The covariant gauges are known to suffer from the Gribov problem: even after fixing a gauge nonperturbatively, there may still exist residual copies which are physically equivalent to each other, called Gribov copies. While the influence of Gribov copies in the relevant quantities such as gluon propagators has been heavily debated in recent studies, the significance of the role they play in the Faddeev-Popov procedure is hardly doubted. We concentrate on Gribov copies in the first Gribov region, i.e., the space of Gribov copies at which the Faddeev-Popov operator is strictly positive (semi)definite. We investigate compact U(1) as the prototypical model of the more complicated standard model group $\mathrm{SU}(N_c)$. With our graphical processing unit implementation of the relaxation method we collect up to a few million Gribov copies per orbit. We show that the numbers of Gribov copies even in the first Gribov region increase exponentially in two, three and four dimensions. Furthermore, we provide strong indication that the number of Gribov copies is gauge orbit dependent.

We present the results of a lattice study of light-cone distribution amplitudes (DAs) of the nucleon and negative parity nucleon resonances using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to $m_{\pi }\simeq 150\mathrm{MeV}$. We find that the three valence quarks in the proton share their momentum in the proportion $37\%:31\%:31\%$, where the larger fraction corresponds to the $u$ quark that carries proton helicity, and determine the value of the wave function at the origin in position space, which turns out to be small compared to the existing estimates based on QCD sum rules. Higher-order moments are constrained by our data and are all compatible with zero within our uncertainties. We also calculate the normalization constants of the higher-twist DAs that are related to the distribution of quark angular momentum. Furthermore, we use the variational method and customized parity projection operators to study the states with negative parity. In this way we are able to separate the contributions of the two lowest states that, as we argue, possibly correspond to $N^{*}(1535)$ and a mixture of $N^{*}(1650)$ and the pion-nucleon continuum, respectively. It turns out that the state that we identify with $N^{*}(1535)$ has a very different DA as compared to both the second observed negative parity state and the nucleon, which implies different electroproduction cross sections at large transferred momenta and may be related to the difference in the decay patterns observed in experiment.

The renormalized next-to-leading-order chiral low-energy constant, $L_{10}^r$, is determined in a complete next-to-next-to-leading-order (NNLO) analysis, using a combination of lattice and continuum data for the flavor $ud$ $V-A$ correlator and results from a recent chiral sum-rule analysis of the flavor-breaking combination of $ud$ and $us$ $V-A$ correlator differences. The analysis also fixes two combinations of NNLO low-energy constants, the determination of which is crucial to the precision achieved for $L_{10}^r$. Using the results of the flavor-breaking chiral $V-A$ sum rule obtained with current versions of the strange hadronic $\tau$ branching fractions as input, we find $L_{10}^r(m_{\rho })=-0.00346(32)$. This result represents the first NNLO determination of $L_{10}^r$, having all inputs under full theoretical and/or experimental control, and the best current precision for this quantity.

Recently, a new perturbative QCD factorization formalism for heavy quarkonium production at a large transverse momentum was proposed. The phenomenological application of this new approach relies on our knowledge of a large number of universal fragmentation functions (FFs) at an input factorization scale ${\mu }_0\gtrsim 2m_Q$ with heavy quark mass $m_Q$, which are nonperturbative, and in principle, should be extracted from data. With heavy quark mass $m_Q\gg {\mathrm{\Lambda }}_{\text{QCD}}$, we calculate these input FFs in terms of nonrelativistic QCD (NRQCD) factorization. We derive contributions to these input FFs through all $S$-wave NRQCD $Q\overline{Q}$ states in a companion paper [Y. -Q. Ma, J. -W. Qiu, and H. Zhang, arXiv:1311.7078 [Phys. Rev. D (to be published)]]. In this paper, we calculate the contributions to the heavy quark-pair FFs from all $P$-wave NRQCD $Q\overline{Q}$ states.

