Lepton-flavor-violating Higgs decay h → μτ and muon anomalous magnetic moment in a general two Higgs doublet model

A two Higgs doublet model (2HDM) is one of minimal extensions of the Standard Model (SM), and it is well-known that the general setup predicts the flavor-violating phenomena, mediated by neutral Higgs interactions. Recently the CMS collaboration has reported an excess of the lepton-flavor-violating Higgs decay in h → μτ channel with a significance of 2.4 σ. We investigate the CMS excess in a general 2HDM with tree-level Flavor Changing Neutral Currents (FCNCs), and discuss its impact on the other physical observations. Especially, we see that the FCNCs relevant to the excess can enhance the neutral Higgs contributions to the muon anomalous magnetic moment, and can resolve the discrepancy between the measured value and the SM prediction. We also find that the couplings to be consistent with the anomaly of the muon magnetic moment as well as the CMS excess in h → μτ predict the sizable rate of τ → μγ, which is within the reach of future B factory.


JHEP05(2015)028
While a Higgs boson has been discovered at the Large Hadron Collider (LHC) experiment [1,2], the whole structure of the Higgs sector is still unknown. Theoretically there is no apparent reason why a Higgs sector with one Higgs doublet is better than the one with more Higgs doublets. Thus, only the experimental research will reveal the true answer.
A two Higgs doublet model (2HDM) is a simple extension of the minimal Higgs sector in the SM. In general, both Higgs doublets couple to fermions, and hence the flavor-changing Higgs interaction is predicted. This is one of the main differences from the SM. Recently the CMS collaboration has reported an excess of lepton-flavor-violating Higgs decay in h → µτ mode [3,4] The SM cannot accommodate such an excess, however, the general 2HDM 1 can explain the excess, as pointed out in refs. [5][6][7]. 2 Therefore, it is worth studying it further, and we find that the µ − τ lepton-flavor-violating Higgs interaction can enhance the neutral Higgs contributions to an anomalous magnetic moment of muon (muon g-2), and hence it can explain the long-standing anomaly of the muon g-2 [15].
In the general 2HDM, we can always take a basis where only one Higgs doublet gets a vacuum expectation value (VEV), so that we can parametrize the Higgs doublets as follows; where G + and G are Nambu-Goldstone bosons, and H + and A are a charged Higgs boson and a CP-odd Higgs boson, respectively. CP-even neutral Higgs bosons φ 1 and φ 2 can mix and form mass eigenstates, h and H (m H > m h ), Here θ βα is the mixing angle. In mass eigenbasis for the fermions, the Yukawa interactions are expressed as follows; is the Cabbibo-Kobayashi-Maskawa (Maki-Nakagawa-Sakata) matrix and the fermions (f L , f R ) (f = u, d, e, ν) are mass eigenstates. ρ ij f are general 3-by-3 complex matrices and can be sources of the Higgsmediated FCNC processes. In the following discussions, we do not adopt the so-called Cheng-Sher ansatz [16] for ρ ij f in order to explore wider parameter space.

