The set of differential equations obeyed by the redshift in the general ${\beta }^{\prime }\ne 0$ Szekeres spacetimes is derived. Transversal components of the ray’s momentum have to be taken into account, which leads to a set of 3 coupled differential equations. It is shown that in a general Szekeres model, and in a general Lemaître-Tolman (L-T) model, generic light rays do not have repeatable paths (RLPs): two rays sent from the same source at different times to the same observer pass through different sequences of intermediate matter particles. The only spacetimes in the Szekeres class in which all rays are RLPs are the Friedmann models. Among the proper Szekeres models, RLPs exist only in the axially symmetric subcases, and in each one the RLPs are the null geodesics that intersect each $t=\mathrm{\text{constant}}$ space on the symmetry axis. In the special models with a 3-dimensional symmetry group (L-T among them), the only RLPs are radial geodesics. This shows that RLPs are very special and in the real Universe should not exist. We present several numerical examples which suggest that the rate of change of positions of objects in the sky, for the studied configuration, is ${10}^{-6}–{10}^{-7}$ arc sec per year. With the current accuracy of direction measurement, this drift would become observable after approximately 10 years of monitoring. More precise future observations will be able, in principle, to detect this effect, but there are basic problems with determining the reference direction that does not change.

We construct a relativistic potential quark model of $D$, $D_s$, $B$, and $B_s$ mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential $V_{\mathrm{Coul}}(r)=-\xi /r$ and the long-range Lorentz-scalar and Lorentz-vector linear potentials $S_{\mathrm{l}.\mathrm{r}.}(r)=(1-\lambda )(\sigma r+V_0)$ and $V_{\mathrm{l}.\mathrm{r}.}(r)=\lambda (\sigma r+V_0)$, where $0\le \lambda <1/2$. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of $D$, $D_s$, $B$, and $B_s$ mesons, which ensure a high accuracy of calculations even for states with the radial quantum number $n_r\sim 1$. We show that the fine structure of $P$-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant ${\alpha }_s$ and the coefficient $\lambda$ of mixing of the long-range scalar and vector potentials $S_{\mathrm{l}.\mathrm{r}.}(r)$ and $V_{\mathrm{l}.\mathrm{r}.}(r)$. The quasiclassical formulas for asymptotic coefficients of wave functions at zero and infinity are obtained.

We improve our description of $\pi \pi$ scattering data by imposing additional requirements on our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of forward dispersion relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy $K_{\ell 4}$ decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost all disagreement with previous chiral perturbation theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.

We present an analysis of the loop-induced magnetic dipole operator in the Randall-Sundrum model of a warped extra dimension with anarchic bulk fermions and an IR brane-localized Higgs. These operators are finite at one-loop order and we explicitly calculate the branching ratio for $\mu \to e\gamma$ using the mixed position/momentum space formalism. The particular bound on the anarchic Yukawa and Kaluza-Klein (KK) scales can depend on the flavor structure of the anarchic matrices. It is possible for a generic model to either be ruled out or unaffected by these bounds without any fine-tuning. We quantify how these models realize this surprising behavior. We also review tree-level lepton flavor bounds in these models and show that these are on the verge of tension with the $\mu \to e\gamma$ bounds from typical models with a 3 TeV Kaluza-Klein scale. Further, we illuminate the nature of the one-loop finiteness of these diagrams and show how to accurately determine the degree of divergence of a five-dimensional loop diagram using both the five-dimensional and KK formalism. This power counting can be obfuscated in the four-dimensional Kaluza-Klein formalism and we explicitly point out subtleties that ensure that the two formalisms agree. Finally, we remark on the existence of a perturbative regime in which these one-loop results give the dominant contribution.

The same complex matrix model calculates both tachyon scattering for the $c=1$ noncritical string at the self-dual radius and certain correlation functions of operators which preserve half the supersymmetry in $\mathcal{N}=4$ super-Yang-Mills theory. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich-Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces.

