Phenomenology of Enhanced Light Quark Yukawa Couplings and the $W^\pm h$ Charge Asymmetry

I propose the measurement of the $W^\pm h$ charge asymmetry as a consistency test for the Standard Model (SM) Higgs, which is sensitive to enhanced Yukawa couplings of the first and second generation quarks. I present a collider analysis for the charge asymmetry in the same-sign lepton final state, $p p \to W^\pm h \to (\ell^\pm \nu) (\ell^\pm \nu jj)$, aimed at discovery significance for the SM $W^\pm h$ production mode in each charge channel with 300 fb$^{-1}$ of 14 TeV LHC data. Using this decay mode, I estimate the statistical precision on the charge asymmetry should reach 0.4\% with 3 ab$^{-1}$ luminosity, enabling a strong consistency test of the SM Higgs hypothesis. I also discuss direct and indirect constraints on light quark Yukawa couplings from direct and indirect probes of the Higgs width as well as Tevatron and Large Hadron Collider Higgs data. While the main effect from enhanced light quark Yukawa couplings is a rapid increase in the total Higgs width, such effects could be mitigated in a global fit to Higgs couplings, leaving the $W^\pm h$ charge asymmetry as a novel signature to test directly the Higgs couplings to light quarks.


I. INTRODUCTION
After the discovery of the Higgs boson in 2012 by the ATLAS and CMS experiments [1,2], the experimental Higgs effort has transitioned to a full-fledged program of Higgs characterization and precision measurements of its couplings to Standard Model (SM) particles. The direct observation of the Higgs to vector bosons has been established at high significance [3][4][5], while decays to taus and bottom quarks have yet to reach discovery significance and direct knowledge about the couplings of the Higgs to first and second generation fermions is utterly lacking.
The most straightforward information about light generation Yukawas would come from direct decays of the Higgs. While these are certainly viable possibilities for the charged leptons [6,7], the inability to distinguish light quark-initiated jets from each other renders this avenue a practical impossibility, with the notable exception of charm tagging. A few studies [8,9] have investigated the prospects for identifying direct decays of Higgs to charm jets, where bottom-and charm-jet tagging work in tandem to disentangle enhanced bottom and charm Yukawa couplings.
Aside from direct decays of the Higgs to light quark jets, the other possibilities for measuring light quark Yukawa couplings come from charm-Higgs associated production [10], which also requires a careful calibration of charm jet tagging efficiencies and a precise determination of Higgs and associated jet backgrounds. The practical applicability of this technique is not well established, however, since a systematic treatment of Higgs and non-Higgs backgrounds is still absent.
An enhanced light quark Yukawa can also lead to significant effects in rare Higgs decays to quark-anti-quark mesons and vector bosons [11][12][13][14]. The impressive control of theoretical uncertainty in these calculations and the corresponding proof of principle searches for such rare decays from Z and Higgs bosons [15][16][17] make it an interesting channel to pursue. In these channels, though, interpreting a deviation from the SM expectation would require knowledge of the Higgs vertices in the so-called indirect contributions. A deviation in the rate for h → J/Ψγ, for example, could be attributed to a nonstandard effective coupling of the Higgs to two photons as well as the charm Yukawa coupling. Hence, the realistic sensitivity of these rare Higgs decays to nonstandard light quark Yukawas suffers not only from the small expected SM rates, but also because the indirectness of the probe necessitates a combination with other Higgs measurements.
Nevertheless, the power of combined fits to Higgs signal strengths cannot be discounted as an important tool in constraining nonstandard Yukawa couplings [8,13,18]. Such combined fits, however, are handicapped by the inability to determine the total width of the Higgs and thus require model-dependent assumptions in order to extract Higgs couplings [19]. For example, the possibility of exotic production modes of the Higgs boson contaminating the Higgs dataset [20] would introduce new physics parameters outside of the coupling deviation framework, spoiling the entire applicability of the κ-framework.
We see that many of the proposed tests of non-standard Yukawa couplings have varied difficulties in experimental applicability or theoretical interpretation. While direct decay tests are best and subject to the least theoretical bias, the only potentially viable channel is the h → cc decay.
