The dilepton production at backward rapidities in $pAu$ and $pp$ collisions at RHIC and LHC energies is investigated in the dipole approach. The results are shown through the nuclear modification ratio $R_{pA}$ considering transverse momentum and rapidity spectra. The dilepton modification ratio presents interesting behavior at the backward rapidities when compared with the already known forward ones, since it is related with the large $x$ kinematical region that is being probed. The rapidity dependence of the nuclear modification ratio in the dilepton production is strongly dependent on the Bjorken $x$ behavior of the nuclear structure function ratio $R_{F_2}=F_2^A/F_2^p$. The $R_{pA}$ transverse momentum dependence at backward rapidities is modified due to the large $x$ nuclear effects: at RHIC energies, for instance, the ratio $R_{pA}$ is reduced as $p_T$ increases, presenting an opposite behavior when compared with the forward one. It implies that the dilepton production at backward rapidities should carry information of the nuclear effects at large Bjorken $x$, as well as that it is useful to investigate the $p_T$ dependence of the observables in this kinematical regime.

Single-spin observables in scattering processes (either analyzing powers or polarizations) are highly constrained by rotational invariance and finite symmetries. For example, it is possible to demonstrate that all single-spin observables are odd under the finite transformation $O=P{A}_{\tau }$ where $P$ is parity and $A_{\tau }$ is a finite symmetry that can be designated “artificial time reversal”. The operators $P$, $O$ and $A_{\tau }$ all have eigenvalues $\pm 1$ so that all single-spin observables can be classified into two distinct categories: (1) P-odd and $A_{\tau }$-even, (2) P-even and $A_{\tau }$-odd. Within the light-quark sector of the standard model, $P$-odd observables are generated from pointlike electroweak processes while $A_{\tau }$-odd observables (neglecting quark mass parameters) come from dynamic spin-orbit correlations within hadrons or within larger composite systems, such as nuclei. The effects of $A_{\tau }$-odd dynamics can be inserted into transverse-momentum dependent constituent distribution functions and, in this paper, we construct the contribution from an orbital quark to the $A_{\tau }$-odd quark parton distribution ${\Delta }^{N}G_{q/p\uparrow }{}^{\mathrm{front}}(x,k_{TN};{\mu }^2)$. Using this distribution, we examine the crucial role of initial- and final-state interactions in the observation of the scattering asymmetries in different hard-scattering processes. This construction provides a geometrical and dynamical interpretation of the Collins conjugation relation between single-spin asymmetries in semi-inclusive deep inelastic scattering and the asymmetries in Drell-Yan production. Finally, our construction allows us to display a significant difference between the calculation of a spin asymmetry generated by a hard-scattering mechanism involving color-singlet exchange (such as a photon) and a calculation of an asymmetry with a hard-scattering exchange involving gluons. This leads to an appreciation of the process-dependence inherent in measurements of single-spin observables.

The Sun is a source of high-energy neutrinos ($E\gtrsim 10\mathrm{GeV}$) produced by cosmic ray interactions in the solar atmosphere. We study the impact of three-flavor oscillations (in vacuum and in matter) on solar atmosphere neutrinos, and calculate their observable fluxes at Earth, as well as their event rates in a kilometer-scale detector in water or ice. We find that peculiar three-flavor oscillation effects in matter, which can occur in the energy range probed by solar atmosphere neutrinos, are significantly suppressed by averaging over the production region and over the neutrino and antineutrino components. In particular, we find that the relation between the neutrino fluxes at the Sun and at the Earth can be approximately expressed in terms of phase-averaged vacuum oscillations, dominated by a single mixing parameter (the angle ${\theta }_{23}$).

Recently, the BES Collaboration observed a broad resonant structure $X(1576)$ with a large width being around 800 MeV and assigned its $J^{PC}$ number to $1^{--}$. We show that the isospin of this resonant structure should be assigned to 1. This state might be a molecule state or a tetraquark state. We study the consequences of a possible $K^{*}(892)-\overline{\kappa }$ molecular interpretation. In this scenario, the broad width can easily be understood. Carefully searching this resonant structure in the $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $J/\psi \to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}{\pi }^0$ decays should be important for understanding the structure of $X(1567)$.

