The structure function of semi-inclusive heavy flavour decays in field theory

Abstract

We consider the decay of a heavy flavour into an inclusive hadronic state X of invariant mass m_X small with respect to its energy E_X, m_X << E_X. The electron spectrum and the hadronic mass distribution in semileptonic b -> u decays, or the photon spectrum in b -> s gamma decays, all require, close to their endpoints, a control over this region. This region is affected both by non-perturbative phenomena related to the Fermi motion of the heavy quark and by perturbative soft gluon radiation in the final state (Sudakov form factor).Fermi motion can be described by the shape function f (m*), which represents the distribution of the effective mass m* of the heavy quark at disintegration time. We perform a factorization with a simple technique in order to consistently separate perturbative from non-perturbative effects. We find that the shape function, contrary to naive expectations,is not a physical distribution, as it is affected by substantial regularization scheme effects, controlling even the leading, double-logarithmic term. It factorizes, however, the bulk of non-perturbative effects in lattice-like regularizations. Some non-perturbative effects are present in the coefficient function even at leading twist, but they are expected to be suppressed on physical grounds. Finally, we clarify a controversial factor of 2 in the evolution kernel of the shape function.

52 pages, 5 figures, LaTeX. More descriptive title. A few minor changes. To be published in Nucl. Phys. B

References in corpus (4)

• Extracting V_{ub} Without Recourse to Structure Functions
• The Resummed Rate for B -> X_s gamma
• Matching of the Shape Function
• Soft-Gluon Resummation in Heavy Quarkonium Physics

Cited by in corpus (19)

• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Present Status of Inclusive Rare B Decays
• Collinear effective theory at subleading order and its application to heavy-light currents
• Dispersion Relation Constrained Partial Wave Analysis of piN Elastic and piN\to\etaN Scattering Data: The Baryon Spectrum
• Inclusive spectra in charmless semileptonic B decays by Dressed Gluon Exponentiation
• Resummed B -> X_u l nu Decay Distributions to Next-to-Leading Order
• Semileptonic and leptonic $B$ decays, circa 2016
• Determination of the CKM matrix elements |V(xb)|
• Brief review on semileptonic B decays
• Progress on semi-leptonic $B_{(s)}$ decays
• Transverse Momentum Distributions in B-Decays
• Status of $|V_{cb}|$ and $|V_{ub}|$ CKM matrix elements
• Reparametrization Invariance in Inclusive Decays of Heavy Hadrons
• Next-to-leading resummed coefficient function for the shape function
• Experimental Status of Semileptonic B Decays - Recent Results from LEP and Comparisons with Y(4S) Experiments
• Radiatively corrected shape function for inclusive heavy hadron decays
• Non-Universal Effects in Semi-Inclusive B Decays
• Determinations of |Vub| with inclusive techniques at LEP
• Transverse Momentum Distribution in b-> s Gamma