Infrared Features of Unquenched Lattice Landau Gauge QCD

The running coupling and the Kugo-Ojima parameter of unquenched lattice Landau gauge are simulated and compared with the continuum theory. Although the running coupling measured by the ghost and gluon dressing function is infrared suppressed, the running coupling has a maximum of α₀ ∼ 2 − 2.5 at around q = 0.5 GeV irrespective of the fermion actions (Wilson fermions and Kogut-Susskind (KS) fermions). The Kugo-Ojima parameter c which saturated to about 0.8 in quenched simulations becomes consistent with 1 in the MILC configurations produced with the use of the Asqtad action, after averaging the dependence on polarization directions caused by the asymmetry of the lattice. The presence of the correction factor 1 + c ₁/q ² in the running coupling depends on the lattice size and the sea quark mass. In the large lattice size and small sea quark mass, c ₁ is confirmed of the order of a few GeV. The MILC configuration of a = 0.09 fm suggests also the presence of dimension-4 condensates with a sign opposite to the dimension-2 condensates. The gluon propagator, the ghost propagator, and the running coupling are compared with recent pQCD results including an anomalous dimension of fields up to the four-loop level.     

Roles of the Color Antisymmetric Ghost Propagator in the Infrared QCD

The results of Coulomb gauge and Landau gauge lattice QCD simulation do not agree completely with continuum theory. There are indications that the ghost propagator in the infrared region has strong fluctuation whose modulus is compatible with that of the color diagonal ghost propagator. After presenting lattice simulation of configurations produced with Kogut–Susskind fermion (MILC collaboration) and those with domain wall fermion (RBC/UKQCD collaboration), I investigate in triple gluon vertex and the ghost–gluon–ghost vertex how the square of the color antisymmetric ghost contributes. Then the effect of the vertex correction to the gluon propagator and the ghost propagator is investigated. Recent Dyson–Schwinger equation analysis suggests the ghost dressing function G(0) = finite and no infrared enhancement or α _G  = 0. But the ghost propagator renormalized by the loop containing a product of color antisymmetric ghost is expected to behave as with with α _G = 0.5, if the fixed point scenario is valid. I interpret the α _G  = 0 solution should contain a vertex correction. The infrared exponent of our lattice Landau gauge gluon propagator of the RBC/UKQCD is α _D  = − 0.5 and that of MILC is about − 0.7. A possible interpretation of the origin of the fluctuation is given.     

The Self-Dual Gauge Fields and the Domain Wall Fermion Zero Modes

A new type of gauge fixing of the Coulomb gauge domain wall fermion system that reduces the fluctuation of the effective running coupling and the effective mass of arbitrary momentum direction including the region outside the cylinder cut region is proposed and tested in the 16³ × 32 × 16 gauge configurations of RBC/UKQCD collaboration. The running coupling at the lowest momentum point does not show infrared suppression and compatible with the experimental data extracted from the JLab collaboration. The source of the fluctuation of the effective mass near momentum p = 0.6 GeV region is expected to be due to the domain wall fermion zero modes.     

QCD coupling constant below 1 GeV in the poincare-covariant model

The behavior of the running coupling constant α _s (Q ²) phenomenologically parameterized in the region of Q < 1 GeV is considered within the framework of the Poincare-covariant quark model in a variety of regimes. An analysis was carried out for pseudoscalar and vector mesons with the lepton masses and decay constants (obtained by the model calculations) required to match their experimental counterparts. It shows that the constant α _s is likely to behave with α_crit = α _s (Q ² = 0) ∼ 0.667 − 0.821 in the case of a frozen regime and α_crit =0.300 − 0.692 for peaked curves, which follows from the experimental values of the leptonic decay constants and masses.     

Electromagnetic form factors of nucleons in a relativistic square-root potential model of independent quarks

The nucleon electromagnetic form factorsG _E ^P (q²),G _M ^P (q²) and the axial-vector form factor G_A(q²) are studied in a relativistic model of independent quarks confined by an equally mixed scalar-vector square root potentialV _q(r)=1/2(1+γ ⁰)(ar ^1/2+ν ₀) taking into account the appropriate centre-of-mass corrections. The respective root-mean-square radii associated withG _E ^P (q²) and G _A (q²) come out as [〈r ²〉 _E ^P ]^1/2=0.86 fm and 〈r _A ² 〉^1/2=0.88 fm. Restoration of chiral symmetry in this model is discussed to derive the pion-nucleon form factorG _πNN(q²) and consequently the pion-nucleon coupling constant is obtained asg _πNN(q²)=12.81 as compared tog _πNN(q²)_exp⋍13.     

