1 / 33

Nucleon parton distributions from lattice QCD

Nucleon parton distributions from lattice QCD. Philipp Hägler. supported by. Motivation. get deeper insight into inner quark and gluon structure of hadrons learn about fundamental aspects and mechanisms of the strong interaction

tekla
Download Presentation

Nucleon parton distributions from lattice QCD

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. Nucleon parton distributionsfrom lattice QCD Philipp Hägler supported by

  2. Motivation • get deeper insight into inner quark and gluon structure of hadrons • learn about fundamental aspects and mechanisms of the strong interaction • facilitate understanding and interpretation of phenomenology of hadron scattering and production; comparison with experiment • make predictions; support search for „new physics“ • provide an approach that is complementary/alternative to the „triumvirate“ pQCD + QCD factorization + experiment as well as other NP-approaches • validate and improve lattice methods and techniques • ...

  3. QCD factorization and observables on the lattice SIDIS DIS DVCS bilocal operators on the light-cone on a Euclidean space-time lattice use manifestly non-local operators off the light-cone on the lattice x-moments matrix elements of local (quark) operators invariant amplitudes approach light-cone limit usingextrapolations/theory (generalized) form factors TMDs (?) x-moments of PDFs, GPDs

  4. Lattice QCD: Introduction Euclidean hadron properties&structure lattice computations form factors Nf=2 and 2+1, many different lattice actions (Wilson, DW,...) with m≈300MeV standard decay constants hadron masses moments of distribution amplitudes polarizabilities hadrons moments of (generalized) PDFs pion, nucleon, ,  k-dependent distributions (TMDs) significant progress in hadron structure calculations on the lattice during last 10 years Lattice gauge theory represents well defined approach to QFT • discretization errors/effects • finite volume errors/effects • large quark masses • ... Lattice QCD is a computational tool which systematic „ab initio“-approach; still with:

  5. Typical „measurements“ on the lattice = vector-, axialvector-, quark spin flip-,(spin-2) graviton-, „spin-n“ coupling quark propagators compute the path-integral using MC methods gauge fields/links U quarks Kentucky (Liu et al.), Collins Bali Schäfer,...

  6. Not quite as trivial as it might appear...

  7. Past and ongoing lattice studies QCDSF/UKQCD RBC/UKQCD LHPC MIT/Cyprus ETMC JLQCD CLS (Mainz) ... pion and nucleon form factors QCDSF/UKQCD LHPC RBC/UKQCD ETMC ... moments of PDFs QCDSF/UKQCD LHPC (ETMC?) ... moments of GPDs „TMDs on the lattice“ PhH, Musch, Negele, Schäfer reviews: Zanotti 0812.3845; Renner 1002.0925 PhH Phys.Rept. 2010 (0912.5483) concentrate on small number of selected results

  8. Isovector momentum fraction substantial systematic uncertainties: renormalization, discretization errors, excited state contamination, ...?

  9. Form factors of the energy momentum tensor QCDSF/UKQCD nf=2 A.Sternbeck, D.Pleiter, J.Zanotti et al. m~180...1000 MeV NP-renormalized [Göckeler et al. 1003.5756] u-d u+d(*) 10 out of ~28 ensembles * [non-singlet, connected only]

  10. Form factors of the energy momentum tensor u-d u+d(*) QCDSF/UKQCD nf=2 A.Sternbeck, D.Pleiter, J.Zanotti et al. * [non-singlet, connected only]

  11. Form factors of the energy momentum tensor QCDSF/UKQCD nf=2 A.Sternbeck, D.Pleiter, J.Zanotti et al. u-d u+d(*) • In summary: • nice data (more to come) • no big surprises • compares well with previous studies(QCDSF [Ohtani et al. 0710.1534], LHPC nf=2+1 [PhH et al. 0705.4295], [Bratt et al. 1001.3620]) • detailed analysis (systematic uncertainties, chiral extrapolations, etc.) in the near future * [non-singlet, connected only]

