Searching for heavy neutrino in terms of tau lepton at future hadron collider

The tau lepton plays important role in the correlation between the low-energy neutrino oscillation data and the lepton flavor structure in heavy neutrino decay. We investigate the lepton flavor signatures with tau lepton at hadron collider through lepton number violating (LNV) processes. In the Type I Seesaw with U$(1)_{\rm B-L}$ extension, we study the pair production of heavy neutrinos via a $Z'$ resonance. We present a detailed assessment of the search sensitivity to the channels with tau lepton in the subsequent decay of heavy neutrinos. For the benchmark model with $Z'$ only coupled to the third generation fermions, we find that the future circular collider (FCC-hh) can discover the LNV signal with tau lepton for $M_{Z'}$ up to 2.2 (3) TeV with the gauge coupling $g'=0.6$ and the integrated luminosity of 3 (30) ab$^{-1}$. The test on the flavor combinations of SM charged leptons would reveal the specific nature of different heavy neutrinos.


I. INTRODUCTION
It is well-known that, in the context of the Standard Model (SM), the non-zero but small Majorana neutrino masses can be realized at leading order through a dimension-five operator [1] κ Λ l L l L HH, where l L and H stand for the SM lepton doublet and the Higgs doublet, respectively. To receive the above "Weinberg operator", the minimal extension of the SM content permits only the Type I, Type II or Type III Seesaw mechanism at tree level [2]. In particular, in Type I Seesaw model [3][4][5][6][7][8][9][10], the neutrino mass matrix is generated by at least two generations of fermionic multiplets as SU(2) L singlet. The new physics scale Λ in Eq. (1) is replaced by the mass of the new multiplets and can be as low as TeV if a small Yukawa coupling κ is allowed.
The new fermionic multiplets in TeV Seesaw mechanisms can be experimentally accessible at the Large Hadron Collider (LHC) (see Ref. [11] and the references therein). Up to now, no significant evidence of such heavy fermions was observed at the LHC and the lower limits on their masses are highly dependent on the mixing between the heavy Majorana neutrinos and the SM leptons. A majority of search results released by ATLAS [12,13] and CMS [14][15][16] were defined by the analysis of electron and/or muon final states from heavy neutrino decay 1 . However, governed by the constraints from neutrino oscillation experiments, the channel with tau lepton in heavy neutrino decay also plays an important role in confirming neutrino mass hierarchies and determining mixing parameters [11,[19][20][21][22][23][24][25][26][27][28]. Recently, several precise reactor measurements lead to more accurate lepton flavor predictions about the Seesaw models. For instance, Double Chooz [29], RENO [30] and in particular Daya Bay [31], have reported non-zero measurements of θ 13 by looking for the disappearance of anti-electron neutrino. T2K and NOvA reported on indications of a non-zero leptonic CP phase [32][33][34]. These experiments provide us up-to-date neutrino oscillation results to investigate the impact on neutrino mass models and consequently examine the lepton flavor signatures to be searched at colliders. Thus, from the experimental point of view, a detailed assessment of the search sensitivity to the channels with tau lepton is in demand at the LHC upgrades.
On the other hand, as proved in Refs. [35,36], requiring all three light neutrinos to be massless is equivalent to requiring lepton number to be conserved at all orders in perturbation theory. In other words, lepton number is nearly conserved in low-scale seesaw models with fermionic singlets in light of non-zero neutrino masses. Tiny neutrino mass is proportional to small lepton number where Z is the new gauge boson of the U(1) (B−L) 3 symmetry and N denotes the heavy neutrino followed by the decay into tau lepton in LNV final states. Suppose a new Z can be discovered through the di-lepton channel in future, one can look for the LNV signal and test the specific nature of heavy neutrinos through this channel. We will show the sensitivity of the search for the above LNV channels in both the high-luminosity LHC (HL-LHC) and future circular hadron collider This paper is organized as follows. In Sec. II, we first describe the U(1) B−L extension and discuss the realization of Type I Seesaw in this model and the constraint from neutrino oscillation experiments on heavy neutrino decay patterns. In Sec. III, we simulate the pair production of heavy neutrinos via Z and its LNV signature with tau lepton at the LHC upgrade. The results of projected sensitivity for heavy neutrinos using tau lepton are also given. Finally, in Sec. IV we summarize our conclusions.
