The thermodynamic singularities of QCD in the plane of complex baryo-chemical potential $\mu$ are studied. Predictions are made using scaling and universality arguments in the vicinity of the massless quark limit. The results are illustrated by a calculation of complex $\mu$ singularities in a random matrix model at finite temperature. Implications for lattice QCD simulations aimed at locating the QCD critical point are discussed.

In this article, we take the point of view that the charmed scalar meson $D_{s0}(2317)$ is the conventional $c\overline{s}$ meson and calculate the strong coupling constant $g_{D_{s0}DK}$ within the framework of the light-cone QCD sum rules approach. The numerical values for the large scalar-$DK$ coupling constant $g_{D_{s0}DK}$ support the hadronic dressing mechanism. Just like the scalar mesons $f_0(980)$ and $a_0(980)$, the $D_{s0}(2317)$ may have small scalar $c\overline{s}$ kernel of the typical $c\overline{s}$ meson size. The strong coupling to the hadronic channels (or the virtual mesons loops) may result in smaller mass than the conventional scalar $c\overline{s}$ meson in the constituent quark models, and enrich the pure $c\overline{s}$ state with other components. The $D_{s0}(2317)$ may spend part (or most part) of its lifetime as virtual $DK$ state.

We have analyzed the production of $WZ$ and $WW$ vector-boson pairs at the LHC. These processes give rise to four-fermion final states, and are particularly sensitive to possible nonstandard trilinear gauge-boson couplings. We have studied the interplay between the influence of these anomalous couplings and the effect of the complete logarithmic electroweak $\mathcal{O}(\alpha )$ corrections. Radiative corrections to the standard model processes in double-pole approximation and nonstandard terms due to trilinear couplings are implemented into a Monte Carlo program for $pp\to 4f(+\gamma )$ with final states involving four or two charged leptons. We numerically investigate purely leptonic final states and find that electroweak corrections can fake new-physics signals, modifying the observables by the same amount and shape, in kinematical regions of statistical significance.

We consider a relativistic particle model in an enlarged relativistic phase space, ${\mathcal{M}}^{18}=(X_{\mu },P_{\mu },{\eta }_{\alpha },{\overline{\eta }}_{\dot{\alpha }},{\sigma }_{\alpha },{\overline{\sigma }}_{\dot{\alpha }},e,\varphi )$, which is derived from the free two-twistor dynamics. The spin sector variables $({\eta }_{\alpha },{\overline{\eta }}_{\dot{\alpha }},{\sigma }_{\alpha },{\overline{\sigma }}_{\dot{\alpha }})$ satisfy two second class constraints and account for the relativistic spin structure, and the pair $(e,\varphi )$ describes the electric charge sector. After introducing the Liouville one-form on ${\mathcal{M}}^{18}$, derived by a nonlinear transformation of the canonical Liouville one-form on the two-twistor space, we analyze the dynamics described by the first and second class constraints. We use a composite orthogonal basis in four-momentum space to obtain the scalars defining the invariant spin projections. The first-quantized theory provides a consistent set of wave equations, determining the mass, spin, invariant spin projection and electric charge of the relativistic particle. The wave function provides a generating functional for free, massive higher spin fields.

Within the superfield approach, we consider the duality between the supersymmetric Maxwell-Chern-Simons and self-dual theories in three spacetime dimensions. Using a gauge embedding method, we construct the dual theory to the self-dual model interacting with a matter superfield, which turns out to be not the Maxwell-Chern-Simons theory coupled to matter, but a more complicated model, with a restricted gauge invariance. We stress the difficulties in dualizing the self-dual field coupled to matter into a theory with complete gauge invariance. After that, we show that the duality, achieved between these two models at the tree level, also holds up to the lowest order quantum corrections.

We consider a six-dimensional space-time, in which two of the dimensions are compactified by a flux. Matter can be localized on a codimension one brane coupled to the bulk gauge field and wrapped around an axis of symmetry of the internal space. By studying the linear perturbations around this background, we show that the gravitational interaction between sources on the brane is described by Einstein 4D gravity at large distances. Our model provides a consistent setup for the study of gravity in the rugby (or football) compactification, without having to deal with the complications of a deltalike, codimension two brane. To our knowledge, this is the first complete study of gravity in a realistic brane model with two extra dimensions, in which the mechanism of stabilization of the extra space is fully taken into account.

We consider the stochastic background of gravitational waves produced by an early generation of Population III stars coupled with a normal mode of star formation at lower redshift. The computation is performed in the framework of hierarchical structure formation and is based on cosmic star formation histories constrained to reproduce the observed star formation rate at redshift $z\lesssim 6$, the observed chemical abundances in damped Lyman alpha absorbers and in the intergalactic medium, and to allow for an early reionization of the Universe at $z\sim 11$ as indicated by the third year results released by WMAP. We find that the normal mode of star formation produces a gravitational wave background which peaks at 300–500 Hz and is within LIGO III sensitivity. The Population III component peaks at lower frequencies (30–100 Hz depending on the model), and could be detected by LIGO III as well as the planned BBO and DECIGO interferometers.

