Preliminary study of the scattering length from lattice QCD

Noncommutative generalizations of a supersymmetry algebra in two dimensions have been introduced earlier in Abbaspur (Int. J. Mod. Phys. A 18:855?C878, 2003; Mod. Phys. Lett. A 18:587?C599, 2003). In this paper we present a field theoretic realization for these algebras in the context of $\mathcal{N}=1$ supersymmetric U(1) gauge theories in two dimensions. We also describe a possible generalization to 4-dimensional theories.     

Volume reflection and volume refraction of relativistic particles in a uniformly bent crystal

The scattering of fast charged particles in a bent crystal has been analyzed in the framework of relativistic classical mechanics. The expressions obtained for the deflection function are in satisfactory agreement with the experimental data for the volume reflection of relativistic protons obtained by Yu. M. Ivanov et al., Phys. Rev. Lett. 97, 144801 (2006); Yu. M. Ivanov et al., Pis’ma Zh. Eksp. Teor. Fiz. 84, 445 (2006) [JETP Lett. 84, 372 (2006)]; and W. Scandale et al., Phys. Rev. Lett. 98, 154801 (2007). The features of the scattering of the particles on ring potentials are considered in a wide range of impact parameters.     

QCD on the Light-Front

Light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x ⁺ = x ⁰ + x ³, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian H _LF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of H _LF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable \({\zeta^2=b^2_\perp x(1-x)}\) , which is conjugate to the invariant mass squared \({{M^2_{q\bar q}}}\) . The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories \({M^2(n, L, S) = 4\kappa^2( n+L +S/2)}\) with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter \({\kappa}\) appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS₅ space with a unique dilaton profile to QCD (3 + 1) at fixed light-front time. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.     

An Alternative Approach to Understanding the Observed Positron Fraction

Space-based observations by PAMELA (Adriani et al., Nature 458, 607, 2009), Fermi-LAT (Ackerman et al., Phys. Rev. Lett. 105, 01103, 2012), and AMS (Aguilar et al., Phys. Rev. Lett. 110, 141102, 2013) have demonstrated that the positron fraction (e+/total-e) increases with increasing energy above about 10 GeV. According to the propagation model for Galactic cosmic rays in widespread use (Moskalenko & Strong, Astrophys. J. 493, 693, 1998), the production of secondary positrons from interaction of cosmic-ray protons and heavier nuclei with the interstellar medium gives a generally falling positron fraction between 10 and 100 GeV, with secondary positrons accounting for only ～20 % of the observed positron fraction at 100 GeV; so some other physical phenomena have been proposed to explain the data. An alternative approach to interpreting the positron observations is to consider these data as presenting an opportunity for re-examining models of Galactic cosmic-ray propagation. Following release of the PAMELA data, three groups published propagation models (Shaviv, et al., Phys. Rev. Lett. 103, 111302, 2009, Cowsik and Burch, Phys. Rev. D. 82, 023009, 2010, Katz et al., Mon. Not. R. Aston. Soc. 405, 1458 2010) in which the observed positron fraction is explained entirely by secondary positrons produced in the interstellar medium. In May of this year, stimulated by the AMS extension of the positron data to higher energy with excellent statistics, two of those groups presented further development of their calculations (Cowsik et al. 2013, Blum et al. 2013), again concluding that the observed positrons can be understood as secondaries. None of the authors of these five papers was registered for the 33rd International Cosmic Ray Conference (ICRC). Although I am not an author of any of these papers, I have some close familiarity with one of these recent papers, so the conference organizers invited me to bring this alternative approach to the attention of the conference. The present paper is a summary of the material I presented, along with a brief comment about reaction at the conference to this approach.     

