Non-perturbative renormalization scheme for the C P -odd three-gluon operator

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 $$ \overline{\mathrm{MS}} $$ 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.

Nucleon electric dipole moment from polarized deep inelastic scattering

“…However, purely-gluonic high-dimensional operators such as O W are quite difficult to deal with theoretically. The most promising approach, the lattice QCD simulation, is not yet at the practical level despite much progress in recent years [5,6]. More phenomenological approaches [7][8][9][10] are subject to large theoretical uncertainties, but at least they can provide concrete numbers that are reasonable in terms of magnitude and can be used as a reference.…”

“…also studied the proton case, but the authors only extracted the sum d p,n 2 + f p,n 2 4. Note that we use the total magnetic moment of the proton as explained earlier 5. We do not know the sign of w. Here we assume it is positive, but if it turns out to be negative, the inequality symbols should be modified accordingly.…”

Electric dipole moments and the search for new physics

“…Alternatively a smearing called 'gradient-flow' can be applied to the discretized matrix elements, which introduces its own hard cutoff scale, but that lets us obtain matrix elements in the continuum. Finally, these continuum quantities have to be converted to the MS-scheme used in phenomenology perturbatively [64][65][66][67][68][69][70]. This last step forces us to work at a fine enough discretization that one has a window between the scale at which perturbation theory becomes reliable and the scale where discretization (or smearing) artifacts dominate.…”

One-loop matching for quark dipole operators in a gradient-flow scheme

“…[42], and our nonperturbative implementation of the hadronic matrix elements required for this program is ongoing [32,37,38,[43][44][45]. Alternative nonperturbative methods for higher-dimensional operators are regularization-independent momentum-subtraction schemes, which have been defined for the qCEDM [46] and the three-gluon operator [47], as well as coordinate-space methods [48]. The mixing of these operators under renormalization was studied first in [49][50][51], then calculated at two loops for the qCEDM in [52] and at two and three loops for the three-gluon operator in [53].…”