In this paper we show that Yang-Mills theory in the Curci-Ferrari-Delbourgo-Jarvis gauge admits some up to now unknown local linear Ward identities. These identities imply some nonrenormalization theorems with practical simplifications for perturbation theory. We show, in particular, that all renormalization factors can be extracted from two-point functions. The Ward identities are shown to be related to supergauge transformations in the superfield formalism for Yang-Mills theory. The case of nonzero Curci-Ferrari mass is also addressed.

Forthcoming photometric redshift surveys should provide an accurate probe of the acoustic peak in the two-point galaxy correlation function, in the form of angular clustering of galaxies within a given shell in redshift space. We investigate the form of the anticipated signal, quantifying the distortions that arise due to projection effects, and, in particular, explore the validity of applying the Limber approximation. A single-integral prescription is presented, which provides an alternative to Limber’s equation, and produces a significantly improved prediction in the regime of interest. The position of the acoustic peak within the angular correlation function relates to the angular diameter distance to the far side of the redshift bin. Thicker redshift bins therefore shift comoving features toward smaller angular scales. As a result, the value of the photometric redshift error acquires a greater significance, particularly at lower redshifts. In order to recover the dark energy equation of state to a level of 1%, we find the total redshift dispersion must be determined to within $\Delta {\sigma }_z\lesssim {10}^{-3}$, which may prove challenging to achieve in practice.

We discuss the creation of massless particles in a Universe, which transits from a radiation-dominated era to any other expansion law. We calculate in detail the generation of gravitons during the transition to a matter-dominated era. We show that the resulting gravitons generated in the standard radiation/matter transition are negligible. We use our result to constrain one or more previous matter-dominated era, or any other expansion law, which may have taken place in the early Universe. We also derive a general formula for the modification of a generic initial graviton spectrum by an early matter-dominated era.

We study the transverse momentum distribution of low-mass lepton pairs produced in hadronic scattering, using the perturbative QCD factorization approach. We argue that the distribution at large transverse momentum, $Q_T\gg Q$, with the pair’s invariant mass $Q$ as low as $Q\sim {\Lambda }_{\mathrm{QCD}}$, can be systematically factorized into universal parton-to-lepton pair fragmentation functions, parton distributions, and perturbatively calculable partonic hard parts evaluated at a short-distance scale $\sim \mathcal{O}(1/Q_T)$. We introduce a model for the input lepton pair fragmentation functions at a scale ${\mu }_0\sim 1\mathrm{GeV}$, which are then evolved perturbatively to scales relevant at the Relativistic Heavy Ion Collider. Using the evolved fragmentation functions, we calculate the transverse momentum distributions in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions at the Relativistic Heavy Ion Collider. We also discuss the sensitivity of the transverse momentum distribution of low-mass lepton pairs to the gluon distribution.

A comparative analysis of the secondary particles output of the main hadronic interaction packages used in simulations of extensive air showers is presented. Special attention is given to the study of events with very energetic leading secondary particles, including diffractive interactions.

We have studied the leptonic decay $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$, via the decay channel ${\tau }^{+}\to e^{+}{\nu }_e{\overline{\nu }}_{\tau }$, using a sample of tagged $D_s^{+}$ decays collected near the $D_s^{*\pm }{D}_s^{\mp }$ peak production energy in $e^{+}{e}^{-}$ collisions with the CLEO-c detector. We obtain $\mathcal{B}(D_s^{+}\to {\tau }^{+}{\nu }_{\tau })=(5.30\pm 0.47\pm 0.22)\%$ and determine the decay constant $f_{D_s}=(252.5\pm 11.1\pm 5.2)\mathrm{MeV}$, where the first uncertainties are statistical and the second are systematic.

