We present a complete study of the leading-twist quark Wigner distributions in the nucleon, discussing both the $\mathsf{T}$-even and $\mathsf{T}$-odd sectors, along with all the possible configurations of the quark and nucleon polarizations. We identify the basic multipole structures associated with each distribution in the transverse phase space, providing a transparent interpretation of the spin-spin and spin-orbit correlations of quarks and nucleons encoded in these functions. Projecting the multipole parametrization of the Wigner functions onto the transverse-position and the transverse-momentum spaces, we find a natural link with the corresponding multipole parametrizations for the generalized parton distributions and transverse-momentum dependent parton distributions, respectively. Finally, we show results for all the distributions in the transverse phase space, introducing a representation that allows one to visualize simultaneously the multipole structures in both the transverse-position and transverse-momentum spaces.

An updated measurement of the single top quark production cross section is presented using the full data set collected by the Collider Detector at Fermilab (CDF), corresponding to $9.5{\mathrm{fb}}^{-1}$ of integrated luminosity from proton-antiproton collisions at 1.96 TeV center-of-mass energy. The events selected contain an imbalance in the total transverse momentum, jets identified as containing $b$ quarks, and no identified leptons. The sum of the $s$- and $t$-channel single top quark cross sections is measured to be $3.53_{-1.16}^{+1.25}\mathrm{pb}$ and a lower limit on the magnitude of the top-to-bottom quark coupling, $|V_{tb}|$ of 0.63, is obtained at the 95% credibility level. These measurements are combined with previously reported CDF results obtained from events with an imbalance in total transverse momentum, jets identified as originating from $b$ quarks, and one identified lepton. The combined cross section is measured to be $3.02_{-0.48}^{+0.49}\mathrm{pb}$ and a lower limit on $|V_{tb}|$ of 0.84 is obtained at the 95% credibility level.

We present a measurement of the branching fraction and the longitudinal polarization fraction of $B^0\to {\rho }^{+}{\rho }^{-}$ decays, as well as the time-dependent $CP$ violating parameters in decays into longitudinally polarized ${\rho }^{+}{\rho }^{-}$ pairs with Belle’s final data set of $772\times {10}^6$ $B\overline{B}$ pairs, at the $\mathrm{\Upsilon }(4S)$ resonance, collected at the asymmetric-energy $e^{+}{e}^{-}$ collider KEKB. We obtain $\mathcal{B}(B^0\to {\rho }^{+}{\rho }^{-})=(28.3\pm 1.5(\text{stat})\pm 1.5(\text{syst}))\times {10}^{-6}$, $f_L=0.988\pm 0.012(\text{stat})\pm 0.023(\text{syst})$, ${\mathcal{A}}_{CP}=0.00\pm 0.10(\text{stat})\pm 0.06(\text{syst})$, ${\mathcal{S}}_{CP}=-0.13\pm 0.15(\text{stat})\pm 0.05(\text{syst})$. We perform an isospin analysis to constrain the Cabibbo-Kobayashi-Maskawa angle ${\varphi }_2$ and obtain two solutions with ${\varphi }_2=(93.7\pm 10.6)°$, being most compatible with other Standard-Model based fits to the data.

The differential cross-section for pair production of top quarks with high transverse momentum is measured in $20.3{\mathrm{fb}}^{-1}$ of proton-proton collisions at a center-of-mass energy of 8 TeV. The measurement is performed for $t\overline{t}$ events in the $\mathrm{lepton}+\mathrm{jets}$ channel. The cross-section is reported as a function of the hadronically decaying top quark transverse momentum for values above 300 GeV. The hadronically decaying top quark is reconstructed as an anti-$k_t$ jet with radius parameter $R=1.0$ and identified with jet substructure techniques. The observed yield is corrected for detector effects to obtain a cross-section at particle level in a fiducial region close to the event selection. A parton-level cross-section extrapolated to the full phase space is also reported for top quarks with transverse momentum above 300 GeV. The predictions of a majority of next-to-leading-order and leading-order matrix-element Monte Carlo generators are found to agree with the measured cross-sections.

We show that both the leading and subleading double soft theorems of the nonlinear sigma model follow from a shift symmetry enforcing Adler’s zero condition in the presence of an unbroken global symmetry. They do not depend on the underlying coset $G/H$ and are universal infrared behaviors of Nambu-Goldstone bosons. Although nonlinear sigma models contain an infinite number of interaction vertices, the double soft limit is determined entirely by a single four-point interaction, together with the existence of Adler’s zeros.

