Looking for a vectorlike B quark at LHC using jet substructure

Vectorlike quarks have been shown to resolve certain long-standing discrepancies pertaining to the bottom sector. We investigate, here, the prospects of identifying the existence of a topless vectorlike doublet $(B,~Y)$, as is preferred by the electroweak precision measurements. Concentrating on single production, $viz.$ $B \bar b$ with $B \to b + Z/H$ subsequently, we find that the fully hadronic decay-channel is susceptible to discovery provided jet substructure observables are used. At the 13 TeV LHC with an integrated luminosity of 300 fb$^{-1}$, a modest value of the chromomagnetic transition moments allows for the exclusion of $M \lesssim 1.8(2.2)$ TeV in the $Z$ and $H$ channels respectively.


Introduction
Over the last three decades, the Standard Model (SM) has been vindicated to an unprecedented degree of accuracy by several experiments, taken singly or in conjunction. These include, but are not limited to, the electroweak precision tests [1], the measurement of the top mass [2] culminating with the discovery of the Higgs particle [3,4]. Yet, certain anomalies persist, starting from the 2.9σ discrepancy in the forward-backward asymmetry (A b F B ) of the b-quark at LEP/SLC [1], a newly updated 4.2σ deviation in the anomalous magnetic moment of the muon [5] to the more recent ones in both charged and neutral-current decays of B-mesons [6]. These are accompanied by the SM's failure in explaining neutrino masses and mixings on the one hand and, on the other, to address questions related to the lightness of the Higgs or the preponderance of matter over antimatter.
Many diverse scenarios going beyond the SM have been proposed to address such issues. Nearubiquitous in all of them are extra fermion fields. With most such fields not being gauge-singlets, non-observation at collider experiments can only mean that they are very heavy. A chiral assignment of quantum numbers (as is the case within the SM) for heavy fields would imply uncomfortably large Yukawa couplings and, hence, an acute tension with not only the electroweak precision tests, but also with Higgs production and decay. Non-chiral fermions, since they allow for gauge-invariant bare mass terms, easily evade such restrictions.
Such vector-like assignments abound in many diverse scenarios [7,8]. Even the simplest supersymmetric construct has them in the form of the Higgsinos. Additional vector-like matter may arise in the quest of enlarging the symmetry, whether gauge [9][10][11][12][13][14], or space-time [15], with the Dirac-like gauginos in the latter suppressing pair production channels and cascade decays that are possible for the usual Majorana-gaugino theories. Similarly, extending the Higgs-sector to obtain an R-symmetric theory has very interesting ramifications [16]. Vector-like matter can also help raise the mass of the SM-like Higgs [17,18] in supersymmetric theories or to alleviate the little hierarchy problem [19]. And, finally, many of the problems that beset gauge-mediated breaking of supersymmetry may be alleviated too [20][21][22][23].
As argued above, to address different issues, a plethora of vector-like fermions have been advocated, either singly 4 or in combinations. For example, these have been invoked to explain the longstanding discrepancy in the muon anomalous moment [44,45] or to address flavour discrepancing pertaining to b-quarks [46][47][48][49]. In the present analysis, we would be concentrating on a single such vector-like quark (VLQ) doublet. Since substantial mixings with the SM quarks are liable to set up too large a FCNC, we assume that it is only with the third-generation that it may participate in Yukawa interactions 5 . Such scenarios had been shown, in Ref. [50], to explain the long-standing problem with A b F B without coming into conflict with any other constraint pertaining to electroweak precision tests. Interestingly, while, of the two quantum number assignments proposed in Ref. [50], one preferred relatively light VLQs (and, hence, would be disfavoured by the absence of signals at the LHC), the other is not only more attractive on theoretical grounds, but also preferred VLQs in the TeV-range.
In the present paper, we are concerned with a VLQ that, amongst other things, is useful in ameliorating the longstanding tension between the global fits to electroweak precision tests [1] and A b F B . The latter, taken in conjunction with the Z → bb branching ratio and the forward-backward asymmetry for the charm-quark requires a substantial new physics effect in the b-sector [51]. This is best brought forward by considering an effective Zbb vertex parameterised by g L,R → g L,R + δg L,R where the tree-level SM couplings are g L = 1/2 + s 2 W /3 ≈ −0.42 and g R = s 2 W /3 ≈ −0.077, with s W being the Weinberg angle. The deviations δg L,R could arise either from quantum corrections (as in the SM) or new physics effects. In terms of the effective couplings, the expressions for R b ≡ Γ(Z → bb)/Γ(Z → hadrons) and A b F B are approximated to the leading order by With the measured value of A b F B being substantially less than the SM prediction, but that for R b being marginally higher, a positive δg R is called for. As was argued in Ref. [50], the required magnitude of deviation is too large to be attributable to loop corrections. On the other hand, a tree-level δg R (along with a tiny, but welcome, δg L ) is naturally generated if the b quark mixes with a VLQ that is part of a SU (2) L -doublet. The standard choice of the hypercharge (Y = 1/6) would require a very large δg R , such that the sign of the effective g R is reversed [50]. The ensuing large mixing has severe ramifications in low-energy physics. This, along with LHC constraints as well as several theoretical considerations [50] implies that Y = −5/6 (leading to a top-less doublet, ψ T L,R = (B Y )) is favoured.
The production and subsequent decays of such VLQs at the LHC has been widely studied in the literature and constraints are imposed from nonobservation [52][53][54][55][56][57][58][59]. While QCD-driven pair-production is bereft of any model-dependence and, naively, expected to be the dominant mode at the LHC, for large masses, the kinematical suppression as well as the suppression due to falling gluon densities quickly limit the sensitivity. Single production, being model-dependent, has the added advantage of providing a window to the ultraviolet completion. A particularly interesting set of couplings that this may probe are the transition magnetic moments, whether of electroweak nature or chromomagnetic. Simple strategies to probe this was developed in Refs. [60,61] and, subsequently, exploited by the CMS collaboration [59,62] to look at a singly-produced VLQ decaying into its SM counterpart and a photon. Somewhat analogous is the case of a VLQ decaying into a bottom quark and a Z [54] or a Higgs boson [56].
While both the pair-production and single-production modes have already been used by the ATLAS and CMS collaboration [56,57,[63][64][65] to impose a lower limit of m B > ∼ 1 − 1.3 TeV [66] for such a VLQ coupling primarily to the b-quark, it still behoves us to look for complementary channels. To this end, we consider the production of such a VLQ, in association with b quark and subsequent decays of VLQ into either a b + Z or a b + H pair, as these modes are associated with a very substantial branching fraction for a large part of the parameter space. With a large m B implying that both the daughters would be highly boosted, the Z (or H) is more likely to manifest itself as a single fat jet rather than two resolved jets. Notwithstanding the subtleties involved in the use of jet substructures, the much larger hadronic branching ratio for the Z and H renders these channels very competitive with the leptonic ones. While fatjet signatures have been investigated in the context of VLQs [67][68][69][70], ours is the first effort to use it for this all hadronic final state.
The rest of the paper has been structured as follows. We begin, in Sec.2, by setting up the formalism and detailing the relevant aspects of the parameter space that we would explore. This is followed, in Sec.3, by a brief recounting of jet substructure as this would be the bedrock of our analysis. The details of the analysis are presented in Sec.4 followed by the concluding Sec.5.

Theoretical Backbone
As we have explained in the preceding section, we would be concentrating on a non-chiral colored SU (2) L fermion field with a hypercharge of −5/6, viz., Ψ L,R ≡ (B , Y ) T L,R . With there being no charge-2/3 quark, several constraints are automatically relaxed. Our motivation being to develop a particular search algorithm, we desist from incorporating the other fields included in Ref. [50], and begin by setting up the formalism and reviewing some immediate consequences.

