Vincenzo Cirigliano

This talk summarizes the progress made since Lattice 2021 in understanding and controlling the contributions of towers of multihadron excited states with mass gaps starting lower than of radial excitations, and in increasing our confidence in the extraction of ground state nucleon matrix elements. The most clear evidence for multihadron excited state contributions (ESC) is in axial/pseudoscalar form factors that are required to satisfy the PCAC relation between them. The talk examines the broader question--which and how many of the theoretically allowed positive parity states N(p)π(−p), N(0)π(0)π(0), N(p)π(0), N(0)π(p), … make significant contributions to a given matrix element? New data for the axial, electric and magnetic form factors are presented. They continue to show trends observed in Ref.[1]. The N2LO χPT analysis of the ESC to the pion-nucleon sigma term, σπN, has been extended to include the Δ as an explicit degree of freedom [2]. The conclusion reached in Ref.[3] that Nπ and Nππ states each contribute about 10 MeV to σπN, and the consistency between the lattice result with Nπ state included and the phenomenological estimate is not changed with this improvement.

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.

We present an overview of searches for violation of lepton flavor universality with a focus on low energy precision probes using pi, K, tau, and nuclear beta decays. We review the current experimental results, summarize the theoretical status within the context of the Standard Model, and discuss future prospects (both experimental and theoretical). We review the implications of these measurements for physics beyond the Standard Model by performing a global model-independent fit to modified W couplings to leptons and four-fermion operators. We also discuss new physics in the context of simplified models and review Standard Model extensions with a focus on those that can explain a possible deviation from unitarity of the Cabibbo-Kobayashi-Maskawa quark mixing matrix.

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.

PoS(LATTICE2021)478 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.