The varying speed of light theory is controversial. It succeeds in explaining some cosmological problems, but, on the other hand, it is excluded by mainstream physics because it will shake the foundation of physics. In the present paper, we devote ourselves to testing whether the speed of light is varying from the observational data of the type Ia supernova, baryon acoustic oscillation, observational $H(z)$ data, and cosmic microwave background. We select the common form $c(t)=c_0{a}^n(t)$ with the contribution of dark energy and matter, where $c_0$ is the current value of speed of light and $n$ is a constant, and consequently we construct a varying speed of light dark energy model (VSLDE). The combined observational data show a trivial constraint $n=-0.0033\pm 0.0045$ at 68.3% confidence level, which indicates that the speed of light may be a constant with high significance. By reconstructing the time variable $c(t)$, we find that the speed of light almost has no variation for redshift $z<{10}^{-1}$. For high-$z$ observations, they are more sensitive to the VSLDE model, but the variation of speed of light is only in order of ${10}^{-2}$. We also introduce the geometrical diagnostic $Om(z)$ to show the difference between the VSLDE and $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) models. The result shows that the current data make it difficult to differentiate them. All the results show that the observational data favor the constant speed of light.

One of the primary objectives for pulsar timing arrays (PTAs) is to detect a stochastic background generated by the incoherent superposition of gravitational waves (GWs), in particular from the cosmic population of supermassive black hole binaries. Current stochastic background searches assume that pulsars in a PTA are separated from each other and the Earth by many GW wavelengths. As more millisecond pulsars are discovered and added to PTAs, some may be separated by only a few radiation wavelengths or less, resulting in correlated GW phase changes between close pulsars in the array. Here we investigate how PTA overlap reduction functions (ORFs), up to quadrupole order, are affected by these additional correlated phase changes, and how they are in turn affected by relaxing the assumption that all pulsars are equidistant from the solar system barycenter. We find that in the low-frequency GW background limit of $f\sim {10}^{-9}\mathrm{Hz}$, and for pulsars at varying distances from the Earth, these additional correlations only affect the ORFs by a few percent for pulsar pairs at large angular separations, as expected. However, when nearby (order 100 pc) pulsars are separated by less than a few degrees, the correlated phase changes can introduce variations of a few tens of percent in the magnitude of the isotropic ORF, and much larger fractional differences in the anisotropic ORFs—up to 188 in the $m=0$, $l=2$ ORF for equidistant pulsars separated by 3°. In fact, the magnitude of most of the anisotropic ORFs is largest at small, but nonzero, pulsar separations. Finally, we write down a small angle approximation for the correlated phase changes which can easily be implemented in search pipelines, and for completeness, examine the behavior of the ORFs for pulsars which lie at a radiation wavelength from the Earth.

Near the tip of the $\tilde{\tau }$ coannihilation strip in the CMSSM with a neutralino lightest supersymmetric particle $\chi$, the astrophysical cold dark matter density constraint forces the $\tilde{\tau }-\chi$ mass difference to be small. If this mass difference is smaller than $m_{\tau }$, the $\tilde{\tau }$ may decay either in the outer part of an LHC detector—the “disappearing track” signature—or be sufficiently long-lived to leave the detector before decaying—the long-lived massive charged-particle signature. We combine searches for these signatures with conventional $E_T^{\text{miss}}$ searches during LHC Run 1, identifying the small remaining parts of the CMSSM $\tilde{\tau }$ coannihilation strip region that have not yet been excluded and discussing how they may be explored during Run 2 of the LHC.

The simplest renormalizable effective field theories with asymmetric dark matter bound states contain two additional gauge singlet fields, one being the dark matter and the other a mediator particle that the dark matter annihilates into. We examine the physics of one such model with a Dirac fermion as the dark matter and a real scalar mediator. For a range of parameters the Yukawa coupling of the dark matter to the mediator gives rise to stable asymmetric dark matter bound states. We derive properties of the bound states including nuggets formed from $N\gg 1$ dark matter particles. We also consider the formation of bound states in the early Universe and direct detection of dark matter bound states. Many of our results also hold for symmetric dark matter.

We study models in which the Higgs sector is extended by a single scalar electroweak multiplet $Z$ with isospin $T=5/2$ (sextet) or $7/2$ (octet) and the same hypercharge as the Standard Model Higgs doublet, in which $Z$ is odd under a global $Z_2$ symmetry. This $Z_2$ symmetry keeps the lightest (neutral) member of $Z$ stable and has interesting implications for phenomenology. We determine the constraints on these models from precision electroweak measurements and Higgs boson decays to two photons. We compute the thermal relic density of the stable member of $Z$ and show that, for masses below 1 TeV, it can make up at most 1% of the dark matter in the Universe. We also show that current dark matter direct detection experiments do not constrain the models, but future ton-scale experiments will probe their parameter space.

