We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

We perform a systematical investigation of the strong decay properties of the low-lying $1P$- and $2D$-wave doubly charmed baryons with the ${}^3{P}_0$ quark pair creation model. The main predictions include: (i) in the ${\mathrm{\Xi }}_{cc}$ and ${\mathrm{\Omega }}_{cc}$ family, the $1P$ $\rho$ mode excitations with $J^P=1/2^{-}$ and $3/2^{-}$ should be the fairly narrow states, while, for the $1P$ $\lambda$ mode excitations, they are most likely to be moderate states with a width of $\mathrm{\Gamma }\sim 100\mathrm{MeV}$. (ii) The $2D_{\rho \rho }$ states mainly decay via emitting a heavy-light meson and the decay widths can reach several tens MeV if their masses are above the threshold of ${\mathrm{\Lambda }}_{c}D$ or ${\mathrm{\Xi }}_{c}D$, respectively. The $2D_{\lambda \lambda }$ states may be broad states with a width of $\mathrm{\Gamma }>100\mathrm{MeV}$.

The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphenelike materials, the surface states of some topological insulators, and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d’Alembertian in marked contrast with usual QEDs. The use of the Bogoliubov-Parasiuk-Hepp-Zimmermann prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultrarelativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity ${\mathcal{C}}^{*}=(92-9{\pi }^2)/(18\pi )$ and the anomalous dimension of the fermion field ${\gamma }_{\psi }(\overline{\alpha },\xi )=2\overline{\alpha }(1-3\xi )/3-16({\zeta }_2{N}_F+4/27){\overline{\alpha }}^2+\mathrm{O}({\overline{\alpha }}^3)$, where $\overline{\alpha }=e^2/(4\pi {)}^2$ and $\xi$ is the gauge-fixing parameter.

We give an estimate of ${\mathrm{\Xi }}_{cc}^{++}$ production rate and transverse momentum spectra in relativistic heavy ion collisions. We use Boltzmann transport equations to describe the dynamical evolution of charm quarks and diquarks inside quark-gluon plasma. In-medium formation and dissociation rates of charm diquarks are calculated from potential nonrelativistic QCD for the diquark sector. We solve the transport equations by Monte Carlo simulations. For 2.76 TeV Pb-Pb collisions with 0–10% centrality, the number of ${\mathrm{\Xi }}_{cc}^{++}$ produced in the transverse momentum range 0–5 GeV and rapidity from $-1$ to 1 is roughly 0.02 per collision. We repeat the calculation with a melting temperature 250 MeV above which no diquarks can be formed. The number of ${\mathrm{\Xi }}_{cc}^{++}$ produced in the same kinematic region is about 0.0125 per collision. We discuss how to study diquarks at finite temperature on a lattice and construct the antitriplet free energy in a gauge invariant but path dependent way. We also comment on extensions of the calculation to other doubly heavy baryons and doubly heavy tetraquarks and the feasibility of experimental measurements.

Exclusive vector meson photoproduction associated with a leading baryon ($B=n,{\mathrm{\Delta }}^{+},{\mathrm{\Delta }}^0$) in $pp$ and $pA$ collisions at RHIC and LHC energies is investigated using the color dipole formalism and taking into account nonlinear effects in the QCD dynamics. In particular, we compute the cross sections for $\rho$, $\varphi$ and $J/\mathrm{\Psi }$ production together with a $\mathrm{\Delta }$ and compare the predictions with those obtained for a leading neutron. Our results show that the $V+\mathrm{\Delta }$ cross section is almost 30% of the $V+n$ one. Our results also show that a future experimental analysis of these processes is, in principle, feasible and can be useful to study leading particle production.

