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Hadron structure and hadronic matter M.Giannini Cortona,13 october 2006

Hadron structure and hadronic matter M.Giannini Cortona,13 october 2006. Introduction Properties of the nucleon Interlude Inclusive and semi-inclusive reactions Quark-antiquark and/or meson cloud effects Conclusion Thanks to colleagues of:

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Hadron structure and hadronic matter M.Giannini Cortona,13 october 2006

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  1. Hadron structure and hadronic matterM.Giannini Cortona,13 october 2006 Introduction Properties of the nucleon Interlude Inclusive and semi-inclusive reactions Quark-antiquark and/or meson cloud effects Conclusion Thanks to colleagues of: Ferrara, Genova, Roma1-2-3, Pavia, Perugia, Trento

  2. Two approaches (very roughly): Microscopic (or systematic): description of hadron properties starting from the dynamics of the particles contained in the hadron - QCD (presently possible only for pQCD) - LQCD (many success, not yet systematic results) - models (eventually based on QCD/LQCD) Phenomenological: parametrization of hadron properties within a theoretical framework, based on general properties of quarks and gluons and/or some aspects of models

  3. Many models have been built and applied to the description of hadron properties: Constituent Quark Models: Isgur-Karl, Capstick Isgur (*) (CQM) algebric U(7) quarks as effective hypercentral (*) degrees of freedom Goldstone Boson Exchange (*) (non zero mass, size?) Instanton interaction ……. Skyrmion Soliton models Chiral models Instanton models (*) …… a systematic approach is more easily followed with CQMs (*) quoted in this talk

  4. Properties of the nucleon • Spectrum • Form factors • Elastic • e. m. transitions • Time-like A system having an excitation spectrum and a size is composite (Ericson-Hüfner 1973)

  5. Nucleon excitation spectrum -> baryon resonances (masses up to 2 GeV) Comment The description of the spectrum is the first task of a model builder: it serves to determine a quark interaction to be used for the description of other physical quantitites LQCD (De Rújula, Georgi, Glashow, 1975) the quark interaction contains a long range spin-independent confinement a short range spin dependent term Spin-independence SU(6) configurations

  6. 3 Constituent quark models for baryons • Isgur-Karl (IK) => Capstick-Isgur (CI) relat. KE, linear three-body confinement + OGE • Glozman-Riska-Plessas (GBE) relat. KE, linear two-body confinement + flavour dependent Goldstone Boson (p, k,..) Exchange (Yukawa type) • Hypercentral CQM (Genova) (hCQM) non relat. KE, linear three-body confinement and coulomb-like +OGE  the interaction can be considered as the hypercentral approximation of the two-body LQCD interaction and/or containing three-body forces Improvements: inclusion of relativistic KE and isospin dependent interaction x - / x x =  +  hyperradius

  7. Goldstone Boson Exchange

  8. x =   hyperradius

  9. Quark-antiquark lattice potential G.S. Bali Phys. Rep. 343, 1 (2001) V = - b/r + c r

  10. Nucleon form factors -> charge and magnetic distribution 4 ff: GpE , GpM , GnE , GnM Renewed experimental interest Jefferson Lab (Hall A) data on GpE/GpM • Important theoretical issue: relativity • Relativistic equation (Bethe-Salpeter like) (Bonn) • Relativistic hamiltonian formulation • according to Dirac (1949): three forms • light front, point form, instant form • (Rome) (Graz-PV, GE) (PV) • main differences: • - realization of the Poincaré group • - number of generators which are interaction dependent

  11. - elastic scattering of polarized electrons on polarized protons • measurement of polarizations asymmetry gives directly the ratio GpE/GpM • discrepancy with Rosenbluth data (?) • linear and strong decrease • pointing towards a zero (!)

  12. Rome group CQM: CI LF WF full curve: with quark ff dotted curve: without quark ff

  13. Graz-Pavia: Point Form Spectator Approximation (PFSA) CQM: GBE Dashed curve: NRIA (Non relativistic impulse approximation) Neutron electric ff: SU(6) violation Dash-dotted confinement only Boffi et al., EPJ A14, 17 (2002) See also the talk by Melde

  14. M.G., E. Santopinto, M. Traini, A. Vassallo, to be published V(x) = - /x + x  and t not much different from the NR case

  15. Boosts to initial and final states • Expansion of current to any order • Conserved current Calculated values! GMp GEp GEn GMn M. De Sanctis, M. G., E. Santopinto, A. Vassallo, nucl-th/0506033

  16. GMp Fit with quark form factors GEn

  17. Interacting quark-diquark model • the effective degrees of freedom are a diquark and a quark- the diquark is thought as two correlated quarks- Regge trajectories-> string model- many states predicted by 3q CQM have been never seen (missing resonances)- q-diquark: no missing states in the lower part of the spectrum very few in the upper part first quantitative constituent q-diquark model encoding the idea of Wilczeck of two types of diquarks: the scalar and vector diquark: E.Santopinto, Phys. Rev. C (2005)

