A universally enhanced light-quarks Yukawa couplings paradigm

We propose that natural TeV-scale new physics (NP) with ${\cal O}(1)$ couplings to the standard model (SM) quarks may lead to a universal enhancement of the Yukawa couplings of all the light quarks, perhaps to a size comparable to that of the SM b-quark Yukawa coupling, i.e., $y_q \sim {\cal O}(y_b^{SM})$ for $q=u,d,c,s$. This scenario is described within an effective field theory (EFT) extension of the SM, for which a potential contribution of certain dimension six effective operators to the light quarks Yukawa couplings is $y_q \sim {\cal O} \left( f \frac{v^2}{\Lambda^2} \right)$, where $v$ is the Higgs vacuum expectation value (VEV), $v=246$ GeV, $\Lambda$ is the typical scale of the underlying heavy NP and $f$ is the corresponding Wilson coefficient which depends on its properties and details. In particular, we study the case of $y_q \sim 0.025 \sim y_b^{SM}$, which is the typical size of the enhanced light-quark Yukawa couplings if the NP scale is around $\Lambda \sim 1.5$ TeV and the NP couplings are natural, i.e., $f \sim {\cal O}(1)$. We also explore this enhanced light quarks Yukawa paradigm in extensions of the SM which contain TeV-scale vector-like quarks and we match them to the specific higher dimensional effective operators in the EFT description. We discuss the constraints on this scenario and the flavor structure of the underlying NP dynamics and suggest some resulting"smoking gun"signals that should be searched for at the LHC, such as multi-Higgs production $pp \to hh,hhh$ and single Higgs production in association with a high $p_T$ jet ($j$) or photon $pp \to hj,h \gamma$ and with a single top-quark $pp \to h t$.


I. INTRODUCTION
After the discovery of the 125 GeV Higgs-like boson, one of the main tasks of the current and future runs of the LHC is to uncover its properties and the physics which underlies its origin. This has led to considerable effort from both the theoretical and experimental sides, in the hunt for the NP, that may address fundamental questions in particle physics, possibly related to the scalar sector of the SM, e.g., the observed hierarchy between the two disparate Planck and EW scales and the flavor and CP structure in the fermion sector.
The Higgs mechanism of the SM suggests that the fermion's Yukawa couplings are proportional to the ratio between their masses and the Higgs VEV (v = 246 GeV), i.e., y f ∝ m f /v. In particular, for the light fermions, where m f /v 1, reactions involving their interaction with the Higgs boson are, in many cases, expected to be vanishingly small and unobservable in the SM. Therefore, any observable signal which can be associated with an enhanced Yukawa coupling of a light fermion would stand out as clear evidence for NP beyond the SM. Indeed, current experimental bounds and Higgs measurements do not exclude the possibility that the Yukawa sector of the SM is modified by TeV-scale NP that directly effect the couplings of the observed 125 GeV Higgs; the current bounds do not exclude Yukawa couplings of the Higgs to the light quarks of the order of the b-quark Yukawa coupling, i.e., allowing y q ∼ O(y SM b ) for q = d, u, s, c [1][2][3][4][5][6].
In this work we propose a framework where the Yukawa interactions of all the light quarks are universally en-hanced, naming it the "Universally Enhanced Higgs Yukawa" paradigm -UEHiggsY paradigm. In particular, we suggest that, if the pattern and size of the Higgs Yukawa interaction Lagrangian is controlled by some TeV-scale underlying NP with natural couplings of O(1), then y q ∼ O(y SM b ) can be universally realized for all q = d, u, s, c, b. We first describe the UEHiggsY paradigm based on an EFT approach and then give an explicit implementation of this mechanism within a renormalizable prescription involving new TeV-scale vector-like quarks (VLQ) with natural O(1) Yukawa-like couplings to the SM quarks.

