Flavor and CP violation in Higgs decays

Flavor violating interactions of the Higgs boson are a generic feature of models with extended electroweak symmetry breaking sectors. Here, we investigate CP violation in these interactions, which can arise from interference of tree-level and 1-loop diagrams. We compute the CP asymmetry in flavor violating Higgs decays in an effective field theory with only one Higgs boson and in a general Type-III Two Higgs Doublet Model (2HDM). We find that large ∼O10%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left(\sim \mathcal{O}\left(10\%\right)\right) $$\end{document} asymmetries are possible in the 2HDM if one of the extra Higgs bosons has a mass similar to the Standard Model Higgs. For the poorly constrained decay modes h → τμ and h → τe, this implies that large lepton charge asymmetries could be detectable at the LHC. We quantify this by comparing the sensitivity of the LHC to existing direct and indirect constraints. Interestingly, detection prospects are best if Higgs mixing is relatively small — a situation that is preferred by the current data. Nevertheless, CP violation in h → τμ or h → τe will only be observable if nonzero rates for these decay modes are measured very soon.


INTRODUCTION
Precision measurements of the Higgs sector of elementary particles are becoming one of the major topics in the physics program at the Large Hadron Collider (LHC).The main goal of these measurements is to search for deviations from Standard Model (SM) expectations that would herald the existence of new physics at the TeV scale, such as additional Higgs bosons, as predicted for example in supersymmetry, secondary sources of electroweak symmetry breaking, for instance due to strong dynamics, or non-standard couplings of the Higgs boson due to higher-dimensional operators.
Many of these extensions of the SM predict the recenly discovered particle [1,2] (hereafter refered to as the Higgs boson) to possess flavor non-diagonal couplings (see for example  and references therein).Existing constraints on some of these couplings are surprisingly weak, especially when couplings to third generation fermions are involved as in the processes h → µτ , h → eτ , t → hc and t → hu.A number of search strategies for flavor violating Higgs couplings has been proposed [14-16, 26, 27] and first experimental searches for top-charm-Higgs couplings have been carried out by ATLAS [28] and CMS [29].
Here we bring the two topics together by investigating Higgs decays that violate flavor and CP.In particular, we consider possible asymmetries between the processes h → i− j+ and h → i+ j− , as parameterized by the observable where i , j = {e, µ, τ } and i = j.This observable offers perhaps the most direct way of searching for CP violation in Higgs decays and does not require considering any differential cross sections.
On the downside, a measurement of A i j CP requires large integrated luminosity due to the smallness of (usually loop-induced) CP violating effects in general, and due to the possible smallness of the decay rates Γ(h → i± j∓ ) themselves.The current 95% CL upper limit on the branching ratios BR(h → τ µ) and BR(h → τ e) is 13% from LHC searches [15,40], while the indirect limit on BR(h → µe) is 2 × 10 −8 [15]. 1 We will therefore not consider the decay h → µe in our phenomenological analysis.
In sec.2, we derive analytic expressions for A i j CP in an effective theory of CP violation in the Higgs sector induced by new particles above the electroweak scale and in several classes of Two Higgs Doublet Models.We will argue that these scenarios are very generic and encompass very large classes of extensions of the SM.We then constrain combined flavor and CP violation in Higgs decays from low-energy observables in sec.3, and we estimate the sensitivity of the LHC in sec.4. We summarize and conclude in sec. 5.

