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Register a new userShort flow-time coefficients of CP-violating operators
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Measurements of a permanent neutron electric dipole moment (EDM) potentially probe Beyond-the-Standard Model (BSM) sources of CP-violation. At low energy the CP-violating BSM interactions are parametrized by flavor-conserving CP-violating operators of dimension higher than four. QCD calculations of the nucleon matrix elements of these operators are required to fully reconstruct the sources and magnitudes of the different CP-violating contributions to the nucleon EDM. Herein we study the quark-chromo electric dipole moment (qCEDM) operator and the three-gluon Weinberg operator. The non-perturbative determination, using lattice QCD, of the nucleon matrix elements of these CP-violating operators is hampered by their short-distance behavior. Under renormalization these operators mix with lower dimensional operators, which induces power divergences in the lattice spacing, as the continuum limit is approached. We study the short-distance behavior of the qCEDM and the Weinberg operators using the gradient flow. We perform a short flow time expansion and determine, in perturbation theory, the expansion coefficients of the linearly-divergent terms stemming from the mixing with the pseudoscalar density and the topological charge, confirming the expectations of the operator product expansion. We introduce a new method to perform calculations at non-zero flow-time for arbitrary values of the external momenta. This method allows us to work in four dimensions for most of the calculations described in this paper, avoiding the complications associated with defining $gamma_5$ in generic d dimensions. We show that leading contributions in the external momenta can be reproduced by defining $gamma_5$ using the t Hooft-Veltman-Breitenlohner-Maison scheme.
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We consider the most general set of $SU(2) times U(1)$ invariant CP-violating operators of dimension six, which contribute to $VVh$ interactions ($V = W, Z, gamma$). Our aim is to constrain any CP-violating new physics above the electroweak scale via the effective couplings that arise when such physics is integrated out. For this purpose, we use, in turn, electroweak precision data, global fits of Higgs data at the Large Hadron Collider and the electric dipole moments of the neutron and the electron. We thus impose constraints mainly on two-parameter and three-parameter spaces. We find that the constraints from the electroweak precision data are the weakest. Among the existing Higgs search channels, considerable constraints come from the diphoton signal strength. We note that potential contribution to $h rightarrow gamma Z$ may in principle be a useful constraining factor, but it can be utilized only in the high energy run. The contributions to electric dipole moments mostly lead to the strongest constraints, though somewhat fine-tuned combinations of more than one parameter with large magnitudes are allowed. We also discuss constraints on gauge boson trilinear couplings which depend on the parameters of the CP-violating operators .
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We calculate the electric dipole moment of the nucleon induced by the QCD theta term. We use the gradient flow to define the topological charge and use $N_f = 2+1$ flavors of dynamical quarks corresponding to pion masses of $700$, $570$, and $410$ MeV, and perform an extrapolation to the physical point based on chiral perturbation theory. We perform calculations at $3$ different lattice spacings in the range of $0.07~{rm fm} < a < 0.11$ fm at a single value of the pion mass, to enable control on discretization effects. We also investigate finite size effects using $2$ different volumes. A novel technique is applied to improve the signal-to-noise ratio in the form factor calculations. The very mild discretization effects observed suggest a continuum-like behavior of the nucleon EDM towards the chiral limit. Under this assumption our results read $d_{n}=-0.00152(71) bartheta e~text{fm}$ and $d_{p}=0.0011(10) bartheta e~text{fm}$. Assuming the theta term is the only source of CP violation, the experimental bound on the neutron electric dipole moment limits $left|barthetaright| < 1.98times 10^{-10}$ ($90%$ CL). A first attempt at calculating the nucleon Schiff moment in the continuum resulted in $S_{p} = 0.50(59)times 10^{-4} bartheta e~text{fm}^3$ and $S_{n} = -0.10(43)times 10^{-4} bartheta e~text{fm}^3$.
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