Radiative Semileptonic Decays of Beautiful Hadrons

TL;DR

This work extends HQET-based analyses of radiative semileptonic decays to a broad set of beauty-hadron channels, showing that heavy-quark spin-flavor symmetry reduces the number of independent SD form factors dramatically compared to the generic Lorentz-invariant case. By matching HQET to HHχPT in the soft and sub-leading soft regions, the authors derive closed-form parameterizations in terms of Isgur-Wise functions and a small set of magnetic-dipole moments, with reparameterization invariance providing powerful constraints that minimize new unknowns. They provide explicit structures for baryon channels ($\Lambda_b\to\Lambda_c$ and $\Lambda_b\to\Lambda_{c1}^{(*)}$) and meson channels ($\bar{B}\to D^{(*)}$, $D^{1/2^+}$, and $D^{3/2^+}$), along with leading and sub-leading soft behaviors and the necessary matching to HHχPT. The results enable precise photon-spectrum predictions and reliable MC implementations for Belle II and LHCb, while identifying the remaining phenomenological inputs (magnetic-dipole coefficients) and the expected size of radiative corrections at realistic photon energies.

Abstract

We derive predictions for the hadronic matrix elements of radiative semileptonic decays of beautiful hadrons within Heavy Quark Effective Theory (HQET), relevant for future measurements at Belle II and LHCb. Our study considers Lambda(b) -> Lambda(c), Lambda(*)(c1) and B -> D(*), D** transitions. The symmetries of HQET highly constrain the number of structure-dependent form factors in all cases. In the soft and sub-leading soft regions, all the form factors are fully determined in terms of non-radiative Isgur-Wise functions and the magnetic dipole moments of the heavy hadrons. The structure of higher order corrections is also briefly discussed.

Figures (4)

• Figure 1: Feynman diagrams contributing to the decay process $\Lambda_b\to \Lambda_c l\bar{\nu}\gamma$. The same diagrams are also the ones relevant for the decay process $\Lambda_b\to \Lambda_{c1}^{(*)} l\bar{\nu}\gamma$. The black square indicates a weak current insertion.
• Figure 2: Feynman diagrams contributing to the decay process $\bar{B}\to D^{**} l\bar{\nu}\gamma$. The black square indicates the weak current insertion.
• Figure 3: HH$\chi$PT Feynman diagrams contributing to the leading soft behavior, i.e. $\mathcal{O}(k^{-1})$. The diagrams are the same either for the meson and for the baryon cases, so that here $H_a$ and $H'_a$ indicate two generic hadronic fields with $SU(3)_V$ index $a$. The black square indicates the weak current insertion.
• Figure 4: HH$\chi$PT Feynman diagrams of magnetic dipole operators contributing to the sub-leading soft behavior, i.e. $\mathcal{O}(k^0)$. Also in this case the diagrams for the meson and baryon case are the same, so that $H_a$ and $H'_a$ are two generic hadron fields with $SU(3)_V$ index $a$. The black square indicate the weak current insertion, while the black circle indicate the insertion of a dim-$5$ magnetic dipole operator.