Low energy effective field theory with only one Higgs boson
We begin by considering the simplest low energy effective field theory (EFT) description of flavor and CP violation in the Higgs sector, where i are charged lepton fields in the mass basis, h is the Higgs boson, and Y h ij is a general, complex 3 × 3 Yukawa matrix.Similar couplings can exist for quarks and neutrinos, but we will here focus on the charged lepton sector, which is most easily accessible at the LHC.
In the SM the couplings of the Higgs with the fermion fields are real and flavor diagonal while several extensions of the SM predict Y h ij = (m i /v)δ ij .Naturalness arguments suggest that the maximal size of the off diagonal elements should be related to the observed hierarchy of fermion masses.For example in [41] in order to avoid tunings, relations like the following have to hold Despite this general expectation one has to remark that the size of the flavor violating couplings is encoded in the details of the ultraviolet theory and in several explicit models larger flavor violating effects will be possible.For this reason, in our approach we are not going to rely on any specific extension and we consider the couplings as free parameters.
The branching ratio for h → i+ j− is given by with and with the SM Higgs width Γ SM = 4.1 MeV for a 125 GeV Higgs boson [42].The Lagrangian (2) leads to non-zero A while the expression for the triangle diagram is Here, p i , p j are the 4-momenta of the final state leptons, m i is the mass of i , and P L = (1 − γ 5 )/2, P R = (1 + γ 5 )/2 are the chirality projection operators.From eqs. ( 6) and ( 7), we can compute A i j CP and find for the phenomenologically most interesting case where i = µ and j = τ is obtained by replacing µ ↔ e in eq. ( 8).
We see that, if only two lepton families (here τ and µ) participate in flavor changing Higgs couplings, A µτ CP is suppressed by the loop factor 1/(8π) and by a factor m 2 τ /m 2 h .When all three lepton generations experience flavor changing Higgs couplings, A µτ CP receives additional contributions that do not depend on lepton masses, but are proportional to a product of three flavor violating Yukawa couplings involving all three flavor combinations eµ, eτ and µτ .Since (|Y µe | 2 + |Y eµ | 2 ) 1/2 is constrained to be smaller than 3.6 × 10 −6 by searches for µ → eγ, µ → e conversion in nuclei, and µ → 3e [13,15], these products are far too small for this source of CP violation to be observable at the LHC.
We conclude that CP violation in flavor changing Higgs couplings is not accessible at the LHC when the additional degrees of freedom responsible for its generation are so heavy that they can be integrated out.We will therefore now consider scenarios in which additional Higgs bosons appear as dynamical degrees of freedom at the LHC.We will show that, in this case, large CP asymmetries are possible.

