In recent years, there has been controversy concerning the anomaly-mediated gaugino mass in the superspace formalism of supergravity. In this paper, we reexamine the gaugino mass term in this formalism by paying particular attention to the symmetry that controls gaugino masses in supergravity. We first discuss super-diffeomorphism invariance of path-integral measures of charged superfields. As we will show, the super-diffeomorphism-invariant measure is not invariant under a super-Weyl transformation, which is the origin of the anomaly-mediated gaugino mass. We show how the anomaly-mediated gaugino mass is expressed as a local operator in a Wilsonian effective action in a super-diffeomorphism-covariant way. We also obtain a gaugino mass term independent of the gauge choice of the fictitious super-Weyl symmetry in the super-Weyl compensator formalism, which reproduces the widely accepted result. We also discuss how to reconcile the gaugino mass term in the local Wilsonian effective action and the gaugino mass term appearing in a nonlocal one-particle irreducible quantum effective action.

The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences between the classical and quantum dynamics. In particular, there are two different sources of quantum effects. Distributional effects, which are also present in the classical evolution of an extended distribution, are due to the fact that all moments cannot be vanishing because of the Heisenberg uncertainty principle. In addition, the noncommutativity of the basic quantum operators add some terms to the quantum equations of motion that explicitly depend on the Planck constant and are not present in the classical setting. These are thus purely quantum effects. Some particular Hamiltonians are analyzed that have very special properties regarding the evolution they generate in the classical and quantum sector. In addition, a large class of inequalities obeyed by high-order statistical moments, and in particular uncertainty relations that bound the information that is possible to obtain from a quantum system, are derived.

The exact Foldy-Wouthuysen transformation is performed in order to study the Dirac field interacting with many possible external fields associated with $CPT$-Lorentz violation. We also derived the calculation of equations of motion as well as the generalized Lorentz force corrected by the mentioned external fields. The main point is the interaction between the Dirac particle and the terms that have the multiplication of the electromagnetic field and the terms that break $CPT$-Lorentz. Finally, with the transformed Hamiltonian we were able to write an expression for the bound state of the theory and analyze it in the atomic experiments context. This result is an analytical expression that gives the possibility of the weakness of $CPT$-Lorentz terms to be compensated by the presence of a strong magnetic field.

We outline how the Wald entropy formula naturally arises in loop quantum gravity based on recently introduced dimension-independent connection variables. The key observation is that in a loop quantization of a generalized gravity theory, the analog of the area operator turns out to measure, morally speaking, the Wald entropy rather than the area. We discuss the explicit example of (higher-dimensional) Lanczos-Lovelock gravity and comment on recent work on finding the correct numerical prefactor of the entropy by comparing it to a semiclassical effective action.

Starting from Maxwell-Weyl algebra we found the transformation rules for generalized space-time coordinates and the differential realization of corresponding generators. By treating local gauge invariance of the Maxwell-Weyl group, we presented the Einstein-Cartan-Weyl gravity with the additional terms containing the gauge fields associated with the antisymmetric generators.

Modified gravity theories on cosmic scales have three key deviations from general relativity. They can cause cosmic acceleration without a physical, highly negative pressure fluid, can cause a gravitational slip between the two metric potentials, and can cause gravitational waves to propagate differently, e.g. with a speed different from the speed of light. We examine whether the deviations in the metric potentials as observable through modified Poisson equations for scalar density perturbations are related to or independent from deviations in the tensor gravitational waves. We show analytically that they are independent instantaneously in covariant Galileon gravity—e.g. at some time one of them can have the general relativity value while the other deviates—though related globally—if one deviates over a finite period, the other at some point shows a deviation. We present expressions for the early-time and late-time de Sitter limits and numerically illustrate their full evolution. This in(ter)dependence of the scalar and tensor deviations highlights complementarity between cosmic structure surveys and future gravitational wave measurements.

We show that in the presence of a chemical potential, black hole evaporation generates baryon number. If the inflaton or Ricci scalar is derivatively coupled to the $B\text{−}L$ current, the expansion of the Universe acts as a chemical potential and splits the energy levels of particles and their antiparticles. The asymmetric Hawking radiation of primordial black holes can thus be used to generate a $B\text{−}L$ asymmetry. If dark matter is produced by the same mechanism, the coincidence between the mass density of visible and dark matter can be naturally explained.