A QCD factorization formalism was recently proposed for evaluating heavy quarkonium production at large $p_T$ at collider energies. With systematically calculated short-distance partonic hard parts and evolution kernels of fragmentation functions (FFs), the predictive power of this factorization approach relies on our knowledge of a large number of universal FFs at an input factorization scale ${\mu }_0\gtrsim 2m_Q$ with heavy quark mass $m_Q$. With the large heavy quark mass, the relative motion of the heavy quark pair inside a heavy quarkonium is effectively nonrelativistic. We evaluate these universal input FFs using nonrelativistic QCD (NRQCD) factorization and express the large number of FFs in terms of a few universal NRQCD long-distance matrix elements with perturbatively calculated coefficients. We derive complete contributions to the single-parton FFs at both $\mathcal{O}({\alpha }_s)$ and $\mathcal{O}({\alpha }_s^2)$ and the heavy quark-pair FFs at $\mathcal{O}({\alpha }_s)$. We present detailed derivation for all contributions involving long-distance matrix elements of $S$-wave NRQCD $Q\overline{Q}$ states ($P$-wave contributions in a companion paper, Y.-Q. Ma, J.-W. Qiu, and H. Zhang, arXiv:1401.0524 [Phys. Rev. D (to be published)]). Our results bridge the gap between the QCD factorization formalism and its phenomenological applications.

We calculate the $O({\alpha }_s)$ corrections to the double differential decay width $d{\mathrm{\Gamma }}_{77}/(d{s}_{1}d{s}_2)$ for the process $\overline{B}\to X_s\gamma \gamma$, originating from diagrams involving the electromagnetic dipole operator ${\mathcal{O}}_7$. The kinematical variables $s_1$ and $s_2$ are defined as $s_i=(p_b-q_i{)}^2/m_b^2$, where $p_b$, $q_1$, $q_2$ are the momenta of the $b$ quark and two photons. We introduce a nonzero mass $m_s$ for the strange quark to regulate configurations where the gluon or one of the photons become collinear with the strange quark and retain terms which are logarithmic in $m_s$, while discarding terms which go to zero in the limit $m_s\to 0$. When combining virtual and bremsstrahlung corrections, the infrared and collinear singularities induced by soft and/or collinear gluons drop out. By our cuts the photons do not become soft, but one of them can become collinear with the strange quark. This implies that in the final result a single logarithm of $m_s$ survives. In principle, the configurations with collinear photon emission could be treated using fragmentation functions. In a related work we find that similar results can be obtained when simply interpreting $m_s$ appearing in the final result as a constituent mass. We do so in the present paper and vary $m_s$ between 400 and 600 MeV in the numerics. This work extends a previous paper by us, where only the leading power terms with respect to the (normalized) hadronic mass $s_3=(p_b-q_1-q_2{)}^2/m_b^2$ were taken into account in the underlying triple differential decay width $d{\mathrm{\Gamma }}_{77}/(d{s}_{1}d{s}_{2}d{s}_3)$.

We show that it is possible to fit all of the HERA deep inelastic scattering data on $F_2^{\gamma p}$ at small values of Bjorken $x$, including the data at very low $Q^2$, using a new model for $F_2^{\gamma p}$ which both includes an asymptotic (high-energy) part that satisfies a saturated Froissart bound behavior, with a vector-dominance-like mass factor in the parametrization, and extends smoothly to $Q^2=0$. We require that the corresponding part of the virtual ${\gamma }^{*}p$ cross section match the known asymptotic part of the real $\gamma p$ cross section at $Q^2=0$, a cross section which is determined by strong interactions and asymptotically satisfies a saturated Froissart bound of the form $\alpha +\beta \ln s+\gamma {\ln }^{2}s$. Using this model for the asymptotic part of $F_2^{\gamma p}$ plus a known valence contribution, we fit the asymptotic high–energy part of the HERA data with $x\le 0.1$ and $W\ge 25\mathrm{GeV}$; the fit is excellent. We find that the mass parameter in the fit lies in the region of the light vector mesons, somewhat above the $\rho$-meson mass, and is compatible with vector dominance. We use this fit to obtain accurate results for the high-energy $ep$ and isoscalar $\nu N$ total cross sections. Both cross sections obey an analytic expression of the type $a+b\ln E+c{\ln }^{2}E+d{\ln }^{3}E$ at large energies $E$ of the incident particle, reflecting the fact that the underlying strong interaction parts of the ${\gamma }^{*}p$, $Z^{*}N$ and $W^{*}N$ cross sections satisfy the saturated Froissart bound. Since approximately 50% of the $\nu N$ center-of-mass (cms) energy is found in $W$—the cms energy of the strongly interacting intermediate vector boson–nucleon system—a study of ultra-high-energy neutrino-nucleon cross sections would allow us, for the first time, to explore strong interactions at incredibly high energies.