JHEP05(2015)028
In the mass eigenstate of Higgs bosons, the interactions are expressed as where and s βα = sin θ βα and c βα = cos θ βα are defined. Note that the SM-like Higgs couplings y hf f approach to the SM ones when c βα gets closer to zero, so that the flavor-violating phenomena mediated by the SM-like Higgs boson can be suppressed in this limit. The current LHC Higgs coupling measurements and search for flavor violation suggest the smallness of the mixing parameter c βα in this framework.
On the other hand, the CMS collaboration reports that there is an excess in h → µτ process [3,4]; where the final state is a sum of µ + τ − and µ − τ + . This might be an evidence of a Flavor Changing Neutral Current (FCNC) involving SM-like neutral Higgs, and, in fact, the flavorviolating coupling ρ e can accommodate the CMS result in our general 2HDM; where Γ h is a total decay width of Higgs boson h and we adopt Γ h = 4.1 MeV in this paper. In order to explain the excess, the size of the flavor mixing should be as follows; Even if the Higgs mixing is small (c βα = 0.01), the O(1) flavor-violating couplingρ µτ can achieve the CMS excess. The next question is what kind of prediction we have, if such a flavor-violating Yukawa coupling exists. One interesting observable predicted by the FCNC is the muon g-2, where the discrepancy between the experimental result and the SM prediction is reported. The CMS excess requires the sizable µ − τ flavor violation, so that it would be possible for the large FCNC to contribute to the muon g-2 through the one-loop diagram involving neutral scalars   where the sign of the ρ τ µ e is fixed to induce the positive contribution to δa µ and the value ofρ µτ is determined to explain the CMS excess of BR(h → µτ ). We have taken m A = m H + = 300 GeV. The cyan (light blue) region is the one within |1σ| (|2σ|) range for the muon g-2 anomaly with the 1σ uncertainty of the CMS h → µτ excess. The dashed is −3σ line. The thick dashed lines correspond to ρ µτ = 0.1, 0.05 and 0.03 with BR(h → µτ )=0.84%, respectively.
assuming that ρ µτ e ρ τ µ e is real, for simplicity. 3 Here we only consider the dominant contributions which are proportional to τ mass m τ . 4 We note that the Yukawa couplings ρ µτ (τ µ) e generate an enhancement of O(m τ /m µ ) in the δa µ , where the m τ dependence comes from the internal τ lepton propagator in one loop diagram shown in figure 1. To maximize a size of the δa µ , while keeping a value of BR(h → µτ ), |ρ µτ e | ∼ |ρ τ µ e | is preferred. 3 If ρ µτ e ρ τ µ e is complex, the electric dipole moment (EDM) of the muon would be induced. The current limit of the muon EDM is |dµ| < 1.8×10 −19 e cm [17], which is expected to be improved up to 1×10 −24 e cm in the future experiments [18,19]. 4 In general, the other Yukawa couplings ρe might contribute to the muon g-2.
Here we have simply assumed that the others are negligible. Here we have assumedρ µτ = ρ µτ e = ±ρ τ µ e where the sign of ρ τ µ e is chosen to realize the positive contribution to δa µ and the value ofρ µτ e is determined to explain the CMS excess of BR(h → µτ ). We have taken m A = m H + = 300 GeV. In the cyan (light blue) region of figure 2, the anomaly of the muon g-2 can be explained within |1σ| (|2σ|) with the 1σ uncertainty of the CMS h → µτ excess. The −3σ line for the muon g-2 anomaly is also shown. Here we adopt the value of the muon g-2 anomaly from ref. [20], δa µ = (26.1 ± 8.0) × 10 −10 . In figure 2, the thick dashed lines correspond toρ µτ = 0.1, 0.05 and 0.03 with BR(h → µτ ) = 0.84%, respectively.

