Low-energy QCD: Chiral coefficients and the quark-quark interaction

A detailed investigation of the low-energy chiral expansion is presented within a model truncation of QCD. The truncation allows for a phenomenological description of the quark-quark interaction in a framework which maintains the global symmetries of QCD and permits a $1/N_c$ expansion. The model dependence of the chiral coefficients is tested for several forms of the quark-quark interaction by varying the form of the running coupling, $\alpha (q^2)$, in the infrared region. The pattern in the coefficients that arises at tree level is consistent with large $N_c$ QCD, and is related to the model truncation.Comment: 28 pages, Latex, 6 postscript figures available on request to [email protected]

Model of supersymmetric quantum field theory with broken parity symmetry

Recently, it was observed that self-interacting scalar quantum field theories having a non-Hermitian interaction term of the form $g(i\phi)^{2+\delta}$, where $\delta$ is a real positive parameter, are physically acceptable in the sense that the energy spectrum is real and bounded below. Such theories possess PT invariance, but they are not symmetric under parity reflection or time reversal separately. This broken parity symmetry is manifested in a nonzero value for $$, even if $\delta$ is an even integer. This paper extends this idea to a two-dimensional supersymmetric quantum field theory whose superpotential is ${\cal S}(\phi)=-ig(i\phi)^{1+\delta}$. The resulting quantum field theory exhibits a broken parity symmetry for all $\delta>0$. However, supersymmetry remains unbroken, which is verified by showing that the ground-state energy density vanishes and that the fermion-boson mass ratio is unity.Comment: 20 pages, REVTeX, 11 postscript figure

Gluon mass generation in the PT-BFM scheme

In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search of infrared finite solutions, paying particular attention to the role of the seagull graph in enforcing transversality, the necessity of introducing massless poles in the three-gluon vertex, and the incorporation of the correct renormalization group properties. In addition, we present a method for regulating the seagull-type contributions based on dimensional regularization; its applicability depends crucially on the asymptotic behavior of the solutions in the deep ultraviolet, and in particular on the anomalous dimension of the dynamically generated gluon mass. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles belonging to different Lorentz structures. The resulting integral equation is then solved numerically, the infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is determined. Various open questions and possible connections with different approaches in the literature are discussed.Comment: 54 pages, 24 figure

Mesons as qbar-q Bound States from Euclidean 2-Point Correlators in the Bethe-Salpeter Approach

We investigate the 2-point correlation function for the vector current. The gluons provide dressings for both the quark self energy as well as the vector vertex function, which are described consistently by the rainbow Dyson-Schwinger equation and the inhomogeneous ladder Bethe-Salpeter equation. The form of the gluon propagator at low momenta is modeled by a 2-parameter ansatz fitting the weak pion decay constant. The quarks are confined in the sense that the quark propagator does not have a pole at timelike momenta. We determine the ground state mass in the vector channel from the Euclidean time Fourier transform of the correlator, which has an exponential falloff at large times. The ground state mass lies around 590 MeV and is almost independent of the model form for the gluon propagator. This method allows us to stay in Euclidean space and to avoid analytic continuation of the quark or gluon propagators into the timelike region.Comment: 21 pages (REVTEX), 8 Postscript figure

Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order

In this paper we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries we obtain reduction transformations and reduced equations to specific examples. We find the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second order nonlinear ODEs.Comment: Accepted for publication in J. Phys. A Math. Theor. 201

The Massive Yang-Mills Model and Diffractive Scattering

We argue that the massive Yang-Mills model of Kunimasa and Goto, Slavnov, and Cornwall, in which massive gauge vector bosons are introduced in a gauge-invariant way without resorting to the Higgs mechanism, may be useful for studying diffractive scattering of strongly interacting particles. We perform in this model explicit calculations of S-matrix elements between quark states, at tree level, one loop, and two loops, and discuss issues of renormalisability and unitarity. In particular, it is shown that the S-matrix element for quark scattering is renormalisable at one-loop order and is only logarithmically non-renormalisable at two loops. The discrepancies in the ultraviolet regime between the one-loop predictions of this model and those of massless QCD are discussed in detail. Also, some of the similarities and differences between the massive Yang-Mills model and theories with a Higgs mechanism are analysed at the level of the S-matrix. Finally, we briefly discuss the high-energy behaviour of the leading-order amplitude for quark-quark elastic scattering in the diffractive region. The above analysis sets up the stage for carrying out a systematic computation of the higher order corrections to the two-gluon exchange model of the Pomeron using massive gluons inside quantum loops.Comment: 38 pages, Latex, with 7 PostScript pictures. Introduction and Section 6 further enlarged, minor typos correcte

The LOFAR pilot surveys for pulsars and fast radio transients

We have conducted two pilot surveys for radio pulsars and fast transients with the Low-Frequency Array (LOFAR) around 140 MHz and here report on the first low-frequency fast-radio burst limit and the discovery of two new pulsars. The first survey, the LOFAR Pilot Pulsar Survey (LPPS), observed a large fraction of the northern sky, ~1.4 x 10^4 sq. deg, with 1-hr dwell times. Each observation covered ~75 sq. deg using 7 independent fields formed by incoherently summing the high-band antenna fields. The second pilot survey, the LOFAR Tied-Array Survey (LOTAS), spanned ~600 sq. deg, with roughly a 5-fold increase in sensitivity compared with LPPS. Using a coherent sum of the 6 LOFAR "Superterp" stations, we formed 19 tied-array beams, together covering 4 sq. deg per pointing. From LPPS we derive a limit on the occurrence, at 142 MHz, of dispersed radio bursts of 107 Jy for the narrowest searched burst duration of 0.66 ms. In LPPS, we re-detected 65 previously known pulsars. LOTAS discovered two pulsars, the first with LOFAR or any digital aperture array. LOTAS also re-detected 27 previously known pulsars. These pilot studies show that LOFAR can efficiently carry out all-sky surveys for pulsars and fast transients, and they set the stage for further surveying efforts using LOFAR and the planned low-frequency component of the Square Kilometer Array.Comment: 18 pages, 10 figures, accepted for A&