Two-loop current–current operator contribution to the non-leptonic QCD penguin amplitude

G Bell,M Beneke,T Huber,Xin-Qiang Li

doi:10.1016/j.physletb.2015.09.037

Abstract

The computation of direct CP asymmetries in charmless B decays at next-to-next-to-leading order (NNLO) in QCD is of interest to ascertain the short-distance contribution. Here we compute the two-loop penguin contractions of the current–current operators Q1,2 and provide a first estimate of NNLO CP asymmetries in penguin-dominated b→s transitions.

Highlights

Non-leptonic exclusive decays of B mesons play a crucial role in studying the CKM mechanism of quark flavour mixing and in quantifying the phenomenon of CP violation
At next-to-leading order we find for the penguin contractions au4|NLO = (−0.0087 − 0.0172i)|Q1,2 + (0.0042 + 0.0041i)|Q3−6 + 0.0083|Q8g, ac4(πK )|NLO = (−0.0131 − 0.0102i)|Q1,2 + (0.0042 + 0.0041i)|Q3−6 + 0.0083|Q8g, (3)
The long- and short-distance contributions can in principle be of the same order and a next-to-nextto-leading order (NNLO) calculation is required to ascertain the perturbative part

Summary

Introduction

Non-leptonic exclusive decays of B mesons play a crucial role in studying the CKM mechanism of quark flavour mixing and in quantifying the phenomenon of CP violation. This calculation is technically very involved since it requires the computation of massive two-loop penguin diagrams – a genuine twoloop, two-scale problem One step towards this goal was recently achieved in [15], where analytic results of all occurring master integrals were derived. At this point it is important to note that the topological tree and penguin amplitudes are not in one-to-one correspondence with the tree (or current-current) operators Qp1,2 and QCD penguin operators Q3−6 of the weak effective Hamiltonian. We shall provide more technical details together with the remaining contributions from the QCD penguin operators Q3−6, which require additional work on infrared subtractions not present for Qp1,2, in a future publication

Outline of the calculation

The topological QCD penguin amplitude

Phenomenology – direct CP asymmetries

Conclusion