Quenched Chiral Perturbation Theory to one loop

Abstract

We calculate the divergences of the generating functional of quenched Chiral Perturbation Theory at one loop, and renormalize the theory by an appropriate definition of the counterterms. We show that the quenched chiral logarithms can be reabsorbed in the renormalization of the B_0 parameter which, at lowest order, is proportional to the vacuum expectation value of the scalar quark density. Finally, we calculate several quantities at one loop to analyze the modifications induced by quenching in the finite part of the one-loop corrections. We point out that some of the finite loop corrections may diverge in the chiral limit.

plain latex, 41 pages, 7 figures. New parts added + other minor changes, version to appear on Nucl. Phys. B

References in corpus (9)

• Chiral Perturbation Theory for the Quenched Approximation of QCD
• Quenched Chiral Logarithms
• Elastic $\pi \pi$ scattering to two loops
• Hadron Scattering Lengths in Lattice QCD
• Quenched Chiral Perturbation Theory for Baryons
• Quenched Chiral Perturbation Theory for Heavy-light Mesons
• Finite-volume two-pion energies and scattering in the quenched approximation
• Quenched Chiral Perturbation Theory for Heavy-Light Mesons
• Quenched Chiral Perturbation Theory for Vector Mesons

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