We derive a supersymmetric renormalization group (RG) equation for the scale-dependent superpotential of the supersymmetric $O(N)$ model in three dimensions. For a supersymmetric optimized regulator function, we solve the RG equation for the superpotential exactly in the large-$N$ limit. The fixed-point solutions are classified by an exactly marginal coupling. In the weakly coupled regime there exists a unique fixed-point solution, for intermediate couplings we find two separate fixed-point solutions and in the strong coupling regime no globally defined fixed-point potentials exist. We determine the exact critical exponents both for the superpotential and the associated scalar potential. Finally, we relate the high-temperature limit of the four-dimensional theory to the Wilson-Fisher fixed point of the purely scalar theory.

It is well known that boundary conditions on quantum fields produce divergences in the renormalized energy-momentum tensor near the boundaries. Although irrelevant for the computation of Casimir forces between different bodies, the self-energy couples to gravity, and the divergences may, in principle, generate large gravitational effects. We present an analysis of the problem in the context of quantum field theory in curved spaces. Our model consists of a quantum scalar field coupled to a classical field that, in a certain limit, imposes Dirichlet boundary conditions on the quantum field. We show that the model is renormalizable and that the divergences in the renormalized energy-momentum tensor disappear for sufficiently smooth interfaces.

We construct renormalization group flow solutions interpolating anti-de Sitter and Schrödinger geometries in Abelian Higgs models obtained from consistent reductions of type IIB supergravity and M theory. We find that $z=2$ Schrödinger geometries can be realized at the minima of scalar potentials of these models, where a scalar charged under $U(1)$ gauge symmetry obtains a nonzero vacuum expectation value. The renormalization group flows are induced by an operator deformation of the dual conformal field theory. The flows are captured by fake superpotentials of the theories.

We discuss qualitative behavior of the $SU(N)$ gauge beta functions in QCD with many massless flavors. Nonperturbative beta functions can be obtained by extracting the renormalized trajectories in the exact renormalization group framework. We examine the renormalization group equations for the general four-fermi couplings as well as the gauge coupling obtained in a simple approximation scheme. It is shown that the gauge beta function possesses not only an IR but also a UV fixed point in the conformal window. These fixed points merge with each other and disappear at the edge of the conformal window. The scaling dimensions of the quark mass operator at the fixed points are also shown.

There is a distinct possibility that current and future cosmological data can be used to constrain Einstein’s theory of gravity on the very largest scales. To be able to do this in a model-independent way, it makes sense to work with a general parameterization of modified gravity. Such an approach would be analogous to the Parameterized Post-Newtonian (PPN) approach which is used on the scale of the Solar System. A few such parameterizations have been proposed and preliminary constraints have been obtained. We show that the majority of such parameterizations are only exactly applicable in the quasistatic regime. On larger scales they fail to encapsulate the full behavior of typical models currently under consideration. We suggest that it may be possible to capture the additions to the ‘Parameterized Post-Friedmann’ (PPF) formalism by treating them akin to fluid perturbations.

The quantum dynamics of the linearly polarized Gowdy $T^3$ model (compact inhomogeneous universes admitting linearly polarized gravitational waves) is analyzed within loop quantum cosmology by means of an effective dynamics. The analysis, performed via analytical and numerical methods, proves that the behavior found in the evolution of vacuum (homogeneous) Bianchi I universes is preserved qualitatively also in the presence of inhomogeneities. More precisely, the initial singularity is replaced by a big bounce which joins deterministically two large classical universes. In addition, we show that the size of the universe at the bounce is at least of the same order of magnitude (roughly speaking) as the size of the corresponding homogeneous universe obtained in the absence of gravitational waves. In particular, a precise lower bound for the ratio of these two sizes is found. Finally, the comparison of the amplitudes of the gravitational wave modes in the distant future and past shows that, statistically (i.e., for large samples of universes), the difference in amplitude is enhanced for nearly homogeneous universes, whereas this difference vanishes in inhomogeneity-dominated cases. The presented analysis constitutes the first systematic effective study of an inhomogeneous system within loop quantum cosmology, and it proves the robustness of the results obtained for homogeneous cosmologies in this context.

Asymptotically warped AdS spacetimes in topologically massive gravity with negative cosmological constant are considered in the case of spacelike stretched warping, where black holes have been shown to exist. We provide a set of asymptotic conditions that accommodate solutions in which the local degree of freedom (the “massive graviton”) is switched on. An exact solution with this property is explicitly exhibited and possesses a slower falloff than the warped AdS black hole. The boundary conditions are invariant under the semidirect product of the Virasoro algebra with a $u(1)$ current algebra. We show that the canonical generators are integrable and finite. When the graviton is not excited, our analysis is compared and contrasted with earlier results obtained through the covariant approach to conserved charges. In particular, we find agreement with the conserved charges of the warped AdS black holes as well as with the central charges in the algebra.

