We extend the $k_{\perp }$-factorization formalism for exclusive photoproduction of vector mesons to the production of electroweak $Z^0$ bosons. Predictions for the $\gamma p\to Z^{0}p$ and $pp\to pp{Z}^0$ reactions are given using an unintegrated gluon distribution tested against deep inelastic data. We show distributions in the $Z^0$ rapidity, transverse momentum of $Z^0$ as well as in relative azimuthal angle between outgoing protons. The contributions of different flavors are discussed. Absorption effects lower the cross section by a factor of 1.5–2, depending on the $Z$-boson rapidity. We also discuss the production of $Z^0$ bosons in central inclusive production. Here rapidity and $(x_{\mathbf{I}\mathbf{P},1},x_{\mathbf{I}\mathbf{P},2})$ distributions of $Z^0$ are calculated. The corresponding cross section is about 3 orders of magnitude larger than that for the purely exclusive process.

Light-cone sum rules for the ${\Lambda }_b\to p$, $\Lambda$ transition form factors are derived from the correlation functions expanded by the twist of the distribution amplitudes of the ${\Lambda }_b$ baryon. In terms of the ${\Lambda }_b$ three-quark distribution amplitude models constrained by the QCD theory, we calculate the form factors at small momentum transfers and compare the results with those estimated in the conventional light-cone sum rules (LCSR) and perturbative QCD approaches. Our results indicate that the two different versions of sum rules can lead to the consistent numbers of form factors responsible for ${\Lambda }_b\to p$ transition. The ${\Lambda }_b\to \Lambda$ transition form factors from LCSR with the asymptotic $\Lambda$ baryon distribution amplitudes are found to be almost 1 order larger than those obtained in the ${\Lambda }_b$-baryon LCSR, implying that the preasymptotic corrections to the baryonic distribution amplitudes are of great importance. Moreover, the SU(3) symmetry breaking effects between the form factors $f_1^{{\Lambda }_b\to p}$ and $f_1^{{\Lambda }_b\to \Lambda }$ are computed as ${28}_{-8}^{+14}\%$ in the framework of ${\Lambda }_b$-baryon LCSR.

With the renewed distribution amplitudes of $\Lambda$, we present a reanalysis on the semileptonic decay ${\Lambda }_c\to \Lambda {\ell }^{+}\nu$ by use of the light-cone sum rule approach with two kinds of interpolating currents. The form factors describing the decay process are obtained and used to predict the decay width. With the inclusion of up to twist-6 contributions the calculations give the decay width $\Gamma =(10.04\pm 0.88)\times {10}^{-14}\mathrm{GeV}$ for Chernyak-Zhitnitsky–type current and $\Gamma =(6.45\pm 1.06)\times {10}^{-14}\mathrm{GeV}$ for Ioffe-type current. The Ioffe-type interpolating current is found to be better for the estimation of the decay rate from a comparison with experimental data.

Using new four-loop results for the heavy quark vacuum polarization and new data for bottom quark production in electron-positron annihilation, an update on the determination of charm- and bottom-quark masses through sum rules has been performed. The previous result for the charm-quark mass, $m_c(3\mathrm{GeV})=0.986(13)\mathrm{GeV}$, based on the lowest moment, is supported by the new results from higher moments which lead to consistent values with comparable errors. The new value for the bottom quark, $m_b(10\mathrm{GeV})=3.610(16)\mathrm{GeV}$, corresponding to $m_b(m_b)=4.163(16)\mathrm{GeV}$, makes use of both the new data and the new perturbative results and is consistent with the earlier determination.

The addition of gauge-singlet fermions to the standard model Lagrangian renders the neutrinos massive and allows one to explain all that is experimentally known about neutrino masses and lepton mixing by varying the values of the Majorana mass parameters $M$ for the gauge singlets and the neutrino Yukawa couplings $\lambda$. Here we explore the region of parameter space where $M$ values are much smaller than the neutrino Dirac masses $\lambda v$. In this region, neutrinos are pseudo-Dirac fermions. We find that current solar data constrain $M$ values to be less than at least ${10}^{-9}\mathrm{eV}$, and discuss the sensitivity of future experiments to tiny gauge-singlet fermion masses. We also discuss a useful basis for analyzing pseudo-Dirac neutrino mixing effects. In particular, we identify a simple relationship between elements of $M$ and the induced enlarged mixing matrix and new mass-squared differences. These allow one to directly relate bounds on the new mass-squared differences to bounds on the singlet fermion Majorana masses.

We study a matrix model which is obtained by dimensional reduction of Chern-Simons theory on $S^3$ to zero dimension. We find that, expanded around a particular background consisting of multiple fuzzy spheres, it reproduces the original theory on $S^3$ in the planar limit. This is viewed as a new type of the large $N$ reduction generalized to curved space.

