The generalized nonextensive statistics proposed by Tsallis have been successfully utilized in many systems where long range interactions are present. For high density quark matter an attractive long range interaction arising from single gluon exchange suggests the formation of a diquark condensate. We study the effects on this color superconducting phase for two quark flavors due to a change to Tsallis statistics. By numerically solving the gap equation we obtain a generalization of the universality condition $\frac{2{\varphi }_0}{T_C}\approx 3.52$ and determine the temperature dependence of the gap. For the Tsallis parameter $q\approx 1$ the specific heat of the gapped fermions is exponential becoming more linear as $q$ increases. This suggests that for larger values of $q$ s-wave color superconductors behave like high $T_c$ superconductors rather than weak superconductors.

It is usually assumed that the high-energy evolution of partons in QCD remains local in coordinate space. In particular, fixed impact-parameter scattering is thought to be in the universality class of one-dimensional reaction-diffusion processes as if the evolutions at different points in the transverse plane became uncorrelated through rapidity evolution. We check this assumption by numerically comparing a toy model with QCD-like impact-parameter dependence to its exact counterpart with uniform evolution in impact-parameter space. We find quantitative differences, but which seem to amount to a mere rescaling of the strong coupling constant. Since the rescaling factor does not show any strong ${\alpha }_s$ dependence, we conclude that locality is well verified, up to subleading terms at small ${\alpha }_s$.

We have evaluated the contribution to the anomalous magnetic moment of the electron from six tenth-order Feynman diagrams which contain eighth-order vacuum-polarization function formed by two light-by-light-scattering diagrams connected by three photons. The integrals are constructed by two different methods. In the first method the subtractive counter terms are used to deal with ultraviolet (UV) singularities together with the requirement of gauge invariance. In the second method, the Ward-Takahashi identity is applied to the light-by-light-scattering amplitudes to eliminate UV singularities. Numerical evaluation confirms that the two methods are consistent with each other within their numerical uncertainties. Combining the two results statistically and adding small contribution from the muons and/or tau leptons, we obtain 0.000 399 9 (18) $(\alpha /\pi {)}^5$. We also evaluated the contribution to the muon $g-2$ from the same set of diagrams and found $-1.26344(14)$ $(\alpha /\pi {)}^5$.

If left-right gauge theory, $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}\times SU(3{)}_C(g_L=g_R)(\equiv G_{2213})$, occurs as an intermediate symmetry in a grand unified theory then, apart from other advantages, it is possible to obtain the seesaw scale necessary to understand small neutrino masses with Majorana coupling of order unity. Barring threshold or nonrenormalizable gravitational effects at the GUT scale, or the assumed presence of additional light scalar particles of unprescribed origin, all other attempts to achieve manifest one-loop gauge coupling unification in supersymmetry $SO(10)$ with such intermediate symmetry have not been successful so far. Attributing this failure to lack of flavor symmetry in the grand unified theory, we show how the spontaneous symmetry breaking of $SO(10)\times S_4$ leads to such left-right intermediate breaking scale extending over the range $M_R\simeq 5\times {10}^9\mathrm{GeV}$ to ${10}^{15}\mathrm{GeV}$. All the charged fermion masses are fitted at the intermediate seesaw scale, $M_N\simeq M_R\simeq 4\times {10}^{13}\mathrm{GeV}$ which is obtained with Majorana coupling $f_0\simeq 1$. Using type-I seesaw and a constrained parametrization in which  $CP$-violation originates only from the quark sector, in addition to other predictions made in the neutrino sector, the reactor mixing angle is found to be ${\theta }_{13}\simeq 3°–5°$ which is in the range accessible to ongoing experiments. The leptonic Dirac phase turns out to be $\delta \simeq 2.9–3.1$ radians with the predicted values of Jarlskog invariant $J_{CP}\simeq 2.95\times {10}^{-5}-{10}^{-3}$.