Electrostatic interaction between two macroparticles in the Poisson-Boltzmann model

Considering the electrostatic energy of the system of two macroparticles in a plasma in the Poisson-Boltzmann model, Resendes et al. [Phys. Lett. A 239, 181 (1998)], Ivanov [Phys. Lett. A 290, 304 (2001)], Gerasimov and Sinkevich {Teplofiz. Vys. Temp. 37, 853 (1999) [High Temp. 37, 823 (1999)]}, and D’achkov {Teplofiz. Vys. Temp. 43, 331 (2005) [High Temp. 43, 322 (2005)]} conclude that attraction between identically charged macroparticles is possible. In the Poisson-Boltzmann model, the distribution of electrons and ions has the Boltzmann form in a self-consistent field that is determined by the Poisson equation. In this work, on the basis of the analysis of the force between two macroparticles in a plasma by using the Maxwell stress tensor, it has been shown that two macroparticles with the same charge always repulse each other in both isothermal and nonisothermal plasmas. The interaction between macroparticles at distances, where Boltzmann exponentials can be linearized, is completely described by the Debye-Hückel theory. The free energy of the system of two particles has been found. It coincides with the Yukawa potential and has no minimum; therefore, such a system is thermodynamically unstable. Since the interaction energy obtained by integrating the interaction force coincides with the free energy of the electric field, the interaction between two macroparticles in the equilibrium plasma is potential.     

Bianchi type-II String Cosmological Model with Magnetic Field in Scale-Covariant Theory of Gravitation

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of scale-covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39, 429, 1977). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento 74, 182, 1983) string cosmological model is obtained in this theory. We use the power law relation between scalar field ? and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.     

Study of the polarization degree for the p ⃗ p → ppη measurement with WASA

Understanding of the production processes of the η meson will strongly rely on the precise determination of spin observables. So far these observables have been determined only for few excess energies and with low statistics (Winter et al. Eur. Phys. J. A18, 355 2003; Czyzykiewicz et al. Phys. Rev. Lett. 98, 122003 2007; Balestra et al. Phys. Rev. C69, 064003 2004). In the year 2010 WASA detector was used for the measurement of the \(\overrightarrow {p}p\rightarrow pp\eta \) reaction with the polarized proton beam of COSY (Moskal and Hodana J. Phys. Conf. Ser 295, 012080 2011). The measurement was done for the excess energy of Q = 15 MeV and Q = 72 MeV. In total about 10⁶ events corresponding to the \(\overrightarrow {p}p\rightarrow pp\eta \) reaction have been collected.     

Light-Front Quantization of the Restricted Gauge Theory of QCD2

In this talk we study the light-front quantization of the restricted gauge theory of QCD₂à la Cho et al.     

A different way to verify the violation of the WWŻB inequality

The solution to Bell theorem for N-qubits was widely studied in [M. ?ukowski, ?. Brukner, Phys. Rev. Lett. 88, 210401 (2002)]. Here we present a different way to obtain the solution of that theorem for the dichotomic experiment. In order to obtain a solution for the Werner-Wolf-?ukowski-Brukner WW?B inequality a new correlation function is proposed. This new correlation function expresses directly the constraints imposed by local theories. We use the general Greenberger-Horne-Zeilinger (GHZ) state, whereof, as it is well known, emerges a family of entangled states that do not violate the WW?B inequality [M. ?ukowski, ?. Brukner, W. Laskowski, M. Wie?niak, Phys. Rev. Lett. 88, 210402 (2002)], i.e. it can be described by a local realistic theory, to illustrate our results.     

Viability of Noether Symmetry of F(R) Theory of Gravity

Recently, we have explored vices and virtues of $R^{\frac{3}{2}}$ term in the action which has in-built Noether symmetry and anticipated that a linear term might improve the situation (Sarkar et al., arXiv:1201.2987 [astro-ph.CO], 2012). In the absence of a conserved current it is extremely difficult to obtain an analytical solution of the said fourth order theory of gravity in the presence of a linear term. Here, we therefore enlarge the configuration space by including a scalar field in addition and also taking some of the anisotropic models (in the absence of a scalar field) into account. We observe that Noether symmetry remains obscure and it does not even reproduce the one that already exists in the literature (Sanyal, Gen. Relativ. Gravit., 37:407, 2005). However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar field (Sanyal, Phys. Lett. B, 624:81, 2005; Mod. Phys. Lett. A, 25:2667, 2010), which simplifies the field equations considerably. Here, we briefly expatiate the non-Noether conserved current and show that indeed the situation is modified.     