II. AN EFT DESCRIPTION OF THE UEHIGGSY PARADIGM
Consider the effective Lagrangian piece corresponding to one of the simplest dimension six effective operators that can generate non-SM Yukawa-like terms: where H (H ≡ iτ 2 H ), q L and u R , d R are the SU(2) SM Higgs, left-handed quark doublets and right-handed quark singlets, respectively. Also, Λ is the NP scale and f i are the corresponding Wilson coefficients which depend on the details of the underlying NP theory. When the above dim.6 operators are added to the SM Yukawa interaction Lagrangian: and EW symmetry is spontaneously broken, one obtains the quark mass matricesM q (q = u, d for up and downquarks, respectively) and the Yukawa couplings in the weak basis. The and couplings in the physical quark mass basis are denoted with a hat: The Yukawa couplings, y ij qqi q j h, are then given by: where m q is the physical quark mass and R(L for all the light quarks (q = d, u, s, c) where m q /v f qH , as well as for the b-quark for which m b /v ∼ f qH . In addition to the modification of the light quarks Yukawa couplings, the effective operators in Eq. 1 also generates new tree-level contact interactions between the SM light quarks and two or three Higgs particles, qqhh and qqhhh. These new couplings are also proportional tô f qH : and may cause large deviations (from the expected SM rates) to the multi-Higgs production channels pp → hh, hhh at the LHC, as will be discussed in section V. The above UEHiggsY paradigm suffers, however, from two potential problems associated with fine-tuning and flavor: fine-tuning: Some degree of fine-tuning is required among the parameters of the Lagrangian pieces L Y SM + ∆L qH in order to simultaneously accommodate the light-quark masses m q m b and the enhanced Yukawa couplings of y q ∼ O(y SM b ). As will be discussed below, this fine-tuning is, however, not worse than the flavor fine-tuning in the SM.
flavor: The Yukawa couplings Y q and Wilson coefficients f qH cannot be diagonalized simultaneously in general. As a result, flavor changing neutral couplings (FCNC) among the SM quarks may appear. This is manifested by the off-diagonal elements of f qH (see Eq. 4), which are a-priori expected to be of O(1). In particular, with Λ ∼ O(1) TeV, we obtain FCNC q i q j h couplings also of the size of the b-quark Yukawa, e.g., y 12 ) (see Eq. 5). We will address this flavor problem in the next section.
As for the fine-tuning issue, it is typically of the order of m q /m b , so that the worst fine-tuning corresponds to the 1st generation quarks, where it is ∼ O(m u,d /m b ) ∼ 10 −3 . To see that, consider the mass and Yukawa coupling of a single light quark q in the presence of the interactions terms in L Y SM + ∆L qH : In particular, fixing m q to its measured/observed value (e.g., m q ∼ 2 MeV for the u-quark) and requiring that 025, the solution to Eqs. 7 and 8 for the corresponding couplings Y q and f qH is: Thus, both f qh and Y q need to be of O(y SM b ) and the resulting fine-tuning is at the level of ∆ q ∼ O(m q /m b ). We therefore see that the UEHiggsY paradigm which arises from natural TeV-scale NP with O(1) couplings, requires technical fine-tuning of the quark-Higgs interaction parameters at the level of ∆ q ∼ O(0.1, 0.01, 0.001) for q = c, s, u/d, respectively. In particular, the finetuning is at most at the per-mill level and is only technical in the sense that the fine-tuned parameters, once fixed, are stable against higher-order corrections (as opposed to the fine-tuning in the SM Higgs potential). In fact, this technical 10 −3 − 10 −1 fine-tuning is comparable to the flavor fine-tuning problem in the SM, which is manifest in the CKM matrix that has no a-priori reason to be close to the identity matrix [7].

III. THE UNDERLYING HEAVY PHYSICS AND FLAVOR
The effective operators in Eq. 1 can be generated by various types of heavy underlying NP which contain new heavy particles that couple to the SM fermions. In Fig. 1 we depict examples of tree-level diagrams in the underlying theory, which can generate the dim. 6 effective operators of Eq. 1 when the heavy fields are integrated out. In particular, the underlaying NP theory may contain heavy VLQ (F 1 and F 2 ) and/or a heavy scalar (Φ) -both have the required quantum numbers to couple to the SM quarks and Higgs fields. Indeed, new heavy scalars and/or vector-like fermions are elementary building blocks of several well motivated beyond the SM scenarios which may address fundamental unresolved theoretical questions in particle physics. As an example for a simple occurrence of the UEHig-gsY framework, we will focus below on the heavy VLQ scenario, which has rich phenomenological implications [8][9][10][11][12][13][14][15][16][17] and may be linked to the mechanism responsible for solving the hierarchy problem [18], as well as to naturalness issues in supersymmetry [19] and in strongly coupled theories where the light Higgs boson is considered to be a pseudo-Nambu-Goldstone boson of an underlying broken global symmetry, e.g., in little Higgs models [20] and in models with partial compositeness [21][22][23]. VLQ dynamics may also be important ingredient of the physics that underlies flavor and CP-violation [7, 9, 11-13, 17, 24].