  18. Results for the Interacting quark-diquark model Quark-diquark interaction: linear + coulomb-like exchange (spin and isospin dependent

  19. Charge form factor of the proton

  20. Time-like Nucleon form factors Observable in Motivations: • Dispersion relations require: GM(q2<0)  GM(q2>0) q2 ∞ • Neutron data from FENICE TL data fit data are obtained after integration over Angles (low statistics) and assuming SL data fit |GE| = |GM| GE unknown  phases of GE & GM unknown

  21. Exp reactions: PANDA Recent interest of DAFNE for upgrade at q2 < (2.5)2 GeV2 working groups of Gr.1 and Gr.3 for triennal INFN plan Various authors + Radici, hep-ex/0603056 submitted a E.P.J C unpolarized The cross section can be written as the sum of a Born (|GE/GM|) and a non Born (2 exchange) term polarized : Born: contains sin(GM-GE) Bianconi, Pasquini, Radici, P.R.D74 (06); hep-ph/0607277

  22. Electromagnetic transitions -> helicity amplitudes for e.m. excitation of nucleon resonances Virtual photon N*,  NR N LF Pace et al.

  23. hCQM, J. Phys. G (1998)

  24. m = 3/2 m = 1/2 Blue curves hCQM Green curves H.O.

  25. N  helicity amplitudes red fit by MAID blue hCQM dashed π cloud contribution (Mainz) GE-MZ coll., EPJA 2004 (Trieste 2003)

  26. please note • the calculated proton radius is about 0.5 fm (value previously obtained by fitting the helicity amplitudes) • not good for elastic form factors (increased by rel. corr.) • there is lack of strength at low Q2 (outer region) in the e.m. transitions • emerging picture: quark core (0.5 fm) plus (meson or sea-quark) cloud

  27. Interlude

  28. Interplay between models and LQCD LQCD: 1) many observables of interest (time-like ff, GPD) cannot be related to quantities calculable on the lattice 2) it is not easy to understand how dynamics is working 3) results are obtained for high quark masses (> 100 MeV for u,d quarks) hence mπ > 350 MeV) Goal: combine LQCD calculations with accurate phenomenological models in order to interpret and eventually guide LQCD results Talk by Cristoforetti Trento-MIT programme Knowing how LQCD observables depend on the quark mass, on can extrapolate Two regimes: Chiral: mπ -> 0 the dependence on quark mass determined by the chiral Perturbation Theory (PT) “Quark model”: large masses (mπ ≥ m ) hadron masses scale with quark masses

  29. transition between the chiral and quark regime which is the origin? at which quark mass m it happens? Studied with the IILM Interacting Instanton Liquid Model Why IILM? - instanton appear to be the dynamical mechanism responsible for the chiral symmetry breaking - masses and electroweak structure of nucleon and pion are correctly reproduced - one phenomenological parameter, instanton size (already known) The transition scale is related to the eigenvalue spectrum of the Dirac operator in an Instanton background The quasi-zero mode spectrum is peaked at m*≈ 80 MeV For mq < m* chiral effects dominates Cristoforetti, Faccioli, Traini, Negele, hep-ph/0605256

  30. Kabc 3-point correlator mq Kabc / rm=0(0) PT predicts it is a constant as a function of the quark mass It can be calculated independently with IILM With IILM one can calculate the nucleon mass for different values of mπ The results agree with the lattice calculations By CP-PACS if the instanton size is 0.32 fm IILM is able to reproduce results in the chiral and quark regime

  31. Inclusive and semi inclusive reactions • Nucleon structure functions • Generalized Parton Distributions (GPD) • Drell-Yan

  32. Leading and higher twist in the moments of the nucleon and deuteron stucture function F2 Simula, Osipenko, Ricco and CLAS coll. two definitions of the moments: Main difference: Nachtmann moments are free from target-mass corrections (which depend on the x-shape of the leading twist) m = nucleon mass twist analysis

  33. proton • LT important at all Q2 • LT dominant for n=2 • HT<~0 at low Q2 • HT>0 at large Q2 • HT comes from partial cancellation of twists with opposite signs n=2 n=4 Similar results for the deuteron n=6 n=8

  34. leading twist moments of the neutron F2 [NPA 766 (2006), in collaboration with S. Kulagin and W. Melnitchouk] nuclear effects in deuteron at moderate and large x (x > 0.1): p (q) = virtual nucleon (photon) 4-momentum pD = deuteron 4-momentum Relativistic deuteron spectral function off shell nucleon structure function - traditional decomposition: usual convolution formula: on-shell nucleon F2 and light-cone momentum distribution in D all the rest: relativistic, off-shell effects, … the decomposition is not unique two models Kulagin-Petti Melnitchouk Differ in Dn(off)