Production tests, like measuring hc + hc production, are fraught with many backgrounds and experimental challenges regarding charm tagging. Indirect tests, whether via Higgs rare decays to quantum chromodynamics (QCD) mesons and vectors or combined coupling fits to Higgs data, are most robust when conducted as consistency tests of the SM.
In the spirit of offering new channels for probing the Standard Model Yukawa couplings, we motivate the charge asymmetry in vector boson associated Higgs production at the LHC. As a proton-proton machine, the LHC handily favors W + h production over W − h production, mainly through the Higgsstrahlung process qq ′ → W ± * → W ± h. At the 14 TeV LHC, for example, for 56 [21, 22]. We point out, however, that this inclusive charge asymmetry is dramatically changed if the light SM quarks have large Yukawa couplings.
Concomitant effects from large light quark Yukawa couplings, such as qq s-channel Higgs production and a rapid increase in the total Higgs width, provide additional channels for indirectly constraining enhanced quark Yukawas.
In Sec. II, we provide a theory motivation and background on Yukawa coupling deviations.
In Sec. III, we discuss the charge asymmetry of pp → W ± h in the SM and the modifications induced by anomalous light quark Yukawa couplings. We then present a collider analysis for same-sign leptons targetting the W ± h charge asymmetry measurement in Sec. IV, demonstrating that the charge asymmetry can be measured at the LHC to subpercent accuracy. We proceed to discuss other phenomenological consequences of enhanced light quark Yukawa couplings and their constraints in Sec. V. We conclude in Sec. VI.

II. YUKAWA DEVIATIONS
The question of fermion mass generation is a central aspect of the structure of the Standard Model. A nonstandard Yukawa coupling in the SM Lagrangian leads to unitarity violation for ff → V V scattering amplitudes. In the Higgs post-discovery phase, and in the absence of direct knowledge of the Yukawa coupling for a given SM fermion f , we can calculate a unitarity bound from ff → W + W − scattering [23] by requiring the partial amplitude satisfies unitarity, |a 0 | ≤ 1/2.
The scale of unitarity violation is then given by where v = 246 GeV is the Higgs vev, ξ = 1/ √ 3 for quarks and ξ = 1 for charged leptons.
This unitarity violation is a general feature in theories with chiral fermion masses arising from spontaneous symmetry breaking if the fermion mass is mismatched with its Yukawa coupling. A stronger bound on E f can be found by studying ff scattering to arbitrary numbers of longitudinal modes of electroweak bosons [24]. Although such a fine-tuned light quark mass is aethestically unappealing, such a mismatch between the quark mass and the Higgs Yukawa coupling cannot be discounted from collider searches for heavy fermions, seeing that limits on vector-like top parters reach only the 1 TeV scale [25,26].
The unitarity bound and inadequacy of the ad-hoc renormalizable Lagrangian can be simultaneously cast into more familiar language by appealing to dimension-6 effective operators for Higgs physics. Here, the SM provides the usual dimension-4 couplings that preserve the mass-coupling relation expected in SM physics, but the fermion masses and their Yukawa couplings get additional contributions from dimension-6 operators. We have where y u and y ′ u , y d and y ′ d are matrices in 3 ⊗ 3 flavor space of Q L and u R and Q L and d R , respectively. The flavor rotations of Q L = (u L , d L ), u R , d R are then used to ensure the mass matrices are diagonal, with f denoting up-type or down-type quarks, and we have expanded H = 1 √ 2 (h + v) about its vev. Importantly, these flavor rotations does not guarantee in general that the Yukawa are diagonal. Simultaneous diagonalization of m f and y ′ f simultaneously is not guaranteed unless they are aligned, and hence without additional assumptions, the Yukawa terms in dimension-6 Higgs effective theory are expected to introduce flavor-changing Higgs couplings. Moreover, phases in y ′ f are not guaranteed to vanish, so we also expect CP violation in Higgs couplings (the overall phase in each Yukawa matrix is not observable). Bounds on both flavor-changing Higgs couplings and CP -violating couplings can be obtained from studying meson mixing [27,28] and electron and neutron dipole moment constraints [29].