In particular, in the VLQ case depicted in diagram (b) of Fig. 1, two types of SU(2) VLQ multiplets are required in order to generate the effective operators of Eq. 1: (F 1 , F 2 ) = (doublet, singlet) and/or (F 1 , F 2 ) = (doublet, triplet). We will adopt a SM-like (doublet, singlet) VLQ setup, assuming three generations of SU(2) VLQ doublets Q i = (U, D) i and the corresponding uptype and down-type SU(2) singlets U i and D i , respectively, carrying the same quantum numbers as the SM quarks doublets and singlets: Q = (3, 2, 1/6), U = (3, 1, 2/3) and D = (3, 1, −1/3). We assume that the VLQ are in their mass basis, having explicit mass terms in the full Lagrangian, i.e., M F (F L F R +F R F L ), with a mass M F =Q,U,D ∼ 1 − 2 TeV (the typical lower bounds on the masses of new VLQ states are in the range 1-1.5 TeV, depending on their mixing with the SM quarks and on their decay pattern [25]). These VLQ will also have in general the following Yukawa-like couplings to the SM Higgs (which upon EWSB also give a small contribution to their masses): whereλ QU andλ QD are 3 × 3 matrices in the VLQ flavor space in their mass basis (we have suppressed the generation index of the VLQ). The Yukawa-like mixing terms of the VLQ with the SM quarks are in general: where, here also,λ U q,Dq,Qu,Qd are all 3 × 3 matrices in the VLQ -SM quarks flavor space and the SM quark fields are also assumed to be in their physical mass basis. With this setup, diagram (a) in Fig. 1 generates the following 3×3 Wilson coefficients/matricesf uH ,f dH (i.e., in the physical quark mass basis) and effective scales of the operators in Eq. 1: Thus (1)), then the Yukawa couplings of all light quarks are universally enhanced, with a typical size of (see Eq. 5): therefore, also generating potentially "dangerous" FCNC q i q j h transitions of the same size, i.e., y ij Indeed, FCNC in the down quark sector and among the 1st and 2nd generations of the up quark sector are severely constrained by experiment -to the level of y 12,21 d < ∼ 10 −5 , y 13,31,23,32 d < ∼ 10 −4 , y 12,21 u < ∼ 10 −5 [26]. This puts stringent constraints on the off-diagonal elements of the Wilson coefficientsf qH . In particular, for Λ ∼ O(1) TeV, these bounds correspond tof ij dH < ∼ 10 −3 − 10 −4 for i = j andf 12,21 uH < ∼ 10 −4 , which therefore, constrain the corresponding flavor changing VLQ coupling to the SM quarks. This observed smallness of FCNC q i → q j transitions is a strong indication that any viable underlying UV completion of the SM, and in particular of the above VLQ scenario, should have a mechanism which strongly suppresses or forbids the above Higgs mediated FC couplings. Such a mechanism is often assumed to be linked to an underlying flavor symmetry which gives flavor selection rules, thus imposing specific flavor textures on the FCNC couplings.
There are several types of mechanisms and/or flavor symmetries that can be applied to our VLQ framework, that will give the desired flavor selection rules. Here we wish to consider simple and rather minimal examples of flavor symmetries which are consistent with both , assuming three different Z3 symmetries due to three types of Z3 charge assignments for the fermion fields in their mass basis. Our notation for the charge assignments is α(ψ k ) = (a, b, c), using k as the generation index, so that α(ψ 1 ) = a, α(ψ 2 ) = b and α(ψ 3 ) = c. See also text.
the current experimental constraints on FCNC and with our UEHiggsY framework. In particular, we introduce a Z 3 flavor symmetry under which the physical states (i.e., mass eigenstates) of the SM quarks and VLQ fields transform as The simplest Z 3 setup, which has no tree-level FCNC and also accommodates the UEHiggsY paradigm is the choice α(ψ k ) = k. In this case, all the Yukawa-like couplings involving the VLQ, i.e.,λ i in Eqs. 11 and 12 as well as the SM Yukawa couplingsŶ u,d are diagonal, so that the Wilson coefficientsf uH andf dH are also diagonal, giving y ij q ∼ y SM b δ ij for q = u, d, c, s, b and no tree-level FCNC. Furthermore, with the UEHiggsY setup of Eqs. 9 and 10 for the diagonal entries ofŶ q andf qH : the Z 3 symmetry with α(ψ k ) = k reproduces the desired quark mass spectrum.
In Table I , will bring about the UEHiggsY scenario with no tree-level FCNC.