We examine $e^{+}{e}^{-}\to D_s^{-}{D}_s^{*+}$ and $D_s^{*-}{D}_s^{+}$ interactions at 4170 MeV using the CLEO-c detector in order to measure the decay constant $f_{D_s^{+}}$ with good precision. Previously our measurements were substantially higher than the most precise lattice based QCD calculation of $(241\pm 3)\mathrm{MeV}$. Here we use the $D_s^{+}\to {\ell }^{+}\nu$ channel, where the ${\ell }^{+}$ designates either a ${\mu }^{+}$ or a ${\tau }^{+}$, when the ${\tau }^{+}\to {\pi }^{+}\overline{\nu }$. Analyzing both modes independently, we determine $\mathcal{B}(D_s^{+}\to {\mu }^{+}\nu )=(0.565\pm 0.045\pm 0.017)\%$, and $\mathcal{B}(D_s^{+}\to {\tau }^{+}\nu )=(6.42\pm 0.81\pm 0.18)\%$. We also analyze them simultaneously to find an effective value of ${\mathcal{B}}^{\mathrm{eff}}(D_s^{+}\to {\mu }^{+}\nu )=(0.591\pm 0.037\pm 0.018)\%$ and $f_{D_s^{+}}=(263.3\pm 8.2\pm 3.9)\mathrm{MeV}$. Combining with the CLEO-c value determined independently using $D_s^{+}\to {\tau }^{+}\nu$, ${\tau }^{+}\to e^{+}\nu \overline{\nu }$ decays, we extract $f_{D_s^{+}}=(259.5\pm 6.6\pm 3.1)\mathrm{MeV}$. Combining with our previous determination of $\mathcal{B}(D^{+}\to {\mu }^{+}\nu )$, we extract the ratio $f_{D_s^{+}}/f_{D^{+}}=1.26\pm 0.06\pm 0.02$. No evidence is found for a $CP$ asymmetry between $\Gamma (D_s^{+}\to {\mu }^{+}\nu )$ and $\Gamma (D_s^{-}\to {\mu }^{-}\nu )$; specifically the fractional difference in rates is measured to be $(4.8\pm 6.1)\%$. Finally, we find $\mathcal{B}(D_s^{+}\to e^{+}\nu )<1.2\times {10}^{-4}$ at 90% confidence level.

The Belle Collaboration recently discovered the first manifestly exotic meson: $Z^{+}(4430)$, which decays into ${\psi }^{\prime }{\pi }^{+}$ and therefore has quark content $c\overline{c}u\overline{d}$. The proximity of its mass to the $D_1{\overline{D}}^{*}$ threshold has motivated the interpretation of the $Z^{+}$ as a charm meson molecule whose constituents are an $S$-wave superposition of $D_1^{+}{\overline{D}}^{*0}$ and $D^{*+}{\overline{D}}_1^0$. If this interpretation is correct, the small ratio of the binding energy of the $Z^{+}$ to the width ${\Gamma }_1$ of its constituent $D_1$ can be exploited to predict properties of its line shapes. Its full width at half maximum in the channel ${\psi }^{\prime }{\pi }^{+}$ should be approximately $\sqrt{3}{\Gamma }_1\approx 35\mathrm{MeV}$, which is consistent with the measured width of the $Z^{+}$. The $Z^{+}$ should also decay into $D^{*}{\overline{D}}^{*}\pi$ through decay of its constituent $D_1$. The peak in the line shape for $D^{*}{\overline{D}}^{*}\pi$ should be at a higher energy than the peak in the line shape for ${\psi }^{\prime }{\pi }^{+}$ by about ${\Gamma }_1/\sqrt{12}\approx 6\mathrm{MeV}$. The line shape in $D^{*}{\overline{D}}^{*}\pi$ should also be broader and asymmetric, with a shoulder on the high energy side that can be attributed to a threshold enhancement in the production of $D_1{\overline{D}}^{*}$.

We extend the one pion exchange model at quark level to include the short distance contributions coming from $\eta$, $\sigma$, $\rho$ and $\omega$ exchange. This formalism is applied to discuss the possible molecular states of $D{\overline{D}}^{*}/\overline{D}{D}^{*}$, $B{\overline{B}}^{*}/\overline{B}{B}^{*}$, $D{D}^{*}$, $B{B}^{*}$, the pseudoscalar-vector systems with $C=B=1$ and $C=-B=1$ respectively. The “$\delta$ function” term contribution and the $S\mathrm{\text{−}}D$ mixing effects have been taken into account. We find the conclusions reached after including the heavier mesons exchange are qualitatively the same as those in the one pion exchange model. The previous suggestion that $1^{++}$ $B{\overline{B}}^{*}/\overline{B}{B}^{*}$ molecule should exist, is confirmed in the one-boson exchange model, whereas $D{D}^{*}$ bound state should not exist. The $D{\overline{D}}^{*}/\overline{D}{D}^{*}$ system can accommodate a $1^{++}$ molecule close to the threshold, the mixing between the molecule and the conventional charmonium has to be considered to identify this state with $X(3872)$. For the $B{B}^{*}$ system, the pseudoscalar-vector systems with $C=B=1$ and $C=-B=1$, near threshold molecular states may exist. These bound states should be rather narrow, isospin is violated and the $I=0$ component is dominant. Experimental search channels for these states are suggested.