We present the calculations of the production of $\widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$ in the minimal supersymmetric standard model at the Large Hadron Collider at center-of-mass energies of 7 and 14 TeV. We discuss the impact of the next-to-leading-order supersymmetric-QCD corrections on the cross sections of $\widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$ production and on the transverse-momentum distributions of the final stop quark. The uncertainties of the leading-order and supersymmetric-QCD corrected cross sections due to the renormalization/factorization scale are studied. Calculations demonstrate that the next-to-leading-order supersymmetric-QCD corrections improve the scale dependence of the leading-order cross sections and enhance significantly the transverse-momentum distributions.

To date the magnetic radius of the proton has been determined only by means of electron-proton scattering, which is not free of controversies. Any existing atomic determinations are irrelevant because they are strongly model dependent. We consider a so-called Zemach contribution to the hyperfine interval in ordinary and muonic hydrogen and derive a self-consistent model-independent value of the magnetic radius of the proton. More accurately, we constrain not a value of the magnetic radius by itself, but its certain combination with the electric-charge radius of the proton, namely, $R_E^2+R_M^2$. The result from the ordinary hydrogen is found to be $R_E^2+R_M^2=1.35(12){\mathrm{fm}}^2$, while the derived muonic value is $1.49(18){\mathrm{fm}}^2$. That allows us to constrain the value of the magnetic radius of proton $R_M=0.78(8)\mathrm{fm}$ at the 10% level.

Recently a high-precision measurement of the Lamb shift in muonic hydrogen has been performed. An accurate value of the proton charge radius can be extracted from this datum with a high accuracy. To do that a sufficient accuracy should be achieved also on the theoretical side, including an appropriate treatment of higher-order proton-structure effects. Here we consider a higher-order contribution of the finite size of the proton to the Lamb shift in muonic hydrogen. Only model-dependent results for this correction have been known up to date. Meanwhile, the involved models are not consistent either with the existing experimental data on the electron-proton scattering or with the value for the electric charge radius of the proton extracted from the Lamb shift in muonic hydrogen. We consider the higher-order contribution of the proton finite size in a model-independent way and eventually derive a self-consistent value of the electric radius of the proton. The reevaluated value of the proton charge radius is found to be $R_E=0.84022(56)\mathrm{fm}$.

Using $2.25\times 10^{8}J/\psi$ events collected with the BESIII detector at the BEPCII storage rings, we observe for the first time the process $J/\psi \to p\overline{p}{a}_0(980)$, $a_0(980)\to {\pi }^0\eta$ with a significance of $6.5\sigma$ ($3.2\sigma$ including systematic uncertainties). The product branching fraction of $J/\psi \to p\overline{p}{a}_0(980)\to p\overline{p}{\pi }^0\eta$ is measured to be $(6.8\pm 1.2\pm 1.3)\times 10^{-5}$, where the first error is statistical and the second is systematic. This measurement provides information on the $a_0$ production near threshold coupling to $p\overline{p}$ and improves the understanding of the dynamics of $J/\psi$ decays to four-body processes.

We evaluate the contribution to $N_{\text{eff}}$ of the extra sterile states in low-scale type I seesaw models (with three extra sterile states). We explore the full parameter space and find that at least two of the heavy states always reach thermalization in the early Universe, while the third one might not thermalize provided the lightest neutrino mass is below $\mathcal{O}({10}^{-3}\mathrm{eV})$. Constraints from cosmology therefore severely restrict the spectra of heavy states in the range 1 eV–100 MeV. The implications for neutrinoless double beta decay are also discussed.

Entanglement is defined between subsystems of a quantum system, and at fixed time two regions of space can be viewed as two subsystems of a relativistic quantum field. The entropy of entanglement between such subsystems is ill-defined unless an ultraviolet cutoff is introduced, but it still diverges in the continuum limit. This behavior is generic for arbitrary finite-energy states, hence a conceptual tension with the finite entanglement entropy typical of nonrelativistic quantum systems. We introduce a novel approach to explain the transition from infinite to finite entanglement, based on coarse graining the spatial resolution of the detectors measuring the field state. We show that states with a finite number of particles become localized, allowing an identification between a region of space and the nonrelativistic degrees of freedom of the particles therein contained, and that the renormalized entropy of finite-energy states reduces to the entanglement entropy of nonrelativistic quantum mechanics.