The third Z 3 symmetry in Table I generates a tree-level u L t R h FCNC coupling (i.e., due tof 13 uH = 0), which is not well constrained and which may yield an interesting signal of exclusive production of the Higgs boson in association with a single top-quark at the LHC. This effect will be discussed in more detail in section V D. Notice also that, while the flavor structures of the SM Yukawa coupling and Wilson coefficients in the down-quark sector are similar in all the three Z 3 symmetries, the up-quark sector corresponding to the third Z 3 symmetry has a rank 2 mass matrix, requiring f 13 uH = 2Ŷ 13 u in order to have a diagonal up-quark mass matrix (i.e., M 13 u = 0). Thus, in this case there are only two non-zero mass eigenvalues in the up-quark sector, so that the UV completion of the VLQ scenario should have another mechanism for generating the top-quark mass, e.g., by coupling the top-quark to another scalar doublet.

IV. CONSTRAINTS FROM THE 125 GEV HIGGS SIGNALS
The measured signals of the 125 GeV Higgs-like particle are sensitive to a variety of new physics scenarios, which may alter the Higgs couplings to the known SM particles involved in its production and decay channels. In particular, modifications of the Higgs Yukawa couplings to the light fermions may lead in general to deviations in both Higgs production and decays.
To see that, we will use the Higgs "signal strength" parameters, which are defined as the ratio between the Higgs production and decay rates and their SM expectations: with (in the narrow Higgs width approximation): where Γ h (Γ h SM ) are the total width of the 125 GeV Higgs(SM Higgs), i represents the parton content in the proton which is involved the production mechanism and f is the Higgs decay final state.
We will consider the signal strength parameters associated with the production processes pp → h and pp → hW, hZ followed by the decays h → γγ, W W , ZZ , τ τ and h → bb, as analysed by the ATLAS and CMS collaborations [27]. [1] In the SM, the s-channel production of the 125 GeV Higgs is dominated by the gluon-fusion production mechanism gg → h. In particular, the SM tree-level qq-fusion production channel, qq → h, is negligible due to the vanishingly small light-quarks SM Yukawa couplings (the effect of the light quarks in the 1-loop ggh coupling is also negligible for our purpose, i.e., at most of O(few %) for the b-quark [6,28]). In the pp → V h channels (V = W, Z), the SM rate is dominated by the s-channel V exchange qq → V → V h.
A different picture arises in our UEHiggsY framework, where the Higgs Yukawa couplings to all the light quarks [1] We neglect Higgs production via pp → tth, which, although included in the ATLAS and CMS fits, are 2-3 orders of magnitudes smaller than the gluon-fusion channel. Also, the vector-boson fusion (VBF) process V V → h is not relevant to our discussion below.
are universally modified/enhanced. Higgs production via qq-fusion becomes important, in particular, the tree-level processes qq → h and t-channel V h production qq → V h (see diagram for qq → γh in Fig. 2 and replace γ → V , V = Z or W ). To study the effect of these new qq-fusion Higgs production channels, we define Yukawa coupling modifiers, κ q , and scale them with the SM bquark yukawa, as follows: where κ f = g hf f /g SM hf f are the couplings modifiers of any of the hf f Higgs decay vertices, R q is defined by and it is understood that σ(qq, gg → h) are convoluted with the corresponding PDF weights and that σ(qq → h) U EHiggsY are calculated at tree-level with the values κ q = 1 for all light flavors q = u, d, c, s (we neglect here the bb-fusion production channel bb → h, which is much smaller than the light quark qq → h-fusion channels for κ b ∼ O(1), i.e., close to its SM value. We have calculated the cross-sections σ(qq → h) using MadGraph5 [35] at LO parton-level, where a dedicated universal FeynRules output (UFO) model for the UEHiggsY framework was produced for the MadGraph5 sessions using FeynRules [36]. We used the MadGraph5 default PDF set and dynamical scale choice for the central value of the factorization (µ F ) and renormalization (µ R ) scales. We find σ(uū, dd, ss, cc → h) U EHiggsY ≈ 33.7, 23.8, 5.4, 4.0 [pb] at the 13 TeV LHC, so that using the N3LO QCD prediction (at the 13 TeV LHC) σ(gg → h) ≈ 48.6 [pb] [33], we obtain q R q ∼ 1.4 and, therefore: where we have added a common K-factor, K q , to the tree-level calculated cross-sections σ(qq → h) U EHiggsY . In particular, with K q ∼ 1.5 (see e.g., [34]) and the UE-HiggsY values κ q = 1 for all q = u, d, c, s, we find that µ U EHiggsY i=gg+qq ∼ 3, so that the 125 GeV Higgs production mechanism is enhanced in the UEHiggsY framework by a factor of O(3) with respect to the SM expectation.