A type-III Higgs doublet model
If not one but two Higgs doublets exist in nature [43] (for a recent review see [44]) and have masses of order 100 GeV, the phenomenology of the Higgs sector becomes considerably richer than in the SM.We will here consider a general "type-III" Two Higgs Doublet Model (2HDM), in which both Higgs doublets Φ 1 and Φ 2 have Yukawa couplings to charged leptons.We work in the Georgi basis [45], in which only Φ 1 acquires a vev so that Φ 1 and Φ 2 can be decomposed according to Here η 1 and η 2 are real scalar fields, A is a real pseudoscalar, H ± are the charged Higgs bosons and G ± , G 0 are Goldstone bosons.The charged lepton Yukawa couplings are given by where L i L denotes the lepton doublets and (δ ij ), (Y ij ) are Yukawa matrices.After electroweak symmetry breaking, the Yukawa couplings become In the most general Two Higgs Doublet Model, η 1 , η 2 and A are not identical to the physical mass eigenstates, which we denote by h 1 , h 2 and h 3 .The two sets of fields are related by an orthogonal transformation with O ∈ SO(3).We denote by h 1 the lightest mass eigenstate, which is usally assumed to approximately resemble the SM Higgs boson.(Occasionally, we will use the notation h and h 1 interchangeably for this physical Higgs state.)In the physical basis, the Lagrangian becomes with For an arbitrary scalar mixing matrix O, the CP asymmetry in h 1 → µτ decays is given by in eq. ( 15) are given by with the loop function and the vectors The angle θ τ is defined according to Y τ τ ≡ |Y τ τ | e iθτ .The analogous expressions for h 1 → eτ are again obtained by simply replacing µ ↔ e in the above expressions.We see that in the general 2HDM, A µτ CP and A eτ CP are unsuppressed except by the loop factor 1/(4π).Therefore the CP asymmetries can easily be of order 10%.If m h 2 m h 1 or m h 3 m h 1 , even larger asymmetries are possible as the last term in square brackets in eqs.( 16) and ( 17) becomes large.Note, however, that in this case, the expansion in m τ /v from eq. ( 15) breaks down, so our analytic expressions are no longer directly applicable.
Eqs. ( 19), ( 20) and ( 21) can be simplified if we parameterize the scalar mixing matrix O in terms of two mixing angles θ 12 and θ 13 , with the definitions c ij ≡ cos θ ij and s ij = sin θ ij .A third mixing angle θ 23 , corresponding to rotations about the 1-axis, is unphysical because it can always be absorbed into a redefinition of the of second Higgs doublet Φ 2 → e iθ 23 Φ 2 .With the explicit parameterization (22), eq. ( 19) becomes We see that R 2 = −R 3 , i.e. that the contributions from h 2 and h 3 to the CP violating loop diagrams tend to cancel each other in the limit m h 2 ≈ m h 3 .The explicit expressions for R V and R L are more lengthy.We now consider several special cases of the general 2HDM.
Case 1: Heavy h 3 Let us first consider a scenario where one of the neutral Higgs mass eigenstates, say h 3 , is much heavier than the other two.The low energy effective Lagrangian for this scenario is (see also eqs. ( 13) and ( 14)) The CP asymmetry is given by with the loop function g(x) from eq. ( 18).We have again neglected diagrams involving electrons.We see that even in this considerably simplified version of the 2HDM, unsuppressed CP violation can occur.
Case 2: Small mixing angles in the scalar sector The observed Standard Model-like nature of the 125 GeV Higgs boson suggests that its mixing with the components of a heavy Higgs doublet should be small.This leads us to consider the limit θ 12 , θ 13 1.The scalar mixing matrix thus becomes and the Yukawa couplings in the physical basis are This leads to the rate for The CP asymmetry is again given by eqs.( 15)-( 17), but with eqs.( 19)-( 21) simplified to Case 3: No CP violation in the scalar sector We now analyze the case where the scalar sector is CP conserving.In the Georgi basis this means that A = h 3 is a mass eigenstate while η 1 and η 2 can have a mixing.This mixing should not be too large so that the lightest mass eigenstate h 1 is mostly η 1 -like and behaves like the SM Higgs boson, in agreement with LHC measurements of Higgs couplings.Nevertheless, h 1 is still allowed to have an η 2 admixture of order 20% as this is the accuracy to which the couplings of the 125 GeV Higgs boson have been measured (see for instance [46]).Thus, sizeable flavor changing Yukawa couplings are still allowed.We are thus led to consider a scalar mixing matrix of the form given by eq. ( 22), with θ 13 = 0 and θ 12 1.With these approximations, A µτ,(0) CP in eq. ( 15) vanishes, and the leading term in the CP asymmetry, generated by loops involving h 2 ≈ η 2 and h 3 = A is given by A µτ,(1) CP : The loop function g(x) is again given by eq. ( 18).Note that eq. ( 32) is again based on the approximation m µ = m e = Y µµ = Y ee = 0. Eq. (32) shows that in the 2HDM without CP violation in the scalar sector the CP asymmetry is always suppressed by m τ /v and by |Y τ τ |.

DIRECT AND INDIRECT CONSTRAINTS
Direct and indirect searches constrain the maximal allowed amount of CP and flavor violation in the Higgs decays accessible at the LHC.In this section we summarize how existing bounds on various low energy and high energy observables constrain BR(h → i j ) × A i j CP .

