On the Drell-Levy-Yan Relation for Fragmentation Functions T. Ito, W.Bentz(Tokai Univ.) K.Yazaki (Tokyo Woman’s University, and RIKEN) A.W.Thomas (JLab)

Slides:

Advertisements

Similar presentations

1 The and -Z Exchange Corrections to Parity Violating Elastic Scattering 周海清 / 东南大学物理系 based on PRL99,262001(2007) in collaboration with C.W.Kao, S.N.Yang.

Advertisements

Lecture 1: basics of lattice QCD Peter Petreczky Lattice regularization and gauge symmetry : Wilson gauge action, fermion doubling Different fermion formulations.

The regularization dependence on the phase diagram in the Nambu-Jona-Lasinio model Hiroaki Kohyama (CYCU)

Chiral 07, Osaka, November 12-16, 2007 Sea-quark flavor asymmetry in the nucleon from a relativistic analysis of the Drell-Yan scattering off nuclei A.

The role of the tetraquark at nonzero temperature Francesco Giacosa in collaboration with A. Heinz, S. Strüber, D. H. Rischke ITP, Goethe University, Frankfurt.

Chiral freedom and the scale of weak interactions.

Polarized structure functions Piet Mulders ‘Lepton scattering and the structure of nucleons and nuclei’ September 16-24, 2004

Quark Hadron Duality and Rein-Sehgal Model † Krzysztof M. Graczyk , Cezary Juszczak, Jan T. Sobczyk Institute of Theoretical Physics Wrocław University,

Functional renormalization – concepts and prospects.

Chiral freedom and the scale of weak interactions.

QCD – from the vacuum to high temperature an analytical approach an analytical approach.

Chiral freedom and the scale of weak interactions.

 Transverse Polarization in STAR Au-Au Collisions Polarization definition and models E896 results STAR analysis STAR results Significance of results Future.

2-nd Vienna Central European Seminar, Nov 25-27, Rare Meson Decays in Theories Beyond the Standard Model A. Ali (DESY), A. V. Borisov, M. V. Sidorova.

New Frontiers in QCD, October 28th, 2011 Based on K. Kim, D. Jido, S.H. Lee PRC 84(2011) K. Kim, Y. Kim, S. Takeuchi, T. Tsukioka PTP 126(2011)735.

Relativistic chiral mean field model for nuclear physics (II) Hiroshi Toki Research Center for Nuclear Physics Osaka University.

Forward - Backward Multiplicity in High Energy Collisions Speaker: Lai Weichang National University of Singapore.

L. R. Dai (Department of Physics, Liaoning Normal University) Z.Y. Zhang, Y.W. Yu (Institute of High Energy Physics, Beijing, China) Nucleon-nucleon interaction.

Monday, Jan. 27, 2003PHYS 5326, Spring 2003 Jae Yu 1 PHYS 5326 – Lecture #4 Monday, Jan. 27, 2003 Dr. Jae Yu 1.Neutrino-Nucleon DIS 2.Formalism of -N DIS.

Hadron to Quark Phase Transition in the Global Color Symmetry Model of QCD Yu-xin Liu Department of Physics, Peking University Collaborators: Guo H., Gao.

Chiral condensate in nuclear matter beyond linear density using chiral Ward identity S.Goda (Kyoto Univ.) D.Jido （ YITP ） 12th International Workshop on.

Eigo Shintani (KEK) (JLQCD Collaboration) KEKPH0712, Dec. 12, 2007.

Inelastic scattering When the scattering is not elastic (new particles are produced) the energy and direction of the scattered electron are independent.

HNP 2011, Pohang, Korea Weak Pion Production and Strangeness Contents on the Hadron Myung-Ki CHEOUN (Soongsil Univ., Korea) and (Soongsil Univ.,

Adnan Bashir Michoacán University, Mexico Michoacán University, Mexico Argonne National Laboratory, USA Kent State University, USA From Free Quarks to.

Jim Stewart DESY Measurement of Quark Polarizations in Transversely and Longitudinally Polarized Nucleons at HERMES for the Hermes collaboration Introduction.

General Discussion some general remarks some questions.