  12. Ju, Jd template figure (update) [JLab Hall A PRL`07; HERMES JHEP`08] lattice results from covariant BChPT extrapolations [Dorati, Gail, Hemmert NPA 2008] * LHPC arXiv:1001.3620 * LHPC PRD `08 0705.4295 * QCDSF (Ohtani et al.) 0710.1534 *,1 QCDSF/UKQCD preliminary Goloskokov&Kroll EPJC`09 0809.4126 Wakamatsu 0908.0972 DiFeJaKr EPJC `05 hep-ph/0408173 (Myhrer&)Thomas PRL`08 0803.2775 1Sternbeck, Pleiter, Zanotti et al. 2011 * [non-singlet, connected only; add. uncertainties due to chiral extrapolations, renormalization]

  13. Transverse momentum distributions (TMDs) in lattice QCD [B. Musch, PhH, J. Negele, A. Schäfer, arXiv:1011.1213 (PRD); PhH, B. Musch, J. Negele, A. Schäfer, EPL 2009 (arXiv:0908.1283) B. Musch, PhD thesis arXiv:0907.2381] HERMES (SIDIS) PRL 2009 motivation on H phenomenology: -SIDIS, DY production • T-odd effects & single-spin azimuthal asymmetries • factorization or correlations in x, k? (test factorization assumption)↔ MC event generators (PYTHIA, HERWIG,.. for LHC, Tevatron) (and COMPASS PLB 2009, 2010) hadron structure: • intrinsic k of quarks & gluons inside hadrons • correlations between momentum, coordinate & spin DOFs conceptual questions related to: -TMD-(QCD)-factorization of semi-inclusive processes -probabilistic interpretation of TMDs; relation to PDFs -relation between TMDs and GPDs -manifestly non-local operators and path geometries on the lattice

  14. Definitions of TMDs and QCD factorization solutions/proposals Mulders et al.1996- („LO“); Anselmino et al., Radicci, Bachetta et al., … 1999- („LO“) Collins 1980- ; Collins&Metz; Collins&Hauptmann; Ji,Ma&Yuan 2004- („NLO“),... Cherednikov&Stefanis(1980s-) 2007- („NLO“); Chay 2007 (EFT, „NLO“) Becher, Neubert 2010 (EFT) ~ „no factorization in terms of TMDs possible“ Aybat&Rogers 2011 („NnLO“?) → Collins („NnLO“?) in "Foundations of Perturbative QCD", (Cambridge University Press) „Not yet published - available from May 2011“ gauge-invariance (regularization and) removal of rapidity/light-cone divergences SIDIS Is there is a unique, commonly accepted exact definition of (SIDIS-)TMDs in terms of (GI) quark- and gluon operators available? !? ? TMD-extractions/ phenomenology

  15. Transverse momentum dependent PDFs - formalism • example: direct • „process independent“ – • Wilson lines parametrization of coordinate space correlators in terms of 9 complex invariant amplitudes define Fourier-transformed amplitudes twist-3 twist-2 notation of [Mulders, Tangermann NPB 1996; Boer, Mulders PRD 57 (1998)] [Musch et al. arXiv:1011.1213 (PRD)] TMDs are part of expansion in , classified according to twist how can TMDs ever be accessed on an Euclidean lattice with hadrons (nearly) at rest?

  16. Transverse momentum dependent PDFs – „extended“ formalism physically more relevant „process dependent“ or „SIDIS“ or „DY“ spatially extended U-shaped links, e.g. access to T-odd structures parametrization of coordinate space correlators in terms of 32 independent complex invariant amplitudes [Goeke, Metz, Schlegel PLB 2005], e.g. Sivers, Boer-Mulders effects the 32 invariant amplitudes can be matched on 32 independent TMDs of twist-2,3,4 [Goeke, Metz, Schlegel PLB 2005] note: the appearance of 32 structures is not a „lattice artefact“

  17. Typical results LHPC, Nf=2+1 DW-valence +staggerd sea

  18. TMDs on the lattice .... Gaussian parametrization and regularization of UV divergencies renormalization (potential power divergencies) ....