It is shown that it is possible to obtain the analytical expression for the effective mixing angle in matter using the formalism which was developed by Kimura, Takamura, and Yokomakura for the neutrino oscillation probability in matter with constant density. If we assume that the imaginary part of the integral of the difference of the energy eigenvalues of the two levels at each level crossing is given by the ratio $\gamma$ of the difference of the energy eigenvalues of the two levels to the derivative of the effective mixing angle at the level crossing, then the nonadiabatic contribution to the oscillation probability can be expressed analytically by this formalism. We give one example in which the energy eigenvalues cannot be expressed as roots of a quadratic equation and we show that our assumption is correct in the approximation of the small mixing angle.

We consider the Wilson-Polchinski exact renormalization group (RG) applied to the generating functional of single-trace operators at a free-fixed point in $d=2+1$ dimensions. By exploiting the rich symmetry structure of free-field theory, we study the geometric nature of the RG equations and the associated Ward identities. The geometry, as expected, is holographic, with anti–de Sitter spacetime emerging correspondent with RG fixed points. The field theory construction gives us a particular vector bundle over the $d+1$-dimensional RG mapping space, called a jet bundle, whose structure group arises from the linear orthogonal bilocal transformations of the bare fields in the path integral. The sources for quadratic operators constitute a connection on this bundle and a section of its endomorphism bundle. Recasting the geometry in terms of the corresponding principal bundle, we arrive at a structure remarkably similar to the Vasiliev theory, where the horizontal part of the connection on the principal bundle is Vasiliev’s higher spin connection, while the vertical part (the Faddeev-Popov ghost) corresponds to the $S$ field. The Vasiliev equations are then, respectively, the RG equations and the Becchi-Rouet-Stora-Tyutin equations, with the RG beta functions encoding bulk interactions. Finally, we remark that a large class of interacting field theories can be studied through integral transforms of our results, and it is natural to organize this in terms of a large $N$ expansion.

We obtain analogs of the Blandford-Znajek split monopole solution for force-free magnetospheres around a slowly rotating Kerr-AdS black hole. For small black holes, we find an analytic solution to first order in the ratio of horizon radius to AdS scale, $r_H/l$, which exhibits a radial Poynting flux and for $r_H/l\to 0$ smoothly approaches the Blandford-Znajek configuration in an asymptotically flat Kerr background. However, for large Kerr-AdS black holes with $r_H/l>1$, namely those for which the bulk black hole holographically describes the thermodynamics of a strongly interacting boundary field theory, the existence of a globally well-defined timelike Killing vector external to the horizon suggests the absence of energy extraction through the Blandford-Znajek process. In this regime, we find that at least for slow rotation the force-free solution still exists but exhibits a range of angular velocities for the field lines, corresponding to the freedom in the dual field theory to rotate a magnetic field through a neutral plasma. As a byproduct of this work, we also obtain an analytic solution for a rotating monopole magnetosphere in pure AdS, analogous to the Michel solution in flat space.

In this paper we have studied the problem of scalar particles pair creation by an electric field in the presence of a minimal length. Two sets of exact solutions for the Klein Gordon equation are given in momentum space. Then the canonical method based on Bogoliubov transformation connecting the “in” with the “out” states is applied to calculate the probability to create a pair of particles and the mean number of created particles. The number of created particles per unit of time per unit of length, which is related directly to the experimental measurements, is calculated. It is shown that, with an electric field less than the critical value, the minimal length minimizes the particle creation. It is also shown that the limit of zero minimal length reproduces the known results corresponding to the ordinary quantum fields.