The Model
The kinetic (including gauge interactions) term for the Ψ L,R fields are exactly analogous to those for the SM quarks. Being vectorial in nature, these quarks can acquire a bare mass M . Furthermore, in view of the strong constraints from flavour physics, the only Yukawa coupling allowed to Ψ L is that with the SM field b R alone(with gauge invariance preventing any such term of Ψ R ). Denoting all the gauge (mass) eigenstates by primed (unprimed) fields, the relevant additional term in the Lagrangian can be written as where H is the SM Higgs doublet. After spontaneous symmetry breaking, the relevant mass terms are expressible as where v is the SM vev. For the sake of simplicity, we have neglected here the much smaller terms connecting b to s , d . Considerations of electroweak precision tests (more specifically, the ρ-parameter) stipulate that y 2 v M . The mass matrix can be diagonalized by a bi-unitary transformation defined by where c L,R ≡ cos θ L,R and s L,R ≡ sin θ L,R . The physical masses and the mixing angles are given by It is worth remembering that, for small mixing angles, It is easy to ascertain (for example, from the very structure of M 2 ) that While m B > m Y , the smallness of the ratio (y 2 v/M ) ensures that the splitting is too small to permit B → Y + W − , and even B → Y + f + f is very small indeed. The electroweak interactions of the mass-eigenstate B are obtained trivially. Restricting ourselves to those that could, potentially, lead to the decay of the B, we have where P L,R = (1 ∓ γ 5 )/2 and g is the SU (2) L gauge coupling. The mixing of quark fields of different isospin (and hypercharge) that generated the interactions of eq.(8) would also result in an alteration of the effective gauge couplings of the eigenstates dominated by the SM quarks. In particular, both of the bbZ couplings g L,R (b) receive nonzero corrections, leading, in turn, to corrections in R b and A b F B (see eq.(1)). The most important parameter, in this context, turns of to be s R [50], with s L playing only a subservient role is ensuring a correct R b . While observables such as R c and Γ had (Z) are affected too, these play even more subservient roles. Thus, R b and A b F B can be used to delineate the appropriate part of the paramater space. With the present scenario relating s L and s R (with s L s R , vide eq.(6)), only one of them is a free parameter. Furthermore, with the aforementioned observables being essentially independent of m B (since one-loop corrections due to the new quarks are too small be of any consequence), the observables under discussion constrain only s R .
We see from eq.(5) that a perturbative limit on the Yukawa coupling y 2 would translate to a bound on s R , scaling approximately as m −1 B . However, stronger constraints arise from observables such as A b F B and R b , as discussed in the preceding section. Although the other precision measurements, such and R c too contribute to the constraints, these have relatively minor roles 6 to play as far as this sector is concerned. For completeness, we quote here the "SM" values of the parameters, defined as the values inferred from the global best-fit [2] to all electroweak precision observables (with quantum corrections incorporated). Restricting ourselves, for brevity's sake, to the most relevant ones, these are R SM b = 0.21576 (0.21629±, 0.00066), A SM F B = 0.1034 (0.0992 ± 0.0016), A SM b = 0.9348 (0.923 ± 0.020), R SM c = 0.17227 (0.1721 ± 0.003), where the numbers in the parentheses refer to the direct experimental measurements [71]. While all the electroweak precision measurements were considered in ref. [50] in deriving the preferred values of the parameters, ref. [7] concentrated on R b and A SM F B in obtaining the "best-fit" value of s R , along with error bands. It should be realised, 6 It should be remembered that with the beams being unpolarized at LEP, A b and A b F B differ essentially by a factor of Ae. At the SLD, though, they differed on account of the polarization, but in a straightforward manner. though, that the other precision electroweak measurements [71], too have an important role to play. In particular, the oblique parameter T (equivalently ρ), receives an additional contribution proportional to s 2 R m 2 B and this translates to a stringent bound on s R ∝ m −1 B especially for larger m B values. The exact results are shown in [7] where experimental value of ∆T and ∆S are taken to be 0.07 ± 0.08 and 0.04 ± 0.07 from [2].
Typically, for m B < ∼ 1 TeV, it is the Z → bb observables that impose stronger constraints, while for m B > ∼ 1 TeV, it is the constraints from the oblique parameters which are stronger, and, for m B > ∼ 1.7 TeV, these tend to rule out the values that best fit the Z → bb observables [7]. Being interested primarily in m B > ∼ 1.2 TeV, we use the corresponding 1σ upper limits.
The presence of such exotic quarks would also serve to alter the effective gluon-gluon-Higgs and photon-photon-Higgs vertices, nominally enhancing the former and suppressing the latter (on account of destructive interference with the W -loop). However, with B being vector-like, its contribution to either loop can only be proportional to the mass term connect it to the SM quark. In other words, in the limit of large m B , the new physics contribution is proportional to s R ; even for its maximum possible value of 0.18(as constrained by the Z-pole observables), a maximal enhancement of 3.2% is admissible in the ggH vertex and a maximal suppression of 0.2% in the γγH vertex. The partial decay width for H → bb suffers a change on two accounts, primarily from the alteration of the Hbb vertex(by a factor of c 2 R ) due to the mixing and, to a much smaller extent, the aforementioned change in H → gg. The cumulative effect is a suppression by less than 6.4%. Consequently, the Higgs branching ratios into other final states are enhanced, at most, by an extra 3.8%. On the experimental side, the production through gg fusion has an uncertainity of about 9% and H → bb has an uncertainity of 10% [72]. If we consider the production of H through Vector-Boson fusion, then the uncertainty in the production cross section is close to 20% [72]. In summary, the LHC measurements in the Higgs sector leads to virtually no worthwhile constraint on this sector. The situation would, of course improve considerably at the HL-LHC.
A very important issue is that of FCNCs involving either of the down-or strange-quarks. The existence of such terms would lead to enhancement of suppressed decays (that, normally, occur only at the loop-level) as also diverse meson-antimeson oscillations. As we have already mentioned in Sec.1, such FCNCs can be suppressed if one posits that the B mixes only with the b. Of course, the fact that, in general, mass terms such as m bs bs or m * db db are nonzero (in the flavour basis) one would still expect some F CN Cs involving the light flavours. The strength thereof would, however, be suppressed. Given the structure of the Cabibbo-Kobayashi-Maskawa matrix, these suppressions, barring large cancellations in the flavour sector, would be O(λ 4 ) or even more severe, where λ is the Cabibbo angle. Such a minimal texture in the quark mixing matrix (as indicated above) is, thus, more than enough to protect one from the FCNC bounds. Indeed, the texture could be perturbed a little to induce tiny tree-level FCNCs connecting the b to the d/s in an effort to address the recently observed anomalies in B-decays. However, since the latter also seemingly involve lepton-flavour violations, we deliberately desist from treading that path.

Transition Chromomagnetic Moment
A consequence of the mixing between fields with different quantum numbers has been the generation of Z-mediated flavour-changing neutral currents. This also explains why the mixing in the lefthanded sector is allowed to be much larger than in the right-handed one. Understandably, the extant SU (3) c ⊗ U (1) em gauge symmetry precludes any such tree-level currents coupling to the photon or the gluons. This, however, does not prevent the generation, as a result of quantum corrections, of gauge invariant terms of the form where g s is the strong coupling constant and G a µν is the field strength tensor for the gluon. Analogous to electromagnetic transition moments, the dimensionless constants κ L,R are determined by the couplings and mass spectrum of the full theory, including all those above the mass scale Λ that have been integrated out. For the sake of simplicity, we consider these to be be real and equal, thereby also eliminating additional sources of CP violation. For our purposes, only the magnitude of κ ≡ κ L,R is relevant (for more details see ref. [73] and references therein), and in the absence of any theoretical knowledge, we shall only assume a phenomenologically guided limit of |κ| < 0.8.

Decay Width and Branching Ratio
With its isospin partner being nearly degenerate with it and all the SM particles being much lighter, B decays are dominated by two-body final states, namely B → bg, B → Zb and B → Hb. The first of these proceeds through the chromomagnetic moment κ. The other two are driven by the mixings 7 s L,R , and for a very large m B , have nearly equal partial widths, a consequence of the Goldstone equivalence theorem. For relatively modest values of m B , though, the two may differ by as much as 20%.
In Fig.1, we depict the total decay width and the major branching fractions for a value of s R that best fits A b FB while being consistent with the oblique parameter constraints. As the top left panel shows, even for a very large value of κ ≡ κ L,R , the ratio Γ/m B < ∼ 0.06, thereby validating the narrow width approximation. We would be using smaller κ values, though. In this paper we study the case of a particularly heavy B decaying to Z/H and a b-jet, with the Z/H manifesting itself as a fatjet. Before going to the detailed analysis, we briefly discuss, in the next section the jet substructure techniques that are useful to detect the properties of such a fatjet.

