A smooth massless limit for supersymmetric QCD

We analyse in detail the behaviour of supersymmetric QCD with a number of flavours M smaller than the number of colours N, for quark masses smaller than the dynamically generated scale Λ. In this regime, we find it useful to move from meson superfields to Nambu–Goldstone-like variables. In particular we work out the mass spectrum and the set of decay constants that specify the interactions of the low-energy theory. We explicitly check that masses and decay constants have a consistent behaviour under decoupling and that they satisfy current algebra requirements. Finally we speculate about the massless limit. For vanishing quark masses, and only in this case, the relation between mesons and Nambu–Goldstone variables becomes singular. When analysed in terms of the Nambu–Goldstone superfields, the massless limit exhibits a spontaneous breaking of the flavour symmetry, with massless Goldstone modes embedded in an M²-dimensional complex moduli space. The symmetry-breaking order parameter is formally infinite, but this has the only effect of turning off the interactions between the chiral superfields. The massive case, for masses smaller than Λ, can be thought of as a perturbation around the massless case, with corrections that can be systematically computed in the effective theory.     

Relaxation of finite, closed systems

On a semi-finite W^*-algebra together with a faithful normal semi-finite trace τ and a one-parameter group of trace preserving ^*-automorphism α_t, we study the limit as t → ∞ of α^*_tψ of a normal state ψ. It is shown that the existence of this limit in the weak sense is determined by the spectral properties of the evolution operator. These results are specialized to finite classical and quantum mechanical systems.     

Spanning Forests and the q-State Potts Model in the Limit q →0

We study the q-state Potts model with nearest-neighbor coupling v=e^βJ−1 in the limit q,v → 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2≤ L ≤ 10, as well as the limiting curves B of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w₀, where w₀ =−1/4 (resp. w₀=−0.1753 ± 0.0002) for the square (resp. triangular) lattice. For w>w₀ we find a non-critical disordered phase that is compatible with the predicted asymptotic freedom as w → +∞. For w0 our results are compatible with a massless Berker–Kadanoff phase with central charge c=−2 and leading thermal scaling dimension x_T,1 = 2 (marginally irrelevant operator). At w=w₀ we find a “first-order critical point”: the first derivative of the free energy is discontinuous at w₀, while the correlation length diverges as w↓ w₀ (and is infinite at w=w₀). The critical ehavior at w=w₀ seems to be the same for both lattices and it differs from that of the Berker–Kadanoff phase: our results suggest that the central charge is c=−1, the leading thermal scaling dimension is x_T,1=0, and the critical exponents are ν=1/d=1/2 and α=1.     

The matrix element of the transverse component of the bilocal vector current and its parton interpretation

In this paper we study the matrix element of the transverse component of the bilocal vector current in the context of deep inelastic scattering. The BJL limit of high energy amplitudes together with light-front current algebra imply the same parton interpretation for its matrix element as that of the plus component. On the other hand, the transverse component depends explicitly on the gluon field operator in QCD, appears as “twist three” and hence its matrix element has no manifest parton interpretation. In this paper we perform calculations in light-front time-ordering perturbative QCD for a dressed quark target to order α_s and demonstrate that the matrix element of the transverse component of the bilocal vector current has the same parton interpretation as that of the plus component.     

On the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper''s operator

Harper's operator is the self-adjoint operator on defined by

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. We first show that the determination of the spectrum of the transition operator on the Cayley graph of the discrete Heisenberg group in its standard presentation, is equivalent to the following upper bond on the norm of H_θ,: H_{θ,≤ 2(1 + √2 + cos(2πθ))}. We then prove this bound by reducing it to a problem on periodic Jacobi matrices, viewing H_θ, as the image of H_θ = U_θ + _θ^* + V_θ + V_θ^* in a suitable representation of the rotation algebra A_θ. We also use powers of H_θ to obtain various upper and lower bounds on H_θ = maxH_θ,. We show that “Fourier coefficients” of H_θ^k in A_θ have a combinatorial interpretation in terms of paths in the square lattice ². This allows us to give some applications to asymptotics of lattice paths combinatorics.     

