We show that the renormalization of the $\mathcal{N}=1$ supersymmetric gauge theory when working in the component formalism, without eliminating auxiliary fields and using a standard covariant gauge, requires a nonlinear renormalization of the auxiliary fields.

We examine in a model-independent manner the measurements that can be performed at $B$ factories with sensitivity to dark matter. If a singlet scalar, pseudoscalar, or vector is present and mediates the standard model-dark matter interaction, it can mediate invisible decays of quarkonium states such as the ${\rm Y}$, $J/\Psi$, and $\eta$. Such scenarios have arisen in the context of supersymmetry, extended Higgs sectors, solutions of the supersymmetric $\mu$ problem, and extra $U(1)$ gauge groups from grand unified theories and string theory. Existing $B$ factories running at the ${\rm Y}(4S)$ can produce lower ${\rm Y}$ resonances by emitting an initial state radiation (ISR) photon. Using a combination of ISR and radiative decays, the initial state of an invisibly decaying quarkonium resonance can be tagged, giving sensitivity to the spin and $CP$ nature of the particle that mediates standard model-dark matter interactions. These measurements can discover or place strong constraints on dark matter scenarios where the dark matter is approximately lighter than the $b$ quark. For the decay chains ${\rm Y}(nS)\to {\pi }^{+}{\pi }^{-}{\rm Y}(1S)$ ($n=2,3$) we analyze the dominant backgrounds and determine that with $400{\mathrm{fb}}^{-1}$ collected at the ${\rm Y}(4S)$, the $B$ factories can limit $\mathrm{BR}({\rm Y}(1S)\to \mathrm{invisible})\lesssim 0.1\%$.

We perform a numerical study of ghost condensation—in the so-called Overhauser channel—for $SU(2)$ lattice gauge theory in minimal Landau gauge. The off-diagonal components of the momentum-space ghost propagator $G^{cd}(p)$ are evaluated for lattice volumes $V=8^4$, ${12}^4$, ${16}^4$, ${20}^4$, ${24}^4$ and for three values of the lattice coupling: $\beta =2.2$, $2.3$, $2.4$. Our data show that the quantity ${\varphi }^b(p)={ϵ}^{bcd}{G}^{cd}(p)/2$ is zero within error bars, being characterized by very large statistical fluctuations. On the contrary, $|{\varphi }^b(p)|$ has relatively small error bars and behaves at small momenta as $L^{-2}{p}^{-z}$, where $L$ is the lattice side in physical units and $z\approx 4$. We argue that the large fluctuations for ${\varphi }^b(p)$ come from spontaneous breaking of a global symmetry and are associated with ghost condensation. It may thus be necessary (in numerical simulations at finite volume) to consider $|{\varphi }^b(p)|$ instead of ${\varphi }^b(p)$, to avoid a null average due to tunneling between different broken vacua. Also, we show that ${\varphi }^b(p)$ is proportional to the Fourier-transformed gluon field components ${\tilde{A}}_{\mu }^b(q)$. This explains the $L^{-2}$ dependence of $|{\varphi }^b(p)|$, as induced by the behavior of $|{\tilde{A}}_{\mu }^b(q)|$. We fit our data for $|{\varphi }^b(p)|$ to the theoretical prediction $(r/L^2+v)/(p^4+v^2)$, obtaining for the ghost condensate $v$ an upper bound of about $0.058{\mathrm{GeV}}^2$. In order to check if $v$ is nonzero in the continuum limit, one probably needs numerical simulations at much larger physical volumes than the ones we consider. As a by-product of our analysis, we perform a careful study of the color structure of the inverse Faddeev-Popov matrix in momentum space.

We investigate the topological charge in $1+1$ dimensional ${\varphi }^4$ theory on a lattice with antiperiodic boundary condition (APBC) in the spatial direction. We propose a simple order parameter for the lattice theory with APBC and we demonstrate its effectiveness. Our study suggests that kink condensation is a possible mechanism for the order-disorder phase transition in the $1+1$ dimensional ${\varphi }^4$ theory. With renormalizations performed on the lattice with periodic boundary condition (PBC), the topological charge in the renormalized theory is given as the ratio of the order parameters in the lattices with APBC and PBC. We present a comparison of topological charges in the bare and the renormalized theory and demonstrate invariance of the charge of the renormalized theory in the broken symmetry phase.

In this work we perform a detailed numerical analysis of ($1+1$) dimensional lattice ${\varphi }^4$ theory. We explore the phase diagram of the theory with two different parametrizations. We find that symmetry breaking occurs only with a negative mass-squared term in the Hamiltonian. The renormalized mass $m_R$ and the field renormalization constant $Z$ are calculated from both coordinate space and momentum space propagators in the broken symmetry phase. The critical coupling for the phase transition and the critical exponents associated with $m_R$, $Z$ and the order parameter are extracted using a finite-size scaling analysis of the data for several volumes. The scaling behavior of $Z$ has the interesting consequence that $⟨{\varphi }_R⟩$ does not scale in $1+1$ dimensions. We also calculate the renormalized coupling constant ${\lambda }_R$ in the broken symmetry phase. The ratio ${\lambda }_R/m_R^2$ does not scale and appears to reach a value independent of the bare parameters in the critical region in the infinite volume limit.

