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Register a new userEstimates of Long-distance Contributions to the $B_s to gamma gamma$ Decay
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We present first calculations of new long-distance contributions to $B_s to gamma gamma$ decay due to intermediate $D_s$ and $D_s^*$ meson states. The relevant $gamma$ vertices are estimated using charge couplings and transition moment couplings. Within our uncertainties, we find that these long-distance contributions could be comparable to the known short-distance contributions. Since they have different Cabibbo-Kobayashi-Maskawa matrix-element factors, there may be an interesting possibility of observing CP violation in this decay.
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The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavour changing neutral current and therefore may only be induced beyond tree level in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential New Physics. To discern such New Physics one must be able to control the errors on the Standard Model prediction of the decay amplitude. These particular decay channels however are dominated by a single photon exchange; this involves a sizeable long-distance hadronic contribution which represents the current major source of theoretical uncertainty. Here we outline our methodology for the computation of the long distance contributions to these rare decay amplitudes using lattice QCD, and present the numerical results of some exploratory studies using the Domain Wall Fermion ensembles of the RBC and UKQCD collaborations.
Neutrinoless double beta decay, if detected, would prove that neutrinos are Majorana fermions and provide the direct evidence for lepton number violation. If such decay would exist in nature, then $pi^-pi^-to ee$ and $pi^-topi^+ ee$ (or equivalently $pi^-e^+topi^+ e^-$) are the two simplest processes accessible via first-principle lattice QCD calculations. In this work, we calculate the long-distance contributions to the $pi^-topi^+ee$ transition amplitude using four ensembles at the physical pion mass with various volumes and lattice spacings. We adopt the infinite-volume reconstruction method to control the finite-volume effects arising from the (almost) massless neutrino. Providing the lattice QCD inputs for chiral perturbation theory, we obtain the low energy constant $g_ u^{pipi}(m_rho)=-10.89(28)_text{stat}(74)_text{sys}$, which is close to $g_ u^{pipi}(m_rho)=-11.96(31)_text{stat}$ determined from the crossed-channel $pi^-pi^-to ee$ decay.
Standard lattice calculations in flavour physics or in studies of hadronic structure are based on the evaluation of matrix elements of local composite operators between hadronic states or the vacuum. In this talk I discuss developments aimed at the computation of long-distance, and hence non-local, contributions to such processes. In particular, I consider the calculation of the $K_L$-$K_S$ mass difference $Delta m_K=m_{K_L}-m_{K_S}$ and the amplitude for the rare-kaon decay processes $Ktopiell^+ell^-$, where the lepton $ell=e$ or $mu$. Lattice calculations of the long-distance contributions to the indirect $CP$-violating parameter $epsilon_K$ and to the rare decays $Ktopi ubar u$ are also beginning. Finally I discuss the possibility of including $O(alpha)$ electromagnetic effects in computations of leptonic and semileptonic decay widths, where the novel feature is the presence of infrared divergences. This implies that contributions to the width from processes with a real photon in the final state must be combined with those with a virtual photon in the amplitude so that the infrared divergences cancel by the Bloch-Nordsieck mechanism. I present a proposed procedure for lattice computations of the $O(alpha)$ contributions with control of the cancellation of the infrared divergences.
The two photon decay width of the neutral pion is analyzed within the combined framework of Chiral Perturbation Theory and the 1/Nc expansion up to order p^6 and p^4 times 1/Nc in the decay amplitude. The eta is explicitly included in the analysis. It is found that the decay width is enhanced by about 4.5% due to the isospin-breaking induced mixing of the pure U(3) states. This effect, which is of leading order in the low energy expansion, is shown to persist nearly unchanged at next to leading order. The chief prediction for the width with its estimated uncertainty is 8.10+-0.08 eV. This prediction at the 1% level makes the upcomming precision measurement of the decay width even more urgent. Observations on the eta and eta can also be made, especially about their mixing, which is shown to be significantly affected by next to leading order corrections.
We examine the effects of R-parity violating (RPV) supersymmetry on the two-photon B decays B -> X_s gamma gamma and B_s -> gamma gamma. We find that, although there are many one-loop RPV diagrams that can contribute to these two-photon B decays, the RPV effect is dominated by a single diagram. This diagram, named here lambda-irreducible, has a distinct topology which is irrelevant for the b -> s gamma amplitude at one-loop and has thus a negligible effect on the one-photon decay B -> X_s gamma. We show that the lambda-irreducible RPV diagram can give BR(B_s -> gamma gamma) ~ 5*10^(-6) and BR(B -> X_s gamma gamma) ~ 6*10^(-7), which is about 16 and 5 times larger than the SM values, respectively. Although the enhancement to the decay width of B -> X_s gamma gamma is not that dramatic, we find that the energy distribution of the two photons is appreciably different from the SM, due to new threshold effects caused by the distinct topology of the RPV lambda-irreducible diagram. Moreover, this diagram significantly changes the forward-backward asymmetry with respect to the softer photon in B -> X_s gamma gamma. Thus, the RPV effect in B -> X_s gamma gamma can be discerned using these observables.
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