Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On soft contributions to the $B^-\to γ^*$ form factors

Aoife Bharucha, Danny van Dyk, Eduardo Velásquez

Abstract

The photoleptonic decay $B^-\to γ\ell^-\barν$ is the simplest low-energy process that probes the substructure of the $B$ meson, making it an excellent candidate to determine the parameters of $B$-meson light-cone distribution amplitudes from experimental data. More recently, the decay $B^-\to γ^*(\to \ell'^-\ell'^+)\ell^-\barν$ has received attention as an alternative probe of these parameters. Both decays are described through a common set of hadronic form factors, which if computed within the framework of QCD factorization give rise to the sensitivity to the $B$-meson light-cone distribution amplitudes. Nevertheless, in this case the form factors still receive so-called soft contributions that can only be estimated but not rigorously computed. In this work, we provide results for the QCD factorization expressions for the form factors, including terms at next-to-leading power in the $b$ quark mass and in the photon energy. We further use these results to estimate the soft contributions within a light-cone sum rule setup. Finally, using numerical results obtained from a benchmark model of the light-cone distribution amplitudes, we show that the soft contributions are under significantly better theoretical control at a mildly spacelike photon virtuality.

On soft contributions to the $B^-\to γ^*$ form factors

Abstract

The photoleptonic decay is the simplest low-energy process that probes the substructure of the meson, making it an excellent candidate to determine the parameters of -meson light-cone distribution amplitudes from experimental data. More recently, the decay has received attention as an alternative probe of these parameters. Both decays are described through a common set of hadronic form factors, which if computed within the framework of QCD factorization give rise to the sensitivity to the -meson light-cone distribution amplitudes. Nevertheless, in this case the form factors still receive so-called soft contributions that can only be estimated but not rigorously computed. In this work, we provide results for the QCD factorization expressions for the form factors, including terms at next-to-leading power in the quark mass and in the photon energy. We further use these results to estimate the soft contributions within a light-cone sum rule setup. Finally, using numerical results obtained from a benchmark model of the light-cone distribution amplitudes, we show that the soft contributions are under significantly better theoretical control at a mildly spacelike photon virtuality.
Paper Structure (13 sections, 50 equations, 2 figures, 2 tables)

This paper contains 13 sections, 50 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Factorization framework and beyond
  3. Leading factorizable contributions
  4. Power corrections and higher-twist contributions
  5. Soft contributions
  6. Numerical results
  7. Conclusion
  8. Details
  9. Final state radiation
  10. Singularity-free hadronic tensor
  11. Projectors onto the form factors
  12. LCDA definitions
  13. LCDA identities

Figures (2)

  • Figure 1: Sketches to illustrate the origin of soft contributions to the photoleptonic decay. In the left sketch, the photon is emitted from the $b$ quark line, which is a power correction to leading QCDF expression; here, soft contributions are not considered. In the right sketch, the photon is emitted from the $u$ quark line. This sketch represents a mechanism that gives rise to soft contributions, resonantly enhanced at $q^2 \simeq m_\rho^2$.
  • Figure 2: The soft contributions for the form factor $F_4$, normalized to the QCDF result. We show the ratio for two fixed values of $q^2$ and as a function of $k^2$. The figure on the left includes only the leading power contribution while the figure on the right include all next-to-leading power contributions.