Charming the Higgs

We show that current Higgs data permit a significantly enhanced Higgs coupling to charm pairs, comparable to the Higgs to bottom pairs coupling in the Standard Model, without resorting to additional new physics sources in Higgs production. With a mild level of the latter current data even allow for the Higgs to charm pairs to be the dominant decay channel. An immediate consequence of such a large charm coupling is a significant reduction of the Higgs signal strengths into the known final states as in particular into bottom pairs. This might reduce the visible vector-boson associated Higgs production rate to a level that could compromise the prospects of ever observing it. We however demonstrate that a significant fraction of this reduced signal can be recovered by jet-flavor-tagging targeted towards charm-flavored jets. Finally we argue that an enhanced Higgs to charm pairs coupling can be obtained in various new physics scenarios in the presence of only a mild accidental cancellation between various contributions.


I. INTRODUCTION
The recent discovery of a Higgs-like particle at the LHC [1,2] is a remarkable success of the Standard Model (SM) of particle physics.The current data imply that the new particle is consistent with the SM predictions [3,4].Still, a lot is yet to be learned regarding the properties of this recently discovered particle.
It is important to study the nature of the Higgs couplings to other SM fields.As the Higgs is rather light, with a mass smaller than that of the top quark and smaller than twice the mass of the W and Z boson, it decays to particles that very weakly interact with it.In fact, the dominant decay mode of the Higgs is to a bottom pair within the SM, and the bottom Yukawa coupling to an on-shell Higgs is O(0.02).This exposes the Higgs branching ratios to a generic susceptibility to any form of new physics.Any deformation of the Higgs couplings to the SM particles, or introduction of additional couplings to new fields, that competes with the small Higgs to bottom coupling will lead to a significant change of the Higgs phenomenology at the LHC.An interesting picture emerges from the potential changes to the existing Higgs couplings to SM particles.The next to leading five couplings beyond the bottom coupling are Higgs couplings to W , Z and τ , which are already measured to decent accuracy, the coupling to gluons which controls the Higgs production cross section, and the coupling to the charm quark.Among those SM states the charm stands out as almost nothing is known experimentally on its coupling to the Higgs boson.
The Higgs branching ratio into charm pairs is O(3%) in the SM, which renders any attempt to directly probe the Higgs to charm coupling at the LHC extremely challenging due to the large multijet background.However, the charm Yukawa coupling is only few times smaller than the bottom one in the SM, about one part in five at the Higgs mass scale [5].Thus, only a factor of few mismatch between the actual charm coupling and its SM value would lead to a significant change of the Higgs phenomenology.Furthermore, despite its small value, the charm mass is not negligible and due to the CKM suppression in bottom decays the charm life time is comparable to that of the bottom quark.Hence, jets originating from charm quarks can in principle be identified at colliders.The ATLAS collaboration, in fact, recently presented new experimental techniques designed to tag charm jets at the LHC [6].The possibility to apply charm-tagging, beyond its plain interest from the SM perspective [7,8], also opens new possibilities to analyze various beyond the SM signals [9][10][11][12].In particular we show in this paper how crucial charm-tagging may be in order to exhume the associated Higgs production signal in the case of a suppressed h → b b branching ratio due to an enhanced Higgs to charm coupling relative to the SM.
There is currently no attempt to directly probe the h → cc channel at colliders and the Higgs to charm coupling is constrained indirectly through the bound on the allowed Higgs "invisible" (more precisely, unobserved) branching ratio.For SM Higgs production cross sections this branching ratio cannot exceed ∼ 20% at 95% confidence level (CL), or ∼ 50% if an additional new physics source of gluon fusion production is assumed [3].This implies a rough upper bound on the Higgs to charm coupling of about three to five times its SM value, assuming no other source of invisible decays other than Higgs decays into the unobserved SM states.Hence, the current data still allow for the h → cc decay channel to be comparable in size with or even to dominate over the h → b b one.