Structure of zero modes in a model of the discrete (2+1)-dimensional nonlinear Schrödinger equation

The structure of the zero modes in a discrete (2+1)-dimensional model of the gauge-invariant nonlinear Schrödinger equation is studied. Including the compactification of the Chern-Simons gauge fields eliminates the difficulties with the continuous model [L. A. Abramyan and A. P. Protogenov, JETP Lett. 64, 859 (1996); L. A. Abramyan, V. I. Berezhiani, and A. P. Protogenov, Phys. Rev. E 56, 6026 (1997)] and leads to a prediction of the existence of a transition region characterized by a hierarchical sequence of collapses which are enumerated by the Chern-Simons coefficient. Using the zero modes in calculating the dependence of the critical power N on the Chern-Simons coefficient, we have found that the transition region lies in the interval 11.703≤N≤12.01.     

Quantum Bianchi Type IX Cosmology in K-Essence Theory

We use one of the simplest forms of the K-essence theory and apply it to the anisotropic Bianchi type IX cosmological model, with a barotropic perfect fluid modeling the usual matter content. We show that the most important contribution of the scalar field occurs during a stiff matter phase. Also, we present a canonical quantization procedure of the theory which can be simplified by reinterpreting the scalar field as an exotic part of the total matter content. The solutions to the Wheeler-DeWitt equation were found using the Bohmian formulation Bohm (Phys. Rev. 85(2):166, 1952) of quantum mechanics, employing the amplitude-real-phase approach Moncrief and Ryan (Phys. Rev. D 44:2375, 1991), where the ansatz for the wave function is of the form Ψ(? ^μ )=χ(?)W(? ^μ ) \(e^{- S(\ell ^{\mu })},\) , where S is the superpotential function, which plays an important role in solving the Hamilton-Jacobi equation.     

Dust ion-acoustic shock-wave structures: Theory and laboratory experiments

An evolutionary theoretical model is developed that describes dust ion-acoustic shock waves in dusty plasma consisting of ions (treated in the hydrodynamic approximation), Boltzmann electrons, and variable-charge dust grains. Account is taken not only of ionization, absorption, momentum loss by electrons and ions in collisions with dust grains, and gas-kinetic pressure effects but also of the processes peculiar to laboratory plasmas. It is shown that the model is capable of describing all the main experimental results on dust ion-acoustic shock waves [Q.-Z. Luo et al., Phys. Plasmas 6, 3455 (1999); Y. Nakamura et al., Phys. Rev. Lett., 83, 1602 (1999)].     

Moduli integrals in liouville gravity

We consider moduli integrals appearing in four-point correlation functions of the (p, q) minimal models coupled to Liouville gravity on a sphere, which is sometimes called 2D minimal gravity or minimal string theory on a sphere. Liouville gravity on a sphere is the quantized metric of the spherical topology in the conformal gauge. Reviewing the previous results on such four-point functions (Y. Ishimoto and Sh. Yamaguchi: Phys. Lett. B607 (2005) 172), we show logarithmic correlation functions of ‘tachyons’ in the Liouville sector, and its moduli integrals of the full correlation functions, in particular in the Majorana fermion model coupled to 2D gravity. Further discussions and related results are given in the final section and in Y. Ishimoto and Al. Zamolodchikov: Theor. Math. Phys.147 (2006) 755.     