Effective theory with only one Higgs boson
Assuming the flavor conserving couplings of the Higgs to quarks and gauge bosons to be at their SM values, we derive in this section the relevant bounds on the Yukawa couplings in the lepton sector.
Let us start by considering constraints coming from direct searches.Since we assume for simplicity that flavor violating new physics affects predominantly the lepton sector, the production cross section σ for the Higgs boson is the same as in the SM.It is therefore straightforward to use existing searches for h → τ + τ − and h → µ + µ − to set bounds on the flavor diagonal couplings Y h τ τ and Y h µµ .The recent CMS analysis [47] finds a signal cross section for h → τ + τ − equal to 0.78 ± 0.27 times the standard model prediction.This means equivalently that has to lie within this range.(Here and in the following, the index SM denotes the SM values of the model parameters and observables.)In a similar way the value of Y h µµ is bounded from the results in [48], where Γ(h → µ + µ − ) has been constrained to be smaller than 7.4 times its SM value.
The most recent constraints on flavor violating couplings to the Higgs boson to leptons have been derived in [15] by recasting an ATLAS search for h → τ + τ − [40] 2).In the 2HDM, the constraints apply equivalently to Y h1 (see eq. ( 14)).We have assumed that Higgs couplings to quarks and gauge bosons are unmodified compared to the SM.
data.They require BR(h → τ ) < 0.13, or equivalently 011, where = e, µ.We expect that a similar analysis including data on h → τ + τ − from the 8 TeV run of the LHC could increase the sensitivity to the Yukawa couplings by about a factor 1.5.A dedicated analysis could do significantly better still (see [16,27] and sec.4).Note that a simple recasting of the existing h → τ τ searches at √ s = 8 TeV is not as promising as it was for the 7 TeV data used in [15].In the case of the latest ATLAS search [49], the reason is the usage of a boosted decision tree which has been trained on SM h → τ τ decays and is therefore expected to be less sensitive to other decay modes, in particular h → τ µ and h → τ e.The latest CMS search for h → τ τ is cutbased, but employs a maximum likelihood method to determine the most likely value of the Higgs mass on an event-by-event basis in spite of the incomplete kinematic information.This method is based on the assumption that any muon or electron in the event originates from a τ decay and is thus accompanied by two neutrinos.Since this is not the case for h → τ µ and h → τ e events, we expect the Higgs mass reconstruction to be very poor for the flavor violating decay channels, leading to significant smearing of our signal and a corresponding loss of sensitivity.
The direct bounds on the flavor-diagonal and flavor-off-diagonal Yukawa couplings are summarized in the upper part of table I.In the lower part, we also show indirect constraints from the radiative decays i → j + γ [13,15].Other indirect observables like the electric and magnetic moments of the electron and the muon give weaker bounds.(The electric dipole moment of the electron leads, however, to a strong constraint on Im(Y eτ Y τ e .)A more detailed discussion can be found, for example, in [13,15,19].