Saturation of Electrostatic Potential: Exactly Solvable 2D Coulomb Models

We test the concepts of renormalized charge and potential saturation, introduced within the framework of highly asymmetric Coulomb mixtures, on exactly solvable Coulomb models. The object of study is the average electrostatic potential induced by a unique “guest” charge immersed in a classical electrolyte, the whole system being in thermal equilibrium at some inverse temperature β. The guest charge is considered to be either an infinite hard wall carrying a uniform surface charge or a charged colloidal particle. The systems are treated as two-dimensional; the electrolyte is modelled by a symmetric two-component plasma (TCP) of point-like ±e charges with logarithmic Coulomb interactions. Two cases are solved exactly: the Debye–Hückel limit β e²→ 0 and the Thirring free-fermion point β e²=2. The results at the free-fermion point can be summarized as follows: (i) The induced electrostatic potential exhibits the asymptotic behavior, at large distances from the guest charge, whose form is different from that obtained in the Debye–Hückel (linear Poisson–Boltzmann) theory. This means that the concept of renormalized charge, developed within the nonlinear Poisson–Boltzmann (PB) theory to describe the screening effect of the electrolyte cloud, fails at the free-fermion point. (ii) In the limit of an infinite bare charge, the induced electrostatic potential saturates at a finite value in every point of the electrolyte region. This fact confirms the previously proposed hypothesis of potential saturation.     

Suppression of the shear viscosity near the critical temperature in hot QCD

We consider QCD near but above critical temperature T_c. The pressure, susceptibilities and the renormalized Polyakov loop — which is an order parameter for the deconfining phase transition — dramatically change up to temperatures a few times T_c. We refer to this region as a “semi”-QGP, where partial confinement plays important role. We show that the shear viscosity η is suppressed by two powers of the Polyakov loop. This suggests that η/T³ decreases markedly as QCD cools down to temperatures near T_c. We also show a ratio of the viscosity to the entropy becomes small near T_c [Y. Hidaka and R.D. Pisarski, Phase," arXiv:0803.0453 [Phys. Rev. D (to be published)]].     

Comparative Regge analysis of Λ,ΣΛ(1520) and Θ<Superscript>+</Superscript> production in γp,πp and pp reactions

Using the Quark-Gluon Strings Model --combined with Regge phenomenology-- we perform a comparative analysis of Λ, Σ⁰, Λ(1520) and Θ⁺ production in binary reactions induced by photon, pion and proton beams on the nucleon. We find that the existing experimental data on the γp↦K⁺Λ differential and total cross-sections can be described very well by the model for photon energies 1-16 GeV and - t < 2 GeV² assuming a dominant contribution of the K^* Regge trajectory. Moreover, using the same parameters we also reproduce the total γp↦K⁺Σ⁰ and γp↦K⁺Λ(1520) cross-sections suggesting a “universality” of the Regge model. In order to check the consistency of the approach we evaluate the differential and total cross-sections for the reaction π^-p↦K⁰Λ which is also found to be dominated by the K^* Regge trajectory. Using the apparent “universality” of the Regge model we extend our scheme to the analysis of the binary reactions γp↦¯⁰Θ⁺, π^-p↦K^-Θ⁺ and pp↦Σ⁺Θ⁺ as well as the exclusive and inclusive Θ⁺ production in the reactions pp↦p¯⁰Θ⁺ and pp↦Θ⁺X. Our detailed studies demonstrate that Θ⁺ production does not follow the “universality” principle, thus suggesting an essentially different internal structure of the exotic baryon relative to conventional hyperons or hyperon resonances.     

