B->V gamma Beyond QCD Factorisation

TL;DR

This work advances the study of exclusive radiative B decays by blending QCD factorisation with dominant beyond-QCD-factorisation effects estimated from light-cone sum rules, including long-distance photon emission and soft-gluon emission from quark loops. It develops a novel approach to compute soft-gluon contributions from light-quark loops via off-shell light-cone sum rules and dispersion techniques, quantified for all $B\to V\gamma$ channels. The authors provide predictions for branching ratios, isospin and CP asymmetries with roughly 20% (30% for certain $B_s$ modes) theoretical uncertainty and derive $|V_{td}/V_{ts}|$ and $\gamma$ from $R_{\rho/\omega}$ measurements, finding results compatible with SM expectations and highlighting observables with strong NP sensitivity, such as time-dependent CP asymmetries in $B\to V\gamma$. The work offers a framework and numerical results that will inform future measurements at B factories, the LHC, and a potential super-flavour factory, while identifying key hadronic inputs and form-factor ratios that control theoretical uncertainties.

Abstract

We calculate the main observables in $B_{u,d}\to (ρ,ω,K^*)γ$ and $B_s\to (\bar K^*,φ)γ$ decays, i.e. branching ratios and CP and isospin asymmetries. We include QCD factorisation results and also the dominant contributions beyond QCD factorisation, namely long-distance photon emission and soft-gluon emission from quark loops. All contributions beyond QCD factorisation are estimated from light-cone sum rules. We devise in particular a method for calculating soft-gluon emission, building on earlier ideas developed for analogous contributions in non-leptonic decays. Our results are relevant for new-physics searches at the $B$ factories, the LHC and a future super-flavour factory. Using current experimental data, we also extract $|V_{td}/V_{ts}|$ and the angle $γ$ of the unitarity triangle. We give detailed tables of theoretical uncertainties of the relevant quantities which facilitates future determinations of these CKM parameters from updated experimental results.

Figures (6)

• Figure 1: (a): WA diagram. The square denotes insertion of the operator $Q_i$. Photon emission from lines other than the $B$ spectator is power-suppressed, except for emission from the final-state quark lines for the operators $Q_{5,6}$, denoted by crosses. (b): soft-gluon emission from a quark loop. Again the square dot denotes the insertion of the operator $Q_i$. There is also a second diagram where the soft gluon is picked up by the $B$ meson.
• Figure 2: Example radiative corrections to weak annihilation. The corrections to the $B$ vertex in (a) are known bellnu and those to the $V$ vertex in (b) are included in $f_V$. For the non-factorisable corrections in (c) only preliminary results are available, see text.
• Figure 3: Leading contribution to the correlation function $\Gamma_V$ in (\ref{['32']}). The black square denotes insertion of the operator $Q_i$ with $i=1,\dots,6$. The $B$ meson momentum is $p_B = p+q$ and the vector meson carries the momentum $p$.
• Figure 4: Left panel: $|V_{td}/V_{ts}|^2$ as function of $R_{\rho/\omega}$, Eq. (\ref{['58']}), in the $|V_{tx}|$ basis, see text. Solid line: central values. Dash-dotted lines: theoretical uncertainty induced by $\xi_\rho = 1.17\pm 0.09$, (\ref{['xirho']}). Dashed lines: other theoretical uncertainties, including those induced by $|V_{ub}|$, $|V_{cb}|$ and the hadronic parameters of Tab. \ref{['tab3']}. Right panel: $\Delta R$ from Eq. (\ref{['delR']}) as function of $|V_{td}/V_{ts}|$ for the $|V_{tx}|$ set of CKM parameters. Solid line: central values. Dashed lines: theoretical uncertainty.
• Figure 7: CP-averaged branching ratios of $B\to(\rho,\omega)\gamma$ as function of $\gamma$, using the effective form factors and central values of other input parameters. (a): $B^\pm \to \rho^\pm\gamma$, (b): $B^0\to \rho^0\gamma$, (c): $B^0\to\omega\gamma$. The boxes indicate the 1$\sigma$ experimental results from BaBar Babar, Tab. \ref{['tab1']}. Note that the resulting value of $\gamma$ from the average of all three channels is $\gamma = (61.0^{+13.5}_{-16.0}({\rm exp})^{+8.9}_{-9.2})^\circ$, Eq. (\ref{['63']}).