Type-III Two Higgs doublet model
Constraining the high dimensional parameter space of the general type-III Two Higgs doublet model discussed in sec.2.2 is a formidable task.Here, our goal is only to explore the region of parameter space where large CP violating effects in flavor violating Higgs decays are possible and detectable at the LHC.We therefore simplify our analysis by assuming the mixing angles θ 12 and θ 13 in the scalar sector to be small, and we set θ 23 to zero (cf.sec.2.2, case 2).We will also assume that Y τ µ and Y µτ are the only nonzero element of the Yukawa matrix Y .This means that the second Higgs doublet couples to SM fermions only through Y τ µ and Y µτ , and that the dominant decay modes of the heavy Higgs mass eigenstates will be h  We have assumed all other entries of the Yukawa matrix Y (including in particular Y µτ ) to vanish.In the left panel, we have assumed m h2 = m h3 , a situation in which no CP violation is expected, while in the right panel, we consider a benchmark scenario with m h3 > m h2 .We show the region excluded by the direct limit on BR(h 1 → τ µ) from LHC data [15] (orange) together with indirect limits from τ → µγ (black dashed).In the right panel, the "Brazilian band" (black curve with green and yellow ±1σ and ±2σ bands) indicates the expected 95% C.L. limit from a search for CP violation at the 13 TeV LHC with an integrated luminosity of 300 fb −1 (see sec. 4 for details).The regions above the band is approximately equal to the region in which evidence for CP violation can be found.The blue dotted contours indicate constant values of the quantity |BR(h 1 → τ µ) × A µτ CP |, which is a measure for the observability of CP violation.The largest CP violating effects are expected for m h2 similar to the mass of the SM-like Higgs boson.(Note that in this case, our plots are only approximate since the underlying analytic expansion from eq. ( 15) breaks down.)(magnetic) dipole moment d µ (a µ ) of the muon are proportional to (Y τ µ Y µτ ) ( (Y τ µ Y µτ )).They are, however not suppressed by the mixing angles θ 12 and θ 13 .However, as we have seen above, large CP violation in h 1 → τ µ is only possible if Y τ µ and Y µτ are very different in magnitude.In this case, dipole moment constraints deteriorate rapidly and we will therefore not consider them further here.
In figs. 2 and 3, we compare the indirect τ → µγ constraints on the Yukawa couplings (black dashed curves) and the direct constraint BR(h 1 → τ µ) < 0.13 [15] (orange shaded region) to the expected BR(h 1 → τ µ) A µτ CP (blue dotted contours).The latter quantity is a measure for the observability of CP violation in h 1 → τ µ decays.We also show the expected sensitivity of the LHC to CP violation in h 1 → τ µ decays (see sec. 4 for details).For illustration, we have here assumed that Y τ µ is the only nonzero element of the Yukawa matrix Y since we see from eqs. ( 16) and ( 17) that a large asymmetry between |Y τ µ | and |Y µτ | maximizes the CP asymmetry.Note that in the left panel of fig.2, no CP violation is expected because we have assumed m h3 = m h2 there.We see from figs. 2 and 3 that the largest observable CP violation is expected when m h2 ∼ m h1 and m h3 much heavier.Moreover, the Higgs mixing angles θ 12 and θ 13 should be small-a situation that is actually preferred by the current LHC data, which is very SM-like.
Finally, we comment on constraints on the charged Higgs bosons H ± whose quantum numbers are the same as those of a left-handed slepton in supersymmetry.Therefore, limits on slepton masses from direct production at the LHC can in principle be recast into limits on the charged  We have assumed all entries of the Yukawa matrix Y other than Y τ µ to vanish.We show the region excluded by the direct limit on BR(h 1 → τ µ) from LHC data [15] (orange) together with indirect limits from τ → µγ (black dashed).The "Brazilian bands" (black curves with green and yellow ±1σ and ±2σ bands) indicate the expected 95% C.L. limits from a search for CP violation at the 13 TeV LHC with an integrated luminosity of 300 fb −1 (see sec. 4 for details).The regions above the bands are approximately equal to the regions in which evidence for CP violation can be found.The blue dotted contours indicate constant values of the quantity |BR(h 1 → τ µ) × A µτ CP |, which is a measure for the observability of CP violation.A search for CP violating effects is most promising if the mixing angles are small.Higgs boson mass m H ± .The ATLAS slepton search in 20.3 fb −1 of 8 TeV data [50] constrains the mass of left-handed sleptons to be m ˜ 300 GeV, assuming a simplified scenarios with massdegenerate left-handed selectrons and smuons, massless neutralinos, and all other SUSY particles very heavy.Comparing slepton pair production in this simplified SUSY model to the production of H ± of the same mass in our 2HDM, we note that H ± production leads to about a factor of 8 fewer events.The reason is that there are two new particles (selectron and smuon) in the SUSY scenario, but only one new particle in the 2HDM.Moreover, pp → H + H − has a branching ratio to the dimuon + MET final state of only 25%-the remainder of the events contains one or two tau leptons.Therefore, the bound on m H ± is significantly weaker than the one on m ˜ , so requiring the charged Higgs bosons to be heavier than 300 GeV is a very conservative assumption.