Ion–ion interactions of LiPF6 and LiBF4 in propylene carbonate solutions

Self-diffusion coefficients of Li⁺ D_Li⁺, PF₆⁻ D_PF6⁻ and solvent propylene carbonate (PC) D_PC in LiPF₆−PC solutions were determined at 298 K by the pulse gradient spin echo (PGSE) NMR technique over the salt concentration range of 0.1–3.0 M (M = mol dm^– 3). The order of the diffusion coefficients was found to be D_Li⁺ < D_PF6⁻ < D_PC over the concentration range examined, and they were monotonically decreased with increasing the salt concentration. Haven ratio Λ/Λ_NMR, where Λ and Λ_NMR represent the ionic conductivity measured electrochemically and that estimated via the Nernst-Einstein equation using the diffusion coefficient, respectively, was evaluated as the measure of the ion–ion interaction in the LiPF₆–PC solutions. Though Λ/Λ_NMR values for LiPF₆-solutions decrease with increasing the salt concentration, they were greater than those for LiBF₄–PC solutions over the whole concentration range examined, which indicates that the ion pair formation ability of PF₆^– ion is weaker than that of the BF₄^– ion. The smaller value of the ionic conductivity for the highly concentrated LiPF₆–PC solution (above 2.0 M) than that of the LiBF₄-solutions can be attributed to the more rapidly increased viscosity relative to the LiBF₄-solution. Classic molecular dynamics (MD) simulations for the respective LiPF₆ and LiBF₄-solution of 0.5 and 1.0 M were also carried out based on the effective pair potentials. Diffusion coefficients, ionic conductivity and Haven ratio for these solutions were calculated from MD trajectories, and they qualitatively agree with those evaluated by experiments. Pair correlation functions g_LiO(r) (for Li⁺–O (PC) pair) and g_LiPF6(r) (for Li⁺–PF₆^– pair) or g_LiBF4(r) (for Li⁺–BF₄^– pair) revealed that the lithium ion weakly forms the contact ion pairs with PF₆^–, whilst strongly with BF₄^–, which supports the present experimental results. Moreover, the simulation results show that both anions in the contact ion pairs predominantly take the monodentate form, which is in contrast to the multidentate coordination predicted by ab initio calculation in gas phase.     

On a Measure on the Inductive Limit of Projection Logics

The aim of the paper is to measure the logic of J-projections from inductive limit of W J-algebras studied. The main result isTheorem. Let А be a W^∗ J-factor of countable type (type of А is different from I₂) and let А be the inductive limit of W^∗ J-factors А_α different from I₂. If (1) А be a W^∗ P-factor or (2) А and all А_α are W^∗ K-factors, then any indefinite measure ν : ∪_αА^h_α→ R can be unique by the strong operator topology extended to an indefinite measure on A^h.     

Light Quark Hadron Mass Scale

With a symmetry procedure based on Noether's theorem, the field equation of motion is obtained from the Dirac Hamiltonian H(D_μ) of a massless quark interacting with a gluon. The equation of motion is the Yang-Mills equation with external current which is spin-dependent and follows from the group algebra. In addition to the pure gauge solution we find a gauge covariant solution which follows from current conservation and sets the mass scale m₀/M = g². This gluon field is due to the density of dipole moments squared and represents four harmonic oscillators with quadratic constraints; the gluon can be written as a string potential or as a 1/x potential with a sharp cutoff. The chiral symmetry group G^spin × G^D gives the light quark hadron degenerate multiplet mass spectrum in terms of m₀[SU(2) × SU(2)] with the spinorial decomposition and the multipole breaks into dipoles. Scaling from atomic lengths it is found that g = em₀/nM for light quarks is the quark charge e/3 renormalized by m₀/M and g is magnetic. Thus quarks occur at the ends of spinning magnetic strings with dipole lengths ∼m₀⁻¹. The mass scale is that of a degenerate magnetic multipole with charge n = 3, 4… .     

Covariant fields: Poincaré group representations and metric structure in the space of quantum states

The representations of the Poincaré group realized over the space of covariant fields transforming according to any irreducible representationD ^(m,n) of the Lorentz group are constructed explicitly with reference to a helicity basis. The representation is indecomposable in the massless case. The form of this representation together with the invariance of two-point Wightman functions of the field (which follows from a weak set of axioms) determines the metric structure in the space of quantum states of the field. This structure is explicitly determined for generalD ^(m,n). Certain particular cases (especially the symmetric traceless tensor field) are discussed in detail. Finally we consider the representation pertaining to massive fields, and examine the passage to the limit of vanishing mass. We present a limiting procedure which leads from the unitary representation of the massive field to the indecomposable non-unitary representation of the massless field.     

Enhancement of the Debye frequency due to a charged-boson exchange model of high temperature superconductors

A simple model of 1-2-3 superconductors in which electrons (holes) in CuO₂ planes interact via exchange with two kinds of bosons is considered. Namely, via one-phonon exchange (weak coupling-Cooper pairing), and via paired holes on oxygen O⁰ from Cu-O chains. The mechanisms of paired holes exchange (“charged bosons”-“O⁰” exchange) considered here in strong coupling leads to the enhancement of the Fröhlich constant g_f (g²_F→Kg²F), and as a consequence to the enhancement of the Debye frequency ω_D^K=f^Kω_D, f^K 1. In the proposed model the exact expression for the constant K is derived.     