Pion mass difference from vacuum polarization E. Shintani, H. Fukaya, S. Hashimoto, J. Noaki, T. Onogi, N. Yamada (for JLQCD Collaboration) December 5,

Nuclear Symmetry Energy from QCD Sum Rule The 5 th APFB Problem in Physics, August 25, 2011 Kie Sang JEONG Su Houng LEE (Theoretical Nuclear and Hadron.

PQCD mechanisms for single (transverse) spin asymmetry in Drell-Yan production PQCD mechanisms for single (transverse) spin asymmetry in Drell-Yan production.

Accessing Orbital Angular Momentum Thru Pion Cloud Itaru Nakagawa RIKEN/RBRC.

1 Keitaro Nagata, Chung-Yuan Christian University Atsushi Hosaka, RCNP, Osaka Univ. Structure of the nucleon and Roper Resonance with Diquark Correlations.

Oct 6, 2008Amaresh Datta (UMass) 1 Double-Longitudinal Spin Asymmetry in Non-identified Charged Hadron Production at pp Collision at √s = 62.4 GeV at Amaresh.

1 Probing Spin and Flavor Structures of the Nucleon with Hadron Beams Flavor and spin structures of the nucleons –Overview and recent results Future prospects.

JPARC DY Workshop, April 7 Ralf Seidl (RBRC) R.Seidl: Transverse Spin 1RIKEN, April 7 In JPARC Drell Yan accessible with: UU(unpolarized beam, unpolarized.

Amand Faessler, Tuebingen1 Chiral Quark Dynamics of Baryons Gutsche, Holstein, Lyubovitskij, + PhD students (Nicmorus, Kuckei, Cheedket, Pumsa-ard, Khosonthongkee,

Thomas Jefferson National Accelerator Facility PAC-25, January 17, 2004, 1 Baldin Sum Rule Hall C: E Q 2 -evolution of GDH integral Hall A: E94-010,

Single-spin asymmetry in interference fragmentation on a transversely polarized hydrogen target at HERMES Tomohiro Kobayashi Tokyo Institute of Technology.

Pentaquark decay width in QCD sum rules F.S. Navarra, M. Nielsen and R.R da Silva University of São Paulo, USP Brazil (  decay width) hep-ph/ (

Tensor and Flavor-singlet Axial Charges and Their Scale Dependencies Hanxin He China Institute of Atomic Energy.

Possible molecular bound state of two charmed baryons - hadronic molecular state of two Λ c s - Wakafumi Meguro, Yan-Rui Liu, Makoto Oka (Tokyo Institute.

GPD and underlying spin structure of the Nucleon M. Wakamatsu and H. Tsujimoto (Osaka Univ.) 1. Introduction Still unsolved fundamental puzzle in hadron.

Convergence of chiral effective theory for nucleon magnetic moments P. Wang, D. B. Leinweber, A. W. Thomas, A. G. Williams and R. Young.

Nuclear Matter Density Dependence of Nucleon Radius and Mass and Quark Condensates in the GCM of QCD Yu-xin Liu Department of Physics, Peking University.

Hadron 2007 Frascati, October 12 th, 2007 P.Faccioli, M.Cristoforetti, M.C.Traini Trento University & I.N.F.N. J. W. Negele M.I.T. P.Faccioli, M.Cristoforetti,

1 NJL model at finite temperature and chemical potential in dimensional regularization T. Fujihara, T. Inagaki, D. Kimura : Hiroshima Univ.. Alexander.

Radiative Decays involving Scalar Mesons Masayasu Harada (Nagoya Univ.) based Japan-US Workshop on “Electromagnetic Meson Production and Chiral Dynamics”

Chiral Approach to the Phi Radiative Decays and the Quark Structure of the Scalar Meson Masayasu Harada (Nagoya Univ.) based HEP-Nuclear Physics Cross.

Choong Sun Kim (C.S. Kim) Department of Physics, Yonsei University, Korea.

Elliptic flow from initial states of fast nuclei. A.B. Kaidalov ITEP, Moscow (based on papers with K.Boreskov and O.Kancheli) K.Boreskov and O.Kancheli)

December 7~11, 2010, BARYONS’10. Contents Motivation –Di-quark Structures in Hadrons Introduction to QCD Sum Rule(QCDSR) QCDSR with Di-quark Eff. Lagrangian.