Motivated by the quest for black holes in anti-de Sitter braneworlds, and, in particular, by the holographic conjecture relating 5D classical bulk solutions with 4D quantum corrected ones, we numerically solve the semiclassical Einstein equations (backreaction equations) with matter fields in the (zero-temperature) Boulware vacuum state. In the absence of an exact analytical expression for $⟨T_{\mu \nu }⟩$ in four dimensions we work within the $s$-wave approximation. Our results show that the quantum corrected solution is very similar to Schwarzschild spacetime until very close to the horizon, but then a bouncing surface for the radial function appears which prevents the formation of an event horizon. We also analyze the behavior of the geometry beyond the bounce, where a curvature singularity arises. In the dual theory, this indicates that the corresponding 5D static classical braneworld solution is not a black hole but rather a naked singularity.

If Newton’s constant $G$ evolves on cosmological timescales as predicted by extended gravity theories then Type Ia supernovae (SnIa) cannot be treated as standard candles. The magnitude-redshift datasets however can still be useful. They can be used to simultaneously fit for both $H(z)$ and $G(z)$ (so that local $G(z)$ constraints are also satisfied) in the context of appropriate parametrizations. Here we demonstrate how this analysis can be done by applying it to the Gold SnIa dataset. We compare the derived effective equation of state parameter $w(z)$ at best fit with the corresponding result obtained by neglecting the evolution $G(z)$. We show that even though the results clearly differ from each other, in both cases the best fit $w(z)$ crosses the phantom divide $w=-1$. We then attempt to reconstruct a scalar-tensor theory that predicts the derived best fit forms of $H(z)$ and $G(z)$. Since the best fit $G(z)$ fixes the scalar-tensor potential evolution $F(z)$, there is no ambiguity in the reconstruction and the potential $U(z)$ can be derived uniquely. The particular reconstructed scalar-tensor theory, however, involves a change of sign of the kinetic term ${\Phi }^{\prime }(z{)}^2$ as in the minimally coupled case.

We present numerical results for the kaon $B$-parameter, $B_K$, determined in the quenched approximation of lattice QCD. Our simulations are performed using domain-wall fermions and the renormalization group improved, DBW2 gauge action which combine to give quarks with good chiral symmetry at finite lattice spacing. Operators are renormalized nonperturbatively using the RI/MOM scheme. We study scaling by performing the simulation on two different lattices with $a^{-1}=1.982(30)$ and 2.914(54) GeV. We combine this quenched scaling study with an earlier calculation of $B_K$ using two flavors of dynamical, domain-wall quarks at a single lattice spacing to obtain $B_K^{\overline{\mathrm{MS}}\mathrm{NDR}}(\mu =2\mathrm{GeV})=0.563(21)(39)(30)$, were the first error is statistical, the second systematic (without quenching errors) and the third estimates the error due to quenching.

We calculate the electromagnetic and the axial form factors of the nucleon within the framework of light cone sum rules (LCSR) to leading order in QCD and including higher-twist corrections. In particular we motivate a certain choice for the interpolating nucleon field. We find that a simple model of the nucleon distribution amplitudes which deviate from their asymptotic shape, but much less compared to the QCD sum rule estimates, allows one to describe the data remarkably well.

Strangeness contents of baryons are calculated within the rigid rotator model for arbitrary number of colors $N_c$. The problem of extrapolation to realistic value $N_c=3$ is noted, based on explicit calculations and comparison of the rigid rotator and rigid oscillator variants of the model. Some features of exotic baryon spectra ({$\overline{10}$}, {27}, and {35}-plets of baryons) obtained in the chiral soliton approach can be understood in terms of simplified quark ($4q\overline{q}$) wave functions. The effective mass of strange antiquark in different $SU(3)$ multiplets of pentaquarks should depend on the particular multiplet, to link the predictions of soliton and quark models. The estimate of the $6_F$ and ${\overline{3}}_F$ diquarks mass difference can be made from comparison with chiral soliton model results for masses of exotic baryons from different $SU(3)$ multiplets. The masses of baryons partners with different values of spin $J$ are also estimated.

We study the single-transverse-spin asymmetry for the Drell-Yan process. We consider production of the lepton pair at large transverse momentum, $q_{\perp }\sim Q$, where $Q$ is the pair’s mass. The spin asymmetry is then of higher twist and may be generated by twist-three quark-gluon correlation functions. Expanding the result for $q_{\perp }\ll Q$, we make contact with the transverse-momentum-dependent QCD factorization involving the so-called Sivers functions. We find that the two mechanisms, quark-gluon correlations on one hand and the Sivers effect on the other, contain the same physics in this region. This ties the two together and imposes an important constraint on phenomenological studies of single-transverse-spin asymmetries.

