1 / 14

“Time-reversal-odd” distribution functions in chiral models with vector mesons

“Time-reversal-odd” distribution functions in chiral models with vector mesons. Alessandro Drago University of Ferrara. Outline. T-odd distributions in QCD Chiral models with vector mesons as dynamical gauge bosons Large N c expansion and the relation. Brodsky, Hwang and Schmidt mechanism.

genera
Download Presentation

“Time-reversal-odd” distribution functions in chiral models with vector mesons

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. “Time-reversal-odd” distribution functionsin chiral modelswith vector mesons Alessandro Drago University of Ferrara

  2. Outline • T-odd distributions in QCD • Chiral models with vector mesons as dynamical gauge bosons • Large Nc expansion and the relation

  3. Brodsky, Hwang and Schmidt mechanism

  4. Gauge link and factorization in Drell-Yan and in DIS (Collins 2002)

  5. From QCD to chiral lagrangians In QCD the two main ingredients are: Gauge theory  Wilson lines Factorization  violation of universality How to compute “T-odd” distributions in chiral models? If we are not using a gauge theory we have no necessity to introduce Wilson lines…

  6. Chiral lagrangians with a hidden local symmetryBando, Kugo, Uehara, Yamawaki, Yanogida 1985 A theorem: “Any nonlinear sigma model based on the manifold G/H is gauge equivalent to a linear model with a Gglobal Hlocal symmetry and the gauge bosons corresponding to the hidden local symmetry Hlocal are composite gauge bosons” For instance: G = SU(2)L SU(2)R H = SU(2)V

  7. What is a hidden symmetry? Kinetic term of a nonlinear sigma model: Under the global SU(2)L X SU(2)R symmetry: We rewrite U(x) in terms of two auxiliary variables: The transformation rules under [SU(2)L XSU(2)R ]global X [SU(2)V]local are:

  8. LV and LA are both invariant under [SU(2)L X SU(2)R ]global X [SU(2)V]local Any linear combination of LV and LA is equivalent to the original kinetic term.

  9. About the  mesons So far we have given no dynamics to V “For simplicity” we add a kinetic term: The  meson acquires a mass via spontaneous breaking of the hidden local SU(2)V symmetry g = g universality M2 = 2 g2 f2 KSRF relation

  10. Introducing matter fields linear representation of Hlocal singlet of Gglobal … is the simplest term After the gauge fixing matter fields transform non-linearly because h(x) has to be restricted to the p - dependent form.

  11. Again about matter fields (quarks) Take a representation r of G whose restriction to H contains r0 Defining c=r(x+) y so that c  r(g) c we have twotypes of quarks: “constituent quarks” y (singlet of Gglobal) “current quarks” c (singlet of Hlocal ) Vector mesons are non-singlet of Hlocal and therefore they are “composed” of constituent quarks y.

  12. Sivers function in -models     : constituent quarks Almost identical to the QCD diagram. has a physical mass. The exchange of a  meson can also be included

  13. The 1/Nc expansion At leading order (1/Nc)0 hedgehog solution (the problem of time reversal has already been solved by the link operators…)

  14. Conclusions “T-odd” distributions can be computed also in chiral models, at least if vector mesons are introduced as gauge bosons. At leading order in 1/Nc : Work to be done: to compute explicitely these distributions. Open problem: if one does not introduce a dynamics associated with the vector mesons, T-odd distributions can still be computed?

More Related