In the heavy quark limit, properties of heavy mesons and doubly heavy baryons are related by heavy quark-diquark symmetry. This problem is reanalyzed in the framework of nonrelativistic QCD (NRQCD). We introduce a novel method for deriving potential NRQCD (pNRQCD) Lagrangians for composite fields from vNRQCD, which contains quarks and antiquarks as explicit degrees of freedom and maintains manifest power counting in the velocity via a label formalism. A Hubbard-Stratonovich transformation is used to eliminate four quark interactions in vNRQCD and then quarks and antiquarks are integrated out to get effective Lagrangians for composite fields. This method is used to rederive Lagrangians for the $Q\overline{Q}$ and $QQ$ sectors of pNRQCD and give a correct derivation of the $O(1/m_Q)$ prediction for the hyperfine splitting of doubly heavy baryons.

We examine the color SU(3) dynamics of $q^4\overline{q}$ system, i.e. of the pentaquark. First we study this system in the model with two-body interaction proportional to the color charges. We construct the potential matrix and show (1) Confinement: the color singlet $q\overline{q}$ potential energy rises infinitely with the separation distance, (2) Stability: All colorless states’ energies are bounded from below, (3) Color singlet clustering: the pentaquark color-singlet state Hamiltonian turns into a sum of a three-quark (baryon) and a quark-antiquark (meson) cluster Hamiltonian, in the limit of asymptotically large separations. We evaluate the four excitation eigenfrequencies of pentaquarks in the harmonic oscillator two-body confining potential and the ground states’ dependence on the quark-antiquark mass ratio. We show that the pentaquark is unlikely to bind even with a top antiquark, in contrast to tetraquarks.

The polarized lepton pair forward-backward asymmetries in $B\to \rho {\ell }^{+}{\ell }^{-}$ decay using a general, model independent form of the four-Fermi interaction is studied. The general expressions for nine double-lepton polarization forward-backward asymmetries are calculated. The study of the forward-backward asymmetries of the doubly polarized lepton pair proves to be a very useful tool in looking for new physics beyond the standard model.

Neutrino emissivities due to direct Urca processes of several spin-one color-superconducting phases of dense quark matter are calculated. In particular, the role of anisotropies and nodes of the gap functions is analyzed. Results for the specific heat as well as for the cooling rates of the color-spin-locked, planar, polar, and $A$ phases are presented and consequences for the physics of neutron stars are briefly discussed. Furthermore, it is shown that the $A$ phase exhibits a helicity order, giving rise to a reflection asymmetry in the neutrino emissivity.

We perform a model independent analysis of the flavor changing strong interaction vertices relevant to the LHC. In particular, the contribution of dimension six operators to single top production in various production processes is discussed, together with possible hints for identifying signals and setting bounds on physics beyond the standard model.

The spectrum of light baryons and mesons has been reproduced recently by Brodsky and Teramond from a holographic dual to QCD inspired in the AdS/CFT correspondence. They associate fluctuations about the AdS geometry with four-dimensional angular momenta of the dual QCD states. We use a similar approach to estimate masses of glueball states with different spins and their excitations. We consider Dirichlet and Neumann boundary conditions and find approximate linear Regge trajectories for these glueballs. In particular the Neumann case is consistent with the Pomeron trajectory.

We perform high-accuracy calculations of the critical exponent $\gamma$ and its subleading exponent for the $3D$ $O(N)$ Dyson’s hierarchical model for $N$ up to 20. We calculate the critical temperatures for the nonlinear sigma model measure $\delta (\overrightarrow{\varphi }.\overrightarrow{\varphi }-1)$. We discuss the possibility of extracting the first coefficients of the $1/N$ expansion from our numerical data. We show that the leading and subleading exponents agree with the Polchinski equation and the equivalent Litim equation, in the local potential approximation, with at least 4 significant digits.

We consider the loop equation in four-dimensional $\mathcal{N}=4$ SYM, which is a functional differential equation for the Wilson loop $W(C)$ and expresses the propagation and the interaction of the string $C$. Our $W(C)$ consists of the scalar and the gaugino fields as well as the gauge field. The loop $C$ is specified by six bosonic coordinates $y^i(s)$ and two fermionic coordinates $\zeta (s)$ and $\eta (s)$ besides the four-dimensional spacetime coordinates $x^{\mu }(s)$. We have successfully determined, to quadratic order in $\zeta$ and $\eta$, the parameters in $W(C)$ and the loop differential operator so that the equation of motion of SYM can be correctly reproduced to give the nonlinear term of $W(C)$. We extract the most singular and linear part of our loop equation and compare it with the Hamiltonian constraint of the string propagating on ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ background.

