The nucleon electric dipole moment with the gradient flow: the θ\theta-term contribution

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.Comment: 32 pages, 14 figures, 2 tables. v2: added 1 plot, 1 table and 1 reference. Typos corrected. Published versio

Baryon mass splittings and strong CP violation in SU(3) Chiral Perturbation Theory

We study $SU(3)$ flavor-breaking corrections to the relation between the octet baryon masses and the nucleon-meson CP-violating interactions induced by the QCD $\bar\theta$ term. We work within the framework of $SU(3)$ chiral perturbation theory and work through next-to-next-to-leading order in the $SU(3)$ chiral expansion, which is $\mathcal{O}(m_q^2)$. At lowest order, the CP-odd couplings induced by the QCD $\bar\theta$ term are determined by mass splittings of the baryon octet, the classic result of Crewther et al. We show that for each isospin-invariant CP-violating nucleon-meson interaction there exists one relation which is respected by loop corrections up to the order we work, while other leading-order relations are violated. With these relations we extract a precise value of the pion-nucleon coupling $\bar g_0$ by using recent lattice QCD evaluations of the proton-neutron mass splitting. In addition, we derive semi-precise values for CP-violating coupling constants between heavier mesons and nucleons with $\sim 30\%$ uncertainty and discuss their phenomenological impact on electric dipole moments of nucleons and nuclei.Comment: 49 pages. Published versio

Electric Dipole Moment Results from lattice QCD

We utilize the gradient flow to define and calculate electric dipole moments induced by the strong QCD $\theta$-term and the dimension-6 Weinberg operator. The gradient flow is a promising tool to simplify the renormalization pattern of local operators. The results of the nucleon electric dipole moments are calculated on PACS-CS gauge fields (available from the ILDG) using $N_{f}=2+1$, of discrete size $32^{3}\times 64$ and spacing $a \simeq 0.09$ fm. These gauge fields use a renormalization-group improved gauge action and a non-perturbatively $O(a)$ improved clover quark action at $\beta = 1.90$, with $c_{SW} = 1.715$. The calculation is performed at pion masses of $m_{\pi} \simeq 411,701$ MeV.Comment: 8 pages, 13 figures, presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017

Electroweak Baryogenesis and the Standard Model Effective Field Theory

We investigate electroweak baryogenesis within the framework of the Standard Model Effective Field Theory. The Standard Model Lagrangian is supplemented by dimension-six operators that facilitate a strong first-order electroweak phase transition and provide sufficient CP violation. Two explicit scenarios are studied that are related via the classical equations of motion and are therefore identical at leading order in the effective field theory expansion. We demonstrate that formally higher-order dimension-eight corrections lead to large modifications of the matter-antimatter asymmetry. The effective field theory expansion breaks down in the modified Higgs sector due to the requirement of a first-order phase transition. We investigate the source of the breakdown in detail and show how it is transferred to the CP-violating sector. We briefly discuss possible modifications of the effective field theory framework.Comment: 21 pages + appendices. V2: Corrected a factor-2 mistake which has changed the results for the baryon asymmetry quantitatively. Main conclusions of the v1 still hol

Indirect Signs of the Peccei-Quinn Mechanism

In the Standard Model, the renormalization of the QCD vacuum angle $\theta$ is extremely tiny, and small $\theta$ is technically natural. In the general Standard Model effective field theory (SMEFT), however, $\Delta\theta$ is quadratically divergent, reflecting the fact that new sources of hadronic CP-violation typically produce $\mathcal O(1)$ threshold corrections to $\theta$. The observation of such CP-violating interactions would therefore be in tension with solutions to the strong CP problem in which $\theta=0$ is an ultraviolet boundary condition, pointing to the Peccei-Quinn mechanism as the explanation for why $\theta$ is small in the infrared. We study the quadratic divergences in $\theta$ arising from dimension-6 SMEFT operators and discuss the discovery prospects for these operators at electric dipole moment experiments, the LHC, and future proton-proton colliders.Comment: 27 pages, 3 figures. Comments welcome