Nevertheless, a large, enhanced diagonal coupling for fermions is readily achieved from Eq. (5). vs.cd PDFs also enhance and dilute, respectively, the charge asymmetry.
Enhanced light quark Yukawa couplings cause the inclusive W ± h charge asymmetry to deviate significantly from the SM expectation. For very large Yukawa enhancements, we can neglect the Higgsstrahlung diagrams in Fig. 1  an enhanced strange Yukawa drives the balanced cs vs.cs PDFs to dominate W ± h production, while the Cabibbo-suppressed us vs.ūs initial states still retains a positive asymmetry. Finally, large down and up quark Yukawas actually enhance the positive charge asymmetry beyond the SM expectation, since the ameliorating effects from second generation quarks in the proton PDFs are weakened.
We adopt the usual κ notation to describe rescalings of the Higgs Yukawa couplings to the first and second generation quarks, y f, eff = κ f y f, SM for f = d, u, s, or c. Throughout this work, we will only consider one Yukawa deviation at a time and will comment briefly in the conclusions about simultaneous deviations in multiple Yukawa couplings. For convenience, we also use theκ f normalization, which rescales κ f into units of y textSM b evaluated at µ = 125 GeV: In Fig. 2, we show the inclusive charge asymmetry for the 14    The gray region shows the bound from the direct Higgs width measurement, Γ H < 1.7 GeV [53], which excludesκ f > 25 for each light quark flavor and is discussed in Sec. V.
Group [32] and renormalized to the Higgs mass via RunDec [33].  6) to rescale κ toκ. The Higgs coupling to W bosons was fixed to the SM value for this scan. We illustrate the mild dependence of the charge asymmetry on PDFs by using two different PDF sets, NNPDF2.3 [34] and CTEQ6L [35].
Measuring the asymmetry at the collider requires tagging the leptonic decay of the W boson and where improvements in hadronic and leptonic τ decays have led to important evidence for the Higgs decays to τ s [5]. The efficacy of these reconstruction methods in the presence an additional lepton and neutrino, however, has not been demonstrated.
We instead explore a new Higgs process, W ± h → (ℓ ± ν)(ℓ ± νjj), taking advantage of the semileptonic decay of the Higgs via W W * . This process has a number of features that make it attractive for measuring the W ± h charge asymmetry. First, this same-sign lepton final state inherits the same charge asymmetry as the inclusive W ± h process. Second, the leading non-Higgs background processes for same-sign leptons are all electroweak processes, in contrast to the h → bb decay discussed before. Finally, although the Higgs resonance is not immediately reconstructible in this decay channel, we have a number of kinematic handles to isolate the Higgs contribution to this final state, which make it eminently suitable to extract the charge asymmetry.
IV. COLLIDER ANALYSIS: SAME-SIGN LEPTONS FROM ASSOCIATED W ± h PRODUCTION Having motivated the possibility and importance of direct tests for light quark Yukawa couplings via their effects in the charge asymmetry of W ± h production, we now present a search for W ± h → ℓ ± ℓ ± / E T + 1 or 2 jets, with ℓ = e or µ, which can be a benchmark process for measuring the charge asymmetry. We emphasize that the charge asymmetry measured in an exclusive Higgs decya mode is at best considered a consistency test of the Standard Model, since large Yukawa deviations in light quark couplings will dilutive the SM Higgs branching fractions, which we address in Sec. V.
Nevertheless, the charge asymmetry of W ± h production is a prediction of the Standard Model that can be affected by deviations in light quark Yukawa couplings.
The primary backgrounds for the ℓ ± ℓ ± / E T + 1 or 2 jets signature are W ± W ± jj, W ± Z, with Z → ℓ ± ℓ ∓ and a lost lepton, and W + W − with charge mis-identification. Note that all of these diboson backgrounds are electroweak processes, giving the benefit that W ± h signal rates are roughly comparable to the background rates. On the other hand, these backgrounds also have their own charge asymmetries, but these can be probed via complementary hadronic channels, inverting selection cuts, or data-driven techniques.
