Within the model of a Lorentz violating extension of the Maxwell sector of the standard model, modified light propagation leads to a change of the resonance frequency of an electromagnetic cavity, allowing cavity tests of Lorentz violation. However, the frequency is also affected by a material-dependent length change of the cavity due to a modified Coulomb potential arising from the same Lorentz violation as well. We derive the frequency change of the cavity taking both into account. The new effects derived are negligible for present experiments, but will be more pronounced in future tests using novel resonator materials.

We study the effects of the violation of the equivalence principle (VEP) or the violation of Lorentz invariance (LIV) in the neutrino sector on the asymmetry between T-conjugate oscillation probabilities, $\Delta P_T\equiv P({\nu }_{\alpha }\to {\nu }_{\beta })-P({\nu }_{\beta }\to {\nu }_{\alpha }),$ in a three-flavor framework. We find that additional mixing due to these mechanisms, while obeying all present bounds, can lead to an observable enhancement, suppression, and/or sign change in $\Delta P_T$ for the preferred energies and baselines of a neutrino factory. The measurement of this asymmetry can be used to establish a new upper limit of the order of ${10}^{-26}$ on VEP or LIV in the $({\nu }_e,{\nu }_{\mu })$ and $({\nu }_e,{\nu }_{\tau })$ sectors.

The spatial momentum dependence of the spectral function for $\pi$ and $\sigma$ at finite temperature is studied by employing the $O\left(4\right)\mathrm{}$ linear sigma model and adopting a resummation technique called optimized perturbation theory (OPT). The poles of the propagators are also searched for. We analyze the spatial momentum dependence of the imaginary part of the self-energy and find that its temperature-dependent part vanishes in the large momentum limit. This is because the energy of the particles in the heat bath which participate in the process becomes large and therefore the Bose distribution function vanishes. We then calculate the spectral functions and search for the poles of the propagators. First, we discuss the temperature dependence for zero spatial momentum. We reproduce the spectral functions in both π and $\sigma$ channels in the previous work and find that the pole, which is responsible for the threshold enhancement of the spectral functions in both π and σ channels, is different from the one for the peak at zero temperature. Second, we discuss the spatial-momentum dependence. When the temperature is low the spatial momentum dependence is also small. As the temperature becomes higher the spatial momentum dependence also becomes large. When the spatial momentum is smaller than the temperature, the spectral functions do not deviate much from those at zero spatial momentum. Once the spatial momentum becomes comparable with the temperature, the deviation becomes considerable. As the momentum becomes much larger than the temperature, thermal effects effectively decrease.

We perform a detailed numerical investigation of the dynamics of a single component “explicitly broken symmetry” $\lambda {\phi }^4$ field theory in 1+1 dimensions, using a Schwinger-Dyson equation truncation scheme based on ignoring vertex corrections. In an earlier paper, we called this the bare vertex approximation (BVA). We assume here that the initial state is described by a Gaussian density matrix peaked around some nonzero value of $〈\phi \mathrm{}\left(0\right)\mathrm{}〉,$ and characterized by a single particle Bose-Einstein distribution function at a given temperature. We compute the evolution of the system using three different approximations: the Hartree approximation, the BVA, and a related two-particle irreducible (2PI) $1/N$ expansion, as a function of coupling strength and initial temperature. In the Hartree approximation, the static phase diagram shows that there is a first order phase transition for this system. As we change the initial starting temperature of the system, we find that the BVA relaxes to a new final temperature and exhibits behavior consistent with a second order phase transition. We find that the average fields equilibrate for arbitrary initial conditions in the BVA, unlike the behavior exhibited by the Hartree approximation, and we illustrate how $〈\phi \mathrm{}\left(t\right)\mathrm{}〉$ and $〈\chi \mathrm{}\left(t\right)\mathrm{}〉$ depend on the initial temperature and on the coupling constant. The Fourier transform of the two-point functions at late times can be fitted by a Bose-Einstein distribution function whose temperature is independent of momentum. We interpret this as evidence for thermalization.

