We study the large-$N_c$ behavior of the critical temperature $T_c$ for chiral symmetry restoration in the framework of the Nambu-Jona-Lasinio model and the linear $\sigma$ model. While in the Nambu-Jona-Lasinio case $T_c$ scales as $N_c^0$ and is, as expected, of the same order as ${\Lambda }_{\mathrm{QCD}}$ (just as the deconfinement phase transition), in the $\sigma$ model the scaling behavior reads $T_c\propto N_c^{1/2}$. We investigate the origin of the different scaling behavior and present two improvements of the $\sigma$ model: (i) a simple, phenomenologically motivated temperature dependence of the parameters and (ii) the coupling to the Polyakov loop. Both approaches lead to the scaling $T_c\propto N_c^0$.

We propose an extension to the standard model where three exotic fermion 5-plets and one scalar 6-plet are added to the particle content. By demanding that all interactions are renormalizable and standard model gauge invariant, we show that the lightest exotic particle in this model can be a dark matter candidate as long as the new 6-plet scalar does not develop a nonzero vacuum expectation value. Furthermore, light neutrino masses are generated radiatively at one-loop while the baryon asymmetry is produced by the $CP$-violating decays of the second lightest exotic particle. We have demonstrated using concrete examples that there is a parameter space where a consistent solution to the problems of baryon asymmetry, dark matter and neutrino masses can be obtained.

We propose a supersymmetric extension of the minimal $B-L$ model where we consider a new $Z_2$-parity under which one right-handed neutrino is assigned odd parity. When the Majorana Yukawa coupling of a $Z_2$-even right-handed neutrino is large, radiative corrections will drive the mass squared of the corresponding right-handed sneutrino to negative values, breaking the $B-L$ gauge symmetry at the TeV scale in a natural way. Additionally, R-parity is broken and thus the conventional supersymmetric dark matter candidate, the neutralino, is no longer viable. Thanks to the $Z_2$-parity, the $Z_2$-odd right-handed neutrino remains a stable dark matter candidate even in the presence of R-parity violation. We demonstrate that the dark matter relic abundance with an enhanced annihilation cross-section by the $B-L$ gauge boson ($Z^{\prime }$) resonance is in accord with the current observations. Therefore, it follows that the mass of this dark matter particle is close to half of the $Z^{\prime }$ boson mass. If the $Z^{\prime }$ boson is discovered at the Large Hadron Collider (LHC), it will give rise to novel probes of dark matter: The observed $Z^{\prime }$ boson mass will delineate a narrow range of allowed dark matter mass. If the $Z^{\prime }$ boson decays to a pair of dark matter particles, a precise measurement of the invisible decay width can reveal the existence of the dark matter particle.

We have been studying QCD with 2 flavors of color-sextet quarks to distinguish whether it is QCD-like or conformal. For comparison, we are now studying QCD with 3 flavors of color-sextet quarks, which is believed to be conformal in the chiral limit. Here, we present the results of simulations of lattice QCD with 3 color-sextet quarks at finite temperatures on lattices of temporal extent $N_t=4$ and 6, with masses small enough to yield access to the chiral limit. As for the 2-flavor case, we find well-separated deconfinement and chiral-symmetry restoration transitions, both of which move to appreciably weaker couplings as $N_t$ is increased from 4 to 6. If this theory is conformal, we would expect there to be a bulk chiral transition at a fixed coupling. For this reason, we conclude that for $N_t=4$ and 6, the chiral and hence the deconfinement transitions are in the strong-coupling domain where the theory is essentially quenched. The similarity between the behaviors of the 2- and 3-flavor theories suggested that the $N_t=4$ and 6 transitions for the 2-flavor theory also lie in the strong-coupling domain. The phase structure of both theories is very similar.

We analyze the phase diagram of hot quark matter in presence of an axial chemical potential, ${\mu }_5$. The latter is introduced to mimic the chirality transitions induced, in hot quantum chromodynamics, by the strong sphaleron configurations. In particular, we study the curvature of the critical line at small ${\mu }_5$, the effects of a finite quark mass and of a vector interaction. Moreover, we build the mixed phase at the first order phase transition line and draw the phase diagram in the chiral density and temperature plane. We finally compute the full topological susceptibility in presence of a background of topological charge.