We consider a 5-dimensional SU(2) gauge theory with fermions in the bulk and with additional SU(2) and U(1) kinetic terms on the branes. The electroweak breaking is obtained by boundary conditions. After deconstruction, fermions in the bulk are eliminated by using their equations of motion. In this way, standard model fermion mass terms and direct couplings to the internal gauge bosons of the moose are generated. The presence of these new couplings gives a new contribution to the ${ϵ}_3$ parameter in addition to the gauge boson term. This allows the possibility of a cancellation between the two contributions, which can be local (site by site) or global. Going back to the continuum, we show that the implementation of local cancellation in any generic warped metric leaves massless fermions. This is due to the presence of one horizon on the infrared brane. However, we can require a global cancellation of the new physics contributions to the ${ϵ}_3$ parameter. This fixes relations among the warp factor and the parameters of the fermion and gauge sectors. It turns out that the warping of the metric does not substantially modify the results obtained in the flat case.

Angular momentum can be defined by rearranging the Komar surface integral in terms of a twist form, encoding the twisting around of space-time due to a rotating mass, and an axial vector. If the axial vector is a coordinate vector and has vanishing transverse divergence, it can be uniquely specified under certain generic conditions. Along a trapping horizon, a conservation law expresses the rate of change of angular momentum of a general black hole in terms of angular momentum densities of matter and gravitational radiation. This identifies the transverse-normal block of an effective gravitational-radiation energy tensor, whose normal-normal block was recently identified in a corresponding energy conservation law. Angular momentum and energy are dual, respectively, to the axial vector and a previously identified vector, the conservation equations taking the same form. Including charge conservation, the three conserved quantities yield definitions of an effective energy, electric potential, angular velocity and surface gravity, satisfying a dynamical version of the so-called first law of black-hole mechanics. A corresponding zeroth law holds for null trapping horizons, resolving an ambiguity in taking the null limit.

Time-independent backreaction corrections of the renormalized expectation value of the stress tensor operator of a massless quantum scalar field, coupled in a two-dimensional spherically symmetric Schwarzschild-de Sitter static black hole metric, are used to obtain its final state. According to the work by Christensen and Fulling, the renormalized stress tensor is found to be determined by the nonlocal contribution of the trace anomaly and some additional parameters. Mathematical derivations of the backreaction equations, in close relation to the work by Bousso and Hawking, show that the scenario of the black hole Hawking radiation is reduced to a remnant, stable, static, Schwarzschild-de Sitter mini black hole which has still new black hole and cosmological shrunk horizons.

We present an approximate metric for a binary black-hole spacetime to construct initial data for numerical relativity. This metric is obtained by asymptotically matching a post-Newtonian metric for a binary system to a perturbed Schwarzschild metric for each hole. In the inner zone near each hole, the metric is given by the Schwarzschild solution plus a quadrupolar perturbation corresponding to an external tidal gravitational field. In the near zone, well outside each black hole but less than a reduced wavelength from the center of mass of the binary, the metric is given by a post-Newtonian expansion including the lowest-order deviations from flat spacetime. When the near zone overlaps each inner zone in a buffer zone, the post-Newtonian and perturbed Schwarzschild metrics can be asymptotically matched to each other. By demanding matching (over a 4-volume in the buffer zone) rather than patching (choosing a particular 2-surface in the buffer zone), we guarantee that the errors are small in all zones. The resulting piecewise metric is made formally $C^{\infty }$ with smooth transition functions so as to obtain the finite extrinsic curvature of a 3-slice. In addition to the metric and extrinsic curvature, we present explicit results for the lapse and the shift, which can be used as initial data for numerical simulations. This initial data is not accurate all the way to the asymptotically flat ends inside each hole, and therefore must be used with evolution codes which employ black hole excision rather than puncture methods. This paper lays the foundations of a method that can be straightforwardly iterated to obtain initial data to higher perturbative order.

Big bang nucleosynthesis in the presence of decaying relic neutral particles is examined in detail. All nonthermal processes important for the determination of light-element abundance yields of ${}^2\mathrm{H}$, ${}^3\mathrm{H}$, ${}^3\mathrm{He}$, ${}^4\mathrm{He}$, ${}^6\mathrm{Li}$, and ${}^7\mathrm{Li}$ are coupled to the thermonuclear fusion reactions to obtain comparatively accurate results. Predicted light-element yields are compared to observationally inferred limits on primordial light-element abundances to infer constraints on the abundances and properties of relic decaying particles with decay times in the interval $0.01\sec \lesssim {\tau }_X\lesssim {10}^{12}\sec$. Decaying particles are typically constrained at early times by ${}^4\mathrm{He}$ or ${}^2\mathrm{H}$, at intermediate times by ${}^6\mathrm{Li}$, and at large times by the ${}^3\mathrm{He}/{}^2\mathrm{H}$ ratio. Constraints are shown for a large number of hadronic branching ratios and decaying particle masses and may be applied to constrain the evolution of the early universe.