H. Kamano , M. Morishita , M. Arima ( Osaka City Univ. )

Nuclear Symmetry Energy in QCD degree of freedom Phys. Rev

Direct Detection of Vector Dark Matter

(Anti)Lambda polarization in SIDIS

Gluon Contribution to Dark Matter Direct Detection

Handout 9 : The Weak Interaction and V-A

Nuclear Physics: the Shell Model Magic Numbers (especially stable)

Nuclear Effects in the Proton-Deuteron Drell-Yan Reaction.

March 16, meeting Y. Koike (BNL/Niigata Univ.)

The Structure of Nuclear force in a chiral quark-diquark model

Transversity Distributions and Tensor Charges of the Nucleon

Introduction and Workshop Charge

Polarized Structure Function of Nucleon and Orbital Angular Momentum

Shapes of proton, spin of proton

Neutron EDM with external electric field

in the Rein-Sehgal Model

A possible approach to the CEP location

Institute of Modern Physics Chinese Academy of Sciences

Presentation transcript:

On the Drell-Levy-Yan Relation for Fragmentation Functions T. Ito, W.Bentz(Tokai Univ.) K.Yazaki (Tokyo Woman’s University, and RIKEN) A.W.Thomas (JLab)

DLY Relation: Case of nucleon Using spectral representations (or the reduction formula), one can show the following relations (“Crossing of nucleon line”): local field operator(fermion type: + sign, boson type: - sign); Choose (i)(current operator) in hadronic tensor, (ii)(quark field) in operator definition of quark distribution → DLY relation can be shown in 2 ways:

DLY Relation: (i) hadronic tensor Hadronic tensors for e p → e’ X, and e + e - → p X Crossing gives: for bosons (fermions). Then the DLY relation follows (0 < z < 1): distribution of quark (q) in hadron (h);fragmentation of q into h

DLY Relation: (ii) operator definition Crossing gives again the DLY relation for bosons (+) and fermions (-). (Here 0 < z < 1) origin of factor 1/6: Average over quark spin and color. Important result: For boson case, at x = 1 ! The “generalized distribution” must be must not vanish positive everywhere:

Numerical calculations: valence quarks Use the NJL model and a simple valence quark picture to calculate the generalized distribution function from the Feynman diagrams (nucleon case) Nucleon ≡ quark + scalar diquark Use pole approximation for diquark propagator. Regularization: Transverse cut-off. Parameters: Constituent quark mass M = 0.4 GeV, cut-off Λ Tr = GeV.

Numerical calculations: sea quarks Include sea quark distributions (or: “unfavored” fragmentation process of sea quarks) as an effect of pion cloud around constituent quarks. For the generalized distribution function, we use the convolution formalism to evaluate diagrams like …… Use pole approximation for diquark and pion propagators; on-shell (parent quark) approximation in the convolution integral.

Generalized u V distribution in proton Results at the NJL model scale Red line: without pion cloud Black line:with pion cloud

Generalized u V distribution in π + Results at the NJL model scale Red line: without pion cloud Black line:with pion cloud

u V distribution in proton Results at Red line: without pion cloud Black line:with pion cloud Blue line:Empirical (MRST)

u V fragmentation into proton Results at Red line: without pion cloud Black line:with pion cloud Blue line:Empirical (M.Hirai et al).

u V distribution in π + Results at Red line: without pion cloud Black line:with pion cloud Blue line:Empirical (P.J.Sutton et al) At x = 1: Input artificially set to zero, in order to use the Q 2 evolution program.

u V fragmentation into π + Results at Red line: without pion cloud Black line:with pion cloud Blue line:Empirical (M.Hirai et al). At z = 1: Input artificially set to zero, in order to use the Q 2 evolution program.

Conclusions DLY relation is based on crossing symmetry, and is very general. It expresses the fragmentation function by the distribution function in the “unphysical” region x > 1. Simple chiral quark model describes the distributions (x 1) by factors of 10 ～ 100. Possible reasons for failure: (i)Point NJL vertex functions (ii) On-shell approximation in convolution integrals (iii) What else ??? Thanks to: S.Kumano, M.Miyama, M.Hirai for Q 2 evolution; M.Strattman for discussions.