On higher derivative corrections of tachyon action

We have examined the momentum expansion of the disk level S-matrix element of two tachyons and two gauge fields to find, up to on-shell ambiguity, the couplings of these fields in the world volume theory of N coincident non-BPS D-branes to all order of α^′. Using the proposal that the action of D-brane–anti-D-brane is given by the projection of the action of two non-BPS D-branes with (−1)^F_L, we find the corresponding couplings in the world volume theory of the brane–anti-brane system. Using these infinite tower of couplings, we then calculate the massless pole of the scattering amplitude of one RR field, two tachyons and one gauge field in the brane–anti-brane theory. We find that the massless pole of the field theory amplitude is exactly equal to the massless pole of the disk level S-matrix element of one RR, two tachyons and one gauge field to all order of α^′. We have also found the couplings of four tachyons to all order of α^′ by examining the S-matrix element of four tachyons.     

Exact results in the two-dimensional U(1)-symmetric Thirring model

A systematic study of the ground state, excitation spectrum, and “isospin-magnetic” properties of the U(1)-Thirring model, based on its exact (Bethe-ansatz) solution, is presented. The exact results obtained for the renormalized mass spectrum in all sectors of the phase diagram of the model allow us to observe a continuous transition from the weak-coupling theory into a strong-coupling (asymptotically free) regime, taking place by varying the coupling constants, g and g. Some questions concerning universality and the relation to other models are discussed.     

Electromagnetic dipole moments and radiative decays of particles from exchange of fermionic unparticles

We construct the propagator for a free fermionic unparticle field from basic considerations of scale and Lorentz invariance. The propagator is fixed up to a normalization factor which is required to recover the result of a free massless fermion field in the canonical limit of the scaling dimension. Two new features appear compared to the bosonic case. The propagator contains both γ and non-γ terms, and there is a relative phase of π/2 between the two in the time-like regime for arbitrary scaling dimension. This should result in additional interference effects on top of the one known in the bosonic case. The non-γ term can mediate chirality flipped transitions that are not suppressed by a light fermion mass but are enhanced by a large bosonic mass in loops, compared to the pure particle case. We employ this last feature to set stringent bounds on the Yukawa couplings between a fermionic unparticle and an ordinary fermion through electromagnetic dipole moments and radiative decays of light fermions.     

Continuum limit of finite temperature λφ3 from lattice Monte Carlo

The φ₃⁴ model at finite temperature is simulated on the lattice. For fixed N_t we compute the transition line for N_s → ∞ by means of finite size scaling techniques. The crossings of a renormalization group trajectory with the transition lines of increasing N_t give a well-defined limit for the critical temperature in the continuum. By considering different RG trajectories, we compute T^c/g as a function of the renormalized parameters.     

Photoproduction of D mesons associated with a leading neutron

The photoproduction of D^*±(2010) mesons associated with a leading neutron has been observed with the ZEUS detector in ep collisions at HERA using an integrated luminosity of 80 pb⁻¹. The neutron carries a large fraction, x_L>0.2, of the incoming proton beam energy and is detected at very small production angles, θ_n<0.8 mrad, an indication of peripheral scattering. The D^* meson is centrally produced with pseudorapidity |η|<1.5, and has a transverse momentum p_T>1.9 GeV, which is large compared to the average transverse momentum of the neutron of 0.22 GeV. The ratio of neutron-tagged to inclusive D^* production is 8.85±0.93(stat.)^+0.48_−0.61(syst.)% in the photon–proton center-of-mass energy range 130<W<280 GeV. The data suggest that the presence of a hard scale enhances the fraction of events with a leading neutron in the final state.     

On integrability of generalized Veronese curves of distributions

Given a 1-parameter family of 1-forms γ(t) = γ₀+tγ₁+ ···+tⁿψ_n, consider the condition dγ(t)γ(t) = 0 (of integrability for the annihilated by γ(t) distribution w(t)). We prove that in order that this condition is satisfied for any t it is sufficient that it is satisfied for N = n + 3 different values of t (the corresponding implication for N = 2n + 1 is obvious). In fact we give a stronger result dealing with distributions of higher codimension. This result is related to the so-called Veronese webs and can be applied in the theory of bihamiltonian structures.