We analyze a spin precession of slow neutrons in the Einstein-Cartan gravity with torsion, chameleon and magnetic field. For the derivation of the Heisenberg equation of motion of the neutron spin we use the effective low-energy potential, derived by Ivanov and Wellenzohn [Phys. Rev. D 92, 125004 (2015)] for slow neutrons, coupled to gravitational, chameleon, and torsion fields to order $1/m$, where $m$ is the neutron mass. In addition to these low-energy interactions we switch on the interaction of slow neutrons with a magnetic field. We show that to linear order approximation with respect to gravitational, chameleon, and torsion fields the Dirac Hamilton operator for fermions (neutrons), moving in spacetimes created by rotating coordinate systems, contains the anti-Hermitian operators of torsion-fermion (neutron) interactions, caused by torsion scalar and tensor space-space-time and time-space-space degrees of freedom. Such anti-Hermitian operators violate $CP$ and $T$ invariance. In the low-energy approximation the $CP$ and $T$ violating torsion-fermion (neutron) interactions appear only to order $O(1/m)$. One may assume that in the rotating Universe and galaxies the obtained anti-Hermitian torsion-fermion interactions might be an origin of (i) violation of $CP$ and $T$ invariance in the Universe and (ii) of baryon asymmetry. We show that anti-Hermitian torsion-fermion interactions of relativistic fermions, violating $CP$ and $T$ invariance, (i) cannot be removed by nonunitary transformations of the Dirac fermion wave functions and (ii) are conformal invariant. According to general requirements of conformal invariance of massive particle theories in gravitational fields [see R. H. Dicke, Phys. Rev. 125, 2163 (1962) and A. J. Silenko, Phys. Rev. D 91, 065012 (2015)], conformal invariance of anti-Hermitian torsion-fermion interactions is valid only if the fermion mass is changed by a conformal factor.

The process of fermion production in the field of a magnetic dipole on a de Sitter expanding universe is analyzed. The amplitude and probability for production of massive fermions are obtained using the exact solution of the Dirac equation written in the momentum-helicity basis. We found that the most probable transitions are those that generate the fermion pair perpendicular to the direction of the magnetic field. The behavior of the probability is graphically studied for large/small values of the expansion factor, and a detailed analysis of the probability in terms of the angle between the momenta vectors of the particle and antiparticle is performed. The phenomenon of fermion production is significant only at a large expansion, which corresponds to the conditions from the early universe. When the expansion factor vanishes, we recover the Minkowski limit where this process is forbidden by the simultaneous energy-momentum conservation.

Massive gravity in the weak field limit is described by the Fierz-Pauli theory with 5 degrees of freedom in four dimensions. In this theory, we calculate the gravitomagnetic effects (potential energy) between two pointlike, spinning sources that also orbit around each other in the limit where the spins and the velocities are small. Spin-spin, spin-orbit and orbit-orbit interactions in massive gravity theory have rather remarkable, discrete differences from their counterparts in general relativity. Our computation is applicable for large distances, for example, for interaction between galaxies or galaxy clusters where massive gravity is expected to play a role. We also extend the computations to quadratic gravity theories in four dimensions and find the lowest order gravitomagnetic effects and show that at small separations quadratic gravity behaves differently than general relativity.

Provided the quantum fluctuations are amplified in the presence of a classical gauge field configuration the resulting curvature perturbations exhibit a mild statistical anisotropy which should be sufficiently weak not to conflict with current observational data. The curvature power spectra induced by weakly anisotropic initial states are computed here for the first time when the electric and the magnetic gauge couplings evolve at different rates as it happens, for instance, in the relativistic theory of van der Waals interactions. After recovering the results valid for coincident gauge couplings, the constraints imposed by the isotropy and the homogeneity of the initial states are discussed. The obtained bounds turn out to be more stringent than naively expected and cannot be ignored when discussing the underlying magnetogenesis scenarios.

We revisit the velocity-dependent one-scale model for topological defect evolution and present a new alternative formulation in terms of a physical (rather than invariant) characteristic length scale. While the two approaches are equivalent (as we explicitly demonstrate), the new one is particularly relevant when studying the evolution of ultrarelativistic defects. Moreover, a comparison of the two provides further insight on the interpretation of the model’s two phenomenological parameters, $c$ related to energy losses and $k$ related to the curvature of the defects. As an illustration of the relevance of the new formulation, we use it to study the evolution of cosmic string and domain wall networks in contracting universes. We show that these networks are ultrarelativistic and conformally contracted, with the physical length scale behaving as $L_{\mathrm{ph}}\propto a$ and the density as $\rho \propto a^{-4}$ (as in a radiation fluid) in both cases. On the other hand, the velocity and invariant length respectively behave as $(\gamma v)\propto a^{-n}$ and $L_{\text{inv}}\propto a^{\frac{4}{4-n}}$, where $n$ is the number of dimensions of the defect’s world sheet. Finally, we also study an alternative friction-dominated scenario and show that the stretching and Kibble regimes identified in the case of expanding universes can also occur for contracting ones.