We study the strong and electromagnetic decay properties of scalar mesons above 1 GeV within a chiral approach. The scalar-isoscalar states are treated as mixed states of quarkonia and glueball configurations. A fit to the experimental mass and decay rates listed by the Particle Data Group is performed to extract phenomenological constraints on the nature of the scalar resonances and to the issue of the glueball decays. A comparison to other experimental results and to other theoretical approaches in the scalar meson sector is discussed.

The radiative $B\to \rho \gamma$, $B\to \omega \gamma$ decay modes are caused by the flavor-changing-neutral-current process, so they give us good insight towards probing the standard model in order to search for new physics. In this paper, we compute the branching ratio, direct $CP$ asymmetry, and isospin breaking effects using the perturbative QCD approach within the standard model.

Recent signals for narrow hadrons containing heavy and light flavors are compared with quark model predictions for spectroscopy, strong decays, and radiative transitions. In particular, the production and identification of excited charmed and $c\overline{s}$ states are examined with emphasis on elucidating the nature of $0^{+}$ and $1^{+}$ states. Roughly 200 strong decay amplitudes of $D$ and $D_s$ states up to 3.3 GeV are presented. Applications include determining flavor content in $\eta$ mesons and the mixing angle in $P$ and $D$ wave states and probes of putative molecular states. We advocate searching for radially excited $D_s^{*}$ states in $B$ decays.

Recently, the gravitational collapse of an infinite cylindrical thin shell of matter in an otherwise empty spacetime with two hypersurface orthogonal Killing vectors was studied by Gonçalves [Phys. Rev. D 65, 084045 (2002)]. By using three alternative criteria for trapped surfaces, the author claimed to have shown that they can never form either outside or on the shell, regardless of the matter content for the shell, except at asymptotical future null infinity. Following Penrose’s original idea, we first define trapped surfaces in cylindrical spacetimes in terms of the expansions of null directions orthogonal to the surfaces and then show that the first criterion used by Gonçalves is incorrect. We also show that his analysis of nonexistence of trapped surfaces in the vacuum is incomplete. To confirm our claim, we present an example that is a solution to the vacuum Einstein field equations and satisfies all the regular conditions imposed by Gonçalves. After extending the solution to the whole spacetime, we show explicitly that trapped surfaces exist in the extended region.

In previous work, we found that necessary and sufficient conditions for large $N_{\mathrm{c}}$ equivalence between parent and daughter theories, for a wide class of orbifold projections of $U(N_{\mathrm{c}})$ gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group factors not be spontaneously broken in the daughter theory. In this paper, we discuss the application of this result to ${\mathbb{Z}}_k$ projections of $\mathcal{N}=1$ supersymmetric Yang-Mills theory in four dimensions, as well as various multiflavor generalizations. ${\mathbb{Z}}_k$ projections with $k>2$ yielding chiral gauge theories violate the symmetry realization conditions needed for large $N_{\mathrm{c}}$ equivalence, due to the spontaneous symmetry breaking of discrete chiral symmetry in the parent super-Yang-Mills theory. But for ${\mathbb{Z}}_2$ projections, we show that previous assertions of large $N_{\mathrm{c}}$ inequivalence, in infinite volume, between the parent and daughter theories were based on incorrect mappings of vacuum energies, theta angles, or connected correlators between the two theories. With the correct identifications, there is no sign of any inconsistency. A subtle but essential feature of the connection between parent and daughter theories involves multivaluedness in the mapping of theta parameters from parent to daughter.

For many physical systems which can be approximated by a classical background field plus small (linearized) quantum fluctuations, a fundamental question concerns the correct description of the backreaction of the quantum fluctuations onto the dynamics of the classical background. We investigate this problem for the example of dilute atomic/molecular Bose-Einstein condensates, for which the microscopic dynamical behavior is under control. It turns out that the effective-action technique does not yield the correct result in general and that the knowledge of the pseudo-energy-momentum tensor $⟨{\widehat{T}}_{\mu \nu }⟩$ is not sufficient to describe quantum backreaction.

Braneworld cosmology supported by a bulk scalar field with an exponential potential is developed. A general class of separable backgrounds for both single and two-brane systems is derived, where the bulk metric components are given by products of world volume and bulk coordinates and the world-volumes represent any anisotropic and inhomogeneous solution to an effective four-dimensional Brans-Dicke theory of gravity. We deduce a cosmic no hair theorem for all ever-expanding, spatially homogeneous Bianchi world volumes and find that the spatially flat and isotropic inflationary scaling solution represents a late-time attractor when the bulk potential is sufficiently flat. The dependence of this result on the separable nature of the bulk metric is investigated by applying the techniques of Hamilton-Jacobi theory to five-dimensional Einstein gravity. We employ the spatial gradient expansion method to determine the asymptotic form of the bulk metric up to third-order in spatial gradients. It is found that the condition for the separable form of the metric to represent the attractor of the system is precisely the same as that for the four-dimensional world-volume to isotropize. We also derive the fourth–order contribution to the Hamilton-Jacobi generating functional. Finally, we conclude by placing our results within the context of the holographic approach to braneworld cosmology.