We consider a large $N$, two-family Calogero and matrix model in the Hamiltonian, collective-field approach. The Bogomol’nyi limit appears and the solutions to the coupled Bogomol’nyi-Prasad-Sommerfeld equations are given by the static soliton configurations. We find all solutions close to constant and construct exact one-parameter solutions in the strong-weak dual case. Full classification of these solutions is presented.

We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates accomplished with the aid of spacetime scalar fields. With our approach we make full contact with, and give a new perspective to, the “evolving constants of motion” program. We are able to directly derive generic properties of observables, especially their dynamics and their Poisson algebra in terms of Dirac brackets, extending earlier results in the literature. We also give a new interpretation of the observables as limits of canonical maps.

It is generally believed that coupling the graviton (a classical Fierz-Pauli massless spin-2 field) to its own energy-momentum tensor successfully recreates the dynamics of the Einstein field equations order by order; however the validity of this idea has recently been brought into doubt [T. Padmanabhan, Int. J. Mod. Phys. D 17, 367 (2008).]. Motivated by this, we present a graviton action for which energy-momentum self-coupling is indeed consistent with the Einstein field equations. The Hilbert energy-momentum tensor for this graviton is calculated explicitly and shown to supply the correct second-order term in the field equations; in contrast, the Fierz-Pauli action fails to supply the correct term. A formalism for perturbative expansions of metric-based gravitational theories is then developed, and these techniques employed to demonstrate that our graviton action is a starting point for a straightforward energy-momentum self-coupling procedure that, order by order, generates the Einstein-Hilbert action (up to a classically irrelevant surface term). The perturbative formalism is extended to include matter and a cosmological constant, and interactions between perturbations of a free matter field and the gravitational field are studied in a vacuum background. Finally, the effect of a nonvacuum background is examined, and the graviton is found to develop a nonvanishing “mass-term” in the action.

We derive new formulas for the spectral energy density and total energy density of massless particles in a general spherically symmetric static metric from a generalized uncertainty principle. Compared with blackbody radiation, the spectral energy density is strongly damped at high frequencies. For large values of $r$, the spectral energy density diminishes when $r$ grows, but at the event horizon, the spectral energy density vanishes and therefore thermodynamic quantities near a black hole, calculated via the generalized uncertainty principle, do not require any cutoff parameter. We find that the total energy density can be expressed in terms of Hurwitz zeta functions. It should be noted that at large $r$ (low local temperature), the difference between the total energy density and the Stefan-Boltzmann law is too small to be observed. However, as $r$ approaches an event horizon, the effect of the generalized uncertainty principle becomes more and more important, which may be observable. As examples, the spectral energy densities in the background metric of a Schwarzschild black hole and of a Schwarzschild black hole plus quintessence are discussed. It is interesting to note that the maximum of the distribution shifts to higher frequencies when the quintessence equation of state parameter $w$ decreases.

To describe dark energy we introduce a fluid model with no free parameter on the microscopic level. The constituents of this fluid are massless particles which are a dynamical realization of the unextended $D=(3+1)$ Galilei algebra. These particles are exotic as they live in an enlarged phase space. Their only interaction is with gravity. A minimal coupling to the gravitational field, satisfying Einstein’s equivalence principle, leads to a dynamically active gravitational mass density of either sign. A two-component model containing matter (baryonic and dark) and dark energy leads, through the cosmological principle, to Friedmann-like equations. Their solutions show a deceleration phase for the early universe and an acceleration phase for the late universe. We predict the Hubble parameter $H(z)/H_0$ and the deceleration parameter $q(z)$ and compare them with available experimental data. We also discuss a reduced model (one-component dark sector) and the inclusion of radiation. Our model shows no stationary modification of Newton’s gravitational potential.

Bekenstein’s tensor-vector-scalar (TeVeS) theory has had considerable success as a relativistic theory of modified Newtonian dynamics. However, recent work suggests that the dynamics of the theory are fundamentally flawed and numerous authors have subsequently begun to consider a generalization of TeVeS where the vector field is given by an Einstein-Æther action. Herein, I develop strong-field solutions of the generalized TeVeS theory, in particular exploring neutron stars as well as neutral and charged black holes. I find that the solutions are identical to the neutron star and black hole solutions of the original TeVeS theory, given a mapping between the parameters of the two theories, and hence provide constraints on these values of the coupling constants. I discuss the consequences of these results in detail including the stability of such spacetimes as well as generalizations to more complicated geometries.

The full moments expansion of the joint probability distribution of an isotropic random field, its gradient, and invariants of the Hessian are presented in 2 and 3D. It allows for explicit expression for the Euler characteristic in ND and computation of extrema counts as functions of the excursion set threshold and the spectral parameter, as illustrated on model examples.