The modified holographic Ricci dark energy coupled to interacting relativistic and non-relativistic dark matter is considered in the nonflat Friedmann-Robertson-Walker universe. Through examining the deceleration parameter, one can find that the transition time of the Universe from decelerating to accelerating phase in the interacting holographic Ricci dark energy model is close to that in the $\mathrm{\Lambda }$ cold dark matter model. The evolution of modified holographic Ricci dark energy’s state parameter and the evolution of dark matter and dark energy’s densities shows that the dark energy holds the dominant position from the near past to the future. By studying the statefinder diagnostic and the evolution of the total pressure, one can find that this model could explain the Universe’s transition from the radiation to accelerating expansion stage through the dust stage. According to the $Om$ diagnostic, it is easy to find that when the interaction is weak and the proportion of relativistic dark matter in total dark matter is small, this model is phantom-like. Through our studying, we find the interaction and the relativistic dark matter’s proportion all have great influence on the evolution of the Universe.

In this paper, we introduce a noncommutative version of the Brans-Dicke (BD) theory and obtain the Hamiltonian equations of motion for a spatially flat Friedmann-Lemaître-Robertson-Walker universe filled with a perfect fluid. We focus on the case where the scalar potential as well as the ordinary matter sector are absent. Then, we investigate gravity-driven acceleration and kinetic inflation in this noncommutative BD cosmology. In contrast to the commutative case, in which the scale factor and BD scalar field are in a power-law form, in the noncommutative case the power-law scalar factor is multiplied by a dynamical exponential warp factor. This warp factor depends on the noncommutative parameter as well as the momentum conjugate associated to the BD scalar field. We show that the BD scalar field and the scale factor effectively depend on the noncommutative parameter. For very small values of this parameter, we obtain an appropriate inflationary solution, which can overcome problems within BD standard cosmology in a more efficient manner. Furthermore, a graceful exit from an early acceleration epoch towards a decelerating radiation epoch is provided. For late times, due to the presence of the noncommutative parameter, we obtain a zero acceleration epoch, which can be interpreted as the coarse-grained explanation.

We consider a two-loop radiative seesaw model with an exact $Z_2\times Z_2^{\prime }$ symmetry, which can stabilize two or three dark matter particles. The model is a simple extension of the inert scalar model of Ma, where the lepton-number violating mass term of the inert scalar, which is required to be small for small neutrino masses, is generated at the one-loop level. The semiannihilation processes of different dark matter particles, which are present when there exist more than three different dark matter particles, not only play an important role for their relic densities but also are responsible for the monochromatic neutrino lines resulting from the dark matter annihilation processes. The monochromatic neutrinos do not suffer from a chiral suppression, and we investigate the observational possibility of the monochromatic neutrino flux from the Sun.

The standard approaches of phenomenology of quantum gravity have usually explicitly violated Lorentz invariance, either in the dispersion relation or in the addition rule for momenta. We investigate whether it is possible in $3+1$ dimensions to have a nonlocal deformation that preserves fully Lorentz invariance, as is the case in $(2+1)\mathrm{D}$ quantum gravity. We answer positively to this question and show for the first time how to construct a homogeneously curved momentum space preserving the full action of the Lorentz group in dimension 4 and higher, despite relaxing locality. We study the property of this relative locality deformation and show that this space leads to a noncommutativity related to Snyder spacetime.

The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Lüscher. While in infinite volume, QED contributions to low-energy charged-particle scattering must be resummed to all orders in perturbation theory (the Coulomb ladder diagrams), in a finite volume the momentum operator is gapped, allowing for a perturbative treatment. The leading QED corrections to the two-particle finite-volume energy quantization condition below the inelastic threshold, as well as approximate formulas for energy eigenvalues, are obtained. In particular, we focus on two spinless hadrons in the $A_1^{+}$ irreducible representation of the cubic group, and truncate the strong interactions to the s-wave. These results are necessary for the analysis of lattice $\mathrm{QCD}+\mathrm{QED}$ calculations of charged-hadron interactions, and can be straightforwardly generalized to other representations of the cubic group, to hadrons with spin, and to include higher partial waves.