Recently it was shown that kink baryons and kink-antikink scattering in the massless Gross-Neveu model are closely related to one- and two-soliton solutions of the sinh-Gordon equation. Here we generalize these findings to the case of $n$ kinks and antikinks. Using the known $n$-soliton solution of the sinh-Gordon equation, we solve the general $n$ kink-antikink scattering problem in the large $N$ Gross-Neveu model analytically, mapping the time-dependent Hartree-Fock approach onto inverse scattering theory.

In this article, we explore the kinematics of timelike geodesic congruences in warped five-dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall-Sundrum anti–de Sitter geometry without and with branes, we find analytical expressions for the expansion scalar and comment on the effects of including thin branes on its evolution. Later, we move on to congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using analytical expressions for the velocity field, we interpret the expansion, shear and rotation (ESR) along the flows, as functions of the extra dimensional coordinate. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer’s point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in backgrounds with a thick brane are solved numerically in order to figure out the role of initial conditions (prescribed on the ESR) and spacetime curvature on the evolution of the ESR.

We propose late-time moduli decay as the common origin of baryons and dark matter. The baryon asymmetry is produced from the decay of new TeV-scale particles, while dark matter is created from the (chain) decay of $R$-parity odd particles without undergoing any annihilation. The baryon and dark matter abundances are mainly controlled by the dilution factor from moduli decay, which is typically in the range ${10}^{-9}–{10}^{-7}$. The exact number densities are determined by simple branching fractions from modulus decay, which are expected to be of similar order in the absence of symmetries. This scenario can naturally lead to the observed baryon asymmetry and, for moderate suppression of the two-body decays of the modulus to $R$-parity odd particles, can also yield the correct dark matter abundance for a dark matter mass in the (5–500) GeV range.

We discuss the stability properties of an autonomous system in loop quantum cosmology. The system is described by a self-interacting scalar field $\varphi$ with positive potential $V$, coupled with a barotropic fluid in the Universe. With $\Gamma =V{V}^{\prime \prime }/V^{\prime 2}$ considered as a function of $\lambda =V^{\prime }/V$, the autonomous system is extended from three dimensions to four dimensions. We find that the dynamic behaviors of a subset, not all, of the fixed points are independent of the form of the potential. Considering the higher-order derivatives of the potential, we get an infinite-dimensional autonomous system, which can describe the dynamical behavior of the scalar field with more general potential. We find that there is just one scalar-field-dominated scaling solution in the loop quantum cosmology scenario.

Single top quark production at the International Linear Collider (ILC) can be used to obtain high precision measurements of the $V_{tb}$ Cabibbo-Kobayashi-Maskawa quark-mixing matrix (CKM) element as well as the effective $tbW$ coupling. We have calculated the QCD correction for the cross section in the context of an effective vector boson approximation. Our results show a $\sim 10\%$ increase due to the strong interaction.

We evaluate differential distributions for the four-body $pp\to nn{\pi }^{+}{\pi }^{+}$ reaction. The amplitude for the process is calculated in the Regge approach including many diagrams. We make predictions for possible future experiments at RHIC and LHC energies. Very large cross sections are found which is partially due to interference of a few mechanisms. Presence of several interfering mechanisms precludes extraction of the elastic ${\pi }^{+}{\pi }^{+}$ scattering cross section. Absorption effects are estimated. Differential distributions in pseudorapidity, rapidity, invariant two-pion mass, transverse-momentum and energy distributions of neutrons are presented for proton-proton collisions at $\sqrt{s}=500\mathrm{GeV}$ (RHIC) and $\sqrt{s}=0.9$, 2.36 and 7 TeV (LHC). Cross sections with experimental cuts are presented.

