In this paper, chiral symmetry breaking and its restoration are investigated in the mean field approximation of Nambu–Jona-Lasinio model. A first-order phase transition exists at low temperature, but is smeared out at high temperature. We discuss the rationality of using susceptibilities as the criteria to determine the crossover region as well as the critical point. Based on our results, it is found that to define a critical band instead of an exclusive line in this region might be a more suitable choice.

Electroweak gauge boson pair production is one of the most important Standard Model processes at the LHC, not only because it is a benchmark process but also by its ability to probe the electroweak interaction directly. We present full next-to-leading order predictions for the production cross sections and distributions of on-shell massive gauge boson pair production in the Standard Model. This includes the QCD and electroweak (EW) corrections. We study the hierarchy between the different channels when looking at the size of the QCD gluon-quark-induced processes and the EW photon-quark-induced processes and provide the first comprehensive explanation of this hierarchy thanks to analytical leading-logarithmic results. We also provide a detailed study of the theoretical uncertainties affecting the total cross section predictions that stem from scale variation, parton distribution function and ${\alpha }_s$ errors. We then compare with the present LHC data.

Earlier studies of the influence of dark matter keV sterile neutrinos on neutrinoless double beta decay concluded that there is no significant modification of the decay rate. These studies have focused only on a mass of the keV sterile neutrino above 2 and 4 keV, respectively, as motivated by certain production mechanisms. On the other hand, alternative production mechanisms have been proposed, which relax the lower limit for the mass, and new experimental data are available, too. For this reason, an updated study is timely and worthwhile. We focus on the most recent data, i.e., the newest Chandra and XMM-Newton observational bounds on the x-ray line originating from radiative keV sterile neutrino decay, as well as the new measurement of the previously unknown leptonic mixing angle ${\theta }_{13}$. While the previous works might have been a little short-sighted, the new observational bounds do indeed render any influences of keV sterile neutrinos on neutrinoless double beta decay small. This conclusion even holds in case not all the dark matter is made up of keV sterile neutrinos.

Studying $e^{-}{e}^{+}\to W^{-}{W}^{+}$ at the one-loop electroweak order, we derive very accurate and simple expressions for the four helicity conserving amplitudes which dominate this process at high energies. The calculations are done in both the standard model and minimal supersymmetric standard model frameworks. Such expressions, called supersimple, nicely emphasize the dynamical contents of each framework. Numerical illustrations are presented, which show the accuracy of this description, and how it can be used for identifying possible additional new physics contributions, like, e.g., anomalous gauge couplings or a new $Z^{\prime }$ vector boson exchange. The procedure is useful even if only the standard model is visible at the future linear collider energies.

At high energies, particles move very fast, so the proper degrees of freedom for the fast gluons moving along the straight lines are Wilson-line operators—infinite gauge factors ordered along the line. In the framework of operator expansion in Wilson lines, the energy dependence of the amplitudes is determined by the rapidity evolution of Wilson lines. We present the next-to-leading order hierarchy of the evolution equations for Wilson-line operators.

The phenomenology of the most general lepton mass matrices obtained through weak basis transformations has been discussed. Using a hierarchical parametrization of these mass matrices, the exact relations for lepton mixing angles have been obtained assuming normal neutrino mass hierarchy and natural structures of lepton mass matrices. The recent three neutrino oscillation data together with the condition of naturalness on the Dirac lepton mass matrices provide a lower bound on the lightest neutrino mass of ${\mathrm{m}}_{\mathrm{v}1}>3\mathrm{meV}$ along with a nonvanishing Dirac $CP$ violating phase.

We apply the dynamical mean field theory (DMFT) approximation to the real, scalar ${\phi }^4$ quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents $\nu$ and $\beta$. We also map out the phase diagram in the most relevant case of four dimensions. In two and three dimensions, DMFT incorrectly predicts a first-order phase transition for all bare quartic couplings, which is problematic, because the second-order nature of the phase transition of lattice ${\phi }^4$ theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behavior away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is second order for small quartic couplings and turns weakly first order as the coupling increases beyond a tricritical value. In dimensions five and higher, DMFT gives qualitatively correct results, predicts reasonable values for the critical exponents and considerably more accurate critical couplings than standard mean field theory. The approximation works best for small values of the quartic coupling. We investigate the change from first- to second-order transition in the local limit of DMFT which is computationally much cheaper. We also discuss technical issues related to the convergence of the nonlinear self-consistency equation solver and the solution of the effective single-site model using Fourier-space Monte Carlo updates in the presence of a ${\phi }^4$ interaction.