where B µ (Y ) and B µ (Y BL ) are the gauge fields (quantum numbers) of U(1) Y and U(1) B−L , respectively. Here we redefine the gauge coupling of B µ as LEP-II sets the lower bound on the Z boson mass in U(1) B−L gauge model, i.e. M Z /g 6 TeV [50]. The most stringent limit comes from the search for dilepton resonance at the LHC with √ s = 13 TeV and the luminosity of 36 fb −1 [37] or 139 fb −1 [51]. Whereas, lower mass limit is set up to 4.2 TeV for the minimal U(1) B−L model [37] and the constraint is also given in the plane On the other hand, in this model, the anomaly-free U(1) extension allows non-universal U(1) charges for the SM fermions. With the presence of three right-handed neutrinos, the most general requirement of the U(1) charges is [52] 3( where Q 1,2,3 are the quark charges and Q e,µ,τ are the lepton charges. To relax the constraint from dilepton channel, there proposed a flavored model under the U(1) (B−L) 3 symmetry where only the third generation fermions are charged with 3Q 3 = −Q τ = 1 and Q 1 = Q 2 = Q e = Q µ = 0 [38,39]. The Z can only be produced through bb → Z and decay into τ + τ − and a pair of one single heavy neutrino. As a result, the above dilepton constraint can be evaded. The constraint from di-tau search [53] is expected to be rather weak [54]. Note that the constraint can also be relaxed by maximizing the ratio The neutrino Yukawa interactions are whereH = iσ 2 H * with H being the SM Higgs doublet. The right-handed neutrino mass matrix The interaction for Z and heavy neutrinos and the eigenstate transformation With a matrix E diagonalizing the charged lepton mass matrix, we can define where U P M N S is the approximate Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mass mixing matrix and the matrix V N transits heavy neutrinos to charged leptons [58].
One can derive a relation between diagonalized neutrino mass matrices and mixing matrices with mass eigenvalues m diag Here the masses and mixing of the light neutrinos in the first term are measurable from the neutrino oscillation experiments, and the second term contains the masses and mixing of the new heavy neutrinos.
The general solution of the V N in Eq. (9) can be parameterized in terms of an arbitrary orthogonal complex matrix Ω, i.e. the Casas-Ibarra parametrization [59] with the orthogonality condition ΩΩ T = I. Using the SM electroweak current for heavy Majorana neutrinos N i , in the mixed mass-flavor basis, we can obtain the partial width of their decay into charged lepton and the asymptotic behavior holds when where = e, µ, τ . Note that, more generally, the Dirac mass matrix can be quite arbitrary with three complex angles parameterizing the orthogonal matrix Ω [40,60]. The above asymptotic behavior of heavy neutrino decay branching ratios is consistent with the Goldstone equivalence theorem and indicates BR(N i → ± W ∓ ) is nearly equal to 25% for any heavy neutrino N i .
The branching fraction of N i (i = 1, 2, 3) decays into each lepton flavor is thus less than 25% for any possible Ω matrix. In one simple case for Ω, i.e. a diagonal unity matrix Ω = I, the results of |V N | 2 are proportional to one and only one light neutrino mass [40]. The branching ratio of N i → ± W ∓ for each lepton flavor is thus independent of neutrino mass [40]. The representative choice of Ω = I can also lead to both the leading and sub-leading decay rate cases in each heavy neutrino decay into certain charged lepton flavor, so one can distinguish different heavy neutrinos [60]. Thus, to reduce the parameter dependence and obtain certain predictions, we take this illustrative case of Casas-Ibarra parametrization with Ω = I in the following study.
In order to understand the implication of the neutrino experiments, we then discuss the neu- where for NH (IH). In addition, the sum of neutrino masses is constrained by combining the Planck, WMAP, highL and BAO data [63] at 95% confidence level (CL) as, By inputting the above experimental constraints to the transiting matrix V N and the above decay width formulas, we can obtain the preferred values for heavy neutrino decay patterns below. In our numerical calculations below, we take the benchmark decay branching ratios of heavy neutrinos with Ω = I for NH and IH as shown in Table I.