We study the flavor-changing quark-graviton vertex that is induced at the one-loop level when gravitational interactions are coupled to the standard model. Because of the conservation of the energy-momentum tensor the corresponding form factors turn out to be finite and gauge invariant. Analytical expressions of the form factors are provided at leading order in the external masses. We show that flavor-changing interactions in gravity are local if the graviton is strictly massless while if the graviton has a small mass long-range interactions inducing a flavor-changing contribution in the Newton potential appear. Flavor-changing processes with massive spin-2 particles are also briefly discussed. These results can be generalized to the case of the lepton-graviton coupling.

We show that there is exact dragging of the axis directions of local inertial frames by a weighted average of the cosmological energy currents via gravitomagnetism for all linear perturbations of all Friedmann-Robertson-Walker (FRW) universes and of Einstein’s static closed universe, and for all energy-momentum-stress tensors and in the presence of a cosmological constant. This includes FRW universes arbitrarily close to the Milne Universe and the de Sitter universe. Hence the postulate formulated by Ernst Mach about the physical cause for the time-evolution of inertial axes is shown to hold in general relativity for linear perturbations of FRW universes.—The time-evolution of local inertial axes (relative to given local fiducial axes) is given experimentally by the precession angular velocity ${\overrightarrow{\Omega }}_{\mathrm{gyro}}$ of local gyroscopes, which in turn gives the operational definition of the gravitomagnetic field: ${\overrightarrow{B}}_{\mathrm{g}}\equiv -2{\overrightarrow{\Omega }}_{\mathrm{gyro}}$. The gravitomagnetic field is caused by energy currents ${\overrightarrow{J}}_{\epsilon }$ via the momentum constraint, Einstein’s $G^{\widehat{0}}{}_{\widehat{i}}$ equation, $(-\Delta +{\mu }^2){\overrightarrow{A}}_{\mathrm{g}}=-16\pi G_{\mathrm{N}}{\overrightarrow{J}}_{\epsilon }$ with ${\overrightarrow{B}}_{\mathrm{g}}=\mathrm{curl}{\overrightarrow{A}}_{\mathrm{g}}$. This equation is analogous to Ampère’s law, but it holds for all time-dependent situations. $\Delta$ is the de Rham-Hodge Laplacian, and $\Delta =-\mathrm{curl}\mathrm{curl}$ for the vorticity sector in Riemannian 3-space.—In the solution for an open universe the $1/r^2$-force of Ampère is replaced by a Yukawa force $Y_{\mu }(r)=(-d/dr)[(1/R)\exp (-\mu r)]$, form-identical for FRW backgrounds with $K=(-1,0)$. Here $r$ is the measured geodesic distance from the gyroscope to the cosmological source, and $2\pi R$ is the measured circumference of the sphere centered at the gyroscope and going through the source point. The scale of the exponential cutoff is the $H$-dot radius, where $H$ is the Hubble rate, dot is the derivative with respect to cosmic time, and ${\mu }^2=-4(dH/dt)$. Analogous results hold in closed FRW universes and in Einstein’s closed static universe.—We list six fundamental tests for the principle formulated by Mach: all of them are explicitly fulfilled by our solutions.—We show that only energy currents in the toroidal vorticity sector with $\ell =1$ can affect the precession of gyroscopes. We show that the harmonic decomposition of toroidal vorticity fields in terms of vector spherical harmonics ${\overrightarrow{X}}_{\ell m}^{-}$ has radial functions which are form-identical for the 3-sphere, the hyperbolic 3-space, and Euclidean 3-space, and are form-identical with the spherical Bessel-, Neumann-, and Hankel functions.—The Appendix gives the de Rham-Hodge Laplacian on vorticity fields in Riemannian 3-spaces by equations connecting the calculus of differential forms with the curl notation. We also give the derivation the Weitzenböck formula for the difference between the de Rham-Hodge Laplacian $\Delta$ and the “rough” Laplacian ${\nabla }^2$ on vector fields.

