The high-energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high-energy neutrino telescopes. Currently, there are several approaches that predict different behaviors for its magnitude for ultrahigh energies. In this paper, we present a comparison between the predictions based on linear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi dynamics, nonlinear QCD, and the imposition of a Froissart-like behavior at high energies. In particular, we update the predictions based on the color glass condensate, presenting for the first time the results for ${\sigma }_{\nu N}$ using the solution of the running coupling Balitsky-Kovchegov equation. Our results demonstrate that the current theoretical uncertainty for the neutrino-nucleon cross section reaches a factor of three for neutrino energies around ${10}^{11}\mathrm{GeV}$ and increases to a factor of five for ${10}^{13}\mathrm{GeV}$.

Observation of the top quark flavor changing neutral process $t\to c+\gamma$ at the LHC would be the signal of physics beyond the standard model. If anomalous $t\to c\gamma$ coupling exists, it will affect the precisely measured $\mathcal{B}(\overline{B}\to X_s\gamma )$. In this paper, we study the effects of a dimension 5 anomalous $tc\gamma$ operator in $\overline{B}\to X_s\gamma$ decay to derive constraints on its possible strength. It is found that, for real anomalous $t\to c\gamma$ coupling ${\kappa }_{tcR}^{\gamma }$, the constraints correspond to the upper bounds $\mathcal{B}(t\to c+\gamma )<6.54\times {10}^{-5}$ (for ${\kappa }_{tcR}^{\gamma }>0$) and $\mathcal{B}(t\to c+\gamma )<8.52\times {10}^{-5}$ (for ${\kappa }_{tcR}^{\gamma }<0$), respectively, which are about the same order as the $5\sigma$ discovery potential of ATLAS ($9.4\times {10}^{-5}$) and slightly lower than that of CMS ($4.1\times {10}^{-4}$) with $10\mathrm{f}{\mathrm{b}}^{-1}$ integrated luminosity operating at $\sqrt{s}=14\mathrm{TeV}$.

The topological susceptibility of the $SU(3)$ random vortex world-surface ensemble, an effective model of infrared Yang-Mills dynamics, is investigated. The model is implemented by composing vortex world surfaces of elementary squares on a hypercubic lattice, supplemented by an appropriate specification of vortex color structure on the world surfaces. Topological charge is generated in this picture by writhe and self-intersection of the vortex world surfaces. Systematic uncertainties in the evaluation of the topological charge, engendered by the hypercubic construction, are discussed. Results for the topological susceptibility are reported as a function of temperature and compared to corresponding measurements in $SU(3)$ lattice Yang-Mills theory. In the confined phase, the topological susceptibility of the random vortex world-surface ensemble appears quantitatively consistent with Yang-Mills theory. As the temperature is raised into the deconfined regime, the topological susceptibility falls off rapidly, but significantly less so than in $SU(3)$ lattice Yang-Mills theory. Possible causes of this deviation, ranging from artefacts of the hypercubic description to more physical sources, such as the adopted vortex dynamics, are discussed.

A generalized translational-invariant noncommutative field theory is analyzed in detail, and a complete description of translational-invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar and nonplanar axial anomalies are obtained.

We analyze the generic structure of Einstein tensor projected onto a 2D spacelike surface $\mathcal{S}$ defined by a unit timelike and spacelike vectors $\mathit{u}$ and $\mathit{n}$, respectively, which describe an accelerated observer (see text). Assuming that flow along $\mathit{u}$ defines an approximate Killing vector $\mathit{\xi }$, we then show that near the corresponding Rindler horizon, the flux $j^a=G_b^a{\xi }^b$ along the ingoing null geodesics $\mathit{k}$, i.e., $\mathit{j}·\mathit{k}$, has a natural thermodynamic interpretation. Moreover, change in the cross-sectional area of the $\mathit{k}$ congruence yields the required change in area of $\mathcal{S}$ under virtual displacements normal to it. The main aim of this paper is to clearly demonstrate how, and why, the content of Einstein equations under such horizon deformations, originally pointed out by Padmanabhan, is essentially different from the result of Jacobson, who employed the so-called Clausius relation in an attempt to derive Einstein equations from such a Clausius relation. More specifically, we show how a very specific geometric term (reminiscent of Hawking’s quasilocal expression for energy of spheres) corresponding to change in gravitational energy arises inevitably in the first law: $\mathrm{d}{E}_G/\mathrm{d}\lambda \propto {\int }_H{\mathrm{d}}^{2}x\sqrt{\sigma }{}^{(2)}R$ (see text)—the contribution of this purely geometric term would be missed in attempts to obtain area (and hence entropy) change by integrating the Raychaudhuri equation.

