We consider a gedanken experiment of the scattering of a current $j=-\frac{1}{4}{F}_{\mu \nu }^i{F}_{\mu \nu }^i$ off a large nucleus to study the gluon saturation at the small-$x$ limit and compute the Sudakov factor of this process through a one-loop calculation. The differential cross section is expressed in terms of the Sudakov resummation, in which the collinear and the rapidity divergences are subtracted.

High-energy evolution equations, such as the Balitsky-Fadin-Kuraev-Lipatov (BFKL), Balitsky-Kovchegov (BK) or Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner equations, aim at resumming the high-energy (next-to-)leading logarithms appearing in QCD perturbative series. However, the standard derivations of these equations are performed in a strict high-energy limit, whereas such equations are then applied to scattering processes at large but finite energies. For this reason, there is typically a slight mismatch between the leading logs resummed by these evolution equations without finite-energy corrections and the leading logs actually present in the perturbative expansion of any observable. That mismatch is one of the sources of large corrections at next-to-leading-order and next-to-leading-logarithmic accuracy. In the case of the BFKL equation in momentum space, this problem is solved by including a kinematical constraint in the kernel, which is the most important finite-energy correction. In this paper, such an improvement of kinematics is performed in mixed space (transverse positions and $k^{+}$) and with a factorization scheme in the light-cone momentum $k^{+}$ (in a frame in which the projectile is right-moving and the target left-moving). This is the usual choice of variables and factorization scheme for the the BK equation. A kinematically improved version of the BK equation is provided, consistent at finite energies. The results presented here are also a necessary step towards having the high-energy limit of QCD (including gluon saturation) quantitatively under control beyond strict leading-logarithmic accuracy.

The top quark, being the heaviest particle of the Standard Model (SM), is a prime candidate of where physics beyond the SM (BSM) might currently hide before our eyes. There are many natural extensions of the SM that rely on top compositeness, and the top quark could follow the paradigm of revealing a substructure when it is probed at high enough momentum transfers. Observing high $p_T$ top final states naturally drives us toward boosted hadronic analyses that can be tackled efficiently with jet substructure techniques. In this paper we analyze the prospects of constraining exemplary nonstandard QCD top interactions in this kinematical regime. We correctly include QCD modifications to additional gluon emission off the boosted top quark and keep track of the modified top tagging efficiencies. We conclude that nonstandard top QCD interactions can be formidably constrained at the LHC 14 TeV. Experimental systematic uncertainties are a major obstacle of the described measurement. Unless significantly improved for the 14 TeV run, they will saturate the direct sensitivity to nonresonant BSM top physics at luminosities of around $100/\mathrm{fb}$.

The most general case of self-induced neutrino flavor evolution is described by a set of kinetic equations for a dense neutrino gas evolving in both space and time. Solutions of these equations have been typically worked out assuming that either the time (in the core-collapse supernova environment) or space (in the early Universe) homogeneity in the initial conditions is preserved through the evolution. In these cases, one can gauge away the homogeneous variable and reduce the dimensionality of the problem. In this paper, we investigate whether small deviations from an initial postulated homogeneity can be amplified by the interacting neutrino gas, leading to a new flavor instability. To this end, we consider a simple two-flavor isotropic neutrino gas evolving in time, and initially composed by only ${\nu }_e$ and ${\overline{\nu }}_e$ with equal densities. In the homogeneous case, this system shows a bimodal instability in the inverted mass hierarchy scheme, leading to the well-studied flavor pendulum behavior. This would lead to periodic pair conversions ${\nu }_e{\overline{\nu }}_e\leftrightarrow {\nu }_x{\overline{\nu }}_x$. To break space homogeneity, we introduce small amplitude space-dependent perturbations in the matter potential. By Fourier transforming the equations of motion with respect to the space coordinate, we then numerically solve a set of coupled equations for the different Fourier modes. We find that even for arbitrarily tiny inhomogeneities, the system evolution runs away from the stable pendulum behavior: the different modes are excited and the space-averaged ensemble evolves towards flavor equilibrium. We finally comment on the role of a time decaying neutrino background density in weakening these results.