FLAVOR AND CP VIOLATING HIGGS DECAYS AT THE LHC
To investigate the sensitivity of future LHC searches to the CP asymmetry A µτ CP in the decay h → τ µ, we follow the strategy proposed in [16].(Results for h → τ e will be very similar.)The search proposed there is sensitive to Higgs boson production through gluon fusion, and is therefore expected to be more sensitive than the alternative strategy proposed in [15], which is optimized for Higgs production through vector boson fusion.We adapt the method outlined in [16] to a hadronic center of mass energy √ s = 13 TeV and an integrated luminosity of 300 fb −1 .We normalize the Higgs production cross section to the gluon fusion cross section from [42].
Following [16], we require exactly one electron (assumed to come from a leptonic τ decay) and  one muon with p T > 30 GeV and |η| < 2.5, and with azimuthal separation ∆φ(e, µ) > 2.7.The azimuthal separation between the muon and the missing transverse momentum, ∆φ(µ, / p T ) must be less than 0.3.The leptons are required to have opposite charge, and events with central high-p T jets (p T > 30 GeV, |η| < 2.5) are vetoed.After this preselection, we classify events as signal-like or background-like based on the p T of the muon and the value of the variable Here, / E obs T is the measured missing energy and / E calc T is the transverse energy of the neutrinos calculated from the momenta of the two charged leptons under the hypothesis of a true h → τ µ decay.In the approximation that all decay products of the τ are collinear, / E calc T is given by where E e and E µ are the energies of the electron and the muon, respectively, p T,e is the transverse momentum of the electron, and θ eµ is the angle between the electron and muon momenta.The dominant backgrounds to the search for h → τ µ are Z + jets production with leptonic decay of the Z, Standard Model diboson (W W , W Z and ZZ) production, single top production and t t production.We simulate the signal and background rates in MadGraph 5 v2.0.0.beta3 [51], followed by parton showering an hadronization in Pythia 6.426 [52].We use the MLM scheme [53] for matching between the matrix element and the parton shower.For detector simulation we use PGS [54] with the default implementation of the CMS detector.
The predicted distributions of r / E T and p T,µ are shown in fig. 4. Our plots confirm that the findings from [16] still hold at √ s = 13 TeV: the p T of the muon tends to be larger for the signal than for the dominant Z +jets background, and the difference between the measured and calculated / E T is typically much smaller for signal events than for background events.: Two-dimensional distribution of signal events (black) and background events (colored).The horizontal axis shows the relative difference between the measured / E T and the / E T calculated from the kinematics of the charged leptons.The vertical axis shows the transverse momentum of the muon.The blue ellipse is the signal region defined in eq.(39).
For the final selection, we require p T,µ − 60 GeV 25 GeV thus restricting the analysis to an ellipse in the p T,µ -r / E T plane (see fig. 5).After this final cut, the total predicted background cross section is while for the signal we obtain in the 2HDM As a crude estimate for the relative accuracy of a measurement of the rate for h → τ µ, we use √ S + B/S, where S and B are the number of signal and background events, respectively, satisfying all preselection cuts as well as the condition (39).For the LHC (300 fb The equivalent numbers for the effective theory from sec.2.1 are obtained by simply setting θ 2  12 + θ 2 13 = 1 in these expressions and replacing Y by Y h .
We emphasize again that the above estimates do not account for systematic uncertainties, which would slightly decrease the sensitivity of a realistic experimental analysis.However, the inclusion of other decay channels-in particular those involving hadronic tau decays and those involving same flavor leptons-can be expected to significantly enhance the sensitivity, so that our limits can still be considered conservative.
For the 2HDM, we show the expected 95% C.L. sensitivity to CP violating signals in h 1 → τ µ decays as "Brazilian bands" in figs. 2 and 3. To compute these bands, we have assumed that the observed rate for h 1 → τ µ decays is at the predicted level at each parameter point, but CP is not violated in the data.In computing the central black curve, we have therefore assumed the observed rates for h 1 → τ + µ − and h 1 → τ − µ + to be identical.For parameter points below the curve, the LHC is then able to disfavor CP violation at the actually predicted level for these parameter points at the 95% C.L. The green (yellow) bands are obtained in a similar way, but allowing for 1σ (2σ) statistical fluctuations of the observed asymmetry away from zero.

CONCLUSIONS
To summarize, we investigated the prospects for discovering a CP asymmetry in the flavorviolating Higgs decays h → τ µ and h → τ e at the LHC.
Flavor violating Yukawa couplings of the SM-like 125 GeV Higgs boson appear quite generally in models with extended electroweak symmetry breaking sectors unless they are forbidden by the introduction of extra symmetries.Low energy constraints are extremely weak for couplings involving τ leptons, so that branching ratios BR(h → τ µ) and BR(h → τ e) of order 10%comparable to BR(h → τ τ ) in the SM-are possible.If the flavor violating Yukawa couplings are complex, CP violation is possible in these decays and would manifest itself as an asymmetry between BR(h → τ + µ − ) and BR(h → τ − µ + ) or between BR(h → τ + e − ) and BR(h → τ − e + ).
We have computed the CP asymmetries for an effective field theory with only one Higgs boson and for a Type-III Two Higgs Doublet Model (2HDM).In the effective theory, the asymmetries are typically suppressed by m 2 τ /m 2 h and/or by the Yukawa couplings Y eµ and Y µe , which are required to be small due to strong constraints from µ → eγ.In the 2HDM, even asymmetries of order few × 10% are possible if one of the new Higgs bosons is similar in mass to the SM Higgs.
We have summarized current direct and indirect constraints on flavor and CP violating Higgs decays involving τ leptons as a function of the parameters of the 2HDM, and we have highlighted the regions of parameter space where a discovery of CP violation could be possible at the LHC (see figs. 2 and 3).Interestingly, we have found that this is the case if Higgs mixing is small-a situation that is preferred due to the so-far SM-like nature of the 125 GeV Higgs boson.On the other hand, CP violation at an observable level would require that the decay h → τ µ or h → τ e would have to be observed very soon.