ADM-like Hamiltonian formulation of gravity in the teleparallel geometry

We present a new Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) meant to serve as the departure point for canonical quantization of the theory. TEGR is considered here as a theory of a cotetrad field on a spacetime. The Hamiltonian formulation is derived by means of an ADM-like $3+1$ decomposition of the field and without any gauge fixing. A complete set of constraints on the phase space and their algebra are presented. The formulation is described in terms of differential forms.     

Thermodynamics and holography of tachyon cosmology

Recently, we have investigated the dynamics of the universe in tachyon cosmology with non-minimal coupling to matter (Farajollahi et al. in Mod Phys Lett A 26(15):1125–1135, 2011; Phys Lett B 711(3–4)15:225–231,2012; Phys Rev D 83:124042, 2011; JCAP 10:014, 20112011; JCAP 05:017, 2011). In particular, for the interacting holographic dark energy (IHDE), the model is studied in Farajollahi et al. (Astrophys Space Sci 336(2):461–467, 2011). In the current work, a significant observational program has been conducted to unveil the model’s thermodynamic properties. Our result shows that the IHDE version of our model better fits the observational data than $\Lambda $ CDM model. The first and generalized second thermodynamics laws for the universe enveloped by cosmological apparent and event horizon are revisited. From the results, both first and generalized second laws, constrained by the observational data, are satisfied on cosmological apparent horizon.In addition, the total entropy is verified with the observation only if the horizon of the universe is taken as apparent horizon. Then, due to validity of generalized second law, the current cosmic acceleration is also predicted.     

The calculation of active Raman modes of α-quartz crystal via density functional theory based on B3LYP Hamiltonian in 6–311+G(2d) basis set?

We obtained an approximation of the force field of ??-quartz crystal using a new idea of applying density functional theory [J Purton, R Jones, C R A Catlow and M Leslie, Phys. Chem. Minerals 19, 392 (1993)]. Our calculations were based on B3LYP Hamiltonian [A N Lazarev and A P Mirgorodsky, Phys. Chem. Minerals 18, 231 (1991)] in 6?311+G(2d) basis set for H₁₆Si₇O₆ cluster and included a unit cell of the lattice. The advantage of our method is the increase in the speed of calculations and the better adaption of simulation results with the experimental data.     

The Standard Model with one universal extra dimension

Effects of universal extra dimensions on Standard Model observables first arise at the one-loop level. The quantization of this class of theories is therefore essential in order to perform predictions. A comprehensive study of the SU _C(3) × SU _L(2) × U _Y(1) Standard Model defined in a space-time manifold with one universal extra dimension, compactified on the oribifold $S^1/Z_2$ , is presented. The fact that the four-dimensional Kaluza–Klein theory is subjected to two types of gauge transformations is stressed and its quantization under the basis of the BRST symmetry discussed. A SU _C(3) × SU _L(2) × U _Y(1)-covariant gauge-fixing procedure for the Kaluza–Klein excitations is introduced. The connection between gauge and mass eigenstate fields is established in an exact way. An exhaustive list of the explicit expressions for all physical couplings induced by the Yang–Mills, Currents, Higgs, and Yukawa sectors is presented. The one-loop renormalizability of the standard Green’s functions, which implies that the Standard Model observables do not depend on a cut-off scale, is stressed.     

Variational Bound States of Screened Potentials

Anumber of years ago, a calculational scheme was introduced by Stubbins [Phys. Rev. A48, 220 (1993)] to compute the energies of both the Hulthén and Yukawa potentials. The method introduces a particular ansatz for solving the Schrödinger equation with screened Coulomb type potentials. In this work, we wish to review the method of Stubbins and to show that it is, in fact, equivalent and a subset of a more systematic (and hence more useful) variational scheme [Zhou et al. Phys. Rev. A51, 3337 (1995)]. This variational approach involves the construction of a basis by taking derivatives of the variational parameters of the system. The eigenvalues of the Hamiltonian matrix are then minimized with respect to these parameters yielding a “best guess” upper bound on the energies.