The total decay widths of heavy Majorana neutrinos are proportional to |V N | 2 ∼ m ν /M N which is small and may lead to long decay length. We calculate the decay length of the Majorna neutrinos by the formula L = 1 Γ E N M N where E N M N is the boost factor and E N is roughly considered to be M Z /2 in the rest frame of Z . Fig. 1 shows the total width (left axis) and decay length (right axis) versus M N for N i (i = 1, 2, 3) and Ω = I. We find that in most of cases the decay length is less than O(1) mm and the heavy neutrinos can be viewed as decaying promptly. Only

III. SEARCHING FOR HEAVY NEUTRINOS WITH TAU LEPTON AT HADRON COLLIDERS
The interesting production at hadron colliders for heavy neutrinos in U(1) extended Type I Seesaw is the pair production of heavy neutrinos through Z resonance as shown in Fig. 2. In the U(1) (B−L) 3 model, the most appealing channel is where = e, µ and the heavy neutrino N can be any one of the mass eigenstates in Table I as they can all involve the third generation coupled to Z . The signal channel we consider includes one electron or muon and one same-sign hadronically decaying tau lepton in the subsequent decay of N . The same-sign W bosons are required to decay hadronically. The U(1) (B−L) 3 model file is produced by FeynRules [64] and is interfaced with MadGraph5 aMC@NLO [65] to generate signal events. The major irreducible SM background is from ttW ± → bbW ± W ± W ∓ with the two same-sign W bosons decaying to one charged lepton = e, µ and one tau lepton, the oppositesign W hadronically decays. The SM backgrounds also include ttZ → bbW + W − Z and W Z+jets with the Z boson leptonic decay. Both the signal and background events are then passed to Pythia 8 [66] and Delphes 3 [67] for parton shower and detector simulation, respectively. We select the events with exactly one electron or muon and one same-sign tau lepton satisfying The jets from W decay are clustered using the anti-k T algorithm in FastJet [68]. If the jets are well isolated, we reconstruct each W boson from two resolved jets with |η(j)| < 2.4 and p T (j) > is not as good as that from (µ, W ). As a result, in the final selection, we only apply the minimal p T cut and the mass window for N µ The cuts for M N τ and the reconstructed Z are not applied.
Given the characteristic features of the signal and backgrounds discussed above, we can use the Gaussian method to calculate the significance where S and B are the signal and background event expectations, respectively. With the proper branching fractions in Table I, the discovered signal events for this channel read as where , L is the integrated luminosity and the factor of 2 accounts for the charge-conjugation of final states. The τ N N denotes the selection efficiency for our signal with one tau lepton. The gray and black curves in Fig. 4 (a) respectively correspond to the sensitivities of σ(pp → Z → N N → µ ± τ ± W ∓ W ∓ ) = 2σ 0 for 5σ discovery and 95% C.L. exclusion, assuming an expected luminosity of 3 ab −1 at 14 TeV TeV. The searches for Z → bb [70] or Z → tt [71] do not place severe constraint due to the suppression by the baryon number. The FCC-hh with the integrated luminosity of 3 (30) ab −1 can probe the LNV signature with tau lepton for the gauge coupling g down to 0.12 (0.07) with M Z = 1 TeV and N = N 3 .
In Fig. 5 we also interpolate the current bounds of Z → τ + τ − [53], Z → bb [70] and Z → tt [71] and estimate their exclusions at future FCC-hh. One can see that the most optimistic channel to directly observe Z is from the Z → τ + τ − channel. However, in the U(1) B−L model, the right-handed neutrinos are needed to cancel the gauge anomalies and the search for LNV signal is important to confirm the existence of the right-handed neutrinos and explain the neutrino masses. Suppose the Z resonance can be discovered through the di-tau channel in future, the search for the pair production of heavy neutrinos we explored would provide crucial information for the LNV nature and mass pattern of the heavy neutrinos.  We study the pair production of heavy neutrinos via Z mediation in the U(1) (B−L) 3 model, with one tau lepton in the subsequent decays: pp → Z → N N → ± τ ± W ∓ W ∓ → ± τ ± + jets.
The τ lepton's hadronic decay is assumed in the above channels. We take into account the realistic