Vincenzo Cirigliano

In a previous work, we showed that unresolved excited state contaminations provide a major source of systematic uncertainty in the calculation of the nucleon electric dipole moment due to the QCD topological term theta. Here we extend the calculation to the quark chromo-electric dipole moment operator (qcEDM). We also show quantitatively the impact of the mixing of the qcEDM with lower-dimensional operators on the lattice. Finally, we present preliminary results from a unitary clover-on-clover calculation for the QCD topological term.

The exponentially falling signal-to-noise ratio in all nucleon correlation functions, and the presence of towers of multihadron excited states with relatively small mass gaps makes extraction of matrix elements of various operators within the ground state nucleon challenging. Theoretically, the allowed positive parity states with the smallest mass gaps are the \(N(\bm p)\pi(-\bm p)\), \(N(\bm 0)\pi(\bm 0)\pi(\bm 0)\), \(N(\bm p)\pi(\bm 0)\), \(N(\bm 0)\pi(\bm p),\ \ldots\), states. A priori, the contribution of these states arises at one loop in chiral perturbation theory (\(\chi\)PT), however, in many cases the contributions are enhanced. In this talk, I will review four such cases: the correlation functions from which the axial form factors, electric and magnetic form factors, the \(\Theta\)-term contribution to neutron electric dipole moment (nEDM), and the pion-nucleon sigma term are extracted. Including appropriate multihadron states in the analysis can lead to significantly different results compared to standard analyses with the mass gaps taken from fits to 2-point functions. The \(\chi\)PT case for \(N \pi\) states is the most clear in the axial/pseudoscalar form factors which need to satisfy the PCAC relation between them. Our analyses, supported by \(\chi\)PT, suggests similarly large effects in the calculations of the \(\Theta\)-term and the pion-nucleon sigma term that have significant phenomenological implications.

We present results for the neutron electric dipole moment due to the dimension 4 and dimension 6 gluonic CP violation, and the isovector quark chromoelectric dipole moment using clover valence quarks on HISQ dynamical ensembles generated by the MILC Collaboration. For the gluonic operators, we use the gradient flow scheme to obtain divergence-free continuum results. For the chromoelectric dipole moment operator, we use the unflowed local operator but discuss how the quadratically divergent mixing with the pseudoscalar operator can be controlled nonperturbatively.

We present an update on our calculations of the matrix elements of the CP violating quark and gluon chromo-EDM operators, as well as the operators these mix with, such as the QCD Theta-term. Their contribution to the neutron EDM is obtained by extrapolating the $F_3$ form factor of a vector current to zero momentum transfer. The calculation is being done using valence Wilson-clover quarks on HISQ background configurations generated by the MILC collaboration.

The quark chromo-electric dipole moment operator and the pseudo-scalar fermion bilinear with which it mixes under renormalization can both be included in a calculation of the electromagnetic form factor of the nucleon using the Schwinger source method. A preliminary calculation of these operators using clover quarks on HISQ lattices generated by MILC collaboration will be presented showing the quality of the signal in the correlators necessary for calculating the neutron electric dipole moment.

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.

We present an update of our analysis of statistical and systematic errors in the calculation of iso-vector scalar, axial and tensor charges of the nucleon. The calculations are done using \(N_f=2+1+1\) flavor HISQ ensembles generated by the MILC Collaboration at three values of the lattice spacing (\(a=0.12,\ 0.09,\) and \(0.06\) fm) and three values of the quark mass (\(M_\pi \approx 310,\ 220\) and \(130\) MeV); and clover fermions for calculating the correlation functions, i.e., we use a clover-on-HISQ lattice formulation. The all-mode-averaging method allows us to increase the statistics by a factor of eight for the same computational cost leading to a better understanding of and control over excited state contamination. Our current results, after extrapolation to the continuum limit and physical pion mass are \(g_A^{u-d} = 1.21(3)\), \(g_T^{u-d} = 1.005(59)\) and \(g_S^{u-d} = 0.95(12) \). Further checks of control over all systematic errors, especially in \(g_A^{u-d}\), are still being performed. Using results for the flavor-diagonal charges, \(g_T^{u} \), \(g_T^{d} \) and \(g_T^{s}\), we analyze contributions of the quark electric dipole moment to the neutron EDM and the consequences for split SUSY model.