This paper studies the way in which confinement leads to chiral symmetry breaking (CSB) through a gap equation. We argue that a combination of entropic effects, related to fluctuations of Wilson loops with massless constituents, and an Abelian gauge invariance of the confinement action as expressed in terms of the usual confining effective propagator $8\pi K_F{\delta }_{\mu \nu }/k^4$, in effect removes infrared singularities coming from use of this propagator in a standard gap equation ($K_F$ is the string tension). Beginning from an Abelian gauge-invariant description of CSB that differs from this standard gap equation, we show how to extract a corresponding gap equation that incorporates both entropic effects and Abelian gauge invariance by replacement of the confining propagator with $8\pi K_F{\delta }_{\mu \nu }/(k^2+m^2{)}^2$. Here the finite mass $m$ turns out to be $\approx M(0)$ [$M(p^2)$ is the running quark mass], based on an extension of an old calculation of the author. This massive propagator gives semiquantitatively two critical properties of confinement: (1) a negative contribution to the confining potential coming from entropy; (2) an infrared cutoff required by Abelian gauge invariance. Entropic effects lead to a $\overline{q}q$ condensate and contribute a negative term $\sim -K_F/M(0)$, essential for a massless pion, to the pion Hamiltonian. The resulting gap equation leads to $M^2(0)\approx K_F/\pi$. We argue that one-gluon exchange is not strong enough in the IR to drive quark CSB, but in any case is necessary to get the correct renormalization-group ultraviolet behavior. We find the standard renormalization-group result with the improvement that the prefactor (related to $⟨\overline{q}q⟩$) can be calculated from the confining solution. Finally, we briefly point out the Minkowski-space virtues of using a principal-part propagator to describe confinement.

We report constraints on the parameters of Yukawa-type corrections to Newtonian gravity from measurements of the gradient of the Casimir force in the configuration of an Au-coated sphere above a Si plate covered with corrugations of trapezoidal shape. For this purpose, the exact expression for the gradient of Yukawa force in the experimental configuration is derived and compared with that obtained using the proximity force approximation. The reported constraints are of almost the same strength as those found previously from several different experiments on the Casimir force and extend over a wide interaction range from 30 to 1260 nm. It is discussed how to make them stronger by replacing the material of the plate.

The dominant contributions to $W^{\mp }{H}^{\pm }$ production at the LHC are the tree-level $b\overline{b}$ annihilation and the $gg$ fusion. We perform for the case of the complex minimal supersymmetric standard model (MSSM) a complete calculation of the next-to-leading order (NLO) electroweak corrections to the $b\overline{b}$ annihilation channel and a consistent combination with other contributions including the standard and supersymmetric-QCD (SUSY-QCD) corrections and the $gg$ fusion, with resummation of the leading radiative corrections to the bottom-Higgs couplings and the neutral Higgs boson propagators. We observe a large $CP$-violating asymmetry, arising mainly from the $gg$ channel.

Directional detection is a promising dark matter search strategy. Indeed, weakly interacting massive particle (WIMP)-induced recoils would present a direction dependence toward the Cygnus constellation, while background-induced recoils exhibit an isotropic distribution in the Galactic rest frame. Taking advantage of these characteristic features, and even in the presence of a sizeable background, it has recently been shown that data from forthcoming directional detectors could lead either to a competitive exclusion or to a conclusive discovery, depending on the value of the WIMP-nucleon cross section. However, it is possible to further exploit these upcoming data by using the strong dependence of the WIMP signal with: the WIMP mass and the local WIMP velocity distribution. Using a Markov chain Monte Carlo analysis of recoil events, we show for the first time the possibility to constrain the unknown WIMP parameters, both from particle physics (mass and cross section) and Galactic halo (velocity dispersion along the three axis), leading to an identification of non-baryonic dark matter.

