The chirally symmetric baryon parity-doublet model can be used as an effective description of the baryon-like objects in the chirally symmetric phase of QCD. Recently it has been found that above the critical temperature higher chiralspin symmetries emerge in QCD. It is demonstrated here that the baryon parity-doublet Lagrangian is manifestly chiralspin-invariant. We construct nucleon interpolators with fixed chiralspin transformation properties that can be used in lattice studies at high T.I. BARYON PARITY DOUBLETS.

Accounting for isospin-breaking corrections is critical for achieving subpercent precision in lattice computations of hadronic observables. A way to include QED and strong-isospin-breaking corrections in lattice QCD calculations is to impose C⋆ boundary conditions in space. Here, we demonstrate the computation of a selection of meson and baryon masses on two QCD and five QCD+QED gauge ensembles in this setup, which preserves locality, gauge and translational invariance all through the calculation. The generation of the gauge ensembles is performed for two volumes, and three different values of the renormalized fine-structure constant at the U-symmetric point, corresponding to the SU(3)-symmetric QCD in the two ensembles where the electromagnetic coupling is turned off. We also present our tuning strategy and, to the extent possible, a cost analysis of the simulations with C⋆ boundary conditions.

Truncating the low-lying modes of the lattice Dirac operator results in an emergence of the chiralspin symmetry SU (2) CS and its flavor extension SU (2N F ) in hadrons. These are symmetries of the quark -chromo-electric interaction and include chiral symmetries as subgroups. Hence the quark -chromo-magnetic interaction, which breaks both symmetries, is located at least predominantly in the near -zero modes. Using as a tool the expansion of propagators into eigenmodes of the Dirac operator we here analytically study effects of a gap in the eigenmode spectrum on baryon correlators. We find that both U (1) A and SU (2) L × SU (2) R emerge automatically if there is a gap around zero. Emergence of larger SU (2) CS and SU (4) symmetries requires in addition a microscopical dynamical input about the higher-lying modes and their symmetry structure.In a number of lattice spectroscopical studies with a chirally-invariant Dirac operator upon artificial truncation of the lowest modes of the Dirac operator [1, 2] a large degeneracy was discovered in mesons [3][4][5] and baryons [6]. Corresponding symmetry groups, SU (2) CS and SU (2N F ) [7,8], turned out to be larger than the chiral symme- (2) CS as subgroups. The chiral-spin transformations from SU (2) CS includes rotations that mix the left-and right-handed components of the quark field. Obviously these symmetries are not symmetries of a free Dirac equation or of the QCD Lagrangian. However, they are symmetries of the Lorentz-invariant fermion charge operator and (in a given reference frame) of the quark -chromo-electric interaction while the interaction of quarks with the chromo-magnetic field and the quark kinetic term break them. Consequently the emergence of SU (2) CS and SU (2N F ) upon truncation of the low-lying modes tells that while the confining quark -electric interaction is distributed among all modes of the Dirac operator, the quark -magnetic interaction is located at least predominantly in the near -zero modes. Some unknown microscopic dynamics should be responsible for this phenomenon.These symmetries emerge naturally, i.e. without any explicit truncation, in hot QCD above the pseudocritical temperature [9][10][11], where the near-zero modes of the Dirac operator are suppressed by temperature [17]. Consequently elementary objects in that range are not free quarks and gluons but rather chirally symmetric quarks bound by the chromo-electric field into color singlet objects, like a "string".According to the Banks-Casher relation [12] the chiral symmetry breaking quark condensate is proportional to the density of the near-zero modes. A gap in the low lying Dirac eigenmode spectrum induces restoration of SU (N F ) L × SU (N F ) R symmetry. It was shown that it also induces restoration of U (1) A in the J = 0 mesons [13]. Analytical study of the J = 0 and J = 1 isovector meson propagators in terms of the eigenmodes of the Dirac operator revealed that all meson correlators that are connected by the U (1) A and/or SU (2) L ×SU (2) R transformations get necessarily ...

RC C R * collaborationWe present two novelties in our analysis of fully dynamical QCD+QED ensembles with C ★ boundary conditions. The first one is the explicit computation of the sign of the Pfaffian. We present an algorithm that provides a significant speedup compared to traditional methods. The second one is a reweighting of the mass in the context of the RHMC. We have tested the techniques on both pure QCD and QCD+QED ensembles with pions at ± ≈ 400 MeV, a lattice spacing of ≈ 0.05 fm, a fine-structure constant of R = 0 and 0.04.

The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS ) via the Banks-Casher relation. At the same time the distribution of the near-zero modes is well described by the Random Matrix Theory (RMT ) with the Gaussian Unitary Ensemble (GUE ). Then it has become a standard lore that a randomness, as observed through distributions of the near-zero modes of the Dirac operator, is a consequence of SBCS. The higher-lying modes of the Dirac operator are not affected by SBCS and are sensitive to confinement physics and related SU (2) CS and SU (2N F ) symmetries. We study the distribution of the near-zero and higher-lying eigenmodes of the overlap Dirac operator within N F = 2 dynamical simulations. We find that both the distributions of the near-zero and higher-lying modes are perfectly described by GUE of RMT. This means that randomness, while consistent with SBCS, is not a consequence of SBCS and is linked to the confining chromo-electric field.

It was established that distribution of the near-zero modes of the Dirac operator is consistent with the Chiral Random Matrix Theory (CRMT) and can be considered as a consequence of spontaneous breaking of chiral symmetry (SBCS) in QCD. The higherlying modes of the Dirac operator carry information about confinement physics and are not affected by SBCS. We study distributions of the near-zero and higher-lying modes of the overlap Dirac operator within N F = 2 dynamical simulations. We find that distributions of both near-zero and higher-lying modes are the same and follow the Gaussian Unitary Ensemble of Random Matrix Theory. This means that randomness, while consistent with SBCS, is not a consequence of SBCS and is related to some more general property of QCD in confinement regime.

RC C R * collaborationWe present preliminary results for the determination of the leading strange and charm quarkconnected contributions to the hadronic vacuum polarization contribution to the muon's 𝑔 − 2. Measurements are performed on the RC ★ collaboration's QCD ensembles, with 3 + 1 flavors of 𝑂 (𝑎) improved Wilson fermions and C ★ boundary conditions. The HVP is computed on a single value of the lattice spacing and two lattice volumes at unphysical pion mass. In addition, we compare the signal-to-noise ratio for different lattice discretizations of the vector current.

We present a preliminary computation of potentials between two static quarks in n f = 2 QCD with O(a) improved Wilson fermions based on Wilson loops. We explore different smearing choices (HYP, HYP2 and APE) and their effect on the signal to noise ratio in the computed static potentials. This is a part of a larger effort concerning, at first, a precise computation of the QCD string breaking parameters and their subsequent utilization for the recent approach based on Born-Oppenheimer approximation (Bicudo et al. 2020 [1]) to study quarkonium resonances and bound states.