We present a model independent study of the chiral condensate evolution in a hadronic gas, in terms of temperature and baryon chemical potential. The meson-meson interactions are described within chiral perturbation theory and the pion-nucleon interaction by means of heavy baryon chiral perturbation theory, both at one loop, and nucleon-nucleon interactions can be safely neglected within our hadronic gas domain of validity. Together with the virial expansion, this provides a systematic expansion at low temperatures and chemical potentials, which includes the physical quark masses. This can serve as a guideline for further studies on the lattice. We also obtain estimates of the critical line of temperature and chemical potential where the chiral condensate melts, which systematically lie somewhat higher than recent lattice calculations but are consistent with several hadronic models. We have also estimated uncertainties due to chiral parameters, heavier hadrons, and higher orders through unitarized chiral perturbation theory.

An evaluation of the principal uncertainties in the computation of neutrino fluxes produced in cosmic ray showers in the atmosphere is presented. The neutrino flux predictions are needed for comparison with experiment to perform neutrino oscillation studies. The paper concentrates on the main limitations which are due to hadron production uncertainties. It also treats primary cosmic ray flux uncertainties, which are at a lower level. The absolute neutrino fluxes are found to have errors of around 15% in the neutrino energy region important for contained events underground. Large cancellations of these errors occur when ratios of fluxes are considered, in particular, the ${\nu }_{\mu }/{\overline{\nu }}_{\mu }$ ratio below $E_{\nu }=1\mathrm{GeV}$, the $({\nu }_{\mu }+{\overline{\nu }}_{\mu })/({\nu }_e+{\overline{\nu }}_e)$ ratio below $E_{\nu }=10\mathrm{GeV}$ and the up/down ratios above $E_{\nu }=1\mathrm{GeV}$ are at the 1% level. A detailed breakdown of the origin of these errors and cancellations is presented.

Based on the latest experimental data of $B\to \pi \pi$ and $\pi K$ modes, a model-independent analytical analysis is presented. The $CP$-averaged branching ratio difference $\Delta R=R_c-R_n$ in $B\to \pi K$ decays with $R_c=2\mathrm{Br}({\pi }^0{K}^{-})/\mathrm{Br}({\pi }^{-}{\overline{K}}^0)$ and $R_n=\mathrm{Br}({\pi }^{+}{K}^{-})/2\mathrm{Br}({\pi }^0{\overline{K}}^0)$ is reduced though it remains larger than the prediction from the standard model (SM) as both measured $R_n$ and $R_c$ are enhanced, which indicates that a room for new physics becomes smaller. The present data of $\pi \pi$ decay reduce the ratio $|C/T|$ from the previous value of $|C/T|\simeq 0.8$ to $|C/T|\simeq 0.65$, which is still larger than the theoretical estimations based on QCD factorization and pQCD. Within SM and flavor SU(3) symmetry, the current $\pi K$ data also diminish the ratio $|C^{\prime }/T^{\prime }|$ from the previous value $|C^{\prime }/T^{\prime }|\simeq 2$ to $|C^{\prime }/T^{\prime }|\simeq 1.16$ with a large strong phase ${\delta }_{C^{\prime }}\simeq -2.65$, while its value remains much larger than the one extracted from the $\pi \pi$ modes. The direct $CP$ violation $A_{CP}({\pi }^0{\overline{K}}^0)$ is predicted to be $A_{CP}({\pi }^0{\overline{K}}^0)=-0.15\pm 0.03$, which is consistent with the present data. Two kinds of new effects in both strong and weak phases of the electroweak penguin diagram are considered. It is found that both cases can reduce the ratio to $|C^{\prime }/T^{\prime }|=0.40\sim 0.80$ and lead to roughly the same predictions for $CP$ violation in ${\pi }^0{K}^0$.

New rate measurements of $B^0$ decays into ${\pi }^0{\pi }^0$, ${\pi }^0\eta$, ${\pi }^0{\eta }^{\prime }$, $\eta \eta$, $\eta {\eta }^{\prime }$, ${\eta }^{\prime }{\eta }^{\prime }$ and $K^{+}{K}^{-}$ are used in conjunction with flavor $SU(3)$ to constrain the coefficients $S$ and $C$ of $\sin \Delta mt$ and $\cos \Delta mt$ in the time-dependent $CP$ asymmetries of $B^0\to {\eta }^{\prime }{K}_S$ and $B^0\to {\pi }^0{K}_S$. Experimental values of $S_{{\eta }^{\prime }K}$ are now seen to be closer to the Standard Model expectations, fully consistent with the new improved bounds.