We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first- and second-order fully relativistic perturbation theory in the synchronous-comoving gauge allows us to go beyond the Newtonian predictions and to calculate relativistic corrections to it. We use an Einstein–de Sitter model, including both growing and decaying modes in our solutions. The impact of our results should be assessed through the implementation of the featured displacement in cosmological $N$-body simulations.

In this paper we will examine the consequence of a canonical theory of quantum dust collapse in $2+1$ dimensions. The solution of the Wheeler-DeWitt equation describing the collapse indicates that collapsing shells outside the apparent horizon are accompanied by outgoing shells within the apparent horizon during their collapse phase and stop collapsing once they reach the apparent horizon. Taking this picture of quantum collapse seriously, we determine a static solution with energy density corresponding to a dust ball whose collapse has terminated at the apparent horizon. We show that the boundary radius of the ball is larger than the Banados-Teitelboim-Zanelli radius confirming that no event horizon is formed. The ball is sustained by radial pressure which we determine and which we attribute to the Unruh radiation within it.

In this paper we present the results of the first low frequency all-sky search of continuous gravitational wave signals conducted on Virgo VSR2 and VSR4 data. The search covered the full sky, a frequency range between 20 and 128 Hz with a range of spin-down between $-1.0\times {10}^{-10}$ and $+1.5\times {10}^{-11}\mathrm{Hz}/\mathrm{s}$, and was based on a hierarchical approach. The starting point was a set of short fast Fourier transforms, of length 8192 s, built from the calibrated strain data. Aggressive data cleaning, in both the time and frequency domains, has been done in order to remove, as much as possible, the effect of disturbances of instrumental origin. On each data set a number of candidates has been selected, using the FrequencyHough transform in an incoherent step. Only coincident candidates among VSR2 and VSR4 have been examined in order to strongly reduce the false alarm probability, and the most significant candidates have been selected. The criteria we have used for candidate selection and for the coincidence step greatly reduce the harmful effect of large instrumental artifacts. Selected candidates have been subject to a follow-up by constructing a new set of longer fast Fourier transforms followed by a further incoherent analysis, still based on the FrequencyHough transform. No evidence for continuous gravitational wave signals was found, and therefore we have set a population-based joint VSR2-VSR4 90% confidence level upper limit on the dimensionless gravitational wave strain in the frequency range between 20 and 128 Hz. This is the first all-sky search for continuous gravitational waves conducted, on data of ground-based interferometric detectors, at frequencies below 50 Hz. We set upper limits in the range between about $10^{-24}$ and $2\times {10}^{-23}$ at most frequencies. Our upper limits on signal strain show an improvement of up to a factor of $\sim 2$ with respect to the results of previous all-sky searches at frequencies below 80 Hz.

Many models on the market allow for particles carrying both lepton number and color, e.g., leptoquarks and leptogluons. Some of the models with this feature can also accommodate color-singlet leptohadrons. We have found that the long-standing discrepancy between the experimental result and the Standard Model prediction for the muon anomalous magnetic moment can be explained by the effect of leptomesons with masses of a few hundred GeV and couplings to the leptons and mesons either of $\mathcal{O}(10^{-2})$ (vector-meson case) or of $\mathcal{O}(1)$ (scalar case). These new particles are testable at the current run of the LHC.

In this paper we report on lattice simulations of $SU(3)$–QCD with nonzero chiral chemical potential. We focus on the influence of the chiral chemical potential on the confinement/deconfinement phase transition and the breaking/restoration of chiral symmetry. The simulation is carried out with dynamical Wilson fermions. We find that the critical temperature rises as the chiral chemical potential grows.