We present the analysis of the renormalization-based evolution of the $CP$-violation observables obtained from the $C$ matrix introduced by Jarlskog. We show that the observables $|\det C|$ and $\mathrm{Tr}{C}^2$ decrease very fast with the energy and their value is reduced at the Planck scale by 5 and 3 orders of magnitude, respectively, with respect to their low-energy values. On the other hand, the Jarlskog Cabibbo-Kobayashi-Maskawa matrix rephasing invariant $J$ increases with energy and at the Planck scale is 25% larger than at low energy. The absolute value of the coefficient $a_{CP}\sim \det C/(\mathrm{Tr}{C}^2{)}^{3/2}$ decreases with energy, and at the Planck scale it is 12% smaller than at low energy. We also find that the pattern of the eigenvalues of the $C$ matrix is such that two eigenvalues almost cancel each other and their absolute values are much bigger than the absolute value of the third eigenvalue. The low rate of $CP$ violation is a consequence of this pattern of the eigenvalues.

Using a sample of dilepton top-quark pair ($t\overline{t}$) candidate events, a study is performed of the production of top-quark pairs together with heavy-flavor (HF) quarks, the sum of $t\overline{t}+b+X$ and $t\overline{t}+c+X$, collectively referred to as $t\overline{t}+\mathrm{HF}$. The data set used corresponds to an integrated luminosity of $4.7{\mathrm{fb}}^{-1}$ of proton-proton collisions at a center-of-mass energy of 7 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. The presence of additional HF ($b$ or $c$) quarks in the $t\overline{t}$ sample is inferred by looking for events with at least three $b$-tagged jets, where two are attributed to the $b$ quarks from the $t\overline{t}$ decays and the third to additional HF production. The dominant background to $t\overline{t}+\mathrm{HF}$ in this sample is $t\overline{t}+\text{jet}$ events in which a light-flavor jet is misidentified as a heavy-flavor jet. To determine the heavy- and light-flavor content of the additional $b$-tagged jets, a fit to the vertex mass distribution of $b$-tagged jets in the sample is performed. The result of the fit shows that $79\pm 14(\text{stat})\pm 22(\text{syst})$ of the 105 selected extra $b$-tagged jets originate from HF quarks, 3 standard deviations away from the hypothesis of zero $t\overline{t}+\mathrm{HF}$ production. The result for extra HF production is quoted as a ratio ($R_{\mathrm{HF}}$) of the cross section for $t\overline{t}+\mathrm{HF}$ production to the cross section for $t\overline{t}$ production with at least one additional jet. Both cross sections are measured in a fiducial kinematic region within the ATLAS acceptance. $R_{\mathrm{HF}}$ is measured to be $[6.2\pm 1.1(\text{stat})\pm 1.8(\text{syst})]\%$ for jets with $p_T>25\mathrm{GeV}$ and $|\eta |<2.5$, in agreement with the expectations from Monte Carlo generators.

We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang–Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansätze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called “power-law” running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.

We show that the total gluon helicity $\mathrm{\Delta }G$ in a polarized nucleon can be calculated on a Euclidean lattice through a universality class of QCD operators that describe the helicity or polarization of the on-shell gluon radiation. We in particular find some operators whose matrix elements in a nucleon of momentum $P^z$ are directly related to $\mathrm{\Delta }G$ with only power-law $(1/P^z{)}^n(n\ge 2)$ corrections.

We investigate the superradiant instability for a charged scalar field in a $D$-dimensional small Reissner–Nordström–anti-de Sitter (RN-AdS) black hole. First, we solve the charged Klein-Gordon equation analytically by a matching method. We show that the general $D$-dimensional quasinormal frequencies depend on the relation between the angular momentum quantum number, $\ell$, and $D$. When $\ell$ is a (non-negative) integer multiple of $D-3$, i.e. $\ell =p(D-3)$, we find an analytical quasinormal frequency formula adding a purely imaginary correction to the AdS normal frequencies. This is the case for all $\ell$ modes in $D=4$. For general $D$ there are two more cases: i) When $\ell$ obeys $\ell =(p+\frac{1}{2})(D-3)$, which can occur for odd $D$, we observe that the matching method fails, since the near- and far-region solutions have different functional dependences. ii) For all other cases, the analytical quasinormal frequency formula gives a complex correction to the AdS normal frequencies. Second, we perform a numerical calculation which confirms the analytical formulas obtained with the matching method and allows us to explore the case where that method failed. In the latter case, as in the former, we verify that all $\ell$ modes for all $D$ may become superradiant, which contradicts a previous claim in the literature.