We present an update of our analysis [1] which includes additional ensembles at different quark masses, lattice spacings and volumes, all with high statistics. We use $N_f=2$ mass-degenerate quark flavors, employing the nonperturbatively improved clover action. The lattice matrix elements are converted to the $\overline{\mathrm{MS}}$ scheme via renormalization factors determined nonperturbatively in the ${\mathrm{RI}}^{\prime }$-MOM scheme. We have systematically investigated excited state contributions, in particular, at the smallest, near physical, pion mass. While our results (with much increased precision) are consistent with Ref. [1], comparing to previous determinations we find that excited state contributions can be significant if the quark smearing is not suitably optimized, in agreement with other recent studies. The difference with respect to the value for $⟨x{⟩}_{u-d}$ extracted from experimental data is reduced but not resolved. Using lattice sizes in the range $L{m}_{\pi }\sim 3.4–6.7$, no significant finite volume effects have been observed. Performing a controlled continuum limit that may remove the discrepancy will require simulations at lattice spacings $a<0.06\mathrm{fm}$.

Since its first observation in 2005, the vector charmonium $Y(4260)$ has turned out to be one of the prime candidates for an exotic state in the charmonium spectrum. It was recently proposed that the $Y(4260)$ should have a prominent $D_1\overline{D}+\mathrm{c}.\mathrm{c}.$ molecular component that is strongly correlated with the production of the charged $Z_c(3900)$. In this paper we demonstrate that the nontrivial cross section line shapes of $e^{+}{e}^{-}\to J/\psi \pi \pi$ and $h_c\pi \pi$ can be naturally explained by the molecular scenario. As a consequence we find a significantly smaller mass for the $Y(4260)$ than previously studied. In the $e^{+}{e}^{-}\to \overline{D}{D}^{*}\pi +\mathrm{c}.\mathrm{c}.$ process, with the inclusion of an additional $S$-wave ${\overline{D}}^{*}\pi$ contribution constrained from data on the $D{\overline{D}}^{*}$ invariant mass distribution, we obtain a good agreement with the data of the angular distributions. We also predict an unusual line shape of $Y(4260)$ in this channel that may serve as a smoking gun for a predominantly molecular nature of $Y(4260)$. Improved measurements of these observables are therefore crucial for a better understanding of the structure of this famous resonance.

We present an update of our determination of the strong coupling ${\alpha }_s$ from the quantum chromodynamics static energy. This updated analysis includes new lattice data, at smaller lattice spacings and reaching shorter distances, the use of better suited perturbative expressions to compare with data in a wider distance range, and a comprehensive and detailed estimate of the error sources that contribute to the uncertainty of the final result. Our updated value for ${\alpha }_s$ at the $Z$-mass scale, $M_Z$, is ${\alpha }_s(M_Z)=0.1166_{-0.0008}^{+0.0012}$, which supersedes our previous result.

Based on the study of the linear response of the fermion propagator in the presence of an external scalar field, we calculate the staggered spin susceptibility in the low-energy limit in the framework of the Dyson-Schwinger approach. We analyze the effect of a finite gauge boson mass on the staggered spin susceptibility in both the Nambu phase and the Wigner phase. It is found that the gauge boson mass suppresses the staggered spin susceptibility in the Wigner phase. In addition, we try to give an explanation for why the antiferromagnetic spin correlation increases when the doping is lowered.

We report the first measurement of the neutrino-oxygen neutral-current quasielastic (NCQE) cross section. It is obtained by observing nuclear deexcitation $\gamma$ rays which follow neutrino-oxygen interactions at the Super-Kamiokande water Cherenkov detector. We use T2K data corresponding to $3.01\times 10^{20}$ protons on target. By selecting only events during the T2K beam window and with well-reconstructed vertices in the fiducial volume, the large background rate from natural radioactivity is dramatically reduced. We observe 43 events in the 4–30 MeV reconstructed energy window, compared with an expectation of 51.0, which includes an estimated 16.2 background events. The background is primarily nonquasielastic neutral-current interactions and has only 1.2 events from natural radioactivity. The flux-averaged NCQE cross section we measure is $1.55\times 10^{-38}{\mathrm{cm}}^2$ with a 68% confidence interval of $(1.22,2.20)\times 10^{-38}{\mathrm{cm}}^2$ at a median neutrino energy of 630 MeV, compared with the theoretical prediction of $2.01\times 10^{-38}{\mathrm{cm}}^2$.