Exclusive radiative and electroweak b->d and b->s penguin decays at NLO

TL;DR

This work provides a comprehensive, next-to-leading-order analysis of exclusive radiative and electroweak b→d and b→s penguin decays within the Standard Model, employing QCD factorization to predict branching fractions, isospin and direct CP asymmetries, and dilepton observables including the forward-backward asymmetry. It extends prior b→s results to b→d transitions by incorporating the necessary up-quark contributions and NNLL corrections, and it studies how these decays constrain CKM parameters, particularly |V_td|/|V_ts|, while highlighting the sensitivity to hadronic form factors and annihilation effects. The paper also compares NNLO-inspired predictions to early experimental results, discusses potential new-physics scenarios that modify C9 and C10 in b→d transitions, and emphasizes the role of future lattice and experimental improvements in sharpening CKM constraints and FCNC tests. Overall, the results provide precise SM benchmarks and identify where measurements of B→ργ and B→ρℓ^+ℓ^− can most effectively probe flavor physics and possible new interactions.

Abstract

We provide Standard Model expectations for the rare radiative decays B->K^* gamma, B->rho gamma and B-> omega gamma, and the electroweak penguin decays B->K^* l^+ l^- and B->rho l^+ l^- at the next-to-leading order (NLO), extending our previous results to b->d transitions. We consider branching fractions, isospin asymmetries and direct CP asymmetries. For the electroweak penguin decays, the lepton-invariant mass spectrum and forward-backward asymmetry is also included. Radiative and electroweak penguin transitions in b->d are mainly interesting in the search for new flavour-changing neutral current interactions, but in addition the B->rho gamma decays provide constraints on the CKM parameters (\barρ,\barη). The potential impact of these constraints is discussed.

Figures (6)

• Figure 1: CP-averaged differential branching ratio for $B^0\to \rho^0\ell^+\ell^-$ at NLO as a function of $q^2$ (solid line, in units of $10^{-9}\,\hbox{GeV}^{-2}$). The light (yellow) band shows the total theoretical uncertainty. In the dark (green) band, the uncertainties related to the CKM parameters and the form factor $A_0^\rho(0)$ are excluded. The dashed line shows the LO result.
• Figure 2: Isospin asymmetry $\Delta(\rho\gamma)$ as a function of the CKM angle $\alpha$. The band displays the total theoretical uncertainty which is mainly due to weak annihilation. The vertical dashed lines limit the range of $\alpha$ obtained from the CKM unitarity triangle fit.
• Figure 3: Isospin asymmetry $\Delta(\rho\,\ell^+\ell^-)$ as a function of $q^2$. The solid (long-dashed) line shows the next-to-leading (leading) order result for $\alpha=94^\circ$. The band represents the hadronic uncertainty. The two dashed lines give $\Delta(\rho\,\ell^+\ell^-)$ for $\alpha=24^\circ$ (lower curve) and $\alpha=164^\circ$ (upper curve).
• Figure 4: Direct CP asymmetry in $B\to\rho^0\gamma$ (solid), $B^+\to\rho^+\gamma$ (long-dashed) and $B\to\omega\gamma$ (short-dashed) decay as a function of the CKM angle $\alpha$. The band shows the theoretical uncertainty for the case of $B\to\rho^0\gamma$. Note that we display minus the CP asymmetry.
• Figure 5: Direct CP asymmetries in $B^0 \to \rho^0\ell^+\ell^-$ (lower set of curves) and $B^+ \to \rho^+\ell^+\ell^-$ as a function of $q^2$. The solid (dashed) curves show the next-to-leading order (leading order) result. The widths of the bands represent the hadronic uncertainty. Note that we display minus the CP asymmetry.