It is found that, except chromomagnetic instability, the gapless 2SC phase also exhibits a paramagnetic response to the perturbation of an external color neutral baryon current. The spontaneously generated baryon current driven by the mismatch is equivalent to the one-plane wave Larkin-Ovchinnikov-Fudde-Ferrell (LOFF) state. We describe the 2SC phase in the nonlinear realization framework, and show that each instability indicates the spontaneous generation of the corresponding pseudo-Nambu-Goldstone current. We show this Nambu-Goldstone currents generation state covers the gluon phase as well as the one-plane wave LOFF state. We further point out that, when the charge neutrality condition is required, there exists a narrow unstable LOFF (Us-LOFF) window, where not only off-diagonal gluons but the diagonal 8th gluon cannot avoid the magnetic instability. We discuss that the diagonal magnetic instability in this Us-LOFF window cannot be cured by an off-diagonal gluon condensate in the color superconducting phase, and it will also show up in some constrained Abelian asymmetric superfluid/superconducting systems.

The Immirzi parameter is a constant appearing in the general-relativity action used as a starting point for the loop quantization of gravity. The parameter is commonly believed not to appear in the equations of motion and not to have any physical effect besides nonperturbatrive quantum gravity. We show that this is not true in general: in the presence of minimally coupled fermions, the parameter appears in the equations of motion: it determines the coupling constant of a four-fermion interaction. Under some general assumptions, there is therefore a relation between the Immirzi parameter and physical effects that are observable in principle, independently from nonperturbative quantum gravity

The Wightman function and the vacuum expectation value of the field square are evaluated for a massive scalar field with a general curvature coupling parameter subject to Robin boundary conditions on two codimension-one parallel branes located on a $(D+1)$-dimensional background spacetime ${\mathrm{AdS}}_{D_1+1}\times \Sigma$ with a warped internal space $\Sigma$. The general case of different Robin coefficients on separate branes is considered. The application of the generalized Abel-Plana formula for the series over zeros of combinations of cylinder functions allows us to manifestly extract the part due to the bulk without boundaries. Unlike the purely anti-de Sitter (AdS) bulk, the vacuum expectation value of the field square induced by a single brane, in addition to the distance from the brane, depends also on the position of the brane in the bulk. The brane induced part in this expectation value vanishes when the brane position tends to the AdS horizon or the AdS boundary. The asymptotic behavior of the vacuum densities near the branes and at large distances is investigated. The contribution of Kaluza-Klein modes along $\Sigma$ is discussed in various limiting cases. In the limit when the curvature radius for the AdS spacetime tends to infinity, we derive the results for two parallel Robin plates on the background spacetime $R^{(D_1,1)}\times \Sigma$. For strong gravitational fields corresponding to large values of the AdS energy scale, both the single brane and interference parts of the expectation values integrated over the internal space are exponentially suppressed. As an example the case $\Sigma =S^1$ is considered, corresponding to the ${\mathrm{AdS}}_{D+1}$ bulk with one compactified dimension. An application to the higher dimensional generalization of the Randall-Sundrum brane model with arbitrary mass terms on the branes is discussed.

The Big Bang Observer (BBO) is a proposed space-based gravitational-wave (GW) mission designed primarily to search for an inflation-generated GW background in the frequency range $\sim {10}^{-1}\mathrm{Hz}–1\mathrm{Hz}$. The major astrophysical foreground in this range is gravitational radiation from inspiralling compact binaries. This foreground is expected to be much larger than the inflation-generated background, so to accomplish its main goal, BBO must be sensitive enough to identify and subtract out practically all such binaries in the observable universe. It is somewhat subtle to decide whether BBO’s current baseline design is sufficiently sensitive for this task, since, at least initially, the dominant noise source impeding identification of any one binary is confusion noise from all the others (rather than instrumental noise). Here we present a self-consistent scheme for deciding whether BBO’s baseline design is indeed adequate for subtracting out the binary foreground. We conclude that the current baseline should be sufficient. However, if BBO’s sensitivity were degraded by a factor 2 from the current baseline, then its ability to detect an underlying primordial background would depend critically on the value of ${\rho }_{\mathrm{th}}$, the threshold signal-to-noise ratio marking the boundary between detectable and undetectable sources. If BBO’s sensitivity were degraded by a factor 4 from the current baseline, it could not detect a primordial background below ${\Omega }_{\mathrm{GW}}\sim {10}^{-15}$. It is impossible to perfectly subtract out each of the binary inspiral waveforms, so an important question is how to deal with the “residual” errors in the post-subtraction data stream. We sketch a strategy of “projecting out” these residual errors, at the cost of some effective bandwidth. We also provide estimates of the sizes of various post-Newtonian effects in the inspiral waveforms that must be accounted for in the BBO analysis.

A generalized gauge fixing which interpolates among the Landau, Coulomb, and maximal Abelian gauges is constructed.