We discuss high-order absorbing constraint preserving boundary conditions for the Z4c formulation of general relativity coupled to the moving puncture family of gauges. We are primarily concerned with the constraint preservation and absorption properties of these conditions. In the frozen coefficient approximation, with an appropriate first-order pseudodifferential reduction, we show that the constraint subsystem is boundary stable on a four-dimensional compact manifold. We analyze the remainder of the initial boundary value problem for a spherical reduction of the Z4c formulation with a particular choice of the puncture gauge. Numerical evidence for the efficacy of the conditions is presented in spherical symmetry.

A stochastic gravitational wave background causes the apparent positions of distant sources to fluctuate, with angular deflections of order the characteristic strain amplitude of the gravitational waves. These fluctuations may be detectable with high precision astrometry, as first suggested by Braginsky et al. in 1990. Several researchers have made order of magnitude estimates of the upper limits obtainable on the gravitational wave spectrum ${\Omega }_{\mathrm{gw}}(f)$, at frequencies of order $f\sim 1{\mathrm{yr}}^{-1}$, both for the future space-based optical interferometry missions GAIA and SIM, and for very long baseline interferometry in radio wavelengths with the SKA. For GAIA, tracking $N\sim {10}^6$ quasars over a time of $T\sim 1\mathrm{yr}$ with an angular accuracy of $\Delta \theta \sim 10\mu$ as would yield a sensitivity level of ${\Omega }_{\mathrm{gw}}\sim (\Delta \theta {)}^2/(N{T}^2{H}_0^2)\sim {10}^{-6}$, which would be comparable with pulsar timing. In this paper we take a first step toward firming up these estimates by computing in detail the statistical properties of the angular deflections caused by a stochastic background. We compute analytically the two-point correlation function of the deflections on the sphere, and the spectrum as a function of frequency and angular scale. The fluctuations are concentrated at low frequencies (for a scale invariant stochastic background), and at large angular scales, starting with the quadrupole. The magnetic-type and electric-type pieces of the fluctuations have equal amounts of power.

The classical Einstein’s gravity can be reformulated from the constrained $U(2,2)$ gauge theory on the ordinary (commutative) four-dimensional spacetime. Here we consider a noncommutative manifold with a symplectic structure and construct a $U(2,2)$ gauge theory on such a manifold by using the covariant coordinate method. Then we use the Seiberg-Witten map to express noncommutative quantities in terms of their commutative counterparts up to the first order in noncommutative parameters. After imposing constraints we obtain a noncommutative gravity theory described by the Lagrangian with up to nonvanishing first-order corrections in noncommutative parameters. This result coincides with our previous one obtained for the noncommutative $SL(2,C)$ gravity.

Nonequilibrium flow of thermally relativistic matter with dissipation is considered in the framework of the relativistic kinetic theory. As an object of the analysis, the supersonic rarefied flow of thermally relativistic matter around the triangle prism is analyzed using the Anderson-Witting model. Obtained numerical results indicate that the flow field changes in accordance with the flow velocity and temperature of the uniform flow owing to both effects derived from the Lorentz contraction and thermally relativistic effects, even when the Mach number of the uniform flow is fixed. The profiles of the heat flux along the stagnation streamline can be approximated on the basis of the relativistic Navier-Stokes-Fourier (NSF) law except for a strong nonequilibrium regime such as the middle of the shock wave and the vicinity of the wall, whereas the profile of the heat flux behind the triangle prism cannot be approximated on the basis of the relativistic NSF law owing to rarefied effects via the expansion behind the triangle prism. Additionally, the heat flux via the gradient of the static pressure is non-negligible owing to thermally relativistic effects. The profile of the dynamic pressure is different from that approximated on the basis of the NSF law, which is obtained by the Eckart decomposition. Finally, variations of convections of the mass and momentum owing to the effects derived from the Lorentz contraction and thermally relativistic effects are numerically confirmed.

