The adaptive aggregation-base domain decomposition multigrid method [A. Frommer et al., SIAM J. Sci. Comput. 36, A1581 (2014)] is extended for two degenerate flavors of twisted mass fermions. By fine-tuning the parameters we achieve a speed-up of the order of a hundred times compared to the conjugate gradient algorithm for the physical value of the pion mass. A thorough analysis of the aggregation parameters is presented, which provides a novel insight into multigrid methods for lattice quantum chromodynamics independently of the fermion discretization.

Dynamical chiral symmetry breaking ($\mathrm{D}\chi \mathrm{SB}$) is studied within ($2+1$)-dimensional QED with $N$ four-component fermions. The leading and next-to-leading orders of the $1/N$ expansion are computed exactly. The analysis is carried out in an arbitrary nonlocal gauge. Resumming the wave-function renormalization constant at the level of the gap equation yields a strong suppression of the gauge dependence of the critical fermion flavor number, $N_c(\xi )$, where $\xi$ is the gauge-fixing parameter, which is such that $\mathrm{D}\chi \mathrm{SB}$ takes place for $N<N_c(\xi )$. Neglecting the weak gauge-dependent terms yields $N_c=2.8469$, while, in the general case, it is found that $N_c(1)=3.0084$ in the Feynman gauge, $N_c(0)=3.0844$ in the Landau gauge, and $N_c(2/3)=3.0377$ in the $\xi =2/3$ gauge where the leading order fermion wave function is finite. These results suggest that $\mathrm{D}\chi \mathrm{SB}$ should take place for integer values $N\le 3$.

The dynamical generation of a fermion gap in graphene is studied at the infra-red Lorentz-invariant fixed point where the system is described by an effective relativistic-like field theory: reduced ${\mathrm{QED}}_{4,3}$ with $N$ four-component fermions ($N=2$ for graphene), where photons are ($3+1$) dimensional and mediate a fully retarded interaction among ($2+1$)-dimensional fermions. A correspondence between reduced ${\mathrm{QED}}_{4,3}$ and ${\mathrm{QED}}_3$ allows us to derive an exact gap equation for ${\mathrm{QED}}_{4,3}$ up to next-to-leading order. Our results show that a dynamical gap is generated for $\alpha >{\alpha }_c$, where $1.03<{\alpha }_c<1.08$ in the case $N=2$ or for $N<N_c$ where $N_c$ is such that ${\alpha }_c\to \infty$ and takes the values $3.24<N_c<3.36$. The striking feature of these results is that they are in good agreement with values found in models with instantaneous Coulomb interaction (including lattice simulations). At the fixed point, $\alpha =1/137\ll {\alpha }_c$, and the system is therefore in the semimetallic regime in accordance with experiments.

In this work, we investigate production of Drell-Yan (DY) pairs in proton-nucleus collisions in kinematic regions where the corresponding coherence length does not exceed the nuclear radius, $R_A$, and the quantum coherence effects should be treated with special care. The results for the nucleus-to-nucleon production ratio available in the literature so far are usually based on the assumption of a very long coherence length (LCL) $l_c\gg R_A$. Since the onset of coherence effects is controlled by the coherence length $l_c$, we estimated its magnitude in various kinematic regions of the DY process and found that the LCL approximation should not be used at small and medium c.m. collision energies ($\sqrt{s}\lesssim 200\mathrm{GeV}$) as well as at large dilepton invariant masses. In order to obtain realistic predictions, we computed for the first time the DY cross section using the generalized color dipole approach based on the rigorous Green function formalism, which naturally incorporates the color transparency and quantum coherence effects and hence allows us to estimate the nuclear shadowing with no restrictions on the CL. In addition to the shadowing effect, we studied a complementary effect of initial state interactions (ISI) that causes an additional suppression at large values of the Feynman variable. Numerical results for the nuclear modification factor accounting for the ISI effect and the finite $l_c$ are compared to the data available from the fixed-target Fermi National Laboratory measurements and a good agreement has been found. Besides, we present new predictions for the nuclear suppression as a function of dilepton rapidity and invariant mass in the kinematic regions that can be probed by the RHIC collider as well as by the planned AFTER@LHC and LHCb fixed-target experiments.