In the so-called “yukawaon” model, the (effective) Yukawa coupling constants $Y_f^{\mathrm{eff}}$ are given by vacuum expectation values (VEVs) of scalars $Y_f$ (yukawaons) with $3\times 3$ components. So far, yukawaons $Y_f$ have been assigned to $\mathbf{6}$ or ${\mathbf{6}}^{*}$ of U(3) family symmetry, so that quarks and leptons were not anomaly free in U(3). In this paper, yukawaons are assigned to $\mathbf{8}+\mathbf{1}$ of U(3), so that quarks and leptons are anomaly free. Since VEV relations among yukawaons are also considerably changed, parameter fitting of the model is renewed. After fixing our free parameters by observed mass ratios, we have only two and one remaining free parameters for quark and lepton mixings, respectively. We obtain successful predictions for the quark and lepton mixing parameters including magnitudes of $CP$ violation. The effective Majorana neutrino mass is also predicted.

We calculate the invariant and helicity amplitudes for the nonleptonic decay ${\Lambda }_b\to \Lambda +J/\psi$, $\psi (2S)$ in the covariant confined quark model. We discuss joint angular decay distributions in the cascade decay ${\Lambda }_b\to \Lambda (\to p{\pi }^{-})+J/\psi$, $\psi (2S)(\to {\ell }^{+}{\ell }^{-})$ and calculate some of the asymmetry parameters that characterize the joint angular decay distribution. We confirm expectations from the naive quark model that the transitions into the ${\lambda }_{\Lambda }=1/2$ helicity states of the daughter baryon $\Lambda$ are strongly suppressed leading to a near maximal negative polarization of the $\Lambda$. For the same reason the azimuthal correlation between the two decay planes spanned by ($p{\pi }^{-}$) and (${\ell }^{+}{\ell }^{-}$) is negligibly small. We provide form factor results for the whole accessible $q^2$ range. Our results are close to lattice results at minimum recoil and light-cone sum rule results at maximum recoil. A new feature of our analysis is that we include lepton mass effects in the calculation, which allows us to also describe the cascade decay ${\Lambda }_b\to \Lambda (\to p{\pi }^{-})+\psi (2S)(\to {\tau }^{+}{\tau }^{-})$.

We perform the transverse-momentum resummation for $W^{+}{W}^{-}$, $ZZ$, and $W^{\pm }Z$ pair productions at the next-to-next-to-leading logarithmic accuracy using soft-collinear effective theory for $\sqrt{S}=8\mathrm{TeV}$ and $\sqrt{S}=14\mathrm{TeV}$ at the LHC, respectively. Importantly, this is the first calculation of $W^{\pm }Z$ transverse-momentum resummation. We also include the nonperturbative effects and discussions on the PDF uncertainties. Comparing with the next-to-leading logarithmic results, the next-to-next-to-leading logarithmic resummation can reduce the dependence of the transverse-momentum distribution on the factorization scales significantly. Finally, we find that our numerical results are consistent with data measured by the CMS Collaboration for the $ZZ$ production, which have thus far only been reported by the LHC experiments for the unfolded transverse-momentum distribution of the gauge boson pair production within theoretical and experimental uncertainties.

We study a few $\Delta F=2$ and $\Delta F=1$ flavor-changing neutral current processes in the minimal 3-3-1 model by considering, besides the neutral vector bosons $Z^{\prime }$, the effects due to one $CP$-even and one $CP$-odd scalar. We find that there are processes in which the interference among all the neutral bosons is constructive or destructive and in others the interference is negligible. We first obtain numerical values for all the unitary matrices that rotate the left- and right-handed quarks and give the correct mass of all the quarks in each charge sector and the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix.

Similar to the superradiant effect in Reissner-Nordström black holes, a charged scalar field can be amplified when impinging on the charged black hole in string theory. According to the black-hole bomb mechanism, the mass term of the incident field can work as the reflecting mirror, which may trigger the instability of the black hole. We study the possible instability triggered by superradiant effects and demonstrate that the charged black hole in string theory is stable against the massive charged scalar perturbation. The reason is that there is no trapping potential well in the black hole exterior, which is separated from the horizon by a potential barrier, and there are no bound states in the superradiant regime.

In this paper, we loosen the zero equation of state of dark matter to a constant $w_{dm}$. By using the currently available cosmic observations, which include the type-Ia supernovae, the baryon acoustic oscillation, the WiggleZ measurements of matter power spectrum, and the cosmic microwave background radiation from the firs release of Planck data through the Markov chain Monte Carlo method, we found the equation of state of dark matter in $3\sigma$ regions: $w_{dm}={0.000707}_{-0.000747-0.00149-0.00196}^{+0.000746+0.00146+0.00193}$. The difference between the minimum of ${\chi }^2$ between the $\Lambda \mathrm{CDM}$ and $\Lambda \mathrm{wDM}$ models is $\Delta {\chi }_{\min }^2=0.446$ for one extra model parameter $w_{dm}$. Although the currently available cosmic observations favor the $\Lambda \mathrm{wDM}$ mildly, no significant deviation from the $\Lambda \mathrm{CDM}$ model is found in $1\sigma$ regions.