In this paper, we discuss the constraint on the relic gravitational waves by both temperature and polarization anisotropies power spectra of cosmic microwave background radiation. Taking into account the instrumental noises of the Planck satellite, we calculate the signal-to-noise ratio $S/N$ by the simulation and the analytic approximation methods. We find that, compared with the $BB$ channel, the value of $S/N$ is much improved in the case where all the power spectra, $TT$, $TE$, $EE$, and $BB$, are considered. If the noise power spectra of the Planck satellite increase for some reason, the value of $S/N$ in the $BB$ channel is much reduced. However, in the latter case where all the power spectra of cosmic microwave background radiation are considered, the value of $S/N$ is less influenced. We also find that the free parameters $A_s$, $n_s$, and $n_t$ have little influence on the value of $S/N$ in both cases.

We investigate ten-dimensional gauge theories whose extra six-dimensional space is a compact coset space, $S/R$, and whose gauge group is a direct product of two Lie groups. We list candidates of the gauge group and embeddings of $R$ into them. After dimensional reduction of the coset space, we find fermion and scalar representations of $G_{\mathrm{GUT}}\times \mathrm{U}(1)$ with $G_{\mathrm{GUT}}=\mathrm{SU}(5)$, $\mathrm{SO}(10)$ and $E_6$, which accommodate all of the standard model particles. We also discuss possibilities to generate distinct Yukawa couplings among the generations using representations with different dimensions for $G_{\mathrm{GUT}}=\mathrm{SO}(10)$ and $E_6$ models.

Coherent ${\pi }^{+}$ and $\pi °$ production in low energy neutrino reactions is discussed in the framework of the partially conserved axial vector current theory . The role of lepton mass effects in suppressing the ${\pi }^{+}$ production is emphasized. Instead of using models of pion nucleus scattering, the available data on pion carbon scattering are implemented for an analysis of the partially conserved axial vector current theory prediction. Our results agree well with the published upper limits for ${\pi }^{+}$ production but are much below the recent MiniBooNE result for $\pi °$ production.

It is argued that the solution space of the equation determining the class of $f(R)$ theories which admit an Einstein static universe should be broadened by including the algebraic roots.

We are interested in the generic behavior of nonlinear sound waves as they approach the surface of a star, here assumed to have the polytropic equation of state $P=K{\rho }^{\Gamma }$. Restricting to spherical symmetry, and considering only the region near the surface, we generalize the methods of Carrier and Greenspan (1958) for the shallow water equations on a sloping beach to this problem. We give a semiquantitative criterion for a shock to form near the surface during the evolution of generic initial data with support away from the surface. We show that in smooth solutions the velocity and the square of the sound speed remain regular functions of Eulerian radius at the surface.

We analyze the breaking of Lorentz invariance in a 3D model of fermion fields self-coupled through four-fermion interactions. The low-energy limit of the theory contains various submodels which are similar to those used in the study of graphene or in the description of irrational charge fractionalization.

We study the stability of Hopfions embedded in a certain modification Ginzburg-Landau model of two equally charged condensates. It has been shown by Ward [Phys. Rev. D 66, 041701(R) (2002)] that a certain modification of the ordinary model results in a system which supports stable topological solitons (Hopfions) for some values of the parameters of the model. We expand the search for stability into a previously uninvestigated region of the parameter space, charting an approximate shape for the stable/unstable boundary and find that, within the accuracy of the numerical methods used, the energy of the stable knot at the boundary is independent of the parameters.

We analyze the problem of negative modes of the Euclidean section of the Reissner-Nordström black hole in four dimensions. We find analytically that a negative mode disappears when the specific heat at constant charge becomes positive. The sector of perturbations analyzed here is included in the canonical partition function of the magnetically charged black hole. The result obeys the usual rule that the partition function is only well-defined when there is local thermodynamical equilibrium. We point out the difficulty in quantizing Einstein-Maxwell theory, where the so-called conformal factor problem is considerably more intricate. Our method, inspired by Kol [Phys. Rev. D 77, 044039 (2008)], allows us to decouple the divergent gauge volume and treat the metric perturbations sector in a gauge-invariant way.

We develop a simple semianalytic model of the star formation rate as a function of time. We estimate the star formation rate for a wide range of values of the cosmological constant, spatial curvature, and primordial density contrast. Our model can predict such parameters in the multiverse, if the underlying theory landscape and the cosmological measure are known.