Turning now to the Higgs decay channels h → γγ, ZZ , W W , bb, τ + τ − and assuming no new physics in the decay (by setting κ f = 1 for f = γ, Z, W, b, τ ), we obtain from Eq. 24: Thus, under the UEHiggsY paradigm with κ q = 1 we have µ γ,Z,W,b,τ U EHiggsY ∼ 0.3, so that the calculated signal strengths of Eq. 19 in these channels are all expected to be the same: Indeed, the best measured signal strengths in the four channels pp → h → γγ, ZZ , W W , τ + τ − have a typical 1σ error of 10-20% and, are, therefore all consistent with the value µ γ,Z,W,b,τ i=gg+qq ∼ 0.93 within 1 − 2σ (for the LHC RUN1 results see [27] and for updated results from RUN2 see e.g., [29]). In particular, the currently measured 125 GeV Higgs signals in these four channels do not constrain the UEHiggsY paradigm with κ q = 1 for all q = u, d, s, c.
Let us next consider the UEHiggsY effect on the measured hV production channel followed by h → bb. This process has currently the best sensitivity to the h → bb decay channel and is used to overcome the large QCD background to the simpler pp → h → bb channel. In particular, in this channel we define µ(pp → hV → bbV ) ≡ R hV →bbV = R hV · µ b , with (V = W, Z): where σ hW , σ hZ ≡ σ(pp → hW + + hW − ), σ(pp → hZ).
As mentioned earlier, in the UEHiggsY framework, the SM s-channel qq → V → hV production channels receives additional tree-level contributions from t-channel q-exchange diagrams, similar to the one depicted for the process qq → hγ in Fig. 2. In particular, calculating the contribution of these diagrams under the UEHiggsY working assumption with κ q = 1 for all q = u, d, c, s, we find R U EHiggsY hV ∼ 1.1 for both V = W and V = Z. Therefore, since µ b U EHiggsY ∼ 0.3 for κ q = 1 (see Eq. 27), the UEHiggsY signal strength parameter in the pp → V h → bbV channel, R hV →bbV , is expected to be appreciably smaller than one (i.e., than its SM value): for both the hW and hZ production channels.
It is interesting to note that the RUN1 best fitted value for the measured signal strength in this channel, pp → hV → bbV , was indeed on the lower side and consistent with the above predicted UEHiggsY value R hV →bbV ∼ 0.33 within about 1σ: the combined ATLAS and CMS analysis of RUN1 data yielded R hV →bbV ∼ 0.65 ± 0.3 [27]. Recent updated ATLAS and CMS analysis in this channel, combining the RUN1 data with about 36 fb −1 of RUN2 data at a center of mass energy of 13 TeV yielded higher values R hV →bbV ∼ 0.9 ± 0.3 [30] and R hV →bbV ∼ 1.06±0.3 [31], respectively, but the errors in this channels are still large.
We thus conclude that, currently, no significant constraints can be imposed on the UEHiggsY paradigm from the measured 125 GeV Higgs signals. We also note that the Higgs Yukawa couplings to the light quarks can also effect the transverse momentum distributions in Higgs production at the LHC [4,6,37]. However, the errors of the currently measured normalized p T (h) in Higgs + jets production are still relatively large, so that this analysis also cannot yet be used to exclude scenarios with κ q ∼ O(1) for the light quarks [4,6] (see also discussion in the next section).

V. HIGGS SIGNALS OF THE UEHIGGSY PARADIGM
Enhanced light-quark Yukawa couplings may have direct consequences in Higgs production and decay phenomenology at the LHC. Here, we wish to discuss at the exploratory level some of the "smoking gun" signals of the UEHiggsY paradigm, associated with the higher dimension effective operators of Eq. 1.
Let us define the normalized cross-section ratios: where F (h) stands for a final state with at least one Higgs. In particular, apart from the pp → h, hV Higgs production channels discussed in the previous section, the UEHiggsY framework potentially effects other processes which involve one or more Higgs particles in the final state. Below we will consider some of the Higgs final states which have a noticeable tree-level sensitivity to the UEHiggsY paradigm and which are also recognized, in general, as sensitive probes of NP [38]: Higgs pair and triple Higgs productions, Higgs + jets production, Higgs + single top associated production and Higgs production with a single photon, i.e., F (h) = hh, hhh, h + nj, ht, hγ. [2] FIG. 2: Sample diagrams for the processes pp → hh, hhh, h+ jet, ht, hγ due to enhanced qqh couplings within the UEHig-gsY paradigm.
Here also, all cross-sections are calculated at LO parton level, using MadGraph5 aMC @NLO [35], with default PDF set and dynamical scale choice for the central value of the factorization and renormalization scales. In addition, following the working assumption of the UEHiggsY paradigm, the effective operators in Eq. 1 are assumed to have a typical scale of Λ ∼ O(1) TeV and couplings f qH ∼ O(1), so that all cross-sections reported below are calculated with qqh Yukawa couplings comparable to the SM b-quark Yukawa, i.e., y qqh = y SM b .