$\mathcal{O}(1)\mathrm{eV}$ sterile neutrino can be responsible for a number of anomalous results of neutrino oscillation experiments. This hypothesis may be tested at short base line neutrino oscillation experiments, several of which are either ongoing or under construction. Here, we concentrate on the so-called gallium anomaly, found by SAGE and GALLEX experiments, and its foreseeable future tests with BEST experiment at Baksan Neutrino Observatory. We start with a revision of the neutrino-gallium cross section that is performed by utilizing the recent measurements of the nuclear final state spectra. We accordingly correct the parameters of gallium anomaly and refine the BEST prospects in testing it and searching for sterile neutrinos. We further evolve the previously proposed idea to investigate the anomaly with ${}^{65}\mathrm{Zn}$ artificial neutrino source as a next option available at BEST and estimate its sensitivity to the sterile neutrino model parameters following the Bayesian approach. We show that after the two stages of operation BEST will make $5\sigma$ discovery of the sterile neutrinos, if they are behind the gallium anomaly.

An analysis of atmospheric neutrino data from all four run periods of Super-Kamiokande optimized for sensitivity to the neutrino mass hierarchy is presented. Confidence intervals for $\mathrm{\Delta }{m}_{32}^2$, ${\sin }^2{\theta }_{23}$, ${\sin }^2{\theta }_{13}$ and ${\delta }_{CP}$ are presented for normal neutrino mass hierarchy and inverted neutrino mass hierarchy hypotheses, based on atmospheric neutrino data alone. Additional constraints from reactor data on ${\theta }_{13}$ and from published binned T2K data on muon neutrino disappearance and electron neutrino appearance are added to the atmospheric neutrino fit to give enhanced constraints on the above parameters. Over the range of parameters allowed at 90% confidence level, the normal mass hierarchy is favored by between 91.9% and 94.5% based on the combined Super-Kamiokande plus T2K result.

In ordinary QCD with light, degenerate, fundamental flavors, $CP$ symmetry is spontaneously broken at $\theta =\pi$, and domain wall solutions connecting the vacua can be constructed in chiral perturbation theory. In some cases the breaking of $CP$ saturates a ’t Hooft anomaly, and anomaly inflow requires nontrivial massless excitations on the domain walls. Analogously, $CP$ can be spontaneously broken in supersymmetric QCD (SQCD) with light flavors and small soft breaking parameters. We study $CP$ breaking and domain walls in softly broken SQCD with $N_f<N$ flavors. Relative to ordinary QCD, the supersymmetric case contains an extra light field, the ${\eta }^{\prime }$, which has interesting effects on the structure of the walls. Vanishing of the $CP$ anomaly is associated with the existence of multiple domain wall trajectories through field space, including walls which support no nontrivial massless excitations. In cases with an anomaly such walls are forbidden, and their absence in the relevant SQCD theories can be seen directly from the geometry of the low energy field space. In the case $N_f=N-1$, multiple approximately Bogomol’nyi–Prasad–Sommerfield walls connect the vacua. Corrections to their tensions can be computed at leading order in the soft breaking parameters, producing a phase diagram for the stable wall trajectory. We also comment on domain walls in the similar case of QCD with an adjoint and fundamental flavors, and on the impact of adding an axion in this theory.

The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bilocal saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean ${\varphi }^6$ model in this work. The phase structure is changed, new phases and relevant operators are found, and certain universality classes are restricted by the bilocal saddle point.

We analyze the concept of causality for the conductivity of graphene described by the Dirac model. It is recalled that the condition of causality leads to the analyticity of conductivity in the upper half-plane of complex frequencies and to the standard symmetry properties for its real and imaginary parts. This results in the Kramers-Kronig relations, which explicit form depends on whether the conductivity has no pole at zero frequency (as in the case of zero temperature when the band gap of graphene is larger than twice the chemical potential) or it has a pole (as in all other cases, specifically, at nonzero temperature). Through the direct analytic calculation it is shown that the real and imaginary parts of graphene conductivity, found recently on the basis of first principles of thermal quantum field theory using the polarization tensor in ($2+1$)-dimensional space-time, satisfy the Kramers-Kronig relations precisely. In so doing, the values of two integrals in the commonly used tables, which are also important for a wider area of dispersion relations in quantum field theory and elementary particle physics, are corrected. The obtained results are not of only fundamental theoretical character, but can be used as a guideline in testing the validity of different phenomenological approaches and for the interpretation of experimental data.