The hadronic decays of the $\tau$ lepton can be used to determine the effective charge ${\alpha }_{\tau }{(m}_{{\tau }^{\prime }}^2)$ for a hypothetical $\tau$ lepton with a mass in the range $0<\mathrm{}{m}_{{\tau }^{\prime }}<m_{\tau }.$ This definition provides a fundamental definition of the QCD coupling at low mass scales. We study the behavior of ${\alpha }_{\tau }$ at low mass scales directly from first principles and without any renormalization-scheme dependence by looking at the experimental data from the OPAL Collaboration. The results are consistent with the freezing of the physical coupling at mass scales ${s=m}_{{\tau }^{\prime }}^2$ of order $1{\mathrm{GeV}}^2$ with a magnitude ${\alpha }_{\tau }\sim 0.9\pm \mathrm{0.1.}$

We derive some properties of the Nambu-Goldstone boson coupling in theories that have CP violation and Majorana masses. We show explicitly that its diagonal coupling to a Majorana fermion is pseudoscalar not scalar. Some potentially useful off-diagonal properties are also derived. We also show, in the process, that the Goldstone theorem often produces interesting and nontrivial identities in matrix theory which may be hard to prove otherwise.

We study the branching ratio of the inclusive $\overrightarrow{b}s{\tau }^{+}{\tau }^{-}$ decay in the general two Higgs doublet model (model III), including the leading order QCD corrections. We find that neutral Higgs mediated tree level diagrams dominate the decay within a reasonable parameter space and the branching ratio could lie between $1.03527\times {10}^{-6}$ and $7.41592\times {10}^{-6},$ which might be measured at the new generation of B experiments.

We demonstrate the viability of improved staggered light quarks in studies of heavy-light systems. Our method for constructing heavy-light operators exploits the close relation between naive and staggered fermions. The new approach is tested on quenched configurations using several staggered actions combined with nonrelativistic heavy quarks. Exploratory calculations of the $B_s$ meson kinetic mass, the hyperfine and $1P\mathrm{-}1S$ splittings in $B_s,$ and the decay constant $f_{B_s}$ are presented and compared to previous quenched lattice studies. An important technical detail, Bayesian curve fitting, is discussed at length.

We calculate the contributions from QED processes involving two virtual photons to the cross sections for $e^{+}{e}^{-}$ annihilation into two charmonium states with the same C parity. Generically, the cross sections are three orders of magnitude smaller than those for charmonia with opposite C parity because they are suppressed by a factor of ${\alpha }^2/{\alpha }_s^2.$ However, if both charmonia have quantum numbers $J^{\mathrm{PC}}{=1\mathrm{}}^{--},$ then there is a contribution to the cross section that involves the fragmentation of each photon into a charmonium. The fragmentation contribution is enhanced by powers of $E_{\mathrm{beam}}{/m}_c,$ the ratio of the beam energy to the charm-quark mass, and this enhancement can compensate for the suppression factor that is associated with the coupling constants. In particular, the predicted cross section for $J/\psi +J/\psi$ at the B factories is larger than that for $J/\psi +{\eta }_c.$

We evaluate the $\overline{B^0}\to J/\psi ({\eta }_c{)D}^{+}{\pi }^{-}$ nonleptonic decay in a phase space region where the pion factors out. This decay might provide a significant background to the decay process $\overline{B^0}\to J/\psi ({\eta }_c{)D}^{\star 0},$ followed by $D^{\star 0}\to D^{+}{\pi }^{-},$ with a slightly off-shell $D^{\star 0}.$ The relevant form factors describing the $\overline{B^0}\to J/\psi ({\eta }_c{)D}^{+}{\mathcal{l}}^{-}{\overline{\nu }}_{\mathcal{l}}$ semileptonic decay, required for the calculations, have been evaluated within the framework of a QCD relativistic potential model. We estimate the branching ratio for the nonleptonic channels, finding $\mathcal{B}\mathcal{R}(\overline{B^0}\to J/\psi D^{+}{\pi }^{-})=3.1\mathrm{}\times {10}^{-8}$ and $\mathcal{B}\mathcal{R}(\overline{B^0}\to {\eta }_c{D}^{+}{\pi }^{-})=3.5\mathrm{}\times {10}^{-8}.$ As a by-product of our calculations, we also quote the $\overline{B^0}\to J/\psi ({\eta }_c{)D}^{+}\mathcal{l}{\nu }_{\mathcal{l}}$ semileptonic decay branching ratio: $\mathcal{B}\mathcal{R}(\overline{B^0}\to J/\psi ({\eta }_c{)D}^{+}\mathcal{l}{\nu }_{\mathcal{l}})\simeq {10}^{-13}.$