In the causal set approach to quantum gravity, Poincaré symmetry is modified by swerving in spacetime, induced by the random lattice discretization of the spacetime structure. The broken translational symmetry at short distances is argued to lead to a residual diffusion in momentum space, whereby a particle can acquire energy and momentum by drift along its mass shell and a system in equilibrium can spontaneously heat up. We consider bounds on the rate of momentum space diffusion coming from astrophysical molecular clouds, nuclear stability and cosmological neutrino background. We find that the strongest limits come from relic neutrinos, which we estimate to constrain the momentum space diffusion constant by $k<{10}^{-61}{\mathrm{GeV}}^3$ for neutrinos with masses $m_{\nu }>0.01\mathrm{eV}$, improving the previously quoted bounds by roughly 17 orders of magnitude.

We calculate in this article the cosmic microwave background (CMB) and matter power spectra of a class of early $f(R)$ cosmologies, which takes the form of $f(R)=R+{\lambda }_1{H}_0^2\exp [R/({\lambda }_2{H}_0^2)]$. Unlike the late-time $f(R)$ cosmologies such as $f(R)=R+\alpha (-R{)}^{\beta }$ ($\beta <0$), the deviation from $\Lambda \mathrm{CDM}$ of this model occurs at a higher redshift (thus the name “early $f(R)$ cosmology”), and this important feature leads to rather different integrated Sachs-Wolfe (ISW) effect and CMB spectrum. The matter power spectrum of this model is, however, again very sensitive to the chosen parameters, and large scale structure (LSS) observations such as Sloan digital sky survey (SDSS) should constrain the parameter space stringently. We expect that our results are applicable at least qualitatively to other models that produce $f(R)$ modification to GR at earlier times (e.g., redshifts $\mathcal{O}(10)\lesssim z\lesssim \mathcal{O}(1)$) than when dark energy begins to dominate—such models are strongly disfavored by data on CMB and matter power spectra.

A class of Einstein-dilaton-axion models is found for which almost all flat expanding homogeneous and isotropic universes undergo recurrent periods of acceleration. We also extend recent results on eternally accelerating open universes.

We use the recently developed tools for an exact bosonization of a finite number $N$ of nonrelativistic fermions to discuss the classic Tomonaga problem. In the case of noninteracting fermions, the bosonized Hamiltonian naturally splits into an $\mathrm{O}(N)$ piece and an O(1) piece. We show that in the large-$N$ and low-energy limit, the $\mathrm{O}(N)$ piece in the Hamiltonian describes a massless relativistic boson, while the O(1) piece gives rise to cubic self-interactions of the boson. At finite $N$ and high energies, the low-energy effective description breaks down and the exact bosonized Hamiltonian must be used. We also comment on the connection between the Tomonaga problem and pure Yang-Mills theory on a cylinder. In the dual context of baby universes and multiple black holes in string theory, we point out that the $\mathrm{O}(N)$ piece in our bosonized Hamiltonian provides a simple understanding of the origin of two different kinds of nonperturbative $\mathrm{O}(e^{-N})$ corrections to the black hole partition function.

Oscillons, extremely long-living localized oscillations of a scalar field, are studied in theories with quartic and sine-Gordon potentials in two spatial dimensions. We present qualitative results concentrating largely on a study in frequency space via Fourier analysis of oscillations. Oscillations take place at a fundamental frequency just below the threshold for the production of radiation, with exponentially suppressed harmonics. The time evolution of the oscillation frequency points indirectly to a life time of at least ${10}^7$ oscillations. We study also elliptical perturbations of the oscillon, which are shown to decay. We finish by presenting results for boosted and colliding oscillons, which point to a surprising persistence and solitonlike behavior.

We derive a direct general map from the luminosity distance $D_L(z)$ to the inhomogeneous matter distribution $M(r)$ in the Lemaitre-Tolman-Bondi (LTB) cosmology and compute several examples. One of our examples explicitly demonstrates that it is possible to tune the LTB cosmological solution to approximately reproduce the luminosity distance curve of a flat Friedmann-Robertson-Walker universe with a cosmological constant. We also discuss how smooth matter distributions can evolve into naked singularities due to shell crossing when the inhomogeneous “curvature” $E(r)$ is a function which changes sign.

Gauge-invariant treatments of the second-order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. These equations imply that the tensor and the vector mode of the second-order metric perturbations may be generated by the scalar-scalar mode coupling of the linear order perturbations as the result of the nonlinear effects of the Einstein equations.