We study the $a_0$ and $\sigma$ mesons with the overlap fermion in the chiral regime with the pion mass as low as 182 MeV in the quenched approximation. After the ${\eta }^{\prime }\pi$ ghost states are separated, we find the $a_0$ mass with the $q\overline{q}$ interpolation field to be almost independent of the quark mass in the region below the strange quark mass. The chirally extrapolated results are consistent with $a_0(1450)$ being the $u\overline{d}$ meson and $K_0^{*}(1430)$ being the $u\overline{s}$ meson with calculated masses at $1.42\pm 0.13\mathrm{GeV}$ and $1.41\pm 0.12\mathrm{GeV}$, respectively. We also calculate the scalar mesonium with a tetraquark interpolation field. In addition to the two-pion scattering states, we find a state at $\sim 550\mathrm{MeV}$. Through the study of volume dependence, we confirm that this state is a one-particle state, in contrast to the two-pion scattering states. This suggests that the observed state is a tetraquark mesonium which is quite possibly the $\sigma (600)$ meson.

We calculate the relation between the bare coupling constant $g_0$ and the $\overline{\mathrm{MS}}$-renormalized coupling $g_{\overline{\mathrm{MS}}}$, $g_0=Z_g(g_0,a\overline{\mu })g_{\overline{\mathrm{MS}}}$, to 2 loops in perturbation theory. We employ the standard Wilson action for gluons and the overlap action for fermions. For convenience, we have worked with the background field technique, which only requires evaluation of 2-point Green’s function for the problem at hand. Our results depend explicitly on the number of fermion flavors ($N_f$) and colors ($N$). Since the dependence of $Z_g$ on the overlap parameter $\rho$ cannot be extracted analytically, we tabulate our results for different values in the allowed range of $\rho$ ($0<\rho <2$), focusing on values which are being used most frequently in simulations. Knowledge of $Z_g$ allows us to derive the 3-loop coefficient of the bare $\beta$-function (${\beta }_L(g_0)$) which, unlike the 1- and 2-loop coefficients, is regularization-dependent. The nontrivial dependence of $Z_g$ and of ${\beta }_L(g_0)$ on $\rho$ is plotted for various choices of $N$, $N_f$.

The potentials between two $B$ mesons are computed in the heavy-quark limit using quenched lattice QCD at $m_{\pi }\sim 400\mathrm{MeV}$. Nonzero central potentials are clearly evident in all four spin-isospin channels, $(I,s_l)=(0,0)$, (0, 1), (1, 0), (1, 1), where $s_l$ is the total spin of the light degrees of freedom. At short distance, we find repulsion in the $I\ne s_l$ channels and attraction in the $I=s_l$ channels. Linear combinations of these potentials that have well-defined spin and isospin in the $t$-channel are found, in three of the four cases, to have substantially smaller uncertainties than the potentials defined with the $s$-channel $(I,s_l)$, and allow quenching artifacts from single hairpin exchange to be isolated. The $B{B}^{*}\pi$ coupling extracted from the long-distance behavior of the finite-volume $t$-channel potential is found to be consistent with quenched calculations of the matrix element of the isovector axial-current. The tensor potentials in both of the $s_l=1$ channels are found to be consistent with zero within calculational uncertainties.

A calculational scheme for obtaining the electric polarizability of the neutron in lattice QCD with dynamical quarks is developed, using the background field approach. The scheme differs substantially from methods previously used in the quenched approximation, the physical reason being that the QCD ensemble is no longer independent of the external electromagnetic field in the dynamical quark case. One is led to compute (certain integrals over) four-point functions. Particular emphasis is also placed on the physical role of constant external gauge fields on a finite lattice; the presence of these fields complicates the extraction of polarizabilities, since it gives rise to an additional shift of the neutron mass unrelated to polarizability effects. The method is tested on a $SU(3)$ flavor-symmetric ensemble furnished by the MILC Collaboration, corresponding to a pion mass of $m_{\pi }=759\mathrm{MeV}$. Disconnected diagrams are evaluated using stochastic estimation. A small negative electric polarizability of $\alpha =(-2.0\pm 0.9)·{10}^{-4}{\mathrm{fm}}^3$ is found for the neutron at this rather large pion mass; this result does not seem implausible in view of the qualitative behavior of $\alpha$ as a function of $m_{\pi }$ suggested by chiral effective theory.

Threshold enhanced perturbative QCD corrections to rapidity distributions of $Z$ and $W^{\pm }$ bosons at hadron colliders are presented using the Sudakov resummed cross sections at ${\mathrm{N}}^3\mathrm{LO}$ level. We have used renormalization group invariance and the mass factorization theorem that these hard scattering cross sections satisfy to construct the QCD amplitudes. We show that these higher order threshold QCD corrections stabilize the theoretical predictions for vector boson production at the LHC under variations of both renormalization and factorization scales.

