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Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil

M. Beneke, Th. Feldmann

TL;DR

This work analyzes heavy-to-light B meson form factors at large recoil, showing that soft contributions collapse to a small set of universal functions and are broken by calculable α_s effects. It introduces a factorization framework with f_i(q^2) = C_i ξ + hard spectator terms and derives explicit α_s corrections to the symmetry relations, including detailed results for B → P and B → V transitions. A numerical study for B → π and B → ρ indicates typical symmetry-breaking corrections around 10% with significant uncertainties dominated by the B-meson distribution amplitude moment ⟨l_+^{-1}⟩_+, and the results are applied to the forward-backward asymmetry zero in B → K^* ℓ^+ℓ^− to constrain the Wilson coefficient C9. The findings provide a more structured, perturbative handle on hadronic uncertainties in rare B decays and connect form-factor symmetries to experimental observables like the FB asymmetry zero.

Abstract

Recently it has been shown that symmetries emerging in the heavy quark and large recoil energy limit impose various relations on form factors that parametrise the decay of B mesons into light mesons. These symmetries are broken by perturbative effects. In this paper we discuss the structure of heavy-to-light form factors including such effects and compute symmetry-breaking corrections to first order in the strong coupling. As an application of our results we consider the forward-backward asymmetry zero in the rare decay B -> V l^+ l^- and the possibility to constrain potential new physics contributions to the Wilson coefficient C_9.

Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil

TL;DR

This work analyzes heavy-to-light B meson form factors at large recoil, showing that soft contributions collapse to a small set of universal functions and are broken by calculable α_s effects. It introduces a factorization framework with f_i(q^2) = C_i ξ + hard spectator terms and derives explicit α_s corrections to the symmetry relations, including detailed results for B → P and B → V transitions. A numerical study for B → π and B → ρ indicates typical symmetry-breaking corrections around 10% with significant uncertainties dominated by the B-meson distribution amplitude moment ⟨l_+^{-1}⟩_+, and the results are applied to the forward-backward asymmetry zero in B → K^* ℓ^+ℓ^− to constrain the Wilson coefficient C9. The findings provide a more structured, perturbative handle on hadronic uncertainties in rare B decays and connect form-factor symmetries to experimental observables like the FB asymmetry zero.

Abstract

Recently it has been shown that symmetries emerging in the heavy quark and large recoil energy limit impose various relations on form factors that parametrise the decay of B mesons into light mesons. These symmetries are broken by perturbative effects. In this paper we discuss the structure of heavy-to-light form factors including such effects and compute symmetry-breaking corrections to first order in the strong coupling. As an application of our results we consider the forward-backward asymmetry zero in the rare decay B -> V l^+ l^- and the possibility to constrain potential new physics contributions to the Wilson coefficient C_9.

Paper Structure

This paper contains 20 sections, 100 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Derivation and discussion of large-recoil symmetries
  3. Recapitulation: heavy-heavy form factors
  4. Heavy-light form factors at large recoil
  5. Calculation of symmetry-breaking corrections
  6. Vertex corrections
  7. Hard spectator interaction
  8. General considerations
  9. $B\to P$ form factors
  10. $B \to V$ form factors
  11. Summary of corrections to form factor ratios
  12. Numerical analysis
  13. Application to the forward-backward asymmetry in $B \to V \ell^+ \ell^-$
  14. Conclusion
  15. Light-cone projections of light mesons
  16. ...and 5 more sections

Figures (3)

  • Figure 1: Different contributions to the $B\to P(V)$ transition. (a) Soft contribution (soft interactions with the spectator antiquark $\bar{q}'$ are not drawn). (b) Hard vertex renormalisation. (c,d) Hard spectator interaction.
  • Figure 2: Corrections to symmetry relations as a function of $q^2$ (three solid lines, see text). Figs. (a)--(g) correspond to the form factor ratios in Eqs. (\ref{['corr1']})-(\ref{['corr3']}) with overall scaling factors divided out, such that the symmetry limit (dotted lines) corresponds to a ratio equal to 1 independent on $q^2$. For illustration we show also results from QCD sum rules Ball:1998tjBall:1998kk (dashed lines). Tensor form factors are renormalized at $\mu=m_b$.
  • Figure 3: Various next-to-leading order contributions to the $B\to K^*\gamma^*$ matrix elements.