No, within a broad class of scenarios. Gravitational-wave (GW) astronomy will open a new window on compact objects such as neutron stars and black holes (BHs). It is often stated that large signal-to-noise detections of ringdown or inspiral waveforms can provide estimates of the masses and spins of compact objects to within fractions of a percent, as well as tests of general relativity. These expectations usually neglect the realistic astrophysical environments in which compact objects live. With the advent of GW astronomy, environmental effects on the GW signal will eventually have to be quantified. Here we present a wide survey of the corrections due to these effects in two situations of great interest for GW astronomy: the BH ringdown emission and the inspiral of two compact objects (especially BH binaries). We mainly focus on future space-based detectors such as eLISA, but many of our results are also valid for ground-based detectors such as aLIGO, aVirgo, and KAGRA. We take into account various effects such as electric charges, magnetic fields, cosmological evolution, possible deviations from general relativity, firewalls, and the effects related to various forms of matter such as accretion disks and dark matter halos. Our analysis predicts the existence of resonances dictated by the external mass distribution, which dominate the very late-time behavior of merger and ringdown waveforms. The mode structure can drastically differ from the vacuum case, yet the BH response to external perturbations is unchanged at the time scales relevant for detectors. This is because, although the vacuum Schwarzschild resonances are no longer quasinormal modes of the system, they still dominate the response at intermediate times. Our results strongly suggest that both parametrized and ringdown searches should use at least two-mode templates. Our analysis of compact binaries shows that environmental effects are typically negligible for most eLISA sources, with the exception of very few special extreme-mass-ratio inspirals. We show, in particular, that accretion and hydrodynamic drag generically dominate over self-force effects for geometrically thin disks, whereas they can be safely neglected for geometrically thick disk environments, which are the most relevant for eLISA. Finally, we discuss how our ignorance of the matter surrounding compact objects implies intrinsic limits on the ability to constrain strong-field deviations from general relativity.

The entropic mechanism for producing nearly scale-invariant density perturbations in a contracting ekpyrotic universe relies on having an unstable scalar potential. Here we develop a variant of this mechanism (recently proposed by Qiu, Gao and Saridakis, and by Li), in which there exists a nontrivial coupling between adiabatic and entropic fields, and where an unstable potential is not required. In the model nearly scale-invariant entropy perturbations are generated first. Remarkably, we find that the bispectrum of these perturbations vanishes, with the values of the non-Gaussianity parameters of local, equilateral and orthogonal type all exactly zero. Subsequently, the entropy perturbations can be converted into curvature perturbations by a variety of mechanisms. The bispectrum of the curvature perturbations depends on the nonlinearity of the conversion process and is thus more model-dependent—however, for an efficient conversion process the final bispectrum remains small. The only distinguishing feature compared to single-field slow-roll inflationary models is that the ekpyrotic phase does not generate significant primordial gravitational waves. Thus the present model provides a perfect match to current data from the PLANCK satellite.

We calculate the time evolution of the expectation value of the energy-momentum tensor for a minimally coupled massless scalar field in cosmological spacetimes, with an application to dark energy in mind. We first study the evolution from inflation until the present, fixing the Bunch-Davies initial condition. The energy density of a quantum field evolves as $\rho \sim 3(H_{I}H{)}^2/32{\pi }^2$ in the matter-dominated (MD) period, where $H_I$ and $H$ are the Hubble parameters during inflation and at each moment. Its equation of state, $w=\rho /p$, changes from a negative value to $w=1/3$ in the radiation-dominated (RD) period, and from $1/3$ to $w=0$ in the MD period. We then consider possible effects of a Planckian universe, which may have existed before inflation, by assuming there was another inflation with the Hubble parameter $H_P(>H_I)$. In this case, modes with wavelengths longer than the current horizon radius are mainly amplified, and the energy density of a quantum field grows with time as $\rho \sim (a/a_0)(H_{P}H{)}^2/32$ in the MD period, where $a$ and $a_0$ are the scale factors at each time and at present. Hence, if $H_P$ is of the order of the Planck scale $M_P$, $\rho$ becomes comparable to the critical density $3(M_{P}H{)}^2$ at the present time. The contribution to $\rho$ from the long wavelength fluctuations generated before the ordinary inflation has $w=-1/3$ in the free field approximation. We mention a possibility that interactions further amplify the energy density and change the equation of state.

We investigate that the two types of the $Q$-balls explain the baryon asymmetry and the dark matter of the Universe in the gauge-mediated supersymmetry breaking. The gauge-mediation type $Q$-balls of one flat direction produce baryon asymmetry, while the new type $Q$-balls of another flat direction become the dark matter. We show that the dark matter new type $Q$-balls are free from the neutron star constraint. The $n=5$ gauge mediation type and $n=6$ new type $Q$-balls are displayed as an example, where the potential is lifted by the superpotential ${\mathrm{\Phi }}^n$. These dark matter $Q$-balls may be detected by future observations, such as in advanced IceCube-like observations.