If neutrinos are Majorana fermions, the lepton mixing parameter space consists of six mixing parameters: three mixing angles and three $CP$-odd phases. A related issue concerns the physical range of the mixing parameters. What values should these take so that all physically distinguishable mixing scenarios are realized? We present a detailed discussion of the lepton mixing parameter space in the case of two and three active neutrinos and in the case of three active and $N$ sterile neutrinos. We emphasize that this question, which has been a source of confusion even among neutrino physicists, is connected to an unambiguous definition of the neutrino mass eigenstates. We find that all Majorana phases can always be constrained to lie between 0 and $\pi$, and that all mixing angles can be chosen positive and at most less than or equal to $\pi /2$ provided the Dirac phases are allowed to vary between $-\pi$ and $\pi$. We illustrate our results with several examples. Finally, we point out that, in the case of new flavor-changing neutrino interactions, the lepton mixing parameter space may need to be enlarged. We properly qualify this statement, and offer concrete examples.

We report the results of a search for the decay $B^0\to K^{*+}{K}^{*-}$ with a sample of $454\pm 5$ million $B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at the Stanford Linear Accelerator Center. We obtain an upper limit at the 90% confidence level on the branching fraction for $\mathcal{B}(B^0\to K^{*+}{K}^{*-})<2.0\times {10}^{-6}$, assuming the decay is fully longitudinally polarized.

Using $385{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at center-of-mass energies around 10.6 GeV, we search for time-integrated $CP$ violation in the Cabibbo-suppressed decays $D^0/{\overline{D}}^0\to {\pi }^{-}{\pi }^{+}{\pi }^0$ and $D^0/{\overline{D}}^0\to K^{-}{K}^{+}{\pi }^0$ with both model-independent and model-dependent methods. Measurements of the asymmetries in amplitudes of flavor states and $CP$ eigenstates provide constraints on theories beyond the standard model, some of which predict $CP$ violation in amplitudes at the 1% level or higher. We find no evidence of $CP$ violation and hence no conflict with the standard model.

Taking into account the recently proposed poly-instanton corrections to the superpotential and combining the racetrack with a Kachru-Kallosh-Linde-Trivedi, respectively, large volume scenario in an intricate manner, we show that we gain exponential control over the parameters in an effective superpotential. This allows us to dynamically stabilize moduli such that a conventional minimal supersymmetric standard model scenario with the string scale lowered to the grand unified theory scale is realized. Depending on the cycles wrapped by the minimal supersymmetric standard model branes, two different scenarios for the hierarchy of soft masses arise. The first one is a supergravity mediated model with $M_{3/2}\simeq 1\mathrm{TeV}$ while the second one features mixed anomaly supergravity mediation with $M_{3/2}\simeq {10}^{10}\mathrm{GeV}$ and split supersymmetry. We also comment on dynamically lowering the scales such that the tree level cosmological constant is of the order $\Lambda =({10}^{-3}\mathrm{eV}{)}^4$.

A class of thick branes in the background of sine-Gordon kinks with a scalar potential $V(\varphi )=p(1+\cos \frac{2\varphi }{q})$ was constructed by R. Koley and S. Kar [Classical Quantum Gravity 22, 753 (2005)]. In this paper, in the background of the warped geometry, we investigate the issue of localization of spin-$1/2$ fermions on these branes in the presence of two types of scalar-fermion couplings: $\eta \overline{\Psi }\varphi \Psi$ and $\eta \overline{\Psi }\sin \varphi \Psi$. By presenting the mass-independent potentials in the corresponding Schrödinger equations, we obtain the lowest Kaluza-Klein modes and a continuous gapless spectrum of Kaluza-Klein states with $m^2>0$ for both types of couplings. For the Yukawa coupling $\eta \overline{\Psi }\varphi \Psi$, the effective potential of the right chiral fermions for positive $q$ and $\eta$ is always positive; hence only the effective potential of the left chiral fermions could trap the corresponding zero mode. This is a well-known conclusion which is discussed extensively in the literature. However, for the coupling $\eta \overline{\Psi }\sin \varphi \Psi$, the effective potential of the right chiral fermions for positive $q$ and $\eta$ is no longer always positive. Although the value of the potential at the location of the brane is still positive, it has a series of wells and barriers on each side, which ensures that the right chiral fermion zero mode could be trapped. Thus we may draw the following remarkable conclusion: for positive $\eta$ and $q$, the potentials of both the left and right chiral fermions could trap the corresponding zero modes under certain restrictions.