Remarkable symmetry properties appear to arise in lattice calculations of correlation functions in which the lowest-lying eigenmodes of the Dirac operator in quark propagators are removed by hand. The Banks-Casher relation ties the chiral condensate to the density of low-lying modes; thus, it is plausible that removal of such modes could lead to a regime where spontaneous chiral symmetry breaking does not occur. Surprising, a pattern of identical correlation functions was observed that is larger than can be explained by a restoration of chiral symmetry. This suggests that a larger symmetry—one that is not present in the QCD Lagrangian—emerges when these modes are removed. Previously it was argued that this emergent symmetry was SU(4). However, when the low-lying modes are removed, the correlation functions of sources in the SU(4) 15-plet of spin-1 mesons appear to coincide with the correlation function of the SU(4) singlet. A natural explanation for this is an emergent symmetry larger than SU(4). In this work, it is shown that there exists no continuous symmetry whose generators in the field theory are spatial integrals of local operators that can account for the full pattern of identical correlation functions unless the apparent coincidence of the singlet channel with the 15-plet is accidental.

We investigate the effects of the violation of the Ginsparg-Wilson (GW) relation in the Möbius domain-wall fermion formulation on the lattice with finite fifth dimension. Using a decomposition in terms of the eigenmodes of its four-dimensional effective Dirac operator, we isolate the GW-violating terms for various physical quantities including the residual mass and the meson susceptibilities relevant for the effective restoration of the axial U(1) symmetry at finite temperature. Numerical result shows that the GW-violating effect is more significant, or even overwhelming, for the quantities that are dominated by the low-lying eigenmodes.

The empirical absence to date of particles obeying parastatistics in high-energy collider experiments might be due to their large masses, weak scale couplings, and lack of gauge couplings. Paraparticles of order $p=2$ must be pair produced, so the lightest such particles are absolutely stable and so are excellent candidates to be associated with dark matter and/or dark energy. If there is a portal to such particles, from a new scalar $A_1$ boson they might be cascade emitted as a pair of para-Majorana neutrinos as in $A_1\to A_2{\breve{\nu }}_{\alpha }{\breve{\nu }}_{\beta }$ or as a pair of neutral spin-zero paraparticles such as in $A_1\to A_2\breve{A}\breve{B}$, where $\breve{B}$ is the anti-paraparticle to $\breve{A}$. In this paper, for an assumed supersymmetric-like “statistics portal” Lagrangian, the associated connected tree diagrams and their parastatistical factors are obtained for the case of order $p=2$ parastatistics. These factors are compared with the corresponding statistical factors for the analogous emission of a nondegenerate or a twofold degenerate pair which obey normal statistics. This shows that diagrams, and diagrammatic thinking, can be useful in perturbatively analyzing paraparticle processes. The parastatistical factor associated with each diagram does require explicit calculation.

In this paper, we present a detailed comparison of the bottom production in gluon-gluon, photon-gluon, photon-photon, Pomeron-gluon, Pomeron-Pomeron and Pomeron-photon interactions at the LHC. The transverse momentum, pseudorapidity and $\xi$ dependencies of the cross sections are calculated at LHC energy using the Forward Physics Monte Carlo, which allows us to obtain realistic predictions for the bottom production with one or two leading intact protons. Moreover, predictions for the kinematical range probed by the LHCb Collaboration are also presented. Our results indicate that the analysis of the single diffractive events is feasible using the Run I LHCb data.

We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ using the decay $B\to D\ell {\nu }_{\ell }$ ($\ell =e,\mu$) based on $711{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}\to \mathrm{\Upsilon }(4S)$ data recorded by the Belle detector and containing $772\times {10}^6$ $B\overline{B}$ pairs. One $B$ meson in the event is fully reconstructed in a hadronic decay mode, while the other, on the signal side, is partially reconstructed from a charged lepton and either a $D^{+}$ or $D^0$ meson in a total of 23 hadronic decay modes. The isospin-averaged branching fraction of the decay $B\to D\ell {\nu }_{\ell }$ is found to be $\mathcal{B}(B^0\to D^{-}{\ell }^{+}{\nu }_{\ell })=(2.31\pm 0.03(\mathrm{stat})\pm 0.11(\mathrm{syst}))\%$. Analyzing the differential decay rate as a function of the hadronic recoil with the parametrization of Caprini, Lellouch, and Neubert and using the form-factor prediction $\mathcal{G}(1)=1.0541\pm 0.0083$ calculated by FNAL/MILC, we obtain ${\eta }_{\mathrm{EW}}|V_{cb}|=(40.12\pm 1.34)\times {10}^{-3}$, where ${\eta }_{\mathrm{EW}}$ is the electroweak correction factor. Alternatively, assuming the model-independent form-factor parametrization of Boyd, Grinstein, and Lebed and using lattice QCD data from the FNAL/MILC and HPQCD collaborations, we find ${\eta }_{\mathrm{EW}}|V_{cb}|=(41.10\pm 1.14)\times {10}^{-3}$.