Using BABAR measurements of the inclusive electron spectrum in $B\to X_{u}e\nu$ decays and the inclusive photon spectrum in $B\to X_s\gamma$ decays, we extract the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$. The extraction is based on theoretical calculations designed to reduce the theoretical uncertainties by exploiting the assumption that the leading shape functions are the same for all $b\to q$ transitions ($q$ is a light quark). The results agree well with the previous analysis, have indeed smaller theoretical errors, but are presently limited by the knowledge of the photon spectrum and the experimental errors on the lepton spectrum.

We evaluate the cross section for $\overline{p}p\to {\ell }^{+}{\ell }^{-}{\pi }^0$ in the forward direction and for a large lepton pair invariant mass. In this kinematical region, the leading-twist amplitude factorizes into a short-distance matrix element, long-distance antiproton-distribution amplitudes, and proton to pion transition distribution amplitudes (TDAs). Using a modeling inspired from the chiral limit for these TDAs, we obtain a first estimate of this cross section, which demonstrates that this process can be measured at GSI-FAIR.

We examine the large-$N_c$ relations which express the electromagnetic $N$-to-$\Delta$ transition quantities in terms of the electromagnetic properties of the nucleon. These relations are based on the known large-$N_c$ relation between the $N\to \Delta$ electric quadrupole moment and the neutron charge radius, and a newly derived large-$N_c$ relation between the electric quadrupole ($E2$) and Coulomb quadrupole ($C2$) transitions. Extending these relations to finite, but small, momentum transfer, we find that the description of the electromagnetic $N\to \Delta$ ratios ($R_{\mathrm{EM}}$ and $R_{\mathrm{SM}}$) in terms of the nucleon form factors predicts a structure which may be ascribed to the effect of the “pion cloud.” These relations also provide useful constraints for the $N\to \Delta$ generalized parton distributions.

We discuss possible ways to observationally detect the superdense cosmic objects composed of hypothetical subconstituent fermions beneath the quark/lepton level, recently proposed by us. The characteristic mass and size of such objects depend on the compositeness scale, and their huge density cannot arise within a context of quarks and leptons alone. Their eventual observation would therefore be a direct vindication of physics beyond the standard model of particle physics, possibly far beyond the reach of the Large Hadron Collider (LHC), in a relatively simple and inexpensive manner. If relic objects of this type exist, they can possibly be detected by present and future x-ray observatories, high-frequency gravitational wave detectors, and seismological detectors. To have a realistic detection rate, i.e., to be observable, they must necessarily constitute a significant fraction of cold dark matter.

We study the quantization of a linear scalar field, whose symmetries are described by the $\kappa$-Poincaré Hopf algebra, via deformed Fock space construction. The one-particle sector of the theory exhibits a natural (Planckian) cutoff for the modes of the field. At the “multiparticle” level the nontrivial coalgebra structure of $\kappa$-Poincaré leads to a deformed bosonization in the construction of Fock space states. These physical states carry energy-momentum charges which are divergenceless and obey a deformed dispersion relation.

Photon geodesics are calculated in a Swiss-cheese model, where the cheese is made of the usual Friedmann-Robertson-Walker (FRW) solution and the holes are constructed from a Lemaître-Tolman-Bondi solution of Einstein’s equations. The observables on which we focus are the changes in the redshift, in the angular-diameter-distance relation, in the luminosity-distance-redshift relation, and in the corresponding distance modulus. We find that redshift effects are suppressed when the hole is small because of a compensation effect acting on the scale of half a hole resulting from the special case of spherical symmetry. However, we find interesting effects in the calculation of the angular distance: strong evolution of the inhomogeneities (as in the approach to caustic formation) causes the photon path to deviate from that of the FRW case. Therefore, the inhomogeneities are able to partly mimic the effects of a dark-energy component. Our results also suggest that the nonlinear effects of caustic formation in cold dark matter models may lead to interesting effects on photon trajectories.

While supernova remnants have been identified as the most likely sources of the galactic cosmic rays, no conclusive observational evidence for this association exists. We show here that IceCube has the possibility of producing incontrovertible evidence by detecting neutrinos produced by the cosmic ray beam interacting with the hydrogen in the vicinity of the supernova shock expanding into the interstellar medium. We show that the observational information on gamma ray fluxes from the Cygnus region, although limited, is sufficient to pinpoint the expected event rate of the neutrinos associated with a single source of 0.5 Crab at the TeV level to within a factor of 2, between 2 and 3.8 neutrinos per year. Finally, we note that recent gamma-ray observations reveal the presence of at least three and possibly up to eight such sources, raising the possibility of seeing more than 10 neutrinos per year from these sources alone.

The newly observed $Z^{+}(4433)$ resonance by BELLE is believed to be a tetraquark bound state made up of $(cu)(\overline{c}\overline{d})$. We propose the bottomed analog of this bound state, namely, by replacing one of the charm quarks by a bottom quark, thus forming $Z_{bc}^{0,\pm ,\pm \pm }$. One of the $Z_{bc}$ is doubly charged. The predicted mass of $Z_{bc}$ is around 7.6 GeV. This doubly charged bound state can be detected by its decay into $B_c^{\pm }{\pi }^{\pm }$. Similarly, we can also replace both charm quark and antiquark of the $Z^{+}(4433)$ by bottom quark and antiquark, respectively, thus forming $Z_{bb}$ the bottomonium analog of $Z^{+}(4433)$. The predicted mass of $Z_{bb}$ is about 10.7 GeV.