We consider the large $N$ spectrum of the quantum mechanical Hamiltonian of two Hermitian matrices coupled via a Yang-Mills interaction. In a framework where one of the matrices is treated exactly and the other is treated as a creation operator impurity, the difference equation associated with the Yang-Mills interaction is derived and solved exactly for two impurities. In this case, the full string tension corrected spectrum depends on two momenta. For a specific value of one of these momenta, the spectrum has the same structure as that of giant magnon bound states. States with general number of impurities are also discussed.

In this work we study the configuration of two perfectly conducting spherical shells. This is a problem of basic importance to make possible development of experimental apparatuses that they make possible to measure the spherical Casimir effect, an open subject. We apply the mode sum method via cutoff exponential function regularization with two independent parameters: one to regularize the infinite order sum of the Bessel functions; other, to regularize the integral that becomes related, due to the argument theorem, with the infinite zero sum of the Bessel functions. We obtain a general expression of the Casimir energy as a quadrature sum. We investigate two immediate limit cases as a consistency test of the expression obtained: that of a spherical shell and that of two parallel plates. In the approximation of a thin spherical shell we obtain an expression that allows to relate our result with that of the proximity-force approximation, supplying a correction to this result.

We present a new two-dimensional numerical code called $\mathtt{N}\mathtt{a}\mathtt{d}\mathtt{a}$ designed to solve the full Einstein equations coupled to the general relativistic hydrodynamics equations. The code is mainly intended for studies of self-gravitating accretion disks (or tori) around black holes, although it is also suitable for regular spacetimes. Concerning technical aspects the Einstein equations are formulated and solved in the code using a formulation of the standard $3+1$ Arnowitt-Deser-Misner canonical formalism system, the so-called Baumgarte-Shapiro Shibata-Nakamura approach. A key feature of the code is that derivative terms in the spacetime evolution equations are computed using a fourth-order centered finite difference approximation in conjunction with the Cartoon method to impose the axisymmetry condition under Cartesian coordinates (the choice in $\mathtt{N}\mathtt{a}\mathtt{d}\mathtt{a}$), and the puncture/moving puncture approach to carry out black hole evolutions. Correspondingly, the general relativistic hydrodynamics equations are written in flux-conservative form and solved with high-resolution, shock-capturing schemes. We perform and discuss a number of tests to assess the accuracy and expected convergence of the code, namely, (single) black hole evolutions, shock tubes, and evolutions of both spherical and rotating relativistic stars in equilibrium, the gravitational collapse of a spherical relativistic star leading to the formation of a black hole. In addition, paving the way for specific applications of the code, we also present results from fully general relativistic numerical simulations of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium.

In this work, we consider different forms of relativistic perfect fluid Lagrangian densities that yield the same gravitational field equations in general relativity (GR). A particularly intriguing example is the case with couplings of the form $[1+f_2(R)]{\mathcal{L}}_m$, where $R$ is the scalar curvature, which induces an extra force that depends on the form of the Lagrangian density. It has been found that, considering the Lagrangian density ${\mathcal{L}}_m=p$, where $p$ is the pressure, the extra-force vanishes. We argue that this is not the unique choice for the matter Lagrangian density, and that more natural forms for ${\mathcal{L}}_m$ do not imply the vanishing of the extra force. Particular attention is paid to the impact on the classical equivalence between different Lagrangian descriptions of a perfect fluid.

A simplified theory of the diagonal Bianchi type I model coupled with a massless scalar field in loop quantum cosmology is constructed according to the $\overline{\mu }$ scheme. Kinematical and physical sectors of the theory are under good analytical control as well as the scalar constraint operator. Although it is possible to compute numerically the nonsingular evolution of the three gravitational degrees of freedom, the naive implementation of the $\overline{\mu }$ scheme to the diagonal Bianchi type I model is problematic. The lack of the full invariance of the theory with respect to the fiducial cell and fiducial metric scaling causes serious problems in the semiclassical limit of the theory. Because of this behavior it is very difficult to extract reasonable physics from the model. The weaknesses of the implementation of the $\overline{\mu }$ scheme to the Bianchi I model do not imply limitations of the $\overline{\mu }$ scheme in the isotropic case.