The outline of the paper is as follows.In the next section we provide a quantitative analysis of the current Higgs data in order to derive the present bounds on the Higgs to charm coupling.We then demonstrate in Sec-tion III that an enhanced charm coupling significantly suppresses the h → b b signal strength in associated Higgs production, mostly through a reduced Higgs branching ratio into bottom pairs, and that the SM level of this signal could be partially or even entirely recovered by enriching the sample with charm-tagged events, depending on the charm-tagging efficiency.In Section IV, we argue that a large Higgs to charm coupling can be obtained under reasonable conditions in various theories beyond the SM where moderate cancellation is present.We present our conclusions in Section V.

II. CONSTRAINTS FROM HIGGS DATA
A Higgs to charm pair coupling significantly larger than in the SM affects both Higgs production cross sections and branching ratios, and is therefore indirectly contrained by current Higgs rate measurements at the LHC.On the one hand a large Higgs to charm coupling implies a universal reduction of all Higgs branching ratios other than into cc final states, provided all other Higgs couplings remain standard.On the other hand Higgs production at hadron colliders is also typically enhanced relative to the SM through a more important charm fusion mechanism occurring at tree-level.(Another effect, though far subdominant, arises in gluon fusion Higgs production through a modified charm-loop contribution.)Therefore, one might expect that there is a charm coupling value for which the enhancement in Higgs production approximately compensates the universal suppression in Higgs decays so that Higgs rates measured at the LHC remain close to the SM predictions.We thus perform a fit of all available Higgs data allowing deviations of the hcc coupling relative to the SM in order to quantitatively determine the largest value presently allowed.
We follow the approach of Ref. [3] to globally fit available Higgs data.We consider both direct data from Higgs rate measurements at the LHC and indirect constraints from electroweak (EW) precision measurements at LEP.We assume that there is only one Higgs scalar h of mass m h = 126 GeV, which is a singlet of the custodial symmetry preserved by EW symmetry breaking (EWSB).The Higgs interactions with other SM particles are assumed to be flavor-conserving and accurately enough parameterized by the effective Lagrangian where interactions to zeroth-order in derivatives are and interactions to next-to-leading order in derivatives are where q = u, d, s, c, b, t and ℓ = e, µ, τ are the SM massive quarks and charged leptons, v = 246 GeV is the EWSB scale, W µ , Z µ , A µ and G µ are the SM gauge fields with the corresponding fields strength tensors.The treelevel SM limit is achieved by c V = c q = c ℓ = 1 and c γγ = c gg = c Zγ = 0 (before the top quark has been integrated out).We neglect CP-odd operators and assume real c q,ℓ coefficients as there is only a weak sensitivity to CP-odd couplings and CP-violating phases in Higgs rate measurements.1 (See e.g.Ref. [15] for a recent update.)The underlying custodial symmetry imposes the following relations among couplings in L 2 [3] where g L and g Y are the SU(2) L and U(1) Y gauge couplings, respectively.In contrast with existing Higgs fits, as in e.g.Refs.[3,4,16,17], we leave the c c as a free parameter of the fit.Current Higgs data are very unlikely to be sensitive to Higgs couplings to e, µ, and u, d, s, as the latter are already very small in the SM.We thus set c e,µ = c u,d,s = 1 in the following.We are left with at most eight independent free parameters: c V , c c,b,t , c τ , c gg , c γγ and c Zγ .