We investigate a model of interacting dark matter and dark energy given by a modified holographic Ricci cutoff in a spatially flat Friedmann-Robertson-Walker space-time. We consider a nonlinear interaction consisting of a significant rational function of the total energy density and its first derivative homogeneous of degree one and show that the effective one-fluid obeys the equation of state of a relaxed Chaplygin gas. So that, the Universe is dominated by pressureless dark matter at early times and undergoes an accelerated expansion in the far future driven by a strong negative pressure. We apply the ${\chi }^2$-statistical method to the observational Hubble data and the Union2 compilation of SNe Ia for constraining the cosmological parameters and analyze the feasibility of the modified holographic Ricci cutoff. By using the new $Om$ diagnostic method, we find that the effective model differs substantially from the $\Lambda$-CDM one, because it gets the accelerated expansion faster than the $\Lambda$-CDM model. Finally, a model with a third component decoupled from the interacting dark sector is presented for studying bounds on the dark energy at early times.

We investigate density perturbations sourced by a curvaton with a generic energy potential. The key feature of a curvaton potential which deviates from a quadratic is that the curvaton experiences a nonuniform onset of its oscillation. This sources additional contributions to the resulting density perturbations, and we especially find that the non-Gaussianity parameter $f_{\mathrm{NL}}$ can become large with either sign no matter whether the curvaton dominates or subdominates the universe when it decays. Such nonquadratic curvaton potentials are required in order to produce a red-tilted density perturbation spectrum (without invoking large-field inflation), and are also motivated by explicit curvaton models based on microscopic physics. We further apply our generic results to the case where the curvaton is a pseudo-Nambu-Goldstone boson of a broken U(1) symmetry, and show that the resulting density perturbations are strongly enhanced towards the hilltop region of the energy potential, accompanied by a mild increase of the non-Gaussianity. Such hilltop Nambu-Goldstone curvatons can produce observationally suggested density perturbations under wide ranges of inflation/reheating scales, and further predict the non-Gaussianity of the density perturbations to lie within the range $10\lesssim f_{\mathrm{NL}}\lesssim 30$.

The extracted value of the relic density has reached the few percent level precision. One can therefore no longer content oneself with calculations of this observable where the annihilation processes are computed at tree level, especially in supersymmetry where radiative corrections are usually large. Implementing full one-loop corrections to all annihilation processes that would be needed in a scan over parameters is a daunting task. On the other hand one may ask whether most of the corrections are taken into account through effective couplings of the neutralino that improve the tree-level calculation and would be easy to implement. We address this issue by concentrating in this first study on the neutralino coupling to (i) fermions and sfermions and (ii) $Z$. After constructing the effective couplings we compare their efficiency to the full one-loop calculation and comment on the failures and success of the approach. As a bonus we point out that large nondecoupling effects of heavy sfermions could in principle be measured in the annihilation process, a point of interest in view of the latest limit on the squark masses from the LHC. We also comment on the scheme dependencies of the one-loop corrected results.

The high mass neutral quantum states envisaged by theories of physics beyond the standard model can, at the hadron colliders, reveal themselves through their decay into a pair of photons. Once such a peak in the diphoton invariant mass distribution is discovered, the determination of its spin through the distinctive photon angular distributions is needed in order to identify the associated nonstandard dynamics. We discuss here the discrimination of the spin-2 Randall-Sundrum graviton excitation against the hypothesis of a spin-0 exchange giving the same number of events under the peak, by means of the angular analysis applied to resonant diphoton events expected to be observed at the LHC. The spin-0 hypothesis is modeled by an effective interaction of a high mass gauge singlet scalar particle interacting with the standard model fields. The basic observable of our analysis is the symmetrically integrated angular asymmetry $A_{\mathrm{CE}}$, calculated for both graviton and scalar $s$-channel exchanges to next-to-leading order in QCD.

The gauge-independent phenomenon of color confinement in Yang-Mills theory likely manifests itself differently in different gauges in terms of the gauge-dependent correlation functions. Therefore, the relation of the infrared structure of the theory to the correlation functions may differ in different gauges. To understand this dependence classes of gauges that are controlled by a single gauge parameter are particularly useful. We present results on propagators and the color-Coulomb potential for the so-called $\lambda$-gauges, which interpolate between the (minimal) Landau gauge and the (minimal complete) Coulomb gauge. Results are reported for the SU(2) lattice gauge theory in three and four space-time dimensions. We investigate especially intermediate and low momenta. We find a continuous evolution of all quantities with the gauge parameter, except at zero $d$-momentum.

