1 / 28

Relation between TMDs and PDFs in the covariant parton model approach

Relation between TMDs and PDFs in the covariant parton model approach. Petr Z a vada Institute of Physics, Prague, Czech Rep. (based on collaboration and discussions with A.Efremov, P.Schweitzer and O.Teryaev). XIX International Workshop on Deep-Inelastic Scattering

chun
Download Presentation

Relation between TMDs and PDFs in the covariant parton model approach

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. Relation between TMDs and PDFs in the covariant parton model approach Petr Zavada Institute of Physics, Prague, Czech Rep. (based on collaboration and discussions with A.Efremov, P.Schweitzer and O.Teryaev) XIX International Workshop on Deep-Inelastic Scattering and Related Subjects, Newport News, Virginia USA April 11-15, 2011

  2. Outline • 3D covariant parton model • PDF-TMD relations • TMDs: numerical predictions • Other effects of LI & RS • Summary

  3. 3D covariant parton model • Model of non-interacting quarks fulfils the requirements of Lorentz invariance & rotationalsymmetry of (3D) quark momentum distribution in the nucleon rest frame. • Model implies relations and rules: • between 3D distributions and structure functions • between structure functions themselves • For example: WW relation, sum rules WW, BC, ELT; helicity↔transversity, transversity↔pretzelosity,... Relations between different TMDs, recently also TMDs↔PDFs See our recent paper and citations therein: A.Efremov, P.Schweitzer, O.Teryaev and P.Z., Phys.Rev.D 83, 054025(2011)

  4. TMDs(TransverseMomentumDependentparton distributions) light-front correlators [A.Efremov, P.Schweitzer, O.Teryaev and P.Z. Phys.Rev.D 80, 014021(2009)]

  5. PDF-TMD relations UNPOLARIZED POLARIZED Knownf1(x), g1(x) allow to predict unknown TMDs For details see: P.Z. Phys.Rev.D 83, 014022 (2011) A.Efremov, P.Schweitzer, O.Teryaev and P.Z. Phys.Rev.D 83, 054025(2011) In this talk we assumem→0

  6. Numerical results: pT/M q(x) 0.10 0.13 0.20 x 0.15 0.18 0.22 0.30 Input for f1(x) MRST LO at 4 GeV2 x pT/M

  7. X 0.15 0.18 0.22 0.30 • Gaussian shape – is supported by phenomenology • <pT2>depends on x, is smaller for sea quarks

  8. What do we know about intrinsic motion? Leptonic data: Models: statistical, covariant <pT>≈0.1 GeV/c ? Hadronic data: SIDIS, Cahn effect <pT> ≈ 0.6 GeV/c Further study is needed!

  9. pT/M g1q(x) 0.10 0.13 0.20 X 0.15 0.18 0.22 0.30 Input for g1: LSS LO at 4 GeV2

  10. Comment In general g1q (x,pT) changes sign at pT=Mx. It is due to the factor: The situation is similar to the g2 (x) case: • With our choice of the light-cone direction: • large x are correlated with large negative p1 • low x are correlated with large positive p1 both expressions have opposite signs for large and lowx E155 experiment

  11. Further effects of Lorentz invariance & rotational symmetry

  12. Cahn effect azimuthal asymmetry proton rest frame Effect is due to nonzero transverse momentum of quarks inside the nucleon

  13. Origin of the effect Transversal motion of the constituents creating a composite target is necessary condition Lepton-quark scattering in one photon exchange approximation W=|Mfi|2 : where Mandelstam variables expressed in the reference frame defined by photon read: pT – transversal momentum with respect to photon axis j azimuthal angle – between leptonic and quark (hadron) production planes y=Pq/Pl=n/l0 ... we are using notation by Anselmino et al., PRD 71, 074006 (2005)

  14. Geometric interpretation Primary reason: for finite Q2 lepton (beam) axis ≠ photon axis s/2=lp=l0p0-|l||p|cosb s1 < s2 [P.Z. Phys.Rev.D 83, 014022 (2011)]

  15. Comment In fact, the effect is more general a+b→ c+d valid for any process 2 → 2 described by invariant probability depending on Mandelstam variables • l – kinematics, W – dynamics…

  16. Measuring of cross-section l+p Measured azimuthal asymmetry gives <pT> Ignoring of longitudinal motion overestimates <pT> !

  17. Kinematical limits (ifand) AND Rest frame: (if pT -distribution is decreasing function) No specific model is assumed!

  18. Summary We discussed some aspects of quark motion inside nucleon within the 3D covariant parton model: We derived the relations between TMDs and PDFs With the use of these relations we calculated the set of unpolarized and polarized TMDs We demonstrated that Lorentz invariance + rotational symmetry represent powerful tool for obtaining new (approximate) relations among distribution functions, including PDFs ↔ TMDs. We discussed also some related kinematical effects.

  19. Thank you !

  20. Backup slides

  21. 3D covariant parton model • General framework

  22. Structure functions • Input: • 3D distribution • functions in the proton rest frame • (starting representation) • Result: • structure • functions • (x=BjorkenxB!)

  23. F1, F2- manifestly covariant form:

  24. g1, g2- manifestly covariant form:

  25. Comments In the limit of usual approach assuming p = xP, (i.e. intrinsic motion is completely supressed) one gets known relations between the structure and distribution functions: We work with a ‘naive’ 3D parton model, which is based on covariant kinematics (and not infinite momentum frame). Main potential: implication of some old and new sum rules and relations among PDF’s and TMDs.

More Related