Several popular Ansätze of lepton mass matrices that contain texture zeros are confronted with current neutrino observational data. We perform a systematic ${\chi }^2$ analysis in a wide class of schemes, considering arbitrary Hermitian charged-lepton mass matrices and symmetric mass matrices for Majorana neutrinos or Hermitian mass matrices for Dirac neutrinos. Our study reveals that several patterns are still consistent with all the observations at the 68.27% confidence level, while some others are disfavored or excluded by the experimental data. The well-known Frampton-Glashow-Marfatia two-zero textures, hybrid textures, and parallel structures (among others) are considered.

We obtain the Misner-Sharp mass in massive gravity for a four-dimensional spacetime with a two-dimensional maximally symmetric subspace via the inverse unified first law method. Significantly, the stress energy is conserved in this case with a general reference metric. Based on this property, we confirm the derived Misner-Sharp mass by the conserved charge method. We find that the existence of the Misner-Sharp mass in this case does not lead to extra constraint for the massive gravity, which is notable in modified gravities. In addition, as a special case, we also investigate the Misner-Sharp mass in the static spacetime. We make a concise discussion of the stability problem in frame of the massive gravity in consideration. Especially, we take the FRW universe into account for investigating the thermodynamics of the massive gravity. The result shows that the massive gravity can be in thermodynamic equilibrium, which fills in the gap in the previous studies of thermodynamics in the massive gravity.

We study the nature of constraints and count the number of degrees of freedom in the nonprojectable version of the $U(1)$ extension of Hořava-Lifshitz gravity, using the standard method of Hamiltonian analysis in the classical field theory. This makes it possible for us to investigate the condition under which the scalar graviton is absent at a fully nonlinear level. We show that the scalar graviton does not exist at the classical level if and only if two specific coupling constants are exactly zero. The operators corresponding to these two coupling constants are marginal for any values of the dynamical critical exponent of the Lifshitz scaling and thus should be generated by quantum corrections even if they are eliminated from the bare action. We thus conclude that the theory in general contains the scalar graviton.

Here we investigate the gravitational lensing in the strong field limit of a Schwarzschild black hole with a solid deficit angle owing to a global monopole within the context of the $f(R)$ gravity theory. We obtain the expressions of the deflection angle and time delay in the forms of elliptic integrals and discuss the asymptotic behavior of the elliptic integrals to find the explicit formulas of the angle and time difference in the strong field limit. We show that the deflection angle and the time delay between multiple images are related not only to the monopole but also to the $f(R)$ correction ${\psi }_0$ by taking the cosmological boundary into account. Some observables such as the minimum impact parameter, the angular separation, the relative magnification, and the compacted angular position are estimated as well. It is intriguing that a tiny modification on standard general relativity will make a remarkable deviation on the angle and the time lag, offering a significant way to explore some possible distinct signatures of the topological soliton and the correction of Einstein’s general relativity.

The neutron split-beam interferometer has proven to be particularly useful in measuring Newtonian gravitational effects such as those studied by Colella, Overhauser, and Werner (COW). The development of the ring laser has led to numerous applications in many areas of physics including a recent general relativistic prediction of frame dragging in the gravitational field produced by the electromagnetic radiation in a ring laser. This paper introduces a new general technique based on a canonical transformation of the Dirac equation for the gravitational field of a general linearized spacetime. Using this technique it is shown that there is a phase shift in the interference of two neutron beams due to the frame-dragging nature of the gravitational field of a ring laser.

We show that there is a special choice of parameters for which the Galileon theory is invariant under an enhanced shift symmetry whose nonlinear part is quadratic in the coordinates. This symmetry fixes the theory to be equivalent to one with only even powers of the field, with no free coefficients, and accounts for the improved soft-limit behavior observed in the quartic Galileon $S$-matrix.

