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Lattice Calculation of New Mesons in the Charm Region and Nucleon Structure

Lattice Calculation of New Mesons in the Charm Region and Nucleon Structure. Synopsis of Lattice QCD Study of X(2317) as a Tetraquark Mesonium Glue and Quark Momenta Renormalization with Sum Rules <x> s , <x> u+d (D.I.), <x 2 >, <x> g Quark and glue angular momenta. 劉 克 非.

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Lattice Calculation of New Mesons in the Charm Region and Nucleon Structure

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  1. Lattice Calculation of New Mesons in the Charm Region and Nucleon Structure • Synopsis of Lattice QCD • Study of X(2317) as a Tetraquark Mesonium • Glue and Quark Momenta • Renormalization with Sum Rules • <x>s, <x>u+d (D.I.), <x2>, <x>g • Quark and glue angular momenta 劉 克 非 • χQCDCollaboration: • A. Alexandru, Y. Chen, T. Doi, S.J. Dong, • T. Draper, M. Gong, I. Horvath, F. Lee, • A. Li, K.F. Liu, N. Mathur, T. Streuer, J.B. Zhang 刘 克 菲

  2. Introduction to Lattice Gauge Theory Path Integral Formulation in Discrete Euclidean Space-Time • Path integral of the partition function of continuum QCD in Minkowski space • Imaginary time with Wick rotation and then • Integrating Grassmann numbers and gives Euclidean partition function • Note the Grassmann number integration • The Green’s function

  3. a Lattice QCD – Path integral in Euclidean Space Why Lattice? • Regularization • Lattice spacing a • Hard cutoff, p ≤ π/a • Scale introduced (dimensional transmutation) • Renormalization • Perturbative • Non-perturbative Regularization independent Scheme Schroedinger functional Current algebra relations • Numerical Simulation • Quantum field theory classical statistical mechanics • Monte Carlo simulation (importance sampling)

  4. Hadron Mass and Decay Constant The two-point Green’s function decays exponentially at large separation of time Mass M= Ep(p=0), decay constant ~ Φ

  5. Nucleon Form Factor The three-point Green’s function for the iso-vector axial current is proportional to asymptotically.

  6. C. Aubin, Lattice ‘09

  7. Hadron Structure withDisconnected Insertion Calculation • Pion-Nucleon Sigma Term, Strangeness Content in N • Quark Spin and Orbital Angular Momentum in Nucleon • Sea Quark Contributions in <x>, and <x2> • Strangeness Electric and Magnetic Form Factors • Muon Anomalous M. M. (g-2) (light-by-light) • Neutron Electric Dipole Moment

  8. Momenta and Angular Momenta of Quarks and Glue • One can decompose the energy momentum tensor into quark part and gluon part gauge invariantly • Nucleon matrix elements can be decomposed as • where the angular momentum is Orbital part X.Ji (1997)

  9. q p p’=p-q Methodology • How to extract T1(q^2) and T2(q^2) ? N.B. we need one more equation to extract T1 and T2 separately (q^2 dependence could be different)

  10. Hadron Structure withQuarks and Glue • Quark and Glue Momentum and Angular Momentum in the Nucleon

  11. Renormalization and Quark-Glue Mixing Momentum and Angular Momentum Sum Rules

  12. Strange Parton Moments • Strange parton distribution is poorly known – H.L. Lai et al. (CTEQ), JHEP 0704:089 (2007) • 0.018 < <x>s < 0.040 • NuTeV measurement of sin2 θW is 3 σ above the standard model strangeness asymmetry, i.e. ? • CTEQ: the sign of is uncertain. • Lattice can calculate

  13. <x>sFull QCD with 2+1 Flavor Clover Fermions mπ = 800, 700, 600 MeV

  14. Quenched 2+1 Flavor Full QCD

  15. Implication on Fitting of PDF Global PDF Fitting à la CTEQ Is there a discrepancy?

  16. Cat’s ears diagrams are suppressed by O(1/Q2).

  17. Large momentum frame • Parton degrees of freedom: valence, connected sea and disconnected sea

  18. Physical Consequences • Is it necessary to separate out the CS from the DS? • Small x behavior (Reggeon exchange, no pomeron exchange) (Pomeron exchange)

  19. 2) Gottfried Sum Rule Violation NMC: two flavor traces ( ) one flavor trace ( ) K.F. Liu and S.J. Dong, PRL 72, 1790 (1994)

  20. 3) Fitting of experimental data CTEQ4, MRST But A better fit where

  21. HERMES – Kaon production in DIS, PL B666, 446 (2008)

  22. Results for <x2> Nf=2+1 Preliminary <x2>(s) <x2>(ud) [DI] MENU2010 @ Willam & Mary

  23. Results for <x>(g) from overlap op Glue Momentum in Nucleon Glue operator from the overlap operator Linear slope corresponds to signal Able to obtain a clear signal of glue in the nucleon. c.f. M.Gockeler et al., Nucl.Phys.Proc.supp..53(1997)324

  24. See Talk 1193 by F. Kunne Horst Fischer DIS2010

  25. Nucleon Spin • Quark spin ΔΣ ~ 30% of proton spin (DIS, Lattice) • Quark orbital angular momentum? (recent lattice calculation ~ 0) • Glue spin ΔG/G small (COMPASS, STAR) ? • Glue orbital angular momentum is small (Brodsky and Gardner) ? Dark Spin ?

  26. Flavor-singlet gA • Quark spin puzzle (dubbed `proton spin crisis’) • NRQM • RQM • Experimentally (EMC, SMC, …

  27. S.J. Dong, J.-F. Lagae, and KFL, PRL 75, 2096 (1995) • DI sea contribution independent of quark mass • This suggests U(1) anomaly at work.

  28. Lattice resolution: U(1) anomaly

  29. Summary • Momentum fraction of quarks (both valence and sea) and gluons have been calculated for quenched and 2+1 flavor dynamical fermions. • Glue mometum fraction is ~ 50%. • g_A ~ 0.25 in agreement with expt. • Glue angular momentum (gauge invariant) is quite small. • Quark orbital angular momentum is small for the valence, but large for the sea quarks.

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