Figure 1 :
Figure 1: Feynman diagrams contributing to flavor and CP violating Higgs boson decays h → i− j+ .In the effective theory model (sec.2.1), only one Higgs boson h ≡ h 1 exists and the bubble diagram (c) does not contribute to the CP asymmetry A i j

CP
through interference of the first two diagrams shown in fig. 1.The bubble diagram (2) (c) exists, but does not contribute to A i j CP .The tree level diagram is given by

Figure 2 :
Figure 2: Direct and indirect constraints on the flavor violating Yukawa couplings Y τ µ in the general type-III 2HDM.We have assumed all other entries of the Yukawa matrix Y (including in particular Y µτ ) to vanish.In the left panel, we have assumed m h2 = m h3 , a situation in which no CP violation is expected, while in the right panel, we consider a benchmark scenario with m h3 > m h2 .We show the region excluded by the direct limit on BR(h 1 → τ µ) from LHC data[15] (orange) together with indirect limits from τ → µγ (black dashed).In the right panel, the "Brazilian band" (black curve with green and yellow ±1σ and ±2σ bands) indicates the expected 95% C.L. limit from a search for CP violation at the 13 TeV LHC with an integrated luminosity of 300 fb −1 (see sec. 4 for details).The regions above the band is approximately equal to the region in which evidence for CP violation can be found.The blue dotted contours indicate constant values of the quantity |BR(h 1 → τ µ) × A µτ CP |, which is a measure for the observability of CP violation.The largest CP violating effects are expected for m h2 similar to the mass of the SM-like Higgs boson.(Note that in this case, our plots are only approximate since the underlying analytic expansion from eq. (15) breaks down.)

Figure 3 :
Figure 3: Direct and indirect constraints on the flavor violating Yukawa couplings Y τ µ in the general type-III 2HDM for fixed Higgs boson masses m h2 and m h3 , but varying Higgs mixing angles.We have assumed all entries of the Yukawa matrix Y other than Y τ µ to vanish.We show the region excluded by the direct limit on BR(h 1 → τ µ) from LHC data[15] (orange) together with indirect limits from τ → µγ (black dashed).The "Brazilian bands" (black curves with green and yellow ±1σ and ±2σ bands) indicate the expected 95% C.L. limits from a search for CP violation at the 13 TeV LHC with an integrated luminosity of 300 fb −1 (see sec. 4 for details).The regions above the bands are approximately equal to the regions in which evidence for CP violation can be found.The blue dotted contours indicate constant values of the quantity |BR(h 1 → τ µ) × A µτ CP |, which is a measure for the observability of CP violation.A search for CP violating effects is most promising if the mixing angles are small.

Figure 4 :
Figure 4: Distributions of (a) the p T of the muon and (b) the relative difference between the measured / E T and the / E T calculated from the kinematics of the charged leptons.

Figure 5
Figure5: Two-dimensional distribution of signal events (black) and background events (colored).The horizontal axis shows the relative difference between the measured / E T and the / E T calculated from the kinematics of the charged leptons.The vertical axis shows the transverse momentum of the muon.The blue ellipse is the signal region defined in eq.(39).
[13,15]..." stands for terms that are second order in m τ /v or first order in m µ /v, m e /v, |Y µµ |, |Y ee |, |Y eµ | or |Y µe |.Setting Y µµ and Y ee to zero is motivated by the observed SM-like nature of the 125 GeV Higgs boson, which suggests that |Y µµ (O 21 + iO 31 ) | and |Y ee (O 21 + iO 31 ) | cannot be larger than few × 10 −2 .Y eµ and Y µe in turn are tightly constrained by searches for lepton flavor violation in µ → eγ, µ → e conversion in nuclei and µ → 3e[13,15](see also sec.2.1).The zeroth and first order terms A

Table I :
in 4.7 fb −1 of 7 TeV LHC Direct and indirect constraints on flavor conserving and flavor violating Yukawa couplings of the SM Higgs bosons in the effective theory eq. ( . 150. 200.250.300.350.400.