Recent CDF and D0 measurements of $B_s^0–{\overline{B}}_s^0$ mixing make it possible to search for $CP$ violation and test $CPT$ symmetry in a variety of $B_s$ decays. Considering both coherent $B_d^0{\overline{B}}_d^0$ decays at the ${\rm Y}(4S)$ resonance and coherent $B_s^0{\overline{B}}_s^0$ decays at the ${\rm Y}(5S)$ resonance, we formulate their time-dependent and time-integrated rates by postulating small $CPT$ violation in $B_d^0–{\overline{B}}_d^0$ and $B_s^0–{\overline{B}}_s^0$ oscillations. We show that the opposite-sign dilepton events from either $C$-odd or $C$-even $B_q^0{\overline{B}}_q^0$ states (for $q=d$ or $s$) can be used to determine or constrain the $CPT$-violating parameter at a super-$B$ factory. The possibility of distinguishing between the effect of $CPT$ violation and that of $\Delta B=-\Delta Q$ transitions is also discussed.

The effects of the peculiar $CP$ conserving phases in unparticle propagators are explored. We find that the phases have a great impact on $CP$ violation. We adopt the decays $B_d\to {\pi }^{+}{\pi }^{-}$ and $B_d\to {\ell }^{-}{\ell }^{+}$ as the illustrators to demonstrate the influences of these phases on the direct $CP$ asymmetries. In particular, we emphasize that unparticle physics is the only model suggested to date that could give the direct $CP$ asymmetries in $B_d\to {\ell }^{-}{\ell }^{+}$ as large as 15%. We also point out that the unparticle phases could be probed in $B\to K^{*}{\ell }^{+}{\ell }^{-}$ decays by using T-odd correlations.

A resonancelike structure in the ${\pi }^{\pm }\psi (2S)$ mass spectrum arising in $B\to K{\pi }^{\pm }\psi (2S)$ has recently been reported. It is noted that the mass of this structure, $4433\pm 4\pm 2\mathrm{MeV}$, is not far from the threshold for production of $D^{*}{\overline{D}}_1(2420)$. A proposed mechanism for production of this state is suggested, and tests are suggested.

Computations of the drag force on a heavy quark moving through a thermal state of strongly coupled $\mathcal{N}=4$ super-Yang-Mills theory have appeared recently. I compare the strength of this effect between $\mathcal{N}=4$ gauge theory and QCD, using the static force between external quarks to normalize the ’t Hooft coupling. Comparing $\mathcal{N}=4$ and QCD at fixed energy density then leads to a relaxation time of roughly $2\mathrm{fm}/c$ for charm quarks moving through a quark-gluon plasma at $T=250\mathrm{MeV}$. This estimate should be regarded as preliminary because of the difficulties of comparing two such different theories.

It has recently been demonstrated that certain types of nontensional stress-energy can live on tensional codimension-2 branes, including gravitational shockwaves and small Schwarzschild black holes. In this paper we generalize the earlier Schwarzschild results, and construct the exact gravitational fields of small rotating black holes on a codimension-2 brane. We focus on the phenomenologically interesting case of a three-brane embedded in a spacetime with two compactified extra dimensions. For a nonzero tension on the brane, we verify that these solutions also show the “lightning rod” effect found in the Schwarzschild solutions, the net effect of which is to rescale the fundamental Planck mass. This allows for larger black hole parameters, such as the event horizon, angular momentum, and lifetime than would be naively expected for a tensionless brane. It is also found that a black hole with angular momentum pointing purely along the brane directions has a smaller horizon angular velocity than the corresponding tensionless case, while a hole with bulk components of angular momentum has a larger angular velocity.

A practical method is suggested for performing renormalized 2 particle irreducible (2PI) resummation at finite temperature using specific renormalization schemes. I examine the consistency of such schemes in the paper. Advantages of the proposed method are that there is no need to solve Bethe-Salpeter equations for 2PI resummation, and there is no explicit diagrammatic resummation of the 2 particle reducible graphs. The proposed method is used to perform a two-loop renormalized 2PI resummation in the finite temperature ${\Phi }^4$ model.

We highlight the conceptual issues that arise when one applies the quasi-Hermitian framework to analyze scattering from localized non-Hermitian potentials, in particular complex square wells or delta functions. When treated in the framework of conventional quantum mechanics, these potentials are generally considered as effective theories, in which probability is not conserved because of processes that have been ignored. However, if they are treated as fundamental theories, the Hilbert-space metric must be changed. In order for the newly defined probability to be conserved, it must differ from the standard one, even at asymptotically large distances from the scattering center, and the mechanism for this is the nonlocality of the new metric, as we show in detail in the model of a single complex delta function. However, properties of distant bound-state systems, which do not interact physically with the non-Hermitian scattering potential, should not be affected. We analyze a model Hamiltonian that supports this contention.