We derive color decompositions of arbitrary tree and one-loop QCD amplitudes into color-ordered objects called primitive amplitudes. Furthermore, we derive general fermion flip and reversion identities spanning the null space among the primitive amplitudes and use them to prove that all color-ordered tree amplitudes of massless QCD can be written as linear combinations of color-ordered tree amplitudes of $\mathcal{N}=4$ super Yang-Mills theory.

We present an all-order proof of the cancellation of infrared (IR) divergences in light-front quantum electrodynamics using a coherent state approach. It is shown, using fermion mass renormalization as an example, that the true IR divergences are eliminated to all orders in a light-front time-ordered perturbative calculation if one uses a coherent state basis instead of the usual Fock basis to calculate the Hamiltonian matrix elements.

By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical notion of temperature for quantum isolated horizons. This is done by demanding that the horizon state satisfying the boundary conditions be a Kubo-Martin-Schwinger state. The exact formula for the temperature can be derived by imposing the reality conditions in the form of the linear simplicity constraints for an imaginary Barbero-Immirzi parameter. Thus, our analysis reveals the connection between the analytic continuation to the Ashtekar self-dual variables and the thermality of the horizon. The horizon thermal equilibrium state can then be used to compute both the entanglement and the Boltzmann entropies. We show that the two provide the same finite answer, which allows us to recover the Bekenstein-Hawking formula in the semiclassical limit. In this way, we shed new light on the microscopic origin of black hole entropy by revealing the equivalence between the near-horizon degrees of freedom entanglement proposal and the state-counting interpretation. The connection with the Connes-Rovelli thermal time proposal for a general relativistic statistical mechanics is worked out.

We construct a four-dimensional de Sitter space up to a conformal transformation by compactifying the anisotropic SD3-brane solution of type IIB string theory on a six-dimensional product space of the form $H_5\times S^1$, where $H_5$ is a five-dimensional hyperbolic space and $S^1$ is a circle. The radius of the hyperbolic space is chosen to be constant. The radius of the circle and the dilaton in four dimensions are time dependent and not constant in general. By different choices of parameters characterizing the SD3-brane solution, either the dilaton or the radius of the circle can be made constant but not both. The form field is also nonvanishing in general, but it can be made to vanish without affecting the solution. This construction might be useful for a better understanding of dS/CFT correspondence as well as for cosmology.

Recent astrophysics observation reveals the existence of some superluminous type Ia supernovae. One natural explanation of such a peculiar phenomenon is to require the progenitor of such a supernova to be a highly super-Chandrasekhar mass white dwarf. Along this line, in this paper, we propose a possible mechanism to explain this phenomenon based on a charged white dwarf. In particular, by choosing suitable new variables and a representative charge distribution, an analytic solution is obtained. The stability issue is also discussed; remarkably, it turns out that the charged white dwarf configuration can be dynamically stable. In the end, we investigate the general relativistic effects and it is shown that the general relativistic effects can be negligible when the mass of the charged white dwarf is below about $3M_{\odot }$.

Spherically symmetric solutions for $f(T)$ gravity models are derived by the so-called Noether symmetry approach. First, we present a full set of Noether symmetries for some minisuperspace models. Then, we compute analytical solutions and find that spherically symmetric solutions in $f(T)$ gravity can be recast in terms of Schwarzschild-like solutions modified by a distortion function depending on a characteristic radius. The obtained solutions are more general than those obtained by the usual solution methods.

Within the context of scalar-tensor gravity, we explore the generalized second law (GSL) of gravitational thermodynamics. We extend the action of ordinary scalar-tensor gravity theory to the case in which there is a nonminimal coupling between the scalar field and the matter field (as a chameleon field). Then we derive the field equations governing the gravity and the scalar field. For a Friedmann-Robertson-Walker universe filled only with ordinary matter, we obtain the modified Friedmann equations as well as the evolution equation of the scalar field. Furthermore, we assume the boundary of the Universe to be enclosed by the dynamical apparent horizon that is in thermal equilibrium with the Hawking temperature. We obtain a general expression for the GSL of thermodynamics in the scalar-tensor gravity model. For some viable scalar-tensor models, we first obtain the evolutionary behaviors of the matter density, the scale factor, the Hubble parameter, the scalar field, and the deceleration parameter, as well as the effective equation of state (EoS) parameter. We conclude that in most of the models, the deceleration parameter approaches a de Sitter regime at late times, as expected. Also, the effective EoS parameter acts like the $\mathrm{\Lambda }\mathrm{CDM}$ model at late times. Finally, we examine the validity of the GSL for the selected models.