An improved generalized suppression factor for gluon emission off a heavy quark is derived within perturbative QCD, which is valid for the full range of rapidity of the radiated gluon and also has no restriction on the scaled mass of the quark with its energy. In the appropriate limit, it correctly reproduces the usual dead cone factor in the forward rapidity region. On the other hand, this improved suppression factor becomes close to unity in the backward direction. This indicates a small suppression of gluon emission in the backward region, which should have an impact on the phenomenology of heavy quark energy loss in the hot and dense matter produced in ultrarelativistic heavy ion collisions.

We present a tetraquark interpretation of the charged bottomonium-like states $Z_b^{\pm }(10610)$ and $Z_b^{\pm }(10650)$, observed by the Belle collaboration in the ${\pi }^{\pm }{\rm Y}(nS)$ $(n=1,2,3)$ and ${\pi }^{\pm }{h}_b(mP)$ $m=1$, 2) invariant mass spectra from the data taken near the peak of the ${\rm Y}(5S)$. In this framework, the underlying processes involve the production and decays of a vector tetraquark $Y_b(10890)$, $e^{+}{e}^{-}\to Y_b(10890)\to [Z_b^{\pm }(10610){\pi }^{\mp },Z_b^{\pm }(10650){\pi }^{\mp }]$ followed by the decays $[Z_b^{\pm }(10610),Z_b^{\pm }(10650)]\to {\pi }^{\pm }{\rm Y}(nS),{\pi }^{\pm }{h}_b(mP)$. Combining the contributions from the meson loops and an effective Hamiltonian, we are able to reproduce the observed masses of the $Z_b^{\pm }(10610)$ and $Z_b^{\pm }(10650)$. The analysis presented here is in agreement with the Belle data and provides crucial tests of the tetraquark hypothesis. We also calculate the corresponding meson-loop effects in the charm sector and find them dynamically suppressed. The charged charmonium-like states $Z_c^{\pm }(3752)$ and $Z_c^{\pm }(3882)$ can be searched for in the decays of the $J^{PC}=1^{--}$ tetraquark state $Y(4260)$ via $Y(4260)\to Z_c^{\pm }(3752){\pi }^{\mp }$ and $Y(4260)\to Z_c^{\pm }(3882){\pi }^{\mp }$, with the subsequent decays $(Z_c^{\pm }(3752),Z_c^{\pm }(3882))\to (J/\psi ,h_c){\pi }^{\pm }$.

We study the energy spectrum of the inclusive bottom-flavored mesons in top-quark decay into a charged-Higgs boson and a massless bottom quark at next-to-leading order (NLO) in the two-Higgs-doublet model. To extract the result we work in the Zero-Mass Variable-Flavor-Number scheme (ZM-VFNs) using realistic nonperturbative fragmentation functions obtained through a global fit to $e^{+}{e}^{-}$ data from CERN LEP1 and SLAC SLC on the Z-boson resonance. We study both the contribution of the bottom quark fragmentation and the gluon fragmentation to produce the bottom-flavored meson ($B$-Meson). We find that the contribution of the gluon leads to an appreciable reduction in decay rate at low values of the $B$-meson energy. It means the NLO corrections are significant.

We search for the $Z_1(4050{)}^{+}$ and $Z_2(4250{)}^{+}$ states, reported by the Belle Collaboration, decaying to ${\chi }_{c1}{\pi }^{+}$ in the decays ${\overline{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ and $B^{+}\to {\chi }_{c1}{K}_S^0{\pi }^{+}$ where ${\chi }_{c1}\to J/\psi \gamma$. The data were collected with the BABAR detector at the SLAC PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider operating at center-of-mass energy 10.58 GeV, and correspond to an integrated luminosity of $429{\mathrm{fb}}^{-1}$. In this analysis, we model the background-subtracted, efficiency-corrected ${\chi }_{c1}{\pi }^{+}$ mass distribution using the $K\pi$ mass distribution and the corresponding normalized $K\pi$ Legendre-polynomial moments, and then test the need for the inclusion of resonant structures in the description of the ${\chi }_{c1}{\pi }^{+}$ mass distribution. No evidence is found for the $Z_1(4050{)}^{+}$ and $Z_2(4250{)}^{+}$ resonances, and 90% confidence level upper limits on the branching fractions are reported for the corresponding $B$-meson decay modes.

