Nonperturbative Aspect of Axial Vector Vertex in the Global Color Symmetry Model

It is shown how the axial vector current of current quarks is related to that of constituent quarks within the framework of the global color symmetry model. Gluon dressing of the axial vector vertex and the quark self-energy functions is described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger-Dyson equation in the rainbow approximation, respectively.Comment: 10 page

Nonperturbative aspects of the quark-photon vertex

The electromagnetic interaction with quarks is investigated through a relativistic, electromagnetic gauge-invariant treatment. Gluon dressing of the quark-photon vertex and the quark self-energy functions is described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger-Dyson equation in the rainbow approximation respectively. Results for the calculation of the quark-photon vertex are presented in both the time-like and space-like regions of photon momentum squared, however emphasis is placed on the space-like region relevant to electron scattering. The treatment presented here simultaneously addresses the role of dynamically generated $q\bar{q}$ vector bound states and the approach to asymptotic behavior. The resulting description is therefore applicable over the entire range of momentum transfers available in electron scattering experiments. Input parameters are limited to the model gluon two-point function, which is chosen to reflect confinement and asymptotic freedom, and are largely constrained by the obtained bound-state spectrum.Comment: 8 figures available on request by email, 25 pages, Revtex, DOE/ER/40561-131-INT94-00-5

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]

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

Meson-Baryon-Baryon Vertex Function and the Ward-Takahashi Identity

Ohta proposed a solution for the well-known difficulty of satisfying the Ward-Takahashi identity for a photo-meson-baryon-baryon amplitude ($\gamma$MBB) when a dressed meson-baryon-baryon (MBB) vertex function is present. He obtained a form for the $\gamma$MBB amplitude which contained, in addition to the usual pole terms, longitudinal seagull terms which were determined entirely by the MBB vertex function. He arrived at his result by using a Lagrangian which yields the MBB vertex function at tree level. We show that such a Lagrangian can be neither hermitian nor charge conjugation invariant. We have been able to reproduce Ohta's result for the $\gamma$MBB amplitude using the Ward-Takahashi identity and no other assumption, dynamical or otherwise, and the most general form for the MBB and $\gamma$MBB vertices. However, contrary to Ohta's finding, we find that the seagull terms are not robust. The seagull terms extracted from the $\gamma$MBB vertex occur unchanged in tree graphs, such as in an exchange current amplitude. But the seagull terms which appear in a loop graph, as in the calculation of an electromagnetic form factor, are, in general, different. The whole procedure says nothing about the transverse part of the ($\gamma$MBB) vertex and its contributions to the amplitudes in question.Comment: A 20 pages Latex file and 16 Postscript figures in an uuencoded format. Use epsf.sty to include the figures into the Latex fil

Electromagnetic form factors of light vector mesons

The electromagnetic form factors G_E(q^2), G_M(q^2), and G_Q(q^2), charge radii, magnetic and quadrupole moments, and decay widths of the light vector mesons rho^+, K^{*+} and K^{*0} are calculated in a Lorentz-covariant, Dyson-Schwinger equation based model using algebraic quark propagators that incorporate confinement, asymptotic freedom, and dynamical chiral symmetry breaking, and vector meson Bethe-Salpeter amplitudes closely related to the pseudoscalar amplitudes obtained from phenomenological studies of pi and K mesons. Calculated static properties of vector mesons include the charge radii and magnetic moments: r_{rho+} = 0.61 fm, r_{K*+} = 0.54 fm, and r^2_{K*0} = -0.048 fm^2; mu_{rho+} = 2.69, mu_{K*+} = 2.37, and mu_{K*0} = -0.40. The calculated static limits of the rho-meson form factors are similar to those obtained from light-front quantum mechanical calculations, but begin to differ above q^2 = 1 GeV^2 due to the dynamical evolution of the quark propagators in our approach.Comment: 8 pages of RevTeX, 5 eps figure

Post-transplantation encapsulating peritoneal sclerosis without inflammation or radiological abnormalities

Background: Post-transplantation encapsulating peritoneal sclerosis (EPS) causing bowel obstruction has been identified as a serious complication after kidney transplantation in patients previously treated with peritoneal dialysis. Systemic inflammation and abnormalities on an abdominal computed tomography (CT) scan are important hallmarks of EPS. To our knowledge, this is the first report of a case being diagnosed with late-onset post-transplantation EPS without systemic inflammation or abnormalities on a CT scan which could only be diagnosed by laparotomy. Case presentation. A 59-year old female presented because of symptoms of bowel obstruction 33 months after kidney transplantation. The patient had a 26-month history of peritoneal dialysis before her first kidney transplantation and was treated with peritoneal dialysis for 4 years before undergoing a second kidney transplantation. Physical examination was unremarkable and laboratory tests showed no signs of systemic inflammation (C-reactive protein <1 mg/L). An abdominal CT scan did not reveal any abnormalities fitting the diagnosis of EPS, except a "feces sign". Given the severity of the progressive symptoms, a diagnostic laparotomy was performed, visualizing a classical EPS. Total peritonectomy and enterolysis were performed, leading to restoration of peristalsis. Conclusion: EPS may occur several years after kidney transplantation in the absence of inflammation and typical radiological abnormalities. Obtaining a diagnosis of post-transplantation EPS is challenging, however, a low threshold for surgical exploration in case of high clinical suspicion and negative findings on the CT scan is mandatory

Shapes of the Proton

A model proton wave function, constructed using Poincare invariance, and constrained by recent electromagnetic form factor data, is used to study the shape of the proton. Spin-dependent quark densities are defined as matrix elements of density operators in proton states of definite spin-polarization, and shown to have an infinite variety of non-spherical shapes. For high momentum quarks with spin parallel to that of the proton, the shape resembles that of a peanut, but for quarks with anti-parallel spin the shape is that of a bagel.Comment: 8 pages, 5 figures, to be submitted to Phys. Rev. C This corrects a few typos and explains some further connections with experiment

Expanding the expressive power of Monadic Second-Order logic on restricted graph classes

We combine integer linear programming and recent advances in Monadic Second-Order model checking to obtain two new algorithmic meta-theorems for graphs of bounded vertex-cover. The first shows that cardMSO1, an extension of the well-known Monadic Second-Order logic by the addition of cardinality constraints, can be solved in FPT time parameterized by vertex cover. The second meta-theorem shows that the MSO partitioning problems introduced by Rao can also be solved in FPT time with the same parameter. The significance of our contribution stems from the fact that these formalisms can describe problems which are W[1]-hard and even NP-hard on graphs of bounded tree-width. Additionally, our algorithms have only an elementary dependence on the parameter and formula. We also show that both results are easily extended from vertex cover to neighborhood diversity.Comment: Accepted for IWOCA 201