Real radiative decays of heavy pseudoscalar mesons

Abstract

We report our ongoing lattice QCD study of radiative leptonic decays of the charged pseudoscalar mesons $D$, $D_s$, $B$, and $B_c \to \ell ν_\ell γ$. We carry out our analysis on a single JLQCD ensemble with lattice spacing $a=0.044~\text{fm}$. This work is a step towards a complete QCD+QED lattice calculation of these modes, aimed at reducing theoretical uncertainties in the extraction of $|V_{cd}|$ and $|V_{cs}|$ and providing first-principles estimates of the corresponding form factors in the $B$ sector.

Figures (4)

• Figure 1: Diagrams contributing to the decay $P \to \ell \nu \gamma$ at leading order in $\alpha_{\text{em}}$. The double square indicates the four-fermion operator from Fermi theory. Here, we focus on the quark-connected contribution in \ref{['fig:quark-connected']}, where the photon can be emitted by either valence quark, and we plan to add the quark-disconnected contribution of \ref{['fig:quark-disconnected']} in the near future. The only non-perturbative contribution entering the final-state radiation in \ref{['fig:lepton-emission']} is the decay constant $f_P$.
• Figure 2: The two quark-connected diagrams that we compute, with the electromagnetic current inserted in either valence quark. To provide more photon momenta we introduce a twist angle $\theta_t$ in one quark line.
• Figure 3: The six heavy-light pseudoscalar meson masses vs the value of the Lorentz invariant $x_\gamma$ in the center-of-mass frame, with the color indicating the photon Fourier mode. \ref{['fig:fourier-modes']} shows the values of $x_\gamma$ that we can access with our methodology relying only on Fourier modes. As shown in \ref{['fig:twist-modes']}, we use twisted boundary conditions to cover additional values of $x_\gamma$. The physical region corresponds to $0 < x_\gamma < 1 - m_\ell^2/m_P^2$, where $m_\ell$ and $m_P$ are the lepton and pseudoscalar meson masses.
• Figure 4: Axial (top panel) and vector (bottom panel) components of the three-point correlator \ref{['eq:3pt']} for the Fourier mode $\pmb{n}=(0,0,1)$ and the states $D$ and $D_s$. The top left plot shows the axial component $C_{3,A}^{11}$ for the $D$ meson as a function of the electromagnetic-current time insertion $t_\gamma + t_W$. The four different colors refer to different source-sink separations $t_W$. The other plots correspond to the vector three-point function $C_{3,V}^{21}$ of the $D$ meson (bottom left), the axial $C_{3,A}^{11}$ of the $D_s$ meson (top right), and the vector $C_{3,V}^{21}$ of the $D_s$ meson (bottom right).