[2] Some of the Higgs signals considered in this section may also be sensitive at 1-loop to modifications of the 3rd generation Yukawa couplings due to the effective operators in Eq. 1, see e.g., [39][40][41][42].
A. Multi-Higgs production pp → hh, hhh Higgs pair production is one of the main targets for NP searches in the Higgs sector at the LHC, primarily due to its sensitivity to the Higgs self coupling in the Higgs potential and to heavy NP in the loop induced couplings of the Higgs to gluons [14,32]. In the SM this process is initiated at LO by 1-loop gluon-fusion diagrams gg → hh, and the corresponding cross-section is σ(pp → hh) ∼ 15 fb at LO, where due to the large QCD corrections, it is typically doubled at NLO [38].
In the UEHiggsY framework, there are additional treelevel diagrams induced by the effective operators of Eq. 1, as depicted in Fig. 2. Settingf ij qH = δ ij (i.e., assuming only flavor diagonal couplings) and Λ ∼ O(1) TeV, we have y q ∼ y SM b for the qqh Yukawa coupling (see Eq. 5) and Γ qq hh ∼ 3y SM b /v for the qqhh couplings (see Eq. 6). For this setup we find at LO and for the 13 TeV LHC: where more than 90% of the enhancement arises from the tree-level diagrams initiated by the u and d quarks.
In particular, the total Higgs production cross-section within the UEHiggsY framework with The current best bounds on the hh production crosssection at the 13 TeV are R hh→bbγγ < ∼ 19 in the hh → bbγγ decay channel (obtained by the CMS collaboration, see [43]) and R hh→bbbb < ∼ 29 in the hh → bbbb decay channel (obtained by the ATLAS collaboration, see [44]).
As was shown in the previous section, in our UEHiggsY framework withf ij qH = δ ij and Λ ∼ O(1) TeV (for which y q ∼ y SM b for q = u, d, c, s, b) the branching ratios for the decays h → bb and h → γγ are decreased by about a factor of three with respect to the SM: BR(h → bb, γγ) ∼ 0.3BR(h → bb, γγ) SM (see Eq. 27 with κ q = 1). Therefore, in these channels we obtain in the UEHiggsY framework: R hh→bbbb = R hh→bbγγ ∼ 100 × (0.3) 2 ∼ 10, which is an order of magnitude larger than the SM rate, but still below the current sensitivity.
For the triple Higgs production channel, pp → hhh, the SM cross-section is around σ(pp → hhh) ∼ 30 ab at LO and about twice larger at NLO [38]. In the UEHiggsY framework (see representative diagrams in Fig. 2) we find that σ(pp → hhh) ∼ 10 [fb], so that: Thus, the expected enhancement over the SM signal in the hhh → bbbbbb decay channel is again R hhh→bbbbbb ∼ O(10). However, since in the UEHiggsY case we have BR(h → bb) ∼ 0.18, the triple Higgs cross-section in this channels is σ(pp → hhh → bbbbbb) ∼ 10 fb · 0.18 3 ∼ 60 [ab] and, therefore, might be difficult to detect even at the HL-LHC with a luminosity of 3000 inverse fb.
B. Higgs + high pT light-jet production pp → hj In general, there is a tree-level SM contribution to the exclusive Higgs + light-jet production, pp → hj, from the hard processes gq → hq, gq → hq and qq → hg, where q = u, d, c or s. However, since the corresponding tree-level diagrams (see e.g., the t-channel diagram for gq → hq in Fig. 2) are proportional to the light-quarks Yukawa couplings, the effect of these light-quark initiated hard-processes on the overall pp → hj cross-section is negligibly small in the SM (i.e., when y q 1 in particular for q = u, d). Thus, the dominant SM contribution to the Higgs + light-jet cross-section arises from the 1-loop gluon-fusion process gg → gh, which, at leading order, is generated mainly by 1-loop top-quark exchanges.
If, on the other hand, y q ∼ y SM b for all q = u, d, c, s, as expected in the UEHiggsY framework, then the contribution (to the pp → hj cross-section) from the quark initiated tree-level process gq → hq, gq → hq and qq → hg becomes appreciably larger. Indeed, in [37] we have shown that the Higgs p T distribution in pp → hj production at the LHC is a rather sensitive probe of the light-quarks Yukawa couplings (and also of other forms of NP in the Higgs-gluon hgg and quark-gluon qqg interactions) and thus of the UEHiggsY paradigm.