Jet-substructure Techniques
Jets are nothing but a cluster of hadrons produced as a result of showering and hadronization following high energy particle collisions and identified using an appropriate jet reconstruction algorithm. With the B quark being very heavy, and its daughters (say, b and Z/H) relatively light, the latter would, typically, be highly boosted. Consequently, the angular separation between the subsequent decay products (of the Z/H in this case) would tend to be small. While this would still not present a problem for the detection of Z → µ + µ − , e + e − , for the dominant decay modes, viz., Z → qq , the closeness would, typically, result in the ensuing jets merging into a single, albeit fat, jet. Fat jets(along with their subjet structures) have been studied in the context of many search strategies, such as those for strongly interacting W bosons [74,75], supersymmetric particles [76,77], heavy resonances decaying to strongly boosted top quarks [78], as well as the Higgs production in association with a W/Z [79,80].
To reconstruct the W/Z/H jets, different algorithms have been used in the literature, whether it be anti-k T [81], Cambridge-Aachen [82] or a combination of both [75]. In the present study, the hadrons are clustered using the 8 anti-k T algorithm [83]. We investigate the variation of the signal efficiency and 7 Since sL sR, the decay B → W t is highly suppressed. 8 The specificity of the hierarchical clustering renders this algorithm more useful for the kind of fat-jets that we are interested in. bh bZ gb Figure 1: The upper left plot shows total decay width as a function of m B using the limit on s R mainly coming from oblique parameters. The other three plots show the branching ratio of B to bH, bZ and bg as a function of m B , for three different values of κ.
the reconstruction of jet substructure variables with two choices of the distance parameter R in the next section. This distance parameter, also known as the jet radius, is an angular cut-off such that a splitting of a parent particle to two daughter particles P → ij will never be combined by the jet algorithm if ∆R ij > R where, ∆R ≡ (∆η) 2 + (∆φ) 2 is the (angular) separation in the azimuth-rapidity plane. Not only should the fat jet arising from the hadronic decay of the Z(H) have a reconstructed jet mass close to m Z (m H ), but it is also expected to resolve into a two-prong substructure. However, some of these properties can be degraded on account of extraneous objects (owing to QCD radiation) that can vitiate jet-reconstruction. Consequently, one needs to use appropriate jet grooming techniques that help in eliminating soft and large-angle QCD radiation. Of many such, we choose to use the jet pruning algorithm [84,85], a popular choice for reconstructing W/Z/H fatjets [81]. While alternative algorithms such as softdrop [86] have also been used [87], it has been shown that the discrimination afforded is very similar [88].

Jet Pruning
In a typical event at the LHC, a very large number of hadronic entities impinge on the detectors. Furthermore, there exist colour reconnections between objects emanating from disparate fundamental processes, hard or soft. The jet reconstruction algorithm, being statistical in nature, cannot always effect an exact differentiation. Pruning is one of the jet-grooming methods to remove those constituents from the jets that carry no significant or useful information. For example, the (invariant) mass of a jet ought to reflect the mass of the primary object, small for a pure QCD jet, and close to the particle mass for a heavy particle. This is facilitated by removing the soft yet large angle constituents of the jet because of the statistically smaller likelihood of their being correlated with the energetic constituents of the jet. Mathematically, at each merging step (j + k → l), we define two constraints given by • softness: p k /p l < z cut for (p k < p j ), and • separation: ∆R jk > R cut .
If both these conditions are met, then we prune (remove) the constituent k and proceed for the next merging. A larger (smaller) value for z cut (R cut ) will result in more aggressive pruning. Clearly, the level of pruning is largely determined by the less aggressive of the two parameters. As for z cut and R cut , the parameters of the pruning algorithm, we choose the default values 9 , namely, z cut = 0.1 and R cut = 0.5 as suggested in Ref. [84]. The pruned jet mass, m J , is computed from the sum of the four-momenta of the components that remain after pruning, and the resultant jet is considered to be a Z(H)-fatjet candidate if m J is commensurate with the Z(H)-mass within the detector resolution limits. And while the irreducible SM backgrounds (with a high-momentum Z(H) would also show similar characteristics, the overwhelmingly stronger pure QCD background would, typically, have jets with much lower masses.

N-subjettiness
Heavy VLQ decays tend to produce top quarks and/or a W , Z, or a Higgs boson with high momenta, causing their respective decay products to merge into a single fat jet [89][90][91]. If the latter is to be resolved into subjets, a naturally important question relates to the precise number of such putative subjets. A good measure of this is N-subjettiness [92] defined as where N is the number of candidate subjets of the jet to be reconstructed. k runs over constituent particles in a given jet with p T,k being their transverse momenta and ∆R j,k the angular separation between a candidate subjet j and a constituent particle k. Furthermore, where R 0 is the characteristic jet-radius. Physically, τ N provides a dimensionless measure of whether a jet can be regarded to be composed of N -subjets. In particular, ratios τ N /τ N −1 are powerful discriminants between jets predicted to have N internal energy clusters and those with fewer clusters. As applied to our case, jets coming from the hadronic decays of the Z(H) tend to have lower values for the ratio τ 21 ≡ τ 2 /τ 1 as compared to QCD or top-jets and, hence, constitutes a good discriminator.

Collider Signatures
As discussed above, we are interested in the single production of the vector-like quark B at the LHC. Several parton-level processes may contribute. In decreasing order of the production cross sections, these are • bg → Bg • qq → bB and gg → bB, with the conjugate process being understood in each case. We would be concentrating here on the third, viz. bB production (dominated by the gluon-fusion contribution). The reason is easy to understand. Since we would be concentrating on fully hadronic cascade decays of the B, each of these channels suffer from large QCD backgrounds. The bB mode, with B → b+Z/H would admit two hard b-tagged jets, thereby offering additional discriminatory power.
To this end, we begin by a detailed discussion, in the next subsection, of the process pp → bB, B → Zb involving the Z-fatjet. The other channel, namely pp → bB, B → Hb shows analogous behaviour and, hence, for the sake of brevity, we do not provide details but only highlight the differences.

Signal: pp → bB, B → Zb (Hb)
We calculate the leading-order on-shell production cross-section 10 in the five flavor scheme (5FS), using the NNPDF23LO1 [93] parton distributions holding the factorisation scale to µ 2 F = 2m 2 B . The final state, being comprised of jets only, largely depends on additional jet radiations. Within this scheme, inclusion of the next-to-leading order effects suppresses the cross-sections by a factor ∼ 0.9 [94] over the mass-range of interest to us. It should also be pointed out at this stage that owing to the relatively modest reach of this mode, uncertainties due to the choice of the parton distributions are relatively small.
In Fig. 2, we plot, as a function of m B , the product σ(pp → bB) × BR(B → bZ). The production cross section is largely dominated by gluon fusion, with both the leading and the subleading (i.e., qq → bB) contributions scaling as κ 2 . On the other hand, increasing κ would also enhance the partial width Γ(B → bg), thereby suppressing the branching fraction for the decay mode of interest, viz. B → bZ. This explains the relatively slow growth of the product with κ in Fig. 2. As a reference point, we choose to work with a benchmark value of κ = 0.5. Analogously, our benchmark points (BP) in the mass-axis read m B =1.2, 1.8 and 2.2 TeV. At the very end, though, we will present the reach in the m B -κ plane.
The signal, thus, comprises of a pair of b-jets accompanied by a Z, whose high momentum would, typically, imply that its decay products coalesce into a further fat jet. Of the two putative b-tagged  jets, one would, typically, be attributed with a transvere momemtum similar in magnitude and in a direction nearly opposite to that of the fat-Z. If an excess in this channel is seen, m B could, presumably, be reconstructed from such pairings.
The second mode, viz. pp → Bb → Hbb, apart from having a nearly identical strength, also has a very similar event topology. The only difference is that, owing to a slightly higher mass of the H (as compared to the Z), its momentum would be marginally smaller and the fraction of events being identified as a fat jet a little lower.

