# The Fifth Annual Large Hadron Collider Physics conference (LHCP2017)

May 15 – 20, 2017
Shanghai Jiao Tong University
Asia/Shanghai timezone
Please bring you passport details to the registration desk to confirm your participation for the excursions

## B \to \pi\pi transition form factor in LCSRs

May 16, 2017, 2:00 PM
2h
Haoran 102 (Shanghai Jiao Tong University)

Xuhui Campus

### Speaker

Shan Cheng (Siegen University)

### Description

We study $B\to\pi\pi$ form factors using QCD light-cone sum rules with $B$-meson distribution amplitudes. These form factors describe the semileptonic decay $B\to \pi\pi \ell\bar{\nu}_{\ell}$, and constitute an essential input in $B\to \pi\pi \ell^+\ell^-$ and $B\to \pi\pi\pi$ decays. We employ the correlation functions where a dipion isospin-one state is interpolated by the vector light-quark current. We obtain sum rules where convolutions of the $P$-wave $\bar{B}^0\to \pi^+\pi^0$ form factors with the time-like pion vector form factor are related to universal $B$-meson distribution amplitudes. These sum rules are valid in the kinematic regime where the dipion state has a large energy and a low invariant mass, and reproduce analytically the known light-cone sum rules for $B\to \rho$ form factors in the limit of $\rho$-dominance with zero width, thus providing a systematics for so-far-unaccounted corrections to $B\to\rho$ transitions. Using data for the pion vector form factor, we estimate finite width-effects and the contribution of excited $\rho$-resonances to the $B\to\pi\pi$ form factors. We find that these contributions amount up to $\sim 20\%$ in the small dipion mass region where they can be effectively regarded as a nonresonant ($P$-wave) background to the $B\to\rho$ transition.

### Primary author

Shan Cheng (Siegen University)

### Co-authors

Prof. Alexander Khodjamirian (Siegen University) Javier Virto (University of Bern)