$\mathcal{N}=1$ $SU(N)$ super-Yang-Mills theory on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ is believed to have a smooth dependence on the circle size $L$. Making $L$ small leads to calculable nonperturbative color confinement, mass gap, and string tensions. For finite $N$, the small-$L$ low-energy dynamics is described by a three-dimensional effective theory. The large-$N$ limit, however, reveals surprises: the infrared dual description is in terms of a theory with an emergent fourth dimension, curiously reminiscent of T-duality in string theory. Here, however, the emergent dimension is a lattice, with momenta related to the ${\mathbb{S}}^1$-winding of the gauge field holonomy, which takes values in ${\mathbb{Z}}_N$. Furthermore, the low-energy description is given by a nontrivial gapless theory, with a space-like $z=2$ Lifshitz scale invariance and operators that pick up anomalous dimensions as $L$ is increased. Supersymmetry-breaking deformations leave the long-distance theory scale-invariant, but change the Lifshitz scaling exponent to $z=1$, and lead to an emergent Lorentz symmetry at small $L$. Adding a small number of fundamental fermion fields leads to matter localized on three-dimensional branes in the emergent four-dimensional theory.

We investigate, in the context of a real massless scalar field in $1+1$ dimensions, models of partially reflecting mirrors simulated by Dirac $\delta -{\delta }^{\prime }$ point interactions. In the literature, these models do not exhibit full transparency at high frequencies. In order to provide a more realistic feature for these models, we propose a modified $\delta -{\delta }^{\prime }$ point interaction that enables full transparency in the limit of high frequencies. Taking this modified $\delta -{\delta }^{\prime }$ model into account, we investigate the Casimir force, comparing our results with those found in the literature.

The $\mathcal{O}({\partial }^2)$ background-independent flow equations for conformally reduced gravity are shown to be equivalent to flow equations naturally adapted to scalar field theory with a wrong-sign kinetic term. This sign change is shown to have a profound effect on the renormalization group properties, broadly resulting in a continuum of fixed points supporting both a discrete and a continuous eigenoperator spectrum, the latter always including relevant directions. The properties at the Gaussian fixed point are understood in particular depth, but also detailed studies of the local potential approximation, and the full $\mathcal{O}({\partial }^2)$ approximation are given. These results are related to evidence for asymptotic safety found by other authors.

In this article, we derive the geodesic equations in the ${\mathrm{U}(1)}^2$ dyonic rotating black hole spacetime. We present their solutions in terms of the Kleinian $\sigma$ function and in special cases in terms of the Weierstraß $\wp$, $\sigma$, and $\zeta$ functions. To give a list of all possible orbits, we analyze the geodesic motion of test particles and light using parametric diagrams and effective potentials.

To study the effect of the anti–de Sitter/conformal field theory correspondence (AdS/CFT) on the primordial inflationary era, we consider a universe filled with a tachyon field in a slow-roll regime. In this context, the background and perturbative parameters characterizing the inflationary era are related to the standard one by correction terms. We show a clear agreement between the theoretical prediction and the observational data for the above-mentioned model. The main results of our work are illustrated for an exponential potential. We show that, for a suitable conformal anomaly coefficient, AdS/CFT correspondence might leave its imprints on the spectrum of the gravitational waves amplitude with a tensor to scalar ratio, $r$, of the perturbations compatible with Planck data.

Correlations between intrinsic galaxy shapes on large scales arise due to the effect of the tidal field of the large-scale structure. Anisotropic primordial non-Gaussianity induces a distinct scale-dependent imprint in these tidal alignments on large scales. Motivated by the observational finding that the alignment strength of luminous red galaxies depends on how galaxy shapes are measured, we study the use of two different shape estimators as a multitracer probe of intrinsic alignments. We show, by means of a Fisher analysis, that this technique promises a significant improvement on anisotropic non-Gaussianity constraints over a single-tracer method. For future weak lensing surveys, the uncertainty in the anisotropic non-Gaussianity parameter, $A_2$, is forecast to be $\sigma (A_2)\approx 50$, $\sim 40\%$ smaller than currently available constraints from the bispectrum of the cosmic microwave background. This corresponds to an improvement of a factor of 4–5 over the uncertainty from a single-tracer analysis.