We provide a well-defined variational principle for three-dimensional flat space Einstein gravity by adding one-half of the Gibbons-Hawking-York boundary term to the bulk action. We check the zero-point function, recovering consistency with thermodynamics of flat space cosmologies. We then apply our result to calculate the one-point functions in flat space Einstein gravity for the vacuum and all flat space cosmologies. The results are compatible with the ones for the zero-mode charges obtained by canonical analysis.

The problem of reconstructing the sky position of compact binary coalescences detected via gravitational waves is a central one for future observations with the ground-based network of gravitational-wave laser interferometers, such as Advanced LIGO and Advanced Virgo. Different techniques for sky localization have been independently developed. They can be divided in two broad categories: fully coherent Bayesian techniques, which are high latency and aimed at in-depth studies of all the parameters of a source, including sky position, and “triangulation-based” techniques, which exploit the data products from the search stage of the analysis to provide an almost real-time approximation of the posterior probability density function of the sky location of a detection candidate. These techniques have previously been applied to data collected during the last science runs of gravitational-wave detectors operating in the so-called initial configuration. Here, we develop and analyze methods for assessing the self consistency of parameter estimation methods and carrying out fair comparisons between different algorithms, addressing issues of efficiency and optimality. These methods are general, and can be applied to parameter estimation problems other than sky localization. We apply these methods to two existing sky localization techniques representing the two above-mentioned categories, using a set of simulated inspiral-only signals from compact binary systems with a total mass of $\le 20M_{\odot }$ and nonspinning components. We compare the relative advantages and costs of the two techniques and show that sky location uncertainties are on average a factor $\approx 20$ smaller for fully coherent techniques than for the specific variant of the triangulation-based technique used during the last science runs, at the expense of a factor $\approx 1000$ longer processing time.

In this paper we study the evolution of cosmological perturbations through a nonsingular bouncing universe using covariant perturbation theory and examine the validity of linear perturbation theory. The bounce is modeled by a two component perfect fluid. Gauge invariant perturbations are defined in terms of the comoving observers. The scalar and vector perturbations become singular at the turning point, which is the boundary of the spacetime region where the null energy condition is violated. Nonadiabatic modes of comoving curvature perturbation diverge at the turning point. The gravitational waves oscillate around the bounce and the turning point. By computing the growth of linearity parameters, it has been shown that the perturbations do not remain linear at the turning point. We also study the matching conditions on scalar perturbations and $\mathcal{V}$, related to the spatial curvature perturbation, is found to be the appropriate variable to be matched across transition surface.

We study scalar fields subject to an equation of the Klein-Gordon type in nonstationary spacetimes, such as those found in cosmology, assuming that all the relevant spatial dependence is contained in the Laplacian. We show that the field description—with a specific canonical pair—and the Fock representation for the quantization of the field are fixed indeed in a unique way (except for unitary transformations that do not affect the physical predictions) if we adopt the combined criterion of (a) imposing the invariance of the vacuum under the group of spatial symmetries of the field equations and (b) requiring a unitary implementation of the dynamics in the quantum theory. Besides, we provide a spacetime interpretation of the field equations as those corresponding to a scalar field in a cosmological spacetime that is conformally ultrastatic. In addition, in the privileged Fock quantization, we investigate the generalization of the evolution of physical states from the hyperbolic dynamical regime to an elliptic regime. In order to do this, we contemplate the possibility of processes with signature change in the spacetime where the field propagates and discuss the behavior of the background geometry when the change happens, proving that the spacetime metric degenerates. Finally, we argue that this kind of signature change leads naturally to a phenomenon of particle creation, with exponential production.