JHEP05(2015)028
In order to explain the anomaly of the muon g-2, the Higgs mixing parameter |s βα | should be close to one, which is consistent with the current Higgs coupling measurements at the LHC experiment. Note that the non-degeneracy among neutral Higgs bosons induces the larger δa µ . Although the non-degeneracy also generates the extra contributions to Peskin-Takeuchi's T-parameter [21][22][23][24], we have found that the small Higgs mixing parameter c βα suppresses the extra contributions in the current scenario when m A is very close to m H + .
As pointed out in refs. [5,25], the Yukawa couplings ρ µτ (τ µ) e would also induce significant contributions to τ → µγ process. The amplitude of τ → µγ process is parametrized by where P R, L (= (1 ± γ 5 )/2) are chirality projection operators, and e, ǫ α , q and u f are the electric charge, a photon polarization vector, a photon momentum, and a spinor of the fermion f , respectively. The branching ratio is given by where α and G F are the fine structure constant and Fermi constant, respectively. The lepton-flavor-violating Higgs contributions to A L and A R are given by , H, A), where A φ L, R (φ = h, H, A, H − ) are the φ contributions at the one loop level. We also include Barr-Zee-type two-loop contributions to A R, L in the numerical analysis, as studied JHEP05(2015)028 in refs. [5,25,26]. 5 When we assume non-zero ρ µτ (τ µ) e as suggested by the CMS excess in h → τ µ, but other ρ f couplings are negligibly small, the predicted branching ratio of τ → µγ is smaller than the current experimental limit (BR(τ → µγ) < 4.4 × 10 −8 at the 90% CL. [27,28]), however, it would be within a reach of the future B-factory. If unknown Yukawa couplings ρ f other than ρ µτ (τ µ) e are non-zero, the branching ratio can be significantly increased. Figure 3 shows the branching ratio of τ → µγ as functions of ρ τ τ e and ρ tt u in the presence of the non-zero ρ µτ (τ µ) e . Note that ρ tt u appears in the Barr-Zee diagrams. Here we have assumed that other ρ f Yukawa couplings are negligible, and m H = 450 GeV, m A = m H + = 300 GeV and s βα = 0.9999 are given. We choose ρ µτ e = −ρ τ µ e to achieve the positive contribution to δa µ and the values of ρ µτ (τ µ) e are determined to explain the CMS excess, BR(h → µτ ) = 0.84%. In figure 3, the line for the current experimental limit BR(τ → µγ) = 4.4 × 10 −8 [27,28] is shown. One sees that the limit strongly constrains ρ τ τ e and ρ tt u , however, they can still be of O(1) if the signs of them are opposite, which is due to a cancellation between the one-and two-loop contributions. The line for a future reference BR(τ → µγ) = 1 × 10 −9 [29] is also shown. As one can see from figure 3, even if ρ tt u = ρ τ τ e = 0 is satisfied, the branching ratio can be as large as 10 −9 . The future improvement on the search for τ → µγ at the level of 10 −9 will be crucial to test this scenario. In passing, the nonzero ρ tt u can contribute to δa µ via the Barr-Zee diagrams. However, it is found that its effect is subdominant.
For other tau decay modes [30], non-zero ρ µτ (τ µ) e couplings induce a correction to τ → µνν mode. We find that the corrction is of O(10 −5 − 10 −3 ) for the parameter space where the muon g-2 can be explained, and it is consistent with the current experimental results. For τ → µll (l = µ, e), the non-zero branching ratios are predicted even if only ρ µτ (τ µ) e are non-zero. The predicted rate, however, is well below the current experimental limit. The rate strongly depends on ρ ll e , and the current limit is setting a strong constraint

JHEP05(2015)028
as ρ ll e 0.01 for the parameter set studied in figure 3. The future improvement of the sensitivity will be very important. 6 A general 2HDM may be also responsible for discrepancies in B → Dτ ν, B → D * τ ν and B → τ ν processes as studied in ref. [31]. The couplings ρ µτ (τ µ) e can contribute to B → Dτ ν, B → D * τ ν and B → τ ν via a charged Higgs mediation if Yukawa couplings ρ u relevant to these processes are sizable. However, since the sizable contribution to the muon g-2 requires ρ µτ e ∼ ρ τ µ e , they also induce the significant contributions to B → Dµν, B → D * µν and B → µν processes, so that it would be difficult to explain these discrepancies, and the relevant Yukawa couplings ρ u(d) should be negligible in our scenario.
In order to explain the muon g-2 anomaly, the relatively light extra Higgs bosons A, H, and H ± are required. They will be expected to be produced at the LHC experiment. The production via quark Yukawa couplings ρ u,d will be possible and important. Furthermore, in the presence of the sizable ρ tt u , the gluon fusion production process for A and H would be dominant. However, it is difficult to predict the production cross section without the detail knowledge of the Yukawa couplings ρ e,u,d . On the other hand, the production via weak interaction such as qq ′ → W ± * → AH ± is less model-dependent as discussed in ref. [32]. The current LHC experimental data would put constraints on various unknown Yukawa couplings ρ f . The detail study will be worth probing this scenario and we will report it in a forthcoming paper [30].
In conclusion, the CMS experiment has reported the excess in h → µτ . Although the definitive statement cannot be made until the statistical significance of this excess becomes higher and the ATLAS collaboration also confirms it, this might be a hint for new physics. The general 2HDM can easily accommodate the excess, which can be induced by the µ − τ lepton-flavor-violating couplings. We have found that the µ − τ flavor violation can significantly enhance the neutral Higgs contributions to the muon g-2, and hence it can explain the anomaly of the muon g-2. In the parameter region where both anomalies for h → µτ and the muon g-2 can be solved, the branching ratio of τ → µγ can be sizable and the search at the future B factory would be crucial to test this scenario. Since the flavor structure of new Yukawa couplings ρ e,u,d is unknown, the further experimental and theoretical studies would be important to reveal the scenario. This will be just a beginning of many of new phenomena beyond the SM.

JHEP05(2015)028
Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.