The Higgs rate measurements at the LHC are presented in the form of signal strengths defined as for each final state f , where σ pp→h and BR h→f are the Higgs production cross section and branching ratio, respectively, while the SM label denotes their corresponding SM predictions.Similar signal strengths measured at the Tevatron are obtained from Eq. ( 5) through the replacement pp → pp.We perform a standard χ 2 analysis in order to fit the coefficients in Eq. ( 1) to current Higgs data.The total χ 2 function is where the index i runs over all measurements of the channel f and correlations between different channels are neglected.µ ex f,i and σ f,i denote the experimental central values and their corresponding standard deviations, respectively.Asymmetric experimental errors are symmetrized for simplicity.We consider the most updated set of Higgs measurements in h → W W * , ZZ * and γγ channels from ATLAS [18], CMS [19] and Tevatron [20] collaborations, as well as the h → τ τ results from CMS [21] and Tevatron [20].We also include the recent h → b b search in vector-boson associated production [22] and in vector-boson fusion at CMS [23], as well as the h → Zγ search at CMS [24].We do not use the recent h → b b and h → τ τ preliminary ATLAS results.However, we checked that the latter does not significantly change our results given the current experimental sensitivity in these channels.µ th f,i are the theoretical signal strength predictions, which incorporate the relative weights of each Higgs production mechanisms as quoted by the experimental collaborations, whenever available.This is the case for all channels that we use except for V h(b b) at CMS for which we assume pure vector-boson associated production.Theoretical predictions for Higgs signal strengths in terms of the effective coefficients in Eq. ( 1) can be found in Ref. [3], while we use the SM Higgs production cross sections and branching ratios of Ref. [25].We however add the following two modifications in order to implement a hcc coupling significantly different than its SM value.First of all, we include the charm loop contribution in the gluon fusion cross section as where numbers are obtained using the running quark masses extracted from Ref. [5].ĉSM gg ≃ 0.012 is obtained by taking the SM limit, c gg → 0 and c t,b,c → 1, in Eq. (7).Then, we include the charm fusion cross section as σ cc→h ≃ 3.0 × 10 −3 |c c | 2 σ SM gg→h , where the charm fusion to gluon fusion cross section ratio is evaluated at next-to-leading order in the QCD coupling and we use MSTW parton distribution functions [26].We transposed the NLO bottom fusion cross section obtained in Ref. [27] in order to estimate σ SM cc→h .
We mainly focus on two different scenarios, where (a) all Higgs couplings but the charm one are SM-like.
(b) all the Higgs couplings but the charm one and c gg are SM-like.
The general case, where all independent parameters are allowed to deviate from the SM is discussed in Appendix A. However, the results are found to be very close to those from case (b) above.Thus, unless explicitly mentioned otherwise, case (b) can be taken as a proxy for the general case.In both cases  to a small interference effect with top and bottom loops in gluon fusion production.Hence, there is almost no sensitivity to the sign of c c .For simplicity we consider positive c c in the following.χ 2 minimization yields c c ≤ 3.7 (7.3) , at 95.4% CL , for case (a) (case (b)) as defined above.The bound in case (b) is obtained upon marginalizing over the c gg coupling.The larger allowed range for the charm coupling in case (b), relative to case (a), is due to a further enhancement of the Higgs production cross section from c gg > 0. δχ2 ≡ χ 2 − χ 2 min as a function of c c for both cases is shown in Fig. 1.The δχ 2 raise in case (b) for c c 3 is due to the further universal suppression in the branching ratios induced by the larger c gg > 0 values required to compensate for the increase in c c .For case (b), we also show in Fig. 2 the 68.3% and 95.4% CL regions in the c c − c gg plane.h → W W * is the most significant channel which dominantly drives the χ 2 fit.Since µ W W * 1 at both ATLAS and CMS experiments, a total Higgs width slightly larger than in the SM is favored.This results in the fact that the χ 2 takes a minimum at a larger charm coupling, c c 1, as shown in Fig. 1.Excluding the h → W W * channel, the remaining average signal strength becomes 1 and the χ 2 fit favors lower values of c c .
We conclude that without additional new physics contributions to Higgs production other than the contribution to charm and gluon fusion, the latter being subdominant, a Higgs to charm coupling as large as about four times its SM value, is consistent with current Higgs data within 95.4% CL.Even larger charm couplings are allowed at 95.4% CL, provided that there is a conjoint O(1) enhancement in gluon fusion production from a new physics source.Such a large hcc coupling would in particular significantly reduce the Higgs branching ratio in bottom pairs.Consequently, suppressed h → b b signals in vector-boson associated Higgs production at ATLAS and CMS experiments are expected as these channels are much less sensitive to gluon fusion and cc fusion production mechanisms.Needless to say even bigger effects are found when the other couplings are allowed to float as well, in particular the higgs to gluons effective coupling.

III. OBSERVABILITY OF h → cc AT THE LHC
We showed in the previous section that a Higgs coupling to cc significantly larger than in the SM is allowed by current Higgs data.We argue here that such a large coupling yields important effects in channels where the Higgs boson decays into bottom pairs.In particular, one expects a significant suppression of µ b b in vector-boson associated prodution, due to a sizable enhancement of BR h→cc relative to the SM.We also demonstrate that the associated production signal can be partially recovered by using the recently developed charm-tagging technique [6].