The isotropic gamma-ray background arises from the contribution of unresolved sources, including members of confirmed source classes and proposed gamma-ray emitters such as the radiation induced by dark matter annihilation and decay. Clues about the properties of the contributing sources are imprinted in the anisotropy characteristics of the gamma-ray background. We use 81 months of Pass 7 Reprocessed data from the Fermi Large Area Telescope to perform a measurement of the anisotropy angular power spectrum of the gamma-ray background. We analyze energies between 0.5 and 500 GeV, extending the range considered in the previous measurement based on 22 months of data. We also compute, for the first time, the cross-correlation angular power spectrum between different energy bins. We find that the derived angular spectra are compatible with being Poissonian, i.e. constant in multipole. Moreover, the energy dependence of the anisotropy suggests that the signal is due to two populations of sources, contributing, respectively, below and above $\sim 2\mathrm{GeV}$. Finally, using data from state-of-the-art numerical simulations to model the dark matter distribution, we constrain the contribution from dark matter annihilation and decay in Galactic and extra-Galactic structures to the measured anisotropy. These constraints are competitive with those that can be derived from the average intensity of the isotropic gamma-ray background.

We consider dark matter physics in a model for the dark sector with extra dark ${\mathrm{U}(1)}_X$ gauge symmetry. The dark sector is composed of exotic fermions that are charged under both dark ${\mathrm{U}(1)}_X$ and the standard model ${\mathrm{SU}(3)}_C\times \mathrm{U}(1{)}_Y$ gauge groups, as well as standard model singlet complex scalars $\mathrm{\Phi }$ and $X$ with nonzero ${\mathrm{U}(1)}_X$ charge. In this model, there are two dark matter candidates—a scalar and a fermion—both of which are stabilized by accidental $Z_2$ symmetry. Their thermal relic density, and direct and indirect detection constraints are discussed in detail and we search for the parameter space of the model accommodating dark matter observations. We also discuss constraints from diphoton resonance searches associated with the scalar field which breaks the dark ${\mathrm{U}(1)}_X$, in a way consistent with dark matter physics. In addition, implications for collider physics are discussed, focusing on the production cross section of the scalar boson.

We analyze the testability of the type II radiative seesaw in which neutrino mass and dark matter (DM) are related at one-loop level. Under the constraints from DM relic density, direct and indirect detection, and invisible Higgs decays, we find three possible regions of DM mass $M_{s_1}$ that can survive the present and even the future experiments: (1) the Higgs resonance region with $M_{s_1}\sim M_h/2$, (2) the Higgs region with $M_{s_1}\sim M_h$, and (3) the coannihilation region with $M_{s_2}\sim M_{s_1}$. Here $s_{1,2}$ are two scalar singlets with the lighter $s_1$ being the DM candidate. Based on DM properties and direct collider constraints, we choose three benchmark points to illustrate the testability of this model at the LHC. We perform a detailed simulation of the four-lepton and trilepton signatures at 13(14) TeV LHC. While both signatures are found to be promising at all benchmark points, the trilepton one is even better: it is possible to reach the $5\sigma$ significance with an integrated luminosity of $100{\mathrm{fb}}^{-1}$.

We analyze a new class of FCNC processes, the $f\to f^{\prime }\overline{\gamma }$ decays of a fermion $f$ into a lighter (same-charge) fermion $f^{\prime }$ plus a massless neutral vector boson, a dark photon $\overline{\gamma }$. A massless dark photon does not interact at tree level with observable fields, and the $f\to f^{\prime }\overline{\gamma }$ decay presents a characteristic signature where the final fermion $f^{\prime }$ is balanced by a massless invisible system. Models recently proposed to explain the exponential spread in the standard-model Yukawa couplings can indeed foresee an extra unbroken dark $U(1)$ gauge group, and the possibility to couple on-shell dark photons to standard-model fermions via one-loop magnetic-dipole kind of FCNC interactions. The latter are suppressed by the characteristic scale related to the mass of heavy messengers, connecting the standard model particles to the dark sector. We compute the corresponding decay rates for the top, bottom, and charm decays ($t\to c\overline{\gamma }$, $u\overline{\gamma }$, $b\to s\overline{\gamma }$, $d\overline{\gamma }$, and $c\to u\overline{\gamma }$), and for the charged-lepton decays ($\tau \to \mu \overline{\gamma }$, $e\overline{\gamma }$, and $\mu \to e\overline{\gamma }$) in terms of model parameters. We find that large branching ratios for both quark and lepton decays are allowed in case the messenger masses are in the discovery range of the LHC. Implications of these new decay channels at present and future collider experiments are briefly discussed.

