arXiv subjects
Publications and source records attributed to Dayanand Mishra.
In this talk, I will present the calculation of LCSR predictions for the $B \to K$ Hadronic Matrix Elements (HME) at low $q^2$ using light meson distribution amplitudes. I will discuss the results obtained.
This article explores the calculation of non-perturbative parameters present in the matrix element of semileptonic inclusive $B$ decays. These are important for the inclusive determination of the Cabbibo-Kobayashi-Maskawa (CKM) parameters in the standard model. We focus on calculating the rate for radiative inclusive decay, $B\to X_c\ell \barν_{\ell}γ$, where $γ$ is hard. Both the radiative and non-radiative ($B\to X_c \ell \barν_{\ell}$) modes are found to require the same non-perturbative parameters. We propose forming ratios from $B\to X_c \ell \barν_{\ell}γ$ and $B\to X_c \ell \barν_{\ell}$ widths in different lepton energy ranges. Our results provide an efficient way to unambiguously calculate the non-perturbative parameters, especially when combined with total width calculations of $B\to X_c \ell \barν_{\ell}$. This is shown explicitly by working to $\mathcal{O}(1/m_b)$ and determining $λ_1$ and $λ_2$.
The non-local effects originating from the charm quark loops at dilepton invariant masses smaller than the charmonium threshold in $B\to K \ell\ell$ are evaluated with light meson distribution amplitudes. The revised estimates with B-meson distribution amplitude within a Light Cone Sum Rule approach yielded results about three orders smaller than the original computation. In view of the importance of these non-factorizable soft gluon effects, both conceptually and phenomenologically, an independent evaluation is necessary. It is found that to twist-4 accuracy, these soft gluon effects vanish when evaluated employing the kaon distribution amplitude. Similar results hold for $B\to K^* \ell\ell$ to the leading twist. This eliminates one of the major sources of potential uncertainty which usually makes it difficult for a clear case of new physics, should the data show deviations from the standard model.
Recently \cite{Horowitz:2022rpp,Horowitz:2022uak}, denominator regularisation (Den. Reg.) scheme has been proposed to handle divergences in quantum field theory. It is shown to yield results as simple as in dimensional regularisation scheme and also shown to be compatible with minimal subtraction scheme by taking several examples in field theory. In this article, we point out some interesting features of this regularisation scheme which appear as a consequence of the requirement of gauge invariance by revisiting QED vacuum polarisation and $H\toγγ$ decay in this regularisation scheme.
Charged current semi-leptonic decays of $B$-meson are important for a precise determination of the CKM elements. The CKM elements $|V_{ub}|$ and $|V_{cb}|$ show a discrepancy between the exclusive and inclusive determinations. These determinations are however masked with hadronic and other uncertainties, and thus can't be unambiguously taken as implying new physics. In the present study, we propose a new observable: the ratio of these two CKM elements, $R_V \equiv \frac{|V_{ub}|}{|V_{cb}|}$, which is found to receive negligible corrections due to hadronic as well as QED effects. Interestingly, $R_V$ as constructed from exclusive determinations of $|V_{ub}|$ and $|V_{cb}|$ agrees quite well with that constructed from the inclusive determinations of these CKM elements. Hence, we propose that $R_V$ is a better and cleaner observable, and can serve as an excellent tool for the test of the Standard Model. We also provide an example of its probing power.
We give detailed results of $\mathcal{O}(α)$ QED corrections (both real emission and virtual corrections) to $B\to K\ell^+\ell^-$ modes. Requiring the real emission to be gauge invariant, the structure of the contact term(s) is fixed. The calculation is done with a fictitious photon mass as the IR regulator and results are shown to be independent of it, establishing cancellation of the soft divergences. Results are presented for a choice of photon energy, $k_{max}$, and photon angle $θ_{cut}$. The QED effects are negative, thereby reducing the rate compared to that without QED effects. Electron channels are shown to receive large corrections ($\mathcal{O}(20\%)$). Impact on lepton flavour universality ratio, $R^{μe}_K$ are also discussed.