Eur. Phys. J. C (2025) 85: 1393
https://doi.org/10.1140/epjc/s10052-025-15141-6

Regular Article - Theoretical Physics

Factorization of multiparticle contributions to amplitudes of B-meson weak decays

¹ D. V. Skobeltsyn Institute of Nuclear Physics, M. V. Lomonosov Moscow State University, 119991, Moscow, Russia
² Joint Institute for Nuclear Research, 141980, Dubna, Russia
³ Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria

^a dmitri_melikhov@gmx.de

Received: 10 September 2025
Accepted: 1 December 2025
Published online: 8 December 2025

Abstract

We show that multiparticle contributions to amplitudes of weak decays of the generic topology (heavy quark hits some intermediate point of the propagator line joining the end-points from which momenta q and $q^{\prime }$ are emitted) is given in the heavy quark limit and at the leading order in ${\alpha }_s$ by the convolution of (i) hard kernel composed of highly virtual propagators of light degrees of freedom and (ii) the B-meson multiparticle wave function, $⟨0|\varphi (x)\varphi (x_1)\cdots \varphi (x_n){\varphi }_b(0)\varphi (x_{n^{\prime }}^{\prime })\cdots \varphi (x_1^{\prime })\varphi (x^{\prime })|B(p)⟩$, in a double-collinear light-cone configuration: the coordinates $x,x_1,\dots ,x_n$ are ordered and aligned along the light-like 4-vector $a_{\mu }$, $a^2=0$, $q_{\mu }\propto a_{\mu }$, while the coordinates $x^{\prime },x_1^{\prime },\dots ,x_{n^{\prime }}^{\prime }$ are ordered and aligned along the light-like 4-vector $a_{\mu }^{\prime }$, $a^{\prime 2}=0$, $q_{\mu }^{\prime }\propto a_{\mu }^{\prime }$, $a^{\prime }a\ne 0$. Corrections to this factorization formula are suppressed by powers of ${\mathrm{\Lambda }}_{\text{QCD}}/M_B$.