We present a simple analytic gravitational solution which describes the holographic dual of a ($2+1$)-dimensional conductor which goes beyond the usual linear response. In particular it includes Joule heating. We find that the nonlinear frequency-dependent conductivity is a constant. Surprisingly, the pressure remains isotropic. We also apply an electric field to a holographic insulator and show that there is a maximum electric field below which it can remain an insulator. Above this critical value, we argue that it becomes a conductor due to pair creation of charged particles. Finally, we study ($1+1$)- and ($3+1$)-dimensional conductors at the nonlinear level; here exact solutions are not available and a perturbative analysis shows that the current becomes time dependent, but in a way that is captured by a time-dependent effective temperature.

We study thermodynamics of entanglement entropy for weakly excited states in certain nonconformal field theories, whose gravity duals are given by nonconformal Dp-branes. We observe that the entanglement entropy of a sufficiently small system in nonconformal backgrounds still obeys a first-law-like relation, just as the anti–de Sitter counterparts investigated in [J. Bhattacharya, M. Nozaki, T. Takayanagi, and T. Ugajin, Phys. Rev. Lett. 110, 091602 (2013)]. The effective temperature is proportional to the inverse of the size of the subsystem. The proportionality is a dimensionless constant which is only determined by the shape of the entangling region and independent of any coupling. This universality is confirmed by working with the 10-dimensional string frame metric as well as the lower-dimensional effective metric. When the entangling region is a strip and translational invariance is broken by metric fluctuations, we derive a first-law-like relation where additional components of the stress energy tensor are involved.

Diverse calculations have shown that a relativistic field confined to a cavity by well-defined boundary conditions can have a negative Casimir or vacuum energy. Why then can one not make a finite system with negative mass by confining the field in some way? We recall, and justify in detail, the not so familiar subdominant trace energy condition for ordinary (baryon-electron nonrelativistic) matter. With its help we show, in two ways, that the mass energy of the cavity structure necessary to enforce the boundary conditions must exceed the magnitude of the negative vacuum energy, so that all systems of the type envisaged necessarily have positive mass energy.

We investigate the three-point correlation functions of Yang-Mills theory in the Landau gauge, with a particular emphasis on the infrared regime. The effect of the Gribov copies is accounted for by adding a mass term for the gluons in the Faddeev-Popov action in the Landau gauge. We perform a one-loop calculation for the ghost-antighost-gluon and three-gluon correlation functions. These analytic results are compared with the available lattice data and give a very satisfying agreement.

We extract gravitational waveforms from numerical simulations of black hole binaries computed using the Spectral Einstein Code. We compare two extraction methods: direct construction of the Newman-Penrose (NP) scalar ${\Psi }_4$ at a finite distance from the source and Cauchy-characteristic extraction (CCE). The direct NP approach is simpler than CCE, but NP waveforms can be contaminated by near-zone effects—unless the waves are extracted at several distances from the source and extrapolated to infinity. Even then, the resulting waveforms can in principle be contaminated by gauge effects. In contrast, CCE directly provides, by construction, gauge-invariant waveforms at future null infinity. We verify the gauge invariance of CCE by running the same physical simulation using two different gauge conditions. We find that these two gauge conditions produce the same CCE waveforms but show differences in extrapolated-${\Psi }_4$ waveforms. We examine data from several different binary configurations and measure the dominant sources of error in the extrapolated-${\Psi }_4$ and CCE waveforms. In some cases, we find that NP waveforms extrapolated to infinity agree with the corresponding CCE waveforms to within the estimated error bars. However, we find that in other cases extrapolated and CCE waveforms disagree, most notably for $m=0$ “memory” modes.

Inspired by the condensed matter analogues of black holes (a.k.a. dumb holes), we study Hawking radiation in the presence of a modified dispersion relation which becomes superluminal at large wave numbers. In the usual stationary coordinates $(t,x)$, one can describe the asymptotic evolution of the wave packets in WKB, but this WKB approximation breaks down in the vicinity of the horizon, thereby allowing for a mixing between initial and final creation and annihilation operators. Thus, one might be tempted to identify this point where WKB breaks down with the moment of particle creation. However, using different coordinates $(\tau ,U)$, we find that one can evolve the waves so that WKB in these coordinates is valid throughout this transition region, which contradicts the above identification of the breakdown of WKB as the cause of the radiation. Instead, our analysis suggests that the tearing apart of the waves into two different asymptotic regions (inside and outside the horizon) is the major ingredient of Hawking radiation.