We identify the following three interesting phenomenological aspects of having a large Higgs to charm coupling.First of all, b b signal strengths in associated production are suppressed due to the larger Higgs width which re-duces the branching ratio into bottom pairs as 2 Eqs. ( 8) and (9) show that enhancing the hcc coupling results in a significant reduction in the Higgs to bottom pairs rate in associated production processes V h( bb) of for case (a) ((b)) respectively, where we assumed SM-like V h production and no acceptance for the other production mechanisms.The suppressed signal in Eq. ( 10) is still consistent at 95.4% CL with all other existing Higgs data.This result makes this final state extremely challenging for the next run of the LHC.Note that in case (b) we include the subdominant Higgs width increase coming from c gg > 0, which further suppresses BR h→b b.
Second, we stress that there is an correlation between the measured µ b b and µ cc signal strengths, as the production cross section is identical for both channels and increasing the Higgs to charm coupling (c c > 1) leads to a suppressed branching ratio into b b and an enhanced one into cc.More precisely the signal strengths into bottom and charm pairs are simply proportional to each other, Deviations of the bottom coupling the SM limit are much more constrained by Higgs data than for the charm coupling (see Eq. (A1)), which yields µ cc ≃ |c c | 2 µ b b.Moreover, we find that this strong correlation remains also in the presence of an additional new physics source of gluon fusion production (c gg = 0), as illustrated in Fig. 3 which shows the regions of the µ b b − µ cc plane consistent within 68.3% and 95.4% CL with Higgs data.The signal strengths in Fig. 3 are evaluated assuming the relative weights of Higgs production mechanisms used by the CMS b b search in associated Higgs production [22].Figure 3 also shows that in the case that c c , c gg and c b are all allowed to vary, the above correlation still endures, albeit in a weaker way.
Finally, we find that the expected combined signal strength into bottom and charm pairs can be relatively enhanced compared to that of only bottom pairs, despite the smaller charm-tagging efficiency.We define the combined signal strength into b b and cc as where ε b and ε c are the tagging efficiencies for bottom and charm jets, respectively.We implicitly assumed in Eq. ( 11) that the only difference between cc and b b analyses is the tagging efficiency, and that, in particular, the production cross section is the same in both cases.We also define the ratio of the combined and bottom only signal strengths as where r cb ≡ ε c /ε b is the ratio of tagging efficiencies of charm-and bottom-flavored jets.Assuming the branching ratio values for a 126 GeV SM Higgs [25], the upper bound from Eq. ( 8) derived from fitting current Higgs data implies for the case (a) ((b)) defined above, where r cb ≃ 0.57 corresponds to ε b ≃ 0.7 [22] together with a prospective charm-tagging efficiency of ε c ≃ 0.4.The parameter R only measures how much combining charm and bottom pairs enhances the associated production signal relative to a sample of bottom pairs only.In particular it is independent of the production cross section by construction.The enhancement in Eq. ( 13) is to be compared with the much reduced signal strength available when only btagging is used to extract the signal, as given in Eq. ( 10).Combining Eqs. ( 10) and ( 13) yields a combined signal strength of for case (a) ((b)), where ε c ≃ 0.4 as well as pure SM-like vector-boson associated production are assumed.
We showed that the expected bottom pair signal strength in associated Higgs production can be significantly reduced, relative to the SM, in the presence of a largely enhanced hcc coupling, since the Higgs decay charm pairs is becoming as important.Moreover, Eq. (13) shows that an increased tagging efficiency for charm jets can bring the measured associated Higgs production signal strength almost back to its SM level.