Discovering the mass of neutrinos is a principle goal in high energy physics and cosmology. In addition to cosmological measurements based on two-point statistics, the neutrino mass can also be estimated by observations of neutrino wakes resulting from the relative motion between cold dark matter (CDM) and neutrinos. Such a detection relies on an accurate reconstruction of the CDM-neutrino relative velocity which is affected by nonlinear structure growth and galaxy bias. We investigate our ability to reconstruct this relative velocity using large $N$-body simulations where we evolve neutrinos as distinct particles alongside the CDM. We find that the CDM velocity power spectrum is overpredicted by linear theory whereas the neutrino velocity power spectrum is underpredicted. The magnitude of the relative velocity observed in the simulations is found to be lower than what is predicted in linear theory. Since neither the CDM nor the neutrino velocity fields are directly observable from galaxy or 21 cm surveys, we test the accuracy of a reconstruction algorithm based on halo density fields and linear theory. Assuming prior knowledge of the halo bias, we find that the reconstructed relative velocities are highly correlated with the simulated ones with correlation coefficients of 0.94, 0.93, 0.92 and 0.88 for neutrinos of mass 0.05, 0.1, 0.2 and 0.4 eV. We confirm that the relative velocity field reconstructed from large scale structure observations such as galaxy or 21 cm surveys can be accurate in direction and, with appropriate scaling, magnitude.

Terrestrial gravity noise, also known as Newtonian noise, produced by ambient seismic and infrasound fields will pose one of the main sensitivity limitations in low-frequency, ground-based, gravitational-wave (GW) detectors. It is estimated that this noise foreground needs to be suppressed by about 3–5 orders of magnitude in the frequency band 10 mHz to 1 Hz, which will be extremely challenging. In this article, we present a new approach that greatly facilitates cancellation of gravity noise in full-tensor GW detectors. The method uses optimal combinations of tensor channels and environmental sensors such as seismometers and microphones to reduce gravity noise. It makes explicit use of the direction of propagation of a GW and can, therefore, either be implemented in directional searches for GWs or in observations of known sources. We show that by using the extra strain channels in full-tensor GW detectors and a modest number of environmental sensors, the Newtonian-noise foreground can be reduced by a few orders of magnitude independent of the GW direction of propagation.

In recent lattice calculations it has been discovered that mesons upon truncation of the quasizero modes of the Dirac operator obey a symmetry larger than the $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_A$ symmetry of the QCD Lagrangian. This symmetry has been suggested to be $SU(4)\supset SU(2{)}_L\times SU(2{)}_R\times U(1{)}_A$ that mixes not only the u- and d-quarks of a given chirality, but also the left- and right-handed components. Here it is demonstrated that bilinear $\overline{q}q$ interpolating fields of a given spin $J\ge 1$ transform into each other according to irreducible representations of $SU(4)$ or, in general, $SU(2N_F)$. This fact together with the coincidence of the correlation functions establishes $SU(4)$ as a symmetry of the $J\ge 1$ mesons upon quasizero mode reduction. It is shown that this symmetry is a symmetry of the confining instantaneous charge-charge interaction in QCD. Different subgroups of $SU(4)$ as well as the $SU(4)$ algebra are explored.

Within an extended chiral constituent quark formalism, we investigate contributions from all possible five-quark components in the octet baryons to the pion-baryon (${\sigma }_{\pi B}$) and strangeness-baryon (${\sigma }_{sB}$) sigma terms: $B\equiv N,\mathrm{\Lambda },\mathrm{\Sigma },\mathrm{\Xi }$. The probabilities of the quark-antiquark components in the ground-state baryon octet wave functions are calculated by taking the baryons to be admixtures of three- and five-quark components, with the relevant transitions handled via the ${}^3{\mathrm{P}}_0$ mechanism. Predictions for ${\sigma }_{\pi B}$ and ${\sigma }_{sB}$ obtained by using input parameters taken from the literature are reported. Our results turn out to be, in general, consistent with the findings via lattice QCD and chiral perturbation theory.