In this work, we investigate black hole (BH) physics in the context of the gravity rainbow. We investigate this through rainbow functions that have been proposed by Amelino-Camelia [Living Rev. Relativity 16, 5 (2013)] and Amelino-Camelia et al. in [Int. J. Mod. Phys. A 12, 607 (1997)]. This modification will give corrections to both the temperature and the entropy of BHs, and hence it changes the picture of Hawking radiation greatly when the size of the BH approaches the Planck scale. It prevents the BH from total evaporation, predicting the existence of a BH remnant, which may resolve the catastrophic behavior of Hawking radiation as the BH mass approaches zero.

In this work, we are going to study the inflationary era of the Universe evolution by using second type of Randall-Sundrum model (RS-II) braneworld gravity. It is supposed that the Universe is dominated by scalar field with noncanonical kinetic terms. The kinetic term is supposed as a power-law function, and the work is performed for two typical cases. Using recent observations, the free parameters of the model are determined. It is shown that theoretical results are in acceptable agreement with observational data. Finally the time period of inflation is derived approximately, and it is found out that the inflation could occur after the five-dimensional Planck time.

To illustrate the complementarity of the linear collider and astrophysics bounds on the light (MeV-scale mass) dark matter (DM), we study the constraints on the magnetic dipole DM from the DM-electron interactions at the proposed International Linear Collider (ILC) and in supernova (SN) 1987A. We in particular focus on the $e^{+}{e}^{-}$ annihilation, which is the common process for producing DM pairs both at the ILC and in the SN. We estimate the bounds on the DM magnetic dipole moment from the monophoton signals at the ILC and also from the energy loss rate due to the freely streaming DM produced in the SN. The SN bounds can be more stringent than those from the ILC by as much as a factor $\mathcal{O}(10^5)$ for a DM mass below $10^2\mathrm{MeV}$. For larger DM masses, on the other hand, SN rapidly loses its sensitivity and the collider constraints can complement the SN constraints.

The landscape of dark matter (DM) direct detection has been profoundly altered by the slew of recent experiments. While some have claimed signals consistent with dark matter, others have seen few, if any, events consistent with dark matter. The results of the putative detections are often incompatible with each other in the context of naive spin-independent scattering, as well as with the null results. In particular, in light of the conflicts between the DM interpretation of the three events recently reported by the CDMS-Si experiment and the first results of the LUX experiment, there is a strong need to revisit the assumptions that go into the DM interpretations of both signals and limits. We attempt to reexamine a number of particle physics, astrophysics and experimental uncertainties. Specifically, we examine exothermic scattering, isospin-dependent couplings, modified halo models through astrophysics-independent techniques, and variations in the assumptions about the scintillation light in liquid xenon. We find that only a highly tuned isospin-dependent scenario remains as a viable explanation of the claimed detections, unless the scintillation properties of LXe are dramatically different from the assumptions used by the LUX experiment.

We consider the status of Higgs inflation in light of the recently announced detection of B modes in the polarization of the cosmic microwave background radiation by the BICEP2 Collaboration. In order for the primordial B-mode signal to be observable by BICEP2, the energy scale of inflation must be high: $V_{\text{inf}}\approx 2\times 10^{16}\mathrm{GeV}$. Higgs inflation generally predicts a small amplitude of tensor perturbations, and therefore it is natural to ask if Higgs inflation might accommodate this new measurement. We find that the answer is essentially no, unless one considers either extreme fine-tuning or possibly adding new beyond the Standard Model fields, which remove some of the more attractive features of the original idea. We also explore the possible importance of a factor that has not previously been explicitly incorporated, namely the gauge dependence of the effective potential used in calculating inflationary observables (e.g., $n_S$ and $r$), to see if this might provide additional wiggle room. Such gauge effects are comparable to the effects of Higgs mass uncertainties and other observables already considered in the analysis, and therefore they are relevant for constraining models. However, they are therefore too small to remove the apparent incompatibility between the BICEP2 observation and the predictions of Higgs inflation.

The recent BICEP2 $B$-mode polarization determination of an inflationary tensor-scalar ratio $r=0.2_{-0.05}^{+0.07}$ is in tension with simple scale-free models of inflation due to a lack of a corresponding low multipole excess in the temperature power spectrum which places a limit of $r_{0.002}<0.11$ (95% C.L.) on such models. Single-field inflationary models that reconcile these two observations, even those where the tilt runs substantially, introduce a scale into the scalar power spectrum. To cancel the tensor excess, and simultaneously remove the excess already present without tensors, ideally the model should introduce this scale as a relatively sharp transition in the tensor-scalar ratio around the horizon at recombination. We consider models which generate such a step in this quantity and find that they can improve the joint fit to the temperature and polarization data by up to $2\mathrm{\Delta }\ln \mathcal{L}\approx -14$ without changing cosmological parameters. Precision $E$-mode polarization measurements should be able to test this explanation.

