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Register a new userNonperturbative Renormalization of the Quark Chromoelectric Dipole Moment with the Gradient Flow:Power Divergences
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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.
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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 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.
Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS-bar scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.
The effect of anomalous chromomagnetic (mu) and chromoelectric couplings (d) of the gluon to the top quark are considered in e+ e- --> t tbar, with unpolarized and longitudinally polarized electron beams. The total cross section, as well as t and tbar polarizations are calculated to order alpha_s in the presence of the anomalous couplings. One of the two linear combinations of t and tbar polarizations is CP even, while the other is CP odd. The limits that could be obtained at a typical future linear collider with an integrated luminosity of 50 1/fb and a total c.m. energy of 500 GeV on the most sensitive CP-even combination of anomalous couplings are estimated as -3 < Re(mu) < 2 for Im(mu) = 0 = d, and sqrt{Im(mu)^2 + |d|^2} < 2.25 for Re(mu) = 0. There is an improvement by roughly a factor of 2 at 1000 GeV. On the other hand, from the CP-odd combination, we derive the possible complementary bounds as -3.6 < Im(mu^* d) < 3.6 for Im(d) = 0, and -10 < Im(d) < 10 for Im(mu^* d) = 0, at a c.m. energy of 500 GeV. The corresponding limit for 1000 GeV is almost an order of magnitude better for Im(mu^* d), though somewhat worse for Im(d). Results for the c.m. energies 500 GeV and 1000 GeV, if combined, would yield independen limits on the two CP-violating parameters of -0.8 < Im(mu^* d) < 0.8 and -11 < Im(d) < 11.
The Fermilab Lattice and MILC collaborations have shown in one-loop lattice QCD perturbation theory that the renormalization constants of vector and axial-vector mixed clover-asqtad currents are closely related to the product of those for clover-clover and asqtad-asqtad (local) vector currents. To be useful for future higher precision calculations this relationship must be valid beyond one-loop and very general. We test its validity nonperturbatively using clover and Highly Improved Staggered (HISQ) strange quarks, utilising the absolute normalization of the HISQ temporal axial current. We find that the renormalization of the mixed current differs from the square root of the product of the pure HISQ and pure clover currents by $2-3%$. We also compare discretization errors between the clover and HISQ formalisms.
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