The excess of data on the total cross section of $\overline{b}b$ production in $\gamma \gamma$ collisions over QCD predictions, observed by L3, OPAL and DELPHI Collaborations at LEP2, has so far defied explanation. The recent final analysis of L3 data has brought important new information concerning the dependence of the observed excess on the $\gamma \gamma$ collisions energy $W_{\gamma \gamma }$. The implications of this dependence are discussed.

The $\mathrm{SU}(3{)}_C\otimes \mathrm{SU}(3{)}_L\otimes \mathrm{U}(1{)}_X$ gauge model with the minimal scalar sector (two Higgs triplets) is studied in detail. One of the vacuum expectation values $u$ is a source of lepton-number violations and a reason for the mixing among the charged gauge bosons—the standard model $W$ and the bilepton (with $L=2$) gauge bosons as well as among neutral non-Hermitian $X^0$ and neutral gauge bosons: the photon, the $Z$, and the new $Z^{\prime }$. Because of these mixings, the lepton-number violating interactions exist in both charged and neutral gauge boson sectors. An exact diagonalization of the neutral gauge boson sector is derived and bilepton mass splitting is also given. The lepton-number violation happens only in the neutrino but not in the charged lepton sector. In this model, lepton-number changing ($\Delta L=\pm 2$) processes exist but only in the neutrino sector. Constraints on vacuum expectation values of the model are estimated and $u\simeq O(1)\mathrm{GeV}$, $v\simeq v_{\mathrm{weak}}=246\mathrm{GeV}$, and $\omega \simeq O(1)\mathrm{TeV}$.

We suggest a supersymmetric (SUSY) explanation of neutrino masses and mixing, where nonrenormalizable interactions in the hidden sector generate lepton number violating Majorana mass terms for both right-chiral sneutrinos and neutrinos. It is found necessary to start with a superpotential including an array of gauge singlet chiral superfields. This leads to nondiagonal $\Delta L=2$ mass terms and almost diagonal SUSY breaking $A$-terms. As a result, the observed pattern of bilarge mixing can be naturally explained by the simultaneous existence of the seesaw mechanism and radiatively induced masses. Allowed ranges of parameters in the gauge singlet sector are delineated, corresponding to each of the cases of normal hierarchy, inverted hierarchy, and degenerate neutrinos.

The process of annihilation of $e^{+}{e}^{-}$ to the three pion final state in the case of moderately high energies is considered. The final state emission of virtual and real photons is considered explicitly. The calculations are performed in QED and the pion sector of the effective chiral Lagrangian. The initial state emission is considered in terms of the lepton structure function. Some numerical estimates are given.

We present arguments suggesting that large size overlapping instantons are the driving mechanism of the confinement-deconfinement phase transition in QCD at nonzero chemical potential $\mu$. The arguments are based on the picture that instantons at very large chemical potential in the weak coupling regime are localized configurations with finite size $\rho \sim {\mu }^{-1}$. At the same time, the same instantons at smaller chemical potential in the strong coupling regime are well represented by the so-called instanton-quarks with fractional topological charge $1/N_c$. We estimate the critical chemical potential ${\mu }_c(T)$ where this phase transition takes place as a function of temperature in the domain where our approach is justified. In this picture, the long standing problem of the “accidental” coincidence of the chiral and deconfinement phase transitions at nonzero temperature (observed in lattice simulations) is naturally resolved. We also derive results at nonzero isospin chemical potential ${\mu }_I$ where direct lattice calculations are possible, and our predictions can be explicitly tested.

We consider simple-pole descriptions of soft elastic scattering for $pp$, $\overline{p}p$, ${\pi }^{\pm }p$ and $K^{\pm }p$. We work at $t$ and $s$ small enough for rescatterings to be effectively absorbed in a simple-pole parametrization, and allow for the presence of a hard Pomeron. After building and discussing an exhaustive dataset, we show that simple poles provide an excellent description of the data in the region $-0.5{\mathrm{GeV}}^2\le t\le -0.1{\mathrm{GeV}}^2$, $6\mathrm{GeV}\le \sqrt{s}\le 63\mathrm{GeV}$. We show that new form factors have to be used, and get information on the trajectories of the soft and hard Pomerons.

We derive a nonperturbative transverse momentum distribution for partons using a potential model to describe the quark-quark interaction inside the proton. We use this distribution in the calculation of the differential cross section of ${\pi }^0$ production for intermediate transverse momentum values in $p-p$ collisions at high energies. Assuming a variable string tension constant for the quark-quark potential we obtain a very good description of the experimental data at different energies. The corresponding values of the mean transverse momentum of the partons are essentially lower than those obtained using a Gaussian transverse momentum parton distribution. Using the same approach we can also describe the proton production data in the Chicago-Princeton experiment. Our analysis indicates that bound state effects may be important for the description of the experimental data in proton-proton collisions.