Factorization of heavy-to-light form factors in soft-collinear effective theory

By Martin Beneke, T. Feldmann. 2003

207 citations recorded by the source corpus.

Abstract Heavy-to-light transition form factors at large recoil energy of the light meson have been conjectured to obey a factorization formula, where the set of form factors is reduced to a smaller number of universal form factors up to hard-scattering corrections. In this paper we extend our previous investigation of heavy-to-light currents in soft-collinear effective theory to final states with invariant mass Λ 2 as is appropriate to exclusive B meson decays. The effective theory contains soft modes and two collinear modes with virtualities of order m b Λ (“hard-collinear”) and  Λ 2 . Integrating out the hard-collinear modes results in the hard spectator-scattering contributions to exclusive B decays. We discuss the representation of heavy-to-light currents in the effective theory after integrating out the hard-collinear scale, and show that the previously conjectured factorization formula is valid to all orders in perturbation theory. The naive factorization of matrix elements in the effective theory into collinear and soft matrix elements may be invalidated by divergences in convolution integrals. In the factorization proof we circumvent the explicit regularization of endpoint divergences by a definition of the universal form factors that includes hard-collinear, collinear and soft effects.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/71cb1dfe07cead95d9a99f9b1cea28f7879bac98

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In Nuclear and High Energy Physics

1. A. Broggio
2. A. Ferroglia
3. T. Becher
4. J. Camalich
5. I. Rothstein
6. S. Jager
7. D. Neill
8. C. Bobeth

Citations in the corpus

• A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory (2012, methodology): “We follow [5, 21] in studying this issue within the context of a toy model of B decays.”
• On B → Vℓℓ at small dilepton invariant mass, power corrections, and new physics (2012, background): “factorization can be proven to all orders [82].”
• Introduction to Soft-Collinear Effective Theory (2014, background): “Indeed, equipping all partons with masses of the order of the typical QCD scale ΛQCD eliminates these low-virtuality modes; however the factorization breaking would then arise from the additional regulators needed in the massive case [172, 174], i.”
• Power-enhanced leading-logarithmic QED corrections to Bq→ μ+μ− (2019, methodology): “A power-counting analysis similar to the one performed in [25] for heavy-to-light meson form factors shows that only two different SCETII operators for each collinear direction are relevant to the power-enhanced correction from the Q9 operator.”
• Effective field theories for heavy quarkonium (2004, background): “…the time-ordered product of currents in SCET (now renamed SCETI) to (non-local) operators of the so-called SCETII, which does not contain collinear modes of virtuality ∼ (1 − z)M2 anymore (see (Beneke and Feldmann, 2004) for a detailed description of the modes involved in SCETI and in SCETII).”