We study the double-charged vector-bilepton pair production and double-charged scalar-bilepton pair production via $p+p\to Y^{++}+Y^{--}+X$ and $p+p\to S_1^{++}+S_1^{--}+X$, where $Y$ and $S_1$ are vector and scalar bileptons, respectively, in the framework of the minimal version of the 3-3-1 model. We compute the photon, $Z$, and $Z^{\prime }$ $s$-channel contributions for the elementary process of bilepton scalar pair production, and to keep the correct unitarity behavior for the elementary $q\overline{q}$ interaction, we include the exotic quark $t$-channel contribution in the vector-bilepton pair production calculation. We explore a mass range for $Z^{\prime }$ and we fix the exotic quark mass within the experimental bounds. In this model, the vector-bilepton mass is directly related to $M_{Z^{\prime }}$ and we consider scalar mass values around the vector-bilepton mass. We show that the total cross section for vector-bilepton production is 3 orders of magnitude larger than for scalar pair production for $\sqrt{s}=7\mathrm{TeV}$ and 14 TeV and we obtain the number of events for the proposed LHC luminosities as a function of the bilepton mass. In addition we present some invariant mass and transverse momentum distributions. When comparing these distributions we observe quite different behavior providing the determination of the bilepton nature. We conclude that one can disentangle the production rates and that the LHC can be capable of detecting these predicted particles as a signal for new physics.

It has been conjectured that the two-dimensional $\mathcal{N}=2$ Wess-Zumino model with a quasihomogeneous superpotential provides the Landau-Ginzburg description of the $\mathcal{N}=2$ superconformal minimal models. For the cubic superpotential $W=\lambda {\Phi }^3/3$, it is expected that the Wess-Zumino model describes $A_2$ model and the chiral superfield $\Phi$ shows the conformal weight $(h,\overline{h})=(1/6,1/6)$ at the IR fixed point. We study this conjecture by a lattice simulation, extracting the weight from the finite volume scaling of the susceptibility of the scalar component in $\Phi$. We adopt a lattice model with the overlap fermion, which possesses a Nicolai map and a discrete $R$-symmetry. We set $a\lambda =0.3$ and generate the scalar field configurations by solving the Nicolai map on $L\times L$ lattices in the range $L=18–32$. To solve the map, we use the Newton-Raphson algorithm with various initial configurations. The result is $1-h-\overline{h}=0.660\pm 0.011$, which is consistent with the conjecture within the statistical error, while a systematic error is estimated as less than 0.5%.

We calculate the chiral condensate of QCD with 2, $2+1$, and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up- and down-quark masses covering a range between 3 and 100 MeV. On $L\sim 1.8–1.9\mathrm{fm}$ lattices at a lattice spacing $\sim 0.11\mathrm{fm}$, we calculate the eigenvalue spectrum of the overlap-Dirac operator. By matching the lattice data with the analytical prediction from chiral perturbation theory at the next-to-leading order, the chiral condensate in the massless limit of up and down quarks is determined.

The Nambu–Jona-Lasinio (NJL)-jet model provides a sound framework for calculating the fragmentation functions in an effective chiral quark theory, where the momentum and isospin sum rules are satisfied without the introduction of ad hoc parameters. Earlier studies of the pion fragmentation functions using the NJL model within this framework showed qualitative agreement with the empirical parametrizations. Here we extend the NJL-jet model by including the strange quark. The corrections to the pion fragmentation functions and corresponding kaon fragmentation functions are calculated using the elementary quark to quark-meson fragmentation functions from NJL. The results for the kaon fragmentation functions exhibit a qualitative agreement with the empirical parametrizations, while the unfavored strange quark fragmentation to pions is shown to be of the same order of magnitude as the unfavored light quark. The results of these studies are expected to provide important guidance for the analysis of a large variety of semi-inclusive data.

We present the next-to-leading order supersymmetric-QCD corrections to the production of a light neutral minimal supersymmetric standard model Higgs boson with a pair of supersymmetric scalar partners of the top quark at next-to-leading order at the LHC. We study the dependence of the lowest order total cross section on both the renormalization/factorization scale and the Higgs mass in the framework of minimal supergravity, taking the point SPS1a as a benchmark, for the numerical calculations. The renormalization/factorization scale dependence of the lowest order total cross section is strong. Including the next-to-leading order supersymmetric-QCD corrections significantly reduces and stabilizes the dependence of the lowest order total cross section on the renormalization/factorization scale.