Exclusive quarkonium photo- and electro-production off the nucleon is studied in the framework of generalized parton distributions (GPDs). The short-distance part of the process is treated at leading order in perturbative Quantum Chromodynamics. The main focus is on the GPD $E$ for gluons. On the basis of different models for $E^g$ we estimate the transverse target spin asymmetry for typical kinematics of a future Electron Ion Collider. We also explore the potential of measuring the polarization of the recoil nucleon.

Cosmological $N$-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic Friedmann-Lemaître-Robinson-Walker cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed [S. R. Green and R. M. Wald, Phys. Rev. D 83, 084020 (2011).], which allows for such nonlinearity at small scales. We propose a relatively straightforward dictionary—which is exact at the linearized level—that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our “ordering scheme” to determine the degree to which the resulting metric and matter distribution solve Einstein’s equation. We find that, within our ordering scheme, Einstein’s equation fails to hold at “order 1” at small scales and at “order $ϵ$” at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein’s equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations to describe relativistic cosmologies, even on scales larger than the Hubble radius.

Astrophysical neutrinos are expected to be produced in the interactions of ultrahigh energy cosmic rays with surrounding photons. The fluxes of the astrophysical neutrinos are highly dependent on the characteristics of the cosmic-ray sources, such as their cosmological distributions. We study possible constraints on the properties of cosmic-ray sources in a model-independent way using experimentally obtained diffuse neutrino flux above 100 PeV. The semianalytic formula is derived to estimate the cosmogenic neutrino fluxes as functions of source evolution parameter and source extension in redshift. The obtained formula converts the upper limits on the neutrino fluxes into the constraints on the cosmic-ray sources. It is found that the recently obtained upper limit on the cosmogenic neutrinos by IceCube constrains the scenarios with strongly evolving ultrahigh energy cosmic-ray sources, and the future limits from a $1{\mathrm{km}}^3$ scale detector are able to further constrain the ultrahigh energy cosmic-rays sources with evolutions comparable to the cosmic star formation rate.

We propose a scheme to investigate whether nonuniform motion degrades entanglement of a relativistic quantum field that is localized both in space and in time. For a Dirichlet scalar field in a cavity in Minkowski space, in small but freely adjustable acceleration of finite but arbitrarily long duration, degradation of observable magnitude occurs for massless transverse quanta of optical wavelength at Earth gravity acceleration and for kaon mass quanta already at microgravity acceleration. We outline a space-based experiment for observing the effect and its gravitational counterpart.

Lin and Liu evaluate the nucleon expectation value of the non-gauge-invariant canonical quark momentum operator on a lattice and obtain zero. They conclude that my argument that, despite the non-gauge-invariance of the operator, its physical matrix elements are gauge-invariant cannot be correct. I show that their result has no bearing on the question of gauge-invariance and also point to an amusing lattice paradox.

It is argued by the author that the canonical form of the quark energy-momentum tensor with a partial derivative instead of the covariant derivative is the correct definition for the quark momentum and angular momentum fraction of the nucleon in covariant quantization. Although it is not manifestly gauge-invariant, its matrix elements in the nucleon will be nonvanishing and are gauge-invariant. We test this idea in the path-integral quantization by calculating correlation functions on the lattice with a gauge-invariant nucleon interpolation field and replacing the gauge link in the quark lattice momentum operator with unity, which corresponds to the partial derivative in the continuum. We find that the ratios of three-point to two-point functions are zero within errors for both the $u$ and $d$ quarks, contrary to the case without setting the gauge links to unity.