The recent detection of the B-mode polarization from the BICEP2 observation, if confirmed to be primordial, seems to be in tension with the upper bound on the amplitude of tensor perturbations from the PLANCK data. We consider a phenomenological model of inflation in which the microscopical properties of the inflationary fluid such as the equation of state $w$ or the sound speed $c_s$ jump in a sharp manner. We show that the amplitude of the scalar perturbations is controlled by a nontrivial combination of $w$ and $c_s$ before and after the phase transition while the tensor perturbations remains nearly intact. With an appropriate choice of the fluid parameters $w$ and $c_s$ one can suppress the scalar perturbation power spectrum on large scales to accommodate a large tensor amplitude.

Within the confined isospin- and density-dependent mass model, we study the properties of strange quark matter (SQM) and quark stars (QSs) in strong magnetic fields. The equation of state of SQM under a constant magnetic field is obtained self-consistently and the pressure perpendicular to the magnetic field is shown to be larger than that parallel to the magnetic field, implying that the properties of magnetized QSs generally depend on both the strength and the orientation of the magnetic fields distributed inside the stars. Using a density-dependent magnetic field profile which is introduced to mimic the magnetic field strength distribution in a star, we study the properties of static spherical QSs by assuming two extreme cases for the magnetic field orientation in the stars, i.e., the radial orientation in which the local magnetic fields are along the radial direction, and the transverse orientation in which the local magnetic fields are randomly oriented but perpendicular to the radial direction. Our results indicate that including the magnetic fields with radial (transverse) orientation can significantly decrease (increase) the maximum mass of QSs, demonstrating the importance of the magnetic field orientation inside the magnetized compact stars.

Vertices describe the interactions between the fundamental degrees of freedom and are therefore of vital importance in many ab initio descriptions of field theory, especially using functional methods. To this end, we present the first lattice study of the thermal behavior of (minimal) Landau-gauge SU(2) Yang-Mills three-point functions, i.e., three-gluon and ghost-gluon vertices. Focusing on the chromomagnetic sector, we find that the phase transition mainly affects the three-gluon vertex, while the ghost-gluon vertex is relatively inert.

We search for infrared zeros of the beta function and evaluate the anomalous dimension of the mass at the associated fixed point for asymptotically free vectorlike fermionic gauge theories with gauge group $SU(N)$. The fixed points of the beta function are studied at the two, three and four loop level in two different explicit schemes. These are the modified regularization invariant scheme and the minimal momentum subtraction scheme. The search is performed in Landau gauge where the beta function of the gauge parameter vanishes. We then compare our findings to earlier identical investigations performed in the modified minimal subtraction scheme. It is found that the value of the anomalous dimension of the mass is smaller at three and four loops than at two loops. This seems to be a generic pattern that is observed in all three different schemes. We then estimate the value of the anomalous dimension to be $\gamma \sim 0.225–0.375$ for twelve fundamental flavors and three colors, $\gamma \sim 0.500–0.593$ for two adjoint flavors and two colors and finally $\gamma \sim 1.12–1.70$ for two two-indexed flavors and three colors with the lower and upper bound set by the minimum and maximum value respectively over all three schemes and at three and four loops. Our analysis suggests that the former two theories lie in the conformal window while the latter belongs to the chirally broken phase.

We formulate a scale-invariant hidden local symmetry (HLS) as a low-energy effective theory of walking technicolor (WTC) which includes the technidilaton, technipions, and technirho mesons as the low-lying spectra. As a benchmark for LHC phenomenology, we in particular focus on the one-family model of WTC having eight technifermion flavors, which can be—at energy scales relevant to the reach of the LHC—described by the scale-invariant HLS based on the manifold $[\mathrm{SU}(8{)}_L\times \mathrm{SU}(8{)}_R{]}_{\text{global}}\times \mathrm{SU}(8{)}_{\text{local}}/\mathrm{SU}(8{)}_V$, where $\mathrm{SU}(8{)}_{\text{local}}$ is the HLS and the global $\mathrm{SU}(8{)}_L\times \mathrm{SU}(8{)}_R$ symmetry is partially gauged by the $\mathrm{SU}(3)\times \mathrm{SU}(2{)}_L\times U(1{)}_Y$ of the standard model. Based on the scale-invariant HLS, we evaluate the coupling properties of the technirho mesons and place limits on the masses from the current LHC data. Then, implications for future LHC phenomenology are discussed by focusing on the technirho mesons produced through the Drell-Yan process. We find that the color-octet technirho decaying to the technidilaton along with the gluon is of interest as the discovery channel at the LHC, which would provide a characteristic signature to probe the one-family WTC.

