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Register a new userThe nucleon electric dipole moment with the gradient flow: the $theta$-term contribution
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We propose a new method to calculate electric dipole moments induced by the strong QCD $theta$-term. The method is based on the gradient flow for gauge fields and is free from renormalization ambiguities. We test our method by computing the nucleon electric dipole moments in pure Yang-Mills theory at several lattice spacings, enabling a first-of-its-kind continuum extrapolation. The method is rather general and can be applied for any quantity computed in a $theta$ vacuum. This first application of the gradient flow has been successful and demonstrates proof-of-principle, thereby providing a novel method to obtain precise results for nucleon and light nuclear electric dipole moments.
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We compute the electric dipole moment of proton and neutron from lattice QCD simulations with N_f=2 flavors of dynamical quarks at imaginary vacuum angle theta. The calculation proceeds via the CP odd form factor F_3. A novel feature of our calculation is that we use partially twisted boundary conditions to extract F_3 at zero momentum transfer. As a byproduct, we test the QCD vacuum at nonvanishing theta.
We evaluate the contribution of the CP violating gluon chromo-electric dipole moment (the so-called Weinberg operator, denoted as $w$) to the electric dipole moment (EDM) of nucleons in the nonrelativistic quark model. The CP-odd interquark potential is modeled by the perturbative one-loop level gluon exchange generated by the Weinberg operator with massive quarks and gluons. The nucleon EDM is obtained by solving the nonrelativistic Schr{o}dinger equation of the three-quark system using the Gaussian expansion method. It is found that the resulting nucleon EDM, which may reasonably be considered as the irreducible contribution, is smaller than the one obtained after $gamma_5$-rotating the anomalous magnetic moment using the CP-odd mass calculated with QCD sum rules. We estimate the total contribution to be $d_n = w times 20 , e , {rm MeV}$ and $d_p = - w times 18 , e , {rm MeV}$ with 60% of theoretical uncertainty.
The connection between a regularization-independent symmetric momentum substraction (RI-$tilde{rm S}$MOM) and the $overline{rm MS}$ scheme for the quark chromo EDM operators is discussed. A method for evaluating the neutron EDM from quark chromoEDM is described. A preliminary study of the signal in the matrix element using clover quarks on a highly improved staggered quark (HISQ) ensemble is shown.
The CP-violating quark chromoelectric dipole moment (qCEDM) operator, contributing to the electric dipole moment (EDM), mixes under renormalization and -- particularly on the lattice -- with the pseudoscalar density. The mixing coefficient is power-divergent with the inverse lattice spacing squared, $1/a^2$, regardless of the lattice action used. We use the gradient flow to define a multiplicatively renormalized qCEDM operator and study its behavior at small flow time. We determine nonperturbatively the linearly divergent coefficient with the flow time, $1/t$, and compare it with the perturbative expansion in the bare and renormalized strong coupling. We also discuss the O($a$) improvement of the qCEDM defined at positive flow time.
We extract the neutron electric dipole moment $vert vec{d}_Nvert$ within the lattice QCD formalism. We analyse one ensemble of $N_f=2+1+1$ twisted mass clover-improved fermions with lattice spacing of $a simeq 0.08 {rm fm}$ and physical values of the quark masses corresponding to a pion mass $m_{pi} simeq 139 {rm MeV}$. The neutron electric dipole moment is extracted by computing the $CP$-odd electromagnetic form factor $F_3(Q^2 to 0)$ through small $theta$-expansion of the action. This approach requires the calculation of the topological charge for which we employ a fermionic definition by means of spectral projectors while we also provide a comparison with the gluonic definition accompanied by the gradient flow. We show that using the topological charge from spectral projectors leads to absolute errors that are more than two times smaller than those provided when the field theoretic definition is employed. We find a value of $vert vec{d}_Nvert = 0.0009(24) theta e cdot {rm fm}$ when using the fermionic definition, which is statistically consistent with zero.
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