We examine the claim of Babak and Grishchuk [S. V. Babak and L. P. Grishchuk, Phys. Rev. D 61, 024038 (1999)] to have solved the problem of localizing the energy and momentum of the gravitational field. After summarizing Grishchuk’s flat-space formulation of gravity, we demonstrate its equivalence to general relativity at the level of the action. Two important transformations are described (diffeomorphisms applied to all fields, and diffeomorphisms applied to the flat-space metric alone) and we argue that both should be considered gauge transformations: they alter the mathematical representation of a physical system, but not the system itself. By examining the transformation properties of the Babak-Grishchuk gravitational energy-momentum tensor under these gauge transformations (infinitesimal and finite) we conclude that this object has no physical significance.

We develop a generating technique for solutions of $U(1{)}^3$ 5D supergravity via dimensional reduction to three dimensions. This theory, which recently attracted attention in connection with black rings, can be viewed as a consistent truncation of the $T^6$ compactification of the 11-dimensional supergravity. Its further reduction to three dimensions accompanied by dualization of the vector fields leads to a 3D gravity coupled sigma model on the homogeneous space $SO(4,4)/SO(4)\times SO(4)$ or $SO(4,4)/SO(2,2)\times SO(2,2)$ depending on the signature of the three-space. We construct a $8\times 8$ matrix representation of these cosets in terms of lower-dimensional blocks. Using it we express a solution generating transformations in terms of potentials and identify those preserving asymptotic conditions relevant to black holes and black rings. As an application we derive the doubly rotating black hole solution with three independent charges. A suitable contraction of the above cosets is used to construct a new representation of the coset $G_{2(2)}/(SL(2,R)\times SL(2,R))$ relevant for minimal five-dimensional supergravity.

We discuss the application of the solitonic techniques to the 5D Einstein-Maxwell gravity. As an illustration we construct a new exact solution describing two concentric rotating dipole black rings. The properties of the solution are investigated.

There has been much recent discussion, and some confusion, regarding the use of existing observational data to estimate the likelihood that next-generation cosmic microwave background (CMB) polarization experiments might detect a nonzero tensor signal, possibly associated with inflation. We examine this issue in detail here in two different ways: (1) first we explore the effect of choice of different parameter priors on the estimation of the tensor-to-scalar ratio $r$ and other parameters describing inflation, and (2) we examine the Bayesian complexity in order to determine how effectively existing data can constrain inflationary parameters. We demonstrate that existing data are not strong enough to render full inflationary parameter estimates in a parametrization- and prior-independent way and that the predicted tensor signal is particularly sensitive to different priors. For parametrizations where the Bayesian complexity is comparable to the number of free parameters we find that a flat prior on the scale of inflation (which is to be distinguished from a flat prior on the tensor-to-scalar ratio) leads us to infer a larger, and in fact slightly nonzero tensor contribution at 68% confidence level. However, no detection is claimed. Our results demonstrate that all that is statistically relevant at the current time is the (slightly enhanced) upper bound on $r$, and we stress that the data remain consistent with $r=0$.

It is well known that anthropic selection from a landscape with a flat prior distribution of cosmological constant $\Lambda$ gives a reasonable fit to observation. However, a realistic model of the multiverse has a physical volume that diverges with time, and the predicted distribution of $\Lambda$ depends on how the spacetime volume is regulated. A very promising method of regulation uses a scale-factor cutoff, which avoids a number of serious problems that arise in other approaches. In particular, the scale-factor cutoff avoids the “youngness problem” (high probability of living in a much younger universe) and the “$Q$ and $G$ catastrophes” (high probability for the primordial density contrast $Q$ and gravitational constant $G$ to have extremely large or small values). We apply the scale-factor cutoff measure to the probability distribution of $\Lambda$, considering both positive and negative values. The results are in good agreement with observation. In particular, the scale-factor cutoff strongly suppresses the probability for values of $\Lambda$ that are more than about 10 times the observed value. We also discuss qualitatively the prediction for the density parameter $\Omega$, indicating that with this measure there is a possibility of detectable negative curvature.