Other backgrounds we do not consider are fully leptonic tt, which we would discard because it requires charge mis-ID and would be killed by b-vetoes. The single vector boson backgrounds, W + jets and Z+ jets, fail because they need a jet faking a lepton or in the case of the Z with charge mis-ID, would still reconstruct the Z peak. We do not consider hard brehmstrahlung and ignore jet faking lepton rates, which eliminates QCD backgrounds.
To enhance the W ± h contribution to the final state, we select exactly two same-sign leptons with p T > 15 GeV, |η| < 2.5. We then select either one or two jets with p T > 20 GeV, |η| < 2.5, where jets are clustered using the anti-k T algorithm [50] with R = 0.4 from FastJet v3.1 [51]. We allow events with only one jet because the second jet from the Higgs decay is too soft or merges with the first jet a significant fraction of the time. Two-jet events are required to be consistent with a hadronic W candidate, 60 GeV < m jj < 100 GeV. Since the subleading lepton typically arises from the Higgs semileptonic decay, we require m T, subleading ℓ,jj < 150 GeV for two jet events.
These cuts are summarized in Table I After our cuts, the W ± h signal asymmetry is 21.0%, while the total charge asymmetry from background contamination is 16.1%. A more careful study of systematic effects, subleading backgrounds, and further reduction of the diboson backgrounds in this channel is certainly warranted but beyond the scope of this work. Optimized cuts would, in particular, help minimize the dominant charge-asymmetric W ± Z background and improve the signal to background discrimination. We expect future studies from additional reconstructable decay modes of the Higgs, such as h → bb, h → ℓ ± ℓ ∓ νν (via ZZ * or W W * ), h → τ ± τ ∓ , and h → γγ will also contribute to the overall sensitivity of measuring the W ± h charge asymmetry.
Extrapolating to 3 ab −1 , we find that the charge asymmetry of the W ± h process can be tested with a statistical precision of ≈ 0.4%, which would be sensitive to higher order theory uncertainties, including PDF errors, and experimental systematic uncertainties, which we have neglected in this treatment. Nevertheless, the observation of the W ± h process in the two independent channels, ℓ + ℓ + + / E T + 1 or 2 jets and ℓ − ℓ − / E T + 1 or 2 jets, provides a direct test on the underlying production process of the W ± h final state and a direct constraint on possibly enhanced light quark Yukawa couplings.
We remark that for non-standard Yukawa couplings, the kinematic distributions for W ± h production are expected to change, resulting in small differences in the quoted efficiencies. For example, with κ d = 1000 (κ u = 1000) the final W ± h signal efficiency increases to 23.0% (23.5%) compared to the SM benchmark efficiency of 21.9%.

CONSTRAINTS
The set of Higgs measurements from the LHC and the Tevatron provide a broad but patchwork picture of Higgs couplings constraints. We emphasize that a direct measurement of Higgs couplings at the LHC is not currently feasible since the total width of the Higgs is unknown, and thus interpreting Higgs measurements requires model assumptions about the underlying Lagrangian dictating the Higgs couplings and possible new light degrees of freedom. For example, the κframework for studying Higgs coupling deviations is invalid when new exotic modes for Higgs production are accessible [20], which cause changes in signal efficiency that are not captured by simple coupling rescalings.

A. Total width constraints
The only direct test for enhanced light quark Yukawa couplings from the LHC is the constraint from the direct measurement of the total Higgs width. From the 7+8 TeV combined analyses using the γγ and 4ℓ channels, ATLAS reported a Higgs total width Γ H constraint of 2.6 GeV at 95% CL [52] and CMS reported a tighter bound of 1.7 GeV [53]. With the latest 13 TeV data, CMS observed a bound of 3.9 GeV (expected 2.7 GeV) in the 4ℓ channel [54] compared to a bound of 3.4 GeV (expected 2.8 GeV) with the Run I dataset, indicating that lineshape measurements of the Higgs have already saturated the resolution expected from the LHC. We remark that the next-generation e + e − Higgs factory machines [55][56][57] will inaugurate the true precision era of Higgs measurements by virtue of being able to tag Higgs-candidate events via the recoil mass method, which can determine the SM Higgs width with 2 − 5% precision [19]. Since light quarks are kinematically accessible decay modes of the 125 GeV Higgs, however, the on-shell decay of the Higgs to light quarks via enhanced Yukawa couplings is untamed for largeκ.