We discuss the expected sensitivity to $Z^{\prime }$ boson effects in the $W^{\pm }$ boson pair production process at the Large Hadron Collider (LHC). The results of a model-dependent analysis of $Z^{\prime }$ boson effects are presented as constraints on the $Z\text{−}{Z}^{\prime }$ mixing angle $\varphi$ and $Z^{\prime }$ boson mass. The process $pp\to W^{+}{W}^{-}+X$ allows us to place stringent constraints on the $Z\text{−}{Z}^{\prime }$ mixing angle. Specifically, we find that the present LHC bounds on the mixing angle are of the order a few times ${10}^{-3}$, which is of the same order as those derived from the electroweak data. These results were derived from analysis of $W$-pair production at $\sqrt{s}=8\mathrm{TeV}$ and integrated luminosity of $20{\mathrm{fb}}^{-1}$. Further improvement on the constraining of this mixing can be achieved from the analysis of data on $WW\to l\nu l^{\prime }{\nu }^{\prime }$ ($l,l^{\prime }=e$ or $\mu$) and $WW\to l\nu jj$ final states collected at the LHC with nominal energy and luminosity, 14 TeV and $100{\mathrm{fb}}^{-1}$, and should be $\varphi \sim {10}^{-4}–{10}^{-3}$.

A theoretical analysis has been performed of the HERMES semi-inclusive deep inelastic data on the difference between ${\pi }^{+}$ and ${\pi }^{-}$ multiplicities. It turns out that the application of a standard perturbative QCD analysis, using, as usual, isospin symmetry for the fragmentation functions, leads to a poor description of the deuteron data at small $z$ values. If one allows a breaking of isospin invariance, a good fit to both proton and deuteron data can be achieved for all measured $z$, but the level of isospin violation, especially at small values of $z$, is simply not credible. We suspect that the problem is a consequence of using the factorized QCD treatment in a kinematic region where it is unjustified.

We apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute to all orders in nuclear opacity the non-Abelian gluon bremsstrahlung of event-by-event fluctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, $v_n^M\{1\}$, and even numbered $2\ell$ gluon distribution, $v_n^M\{2\ell \}$, inclusive distributions in high-energy $p+A$ reactions as a function of harmonic $n$, target recoil cluster number, $M$, and gluon number, $2\ell$, at the RHIC and LHC. Multiple resolved clusters of recoiling target beam jets together with the projectile beam jet form color scintillation antenna (CSA) arrays that lead to characteristic boost-noninvariant trapezoidal rapidity distributions in asymmetric $B+A$ nuclear collisions. The scaling of the intrinsically azimuthally anisotropic and long range in $\eta$ nature of the non-Abelian bremsstrahlung leads to $v_n$ moments that are similar to results from hydrodynamic models, but due entirely to non-Abelian wave interference phenomena sourced by the fluctuating CSA. Our analytic nonflow solutions are similar to recent numerical saturation model predictions but differ by predicting a simple power-law hierarchy of both even and odd $v_n$ without invoking $k_T$ factorization. A test of the CSA mechanism is the predicted nearly linear $\eta$ rapidity dependence of the $v_n(k_T,\eta )$. Non-Abelian beam jet bremsstrahlung may, thus, provide a simple analytic solution to the beam energy scan puzzle of the near $\sqrt{s}$ independence of $v_n(p_T)$ moments observed down to 10 AGeV, where large-$x$ valence-quark beam jets dominate inelastic dynamics. Recoil bremsstrahlung from multiple independent CSA clusters could also provide a partial explanation for the unexpected similarity of $v_n$ in $p(D)+A$ and noncentral $A+A$ at the same $dN/d\eta$ multiplicity as observed at the RHIC and LHC.

We discuss, within the simplified context provided by the polymeric harmonic oscillator, a construction leading to a separable Hilbert space that preserves some of the most important features of the spectrum of the Hamiltonian operator. This construction may be applied to other polymer quantum mechanical systems, including those of loop quantum cosmology, and is likely generalizable to certain formulations of full loop quantum gravity. It is helpful to sidestep some of the physically relevant issues that appear in that context, in particular those related to superselection and the definition of suitable ensembles for the statistical mechanics of these types of systems.