Evolution of Weinberg’s gluonicCP-violation operator

Abstract

The renormalization-group evolution of Weinberg's purely gluonic dimension-6 CP-violating operator is computed to first order in the QCD coupling constant, including its mixing with the quark color electric dipole moment. Our result for the anomalous dimension of the quark operator agrees with several previous calculations. For the gluonic operator, we find the anomalous dimension to have the same magnitude but opposite sign as a previous calculation. This significantly relaxes the constraints imposed on extensions of the standard model by experimental measurements of the neutron electric dipole moment.PACS numbers: U.30. Er, 12.38.Bx, 13.40.Fn It was recently pointed out by Weinberg ] that there is a CP-violating operator of dimension 6 that is constructed out of gluon fields only. It can therefore give a contribution to the neutron electric dipole moment that is not suppressed by any light-quark masses or mixing angles. This gluonic operator OG can be induced as a term in the low-energy effective Hamiltonian by exchange of heavy Higgs bosons, 1,2 by the exchange of gluinos in supersymmetric models, 3 or by exchange of gauge bosons in leftright symmetric models. 4 The consideration of the operator OQ allows the constraints on CP violation from experimental limits on the neutron electric dipole moment to be tightened significantly. A recent calculation of the renormalization-group evolution of OG found it to have a large anomalous dimension, 5 so its coefficient is magnified enormously by renormalization-group evolution from the heavy mass scale down to the hadronic scale. By including this factor, which can be as large as 800, and imposing a naturalness condition on the source of CP violation, one can rule out a number of extensions of the standard model. I3,4 Since the renormalization of the operator OQ has such a dramatic effect, it is important to check the calculation of its anomalous dimension and to investigate the effects of mixing with other operators. In this Letter, we calculate the renormalization-group evolution of OQ to first order in the QCD coupling constant, including its mixing with the quark color electric dipole moment operator O q . Our result for the anomalous dimension of O q agrees with several previous calculations. For the gluonic operator OQ, we find the anomalous dimension to have the same magnitude but opposite sign as the previous calculation. This changes an enhancement factor of 800 into a suppression by 800, significantly relaxing the constraints imposed on extensions of the standard model. We also show that renormalization-group mixing between OG and O q can be neglected, but that the color electric dipole moment of a heavy quark can induce significant corrections to the coefficient of OG by the matching conditions at the heavy-quark threshold.The purely gluonic dimension-6 CP-violating operator discovered by Weinberg iswhere // is the renormalization scale and our convention is ,f OI23 = + 1. Under renormalization-group evolution, it mixes with the quark color electric dip...

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