Backgrounds
While the SM backgrounds to the two aforementioned signal channels are similar, they, understandably, contribute differently in the two cases. We begin by discussing the case that suffers larger backgrounds, namely the Zbb channel. The major SM backgrounds arise from the processes detailed beow.
• W/Z production accompanied by multijets : As with the signal, the fatjet would arise, mostly, from the hadronic decays of the vector boson, with a rather subdominant contribution from events wherein some of the jets accompanying the W/Z are reconstructed as a fatjet. While the corresponding SM cross sections are very large, viz., for Z+jets, it is 6.3×10 4 pb (NNLO) [95,96] and 1.95×10 5 pb (NLO) for W +jets [97], note that requiring these additional jets to be b-tagged would result in a severe suppression.
• tt + jets : If the radius parameter R is small enough, then the two-prong hadronic decay of one of W 's emanating from the top decay could be reconstructed as a fatjet. Despite the smaller production cross section (≈ 990 pb at N 3 LO [98]), this would be expected to be a major background owing to the automatic presence of two b-jets.
• QCD n-jets (n ≥ 4) with none being b-or c-like: This, of course, is very large indeed (∼ 10 8 pb). And even with the requirement that two (or more) of these jets should reconstruct to close to m Z , the wide jetmass distribution means that a non-negligible fraction would satisfy the cuts. However, with the cross-section being an even stronger function of p min T than the preceding background contribution, a strong cut is likely to be useful. However, once we impose the condition that at least two jets are b-like, the small mistagging probability ( < ∼ 10 −3 for each of u, d, s, g [99]) ensures that this background is not of any importance.
• Semi-inclusive bb+ n (n > 1) jets : Mainly QCD driven, the cross section is very large (∼ 10 5 pb) and depends crucially on the number of jets in the final state and on the minimum p T (p min T ) allowed to the jets. Calculated using MadGraph, the cross sections have been validated against Refs. [100,101]. To this, we also add the contribution from cc+ n (n > 1) jets, where the charm is misstagged as a b-jet.
• Semi-inclusive V V production (V = W/Z) : Diboson (W W , W Z and ZZ) production processes with a boosted gauge boson decaying hadronically can also mimic the fatjet signal. The cross sections for the aforementioned processes, at the NLO level, respectively are 119 pb, 47 pb and 16 pb [102].
For our analysis, though, we consider the semi-inclusive version with upto two extra jets, with the latter being required to satisfy p T (j) > 30 GeV and |η(j)| < 2.5 and, in the case of two jets, ∆R(j, j) ≥ 0.4 as well. Considered at the LO level, using the 5 flavour scheme and MLM matching the corresponding cross sections are found to be ∼ 120 pb, ∼ 55 pb and ∼ 16 pb respectively. As we would see later, these processes lead only to a minor component of the total background, mainly from W Z and ZZ events.
• Semi-inclusive HV production: Quite analogous to the previous set, these processes may contribute to the background for either signal channels, depending on whether the hadronic decays of Higgs or the W/Z boson are identified as the fatjet. The cross section for inclusive HZ process is ∼ 1 pb and HW is ∼ 1.8 pb at LO (when the cuts mentioned in the context of V V production above are imposed). While the higher order corrections can be found in ref. [103] and the references therein, this contribution is subdominant even in the context of the Hbb mode.
• Single top production: Despite being semiweak processes, the total cross section (σ tW = 83.1 pb, σ tb = 248 pb and σ tj = 12.35 pb at NNLO [104]) is quite comparable to the QCD-driven tt cross section, in a large part on account of the phase space. However, once the large p min T criterion is imposed, the contribution is suppressed to a great degree.
As the kinematic distributions for the inclusive n-jet cross sections are somewhat similar to the inclusive bb events (both being largely QCD-driven), we, henceforth, merge the two and term it "Inclusive bb". Of course, in doing this, tagging efficiency and/or mistagging probability (as the case may be) are duly taken care of. Furthermore, we would subsume the relatively smaller contributions accruing from inclusive-V V , V H and single top events into an "Others" category.
For the H-fatjet channel, some quantitative changes in the background profile turn out to be crucial. For example, with m H varying significantly from m Z , the fraction of the electroweak gauge bosons (whether emanating from hard V +jets or hard V V + X production or from the decay of tops), reconstructing as a H-fatjet reduces considerably. On the other hand, new processes such as inclusive H-production (whether QCD-initiated or as a result of vector-boson fusion) and Higgsstrahlung processes (W H, ZH or even ttH) now need to be considered. Fortunately, the corresponding cross sections are much lower, especially for the event topology that we need to consider. Naively, this would already suggest that the Higgs-channel would be the more sensitive one.

Details of Simulation
Implementing the model in FeynRules [105,106], we generate signal and background events at the tree order using MadGraph [107] interfaced with PYTHIA8 [108] for parton showering and fragmentation. A given hard process contributing to either signal or background is generated with up to two additional partons to account for QCD radiations. To avoid possible inconsistencies (such as overcounting) arising from interfacing such matrix elements with parton showering algorithms, we employ the MLM matching scheme [109,110] with matching parameters as suggested in refs. [111,112]. Signal events are simulated for mass points in the range m B ∈ [0.8, 3] TeV. The events are passed through DELPHES 3 [113], in order to implement detector effects and applying reconstruction algorithms. Jets are reconstructed using the anti-k T algorithm [83] in FastJet [114], with p T > 30 GeV and R = 0.5(0.8). We impose ∆R(j, j) > 0.4 and η < 2.5 on the jets. For other parameters, we use the default CMS card. To identify b-jets, we use a b-tagging module inside DELPHES, with the (p T , η)dependent tagging efficiency being in the 70-80% range. The probability of mistagging a charm as b-jet is 10% while for the other quarks and gluons, it is 0.1% or less. A lepton is considered to be visible and isolated only if it simultaneously satisfies p T > 10 GeV, |η| < 2.5 and ∆R( , j) > 0.4 for all the jets in the event.
We implement jet substructure techniques to distinguish the fatjets from ordinary ones. The former are reconstructed and identified with the FastJet module demanding p T > 200 GeV and η < 2.4. As for the radius parameter R, we investigate the performance for different values but, for brevity's sake, present the result for only two choices. The first, namely, R = 0.8, is a more conventional choice and enables tracking down the decay products of Z even when the latter is not highly boosted. The second choice, viz. R = 0.5, is aimed towards reconstructing a heavily boosted Z. This is expected to be particularly useful for large m B . For other parameters of the jet-substructure observables, as mentioned in Section 3, we follow Ref. [65].
Since jet energy measurements are very crucial for our analysis, it is important to consider the energy resolutions, expecially in the context of the hadronic calorimeter. This, however, depends on the particular detector being considered, and, furthermore on whether one is considering the barrel, endcap or the forward region [115,116]. Multiple sources (such as stochastic term, white noise etc.) contribute: with the terms to be added in quadrature. The constants a s,w,C depend on the details of the detector (and the geometric location within), and typically a s ∈ (0.5, 0.65), a C ∈ (0.03, 0.06) and a w < ∼ 5. Similar expressions hold for the electromagnetic calorimeter as well, but with smaller a i . However, since we are not interested in either photons or e ± , the resolution of the electromagnetic calorimeter is of little interest to us.
In addition, the granularity of the detectors implies a finite angular resolution. This, in principle, would be significant for the measurement of both the missing transverse momentum, and, more importantly, the invariant mass of a jet pair. However, in practice, these uncertainties are of little concern in view of the relatively large error in the jet energy measurements.