We report on the observation of a significant deficit of cosmic rays from the direction of the Moon with the IceCube detector. The study of this “Moon shadow” is used to characterize the angular resolution and absolute pointing capabilities of the detector. The detection is based on data taken in two periods before the completion of the detector: between April 2008 and May 2009, when IceCube operated in a partial configuration with 40 detector strings deployed in the South Pole ice, and between May 2009 and May 2010 when the detector operated with 59 strings. Using two independent analysis methods, the Moon shadow has been observed to high significance ($>6\sigma$) in both detector configurations. The observed location of the shadow center is within 0.2° of its expected position when geomagnetic deflection effects are taken into account. This measurement validates the directional reconstruction capabilities of IceCube.

We demonstrate that light charged and extra neutral scalars in the (100–200) GeV mass range pass the potentially dangerous flavor constraints in a particular class of two-Higgs-doublet model which has appropriately suppressed flavor-changing neutral currents at tree level. We study their decay branching ratios into various fermionic final states and comment on the possibility of their detection in the collider experiments. We also remark on how their trademark decay signatures can be used to discriminate them from the light nonstandard scalars predicted in other two-Higgs-doublet models.

We revisit the $\mathrm{\Delta }F=2$ transitions in the $K$ and $B_{d,s}$ neutral meson systems in the context of the minimal left-right symmetric model. We take into account, in addition to up-to-date phenomenological data, the contributions related to the renormalization of the flavor-changing neutral Higgs tree-level amplitude. These contributions were neglected in recent discussions, albeit formally needed in order to obtain a gauge-independent result. Their impact on the minimal LR model is crucial and twofold. First, the effects are relevant in $B$ meson oscillations, for both CP conserving and CP violating observables, so that for the first time these imply constraints on the LR scenario which compete with those of the $K$ sector (plagued by long-distance uncertainties). Second, they sizably contribute to the indirect kaon CP violation parameter $ϵ$. We discuss the bounds from $B$ and $K$ mesons in both cases of LR symmetry: generalized parity ($\mathcal{P}$) and charge conjugation ($\mathcal{C}$). In the case of $\mathcal{P}$, the interplay between the CP-violation parameters $ϵ$ and ${ϵ}^{\prime }$ leads us to rule out the regime of very hierarchical bidoublet vacuum expectation values $v_2/v_1<m_b/m_t\simeq 0.02$. In general, by minimizing the scalar field contribution up to the limit of the perturbative regime and by definite values of the relevant CP phases in the charged right-handed currents, we find that a right-handed gauge boson $W_R$ as light as 3 TeV is allowed at the 95% C. L. This is well within the reach of direct detection at the next LHC run. If not discovered, within a decade the upgraded LHCb and Super B factories may reach an indirect sensitivity to a left-right scale of 8 TeV.

We study the $W^{\prime }$ phenomenology in composite Higgs/Warped extra-dimensional models focusing on the effect of fermionic resonances at $\sim 1\mathrm{TeV}$. After deriving the existing bounds from the current LHC-8 analyses, we highlight the most promising signatures for $W^{\prime }$ discovery at the 14 TeV LHC. We find in particular very promising the study of $W^{\prime }$ decay modes into vectorlike top partners, specifically the decay into a doublet of custodian heavy fermions, $T_{5/3}{T}_{2/3}$, and the decay into a heavy fermion plus a Standard Model quark. We perform a detailed parton-level analysis of the channel $W^{\prime }\to T_{5/3}{T}_{2/3}$ in the same-sign dilepton final state, finding that it is a very promising signature to test the region at high $W^{\prime }$ mass, $m_{W^{\prime }}\gtrsim 2\mathrm{TeV}$, and of the $W^{\prime }\to Tb$ mode, which is one of the best channels to test the intermediate $W^{\prime }$ mass region and that, already with the LHC-8 data, could extend the present exclusion bounds.

We explore the phase structure and symmetry breaking in four-dimensional SU(3) gauge theory with one spatial compact dimension on the lattice ($16^3\times 4$ lattice) in the presence of fermions in the adjoint representation with periodic boundary conditions. We estimate numerically the density plots of the Polyakov loop eigenvalues phases, which reflect the location of minima of the effective potential in the Hosotani mechanism. We find strong indications that the four phases found on the lattice correspond to $SU(3)$-confined, $SU(3)$-deconfined, $SU(2)\times U(1)$, and $U(1)\times U(1)$ phases predicted by the one-loop perturbative calculation. The case with fermions in the fundamental representation with general boundary conditions, equivalent to the case of imaginary chemical potentials, is also found to support the $Z_3$ symmetry breaking in the effective potential analysis.