We present the results of 74 new simulations of nonprecessing spinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/7\le q\le 1$ and individual spins covering the parameter space $-0.95\le {\alpha }_{1,2}\le 0.95$. We supplement those runs with 107 previous simulations to study the hangup effect in black hole mergers, i.e. the delay or prompt merger of spinning holes with respect to nonspinning binaries. We perform the numerical evolution for typically the last ten orbits before the merger and down to the formation of the final remnant black hole. This allows us to study the hangup effect for unequal mass binaries leading us to identify the spin variable that controls the number of orbits before merger as ${\overrightarrow{S}}_{\mathrm{hu}}·\widehat{L}$, where ${\overrightarrow{S}}_{\mathrm{hu}}=(1+\frac{1}{2}\frac{m_2}{m_1}){\overrightarrow{S}}_1+(1+\frac{1}{2}\frac{m_1}{m_2}){\overrightarrow{S}}_2$. We also combine the total results of those 181 simulations to obtain improved fitting formulas for the remnant final black hole mass, spin and recoil velocity as well as for the peak luminosity and peak frequency of the gravitational strain, and find new correlations among them. This accurate new set of simulations enhances the number of available numerical relativity waveforms available for parameter estimation of gravitational wave observations.

Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the most general matter Lagrangian allowed by the symmetries is considered, dynamical restrictions arise on their functional dependence. The field equations are obtained and the conservation laws associated with the symmetries are derived. It is found that, analogous to torsion-free unimodular gravity, the field equation for the vierbein is traceless; nevertheless, torsion is algebraically related to the spin density as in standard Einstein-Cartan theory. The particular example of massless Dirac spinors is studied, and comparisons with standard Einstein-Cartan theory are shown.

We study the effects of failure to equilibrate the squared topological charge $Q^2$ on lattice calculations of pseudoscalar masses and decay constants. The analysis is based on chiral perturbation theory calculations of the dependence of these quantities on the QCD vacuum angle $\theta$. For the light-light partially quenched case, we rederive the known chiral perturbation theory results of Aoki and Fukaya, but using the nonperturbatively valid chiral theory worked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. We then extend these calculations to heavy-light mesons. Results when staggered taste violations are important are also presented. The derived $Q^2$ dependence is compared to that of simulations using the MILC Collaboration’s ensembles of lattices with four flavors of dynamical highly improved staggered quarks. We find agreement, albeit with large statistical errors. These results can be used to correct for the leading effects of unequilibrated $Q^2$, or to make estimates of the systematic error coming from the failure to equilibrate $Q^2$. In an appendix, we show that the partially quenched chiral theory may be extended beyond a lower bound on valence masses discovered by Sharpe and Shoresh. Subtleties occurring when a sea-quark mass vanishes are discussed in another appendix.

We present the results of the first lattice QCD calculation of the $K\to \pi$ matrix elements of the chromomagnetic operator $O_{\mathrm{CM}}=g\overline{s}{\sigma }_{\mu \nu }{G}_{\mu \nu }d$, which appears in the effective Hamiltonian describing $\mathrm{\Delta }S=1$ transitions in and beyond the standard model. Having dimension five, the chromomagnetic operator is characterized by a rich pattern of mixing with operators of equal and lower dimensionality. The multiplicative renormalization factor as well as the mixing coefficients with the operators of equal dimension have been computed at one loop in perturbation theory. The power divergent coefficients controlling the mixing with operators of lower dimension have been determined nonperturbatively, by imposing suitable subtraction conditions. The numerical simulations have been carried out using the gauge field configurations produced by the European Twisted Mass Collaboration with $N_f=2+1+1$ dynamical quarks at three values of the lattice spacing. Our result for the $B$ parameter of the chromomagnetic operator at the physical pion and kaon point is $B_{\mathrm{CMO}}^{K\pi }=0.273(69)$, while in the SU(3) chiral limit we obtain $B_{\mathrm{CMO}}=0.076(23)$. Our findings are significantly smaller than the model-dependent estimate $B_{\mathrm{CMO}}\sim 1–4$, currently used in phenomenological analyses, and improve the uncertainty on this important phenomenological quantity.