Signal and Background Profiles for Different Choices of R
With the profiles (both signal and backgrounds) for the two channels, viz. Z or H, being quite similar, for the sake of brevity, we discuss only the former. This choice is also occasioned by the fact that this would turn out to be the one with the worse signal-to-background ratio.
Since the hard process corresponding to our signal comprises of a fat jet accompanied by another pair of b-tagged jets, we preselect events with a minimum of three relatively central (|η| < 2.5) jets, each with a minimum transverse momentum 11 p T > 30 GeV, demanding that they be separated by at least ∆R(j, j) > 0.4. Arranging them in the descending order of p T , as j 0 , j 1 , j 2 , j 3 . . . , we display, in the top panel of Fig. 3, the p T distributions of the leading (j 0 ), sub-leading (j 1 ) and sub-sub-leading (j 2 ) jets for each of the three benchmark points. For a more massive B-quark, its decay products would be more energetic in its rest frame, resulting in a harder p T spectrum. For the two leading jets, this is reflected by the top left and top center panels of Fig. 3. jets. The distribution for the sub-sub-leading jet (top right in Fig. 3) is a little more intricate. For most signal events, this jet would originate from the primary b (produced in association with the B). This explains the similarity in the three normalized spectra. It should also be realized that, as m B grows large, it provides a scale for the kinematics, and a somewhat large p T (B) = p T (b) would not cause significant suppression. This explains the slightly harder p T (j 2 ) spectrum for larger m B .
While the decay of a very massive B would result in very energetic daughters, not all of the energy would be manifested in the form of transverse momenta. In view of this, we also investigate the energy of the three jets(as defined in the laboratory frame). Although such a variable is not very popular in the context of a hadronic collider (owing to the lack of information of the longitudinal momentum of the subprocess center-of-mass), we would find this to be useful. The middle panel of Fig.3 exhibits the distribution in E j for each of the three leading jets. Qualitatively, the features of the p T distributions are replicated except that the spectra are hardened (understandably) and sharpened.
The relative hardness of the individual p T spectra is also reflected (Fig.3, bottom left) by that for H T (≡ jets p T ), the scalar sum of the individual jet p T s. Note, though, that the difference between those for the three benchmark plots is somewhat obscured by the inclusion of all jets in H T , not just the leading three. Much the same story is repeated by the distribution in the sum of all jet energies (Fig.3, bottom center). Another potentially interesting kinematic variable is the missing transverse energy (MET). In the present context, it could arise from two sources, the first being the neutrinos that result from leptonic decays, whether that of an entity involved in a hard process or from the hadrons in the cascade. A second, and given the large jet energies, often more important source is the mismeasurement of jet energies (as described in the preceding subsection). A third possible source is the event of a jet constituent not being registered in the detector, including the possibility of entities passing through detector gaps. Short of a full detector simulation, though, we cannot include the last-mentioned contribution. However, it is not expected to be a large effect. As we see in Fig.3, the MET, typically, tends to be not too large (a consequence of there not being a hard invisible particle in the event) and its distribution has only a relatively small dependence on m B .
We turn, now, to a discussion of the various contributions to the background. In Fig.4, we display the corresponding kinematic distributions. The p T and energy distributions for the backgrounds are much softer than those for the signal. This, of course, is expected as far as the two leading jets j 0,1 are concerned, simply on account of the large m B that we are interested in. As far as j 2 is concerned, the relative hardness of the signal profile can be understood by realizing that it is m B that provides the dominant scale in the production and a momenta of a few hundred GeVs does not exact too large a 11 We impose a stronger pT cut later on.  price. Consequently, harder cuts on p T j or E j are expected to improve the signal-to-background ratio. It should be realized, though, that the p T distributions for inclusive tt production are relatively wider than those for the other backgrounds. This difference is even more stark for the H T distribution and, thus, a cut on H T would not preferentially remove this background over the signal. As this feature has its origin in the large number of jets resulting from inclusive tt production 12 , it might seem that a restriction on the maximum number of hard jets might be useful in improving the signal-to-background ratio. This, however, is not a good option as, apart from the cut-definition sensitivity bringing into question the infrared safety, an inordinately large fraction would be lost from an already small signal size. Instead, a cut on H T , augmented by a minimum requirement for j E j (see Fig.4, lower center) would serve the purpose better. Also displayed, in the lower right panel, is the distribution in the MET for each of the individual contributions to the background. It can be easily ascertained that it is only the inclusive tt process that has an MET spectrum significantly harder than that for the signal, the reason being attributable to both the possible presence of neutrinos in the former set of events as also the large number of jets, each with its associated energy resolution.
The analysis presented so far corresponds to a particular choice of the jet radius R used for jet reconstruction, namely R = 0.5. Had we chosen a somewhat different value, the aforementioned distributions would suffer only relatively small quantitative changes and no major qualitative ones. The rationale for our choice, as compared to the more canonical R = 0.8 would become manifest soon.
At this stage, we make our first identification of a fat Z-jet, selecting only those events that contain a jet, termed J Z , that satisfies the twin conditions of 13 As the Z would need to be highly boosted for its daughters to coalesce into a single (fat) jet, the requirement on its p T is not expected to lead to a significant loss of signal. Note that, even for the signal, not all events would contain such a jet. For one, some of the putative Z-jets could merge with other jets (or incorporate hadrons with a different origin), thereby augmenting its mass to beyond 105 GeV. Similarly, some of its constituents may go missing in the jet reconstruction algorithm. Finally, there is the probability of a jet energy mismeasurement. As Table 1 shows, only in 35%-50% of the signal events, is a Z actually reconstructed as a fatjet. Fortunately, though, the probability of reconstruction is much smaller for the background events (see Table 1). This suppression is, understandably, extreme for the potentially largest contributors to the backround, namely inclusive 14 bb and QCD n-jets, as there are no gauge-bosons in such events. The large suppression for the tt and diboson backrounds owes itself to two factors. For one, the top-production events have only W 's and not a Z, whereas, of the diboson events, only a fraction have Z's. Secondly, a relatively small fraction of these gauge bosons have a p T sufficiently large for the daughter to coalesce into a fatjet defined using R = 0.8. For our favoured choice, namely R = 0.5, this fraction is smaller still.  Table 1: The fraction of events where one of the three leading jets can be identified as fatjet with p T > 200 GeV. Jets are reconstructed with a raduius R = 0.5 with the parenthetical numbers denoting results for R = 0.8.

Signal Events
It is also instructive to examine the distribution of the fatjet within the three leading jets. As for the signal events, a priori, one would imagine that, the Z is as likely to lead to j 1 as compared to j 0 . While this is indeed true, the differing rates in Table 1 can be understood by realizing that if J Z is to be identified with j 1 , it would require that j 0 must have a p T substantially larger than 200 GeV. Naturally, only a smaller draction of events would satisfy this. Similar arguments also explain the much fewer incidences of j 2 (or, j 3,4 etc, if the exist) being identified as the fatjet. 13 The identification of a fat H-jet, appropriate for the other channel, proceeds analogously, with m(JH ) ∈ [110,140] GeV.
14 Note that we have not yet imposed b-tagging requirement.
Particularly important, in this analysis, is our choice of the jet radius R. With the gauge bosons from such background events not being highly boosted, the choice R = 0.5 implies that the daughters of the gauge boson are more likely to be reconstructed as two independent jets rather than a single fatjet. This has to be contrasted with the case of the signal where the Z tends to be highly boosted. Sure enough, an increase to R = 0.8 would significantly enhance the probability for background as opposed to a very small increase for the signal events (see Table 1). This vindicates our use of R = 0.5.
In Fig.5, we display a few kinematic distributions of importance constructed for events that do contain a fatjet as defined by eq. (12). Even a cursory comparison of the two leftmost panels establishes that a much stronger restriction on the J Z transverse momentum, such as p T (J Z ) > 400 (500) GeV would significantly reduce the background without impinging much on the signal strength. Also shown in Fig.5 are ratios of the missing transverse momentum MET with H T (central panels) and the p T of the leading b-tagged jet. Despite the former having remarkably different structure for the signal and backgrounds, a restriction on this ratio so as to enhance the signal-to-background ratio would, simultaneously, reduce the total size of the signal drastically. On the other hand, the ratio MET/p T would turn out to be an useful discriminant. Once the fatjet J Z has been identified in the correct mass window, we consider, next, the two hardest of the remaining jets. The one with the maximal azimuthal separation with J Z is christened J 1 and the other as J 2 . This identification is particularly useful in identifying the signal events. With the very heavy B, typically being produced with a relatively small transverse momentum, viz. p T (B) m B , its daughters (J Z and the putative J 1 ) are likely to be produced with ∆φ(J Z , J 1 ) ∼ π, as is seen in Fig 6(left). Consequently, the corresponding ∆R too tends to be large as in Fig 6(right). Such a strong preference is not expected of the background events. That ∆φ(J Z , J 2 ) has a slight preference for large values as well is understandable, for the b produced alongwith the B would have a small momentum too; consequently, momentum conservation would stipulate that the transverse component would prefer to be opposite that of the leading transverse momentum in the event, namely that of J Z . It might seem, though, that analogous arguments would hold for the backgrounds too. This is only partially true though, for some of the contributions tend to have a larger sphericity. And, finally, in the event of multijet events, we find that the probability of the true b-daughter of the decaying B not leading to J 1 is much less than 1%, thereby establishing the robustness of the identification.