Based on a spin-flavor extension of chiral symmetry, a novel $s$-wave meson-meson interaction involving members of the $\rho$ nonet and of the $\pi$ octet is introduced, and its predictions are analyzed. The starting point is the SU(6) version of the SU(3)-flavor Weinberg-Tomozawa Lagrangian. SU(6) symmetry-breaking terms are then included to account for the physical meson masses and decay constants in a way that preserves (broken) chiral symmetry. Next, the $T$-matrix amplitudes are obtained by solving the Bethe-Salpeter equation in a coupled-channel scheme, and the poles are identified with their possible Particle Data Group counterparts. It is shown that most of the low-lying even-parity Particle Data Group meson resonances, especially in the $J^P=0^{+}$ and $1^{+}$ sectors, can be classified according to multiplets of SU(6). The $f_0(1500)$, $f_1(1420)$, and some $0^{+}(2^{++})$ resonances cannot be accommodated within this scheme, and thus they would be clear candidates to be glueballs or hybrids. Finally, we predict the existence of five exotic resonances ($I\ge 3/2$ and/or $|Y|=2$) with masses in the range of 1.4–1.6 GeV, which would complete the ${27}_1$, ${10}_3$, and ${10}_3^{*}$ multiplets of $\mathrm{SU}(3)\otimes \mathrm{SU}(2)$.

We study natural composite cold dark matter candidates which are pseudo-Nambu-Goldstone bosons (pNGB) in models of dynamical electroweak symmetry breaking. Some of these can have a significant thermal relic abundance, while others must be mainly asymmetric dark matter. By considering the thermal abundance alone we find a lower bound of $m_W$ on the pNGB mass when the (composite) Higgs is heavier than 115 GeV. Being pNGBs, the dark matter candidates are in general light enough to be produced at the LHC.

In the leptophilic model, one Higgs doublet couples to quarks and another couples to leptons. We study the supersymmetric version of this model, concentrating on the tightly constrained Higgs sector, which has four doublets. Constraints from perturbativity, unitarity, and LEP bounds are considered. It is found that the lightest Higgs, $h$, can have a mass well below 114 GeV, and for masses below 100 GeV will have a substantially enhanced branching ratio into $\tau$ pairs. For this region of parameter space, traditional production mechanisms (Higgs-strahlung, W fusion, and gluon fusion) are suppressed, but it may be produced in the decay of heavier particles. The second lightest Higgs has a mass of approximately 110 GeV for virtually all of parameter space, with standard model couplings, and thus an increase of a few GeV in the current lower bound on the standard model Higgs mass would rule out the model. The two heavier Higgs are both gauge phobic, one decays almost entirely into $b\overline{b}$ and can be produced via gluon fusion while the other decays almost entirely into ${\tau }^{+}{\tau }^{-}$ but cannot be easily produced.

We study chiral symmetry breaking using the standard gap equation, supplemented with the infrared-finite gluon propagator and ghost dressing function obtained from large-volume lattice simulations. One of the most important ingredients of this analysis is the non-Abelian quark-gluon vertex, which controls the way the ghost sector enters into the gap equation. Specifically, this vertex introduces a numerically crucial dependence on the ghost dressing function and the quark-ghost scattering amplitude. This latter quantity satisfies its own, previously unexplored, dynamical equation, which may be decomposed into individual integral equations for its various form factors. In particular, the scalar form factor is obtained from an approximate version of the “one-loop dressed” integral equation, and its numerical impact turns out to be rather considerable. The detailed numerical analysis of the resulting gap equation reveals that the constituent quark mass obtained is about 300 MeV, while fermions in the adjoint representation acquire a mass in the range of (750–962) MeV.

In a recent paper, we have shown that the way of gauge-invariant decomposition of the nucleon spin is not necessarily unique, but there still exists a preferable decomposition from the observational viewpoint. What was not complete in this argument is a fully satisfactory answer to the following questions. Does the proposed gauge-invariant decomposition, especially the decomposition of the gluon total angular momentum into its spin and orbital parts, correspond to observables which can be extracted from high-energy deep-inelastic-scattering measurements ? Is this decomposition not only gauge invariant but also Lorentz frame independent, so that it is legitimately thought to reflect an intrinsic property of the nucleon? We show that we can answer both of these questions affirmatively by making full use of a gauge-invariant decomposition of the covariant angular-momentum tensor of QCD in an arbitrary Lorentz frame.

