Dan Pirjol

An effective field theory for collinear and soft gluons: Heavy to light decays

We construct the Lagrangian for an effective theory of highly energetic quarks with energy Q, interacting with collinear and soft gluons. This theory has two low energy scales, the transverse momentum of the collinear particles,

Soft collinear factorization in effective field theory

{p}_{\ensuremath{\perp}},

Hard scattering factorization from effective field theory

and the scale

B → M 1 M 2 : Factorization, charming penguins, strong phases, and polarization

{p}_{\ensuremath{\perp}}^{2}/Q.

Proof of Factorization for B --> Dpi

The heavy to light currents are matched onto operators in the effective theory at one loop and the renormalization group equations for the corresponding Wilson coefficients are solved. This running is used to sum Sudakov logarithms in inclusive

Exclusive rare B → K * ℓ + ℓ − decays at low recoil: Controlling the long-distance effects

\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}\ensuremath{\gamma}

Factorization and end point singularities in heavy-to-light decays

and

Reparameterization Invariance for Collinear Operators

\stackrel{\ensuremath{\rightarrow}}{B}{X}_{u}l\overline{\ensuremath{\nu}}

Radiative leptonic decays of B mesons in QCD

decays. We also show that the interactions with collinear gluons preserve the relations for the soft part of the form factors for heavy-to-light decays found by Charles et al. [Phys. Rev. D 60, 014001 (1999)], establishing these relations in the large energy limit of QCD.

Factorization in leptonic radiative B→γeν decays

The factorization of soft and ultrasoft gluons from collinear particles is shown at the level of operators in an effective field theory. Exclusive hadronic factorization and inclusive partonic factorization follow as special cases. The leading order Lagrangian is derived using power counting and gauge invariance in the effective theory. Several species of gluons are required, and softer gluons appear as background fields to gluons with harder momenta. Two examples are given: the factorization of soft gluons in B->D pi, and the soft-collinear convolution for the B->Xs gamma spectrum.