Fatjet Characteristics for Signal and Background
In the preceding subsection, we have demonstrated the importance of demanding a fat jet(J Z ) in the signal. The criteria to define a jet to be a fat one, though, were ad hoc in nature. We, now, reexamine such issues, aiming to best define it. To this end, we take a few steps back, not only relaxing the criteria on the fatjet mass (as described in the preceding subsection), but also reconsidering the radius R used to define jets. To begin with, we consider the popular choice of R = 0.8. In Fig.8, we display two important characteristics of the putative fatjet, requiring it only to satisfy p T > 500 GeV. The left panels show the distributions without any further cuts, the top one for the jet mass, and the bottom one for the ratio of two subjettiness parameters (see eqn.10), viz. τ 21 ≡ τ 2 /τ 1 . While there exists a peak at m Z , there is a hint of a second peak a little below 40 GeV. The latter can be understood in terms of relatively hard and asymmetric QCD radiations. The expectation value of the mass of such jets (calculated, for example, by considering the q → qg splitting function and then performing the θ and z integrations) is given by [117] m 2 = 3α s 8π C F p 2 T R 2 (13) and, hence, the mass scales linearly with jet p T and the radius parameter R. That the low-energy peaks in Fig.8 are indeed QCD-driven is also attested to by the gradual drop around the central value [117], as distinct from sharp peak corresponding to an on-shell particle decay. Such an origin also explains why the peak is more pronounced for smaller m B . Notwithstanding our ability to explain the secondary peak, its very presence and size seems to argue against the identification of the fatjet as a two-pronged decay. Similarly, the τ 21 distribution does not show any inclination for τ 21 < 0.5, as a two-prong system should, ideally, favour. It is interesting to consider, at this stage, the situation for jet reconstruction using R = 0.5, as detailed in Fig.9. The aforementioned secondary peak (at m J < ∼ 40 GeV) is even more pronounced now, thanks to the fact that such an R calls for narrower jets. Quite analogously, the preference for τ 21 > 0.5 is strengthened. Both these arguments would seem to call for R = 0.8 being a better choice. This is, however, belied by an examination of the right panels for both Figs.8&9. The top right panels in both clearly demonstrate that a cut 15 on τ 21 strongly accentuates the Z-peak, simultaneously obliterating the secondary peak at low m J . Analogously, requiring the jet mass to lie in the 80 GeV ≤ m J ≤ 105 GeV window results in the τ 21 distribution showing a clear bias for τ 21 < 0.5 (bottom right panels). Both these observations are as expected, for it is only such events that should show up as two-prong decays of the Z. Indeed, were we to consider a two-dimensional distribution (in the τ 21 -m J plane), the event rate would show a clear correlation between these two kinematic variables.
It is interesting to note that the τ 21 distribution, after effecting the fatjet mass window restriction, is slightly flatter for a larger m B . This holds true for both choices of R (see Figs. 8 & 9) and is but a consequence of the fact that as the fatjet is boosted more and more, the distinction between one-prong and two-prong configurations is progressively blurred. This can be understood by examining the Z decay into a qq pair which, through their subsequent radiation, putatively lead to the two smaller cones within the fatjet. In calculating τ 2 (see eq.10) two subjet axes are assigned along the direction of these two cones. For an individual fatjet constituent, the minimum of the two ∆Rs between the constituent and the assigned axes contrubutes to τ 2 . Consequently, the value of τ 2 tends to be small. On the other hand, in calculating τ 1 , only one subjet axis is defined and assigned along the direction of the fatjet. Consequently τ 1 for m B = 1.8 TeV is smaller than that for m B = 1.2 TeV resuling in a flatter τ 21 distribution for the former case It should be further noticed that the τ 21 distribution is sharper in Fig.9 compared to Fig.8. Again, this was to be expected given that a smaller value of R will allow for smaller amount of secondary radiations within the cone. As we shall shortly see, the situation is markedly different for the topdecays contributing to the background and, together, this prompts us to adopt R = 0.5 as the definitive requirement. As for the jet-mass requiremnt, clearly the choice [80,105] GeV would be better than, say the [65,105] GeV one (as adopted in various analyses, on account of the former discriminating against W -backrounds (whether from direct W production or from top-decays). Finally, we find the p T > 500 GeV requirement to be a nearly optimal one.
We, now, consider the corresponding fatjet characteristics for the leading contributions to the background, once again for both R = 0.8 (Fig.10) and R = 0.5 (Fig.11). Concentrating on the top-left panel of Fig.10, both the tt and the single-top contribution clearly show a peak at Fig.10. The latter, in addition, shows a stronger peak close to the gauge boson masses. While, naively, one would also have expected the tt events to also show the second peak, courtesy the W in the decay chain, note that the large p T demanded of the fatjet would mean that the W and the b would tend to coalesce into a single jet. The use of R = 0.5, instead, altogether removes the peak at m J ≈ m t (see Fig.11). This can be understood by realizing that the radius parameter is essentially set by R ∼ m J /E J . For R = 0.8, the large p T that has been demanded of the top (putative fatjet) allows it to decay within R; and once the three prong nature of the top is resolved, it is identified as a fatjet. For the reconstruction of t-quark (as a fatjet) within a smaller radius of R = 0.5, a much higher energy is required of the top and only a small fraction of events would satisfy this. Rather, the fraction of events with m J close to m W,Z is enhanced. Once again, the strong peaks at small m J can be understood in terms of the secondary QCD radiation (see discussion surrounding eqn.13). It is interesting to note that Figure 10: As in Fig.8, but for the leading contributions to the background with R = 0.8.
neither of the two aforementioned plots shows a peak at m J ≈ m t for the inclusive tt events. This can be understood by realizing that only a small fraction of such events would boast of a top with a p T sufficiently large enough for the top to be manifested as a fat jet.
In the bottom panels of both Fig.10 and Fig.11, we plot the distributions of τ 21 before any m J cut (left) and after requiring m J ∈ [80, 105] GeV (right). Before the cut, none of the contributors to the background show a preference for τ 21 < 0.5. Even on imposition of the cut, it is only the single-top production that exhibits this preference, primarily on account of the W . Similarly, for the V + jets contribution, the m J cut better accentuates the two-prong nature for R = 0.5 (than for R = 0.8).
An analogous enhancement does not occur for the tt background (especially for R = 0.8) as a large fraction of the fatjet reconstruction, before the cut, would be associated with the entire top. The QCD jets being a diffuse spray of large angle radiation, the τ 21 distribution for the inclusive bb events is, understandably, quite flat.
It might seem surprising that the top left panels of both Fig.10 and Fig.11 do not show a peak in the m J ∈ [80,105] GeV for the V +jets background. This can be understood by realizing that the gauge Figure 11: As in Fig.9, but for the leading contributions to the background with R = 0.5.
boson, very often, has a slightly smaller p T than the leading QCD jet(s). Furthermore, the secondary radiation off the leading parton often leads to these being identified as the fatjet, especially when a strong cut is applied on the fatjet p T . Consequently, the peak is smeared to a great extent. When the τ 21 restriction is applied, the peak duly stands out.
With the event topology for bH being similar to bZ, and given that the difference m H − m Z m B , we would expect the Higgs too to lead to a fatjet. So, in Fig 12, we present the jetmass and the τ 21 plots for the choice R = 0.5 for the Higgs scenario after putting a cut of τ 21 < 0.4 on the former and a cut of 110 < m J < 140 on the later. We see that the Higgs-mass and the two-prong behavior are correctly identified. A comparison of the results for the choices R = 0.5 and R = 0.8 leads us to conclusions similar to those reached for the Z-fatjet case with the τ 21 distribution for R = 0.8 being flatter than the R = 0.5 case in the Higgs fatjet mass window. It is also evident from the background plots (left figures of Fig.10 ) that in the jet mass region of  the backgrounds are expected to be much smaller. The rest of the behaviour of the backgrounds remain same and, hence, we do not show them separately.