IV. CHARM COUPLING BEYOND THE SM
Modified Higgs couplings to fermions can arise in many theories beyond the SM.We consider here different theoretical frameworks which illustrate the possibility of having a Higgs to charm coupling significantly larger than within the SM.We begin with an effective field theory (EFT) discussion, where new physics above the weak scale is described by a set of higher-dimensional operators, in order to stress that Higgs coupling to charm is a priori not necessarily related to the small charm mass.We then discuss how much the Higgs to charm coupling can deviate from the SM within specific new physics scenarios.In particular, we show that it is possible to obtain c c of order few, with all other couplings SM-like, in a two Higgs doublet model (2HDM) with minimal flavor violation (MFV) and in a General MFV (GMFV) [28] scenario with only one Higgs doublet.We finally comment on composite models where the Higgs field is realized as a pseudo-Nambu-Goldstone boson (pNGB).
Within the EFT framework the Higgs to charm coupling is modified in the presence of a dimension six operator.The relevant operators in the up-type quark sector are where the first term is the marginal up-type Yukawa operator of the SM and the second term is a dimension six operator suppressed by the new physics scale Λ. Q i and U i , with i = 1, 2, 3, are the SM quark lefthanded doublets and right-handed singlets, respectively, and H is the Higgs doublet, with H = iσ 2 H * .λ u and g u are generic complex 3 × 3 matrices in flavor space.
Setting the Higgs field to its vacuum expectation value H = (0, (v+h)/ √ 2) T , the mass and linear Higgs coupling matrices are respectively We assume for convenience that λ u and g u are aligned and that only g u 22 = 0 in the mass basis.In this case the deviation from the SM Higgs to charm coupling is simply where we defined y c ≡ √ 2 m c /v ≃ 3.6 × 10 −3 , m c being the running charm quark at the Higgs mass scale [5].Naive dimensional analysis suggests that the effective description breaks down at the scale Λ for g u 22 ∼ 16π 2 .As a function of the Higgs to charm coupling modification this scale is Assuming the upper bound on c c in Eq. ( 8), we find that the cutoff scale can be as high as Λ 38 (25) TeV for case (a) ((b)).These scales are sufficiently high so that it is possible that the associated new physics dynamics at the cut-off leaves no direct signatures at the LHC other than a significantly enhanced Higgs to charm coupling.
We now focus on some specific new physics scenarios.Consider a 2HDM with MFV [29,30].In this setup, the MFV ansatz allows to write the SM-like Higgs couplings to fermions as an expansion in the spurionic parameters which break the flavor symmetry group.Following notations of Ref. [31], the charm and top quark couplings to the SM-like Higgs boson are where y i ≡ √ 2 m i /v, V ij are the CKM matrix elements and A U S , B U S and C U S are O(1) coefficients.O(y 4 i ) and higher contributions were neglected in Eq. (20).Assuming for instance A U S ≃ 4 and B U S ≃ −3, Eq. ( 20) yields c c ≃ 4 and c t ≃ 1.Moreover, in the limit where all the heavier Higgs states are decoupled, c V ≃ 1 [32].Therefore, a significantly larger charm coupling, with all other couplings close to their SM values, can be obtained at the expense of a mild cancellation, at the level of one part in few, among unknown O(1) coefficients.