Based on the measurements of ${(D}_s^{+}{,D}^{+})\to f_0\mathrm{}(1370)\mathrm{}{\pi }^{+}$ we determine, in a model independent way, the allowed $s\overline{s}$ content in the scalar meson $f_0\mathrm{}\left(1370\right).$ We find that, on the one hand, if this isoscalar resonance is a pure $n\mathrm{n̄}$ state $\left[n\mathrm{n̄}\equiv \right(uū+d\overline{d})/\sqrt{2}],$ a very large W-annihilation term will be needed to accommodate $D_s^{+}\to f_0\mathrm{}\left(1370\right)\mathrm{}{\pi }^{+}.$ On the other hand, the $s\overline{s}$ component of $f_0\mathrm{}\left(1370\right)\mathrm{}$ should be small enough to avoid excessive $D_s^{+}\to f_0\mathrm{}\left(1370\right)\mathrm{}{\pi }^{+}$ induced from the external W emission. Measurement of $f_0\mathrm{}\left(1370\right)\mathrm{}$ production in the decay $D_s^{+}\to K^{+}{K}^{-}{\pi }^{+}$ will be useful to test the above picture. For the decay $D^0\to f_0\mathrm{}\left(1370\right)\mathrm{}{K}^0$ which is kinematically barely or even not allowed, depending on the mass of $f_0\mathrm{}\left(1370\right),$ we find that the finite width effect of $f_0\mathrm{}\left(1370\right)\mathrm{}$ plays a crucial role on the resonant three-body decay $D^0\to f_0\mathrm{}\left(1370\right)\mathrm{}{K}^0\to {\pi }^{+}{\pi }^{-}{K}^0.$

Analytic models for hadron-hadron scattering are characterized by simple analytical parametrizations for the forward amplitudes and the use of dispersion relation techniques to study the total cross section ${\sigma }_{\mathrm{tot}}$ and the $\rho$ parameter (the ratio between the real and imaginary parts of the forward amplitude). In this paper we investigate simultaneously four aspects related to the application of the model to $\mathrm{pp}$ and $\overline{p}p$ scattering, from accelerator to cosmic-ray energies: (1) the effect of different estimations for ${\sigma }_{\mathrm{tot}}$ from cosmic-ray experiments; (2) the differences between individual and global (simultaneous) fits to ${\sigma }_{\mathrm{tot}}$ and $\rho ;$ (3) the role of the subtraction constant in the dispersion relations; (4) the effect of distinct asymptotic inputs from different analytic models. This is done by using as a framework the single Pomeron and the maximal odderon parametrizations for the total cross section. Our main conclusions are the following: (1) Despite the small influence from different cosmic-ray estimations, the results allow us to extract an upper bound for the soft Pomeron intercept: $1+\epsilon =1.094;$ (2) although global fits present good statistical results, in general, this procedure constrains the rise of ${\sigma }_{\mathrm{tot}};$ (3) the subtraction constant as a free parameter affects the fit results at both low and high energies; (4) independently of the cosmic-ray information used and the subtraction constant, global fits with the odderon parametrization predict that, above $\sqrt{s}\approx 70\mathrm{GeV},$ ${\rho }_{\mathrm{pp}}\mathrm{}\left(s\right)\mathrm{}$ becomes greater than ${\rho }_{\overline{p}p}\mathrm{}\left(s\right),$ and this result is in complete agreement with all the data presently available. In particular, we infer ${\rho }_{\mathrm{pp}}=0.134\mathrm{}\pm 0.005$ at $\sqrt{s}=200\mathrm{}\mathrm{GeV}$ and $0.151\pm 0.007$ at 500 GeV (BNL RHIC energies). A detailed discussion of the procedures used and all the results obtained is also presented.

We consider the solution of the Bethe-Salpeter equation in the Euclidean metric for a $\overline{q}q$ vector meson in the circumstance where the dressed quark propagators have timelike complex conjugate mass poles. This approximates features encountered in recent QCD modeling via the Dyson-Schwinger equations; the absence of real mass poles simulates quark confinement. The analytic continuation in the total momentum necessary to reach the mass shell for a meson sufficiently heavier than 1 GeV leads to the quark poles being within the integration domain for two variables in the standard approach. Through Feynman integral techniques, we show how the analytic continuation can be implemented in a way suitable for a practical numerical solution. We show that the would-be $\overline{q}q$ width to the meson generated from one quark pole is exactly canceled by the effect of the conjugate partner pole; the meson mass remains real and there is no spurious $\overline{q}q$ production threshold. The ladder kernel we employ is consistent with one-loop perturbative QCD and has a two-parameter infrared structure found to be successful in recent studies of the light SU(3) meson sector.

