Renormalization of the next-to-leading-power γγ→ h and gg→ h soft quark functions
arxiv(2024)
摘要
We calculate directly in position space the one-loop renormalization kernels
of the soft operators O_γ and O_g that appear in the soft-quark
contributions to, respectively, the subleading-power γγ→ h and
gg→ h form factors mediated by the b-quark. We present an IR/rapidity
divergence-free definition for O_g and demonstrate that with a correspondent
definition of the collinear function, a consistent factorization theorem is
recovered. Using conformal symmetry techniques, we establish a relation between
the evolution kernels of the leading-twist heavy-light light-ray operator,
whose matrix element defines the B-meson light-cone distribution amplitude
(LCDA), and O_γ to all orders in perturbation theory. Application of
this relation allows us to bootstrap the kernel of O_γ to the two-loop
level. We construct an ansatz for the kernel of O_g at higher orders. We test
this ansatz against the consistency requirement at two-loop and find they
differ only by a particular constant.
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