We present next-to-leading order (NLO) perturbative-QCD calculations of the cross sections for $\ell N\to hX$ and $\ell N\to \mathrm{jet}X$. The main feature of these processes is that the scattered lepton is not observed, so that the hard scale that makes them perturbative is set by the transverse momentum of the hadron or jet. Kinematically, the two processes thus become direct analogs of single-inclusive production in hadronic collisions which, as has been pointed out in the literature, makes them promising tools for exploring transverse spin phenomena in QCD when the incident nucleon is transversely polarized. We find that the NLO corrections are sizable for the spin-averaged cross section. We also investigate in how far the scattering is dominated by the exchange of almost real (Weizsäcker-Williams) photons. We present numerical estimates of the cross sections for present-day fixed target experiments and for a possible future electron-ion collider.

We consider the phase diagram of QCD at very high baryon density and at zero temperature in the presence of a strong magnetic field. The state of matter at such high densities and low temperatures is believed to be a phase known as the color-flavor locked phase which breaks color and electromagnetic gauge invariance, leaving a linear combination of them, denoted as $U(1{)}_{\widetilde{em}}$, unbroken. Of the nine quarks (three flavors and three colors), five are neutral under this unbroken generator and four are oppositely charged (two with a charge of $+1$ and two with $-1$). In the presence of a magnetic field corresponding to $U(1{)}_{\widetilde{em}}$, however, the properties of the condensate change and a new phase known as the magnetic color-flavor locked (MCFL) phase is realized. This phase breaks an approximate $SU(3{)}_C\times SU(2{)}_L\times SU(2{)}_R\times U(1{)}_B\times U(1{)}_A^{-}$ symmetry of the Lagrangian to $SU(2{)}_{C+L+R}\times U(1{)}_{\widetilde{em}}$ giving rise to six Goldstone modes, five of which are pseudo Goldstone modes. These Goldstone modes are composed of excitations that correspond to both neutral quarks and charged quarks. Hence it is natural to expect that the propagators of these Goldstone modes are affected in the presence of a magnetic field, and their speed becomes considerably anisotropic. Although this anisotropy is self-evident from symmetry arguments, it has not been quantified yet. We calculate this anisotropy in the speed of the Goldstone modes using a Nambu–Jona-Lasinio model type of interaction between the quarks and comment on the impact of such anisotropic modes on transport properties of the MCFL phase.

We use canonical formalism to study the fermion determinant in different three-dimensional Abelian gauge-field backgrounds that contain nonzero magnetic and electric flux in order to understand the nonperturbative contributions to the parity-odd and parity-even parts of the phase. We show that a certain phase associated with free fermion propagation along a closed path in a momentum torus is responsible for the parity anomaly in a background with nonzero electric flux. We consider perturbations around backgrounds with nonzero magnetic flux to understand the structure of the parity-breaking perturbative term at finite temperature and mass.

Due to internal symmetries of its ghost sector, the Poincaré generators of the Gribov-Zwanziger (GZ) model are not unique. The model apparently has two linearly independent symmetric and conserved energy-momentum tensors. We show that these energy-momentum tensors are physically equivalent and differ by unobservable conserved currents only. There is a single physical energy-momentum operator that is invariant under all symmetries of the ghost sector, including Becchi-Rouet-Stora-Tyutin (BRST). This resolves concerns about Poincaré invariance raised by the explicit $x$-dependence of the BRST operator. The energy, momentum, and angular momentum of physical states are well-defined quantities that vanish for the ground state of this theory. We obtain and discuss the physical Ward identities resulting from Poincaré invariance.

We address the issue of Becchi-Rouet-Stora-Tyutin (BRST) symmetry breaking in the Gribov-Zwanziger (GZ) model, a local, renormalizable, nonperturbative approach to QCD. Explicit calculation of several examples reveals that BRST symmetry breaking apparently afflicts the unphysical sector of the theory, but may be unbroken where needed, in cases of physical interest. Specifically, the BRST-exact part of the conserved energy-momentum tensor and the BRST-exact term in the Kugo-Ojima confinement condition both have a vanishing expectation value. We analyze the origin of the breaking of BRST symmetry in the GZ model and obtain a useful sufficient condition that determines which operators preserve BRST. Observables of the GZ theory are required to be invariant under a certain group of symmetries that includes not only BRST but also others. The definition of observables is thereby sharpened and excludes all operators known to us that break BRST invariance. We take as a hypothesis that BRST symmetry is unbroken by this class of observables. If the hypothesis holds, BRST breaking is relegated to the unphysical sector of the GZ theory, and its physical states are obtained by the usual cohomological BRST construction. The fact that the horizon condition and the Kugo-Ojima confinement criterion coincide assures that color is confined in the GZ theory.