We can thus use the CMS Γ H < 1.7 GeV constraint [53] to bound the individual light quark Yukawa couplings: using the renormalized quark masses calculated from RunDec [33]. These translate tō

B. Inclusive charge asymmetry
At the fully inclusive level, the Higgs Yukawa couplings can be tested via the proposed charge asymmetry measurement. While more stringent constraints on the light quark Yukawa couplings can be obtained from global fits combining all Higgs data, these global fits suffer from the requirement of a theoretical model dependence, most commonly the κ framework.
We point out, however, that absent deviations in light quark Yukawa couplings the fully inclusive charge asymmetry also provides a model-independent measurement of the Higgs coupling to W bosons. Fully inclusive Higgs production processes are not normally considered at hadronic colliders because of the inability to ascertain the Higgs contribution independent of the Higgs decay mode.
This is analogous to the recoil mass method advocated for e + e − Higgs factories, which allows a fully inclusive rate measurement sensitive to the hZZ coupling. At the moment, though, there is no practical proposal for measuring such an inclusive variable in any Higgs process and all Higgs data stems from analyses for specific Higgs decays, and so the intriguing possibility of a fully inclusive Higgs measurement to extract a Higgs production coupling remains remote.

C. Exclusive Higgs measurements and current constraints
In Eq. (3), we only introduced new physics operators that modified the mass generation and Yukawa couplings of the SM quarks, leaving the Higgs-vector couplings untouched. As a result, enhanced Yukawa couplings lead to increased rates for σ(qq ′ → W ± h) and σ(qq → h) production, but the effective signal strengths µ W h and µ gg of exclusive Higgs decays to a particular X final state are depleted according to where we have included s-channel qq Higgs production in the overall gluon fusion rate. We remark that the gluon fusion and qq annihilation production modes can be possibly disentangled at the LHC by studying Higgs candidate kinematics [61][62][63], while the qq decay can also possibly be probed at e + e − Higgs factories [64].
Solely turning on large Yukawa couplings for light quarks is hence strongly constrained by combined coupling fits using current Higgs data, since the increased production rates from the which can be converted tō κ d < 1.24,κ u < 0.54,κ s < 1.03,κ c < 1.14 , vectors can also relieve the bounds above, although concrete possibilities are limited [68]. A global analysis performed in Ref. [13], allowing all Higgs couplings to vary, has derived the constraints κ d < 1.4,κ u < 1.3,κ s < 1.4, andκ c < 1.4.
We note that the Tevatron also provides constraints on enhanced light quark Yukawa couplings given the nature of the machine as a proton-anti-proton collider. The primary search channel at the Tevatron sensitive to s-channel Higgs production was the W W * decay mode [69] We hence motivated the possible measurement of the W ± h charge asymmetry in the exclusive mode W ± h → ℓ ± ℓ ± / E T + 1 or 2 jets, which is a clean same-sign dilepton final state that inherits the same charge asymmetry as the original Higgs production process. After accounting for the main backgrounds from electroweak diboson production, we estimate that the individual ++ and −− final states reach a statistical 5σ significance each with 300 fb −1 of 14 TeV LHC data. Even though the Higgs boson is not fully reconstructed in this decay, the clean same-sign dilepton signature can be readily extrapolated to the expected 3 ab −1 high luminosity run, enabling a statistical precision on the exclusive charge asymmetry of 0.4%. If the measured asymmetry deviates from the SM expectation, then a likely interpretation would be an enhanced SM light quark Yukawa counterbalanced by additional new physics effects that preserve rough current consistency of the