Calculation of Magnetic Penguin Amplitudes in B --> φK Decays Using PQCD Approach

New physics contributions to B decays often arise through chromo-magnetic penguin operators. To look for new physics effects in B decays, it is useful to be able to estimate the hadronic matrix elements for the chromo-magnetic operator. We compute this contribution to B --> φ K decays using PQCD methods. It is shown that, if the Wilson coefficient of the new physics is same order of magnitude as that of the Standard Model, this operator gives a non-negligible contribution compared to that of the Standard Model (about 30%). We also investigate the value of q², which is the momentum transferred by the gluon in the chromo-magnetic penguin operator. We find that the expectation value <q²> is approximately M²_B/4, in agreement with a naive guess. This result, however, is very sensitive to the scale dependence of the Wilson coefficient. We also show that the matrix element for the chromo-magnetic penguin operator is independent of the choice of energy scale to a very good approximation.