A Condensed Matter Interpretation of SM Fermions and Gauge Fields

We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ³), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ³) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3)⊗ℂ)(ℤ³). This space allows a simple physical interpretation as a phase space of a lattice of cells. We find the SM SU(3) _c ×SU(2) _L ×U(1) _Y action on (Aff(3)⊗ℂ⊗Λ)(ℝ³) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ₂-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ₂-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.     

Baryon-charge transfer and production asymmetry of Λ0/ [`(L)] 0\bar \Lambda ^0 in hadron interactions

Predictions were made for asymmetry between production spectra of Λ⁰ and at the energy of LHC experiments. The value of A(s) should be situated in the corridor between two curves calculated in the quark-gluon string model with two possible values of intercept α _SJ(0) = 0.5 and 0.9. Both curves describe the asymmetries measured at lower energies up to RHIC experiments. The data of the H1 experiment can be fitted only with α _SJ(0) = 0.9. The text was submitted by the author in English.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

High-spin states of<Superscript>125</Superscript>Sb: Particle-core excitation coupling

Excited states of¹²⁵Sb have been studied using in-beam γ spectroscopy techniques via the¹²⁴Sn(⁷Li, α2n) reaction at a beam energy of 32 MeV. A high-spin level scheme including 21 new γ-transitions and 14 new excited states have been established. Three isomers have been identified at 1970, 2110 and 2471 keV and the ranges of their half-lives have been estimated from the delayed coincidence data. The level structure of¹²⁵Sb is discussed in terms of particle-core excitation coupling. With the help of empirical shell model calculations the three isomers are proposed to have three-quasiparticle πg_7/2⊗v(h _11/2 s _1/2)₅₋, πg_7/2⊗v(h _11/2 d _3/2)₇₋ and πg_7/2⊗v(h ₁₁^2/2)₁₀ ⁺ configurations, respectively.     

A non-perturbative calculation of the infrared limit of the axial gauge gluon propagator (I)

We describe a non-perturbative study of the infrared behavior of the axial gauge gluon propagator based on the Dyson equation and Ward identities. We conclude that the propagator Δ_μν(q) displays a q^?4 singularity in the infrared limit, and that consequently the axial gauge running coupling constant g_A²)(q) displays a q^?2 singularity in the same limit. The only assumption necessary to obtain this conclusion is that the transverse part of the triple-gluon vertex function does not dominate the longitudinal part in the infrared regime.     

Mirror supersymmetry in the space of (super) extended Poincaré algebras p(p,q)

We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and ₂-graded Lie algebras g = g₀ + g₁, where g₀ = s₀(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V = ^{p, q} of signature (p, q) and g₁ is a spin 1/2 s₀(V)-module extended to a s₀-module with kernel V.As a result of the classification, we obtain, if g₁ = S is the spinor module, the numbers L ⁺(n, s) (resp. L ^–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L ⁺(–n, s)=L ^– (n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University).     

Slope parameter and scaling of differential cross-section of Λ-p scattering

The claim of Mohapatra and Maharana thattb(s) is a better scaling variable thant(lns)² is put to test in the case of Λ-p scattering, after parametrizingb(s) asC ₁ +C ₂(lns)α. It was observed that in this case the data also prefer anα value which is close to those obtained by Mohapatra and Maharana for other scattering processes.     

UA(1) anomaly and $ \eta^{{\prime}}_{}$ -mass from an infrared singular quark-gluon vertex

The U _A(1) problem of QCD is inevitably tied to the infrared behaviour of quarks and gluons with its most visible effect being the -mass. A dimensional argument of Kogut and Susskind showed that the mixing of the pseudoscalar flavour-singlet mesons with gluons can provide a screening of the Goldstone pole in this channel if the full quark-quark interaction is strongly infrared singular as ∼ 1/k ⁴ . We investigate this idea using previously obtained results for the Landau gauge ghost and gluon propagator, together with recent determinations for the singular behaviour of the quark-gluon vertex. We find that, even with an infrared vanishing gluon propagator, the singular structure of the quark-gluon vertex for certain kinematics is apposite for yielding a non-zero screening mass.     