  19. l2-dependence of the (renormalized) invariant amplitudes [B. Musch, PhH, J. Negele, A. Schäfer, arXiv:1011.1213 (PRD)] unpolarized unpolarized

  20. l2-dependence of the (renormalized) invariant amplitudes long. polarized long. polarized worm-gear worm-gear

  21. l2-dependence of the (renormalized) invariant amplitudes

  22. l2-dependence of the (renormalized) invariant amplitudes „pretz....“ „pretz....“ transversity transversity compare e.g. to models: Pasquini et al PRD 2008, Bacchetta et al.,...

  23. Correlations in

  24. GPDs genuine effect of intrinsic transverse momentum of quarks Intrinsic transverse momentum densities of the nucleon [Boglione, Mulders PRD 60 (1999), Diehl, PhH EPJC 44 (2005)] PhH, B. Musch et al. EPL 2009, arXiv:0908.1283

  25. Preliminary results for extended gauge links [calculations and results by Berni Musch (JLab)]

  26. move gauge link to infinity; ‚final state interactions‘ • approach the light-cone; • -moments note: limit anyway not defined without regulator [see e.g. BaBoDiMu 0803.0227] ↔ work at finite with the Collins-Soper parameter ζ CS evolution [CS NPB 1981, IdJiMaYu hep-ph/0406302] note: regularizes rapidity divergences note: soft factors cancel out in amplitude-ratios T-odd effects and transverse momentum shifts

  27. Sivers transverse momentum shift

  28. Boer-Mulders transverse momentum shift

  29. ? Boer-Mulders transverse momentum shift – ζ-dependence

  30. Relation to deformed quark impact parameter distributions negative Boer-Mulders function for up- and down quarks in the proton and the pion [hep-lat/0612032], [0708.2249] if preliminary TMD-results hold, a consistent picture could be emerging tensor GPDs of the nucleon and pion on the lattice [QCDSF (PhH et al.) hep-lat/0612032, (BrDiHä et al.) 0708.2249] chromodynamic lensing [Burkardt hep-ph/0302144, 0811.1206] +

  31. Summary & Outlook ongoing promising efforts in computation of moments of GPDs on the lattice first direct lattice calculations of non-local operators related to TMDs first exploratory lattice study of „T-odd“ effects investigations of systematic effects are in progress and should to be intensified NP-renormalization, excited states, disconnected contributions,... with respect to invariant amplitudes/TMDs study η→limit ζ-evolution study different/additional link structures employ larger momenta P x (l·P)-dependence; (x,k)-correlations different pion masses, chiral extr. ...

  32. work done in collaboration with/based on results from B. Bistrovic, J. Bratt, J.W. Negele, A. Pochinsky, S. Syritsyn (MIT) R.G. Edwards, B. Musch, D.G. Richards (JLab) K. Orginos (W&M) M. Engelhardt (New Mexico) G. Fleming, M. Lin (Yale), H.-W. Lin (INT), H. Meyer (Mainz), D.B. Renner (DESY Zeuthen), M. Procura (TUM), W. Schroers (LHPC) D. Brömmel (Southampton), M. Diehl (DESY), M. Göckeler, M. Gürtler, Th. Hemmert, A. Schäfer, A. Sternbeck, F. Winter (Regensburg U.) R. Horsley, J. Zanotti (Edinburgh U.) Y. Nakamura (Regensburg) P. Rakow (Liverpool U.) D. Pleiter, G. Schierholz (DESY) H. Stüben (ZIB); M. Ohtani (Tokyo) (QCDSF/UKQCD) M. Altenbuchinger, B. Musch (→JLab), W. Weise (T39, TUM) (additional) references: QCDSF: PoS(LAT2006)120; 0710.1534; PRL 98 222001 (2007); PRD 74:094508,2006 (hep-lat/0603028); PRL 2008 (0708.2249); LHPC: PRL 96 502001 (2006) ; PRD 77, 094502 (2008), 0810.1933; PRD81:034507, 2010 (0907.4194); 1001.3620; PhH Phys.Rep. 2010 (0912.5483); 1011.1213

More Related