Abstract
We define a regularization-independent momentum-subtraction scheme for the C P -odd three-gluon operator at dimension six. This operator appears in effective field theories for heavy physics beyond the Standard Model, describing the indirect effect of new sources of C P-violation at low energies. In a hadronic context, it induces permanent electric dipole moments. The hadronic matrix elements of the three-gluon operator are non-perturbative objects that should ideally be evaluated with lattice QCD. We define a non-perturbative renormalization scheme that can be implemented on the lattice and we compute the scheme transformation to overline{mathrm{MS}} at one loop. Our calculation can be used as an interface to future lattice-QCD calculations of the matrix elements of the three-gluon operator, in order to obtain theoretically robust constraints on physics beyond the Standard Model from measurements of the neutron electric dipole moment.
Highlights
Permanent electric dipole moments (EDMs) of non-degenerate systems break the symmetries of parity (P ) and time reversal (T ), and in Lorentz-invariant theories, the combination of charge conjugation and parity (CP )
We present the complete basis of operators that renormalize the gluon chromo-electric dipole moment (gCEDM) operator at leading order in the QED coupling
The CP -odd three-gluon operator gives the main contribution to the nucleon EDM in several beyond the Standard Model scenarios, especially when CP is violated in the interactions of heavy particles, such as the Higgs [48, 85] or the Higgs and the top quark [86]
Summary
Permanent electric dipole moments (EDMs) of non-degenerate systems break the symmetries of parity (P ) and time reversal (T ), and in Lorentz-invariant theories, the combination of charge conjugation and parity (CP ). Lattice QCD (LQCD) has emerged as a powerful tool to compute hadronic matrix elements, in which all sources of systematic uncertainty can be quantified, controlled, and improved This has led to the first LQCD calculations of the nucleon EDM from the u- and d-quark EDMs [33], with few-percent uncertainties, and to the first estimates of the nucleon EDM induced by the QCD θterm [34,35,36,37,38,39,40,41] and by the quark CEDM [42, 43]. More details on the operator basis construction are provided in the appendices
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