We apply a self-consistent relativistic mean-field variational “Gaussian functional” (or optimized one-loop perturbation theory, or $\mathrm{Hartree}+\mathrm{RPA}$) approximation to the extended $N_f=2$ linear $\sigma$ model with spontaneously and explicitly broken chiral $\mathrm{S}{\mathrm{U}}_{\mathrm{R}}(2)\times \mathrm{S}{\mathrm{U}}_{\mathrm{L}}(2)\times {\mathrm{U}}_{\mathrm{A}}(1)\equiv \mathrm{O}(4)\times \mathrm{O}(2)$ symmetry. We set up the self-consistency, or gap equations that dress up the bare fields with “cactus tree” loop diagrams, and the Bethe-Salpeter equations that provide further dressing with one-loop irreducible diagrams. In a previous publication [V. Dmitrašinović and I. Nakamura, J. Math. Phys. (N.Y.) 44, 2839 (2003).] we have already shown the ability of this approximation to create composite (i.e., bound and/or resonance) states. With explicit $\mathrm{S}{\mathrm{U}}_{\mathrm{R}}(2)\times \mathrm{S}{\mathrm{U}}_{\mathrm{L}}(2)\times {\mathrm{U}}_{\mathrm{A}}(1)$ chiral symmetry breaking first we consider how the ${\mathrm{U}}_{\mathrm{A}}(1)$ symmetry induced scalar-pseudoscalar meson mass relation that is known to hold in fermionic chiral models is modified by the bosonic gap equations. Then we solve the gap and Bethe-Salpeter equations numerically and discuss the solutions’ properties and the particle content of the theory. We show that in the strong-coupling regime two, sometimes even three solutions to the $\eta$ meson channel Bethe-Salpeter equation may coexist.

In this paper we study the decoherence of the semiclassical branches of an accelerated universe. We use a third quantization formalism to analyze the decoherence between two branches of a parent universe caused by their interaction with the vacuum fluctuations of the space-time and with other parent universes in a multiverse scenario.

We explore the model-independent constraints from cosmology on a dark-matter particle with no prominent standard model interactions that interacts and thermalizes with other particles in a hidden sector. Without specifying detailed hidden-sector particle physics, we characterize the relevant physics by the annihilation cross-section, mass, and temperature ratio of the hidden-to-visible sectors. While encompassing the standard cold weakly interacting massive particle (WIMP) scenario, we do not require the freeze-out process to be nonrelativistic. Rather, freeze-out may also occur when dark-matter particles are semirelativistic or relativistic. We solve the Boltzmann equation to find the conditions that hidden-sector dark matter accounts for the observed dark-matter density, satisfies the Tremaine-Gunn bound on dark-matter phase-space density, and has a free-streaming length consistent with cosmological constraints on the matter power spectrum. We show that for masses $\lesssim 1.5\mathrm{keV}$, no region of parameter space satisfies all these constraints. This is a gravitationally mediated lower bound on the dark-matter mass for any model in which the primary component of dark matter once had efficient interactions—even if it has never been in equilibrium with the standard model.

Exclusive diffractive production of real photons and vector mesons in $ep$ collisions has been studied at HERA in a wide kinematic range. Here we present and discuss a Regge-type model of real photon production (deeply virtual Compton scattering), as well as production of vector mesons treated on the same footing by using an extension of a factorized Regge-pole model proposed earlier. The model has been fitted to the HERA data. Despite the very small number of the free parameters, the model gives a satisfactory description of the experimental data, both for the total cross section as a function of the photon virtuality $Q^2$ or the energy $W$ in the center of mass of the ${\gamma }^{*}p$ system, and the differential cross sections as a function of the squared four-momentum transfer $t$ with fixed $Q^2$ and $W$.

The heavy fourth-generation Majorana neutrino can be stable and contribute to a small fraction of the relic density of dark matter (DM) in the Universe. Because of its strong coupling to the standard model particles, it can be probed by the current direct and indirect DM detection experiments even it is a subdominant component of the whole halo DM. Assuming that it contributes to the same fraction of the local halo DM density as that of the DM relic density in the Universe, we show that the current Xenon100 data constrain the mass of the stable Majorana neutrino to be greater than the mass of the top quark. In the mass range from 200 GeV to a few hundred GeV, the effective spin-independent cross section for the neutrino elastic-scattering off nucleon is insensitive to the neutrino mass and mixing, and is predicted to be $\sim 1.5\times {10}^{-44}{\mathrm{cm}}^2$, which can be reached by the direct DM detection experiments soon. In the same mass region the predicted effective spin-dependent cross section for the heavy neutrino scattering off proton is in the range of $2\times {10}^{-40}{\mathrm{cm}}^2\sim 2\times {10}^{-39}{\mathrm{cm}}^2$, which is within the reach of the ongoing DM indirect search experiments such as IceCube. We demonstrate such properties of the heavy neutrino DM in a fourth-generation model with the stability of the fourth Majorana neutrino protected by an additional generation-dependent $U(1)$ gauge symmetry.