Result
We begin by discussing the Z-fatjet channel in detail. The analysis for the H-fatjet channel (presented thereafter) follows analogously with some subtle differences, which would be highlighted. Thereafter, we the delineate the part of the parameter space that could be ruled out by either channel or even lead to a discovery.

The Z-fatjet Channel
As we have already discussed, the R = 0.5 choice is not only more commensurate with the two-prong nature of the signal, while suppressing the contributions from the tt background, but also allows for the imposition of a stronger cut on τ 21 , so as to further reduce the backgrounds. Consequently, we would largely concentrate on this choice, and comment only briefly on the results for R = 0.8. Guided by the kinematic distributions for the signal and background events, as described earlier, we now discuss the selection cuts, in the order these are imposed, alongwith the effects these have.
• Selection 1 (S 1 ): We require at least three jets, imposing a veto on isolated leptons satisfying Ordering them according to the transverse momenta, the three leading jets must not only satisfy but also marginally stronger requirements on their total energy (in the laboratory-fixed frame), namely E(j 0 ) > 500 GeV , In addition, we require that H T jets > 1000 GeV and jets E > 1200 GeV .
• Selection 2 (S 2 ): We require that at least one of the jets from the preceding stage gets resolved into a fat jet J Z satisfying m J ∈ [80,105] GeV and p T (J Z ) > 500 GeV (18) Of the remaining jets (from amongst j 0,1,2 ), we name the one with the maximal azimuthal separation with J Z as J 1 and demand that ∆φ(J Z , J 1 ) > 2.5.
• Selection 3 (S 3 ): Of the jets that have not been identified as a fat jet, we demand that at least two be b-tagged. In other words, we consider the semi-inclusive final state N b ≥ 2 (where we do not make any demand on the identity of the others). In addition, we demand that the ratio of the MET and the p T of the leading b-jet be less than unity.
• Selection 4 (S 4 ): At this stage, we optimize the fatjet characteristics by effecting a single fatjet selection in terms of τ 21 . We consider two choices, namely (a) τ 21 < 0.5 or The devolution of the signal cross section, as the selection criteria are applied consecutively, are summarised in Table 2. The corresponding numbers for the backgrounds are presented too 16 As even a cursory comparison of these tables with the cross sections discussed in Sec.4.2 shows, S 1 itself results in a severe preferential suppression of the background as compared to the signal. The subsequent imposition of S 2 retains ∼45-70% of the signal events, while rejecting nearly 90% of the total background 17 that survives S 1 .   As is evident from the tables, the signal-to-background ratio improves significantly once N b ≥ 2 is demanded, with the improvement being driven by that in the major channel, namely QCD-driven 16 A caveat needs to be enetered here. Keeping the S3 selection in mind, we deliberately omitted, from the table, the multijet QCD events where the final state does not contain either of a bb or a cc pair. As argued earlier, such backgrounds are too small to be of any consequence here. 17 It is obvious, though, that the suppression works differently for the individual contributions to the background.
inclusive-bb production. This can be understood by realizing that the additional jets in such processes would often appear close to one of the b-or b-induced ones and, together, would constitute the fat jet (thereby leaving only one b-tagged jet amongst the rest). It should be pointed out at this stage that the remaining component of S 3 , namely MET/p T ≤ 1 for the leading b-tagged jet, is particularly effective in reducing the background contributions. A relatively large value of this ratio, especially for the inclusive tt production background, has two primary sources. For one, such processes are associated with multiple jets, with the associated MET accruing primarily from jet-energy mismeasurements. As for the events associated with semileptonic decays of the top, note that if the associated lepton be the electron or the muon, then an event with a large p T carried by the neutrino would, most likely, be eliminated by the isolated lepton veto. This, however, does not hold for the tau-events, primarily because of the large semileptonic branching fraction for the latter and also because the leptonic decays tend to leave smaller momenta for the ensuing electron/muon. Thus, such events account for a large fraction of the high-MET background events.
As for selection S 4 , since it pertains only to the fatjet, it is naturally independent of the value of N b . Furthermore, the alternative (a) is, understandably, less restrictive as compared to (b). As can be seen from a comparison of the two units of Tables 2, imposing S 4 (a) would retain roughly ∼ 53% of the total background, but as much as 70-80% of the signal (depending on m B ). The corresponding numbers for S 4 (b) are ∼ 33% and 64-70% respectively. The somewhat larger improvement due to S 4 (b) can be traced to the fact that the stronger τ 21 cut is better able to selectively choose the two-prong fatjets. While a still stronger cut would further improve the signal-to-background ratio, it would be at the cost of signal strength and the consequent loss in the significance. Indeed, S 4 (b) represents a near-optimal choice. To understand the differing strength of S 4 (a, b) when applied to the different contributions to the background, we draw attention to the fact that the two prong nature is dominant only for the single-top background (see the discussion in Sec.4.5 and, in particular, Fig.11). In comparison, the signal tends to exhibit a more pronounced two prong nature (Fig.9). For m B > ∼ 2 TeV, though, there is little advantage in applying S 4 , a consequence of the flattening of the τ 21 distribution as discussed in Sec.4.5.
To further enhance the significance, we consider the invariant mass M inv ≡ m(J Z , J 1 ), with J 1 defined as in selection S 2 . Since, for the signal events, these two jets are expected to have arisen from the decay of the B, we concentrate on intervals |M inv − m B | ≤ 3Γ B , for a given m B . For κ = 0.5, the total widths Γ B (as calculated in Sec.2.3), for the benchmark points m B = 1.2, 1.8 and 2.2 TeV are 32, 66.5 and 90 GeV respectively. As even a cursory examination of Table 3 shows, this restriction on M inv is extremely useful in accentuating the signal-to-noise ratio. Calculated for an integrated luminosity of 300 fb −1 , the consequent discovery significances (defined as σ ≡ S/ √ B, where S (B) represent the total number of signal(background) events) are also presented in Table 3.
It is instructive to peruse Table 3 carefully. For one, the cut S 4 (a) would result in smaller significance values as compared to those for the alternative, namely, S 4 (b). This is just a vindication of our earlier argument that a stronger cut on the subjettiness ratio τ 21 preferentially removes the background events. An analogous (and expected) feature is afforded by a comparison with the significance reach for R = 0.8, presented in Table 3 for a cut of τ 21 > 0.5. With the Z-fatjet getting progressively more collimated as m B increases, an increase in R (from 0.5 to 0.8) would not imply a significant increase in the number of signal events, catching only a few extra events with larger radiation. On the contrary, a much larger fraction of the background events, especially those accruing from top decays, would now be accepted by the algorithm, leading to a significant decrease in the ensuing significance.

R=0.5, b-jet≥ 2 After S 3
After S 4 (b) m B ± 3Γ B (TeV) 1.  Table 3: The signal and total background cross section after S 3 and S 4 (b) in the |m(J Z , J 1 ) − M B | ≤ 3Γ B bin for κ = 0.5 is presented for the Z-fatjet signal (B→bZ). The comparison among the significances(σ), evaluated at 300 fb −1 is also shown for b-jet ≥ 2. We also quote the significance(σ), evaluated at 300 fb −1 for R = 0.8 for comparison.