Based on the second-order nonlinear theory of perturbations in nonzero $\Lambda$ flat cosmological models, we study the gravitational effects of local inhomogeneities on cosmic microwave background (CMB) anisotropies. As the local inhomogeneities we consider first large-scale dipole and quadrupole distributions of galaxies around us and next an isolated cluster-scale matter distribution. It is found that, due to the second-order integral Sachs-Wolfe effect, the north-south asymmetry of CMB anisotropies and non-Gaussian signatures (in terms of scale-dependent estimators of kurtosis) in a spotlike object are caused from these matter distributions along light paths. Our theoretical results seem to be consistent with recent various observational results which have been shown by Hansen et al., Eriksen et al., Vielva et al. and Cruz et al.

We examine the dynamics of inflation driven by multiple, interacting scalar fields and derive a multifield version of the Hubble slow roll expansion. We show that the properties of this expansion naturally generalize those of the single field case. We present an analogous hierarchy of slow roll parameters, and derive the system of flow equations that describes their evolution, and show that when this system is truncated at finite order, it can always be solved exactly. Lastly, we express the scalar and tensor perturbation spectra in terms of the slow roll parameters.

The mixing of ${\eta }_c$ and the lowest mass pseudoscalar glueball is estimated within the framework of the instanton liquid model. It is demonstrated that the mixing is large and may explain the difference between the observed mass of the glueball candidate X(1835) and the theoretical prediction of the QCD sum rule analysis.

The complete one-loop electroweak corrections to charged Higgs boson pair production in $\gamma \gamma$ collision mode at linear colliders in the minimal supersymmetric standard model (MSSM), are calculated in this paper. We discuss the dependence of the corrections to the subprocess $\gamma \gamma \to H^{+}{H}^{-}$ on the related parameters, such as the colliding energy, charged Higgs boson mass $M_{H^{\pm }}$ and some supersymmetric parameters $\tan \beta$, $M_{\mathrm{SUSY}}$ and gaugino mass parameter $M_2$. We find that the corrections generally reduce the Born cross sections and the relative one-loop corrections to both the subprocess typically in the range of $-10\%$ to $-30\%$. We also present the numerical results at the SPS1a’ point from the supersymmetry parameter analysis (SPA) project. We conclude that the full one-loop electroweak corrections to subprocess $\gamma \gamma \to H^{+}{H}^{-}$ and the parent process $e^{+}{e}^{-}\to \gamma \gamma \to H^{+}{H}^{-}$ are significant and therefore should be considered in precise analysis of charged Higgs boson pair productions via $\gamma \gamma$ collision at future linear colliders.

We study chargino production at a muon collider with longitudinally polarized beams and center of mass energies around the heavy neutral Higgs boson resonances. We show that the interference of the $CP$ even and $CP$ odd Higgs bosons can be analyzed using the energy distributions of the lepton or $W$ boson from the chargino two-body decays ${\tilde{\chi }}_j^{\pm }\to {\ell }^{\pm }{\tilde{\nu }}_{\ell }$ or ${\tilde{\chi }}_j^{\pm }\to W^{\pm }{\tilde{\chi }}_1^0$, respectively. The energy distributions depend on the longitudinal polarization of the decaying chargino, which are correlated to the muon beam polarizations. We define asymmetries in these energy distributions which allow a determination of the $H$ and $A$ couplings to the charginos and, in particular, of their relative phase. We analyze the asymmetries, cross sections and branching ratios in $CP$ conserving Minimal Supersymmetric Standard Model scenarios. For nearly degenerate Higgs bosons we find maximal asymmetries which can be measured with high statistical significance.

We discuss the apparent conflict between reflection positivity and positivity of the topological susceptibility in two-dimensional nonlinear sigma models and in four-dimensional gauge theories. We pay special attention to the fact that this apparent conflict is already present on the lattice; its resolution puts some nontrivial restrictions on the short-distance behavior of the lattice correlator. It is found that these restrictions can be satisfied both in the case of asymptotic freedom and the dissident scenario of a critical point at finite coupling.

We determine the masses and magnetic moments of the octet baryons in chiral perturbation theory formulated for a mixed lattice action of Ginsparg-Wilson valence quarks and staggered sea quarks. Taste-symmetry breaking does not occur at next-to-leading order in the combined lattice spacing and chiral expansion. Expressions derived for masses and magnetic moments are required for addressing lattice artifacts in mixed-action simulations of these observables.

We derive the two-point spectral correlation function of the Dirac operator with a specific external source in the $ϵ$ regime of QCD. This correlation function has a unique and strong dependence on $F_{\pi }$, and thus provides an novel way to extract $F_{\pi }$ from lattice simulations. We test the method in a quenched lattice simulation with staggered fermions.