In this paper we describe a new integration method for the groups $U(N)$ and $SU(N)$, for which we verified numerically that it is polynomially exact for $N\le 3$. The method is applied to the example of one-dimensional QCD with a chemical potential. We explore, in particular, regions of the parameter space in which the sign problem appears due the presence of the chemical potential. While Markov chain Monte Carlo fails in this region, our new integration method still provides results for the chiral condensate on arbitrary precision, demonstrating clearly that it overcomes the sign problem. Furthermore, we demonstrate that also in other regions of parameter space our new method leads to errors which are reduced by orders of magnitude.

We investigate the critical endline of the finite temperature phase transition of QCD around the SU(3)-flavor symmetric point at zero chemical potential. We employ the renormalization-group improved Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson-clover fermion action. The critical endline is determined by using the intersection point of kurtosis, employing the multiparameter, multiensemble reweighting method to calculate observables off the SU(3)-symmetric point, at the temporal size $N_{\mathrm{T}}=6$ and lattice spacing as low as $a\approx 0.19\mathrm{fm}$. We confirm that the slope of the critical endline takes the value of $-2$, and find that the second derivative is positive, at the SU(3)-flavor symmetric point on the Columbia plot parametrized with the strange quark mass $m_{\mathrm{s}}$ and degenerated up-down quark mass $m_{\mathrm{l}}$.

A picture of confinement in QCD based on a condensate of thick vortices with fluxes in the center of the gauge group (center vortices) is studied. Previous concrete model realizations of this picture utilized a hypercubic space-time scaffolding, which, together with many advantages, also has some disadvantages, e.g., in the treatment of vortex topological charge. In the present work, we explore a center vortex model which does not rely on such a scaffolding. Vortices are represented by closed random lines in continuous $2+1$-dimensional space-time. These random lines are modeled as being piecewise linear, and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a torus with periodic boundary conditions. Besides moving, growing, and shrinking of the vortex configurations, also reconnections are allowed. Our ensemble therefore contains not a fixed but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining phase transition. We study both vortex percolation and the potential $V(R)$ between the quark and antiquark as a function of distance $R$ at different vortex densities, vortex segment lengths, reconnection conditions, and at different temperatures. We find three deconfinement phase transitions, as a function of density, as a function of vortex segment length, and as a function of temperature.

We investigate the valence quark distribution function of the pion $v^{\pi }(x,Q^2)$ in the framework of the chiral constituent quark model and evaluate the meson cloud effects on $v^{\pi }(x,Q^2)$. We explicitly demonstrate how the meson cloud effects affect $v^{\pi }(x,Q^2)$ in detail. We find that the meson cloud correction causes an overall 32% reduction of the valence quark distribution and an enhancement at the small Bjorken $x$ regime. Besides, we also find that the dressing effect of the meson cloud will make the valence quark distribution to be softer in the large $x$ region.

The QCD string model is employed to evaluate the masses of orbitally and radially excited heavy-light mesons and lightest hybrids in the spectrum of charmonium and bottomonium. The number of parameters of the model is reduced to only seven which are the string tension, the two values of the strong coupling constant (one for heavy-light and $\overline{c}c$ mesons and one for $\overline{b}b$ mesons), and the four overall spectrum shift constants which depend on the quark contents of the particular meson or hybrid family. A few well-established states in the spectrum of heavy-light and heavy-heavy mesons are used to fix these parameters, and then the masses of other mesons and hybrids come out as predictions of the model which are confronted with the existing experimental data, and a few suggestions are made concerning yet not measured quantum numbers of some states in the spectrum of charmonium and bottomonium.

The $e^{+}{e}^{-}\to K^{+}{K}^{-}$ cross section is measured in the center-of-mass energy range 1.05–2.00 GeV at the SND detector. The measurement is based on data with an integrated luminosity of $35{\mathrm{pb}}^{-1}$ collected at the VEPP-2000 $e^{+}{e}^{-}$-collider. The obtained results are consistent with the previous most accurate data obtained in the BABAR experiment and have a comparable accuracy.