We present a study of correlations among conserved charges like baryon number, electric charge and strangeness in the framework of $2+1$ flavor Polyakov loop extended Nambu–Jona-Lasinio model at vanishing chemical potentials, up to fourth order. Correlations up to second order have been measured in lattice QCD, which compares well with our estimates given the inherent difference in the pion masses in the two systems. Possible physical implications of these correlations and their importance in understanding the matter obtained in heavy-ion collisions are discussed. We also present a comparison of the results with the commonly used unbound effective potential in the quark sector of this model.

We study a supersymmetric version of the seesaw mechanism type III. The model consists of the minimal supersymmetric extension of the standard model particle content plus three copies of $\mathbf{24}$ superfields. The fermionic part of the $SU(2)$ triplet contained in the $\mathbf{24}$ is responsible for the type-III seesaw, which is used to explain the observed neutrino masses and mixings. Complete copies of $\mathbf{24}$ are introduced to maintain gauge coupling unification. These additional states change the beta functions of the gauge couplings above the seesaw scale. Using minimal Supergravity boundary conditions, we calculate the resulting supersymmetric mass spectra at the electroweak scale using full 2-loop renormalization group equations. We show that the resulting spectrum can be quite different compared to the usual minimal Supergravity spectrum. We discuss how this might be used to obtain information on the seesaw scale from mass measurements. Constraints on the model space due to limits on lepton flavour violating decays are discussed. The main constraints come from the bounds on $\mu \to e\gamma$ but there are also regions where the decay $\tau \to \mu \gamma$ gives stronger constraints. We also calculate the regions allowed by the dark matter constraint. For the sake of completeness, we compare our results with those for the supersymmetric seesaw type II and, to some extent, with type I.

We present the general form of the unitary matrices keeping invariant the Majorana neutrino mass matrix of specific texture suitable for explaining oscillation data. In the case of the tri-bimaximal pattern with two degenerate masses, we give a specific realization of the underlying $U(1)$ symmetry which can be uplifted to a symmetry in a complete theory including charged leptons. For this, we present a model with three light SM-like Higgs doublets and one heavy Higgs triplet and find that one can accommodate the hierarchy of the charged-lepton masses. The lepton mass spectrum can also be achieved in another model extending the SM with three SM-singlet scalars transforming nontrivially under the flavor symmetry. We discuss how such a model has room for generating enough baryon asymmetry through leptogenesis in the framework of type-I and -II seesaw mechanisms.

D3-branes are often a necessary ingredient in global compactifications of F-theory. In minimal realizations of flavor hierarchies in F-theory GUT models, suitable fluxes are turned on, which in turn attract D3-branes to the Yukawa points. Of particular importance are “E-type” Yukawa points, as they are required to realize a large top quark mass. In this paper we study the worldvolume theory of a D3-brane probing such an E-point. D3-brane probes of isolated exceptional singularities lead to strongly coupled $\mathcal{N}=2$ conformal field theories (CFTs) of the type found by Minahan and Nemeschansky. We show that the local data of an E-point probe theory determine an $\mathcal{N}=1$ deformation of the original $\mathcal{N}=2$ theory which couples this strongly interacting CFT to a free hypermultiplet. Monodromy in the seven-brane configuration translates to a novel class of deformations of the CFT. We study how the probe theory couples to the standard model, determining the most relevant F-term couplings, the effect of the probe on the running of the standard model gauge couplings, as well as possible sources of kinetic mixing with the standard mModel.

We study the beta functions of the leading, two-derivative terms of the left-gauged $SU(N)$ nonlinear $\sigma$ model in $d$ dimensions. In $d>2$, we find the usual Gaussian ultraviolet fixed point for the gauge coupling and an attractive non-Gaussian fixed point for the Goldstone boson coupling. The position of the latter fixed point controls the chiral expansion, unitarity and the strength of the tree-level Goldstone boson scattering amplitudes. For large $N$ the model is weakly coupled, unitary at all energies and well described by the lowest order of chiral perturbation theory. Attention is paid to the gauge and scheme dependence of the results.