In particular, we have defined in [37] the signal strength for pp → hj, followed by the Higgs decay h → f f , where f can be any of the SM Higgs decay products (e.g., f = b, τ, γ, W, Z): whereσ is the p T -dependent "cumulative cross-section", satisfying a given lower Higgs p T cut: and found that, in a NP scenario where y q ∼ y SM b for all q = u, d, c, s (which corresponds to the UEHiggsY framework discussed here), the above signal strength is significantly smaller than its SM value at the large p T (h) regime: for f = b, τ, γ, W, Z and with a p T (h) cut in the range p cut T ∼ 200 − 1000 GeV.
C. Higgs-photon associated production pp → hγ In the SM, the leading contribution to the exclusive pp → hγ production channel is the tree-level t-channel hard processes cc, bb → hγ (shown by the diagram for qq → hγ in Fig. 2 with q = c, b), which give a rather small cross-section of σ(pp → hγ) ∼ O(0.1) [fb] with a 30 GeV p T (γ)-cut at the 13 TeV LHC [45,46]. The 1-loop SM (EW) diagrams contributing to the light-quark annihilation channels, e.g., uū, dd → hγ, are more than an order of magnitude smaller than the tree-level bb-fusion production channel [45] and the amplitude for the gluon-fusion production channel gg → hγ vanishes due to Furry's theorem.
In our UEHiggsY framework, the exclusive channel pp → hγ has an appreciably larger rate due to the treelevel (t-channel) light-quark fusion diagrams qq → hγ shown in Fig. 2 (i.e., with q = u, d, s, c), which are enhanced by the O(y SM b ) qqh Yukawa couplings. In particular, setting againf ij qH = δ ij and Λ = 1.5 TeV (leading to y q ∼ y SM b ), we get σ(pp → hγ) ∼ 1250 [fb], at the 13 TeV LHC and with p T (γ) > 30 GeV. Thus, for the exclusive pp → hγ production channel we find: where about 80% of the enhancement arises from the tree-level uū-fusion diagrams.
We note that the exclusive pp → hγ channel is potentially sensitive to other variants of underlying NP which can be parameterized by different forms of higher dimensional effective operators, i.e., other than the ones associated with the UEHiggsY paradigm in Eq. 1, [48]. In particular, [48] finds that σ(pp → hγ) ∼ O (10) [fb] can be realized by other types of NP with a typical scale of Λ ∼ 1 TeV and Wilson coefficients of O(1). This is more than an order of magnitude smaller than the effect expected in the UEHiggsY case.
Clearly, differential distributions (e.g., such as the photon transverse momentum distribution [48]) may provide extra handles for disentangling the various types of NP that can effect the hγ production channel at the LHC. This is, however, beyond the scope of this work.
D. Higgs-single top associated production pp → th The main SM production channels of a Higgs boson in association with a single top quark at hadron colliders are inclusive and have, at LO, two distinguishable underlying hard processes, which include an extra quark/jet accompanying the ht in the final state [38]: [3] the dominant t-channel process which is initiated by bWfusion, bW → ht + j, where the extra jet accompanies the virtual space-like W -boson, and the s-channel qqfusion hard-process with a virtual time-like W -boson, qq → W → th + j b , where q, q are light quarks (i.e., primarily u,d and c,s) and j b is a b-quark jet. The tchannel process is very sensitive to the magnitude and sign of the tth Yukawa coupling [49], and at LO in the SM has a cross-section of σ(pp → ht + j) SM ∼ 75 [fb]. The cross-section for the s-channel process, pp → ht + j b , is about 25 times smaller [38].
The exclusive th production channels, pp → ht and pp → ht, involve in the SM the extremely small 1-loop FC tuh and/or tch vertices and are, therefore, negligibly small with no observable consequences. On the other hand, in the UEHiggsY framework we have for the FC tuh coupling (assuming for simplicity thatf 13 uH =f 31 uH ): and similarly for the tch coupling, where = v 2 /Λ 2 . Thus, with Λ ∼ 1.5 TeV and natural underlying NP (i.e.,f 13 uH ∼ O(1)), we expect the UEHiggsY FC tuh and tch couplings to be typically of the size of the SM b-quark Yukawa coupling, ξ tu,tc ∼ y SM b , in which case the exclusive channel pp → th has a rate many orders of magnitudes larger than the SM rate, due to the tree-level ug(cg)-fusion FC diagrams u(c)g → th (see Fig. 2).