A model independent study of the minimal flavor violation (MFV) framework is presented, where the only sources of flavor breaking at low energy are the up and down Yukawa matrices. Two limits are identified for the Yukawa coupling expansion: linear MFV, where it is truncated at the leading terms, and nonlinear MFV, where such a truncation is not possible due to large third generation Yukawa couplings. These are then resummed to all orders using nonlinear $\sigma$-model techniques familiar from models of collective breaking. Generically, flavor-diagonal $CP$ violating (CPV) sources in the UV can induce $O(1)$ CPV in processes involving third generation quarks. Because of a residual $U(2)$ symmetry, the extra CPV in $B_d-{\overline{B}}_d$ mixing is bounded by CPV in $B_s-{\overline{B}}_s$ mixing. If operators with right-handed light quarks are subdominant, the extra CPV is equal in the two systems, and is negligible in processes involving only the first two generations. We find large enhancements in the up-type sector, both in CPV in $D-\overline{D}$ mixing and in top flavor violation.

Just one decaying dark matter chiral multiplet $N$ is introduced at the TeV scale beyond the minimal supersymmetric standard model. A heavy axino needed for the strong $CP$ solution, decaying to $N$ and minimal supersymmetric standard model particles, enables us to calculate its abundance in the scenario that the heavy axino, once dominating the energy density of the Universe, decays after the lightest supersymmetric particle decouples. Dimension 6 interactions arising from the mass scale of $E^{\pm }$ allow the lifetime of the fermionic or the bosonic superpartner of $N$ in the ${10}^{27}\mathrm{s}$ range to be compatible with the recent astrophysical bounds. A diagrammatic strategy obtaining a suppression factor $1/M^2$ is also given.

We apply black-box methods, i.e. where the performance of the method does not depend upon initial guesses, to extract excited-state energies from Euclidean-time hadron correlation functions. In particular, we extend the widely used effective-mass method to incorporate multiple correlation functions and produce effective-mass estimates for multiple excited states. In general, these excited-state effective masses will be determined by finding the roots of some polynomial. We demonstrate the method using sample lattice data to determine excited-state energies of the nucleon and compare the results to other energy-level finding techniques.

The inverse seesaw mechanism with three pairs of gauge-singlet neutrinos offers a natural interpretation of the tiny masses of three active neutrinos at the TeV scale. We combine this picture with the newly proposed Friedberg-Lee (FL) symmetry in order to understand the observed pattern of neutrino mixing. We show that the FL symmetry requires only two pairs of the gauge-singlet neutrinos to be massive, implying that one active neutrino must be massless. We propose a phenomenological ansatz with broken FL symmetry and exact $\mu \mathrm{\text{−}}\tau$ symmetry in the gauge-singlet neutrino sector, and obtain the tribimaximal neutrino mixing pattern by means of the inverse seesaw relation. We demonstrate that nonunitary corrections to this result can possibly reach the percent level, and a soft breaking of $\mu \mathrm{\text{−}}\tau$ symmetry can give rise to $CP$ violation in such a TeV-scale seesaw scenario.

We discuss short-baseline and very-short-baseline ${\nu }_e$ disappearance at a neutrino factory. We take into account geometric effects, such as from averaging over the decay straights, and the uncertainties of the cross sections. We follow an approach similar to reactor experiments with two detectors: we use two sets of near detectors at different distances to cancel systematics. We demonstrate that such a setup is very robust with respect to systematics, and can have excellent sensitivities to the effective mixing angle and squared-mass splitting. In addition, we allow for $CPT$ invariance violation, which can be tested (depending on the parameters) up to a 0.1% level.

We prove a no-ghost theorem for a bosonic string propagating in Nappi-Witten spacetime. This is achieved in two steps. We first demonstrate unitarity for a class of $\mathrm{NW}/U(1)$ modules: the norm of any state which is primary with respect to a chosen timelike $U(1)$ is non-negative. We then show that physical states–states satisfying the Virasoro constraints–in a class of modules of an affinisation of the Nappi-Witten algebra are contained in the $\mathrm{NW}/U(1)$ modules. Similar to the case of strings on ${\mathrm{AdS}}_3$, in order to saturate the spectrum obtained in light-cone quantization we are led to include modules with energy not bounded from below, which are related to modules with energy bounded from below by spectral flow automorphisms.

In this article we calculate the leading order shear viscosity in QCD using the resummed three-particle irreducible effective action. We work to 3-loop order in the effective action. We show that the integral equations that resum the pinch and collinear contributions are produced naturally by the formalism. All leading order terms are included, without the need for any kind of power counting arguments.