In this work we evaluate the production rate of the charmed baryon ${\Lambda }_c(2940{)}^{+}$ at PANDA. For possible assignments of ${\Lambda }_c(2940{)}^{+}$: $J^P=1/2^{\pm }$, $3/2^{\pm }$ and $5/2^{\pm }$, the total cross section of $p\overline{p}\to {\overline{\Lambda }}_c{\Lambda }_c(2940{)}^{+}$ is estimated, which may exceed 1 nb. With the designed luminosity ($2\times {10}^{-32}{\mathrm{cm}}^{-2}/\mathrm{s}$) of PANDA, our estimate indicates that ten thousand events per day if ${\Lambda }_c(2940{)}^{+}$ is of $J^P=1/2^{+}$ or ${10}^8$ per day if it is of $J^P=5/2^{+}$ can be expected. Those values actually set the lower and upper limits of the ${\Lambda }_c(2940{)}^{+}$ production. In addition, we present the Dalitz plot and carry out a rough background analysis of the ${\Lambda }_c(2940{)}^{+}$ production in the $p\overline{p}\to D^{0}p{\overline{\Lambda }}_c$ and $p\overline{p}\to {\Sigma }_c^{0,++}{\pi }^{+,-}{\overline{\Lambda }}_c$ processes, which would provide valuable information for accurate determination of the ${\Lambda }_c(2940{)}^{+}$ identity.

We examine measurements of time-dependent $CP$ asymmetries that could be made in new and future flavour facilities. In charm decays, where they can provide a unique insight into the flavor changing structure of the Standard Model, we examine a number of decays to $CP$ eigenstates and describe a framework that can be used to interpret the measurements. Such measurements can provide a precise determination of the charm mixing phase, as well as constraints on the Standard Model description of $CP$ violation an possible new physics contributions. We make a preliminary assessment, based on statistical considerations, of the relative capabilities of LHCb with data from $pp$ collisions, with Belle II and Super B using data from $B_d$, $B_s$ and charm thresholds. We discuss the measurements required to perform direct and indirect tests of the charm unitarity triangle and its relationship with the usual $B_d$ triangle. We find that, while theoretical and experimental systematic uncertainties may limit their interpretation, useful information on the unknown charm mixing phase, and on the possible existence of new physics can be obtained. We point out that, for $B_d$ decays, current experimental bounds on $\Delta {\Gamma }_{B_d}$ will translate into a significant systematic uncertainty on future measurements of $\sin 2\beta$ from $b\to c\overline{c}s$ decays. The possibilities for simplified $B_s$ decay asymmetry measurements at Super B and Belle II are also reviewed.

Pion-pion scattering is studied in a generalized linear sigma model which contains two scalar nonets (one of quark-antiquark type and the other of diquark-antidiquark type) and two corresponding pseudoscalar nonets. An interesting feature concerns the mixing of the four isosinglet scalar mesons which yield poles in the scattering amplitude. Some realism is introduced by enforcing exact unitarity via the K-matrix method. It is shown that a reasonable agreement with experimental data is obtained up to about 1 GeV. The poles in the unitarized scattering amplitude are studied in some detail. The lowest pole clearly represents the sigma meson (or $f_0(600)$) with a mass and decay width around 500 MeV. The second pole invites comparison with the $f_0(980)$ which has a mass around 1 GeV and decay width around 100 MeV. The third and fourth poles, resemble some of the isosinglet state in the complicated 1–2 GeV region. Some comparison is made to the situation in the usual SU(3) linear sigma model with a single scalar nonet.

The analysis of the recent neutral-current neutrino-nucleus scattering cross sections measured by the MiniBooNE Collaboration requires relativistic theoretical descriptions also accounting for the role of final-state interactions. In this work, we evaluate differential cross sections with the relativistic distorted-wave impulse approximation and with the relativistic Green’s function model to investigate the sensitivity to final-state interactions. The role of the strange-quark content of the nucleon form factors is also discussed.

An electron antineutrino mass has been measured in tritium $\beta$ decay in the Troitsk $\nu$-mass experiment. The setup consists of a windowless gaseous tritium source and an electrostatic electron spectrometer. The whole data set acquired from 1994 to 2004 was reanalyzed. A thorough selection of data with the reliable experimental conditions has been performed. We checked every known systematic effect and obtained the following experimental estimate for neutrino mass squared $m_{\nu }^2=-0.67\pm 2.53{\mathrm{eV}}^2$. This gives an experimental upper sensitivity limit of $m_{\nu }<2.2\mathrm{eV}$, 95% C.L. and upper limit estimates $m_{\nu }<2.12\mathrm{eV}$, 95% C.L. for Bayesian statistics and $m_{\nu }<2.05\mathrm{eV}$, 95% C.L. for the Feldman and Cousins approach.

A multivariate likelihood method to measure electroweak couplings with the Drell–Yan process at the LHC is presented. The process is described by the dilepton rapidity, invariant mass, and decay angle distributions. The decay angle ambiguity due to the unknown assignment of the scattered constituent quark and antiquark to the two protons in a collision is resolved statistically using correlations between the observables. The method is applied to a sample of dimuon events from proton-proton collisions at $\sqrt{s}=7\mathrm{TeV}$ collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of $1.1{\mathrm{fb}}^{-1}$. From the dominant $u\overline{u}$, $d\overline{d}\to {\gamma }^{*}/Z\to {\mu }^{-}{\mu }^{+}$ process, the effective weak mixing angle parameter is measured to be ${sin}^2{\theta }_{\mathrm{eff}}=0.2287\pm 0.0020(\mathrm{stat}.)\pm 0.0025(\mathrm{syst}.)$. This result is consistent with measurements from other processes, as expected within the standard model.