Collinear effective theory at subleading order and its application to heavy-light currents
Abstract
We consider an effective theory of highly energetic quarks with energy E, interacting with collinear and soft gluons. By integrating out collinear degrees of freedom from an energetic, massless quark, we construct a collinear effective theory to subleading order. The collinear effective theory offers a systematic expansion in power series of a small parameter lambda=p_{\perp}/E, where p_{\perp} is the transverse momentum of a collinear particle. We construct the effective Lagrangian to first order in lambda, and discuss its features including additional symmetries such as the reparameterization invariance and the collinear gauge invariance. These symmetries constrain the structure of the effective theory, and one of the constraints is that the effective Lagrangian at order lambda is not renormalized to all orders in alpha_s. Heavy-light currents can be matched from the full theory onto the operators in the collinear effective theory at one loop and to order lambda. We obtain heavy-light current operators in the effective theory to order lambda and calculate their Wilson coefficients. And the renormalization group equations for the Wilson coefficients are solved. As an application, we calculate the form factors for decays of B mesons to light energetic mesons to order lambda and at leading-logarithmic order in \alpha_s.Keywords
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