A two-Higgs-doublet model facing experimental hints

Physics beyond the Standard Model has so far eluded our experimental probes. Nevertheless, a number of interesting anomalies have accumulated that can be taken as hints towards new physics: BaBar, Belle, and LHCb have found deviations of approximately 3.8σ in B → Dτν and B → D∗τν; the anomalous magnetic moment of the muon differs by about 3σ from the theoretic prediction; the branching ratio for τ→ μνν is about 2σ above the Standard Model expectation; and CMS and ATLAS found hints for a non-zero decay rate of h → μτ at 2.6σ. Here we consider these processes within a lepton-specific two-Higgs doublet model with additional non-standard Yukawa couplings and show how (and which of) these excesses can be accommodated.


Introduction
This talk is based on Ref. [1], where a more detailed discussion can be found.Tests of flavor universality or flavor violation serve as a useful tool to search for physics beyond the Standard Model (SM), seeing as the SM predictions are precisely known.Some experiments have reported on deviations from the SM, which we list below.
One possible new-physics explanation comes in the form of a charged scalar [5][6][7].
Each anomaly individually can be accommodated in SM extensions by scalars, e.g.2HDMs.The goal of our study is to see if all four anomalies can be explained simultaneously with a fairly minimal model.

Modified 2HDM-X
We will study a lepton-specific 2HDM (2HDM-X), defined by the Yukawa couplings in the Lagrangian with additional couplings that break the type-X structure The scalar interactions with fermions after electroweak breaking can be written as where the couplings -in the limit of large tan β of interest here -are given by V denotes the Cabibbo-Kobayashi-Maskawa mixing matrix, v 174 GeV the vacuum expectation value, and the matrices parametrize the deviation from the type-X structure ( f and ξ f are related by fermion rotations).On phenomenological grounds, we take d = 0 and both u and of the form where × denotes a non-zero entry, allowing for lepton flavor violation in the μ-τ sector.

Phenomenology
In this section we address the constraints on our model and its potential to resolve the experimental anomalies outlined above.

Tau decays τ → νν
Decays of the tau are modified at tree-level by the charged scalar H + (including a change in the Michel parameter η) [24][25][26] and at loop-level through a modified Wτν coupling g Wτν → g Wτν (1 + δg) [21,24,25]: with the 2HDM couplings [21] z ≡ v 2 m 2 The experimentally allowed regions are shown in Fig. 1.In the SM we have δg = z = 0, which is disfavored by τ → μνν at more than 2σ (with PDG values).In the 2HDM-X one has δg ≤ 0 and z > 0, which makes Δ μ even worse and puts pressure on the 2HDM-X and 2HDM-II (which has the same lepton couplings).In our modified 2HDM-X, we can however flip the sign of the tau coupling via

Magnetic moment a μ and h → μτ
It has been shown that a light pseudoscalar in the 2HDM-X with large tan β can resolve the Δa μ anomaly via its contribution in a Barr-Zee diagram [36], see for example Refs.[19][20][21].As seen above, we need to flip the sign of the tau coupling to the new scalars in order to alleviate the τ → μνν discrepancy.Because of this, it is the non-SMlike CP-even scalar that can resolve the Δa μ anomaly in our model (and not the pseudoscalar).The pseudoscalar then needs to be heavier than the scalar in order not to cancel the contribution to Δa μ (see Fig 2).
The same Barr-Zee diagrams that give the desired Δa μ also lead to τ → μγ decays in case 32 0 (as required for h → μτ).If we want to explain h → μτ, the τ → μγ rate needs to be tuned to small values using m H m A , which necessarily also suppresses the contribution to Δa μ (see Fig 2).As a result, it is possible within our modified 2HDM-X to resolve the anomalies in τ → μνν and Δa μ or to resolve τ → μνν and h → μτ, but not both at the same time, at least without introducing more parameters.

Tauonic B decays
The relevant effective Hamiltonian for the semileptonic B decays in our model is . The lighter regions correspond to 2σ experimental uncertainties while the darker regions are correspond to 1σ [1].
These Wilson coefficients affect the two ratios R(D ( * ) ) in the following way [4,37,38], leading to the allowed regions of Fig. 3.As can be seen, our new-physics model from Eq. ( 26) has the right structure to easily resolve the anomaly, e.g. with real

Conclusions
We addressed the measured anomalies in R(D ( * ) ) (3.8σ), a μ (∼ 3σ), τ → μνν (2.4σ), and h → μτ (2.6σ) within a simple two-Higgs-doublet model.The Yukawa structure of our model is close to the lepton-specific 2HDM 1 Efficiency corrections to R(D) due to the BaBar detector [2] are important in the case of large contributions from C cb R,L , i.e. if one wants to explain R(D) with destructive interference with the SM contribution.As shown in Ref. [39], these corrections can be effectively taken into account by multiplying the quadratic term in C cb R,L of Eq. ( 27) by an approximate factor of 1.5 (not included in Eq. ( 27)).For m H m A , the allowed regions from τ → μνν would be slightly larger [1].
(type X), but with some additional Yukawa couplings involving third-generation fermions that give rise to the b-c (necessary for R(D ( * ) )) and μ-τ transitions (relevant for h → μτ) as well as corrections to ττ couplings (important for τ → μνν).
The charged scalar H + influences R(D ( * ) ) and τ → μνν and can resolve both deviations simultaneously (see Fig. 4), as long as the sign of the tau coupling is flipped, meaning 33 > m τ /v.Because of this, a light scalar (not pseudoscalar) is needed to resolve the Δa μ anomaly, which then induces the top decay t → Hc [1].h → μτ can only be explained if we give up on Δa μ , otherwise the rate τ → μγ would be too large.
It remains to be seen which of these anomalies stand the test of time and which are simply statistical fluctuations.The fact that some of them can be explained rather naturally within a fairly minimal model gives however hope that we are on the verge of something interesting.

Figure 4 .
Figure 4. Allowed regions in the tan β-v/m τ 33 plane from R(D ( * ) ) and τ → μνν at the 2σ level.The yellow region is allowed by τ → μνν using the HFAG result for m H = 30 GeV and m A = 200 GeV, while the (darker) blue one is the allowed region using the PDG result.The red, orange, green, and magenta bands correspond to the allowed regions by R(D ( * ) ) for different values of u 32 .The gray region is excluded by Z → ττ and τ → eνν.For m H m A , the allowed regions from τ → μνν would be slightly larger[1].