The H-fatjet Channel
We, now, consider the second possibility, namely when the vector-like quark decays in the B → Hb channel. As we have discussed earlier, Br(B → Hb) ≈ Br(B → Zb) and, with the hadronic branching fraction of the Higgs not being too different from that of the Z, nominally, the signal strengths should be similar. On the other hand, many of the SM backgrounds, such as those originating from W/Z or top-production, are expected to reduce drastically, on account of these peaking away from m H . In other words, the naive expectation would be that this signal (comprising of one H-fatjet with two additional jets) would be significantly more visible against the background, as compared to that in the previous section. We would see, though, that this is borne out to a great extent, though not to the degree that a naive estimate would indicate.
With the mass difference m H − m Z m B , one would expect the signal profile to be quite similar in the two cases. Consequently, we retain all the earlier selection cuts, except for making the obvious alteration in S 2 , which, for the H-fatjet, now reads m J ∈ [110,140] GeV and p T (J H ) > 500 GeV .
The devolution of the cross section, as the selection criteria are applied consecutively, is summarised in Table 4 for both the signal benchmark points as well as the backgrounds. Since our methodology is virtually identical to that in the preceding subsection, much of the details are very analogous, and we shall just concentrate on identifying the major differences.
That the backgrounds, on application of the cut S 1 alone, should remain identical to those in Table 2 is obvious. At this stage, the signal too remains very close to that in the previous case, a testament to the near equality of the raw signal strengths. This near equality is altered significantly on the imposition of S 2 , and is a consequence of the slightly higher mass of the Higgs as compared to the Z. Note that the demand for a two-prong jet of mass 110-140 GeV indirectly translates to a minimum p T requirement (since ∆R ≈ 2m J /p T ). Consequently a non-negligible fraction of events containing a putative fatjet with p T > 500 GeV would no longer be reconstructed as one. Of course, this effect can be offset by allowing for a larger R. However, such a choice would also entail a larger background count. Furthermore, the somewhat flatter τ 21 distribution that, say R = 0.8 entails (see Sec. 4.5), renders the S 4 (a/b) cuts less effective.
S 3 , being only a requirement of the non-fatjet components of the event being b-tagged, understandably has nearly equal efficiency for the two channels. The small difference in efficiencies is attributable to  the slightly different phase space distributions of the b emanating from the heavy B-decay. And while the S 4 cut is expected to have a different efficiency in the two cases, owing to a difference in the corresponding τ 21 distributions, the effect is relatively small.
1.   Table 3 but for H-fatjet (B→bH) channel As in the preceding case, the significance can be further enhanced by restricting the invariant mass M inv ≡ m(J H , J 1 ) to the interval |M inv − m B | ≤ 3Γ B . The consequent discovery significances, as calculated for an integrated luminosity of 300 fb −1 are presented in Table 5. Note that we obtain marginally better significance in the J H scenario for m B > 1.8 TeV, compared to J Z channel, primarily due to extra suppression of the background. Once again, a stronger cut on the subjettiness ratio τ 21 preferentially removes the background events and, for brevity's sake, we present the results only for S 4 (b). And, as in the previous case, the use of a larger R only serves to dilute the significance.

Discovery Projection
It is interesting to note that, notwithstanding the differences in the effective efficiencies for the signal and background events, the two channels have very similar sensitivities. With the search strategy being very similar too, it is, thus, worthwhile to combine the two sets of results to reach an enhanced sensitivity and this is what we now embark on.  We demonstrate the significance as a function of m B in Fig 13 for κ = 0.5 for an integrated luminosity of 300 fb −1 It is ≥ 3σ for VLQ masses < 2.2(2.0) TeV and ≥ 5σ for VLQ masses < 2.05(1.84) TeV in the J H (J Z ) channel. Clearly, upto 1.6 TeV, both the channels predict almost same significance, but thereafter the H-fatjet channel is clearly the more sensitive one. This small difference in significance at smaller m B values was expected because of the more restrictive nature of S 2 cut in the case of H, already discussed in Sec.4.6.2. Combining the two channels, the joint significance reach is ≥ 5σ (≥ 3σ) for VLQ masses < 2.12(2.42) TeV. In Fig 14 we have plotted the contours of 3σ and 5σ significance in the κ vs. m B plane for both J Z and J H channels. It is obvious from the plot that with the J H channel alone, it is possible to probe smaller values of κ with 3/5σ significance at a fixed m B .

Conclusions and Outlook
Non-chiral (or vector-like) fermions have been invoked in a multitude of theories, to address a medley of issues. The more theoretical concerns range from dynamical breaking of the electroweak symmetry or alleviating the little hieracrchy problem in a class of theories to models providing a portal for Dark Matter. Concerns that are more immediate include explaining muon or electron anomalous magnetic moments or several puzzles in flavour physics. In particular, topless vector-like doublets (B, Y ) have been shown to provide a redressal of the tension between global fits to electroweak precision tests and the forward backward asymmetry in bb production at LEP/SLC.
In our quest to examine the status of such resolutions, we begin by delineating the constraints on the mixings of the B with light counterparts, as obtained from measurements of electroweak precision variables and other flavour-sector processes. Such an exercise also helps determine the branching fractions for the B-quark decays. We, then, investigate possible LHC signatures of such a B-quark.
The very structure of such theories imply a sizable a transition chromomagnetic moment κ, allowing for single-production such as gg → bB. Despite the smallness of κ, such a production channel could easily dominate QCD-driven pair production for significantly large m B .
In this paper, we have concentrated on the the single production of such a B in association with a bottom-jet, with the B, subsequently decaying to a Z/H boson and another b-jet. While such channels would be expected to be overwhelmed by large backgrounds (unless the Z decays hadronically), for a sufficiently large mass m B (such as to evade the current experimental limits), the bosonic daughter is boosted so as to often manifest itself as a fatjet. Exploiting this feature, we have striven to identify both the kinematic features as well as the optimal jet reconstruction algorithms. In particular, the two-prong nature of the Z/H-fatjet is best evinced by the choice R = 0.5 for the radius parameter, rather than the more conventional R = 0.8. Complemented by the use of the subjettiness ratio τ 21 as well as the imposition of a differential of cuts on the transverse momenta (a very stiff one for the fatjet and more moderate ones for the two subleading jets), the signal-to-background ratio can be improved to a great extent. As a final discriminator, we use the fact that the fatjet J Z/H and the jet with the maximal azimuthal separation from it should, preferentially, reconstruct the mass of the B.
The consequent significance ratio is quite handsome in either of the channels (Z/H) and, together, amount to more than 3σ for m B ∼ 2.5 TeV with an integrated luminosity of only 300 fb −1 . The HL-LHC option would, understandably, push up the limit significantly. It is worthwhile to notice that it is the Higgs channel is the more sensitive one, a consequence of the twin facts that the branching fractions Br(B → b + Z/H) are very similar and that the SM backgrounds for the Higgs-fatjet channel are significantly smaller.
A key component of our search strategy is the requirement that at least two of the high-p T jets, other than the fatjet, should be b-tagged (i.e., N b ≥ 2) While this was particularly useful in suppressing the SM backgrounds, the adoption of this criterion also meant that some of the potential signal processes too had to be left out as discussed in Sec.4. Indeed, as Fig. 15 shows, the resonant production channel pp → B and even pp → gB have cross sections significantly larger than that for the channel we worked with. However, with the QCD-multijet background now increasing manifolds, the pursual of such channels would require analyses much more sophisticated than what we have used here. There is hope, though, that machine learning techniques could unmask the corresponding signal and we hope to return to this question at a later date.
Potentially much more interesting is the channel pp → BZ. As can be seen from even overtakes it. While one b-jet is now lost, it is now compensated by a Z (H), which has its own distinct signature, even for hadronic decays. This, potentially would substantially increase the signal-to-background ratio, primarily on account of a much reduced background.
Similarly, the production of a much heavier B (than what we have considered) is severely suppressed at the LHC. This, though, would not be the case at a future circular collider. In paricular, note that the pp → BZ mode now dominates over our chosen mode starting with a much smaller m B . However, such a machine would have its own imprint on multiple issues such as the nature of QCD radiation, the efficiencies etc., and a naive extension of our analysis would not be tenable. In particular, new jet substructure observables might be called for. These are only a subset of open questions that we hope to address in future.