We survey the nonlocked color-flavor-spin channels for quark-quark (color superconducting) condensates in QCD, using a Nambu–Jona-Lasinio model. We also study isotropic quark-antiquark (mesonic) condensates. We make mean-field estimates of the strength and sign of the self-interaction of each condensate, using four-fermion interaction vertices based on known QCD interactions. For the attractive quark pairing channels, we solve the mean-field gap equations to obtain the size of the gap as a function of quark density. We also calculate the dispersion relations for the quasiquarks, in order to see how fully gapped the spectrum of fermionic excitations will be. We use our results to specify the likely pairing patterns in neutral quark matter, and comment on possible phenomenological consequences.

If three right-handed neutrinos are added to the standard model, then, for the three known generations, there are six quarks and six leptons. It is then natural to assume that the symmetry considerations that have been applied to the quark matrices are also valid for the lepton mass matrices. Under this assumption, the solar and atmospheric neutrino data can be used to determine the individual neutrino masses. Using the ${\chi }^2$ fit, it is found that the mass of the lightest neutrino is (2–$5)\times {10}^{-3}\mathrm{eV},$ that of the next heavier neutrino is (10–$13)\times {10}^{-3}\mathrm{eV},$ while the mass of the heaviest neutrino is (52–$54)\times {10}^{-3}\mathrm{eV}.$

We study the domain of validity of a Schwinger-Dyson approach to nonequilibrium dynamics when $〈\phi \mathrm{}\left(x\right)\mathrm{}〉\ne 0.$ We perform exact numerical simulations of the one- and two-point functions of a single component $\lambda {\phi }^4$ field theory in $1+1$ dimensions in the classical field theory case. We compare these results to two self-consistent truncations of the Schwinger-Dyson equations which ignore three-point vertex function corrections. The first approximation, which we called the bare vertex approximation, sets the three-point function to one. It gives a promising description for $〈\phi \mathrm{}\left(x\right)\mathrm{}〉=\phi \mathrm{}\left(t\right).$ The second approximation, which ignores higher in $1/N$ corrections to the 2PI generating functional is not as accurate for $\phi \mathrm{}\left(t\right)\mathrm{}$ for the case $N=1.\mathrm{}$ Both approximations have serious deficiencies in describing the two-point function when $\phi \mathrm{}\left(0\right)\mathrm{}\gtrsim \mathrm{0.4.}$

We propose a formula to determine the first moment of difference between the polarized $ū$ and $\overline{d}$ quarks in the nucleon, i.e., $\Delta ū-\Delta \overline{d}$ from the Drell-Yan processes in collisions of unpolarized hadrons with longitudinally polarized nucleons by measuring outgoing lepton helicities. As coefficients in the differential cross section depend on the u- and d-quark numbers in the unpolarized hadron beam, the difference $\Delta ū-\Delta \overline{d}$ can be independently tested by changing the hadron beam. Moreover, a formula for estimating the K factor in Drell-Yan processes is also suggested.

We examine the recently found equivalence for the response of a static scalar source interacting with a massless Klein-Gordon field when the source is (i) static in Schwarzschild spacetime, in the Unruh vacuum associated with the Hawking radiation, and (ii) uniformly accelerated in Minkowski spacetime, in the inertial vacuum, provided that the source’s proper acceleration is the same in both cases. It is shown that this equivalence is broken when the massless Klein-Gordon field is replaced by a massive one.

We study nonsupersymmetric fermion mass and condensate deformations of the AdS conformal field theory correspondence. The five dimensional supergravity flows are lifted to a complete and remarkably simple ten dimensional background. A brane probe analysis shows that when all the fermions have an equal mass a positive mass is generated for all six scalar fields leaving nonsupersymmetric Yang-Mills theory in the deep infrared. We numerically determine the potential, produced by the background, in the Schrödinger equation relevant to the study of $O^{++}$ glueballs. The potential is a bounded well, providing evidence of stability and for a discrete, confined spectrum. The geometry can also describe the supergravity background around an (unstable) fuzzy 5-brane.

We find the parameters of the MSSM in terms of bulk supergravity fields for the D-brane model of Berenstein, Jejjala, and Leigh. The model consists of a D3-brane at the singularity of a non-Abelian orbifold ${\Delta }_{27},$ which gives the particles of the supersymmetric standard model. We compute the action for the D-brane fields in the presence of both supersymmetric and supersymmetry breaking background fluxes. We get quark, lepton, gaugino, Higgsino, scalar partners and Higgs boson masses as well as soft trilinear couplings as functions of the background fields. This work develops a framework for connecting MSSM phenomenology to brane compactifications.