We investigate the effects of the background primordial magnetic field (PMF) on the cosmic microwave background (CMB). The sound speed of the tightly coupled photon-baryon fluid is increased by the background PMF. The increased sound speed causes the odd peaks of the CMB temperature fluctuations to be suppressed and the CMB peak positions to be shifted to a larger scale. The background PMF causes a stronger decaying potential and increases the amplitude of the CMB. These two effects of the background PMF on a smaller scale cancel out, and the overall effects of the background PMF are the suppression of the CMB around the first peak and the shifting of peaks to a larger scale. We also discuss obtaining information about the PMF generation mechanisms, and we examine the nonlinear evolution of the PMF by the constraint on the maximum scale for the PMF distributions. Finally, we discuss degeneracies between the PMF parameters and the standard cosmological parameters.

In this paper I exhibit a class of reflection-positive Euclidean invariant four-point functions that can be used to formulate a Poincaré invariant quantum theory. I demonstrate the existence of scattering wave operators, which can be calculated without analytic continuation in this representation.

We present a $2+1$-flavor lattice QCD calculation of the electromagnetic Dirac and Pauli form factors of the octet baryons. The magnetic Sachs form factor is extrapolated at six fixed values of $Q^2$ to the physical pseudoscalar masses and infinite volume using a formulation based on heavy-baryon chiral perturbation theory with finite-range regularization. We properly account for omitted disconnected quark contractions using a partially quenched effective field theory formalism. The results compare well with the experimental form factors of the nucleon and the magnetic moments of the octet baryons.

The axial magnetic effect is the generation of an equilibrium dissipationless energy flow of chiral fermions in the direction of the axial (chiral) magnetic field. At finite temperature the dissipationless energy transfer may be realized in the absence of any chemical potentials. We numerically study the temperature behavior of the axial magnetic effect in quenched $SU(2)$ lattice gauge theory. We show that in the confinement (hadron) phase the effect is absent. In the deconfinement transition region the conductivity quickly increases, reaching the asymptotic $T^2$ behavior in a deep deconfinement (plasma) phase. Apart from an overall proportionality factor, our results qualitatively agree with theoretical predictions for the behavior of the energy flow as a function of temperature and strength of the axial magnetic field.

A relativistic world-line Hamiltonian for strongly interacting $3q$ systems in a magnetic field is derived from the path integral for the corresponding Green’s function. The neutral baryon Hamiltonian in the magnetic field obeys the pseudomomentum conservation and allows a factorization of the c.m. and internal motion. The resulting expression for the baryon mass in the magnetic field is written explicitly with the account of hyperfine, one pion exchange, and one gluon exchange (color Coulomb) interaction. The neutron mass is fast decreasing with the magnetic field, losing $1/2$ of its value at $eB\sim 0.25{\mathrm{GeV}}^2$ and is nearly zero at $eB\sim 0.5{\mathrm{GeV}}^2$. Possible physical consequences of the calculated mass trajectory of the neutron, $M_n(B)$, are presented and discussed.

We present the first calculation of inclusive jet photoproduction with approximate next-to-next-to-leading-order contributions, obtained from a unified threshold resummation formalism. The leading coefficients for direct photoproduction are computed analytically. Together with the coefficients pertinent to parton-parton scattering, they are shown to agree with those appearing in our full next-to-leading-order calculations. For hadron-hadron scattering, numerical agreement is found with a previous calculation of jet production at the Tevatron. We show that the direct and resolved approximate next-to-next-to-leading-order contributions considerably improve the description of final ZEUS data on jet photoproduction and that the error on the determination of the strong coupling constant is significantly reduced.

In a relativistic quark model we study the structure of the $N(1710)$ resonance, and the ${\gamma }^{*}N\to N(1710)$ reaction focusing on the high momentum transfer region, where the valence quark degrees of freedom are expected to be dominant. The $N(1710)$ resonance, a state with spin 1/2 and positive parity ($J^P={\frac{1}{2}}^{+}$), can possibly be interpreted as the second radial excitation of the nucleon, after the Roper, $N(1440)$. We calculate the ${\gamma }^{*}N\to N(1710)$ helicity amplitudes, and predict that they are almost identical to those of the ${\gamma }^{*}N\to N(1440)$ reaction in the high momentum transfer region. Thus, future measurement of the helicity amplitudes for the ${\gamma }^{*}N\to N(1710)$ reaction can give a significant hint on the internal structure of the $N(1710)$ state.