The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering Hathrell’s renormalization group equations for massless QED in curved space, we determine the gravitational counterterms and the conformal anomalies as well near four dimensions. As conjectured for conformal couplings in the 1970s, we show that at all orders of the perturbation they can be combined into two forms only: the square of the Weyl tensor in $D$ dimensions and $E_D=G_4+(D-4)\chi (D)H^2-4\chi (D){\nabla }^{2}H$, where $G_4$ is the usual Euler density, $H=R/(D-1)$ is the rescaled scalar curvature, and $\chi (D)$ is a finite function of $D$ only. The number of the dimensionless gravitational couplings is also reduced to two. $\chi (D)$ can be determined order by order in series of $D-4$, whose first several coefficients are calculated. It has a universal value of $1/2$ at $D=4$. The familiar ambiguous ${\nabla }^{2}R$ term is fixed. At the $D\to 4$ limit, the conformal anomaly $E_D$ just yields the combination $E_4=G_4-2{\nabla }^{2}R/3$, which induces Riegert’s effective action.

The baryon acoustic oscillation (BAO), known as one of the largest cosmological objects, is now recognized as a standard cosmological tool to measure geometric distances via the Alcock-Paczynski effect, by which the observed BAO exhibits characteristic anisotropies in addition to the redshift distortions. This implies that once we know the correct distances to the observed BAO, the tip points of baryon acoustic peaks in the anisotropic correlation function of galaxies, $\xi (\sigma ,\pi )$, can form a great circle (hereafter the two-dimensional BAO circle) in the $\sigma$ and $\pi$ plane, where $\sigma$ and $\pi$ are the separation of the galaxy pair parallel and perpendicular to the line of sight, respectively. This two-dimensional BAO circle remains unchanged under the variations of the unknown galaxy bias and/or coherent motion, while it varies transversely and radially with respect to the variations of $D_A$ and $H^{-1}$, respectively. Hereby the ratio between the transverse distance $D_A$ and the radial distance $H^{-1}$ reproduces the intrinsic shape of the two-dimensional BAO circle, which is a priori given by the known broadband shape of spectra. All BAO peaks of $\xi (\sigma ,\pi )$ are precisely calculated with the improved theoretical model of redshift distortion. We test this broadband Alcock-Paczynski method using baryon oscillation spectroscopic survey–like mock catalogues. The transverse and radial distances are probed in precision of several percentage fractional errors, and the coherent motion is observed to match with the fiducial values accurately.

We study flat Friedmann–Robertson–Walker models with a perfect fluid matter source and a scalar field nonminimally coupled to matter having a double exponential potential. It is shown that the scalar field almost always diverges to infinity. Under conditions on the parameter space, we show that the model is able to give an acceptable cosmological history of our Universe, that is, a transient matter era followed by an accelerating future attractor. It is found that only a very weak coupling can lead to viable cosmology. We study in the Einstein frame the cosmological viability of the asymptotic form of a class of $f(R)$ theories predicting acceleration. The role of the coupling constant is briefly discussed.

We show that recently proposed white dwarf models with masses well in excess of the Chandrasekhar limit, based on modifying the equation of state by a superstrong magnetic field in the center, are very far from equilibrium because of the neglect of Lorentz forces. An upper bound on the central magnetic fields, from a spherically averaged hydrostatic equation, is much smaller than the values assumed. Robust estimates of the Lorentz forces are also made without assuming spherical averaging. These again bear out the results obtained from a spherically averaged model. In our assessment, these estimates rule out the possibility that magnetic tension could change the situation in favor of larger magnetic fields. We conclude that such super-Chandrasekhar models are unphysical, and exploration of their astrophysical consequences is premature.

Inspired by the very recent LHCb measurements of $B_s\to J/\psi f_1(1285)$ and the good agreement between the perturbative QCD predictions and the data for many $B\to J/\psi V$ decays, we here investigate the $B_s\to J/\psi f_1(1285)$ and $B_s\to J/\psi f_1(1420)$ decays for the first time by employing the perturbative QCD (pQCD) approach, in which the $1^3{P}_1$ states $f_1(1285)$ and $f_1(1420)$ are believed to be the mixture of flavor singlet $f_1$ and octet $f_8$ or of quark-flavor states $f_{1q}$ and $f_{1s}$. We show that the pQCD predictions for the branching ratio of $B_s\to J/\psi f_1(1285)$ agree well with the data within errors for the mixing angle ${\theta }_{{}^3{P}_1}\approx 20°({\varphi }_{{}^3{P}_1}\approx 15°)$ between $f_1(f_{1q})$ and $f_8(f_{1s})$ states. Furthermore, the branching ratio of $B_s\to J/\psi f_1(1420)$ and the large transverse polarization fractions in these two considered channels are also predicted and will be tested by the LHC and the forthcoming Super-B factory experiments. Based on the decay rates of $B_s\to J/\psi f_1(1285)$ and $B_s\to J/\psi f_1(1420)$ decay modes predicted in the pQCD approach, the extracted mixing angle between $f_1(1285)$ and $f_1(1420)$ is basically consistent with currently available experimental measurements and lattice QCD analysis within still large theoretical errors.

