Meson masses in electromagnetic fields with Wilson fermions

We determine the light meson spectrum in QCD in the presence of background magnetic fields using quenched Wilson fermions. Our continuum extrapolated results indicate a monotonous reduction of the connected neutral pion mass as the magnetic field grows. The vector meson mass is found to remain nonzero, a finding relevant for the conjectured rho-meson condensation at strong magnetic fields. The continuum extrapolation was facilitated by adding a novel magnetic field-dependent improvement term to the additive quark mass renormalization. Without this term, sizable lattice artifacts that would deceptively indicate an unphysical rise of the connected neutral pion mass for strong magnetic fields are present. We also investigate the impact of these lattice artifacts on further observables like magnetic polarizabilities and discuss the magnetic field-induced mixing between rho-mesons and pions. We also derive Ward-Takashi identities for QCD thorn QED both in the continuum formulation and for ( order a-improved) Wilson fermions

Weak Decay of Magnetized Pions

The leptonic decay of charged pions is investigated in the presence of background magnetic fields. In this situation, Lorentz symmetry is broken, and new fundamental decay constants need to be introduced, associated with the decay via the vector part of the electroweak current. We calculate the magnetic field dependence of both the usual and a new decay constant nonperturbatively on the lattice. We employ both Wilson and staggered quarks and extrapolate the results to the continuum limit. With this nonperturbative input, we calculate the tree level electroweak amplitude for the full decay rate in strong magnetic fields. We find that the muonic decay of the charged pion is enhanced drastically by the magnetic field. We comment on possible astrophysical implications

Nucleon mass and sigma term from lattice QCD with two light fermion flavors

We analyze Nf=2 nucleon mass data with respect to their dependence on the pion mass down to mpi = 157 MeV and compare it with predictions from covariant baryon chiral perturbation theory (BChPT). A novel feature of our approach is that we fit the nucleon mass data simultaneously with the directly obtained pion-nucleon sigma-term. Our lattice data below mpi = 435 MeV is well described by O(p^4) BChPT and we find sigma=37(8)(6) MeV for the sigma-term at the physical point. Using the nucleon mass to set the scale we obtain a Sommer parameter of r_0=0.501(10)(11) fm.Comment: 26 pages, 11 figures, 5 tables. Version to appear in NPB with a few more details on the fit parameter

Weak Decay of Magnetized Pions

Bali G S, Brandt B B, Endrödi G, Gläßle B. Weak Decay of Magnetized Pions. Physical Review Letters. 2018;121(7): 072001.The leptonic decay of charged pions is investigated in the presence of background magnetic fields. In this situation, Lorentz symmetry is broken, and new fundamental decay constants need to be introduced, associated with the decay via the vector part of the electroweak current. We calculate the magnetic field dependence of both the usual and a new decay constant nonperturbatively on the lattice. We employ both Wilson and staggered quarks and extrapolate the results to the continuum limit. With this nonperturbative input, we calculate the tree level electroweak amplitude for the full decay rate in strong magnetic fields. We find that the muonic decay of the charged pion is enhanced drastically by the magnetic field. We comment on possible astrophysical implications

Meson masses in electromagnetic fields with Wilson fermions

Bali G S, Brandt B B, Endrödi G, Gläßle B. Meson masses in electromagnetic fields with Wilson fermions. Physical Review D. 2018;97(3): 034505.We determine the light meson spectrum in QCD in the presence of background magnetic fields using quenched Wilson fermions. Our continuum extrapolated results indicate a monotonous reduction of the connected neutral pion mass as the magnetic field grows. The vector meson mass is found to remain nonzero, a finding relevant for the conjectured ρ-meson condensation at strong magnetic fields. The continuum extrapolation was facilitated by adding a novel magnetic field–dependent improvement term to the additive quark mass renormalization. Without this term, sizable lattice artifacts that would deceptively indicate an unphysical rise of the connected neutral pion mass for strong magnetic fields are present. We also investigate the impact of these lattice artifacts on further observables like magnetic polarizabilities and discuss the magnetic field–induced mixing between ρ-mesons and pions. We also derive Ward-Takashi identities for QCD+QED both in the continuum formulation and for (order a–improved) Wilson fermions

Computational tools for solving a marginal problem with applications in Bell non-locality and causal modeling

Marginal problems naturally arise in a variety of different fields: basically, the question is whether some marginal/partial information is compatible with a joint probability distribution. To this aim, the characterization of marginal sets via quantifier elimination and polyhedral projection algorithms is of primal importance. In this work, before considering specific problems, we review polyhedral projection algorithms with focus on applications in information theory, and, alongside known algorithms, we also present a newly developed geometric algorithm which walks along the face lattice of the polyhedron in the projection space. One important application of this is in the field of quantum non-locality, where marginal problems arise in the computation of Bell inequalities. We apply the discussed algorithms to discover many tight entropic Bell inequalities of the tripartite Bell scenario as well as more complex networks arising in the field of causal inference. Finally, we analyze the usefulness of these inequalities as nonlocality witnesses by searching for violating quantum states