Shape and soft functions of HQET and SCET in the 't Hooft Model

Abstract

The main application of Heavy Quark Effective Theory (HQET) and of Soft Collinear Effective Theory (SCET) is in establishing factorization theorems for exclusive and semi-inclusive decays of heavy mesons. However, the calculation of the soft factors from the HQET or SCET factorization relations is, as usual, impeded by the non-perturbative aspect of the strong interactions. In the hope of gaining some insights into some of these quantities we compute them in the 't Hooft model. We find that the B-meson shape function is exactly given by the square of the B-meson light-cone wave-function. The structure of the B-pi structure function is more complicated: it is given by the product of wave-functions or by a resonant sum depending on the kinematics. The result simplifies dramatically in the chiral limit, where it can be compared with general arguments based on Heavy Meson-Chiral Perturbation theory. No attempt is made to use these results for applications to phenomenology.

arXiv comment17 pages, 5 figures

References in corpus (29)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Invariant Operators in Collinear Effective Theory
• Inclusive Semileptonic B and Polarized Lambda_b Decays from QCD
• Nonperturbative Corrections to Inclusive Beauty and Charm Decays: QCD versus Phenomenological Models
• Asymptotics of Heavy-Meson Form Factors
• Differential Distributions in Semileptonic Decays of the Heavy Flavors in QCD
• On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays
• Analysis of the Photon Spectrum in Inclusive $B\to X_s\gamma$ Decays
• Factorization of heavy-to-light form factors in soft-collinear effective theory
• Factorization and Endpoint Singularities in Heavy-to-Light decays
• Sudakov Resummation for Subleading SCET Currents and Heavy-to-Light Form Factors
• A Complete Basis for Power Suppressed Collinear-Ultrasoft Operators
• Resummation of Nonperturbative Corrections to the Lepton Spectrum in Inclusive $B\to X\ell \bar{\nu }$ Decays
• Factorization and the Soft Overlap Contribution to Heavy-to-Light Form Factors
• The photon polarization in B -> X gamma in the standard model
• Comment on Quark Masses in SCET
• Heavy flavor decays, OPE and duality in two-Dimensional 't Hooft model
• Explicit Quark-hadron Duality in Heavy-light Meson Weak Decays in the 't Hooft Model
• The CP asymmetry in B^0(t) -> K_S π^0 γin the Standard Model
• Rare radiative exclusive B decays in soft-collinear effective theory
• Heavy Mesons in Two Dimensions
• Subleading collinear operators and their matrix elements
• Form Factors in the Heavy Quark and Chiral Limit: Pole dominance in $\bar{B}\to \pi e{\bar{\nu }}_e$
• Factorization in B -> K pi e+e- decays
• Global duality in heavy flavor decays in the 't Hooft model
• Chiral symmetry and exclusive B decays in the SCET
• Global duality in heavy flavor hadronic decays

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