Effect of electron-phonon interaction and temperature dependence of resistivity in some heavy fermion systems

Here we have considered the electron-phonon interaction in the Periodic Anderson Model (PAM) to describe the temperature dependence of resistivity in some heavy fermion (HF) systems. Since the resistivity is related to the imaginary part of the electron self energy, the expression of the same is evaluated from electron Green function by the double time temperature dependant Green function technique of the Zubarev type. In order to understand the effect of electron-phonon interaction in these systems, we couple the phonons to both the f-electrons as well as to the electrons of the hybridization band of both conduction and f-electrons. The influence of various model parameters, namely, the position of 4f level E ₀, the electron-phonon coupling strengths f ₁(q) and f ₂(q), the effecting coupling strength g = N(0)γ ₀²/ω ₀ have been studied on the temperature dependence of resistivity in HF systems. The numerical analysis is performed for q = 0 and for finite temperature in the static limit. The analysis of the results gives satisfactorily in comparison to the experimental observations.     

Specific heat of the harmonic oscillator within generalized equilibrium statistics

Summary Within the generalized equilibrium statistics recently introduced by Tsallis (p _n ∝[1−β(q−-1) _εn ]^1/(q−)), we calculate the thermal dependence of the specific heat corresponding to a harmonic-oscillator-like spectrum, namely ε _n ω(n−α) (∀ω>0,n=0,1,2,...). The influences ofq and α are exhibited. Physically inaccessible and/or thermally frozen gaps are obtained in the low-temperature region, and, forq>1, oscillations are observed in the high-temperature region. The specific heat of the two-level system is also shown.     

Coupling running through the looking-glass of dimensional reduction

The dimensional reduction, in a form of transition from four to two dimensions, was used in the 90s of the past century in a context of the HE Regge scattering. Recently, it has got a new impetus in quantum gravity where it opens the way to renormalizability and finite short-distance behaviour. We consider a QFT model gφ⁴ with running coupling defined in both domains of different dimensionality; the $ \bar g $ \bar g (q ²) evolutions being duly correlated at the reduction scale q ∼ M. Beyond this scale, in the deep UV 2-dimensional region, the running coupling does not increase any more. Instead, it slightly decreases and tends to a finite value $ \bar g $ \bar g ₂(∞) < $ \bar g $ \bar g ₂(M ²) from above. As a result, the global evolution picture looks quite peculiar and proposes a base for the modified scenario of gauge couplings behavior with UV fixed points provided by dimensional reduction instead of leptoquarks.     

Improvement of perturbation theory in QCD for e + e − →hadrons and the problem of α s freezing

A method of improving perturbation theory in QCD is developed which can be applied to any polarization operator. The case of the polarization operator Π(q ²), corresponding to the process e ⁺ e ⁻→ hadrons, is considered in detail. By the use of the analytical properties of Π(q ²) and a perturbation expansion of Π(q ²) for q ²<0, the function ImΠ(q ²) at q ²>0 is defined in such a way that the infrared pole is eliminated. The convergence of the perturbation series for R(q ²)=σ(e ⁺ e ⁻ →hadrons)/(e ⁺ e ⁻→μ ⁺ μ ⁻) is improved. After substitution of R(q ²) into the dispersion relation an improved Adler function D(q ²) is obtained, having no infrared pole and a frozen α _s (q ²). Good agreement with experiment is achieved. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 167–170 (10 August 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The string coupling accelerates the expansion of the universed

Generic cosmological models in non-critical string theory have a time-dependent dilaton background at a late epoch. The cosmological deceleration parameter q ₀ is given by the square of the string coupling, g _s ², up to a negative sign. Hence the expansion of the Universe must accelerate eventually, and the observed value of q ₀ corresponds to g _s ² ∼ 0.6. In this scenario, the string coupling is asymptotically free at large times, but its present rate of change is imperceptibly small. First Award in the 2005 Essay Competition of the Gravity Research Foundation. - Ed.