Consider now a model with one Higgs doublet in the GMFV framework [28], in which large top Yukawa effects are resummed to all orders.We define our notations in Appendix B. In the mass basis, the up-type quark mass and linear Higgs interaction matrices become M u ≃ λv/ √ 2×diag y u (γ + ζx), y c (γ + ζx), 1 + rx and to leading order in λ C ≃ 0.23, the sine of the Cabibbo angle and in x ≡ v 2 /(2Λ 2 ) , with Λ the GMFV scale, we find where w ≡ η − γr + α * (ζ − γr).Equation ( 21) yields the following Higgs to charm coupling ratio in GMFV and in the SM As λ, ζ ∼ O(1) and x 1, c c > 1 can be obtained for not too small value of x.As in all the above cases the coupling enhancement is at the cost of a moderate accidental cancelation among O(1) couplings.Note that the GMFV scale is constrained through the off-diagonal entries in Eq. ( 21) by a series of flavor changing observables analysed in Ref. [15].However, constraints from singletop production, neutral D meson mixing, flavor changing top decay t → hj and neutron electric dipole moment (assuming O(1) phases in the fundamental parameters) are satisfied for x 1 since GMFV contributions are suppressed by λ 2 C , λ 5 C , λ 2 C and y u λ 6 C , respectively.Consider finally composite pNGB Higgs models.Modifications of Higgs couplings to up-type quark in composite Higgs models is parameterized by the effective Lagrangian in Eq. ( 15) with Λ remplaced by the global symmetry breaking scale f , the "decay constant" of the pNGB Higgs [33].The dimension six coefficient in Eq. ( 15) receives two types of contributions from the composite dynamics, g u = g u h + g u ψ .The first term is a direct contribution from the non-linear Higgs dynamics and it is aligned with the marginal operator g u h ∝ λ u .The second term arises from the presence of light fermionic resonances from the strong dynamics.It is generically misaligned with λ u and its entries scale like g u ψ ∼ λ u ǫ 2 (g ψ f /m ψ ) 2 , where g ψ < 4π and m ψ are respectively a typical strong coupling and a resonance mass of the strong dynamics, and ǫ < 1 is the degree of the compositeness of the SM quarks.Neglecting flavor violation for simplicity and assuming relatively composite righthanded charm quark, the Higgs to charm coupling is [34] where ǫ c is the right-handed charm degree of compositeness.The symmetry breaking scale f is constrained by EW precision parameters to be f 750 GeV (see e.g.[35,36] for a recent analysis).Hence, in the absence of light composite resonances associated with the charm quark, the Higgs to charm coupling is not expected to deviate significantly from its SM value.However, if light charm partner resonances are present a larger Higgs to charm can be obtained.Current bounds on the charm partner mass from direct searches at the LHC are m ψ O(500 GeV) [12].Hence, for a fully composite charm quark ǫ c ≃ 1, g ψ ∼ 4π a largely enhanced hcc coupling is possible.

V. CONCLUSIONS
We pointed out that the Higgs to charm coupling can be significantly enhanced, relative to its SM value, without conflicting with current Higgs data.As the dominant decay mode of the SM Higgs into bottom quarks is characterized by a rather small coupling, a moderate enhancement of the charm coupling is sufficient to yield dramatic changes in the Higgs phenomenology at the LHC.In particular, we find that current data even allow for the h → cc mode to become the dominant Higgs decay channel.This results in the h → b b signal strength being reduced down to O(40%) level, which renders observation of this channel rather challenging for the next LHC run.However, we argued that a realistic prospective form of charm-tagging would allow to not only resurrect part of the lost b b signal but also to obtain signal strengths in the associated Higgs production channels which are close to the SM expectations by combining both charm and bottom pairs.We also briefly demonstrated that within several SM extensions an enhanced Higgs to charm coupling can be obtained through a moderate accidental cancellation between O(1) couplings of the theory.

FIG. 1 :
FIG.1:δχ 2 = χ 2 − χ 2min as a function of the Higgs to charm pairs coupling cc.The black and red curves correspond respectively to case (a), where all Higgs coupling but cc are SM-like, and case (b), where only cc and cgg deviate from the SM and marginalizing over the latter.Horizontal dashed lines denotes the 68.3% and 95.4% CL (δχ 2 = 1 and 4, respectively).

FIG. 2 :
FIG.2: 68.3% (solid) and 95.4% (dashed) CL regions in the cc − cgg plane in case (b) where only the Higgs to charm and Higgs to gluon couplings are allowed to deviate from their SM values.The red dot represents the best fit point.ĉSM gg ≃ 0.012 .

, c b 1 68. 3 CL, c b 1 best fit, c b 1 95. 4 CL, c b 1 68. 3 CL, c b 1 best fit, c b 1 FIG. 3 :
FIG.3: Correlation between µcc and µ b b signal strengths in the presence of an enhance Higgs to charm coupling relative the SM.Relative weights of each Higgs production mechanisms from the CMS analysis[22] are assumed for both signal strengths.The red dot represents the best fit point and the solid (dashed) black line is the 68.3 (95.4)%CL contour derived from fitting current Higgs data for case (b), where only cc and cgg are not SM-like.The solid (dashed) gray contour delineates the allowed 68.3 (95.4)%CL region for the more general case where c b is allowed to vary as well.