An earlier extraction from the HERMES experiment of the polarization-averaged parton distribution of strange quarks in the nucleon has been reevaluated using final data on the multiplicities of charged kaons in semi-inclusive deep-inelastic scattering obtained with a kinematically more comprehensive method of correcting for experimental effects. General features of the distribution are confirmed, but the rise at low $x$ is less pronounced than previously reported.

We study the timelike virtual Compton scattering process with a linearly polarized photon beam, in the generalized Bjorken scaling region and in the medium energy range, which will be studied intensely at JLab12 experiments. We define new observables and show how they should help to access the polarized quark and gluon generalized parton distributions.

We calculate new constraints on extra neutrino interactions via light Abelian vector bosons, where the boson mass arises from a Stuckelberg mechanism. We use the requirement that $Z$, $W$, and kaon decays, as well as electron-neutrino scattering, are not altered by the new interactions beyond what is allowed by experimental uncertainties. These constraints are strong and apply to neutrinophilic dark matter, where interactions of neutrinos and dark matter via a new gauge boson are important. In particular, we show that models where neutrino interactions are needed to solve the small-scale structure problems in the $\mathrm{\Lambda }\mathrm{CDM}$ cosmology are constrained.

Compared to $\mu \to e\gamma$ and $\mu \to eee$, the process $\mu \to e$ conversion in nuclei receives enhanced contributions from Higgs-induced lepton flavor violation. Upcoming $\mu \to e$ conversion experiments with drastically increased sensitivity will be able to put extremely stringent bounds on Higgs-mediated $\mu \to e$ transitions. We point out that the theoretical uncertainties associated with these Higgs effects, encoded in the couplings of quark scalar operators to the nucleon, can be accurately assessed using our recently developed approach based on $SU(2)$ chiral perturbation theory that cleanly separates two- and three-flavor observables. We emphasize that with input from lattice QCD for the coupling to strangeness $f_s^N$, hadronic uncertainties are appreciably reduced compared to the traditional approach where $f_s^N$ is determined from the pion-nucleon $\sigma$ term by means of an $SU(3)$ relation. We illustrate this point by considering Higgs-mediated lepton flavor violation in the standard model supplemented with higher-dimensional operators, the two-Higgs-doublet model with generic Yukawa couplings, and the minimal supersymmetric standard model. Furthermore, we compare bounds from present and future $\mu \to e$ conversion and $\mu \to e\gamma$ experiments.

The latest data from the ACME Collaboration have put a stringent constraint on the electric dipole moment $d_e$ of the electron. Nevertheless, the standard model (SM) prediction for $d_e$ is many orders of magnitude below the new result, making this observable a powerful probe for physics beyond the SM. We carry out a model-independent study of $d_e$ in the SM with right-handed neutrinos and its extension with the neutrino seesaw mechanism under the framework of minimal flavor violation. We find that $d_e$ crucially depends on whether neutrinos are Dirac or Majorana particles. In the Majorana case, $d_e$ can reach its experimental bound, and it constrains the scale of minimal flavor violation to be above a few hundred GeV or more. We also explore extra $CP$-violating sources in the Yukawa couplings of the right-handed neutrinos. Such new sources can have important effects on $d_e$.

We report a measurement of $D^0\text{−}{\overline{D}}^0$ mixing parameters and a search for indirect $CP$ violation through a time-dependent amplitude analysis of $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ decays. The results are based on $921{\mathrm{fb}}^{-1}$ of data accumulated with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. Assuming $CP$ conservation, we measure the mixing parameters $x=(0.56\pm {0.19}_{-0.09-0.09}^{+0.03+0.06})\%$ and $y=(0.30\pm {0.15}_{-0.05-0.06}^{+0.04+0.03})\%$, where the errors are statistical, experimental systematic, and systematic due to the amplitude model, respectively. With $CP$ violation allowed, the parameters $|q/p|={0.90}_{-0.15-0.04-0.05}^{+0.16+0.05+0.06}$ and $\arg (q/p)=(-6\pm 11\pm 3_{-4}^{+3})°$ are found to be consistent with conservation of $CP$ symmetry in mixing and in the interference between mixing and decay, respectively.

The induction of a Lorentz- and CPT-violating Chern-Simons-like term in a fermionic theory embedded in linearized quantum gravity is reassessed. We explicitly show that gauge symmetry on underlying Feynman diagrams does not fix the arbitrariness inherent to such induced term at one loop order. We present the calculation in a nonperturbative expansion in the Lorentz-violating parameter $b_{\mu }$ and within a framework which, besides operating in the physical dimension, judiciously parametrizes regularization dependent arbitrary parameters usually fixed by symmetries.

