Note on gauge and gravitational anomalies of discrete ZNZ_N symmetries

In this note, we discuss the consistency conditions which a discrete $Z_N$ symmetry should satisfy in order that it is not violated by gauge and gravitational instantons. As examples, we enlist all the $Z_N$ ${\cal R}$-symmetries as well as non-${\cal R}$ $Z_N$ symmetries (N=2,3,4) in the minimally supersymmetric standard model (MSSM) that are free from gauge and gravitational anomalies. We show that there exists non-anomalous discrete symmetries that forbid Baryon number violation up to dimension 6 level (in superspace). We also observe that there exists no non-anomalous $Z_3$ ${\cal R}$-symmetry in the MSSM. Furthermore, we point out that in a theory with one Majorana spin 3/2 gravitino, a large class of $Z_4$ ${\cal R}$-symmetries are violated in the presence of Eguchi-Hanson (EH) gravitational instanton. This is also in general true for higher $Z_N$ ${\cal R}$-symmetries. We also notice that in 4 dimensional ${\cal N}=1$ supergravity, the global $U(1)$ ${\cal R}$-symmetry is always violated by the EH instanton irrespective of the matter content of the theory.Comment: Version to appear in JHE

Lepton Electric Dipole Moment and Strong CP Violation

Contribution of the strong CP angle, $\bar\theta$, to the Wilson Coefficients of electron and muon electric dipole moment (EDM) operators are discussed. Previously, $\bar\theta$ contribution to the electron EDM operator was calculated by Choi and Hong. However, the effect of CP-violating three meson coupling was missing there. We include this missing contribution for the first time in the literature, and reevaluate the Wilson coefficients of the lepton EDM operator. We obtain $d_e = - (2.2-8.6) \times 10^{-28} \bar\theta$ e-cm which is 15 - 70 % of the result obtained in Choi and Hong. We also estimated the muon EDM as $d_\mu = - (0.5-1.8) \times 10^{-25} \bar\theta$ e-cm. Using $|\bar\theta| \lesssim 10^{-10}$ suggested by the neutron EDM measurements, we obtain $|d_e| \lesssim 8.6 \times 10^{-38}$ e-cm and $|d_\mu| \lesssim 1.8 \times 10^{-35}$ e-cm. The $\bar\theta$ contribution to the muon EDM is much below the sensitivities of the current and near future experiments. Our result shows that the $\bar\theta$ contribution to $d_{e,\mu}$ can be larger than the CKM contributions by many orders of magnitude.Comment: 10 pages, 2 figures; v3: version published, reference adde

Role of Tensor operators in RKR_K and RK∗R_{K^*}

The recent LHCb measurement of $R_{K^*}$ in two $q^2$ bins, when combined with the earlier measurement of $R_K$, strongly suggests lepton flavour non-universal new physics in semi-leptonic $B$ meson decays. Motivated by these intriguing hints of new physics, several authors have considered vector, axial vector, scalar and pseudo scalar operators as possible explanations of these measurements. However, tensor operators have widely been neglected in this context. In this paper, we consider the effect of tensor operators in $R_K$ and $R_{K^*}$. We find that, unlike other local operators, tensor operators can comfortably produce both of $R_{K^*} ^{\rm low}$ and $R_{K^*} ^{\rm central}$ close to their experimental central values. However, a simultaneous explanation of $R_K$ is not possible with only Tensor operators, and other vector or axial vector operators are needed. In fact, we find that combination of vector and tensor operators can provide simultaneous explanations of all the anomalies comfortably at the $1 \sigma$ level, a scenario which is hard to achieve with only vector or axial vector operators. We also comment on the compatibility of the various new physics solutions with the measurements of the inclusive decay $B_d \to X_s \ell^+ \ell^-$.Comment: Version to appear in PL

Nonuniversality of indirect CP asymmetries in D→ππ,KKD \to \pi\pi, KK decays

We point out that, if the direct CP asymmetries in the $D \to \pi^+ \pi^-$ and $D \to K^+ K^-$ decays are unequal, the indirect CP asymmetries as measured in these modes are necessarily unequal. This nonuniversality of indirect CP asymmetries can be significant with the right amount of new physics contributions, a scenario that may be fine-tuned, but is still viable. A model-independent fit to the current data allows different indirect CP asymmetries in the above two decays. This could even be contributing to the apparent tension between the difference CP asymmetries $\Delta A_{\rm CP}$ measured through the pion-tagged and muon-tagged data samples at the LHCb. This also implies that the measurements of $A_\Gamma$ and $y_{\rm CP}$ in the $\pi^+ \pi^-$ and $K^+ K^-$ decay modes can be different, and averaging over these two modes should be avoided. In any case, the complete analysis of CP violation measurements in the $D$ meson sector needs to take into account the possibility of different indirect CP asymmetries in the $\pi^+\pi^-$ and $K^+ K^-$ channels.Comment: 23 pages, 14 Postscript figures, matches published versio

Hint of Lepton Flavour Non-Universality in BB Meson Decays

The LHCb collaboration has recently presented their result on R_K = BR(B+ -> K+ mu+ mu-)/ BR(B+ -> K+ e+ e-) for the dilepton invariant mass bin m_{ll}^2 = 1-6 GeV^2 (l = mu, e). The measurement shows an intriguing 2.6 sigma deviation from the Standard Model (SM) prediction. In view of this, we study model independent New Physics (NP) explanations of R_K consistent with other measurements involving b -> s l l transition, relaxing the assumption of lepton universality. We perform a Bayesian statistical fit to the NP Wilson Coefficients and compare the Bayes Factors of the different hypotheses in order to quantify their goodness-of-fit. We show that the data slightly favours NP in the muon sector over NP in the electron sector.Comment: Final version, to appear in JHE