We consider unfavored light quark/antiquark to $D$ meson fragmentation. We discuss nonperturbative effects for small transverse momenta. The asymmetry for $D^{+}$ and $D^{-}$ production measured by the LHCb collaboration provides natural constraints on the parton (quark/antiquark) fragmentation functions. We find that already a fraction of $q/\overline{q}\to D$ fragmentation probability is sufficient to account for the measured asymmetry. We make predictions for similar asymmetry for neutral $D$ mesons. Large $D$-meson production asymmetries are found for large $x_F$ which is related to dominance of light quark/antiquark $q/\overline{q}\to D$ fragmentation over the standard $c\to D$ fragmentation. As a consequence, prompt atmospheric neutrino flux at high neutrino energies can be much larger than for the conventional $c\to D$ fragmentation. The latter can constitute a sizeable background for the cosmic neutrinos claimed to be observed recently by the IceCube Observatory. Large rapidity-dependent $D^{+}/D^{-}$ and $D^0/{\overline{D}}^0$ asymmetries are predicted for low ($\sqrt{s}=20–100\mathrm{GeV}$) energies. The $q/\overline{q}\to D$ fragmentation leads to enhanced production of $D$ mesons at low energies. At $\sqrt{s}=20\mathrm{GeV}$ the enhancement factor with respect to the conventional contribution is larger than a factor of five. In the considered picture the large-$x_F$ $D$ mesons are produced dominantly via fragmentation of light quarks/antiquarks. Predictions for fixed target $p+{}^4\mathrm{He}$ collisions relevant for a fixed target LHCb experiment are presented.

We construct the holographic renormalization group (RG) flow of thermoelectric conductivities when the translational symmetry is broken. The RG flow is probed by the intrinsic observers hovering on the sliding radial membranes. We obtain the RG flow by solving a matrix-form Riccati equation. The RG flow provides a high-efficient numerical method to calculate the thermoelectric conductivities of strongly coupled systems with momentum dissipation. As an illustration, we recover the AC thermoelectric conductivities in the Einstein-Maxwell-axion model. Moreover, in several homogeneous and isotropic holographic models which dissipate the momentum and have the finite density, it is found that the RG flow of a particular combination of DC thermoelectric conductivities does not run. As a result, the DC thermal conductivity on the boundary field theory can be derived analytically, without using the conserved thermal current.

We compute semiclassical corrections to the energy of rotating open Nambu-Goto strings with and without masses at the ends, using methods from quantum field theory on curved space-times.

We study duality in $\mathcal{N}=1$ supersymmetric QCD in the non-Abelian Coulomb phase, order-by-order in scheme-independent series expansions. Using exact results, we show how the dimensions of various fundamental and composite chiral superfields, and the quantities $a$, $c$, $a/c$, and $b$ at superconformal fixed points of the renormalization group emerge in scheme-independent series expansions in the electric and magnetic theories. We further demonstrate that truncations of these series expansions to modest order yield very accurate approximations to these quantities and suggest possible implications for nonsupersymmetric theories.

This paper is a follow-up on two previous ones, in which properties of blueshifted rays were investigated in Lemaître–Tolman (L–T) and quasispherical Szekeres (QSS) spacetimes. In the present paper, an axially symmetric QSS deformation is superposed on such a L–T background that was proved, in the first paper, to mimic several properties of gamma-ray bursts. The present model makes $z$ closer to $-1$ than in the background L–T spacetime, and, as implied by the second paper, strong blueshifts exist in it only along two opposite directions. The QSS region is matched into a Friedmann background. The big bang (BB) function $t_B(r)$, which is constant in the Friedmann region, has a gate-shaped hump in the QSS region. Since a QSS island generates stronger blueshifts than a L–T island, the BB hump can be made lower—then, it is further removed from the observer and implies a smaller observed angular radius of the source. Consequently, more sources can be fitted into the sky—all these facts are confirmed by numerical computations. Null geodesics reaching present observers from different directions relative to the BB hump are numerically calculated. Patterns of redshift across the image of the source and along the rays are displayed.

We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a $D$-dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a ($D-2$)-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations.