Isospin density and thermal corrections for several condensates are discussed, at the one-loop level, in the frame of chiral dynamics with pionic degrees of freedom. The evolution of such objects gives an additional insight into the condensed-pion phase transition that occurs basically when $|{\mu }_{\mathrm{I}}|>m_{\pi }$, $|{\mu }_{\mathrm{I}}|$ being the isospin chemical potential. Calculations are done in both phases, showing a good agreement with lattice results for such condensates.

Compact results are obtained for tree-level non-MHV amplitudes of six fermions and of four fermions and two gluons, by using extended BCF/BCFW rules. Combining with previous results, complete set of tree amplitudes of six partons are now available in compact forms.

We analyze the electromagnetic contributions to the octet and decuplet baryon masses using the heavy-baryon approximation in chiral effective field theory and methods we developed in earlier analyses of the baryon masses and magnetic moments. Our methods connect simply to Morpurgo’s general parametrization of the electromagnetic contributions and to semirelativistic quark models. Our calculations are carried out including the one-loop mesonic corrections to the basic electromagnetic interactions, so to two loops overall. We find that to this order in the chiral loop expansion there are no three-body contributions. The Coleman-Glashow relation and other sum rules derived in quark models with only two-body terms therefore continue to hold, and violations involve at least three-loop processes and can be expected to be quite small. We present the complete formal results and some estimates of the matrix elements here. Numerical calculations will be presented separately.

We report on a search for pair production of first-generation scalar leptoquarks (LQ) in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ using an integrated luminosity of $252{\mathrm{pb}}^{-1}$ collected at the Fermilab Tevatron collider by the D0 detector. We observe no evidence for LQ production in the topologies arising from $\mathrm{LQ}\overline{\mathrm{LQ}}\to eqeq$ and $\mathrm{LQ}\overline{\mathrm{LQ}}\to eq\nu q$, and derive 95% C.L. lower limits on the LQ mass as a function of $\beta$, where $\beta$ is the branching fraction for $\mathrm{LQ}\to eq$. The limits are 241 and $218\mathrm{GeV}/c^2$ for $\beta =1$ and 0.5, respectively. These results are combined with those obtained by D0 at $\sqrt{s}=1.8\mathrm{TeV}$, which increases these LQ mass limits to 256 and $234\mathrm{GeV}/c^2$.

Weakly Interacting Massive Particles (WIMPs) of mass $m$ freeze-out at a temperature $T_f\simeq m/25$, i.e. in the range 400 MeV–40 GeV for a particle in the typical mass range 10–1000 GeV. The WIMP relic density, which depends on the effective number of relativistic degrees of freedom at $T_f$, may be measured to better than $1\%$ by Planck, warranting comparable theoretical precision. Recent theoretical and experimental advances in the understanding of high-temperature QCD show that the quark gluon plasma departs significantly from ideal behavior up to temperatures of several GeV, necessitating an improvement of the cosmological equation of state over those currently used. We discuss how this increases the relic density by approximately 1.5–$3.5\%$ in benchmark mSUGRA models, with an uncertainty in the QCD corrections of 0.5–$1\%$. We point out what further work is required to achieve a theoretical accuracy comparable with the expected observational precision, and speculate that the effective number of degrees of freedom at $T_f$ may become measurable in the foreseeable future.

A new method for calculating the coefficient functions of the operator product expansion is proposed which does not depend explicitly on elementary fields. Coefficient functions are defined entirely in terms of composite operators. The method is illustrated in the case of QCD nonsinglet operators.

The precise quark mass dependence of the one-loop effective action in an instanton background has recently been computed [Phys. Rev. Lett. 94, 072001 (2005).]. The result interpolates smoothly between the previously known extreme small and large mass limits. The computational method makes use of the fact that the single instanton background has radial symmetry, so that the computation can be reduced to a sum over partial waves of logarithms of radial determinants, each of which can be computed numerically in an efficient manner. The bare sum over partial waves is divergent and must be regulated and renormalized. In this paper we provide more details of this computation, including both the renormalization procedure and the numerical approach. We conclude with comparisons of our precise numerical results with a simple interpolating function that connects the small and large mass limits, and with the leading order of the derivative expansion.

Whether one starts from the analytic S-matrix definition or the requirement of gauge-parameter independence in renormalization theory, a relativistic resonance is given by a pole at a complex value $s_R$ of the energy squared $s$. The complex number $s_R$ does not define the mass and the width separately, and the pole definition alone is also not sufficient to describe the interference of two or more Breit-Wigner resonances as observed in experiments. To achieve this and obtain a unified theory of relativistic resonances and decay, we invoke the decaying particle aspect of a resonance and associate to each pole a space of relativistic Gamow kets. The Gamow kets transform irreducibly under causal Poincaré transformations and have an exponential time evolution. Therefore one can choose of the many possible width parameters, the width ${\Gamma }_R$ of the relativistic resonance such that the lifetime $\tau =\hslash /{\Gamma }_R$. This leads to the parametrization $s_R=(M_R-i{\Gamma }_R/2{)}^2$ and uniquely defines these $(M_R,{\Gamma }_R)$ as the mass and width parameters for a resonance. Further it leads to the following new results: Two poles in the same partial wave are given by the sum of two Breit-Wigner amplitudes and by a superposition of two Gamow vectors with each Gamow vector corresponding to one Breit-Wigner amplitude. In addition to the sum of Breit-Wigner amplitudes, the scattering amplitude contains a background amplitude representing direct production of the final state (contact terms). This contact amplitude is associated to a background vector representing the nonexponential energy continuum; omitting it gives the two interfering exponentials of the Weisskopf-Wigner methods. To accomplish all this required a minor modification in the foundation of quantum theory, which led to a quantum theory that contains the time asymmetry of causality.

Light-cone gauge manifestly supersymmetric formulation of 11 dimensional supergravity is developed. The formulation is given entirely in terms of light-cone scalar superfield, allowing us to treat all component fields on an equal footing. All higher derivative on mass-shell manifestly supersymmetric $4$-point functions invariant with respect to linear supersymmetry transformations and corresponding (in gravitational bosonic sector) to terms constructed from four Riemann tensors and derivatives are found. Superspace representation for $4$-point scattering amplitudes is also obtained. Superfield representation of linearized interaction vertex of superparticle and supergravity fields is presented. All $4$-point higher derivative interaction vertices of ten-dimensional supersymmetric Yang-Mills theory are also determined.

Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green’s function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from “quasinormal” modes of the self-similar system as well as “high-frequency” waves are clarified. We find a characteristic power-law time evolution of the outgoing energy flux which appears just before naked singularity formation and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.

This is the second of two companion papers on the interior structure of self-similar accreting charged black holes. In the first paper, the black hole was allowed to accrete only a single fluid of charged baryons. In this second paper, the black hole is allowed to accrete in addition a neutral fluid of almost noninteracting dark matter. Relativistic streaming between outgoing baryons and ingoing dark matter leads to mass inflation near the inner horizon. When enough dark matter has been accreted that the center-of-mass frame near the inner horizon is ingoing, then mass inflation ceases and the fluid collapses to a central singularity. A null singularity does not form on the Cauchy horizon. Although the simultaneous presence of ingoing and outgoing fluids near the inner horizon is essential to mass inflation, reducing one or the other of the ingoing dark matter or outgoing baryonic streams to a trace relative to the other stream makes mass inflation more extreme, not the other way around as one might naively have expected. Consequently, if the dark matter has a finite cross section for being absorbed into the baryonic fluid, then the reduction of the amount of ingoing dark matter merely makes inflation more extreme, the interior mass exponentiating more rapidly and to a larger value before mass inflation ceases. However, if the dark matter absorption cross section is effectively infinite at high collision energy, so that the ingoing dark matter stream disappears completely, then the outgoing baryonic fluid can drop through the Cauchy horizon. In all cases, as the baryons and the dark matter voyage to their diverse fates inside the black hole, they only ever see a finite amount of time pass by in the outside universe. Thus the solutions do not depend on what happens in the infinite past or future. We discuss in some detail the physical mechanism that drives mass inflation. Although the gravitational force is inward, inward means opposite direction for ingoing and outgoing fluids near the inner horizon. Mass inflation is driven by a feedback loop in which the general relativistic contribution to the gravitational force sourced by the radial pressure accelerates the ingoing and outgoing fluids through each other, which increases the radial pressure, which increases the gravitational force.

An extensive investigation is made of the interior structure of self-similar accreting charged black holes. In this, the first of two papers, the black hole is assumed to accrete a charged, electrically conducting, relativistic baryonic fluid. The mass and charge of the black hole are generated self-consistently by the accreted material. The accreted baryonic fluid undergoes one of two possible fates: either it plunges directly to the spacelike singularity at zero radius, or else it drops through the Cauchy horizon. The baryons fall directly to the singularity if the conductivity either exceeds a certain continuum threshold ${\kappa }_{\infty }$, or else equals one of an infinite spectrum ${\kappa }_n$ of discrete values. Between the discrete values ${\kappa }_n$, the solution is characterized by the number of times that the baryonic fluid cycles between ingoing and outgoing. If the conductivity is at the continuum threshold ${\kappa }_{\infty }$, then the solution cycles repeatedly between ingoing and outgoing, displaying a discrete self-similarity reminiscent of that observed in critical collapse. Below the continuum threshold ${\kappa }_{\infty }$, and except at the discrete values ${\kappa }_n$, the baryonic fluid drops through the Cauchy horizon, and in this case undergoes a shock, downstream of which the solution terminates at an irregular sonic point where the proper acceleration diverges, and there is no consistent self-similar continuation to zero radius. As far as the solution can be followed inside the Cauchy horizon, the radial direction is timelike. If the radial direction remains timelike to zero radius (which cannot be confirmed because the self-similar solutions terminate), then there is presumably a spacelike singularity at zero radius inside the Cauchy horizon, which is distinctly different from the vacuum (Reissner-Nordström) solution for a charged black hole.

New families of exact general relativistic thick disks are constructed using the “displace, cut, fill, and reflect” method. A class of functions used to fill the disks is derived imposing conditions on the first and second derivatives to generate physically acceptable disks. The analysis of the function’s curvature further restricts the ranges of the free parameters that allow physically acceptable disks. Then this class of functions together with the Schwarzschild metric is employed to construct thick disks in isotropic, Weyl and Schwarzschild canonical coordinates. In these last coordinates an additional function must be added to one of the metric coefficients to generate exact disks. Disks in isotropic and Weyl coordinates satisfy all energy conditions, but those in Schwarzschild canonical coordinates do not satisfy the dominant energy condition.

We apply an extended version of the method developed by Chimento and Jakubi [Int. J. Mod. Phys. D 5, 71 (1996)], to derive exact cosmological (flat) Friedmann-Robertson-Walker solutions in RS2 brane models with a perfect fluid of ordinary matter plus a scalar field fluid trapped on the brane. We found new exact solutions, which could serve to unify inflation and quintessence in a common theoretical framework.

We analyze the energy extraction by the Penrose process in higher dimensions. Our result shows the efficiency of the process from higher dimensional black holes and black rings can be rather high compared with that in the four-dimensional Kerr black hole. In particular, if one rotation parameter vanishes, the maximum efficiency becomes infinitely large because the angular momentum is not bounded from above. We also apply a catastrophe theory to analyze the stability of black rings. It indicates a branch of black rings with higher rotational energy is unstable, which should be a different type of instability from the Gregory-Laflamme one.

We derive strong bounds on any possible large-scale spatial variation in the values of physical constants whose space-time evolution is driven by a scalar field. These limits are imposed by the isotropy of the microwave background on large angular scales in theories which describe space and time variations in the fine structure constant, $\alpha$, the electron-proton mass ratio, $\mu$, and the Newtonian gravitational constant, $G$. Large-scale spatial fluctuations in the fine structure constant are bounded by $\delta \alpha /\alpha \lesssim 2\times {10}^{-9}$ and $\delta \alpha /\alpha \lesssim 1.2\times {10}^{-8}$ in the Bekenstein-Sandvik-Barrow-Magueijo and varying-speed-of-light theories, respectively, fluctuations in the electron-proton mass ratio by $\delta \mu /\mu \lesssim 9\times {10}^{-5}$ in the Barrow-Magueijo theory and fluctuations in $G$ by $\delta G/G\lesssim 3.6\times {10}^{-10}$ in the Brans-Dicke theory. These derived bounds are significantly stronger than any obtainable by direct observations of astrophysical objects at the present time.

We propose a hybrid inflation scenario in which the singlet sneutrino, the superpartner of the right-handed neutrino, plays the role of the inflaton. We study a minimal model of sneutrino hybrid inflation in supergravity, where we find a spectral index $n_{\mathrm{s}}\approx 1+2\gamma$ with $|\gamma |\lesssim 0.02$, and predict a running spectral index $|\mathrm{d}{n}_{\mathrm{s}}/\mathrm{d}\ln k|\ll |\gamma |$ and a tensor-to-scalar ratio $r\ll {\gamma }^2$ for field values well below the Planck scale. In our scenario, the baryon asymmetry of our universe can be explained via nonthermal leptogenesis and a low reheat temperature $T_{\mathrm{RH}}\approx {10}^6$ GeV can be realized.

We show by explicit computation that the recently discovered duality invariance of $D=4$ linearized gravity is lost, already at first self-interacting, cubic approximation of general relativity. In contrast, the cubic Yang-Mills extension of Maxwell does admit a simple deformed duality.

In the framework of perturbative QCD approach, we calculate the branching ratio and $CP$ asymmetry for $B_s^0({\overline{B}}_s)\to {\pi }^{\pm }{K}^{\mp }$ and $B_s({\overline{B}}_s)\to {\pi }^0{\overline{K}}^0(K^0)$ decays. Besides the usual factorizable diagrams, both nonfactorizable and annihilation type contributions are taken into account. We find that (a) the branching ratio of $B_s^0({\overline{B}}_s)\to {\pi }^{\pm }{K}^{\mp }$ is about $(6-10)\times {10}^{-6}$; $Br(B_s({\overline{B}}_s)\to {\pi }^0{\overline{K}}^0(K^0))$ about $(1-3)\times {10}^{-7}$; and (b) there are large $CP$ asymmetries in the two processes, which can be tested in the near future LHC-b experiments at CERN and BTeV experiments at Fermilab.

Roles of instanton induced interactions (III) in the masses of pentaquark baryons, ${\Theta }^{+}$ ($J=1/2$ and $3/2$) and ${\Xi }^{--}$, and a dibaryon, $H$, are discussed using the MIT bag model. It is shown that the two-body terms in III give a strong attraction mainly due to the increase of the number of flavor antisymmetric quark pairs in multiquark systems. In contrast, the three-body $u$-$d$-$s$ interaction is repulsive. It is found that III lowers the mass of negative-parity ${\Theta }^{+}$ as much as 100 MeV from the mass predicted by the bag model without III. We also consider possible quark model configurations for positive-parity ${\Theta }^{+}$ under III.