  35. neutron leading twist good statistical and systematic precision n=2 n=4 at large Q2 good agreement with neutron moments obtained from existing NLO PDF’s n=6 n=8 at low Q2 the extracted LT runs faster than the PDF prediction @ NLO

  36. Generalized Parton Distributions (GPD)

  37. GPDs depend on two momentum fractions and unpol. long. pol. GPDs transv. pol. Generalized Parton Distributions in Exclusive Virtual Photoproduction *(q) , *, , , . . . hard Q2 = -q2 >> t = (P-P’)2 << x +  x -  soft GPDs P,S P’,S’ P,S P’,S’ t + G = +5 is+5 (chiral odd) average fraction of the longitudinal momentum carried by partons skewness parameter: fraction of longitudinal momentum transfer t-channel momentum transfer squared

  38. Parton interpretation of GPD Quark-antiquark DGLAP ERLB DGLAP ERLB Efremov-Radyshkin-Brodsky-Lepage DGLAP Dokschitzer-Gribov-Lipatov-Altarelli-Parisi

  39. Non pol GPD for u,d quarks (similar results for helicity GPD) GBE model hCQM with relat. KE no OGE Light cone wave functions Fixed t = -0.5 GeV2  = 0 (solid) 0.1 (dashed) 0.2 (dotted) Boffi, Pasquini, Traini NP B, 2003 & 2004

  40. In the forward limit f1q (unpolarized distribution) g1q (longitudinal polarization or helicity distribution) h1q (transverse polarization or transversity distribution) - Assuming that the calculated GPQ correspond to the hadronic scale m02 ≈ 0.1 GeV2 - Performing a NLO evolution up to Q2 = 3 GeV2 one can calculate the measured asymmetries Beyond x=0.3 (valence quarks only) Dashed curves: no evolution

  41. Chiral-odd GPD Pavia group: overlap representation instant form wf rel hCQM (no OGE) Fixed t = -0.5 GeV2  = 0 (solid) 0.1 (dashed) 0.2 (dotted) See talk by Pincetti Scopetta Vento Quarks are complex systems containing partons of any type Convolution of the quark GPD with the NR IK CQM wf Respect of: forward condition, integral of , polynomial condition Scopetta Simple MIT bag model (only HT is non vanishing)

  42. HT HT Scopetta-Vento PR D71 (2005) Scopetta PR D72 (2005)

  43. Motivations for SIDIS spin asymmetry Radici et al. Goal: - integrate over PhT=(P1+P2)T; asimmetry in RT=(P1-P2)T, that is in R ; - extract transversity h1 through coming from the interference of the hadron pair (h1h2) produced in s or in p wave Dihadron fragm Function DiFF from e+e- ()()X in the Belle experiment (KEK) pp collisions possible at RHIC-II Problem (Jaffe) change of sign? s-p interf. from  elastic phase shifts spectator model calculation of from Im [ interf. of two channels ] confronto con Hermes e Compass Bacchetta-Radici

  44. DRELL - YAN

  45. Spin asymmetry in (polarized) Drell-Yan Spin asymmetries in collisions with transversely polarized hadrons: First measure at BNL in ‘76 At high energies asymmetries reach 40% (not explained by pQCD) Sivers effect Collins-Soper frame Boer-Mulders function + less important terms transversity h1 can be extracted

  46. In a series of papers by Bianconi and Radici: Monte Carlo Simulations and measurability of the various effects (Sivers, Boer Mulders, transversity h1) in different kinematical conditions PAX / ASSIA at GSI, RHIC-II, COMPASS test on the change of sign of the Sivers function in SIDIS and Drell-Yan (predicted by general properties) 100.000 - events (black triangles) 25.000 + events (open blue triangles) The corresponding squares are obtained changing the sign of the Sivers function, obtained from the parametrization of P.R.D73 (06) 034018 Statistical error bars x2 is the parton momentum in p↑

  47. Di Salvo General parametrization of the correlator entering in the cross section (in particular the twist 2 T-even component) Comparison with the density matrix of a confined quark (interaction free but with transverse momentum) simple relations valid also after Evolution (Polyakov) choice (normalization) nucleon momentum for The asymmetry turns out to be That is proportional to 1/Q2

  48. ATT/aTT > 0.2 Models predict |h1u|>>|h1d| Drago ATT for PAX kinematic conditions PAX: M2~10-100 GeV2, s~45-200 GeV2, τ=x1x2=M2/s~0.05-0.6 →Exploration ofvalence quarks(h1q(x,Q2) large)

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