The existence of stable bound orbits of test particles is one of the most characteristic properties in black hole spacetimes. In higher-dimensional black holes, due to the dependence of gravity on the spacetime dimensions, there is no stable bound orbit balanced by Newtonian gravitational monopole force and centrifugal force, although this balance occurs in the four-dimensional Kerr black hole. In this paper, however, the existence of stable bound orbits of massive and massless particles is shown in six-dimensional singly spinning Myers-Perry black holes with a value of the spin parameter larger than a critical value. The innermost stable bound orbits and the outermost stable bound orbits are found on the rotational axis.

This article details the computation of the two-point correlators of the convergence, $E$ and $B$ modes of the cosmic shear induced by the weak lensing by large scale structure assuming that the background spacetime is spatially homogeneous and anisotropic. After detailing the perturbation equations and the general theory of weak lensing in an anisotropic universe, it develops a weak shear approximation scheme in which one can compute analytically the evolution of the Jacobi matrix. It allows one to compute the angular power spectrum of the $E$ and $B$ modes. In the linear regime, the existence of $B$ modes is a direct tracer of a late-time anisotropy and their angular power spectrum scales as the square of the shear. It is then demonstrated that there must also exist off-diagonal correlations between the $E$ modes, $B$ modes and convergence that are linear in the geometrical shear and allow one to reconstruct the eigendirections of expansion. These spectra can be measured in future large scale surveys, such as Euclid and Square Kilometre Array, and offer a new tool to test the isotropy of the expansion of the universe at low redshift.

We investigate the formation of light nuclei with the nuclear mass number less than or equal to four in $2+1$ flavor QCD using a nonperturbative improved Wilson quark and Iwasaki gauge actions. The quark mass is decreased from our previous work to the one corresponding to the pion mass of 0.30 GeV. In each multinucleon channel, the energy shift of the ground state relative to the assembly of free nucleons is calculated on two volumes, whose spatial extents are 4.3 and 5.8 fm. From the volume dependence of the energy shift, we distinguish a bound state of multinucleons from an attractive scattering state. We find that all the ground states measured in this calculation are bound states. As in the previous studies at larger $m_{\pi }$, our result indicates that at $m_{\pi }=0.30\mathrm{GeV}$ the effective interaction between nucleons in the light nuclei is relatively stronger than the one in nature, since the results for the binding energies are larger than the experimental values and a bound state appears in the dineutron channel, which is not observed in experiment. Possible sources of systematic error in this calculation are discussed.

We study constraints on left-right symmetric models from searches of semileptonic decays of $D$, $D_s$, and $B$ mesons, mediated by heavy neutrinos $N$ with masses $m_N\sim \mathrm{GeV}$ that go on their mass shell leading to a resonant enhancement of the rates. Using these processes, we examine, as a function of $m_N$ and $M_{W_R}$, the physics reach of the recently proposed high-intensity beam dump experiment SHiP, which is expected to produce a large sample of $D_s$ mesons. We compare these results with the corresponding reach of neutrinoless double beta decay experiments, as well as like-sign dilepton searches with displaced vertices at the LHC. We conclude that the SHiP experiment has clear advantages in probing the left-right symmetric models for heavy neutrinos in the GeV mass range.

We present a framework to combine data from the latest neutrinoless double-$\beta$ decay experiments for multiple isotopes and derive a limit on the effective neutrino mass $m_{\beta \beta }$ using the experimental energy distributions. The combined limits on $m_{\beta \beta }$ range between 130 and 310 meV, where the spread is due to different model calculations of nuclear matrix elements. The statistical consistency ($p$ values) between this result and the signal observation claimed by the Heidelberg-Moscow experiment is derived. The limits on $m_{\beta \beta }$ are also evaluated in a ($3+1$) sterile neutrino model, assuming all neutrinos are Majorana particles.