Defining here the ratios: we find R th/thj ,Rt h/thj → 0 in the SM, while R th/thj ∼ 2 andRt h/thj ∼ 0.8 in the UEHiggsY case. Notice also that the asymmetric production of th versesth in the UEHiggsY framework is different then the corresponding asymmetry in the SM channels thj and thj. In particular, while in the UEHiggsY case the th production rate is about 5 times larger than theth rate, in the SM the thj production rate is less than 2 times larger than thē thj rate (see [38]). Indeed, the CMS collaboration had recently performed a dedicated search for the exclusive FC single top -Higgs [3] Another sub-leading single top production channel in the SM is the associated production of th with an on-shell W boson in the final state, pp → thW . associated production channel pp → th at the 13 TeV LHC with a data sample of 35.9 fb −1 [50]. No significant deviation from the predicted background was observed and bounds on the FC couplings ξ tu and/or ξ tc were obtained. In particular, the bounds were reported on the branching ratios of the corresponding FC decay channels t → uh, ch, which, when translated to the FC couplings (see derivation below), give ξ tu , ξ tc < ∼ 0.09. This bound is more than 4 times larger than the expected strength of these FC couplings in the UEHiggsY framework with which the above values for R th/thj andRt h/thj were obtained (recall that, within the UEHiggs paradigm, we expect ξ tu , ξ tc ∼ y SM b ∼ 0.02). In other words, the currently reported sensitivity to the exclusive th final state is σ(pp → th+th) < ∼ 16×σ(pp → th+th) U EHiggsY , since the corresponding UEHiggsY predicted cross-section scales as ξ 2 tu,tc . Finally, we note that the currently best direct bounds on ξ tu and ξ tc were obtained by the ATLAS collaboration, which analysed the FC top-quark decays t → uh, ch in pp → tt events at a center of mass energy of 13 TeV and with 36.1 fb −1 [51]. They found BR(t → uh) < 2.4 · 10 −3 and BR(t → ch) < 2.2 · 10 −3 .
Using Eq. 38, we have (for m u,c /m t → 0): where Γ t is the total width of the top-quark. Thus, the above cited ATLAS bounds translate into the bounds ξ tu , ξ tc < ∼ 0.06, allowing FC tuh and tch couplings about 3 times larger than the b-quark Yukawa coupling, i.e., ξ tu , ξ tc < ∼ 3y SM b , which do not rule out the UEHiggsY paradigm with the values ξ tu , ξ tc ∼ y SM b .
In Table II we summarize our predictions for the Higgs signals considered in this chapter in the UEHiggsY framework, as well as the corresponding SM predictions and the current limits and sensitivities to some of these signals from the LHC RUN2.

VI. SUMMARY
We have proposed a new framework where the Yukawa couplings of the light quarks of the 1st and 2nd generations, q = u, d, c, s, can be as large as the b-quark Yukawa, thus decoupling them from the SM Higgs mechanism, within which a Yukawa coupling of a fermion is proportional to its mass. We have shown that this scenario (which we named the "UEHiggsY paradigm") is natural, if the typical scale of the NP which is responsible for the enhancement of the light quarks Yukawa couplings is around 1-2 TeV and the heavy (and decoupled) degrees of freedom in the underlying theory have natural couplings of O(1) with the SM quarks. We have studied the UE-HiggsY paradigm in an EFT setup, where dimension six effective operators yield a Yukawa term y q ∼ O f v 2 Λ 2 , √ s = 13 TeV (RUN2) Higgs signal SM prediction our UEHiggsY prediction Current limit/sensitivity R hV →bbV = σ(pp→hV →bbV ) σ(pp→hV →bbV ) SM  The cases where we did not find an experimental bound/measurement are marked by "None". The -LHC experimental groups are encouraged to perform a dedicated search in these channels, e.g., the exclusive pp → hγ, which may also be important for the search of heavy resonances [52].
where Λ is the typical NP scale and f is a dimensionless coefficient (i.e., the Wilson coefficient in the EFT expansion), which depends on the properties and details of the underlying NP dynamics. In particular, with Λ ). We also explore the UEHiggsY scenario in extensions of the SM which contain TeV-scale vector-like quarks (VLQ) with a typical mass of 1-2 TeV, which we matched to the higher dimensional EFT operators. We then discuss the flavor structure of the UEHiggsY Yukawa textures and, in particular, of the VLQ extension, and the sensitivity of the measured 125 GeV Higgs signals to this paradigm.
Finally, we suggest some "smoking gun" signals of the UEHiggsY paradigm that should be accessible to the future LHC runs: multi-Higgs production pp → hh, hhh and single Higgs production in association with a high p T jet or photon pp → hj, hγ and with a single top-quark pp → ht.