Search results for "Mathematical physics"
showing 10 items of 2687 documents
Chiral Perturbation Theory with tensor sources
2007
23 pages, 1 figure.-- ISI Article Identifier: 000249788800051.-- ArXiv pre-print available at: http://arxiv.org/abs/0705.2948
The sunset diagram in SU(3) chiral perturbation theory
1996
A general procedure for the calculation of a class of two-loop Feynman diagrams is described. These are two-point functions containing three massive propagators, raised to integer powers, in the denominator, and arbitrary polynomials of the loop momenta in the numerator. The ultraviolet divergent parts are calculated analytically, while the remaining finite parts are obtained by a one-dimensional numerical integration, both below and above the threshold. Integrals of this type occur, for example, in chiral perturbation theory at order p^6.
Renormalization of relativistic baryon chiral perturbation theory and power counting
2003
We discuss a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. The method involves finite subtractions of dimensionally regularized diagrams beyond the standard $\bar{\rm MS}$ scheme of chiral perturbation theory to remove contributions violating the power counting. This is achieved by a suitable renormalization of the parameters of the most general effective Lagrangian. In addition to simplicity our method has the benefit that it can be easily applied to multiloop diagrams. As an application we discuss the mass and the scalar form factor of the nucleon and compare the results with the e…
Hadron structure in the description of electromagnetic reactions
2002
The description of electromagnetic reactions at intermediate energies, such as pion electroproduction or (virtual) Compton scattering, traditionally starts from covariant tree-level Feynman diagrams (Born or pole terms). Internal hadron structure is included by means of (on-shell) form factors in the vertices while free propagators are used. To overcome problems with gauge invariance, simple prescriptions, such as, choosing ${F}_{1}^{V}{(q}^{2}{)=F}_{\ensuremath{\pi}}{(q}^{2})$ in pion electroproduction or the ``minimal substitution,'' are used. We discuss the inherent assumptions of such approaches and study the general structure of electromagnetic vertices and propagators for pions and nu…
Bethe-Salpeter approach for unitarized chiral perturbation theory
2000
The Bethe-Salpeter equation restores exact elastic unitarity in the $s-$ channel by summing up an infinite set of chiral loops. We use this equation to show how a chiral expansion can be undertaken in the two particle irreducible amplitude and the propagators accomplishing exact elastic unitarity at any step. Renormalizability of the amplitudes can be achieved by allowing for an infinite set of counter-terms as it is the case in ordinary Chiral Perturbation Theory. Crossing constraints can be imposed on the parameters to a given order. Within this framework, we calculate the leading and next-to-leading contributions to the elastic $\pi \pi$ scattering amplitudes, for all isospin channels, a…
Universal Bounds for SU(3) Low Energy Constants
2008
In this paper bounds for L_1, L_2 and L_3 are obtained in Chiral Perturbation Theory with three flavours. At the same time we test the compatibility of this theory with axiomatic principles. Following a recent paper we use dispersion relations to write positivity conditions that translate into bounds for the chiral low energy constants. As a first approach we consider the exact SU(3)_V limit and notice that if a common mass of the order of that of the kaon is adopted for the octet of pseudo-Goldstone bosons the bounds have very large O(p^6) corrections. Once the positivity conditions are adapted to account for different masses, we correct the previous bounds for a physical kaon mass and fin…
On the singular behaviour of scattering amplitudes in quantum field theory
2014
We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.
S-waveKK*interactions in a finite volume and thef1(1285)
2015
Lattice QCD simulations provide a promising way to disentangle different interpretations of hadronic resonances, which might be of particular relevance to understand the nature of the so-called XY Z particles. Recent studies have shown that in addition to the well-established naive quark model picture, the axial-vector meson f1(1285) can also be understood as a dynamically generated state built upon the KK ∗ interaction. In this work, we calculate the energy levels of the KK ∗ system in the f1(1285) channel in finite volume using the chiral unitary approach. We propose to calculate the loop function in the dimensional regularization scheme, which is equivalent to the hybrid approach adopted…
Gluon mass through ghost synergy
2011
In this work we compute, at the "one-loop-dressed" level, the nonperturbative contribution of the ghost loops to the self-energy of the gluon propagator, in the Landau gauge. This is accomplished within the PT-BFM formalism, which guarantees the gauge-invariance of the emerging answer. In particular, the contribution of the ghost-loops is automatically transverse, by virtue of the QED-like Ward identities satisfied in this framework. Using as nonperturbative input the available lattice data for the ghost dressing function, we show that the ghost contributions have a rather sizable effect on the overall shape of the gluon propagator, both for $d=3,4$. Then, by exploiting a recently introduce…
Indirect determination of the Kugo-Ojima function from lattice data
2009
We study the structure and non-perturbative properties of a special Green's function, u(q), whose infrared behavior has traditionally served as the standard criterion for the realization of the Kugo-Ojima confinement mechanism. It turns out that, in the Landau gauge, u(q) can be determined from a dynamical equation, whose main ingredients are the gluon propagator and the ghost dressing function, integrated over all physical momenta. Using as input for these two (infrared finite) quantities recent lattice data, we obtain an indirect determination of u(q). The results of this mixed procedure are in excellent agreement with those found previously on the lattice, through a direct simulation of …