We point out that, if the direct $CP$ asymmetries in the $D\to {\pi }^{+}{\pi }^{-}$ and $D\to K^{+}{K}^{-}$ decays are unequal, the indirect $CP$ asymmetries as measured in these modes are necessarily unequal. This nonuniversality of indirect $CP$ asymmetries can be significant with the right amount of new physics contributions, a scenario that may be fine-tuned but is still viable. A model-independent fit to the current data allows different indirect $CP$ asymmetries in the above two decays. This could even be contributing to the apparent tension between the difference $CP$ asymmetries $\mathrm{\Delta }{A}_{CP}$ measured through the pion-tagged and muon-tagged data samples at the LHCb. This also implies that the measurements of $A_{\mathrm{\Gamma }}$ and $y_{CP}$ in the ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ decay modes can be different, and averaging over these two modes should be avoided. In any case, the complete analysis of $CP$ violation measurements in the $D$ meson sector should take into account the possibility of different indirect $CP$ asymmetries in the ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ channels.

The production of new gauge bosons is a standard benchmark for the exploration of the physics capabilities of future colliders. The $\sqrt{s}=100\mathrm{TeV}$ future hadron collider will make a major step in our ability to search for and explore the properties of such new states. In this paper, employing traditional models to make contact with the past and more recent literature, we not only establish in detail the discovery and exclusion reaches for both the $Z^{\prime }$ and $W^{\prime }$ within these models, but, more importantly, we also examine the capability of the future hadron collider to extract information relevant for the determination of the couplings of the $Z^{\prime }$ to the fermions of the Standard Model as well as the helicity of the corresponding $W^{\prime }$ couplings. This is a necessary first step in determining the nature of the underlying theory, which gave rise to these states.

The presence of a bosonic resonance near 125 GeV has been firmly established at the Large Hadron Collider. Understanding the exact nature of this boson is a priority. The task now is to verify whether the boson is indeed the scalar Higgs as proposed in the Standard Model of particle physics, or something more esoteric as proposed in the plethora of extensions to the Standard Model. This requires a verification that the boson is a $J^{PC}=0^{++}$ state with couplings precisely as predicted by the Standard Model. Since a non-Standard Model boson can in some cases mimic the Standard Model Higgs in its couplings to gauge bosons, it is essential to rule out any anomalous behavior in its gauge couplings. We present a step by step methodology to determine the properties of this resonance without making any assumptions about its couplings. We present the analysis in terms of uniangular distributions which lead to angular asymmetries that allow for the extraction of the couplings of the 125–126 GeV resonance to $Z$ bosons. We show analytically and numerically, that these asymmetries can unambiguously confirm whether the new boson is indeed the Standard Model Higgs boson.

We present results for the $Z$ boson and $W$ boson transverse momentum ($p_T$) distributions for large $p_T$ at LHC and Tevatron energies. We calculate complete next-to-leading-order QCD corrections as well as soft-gluon corrections at next-to-next-to-leading order (NNLO) to the differential cross section. The NNLO soft-gluon contributions are derived from next-to-next-to-leading-logarithm resummation at two loops. We find enhancements of the $p_T$ distributions and reductions of the scale dependence when the NNLO corrections are included.

The standard three-neutrino ($3\nu$) oscillation framework is being increasingly refined by results coming from different sets of experiments, using neutrinos from solar, atmospheric, accelerator and reactor sources. At present, each of the known oscillation parameters [the two squared mass gaps $(\delta m^2,\mathrm{\Delta }{m}^2)$ and the three mixing angles $({\theta }_{12},{\theta }_{13},{\theta }_{23})$] is dominantly determined by a single class of experiments. Conversely, the unknown parameters (the mass hierarchy, the ${\theta }_{23}$ octant and the CP-violating phase $\delta$) can currently be constrained only through a combined analysis of various (eventually all) classes of experiments. In the light of recent new results coming from reactor and accelerator experiments, and of their interplay with solar and atmospheric data, we update the estimated $N\sigma$ ranges of the known $3\nu$ parameters and revisit the status of the unknown ones. Concerning the hierarchy, no significant difference emerges between normal and inverted mass ordering. A slight overall preference is found for ${\theta }_{23}$ in the first octant and for nonzero CP violation with $\sin \delta <0$; however, for both parameters, such preference exceeds $1\sigma$ only for normal hierarchy. We also discuss the correlations and stability of the oscillation parameters within different combinations of data sets.