We consider the high-temperature limit of the Casimir interaction between a Dirichlet sphere and a Dirichlet plate due to the vacuum fluctuations of a scalar field in $(D+1)$-dimensional Minkowski spacetime. The high-temperature leading term of the Casimir free interaction energy is known as the classical term, since it does not depend on the Planck constant $\hslash$. From the functional representation of the zero-temperature Casimir interaction energy, we use Matsubara formalism to derive the finite-temperature Casimir free energy and obtain the classical term. It can be expressed as a weighted sum over logarithms of determinants. Using similarity transforms of matrices, we reexpress this classical term as an infinite series. This series is then computed exactly using a generalized Abel-Plana summation formula. From this, we deduce the short-distance asymptotic expansions of the classical Casimir interaction force. As expected, the leading term agrees with the proximity force approximation. The next two terms in the asymptotic expansion are also computed. It is observed that the ratio of the next-to-leading-order term to the leading-order term is proportional to the dimension of spacetime. Hence, a larger correction to the proximity force approximation is expected in spacetime with higher dimensions. This is similar to a previous result deduced for the zero-temperature case.

We discuss cosmological effects of the quantum loops of massless particles, which lead to temporal nonlocalities in the equations of motion governing the scale factor $a(t)$. For the effects discussed here, loops cause the evolution of $a(t)$ to depend on the memory of the curvature in the past with a weight that scales initially as $1/(t-t^{\prime })$. As one of our primary examples, we discuss the situation with a large number of light particles, such that these effects occur in a region where gravity may still be treated classically. However, we also describe the effect of quantum graviton loops and the full set of Standard Model particles. We show that these effects decrease with time in an expanding phase, leading to classical behavior at late time. In a contracting phase, within our approximations the quantum results can lead to a bouncelike behavior at scales below the Planck mass, avoiding the singularities required classically by the Hawking-Penrose theorems. For conformally invariant fields, such as the Standard Model with a conformally coupled Higgs, this result is purely nonlocal and parameter independent.

We present the practical step-by-step procedure for constructing canonical gravitational dynamics and kinematics directly from any previously specified quantizable classical matter dynamics, and then illustrate the application of this recipe by way of two completely worked case studies. Following the same procedure, any phenomenological proposal for fundamental matter dynamics must be supplemented with a suitable gravity theory providing the coefficients and kinematical interpretation of the matter theory, before any of the two theories can be meaningfully compared to experimental data.

A self-interacting SU(2) doublet of complex scalar fields, minimally coupled to Einstein-Gauss-Bonnet gravity is considered in five space-time dimensions. The classical equations admit two families of solitons corresponding to spinning and nonspinning bosons stars. For generic values of the coupling constants the solutions are constructed numerically and agree with exact results that are available in special limits of the parameters. It is shown that the pattern of boson stars related to Einstein gravity is significantly affected by the Gauss-Bonnet term.

We explore a new mechanism of slowing down the rotation of neutron stars via accretion of millicharged dark matter. We find that this mechanism yields pulsar braking indices that can be substantially smaller than the standard $n\sim 3$ of the magnetic dipole radiation model for millicharged dark matter particles that are not excluded by existing experimental constraints thus accommodating existing observations.

In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so-called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach, one necessarily introduces an additional hypersurface choice to the problem. Using our mixed and pure tensors approach, we are able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hypersurface dependence inherent to the covariant approach. Finally, through the use of this map, we define full nonlinear tensors that at first order correspond to the three known gauge invariant variables $\mathrm{\Phi }$, $\mathrm{\Psi }$ and $\mathrm{\Xi }$, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hypersurface invariant variables at any order.

The origin of tiny neutrino masses and the baryon number asymmetry of the Universe are naturally interpreted by the canonical seesaw and leptogenesis mechanisms, in which there are the heavy Majorana neutrino mass matrix $M_{\mathrm{R}}$, the Dirac neutrino mass matrix $M_{\mathrm{D}}$, the charged-lepton mass matrix $M_{\ell }$, and the effective (light) neutrino mass matrix $M_{\nu }$. We find that $\mathrm{Im}(\det [M_{\mathrm{D}}^{†}{M}_{\mathrm{D}},M_{\mathrm{R}}^{†}{M}_{\mathrm{R}}])$, $\mathrm{Im}(\det [M_{\ell }{M}_{\ell }^{†},M_{\nu }{M}_{\nu }^{†}])$, and $\mathrm{Im}(\det [M_{\ell }{M}_{\ell }^{†},M_{\mathrm{D}}{M}_{\mathrm{D}}^{†}])$ can serve as a basis-independent measure of $CP$ violation associated with lepton-number-violating decays of heavy neutrinos, flavor oscillations of light neutrinos, and lepton-flavor-violating decays of charged leptons, respectively. We first calculate these quantities with the help of a standard parametrization of the $6\times 6$ flavor mixing matrix, then discuss their implications on both leptogenesis and $CP$ violation at low energy scales. A comparison is also made with the weak-basis invariants of leptogenesis, as proposed by Branco et al.