Resolving infrared singularities of QCD through the vertex paradigm
Abstract
We furnish details and extensions for the vertex paradigm and related ideas. The vertex paradigm is a method for dealing nonperturbatively with the SchwingerDyson equations (SDE) of asymptoticallyfree (AF) gauge theories such as QCD, even in the face of necessary approximations. It provides a useful truncation for the infinitelymany SDE of the gauge and renormalizationgroup invariant Pinch Technique (PTRGI). We implement the vertex paradigm by successive approximations at the onedressedloop level, postulating input treelevel gluon and ghost propagators and a 3gluon vertex that are wellbehaved in the infrared and also satisfy several crucial PTRGI Ward identities that are QEDlike and ghostfree. Good IR behavior is assured by including a (nonrunning) gaugeinvariant dynamical gluon and ghost mass as part of the input. The nontrivial part of the vertex paradigm is that, with our inputs, the oneloop output vertex then satisfies the correct Ward identity from which we can construct the output gluon propagator, by taking account of NambuGoldstonelike massless scalars and related technical problems that arise whenever there is dynamical gluon mass generation. The oneloop outputs show a number of desirable features: They are PTRGI; free of any reference to a coupling (dimensional transmutation); satisfy the ghostfree Ward identities connecting them; give exactly the known oneloop UV behavior; and are free of IR singularities. We give a much simpler illustration of the main principles of the vertex paradigm in a modified $\phi^3_6$ model that is AF. Our successiveapproximation scheme is not designed to estimate the gluon dynamical mass, but it shows that there is a lower limit to the mass below which the AF theory breaks down.
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.2214
 Bibcode:
 2014arXiv1410.2214C
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 25 pages, 10 figures, revtex4