We discuss possible destinations from the chromomagnetic instability in color superconductors with Fermi surface mismatch $\delta \mu$. In the two-flavor superconducting (2SC) phase we calculate the effective potential for color vector potentials ${\mathit{A}}_{\alpha }$ which are interpreted as the net momenta $\mathit{q}$ of pairing in the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) phase. When $1/\sqrt{2}<\delta \mu /\Delta <1$ where $\Delta$ is the gap energy, the effective potential suggests that the instability leads to a LOFF-like state which is characterized by color-rotated phase oscillations with small $\mathit{q}$. In the vicinity of $\delta \mu /\Delta =1/\sqrt{2}$ the magnitude of $\mathit{q}$ continuously increases from zero as the effective potential has negative larger curvature at vanishing ${\mathit{A}}_{\alpha }$ that is the Meissner mass squared. In the gapless 2SC (g2SC) phase, in contrast, the effective potential has a minimum at $g{\mathit{A}}_{\alpha }\sim \delta \mu \sim \Delta$ even when the negative Meissner mass squared is infinitesimally small. Our results imply that the chromomagnetic instability found in the gapless phase drives the system toward the LOFF state with $\mathit{q}\sim \delta \mu$.

A general equation for the probability distribution of parallel transporters on the gauge group manifold is derived using the cumulant expansion theorem. This equation is shown to have a general form known as the Kramers-Moyall cumulant expansion in the theory of random walks, the coefficients of the expansion being directly related to nonperturbative cumulants of the shifted curvature tensor. In the limit of a gaussian-dominated QCD vacuum the obtained equation reduces to the well-known heat kernel equation on the group manifold.

We analyze a toy model which has a structure similar to that of the recently found QCD evolution equations, but without transverse dimensions. We develop two different but equivalent methods in order to compute the leading-order and next-to-leading-order Pomeron loop diagrams. In addition to the leading-order result which has been derived within other toy models [A. H. Mueller, Nucl. Phys. B437, 107 (1995).][A. H. Mueller and G. P. Salam, Nucl. Phys. B475, 293 (1996).], we can also calculate the next-to-leading-order contribution which provides the (${\alpha }_s^2\alpha Y$) correction. We interpret this result and discuss its possible implications for the four-dimensional QCD evolution.

The magnetic moments of ground state single, double and triple heavy baryons containing charm or bottom quarks are calculated in a relativistic three-quark model, which, in the heavy-quark limit, is consistent with heavy-quark effective theory and heavy hadron chiral perturbation theory. The internal quark structure of baryons is modeled by baryonic three-quark currents with a spin-flavor structure patterned according to standard covariant baryonic wave functions and currents used in QCD sum rule calculations.

We analyze the constraint structure of a spin-$3/2$ particle interacting with a pseudoscalar. Requiring the self consistency of the considered effective field theory imposes restrictions on the possible interaction terms. In the present case we derive two constraints among the three lowest-order $\pi \Delta$ interaction terms. From these constraints we find that the total Lagrangian is invariant under the so-called point transformation. On the other hand, demanding the invariance under the point transformation alone is less stringent and produces only classes of relations among the coupling constants.

We calculate the scalar form factor of the proton in the framework of the light-cone QCD sum rules approach with the three valence quark light-cone distribution amplitudes up to twist-6 and observe the scalar form factor $\sigma (t=-Q^2)$ at intermediate and large momentum transfers $Q^2>2{\mathrm{GeV}}^2$ has significant contributions from the end point (or soft) terms. The numerical values for the $\sigma (t=-Q^2)$ are compatible with the calculations from the chiral quark model and lattice QCD at the region $Q^2>2{\mathrm{GeV}}^2$.

Nonvanishing $U_{e3}$ has been theoretically related to a certain flavor symmetry breaking in the neutrino sector. We propose a scenario to break the $\mu -\tau$ symmetry so as to accommodate the nonvanishing $U_{e3}$. Our scenario is constructed in the context of a seesaw model, and the $\mu -\tau$ symmetry breaking is achieved by introducing a $CP$ phase in the Dirac Yukawa matrix. We also show how the deviation of ${\theta }_{23}$ from the maximal mixing and nonvanishing $U_{e3}$ depend on the $CP$ phase. Neutrino mixings and the neutrino mass-squared differences are discussed, and the amplitude in neutrinoless double beta decay $m_{ee}$ are also predicted. We found that a tiny breaking of the $\mu -\tau$ symmetry due to mass splitting between two degenerate heavy Majorana neutrinos on top of the Dirac $CP$ phase can lead to successful leptogenesis. We examine how leptogenesis can be related with low energy neutrino measurement, and show that our predictions for $U_{e3}$ and $m_{ee}$ can be constrained by the current observation of baryon asymmetry.