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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: Ferrara, Genova, Roma1-2-3, Pavia, Perugia, Trento

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Two approaches (very roughly): 1)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) 2)Phenomenological: parametrization of hadron properties within a theoretical framework, based on general properties of quarks and gluons and/or some aspects of models

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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

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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)

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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

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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 ( 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 = + hyperradius x - / x

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Goldstone Boson Exchange

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x = hyperradius

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

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Nucleon form factors -> charge and magnetic distribution 4 ff: G p E, G p M, G n E, G n M Renewed experimental interest Jefferson Lab (Hall A) data on G p E /G p M 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

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- elastic scattering of polarized electrons on polarized protons - measurement of polarizations asymmetry gives directly the ratio G p E /G p M - discrepancy with Rosenbluth data (?) - linear and strong decrease - pointing towards a zero (!)

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

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

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

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GEpGEp GEnGEn GMnGMn GMpGMp Calculated values! Boosts to initial and final states Expansion of current to any order Conserved current M. De Sanctis, M. G., E. Santopinto, A. Vassallo, nucl-th/0506033

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Fit with quark form factors GMpGMp GEnGEn

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-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 Interacting quark-diquark model 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)

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

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Charge form factor of the proton

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Time-like Nucleon form factors Observable in TL data fit SL data fit Motivations: -Dispersion relations require: G M (q 2 0) q 2 ∞ - Neutron data from FENICE data are obtained after integration over Angles (low statistics) and assuming |G E | = |G M | G E unknown phases of G E & G M unknown

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

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

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hCQM, J. Phys. G (1998)

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

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

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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 Q 2 (outer region) in the e.m. transitions emerging picture: quark core (0.5 fm) plus (meson or sea-quark) cloud

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Interlude

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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 m π > 350 MeV) Goal: combine LQCD calculations with accurate phenomenological models in order to interpret and eventually guide LQCD results Trento-MIT programme Knowing how LQCD observables depend on the quark mass, on can extrapolate Two regimes: Chiral: m π -> 0 the dependence on quark mass determined by the chiral Perturbation Theory ( PT) “Quark model”: large masses (m π ≥ m ) hadron masses scale with quark masses Talk by Cristoforetti

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Cristoforetti, Faccioli, Traini, Negele, hep-ph/0605256 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 m q < m* chiral effects dominates

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PT predicts it is a constant as a function of the quark mass It can be calculated independently with IILM m q K abc / m=0 (0) K abc 3-point correlator With IILM one can calculate the nucleon mass for different values of m π 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

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

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Leading and higher twist in the moments of the nucleon and deuteron stucture function F 2 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

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

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leading twist moments of the neutron F 2 [NPA 766 (2006), in collaboration with S. Kulagin and W. Melnitchouk] p (q) = virtual nucleon (photon) 4-momentum p D = deuteron 4-momentum nuclear effects in deuteron at moderate and large x (x > 0.1): all the rest: relativistic, off-shell effects, … usual convolution formula: on-shell nucleon F 2 and light-cone momentum distribution in D - traditional decomposition: the decomposition is not unique two models off shell nucleon structure function Relativistic deuteron spectral function Kulagin-Petti Melnitchouk Differ in n (off)

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

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Generalized Parton Distributions (GPD)

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

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

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Light cone wave functions GBE model hCQM with relat. KE no OGE Boffi, Pasquini, Traini NP B, 2003 & 2004 Non pol GPD for u,d quarks (similar results for helicity GPD) Fixed t = -0.5 GeV 2 = 0 (solid) 0.1 (dashed) 0.2 (dotted)

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In the forward limit f 1 q (unpolarized distribution) - Assuming that the calculated GPQ correspond to the hadronic scale 0 2 ≈ 0.1 GeV 2 - Performing a NLO evolution up to Q 2 = 3 GeV 2 Beyond x=0.3 (valence quarks only) one can calculate the measured asymmetries Dashed curves: no evolution g 1 q (longitudinal polarization or helicity distribution) h 1 q (transverse polarization or transversity distribution)

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Chiral-odd GPD Pavia group: overlap representation instant form wf rel hCQM (no OGE) Fixed t = -0.5 GeV 2 = 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 ScopettaSimple MIT bag model (only H T is non vanishing)

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Scopetta-Vento PR D71 (2005) Scopetta PR D72 (2005) HTHT HTHT

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SIDIS spin asymmetry Goal: - integrate over P hT =(P 1 +P 2 ) T ; asimmetry in R T =(P 1 -P 2 ) T, that is in R ; - extract transversity h 1 through coming from the interference of the hadron pair (h 1 h 2 ) produced in s or in p wave Motivations for from e + e - ( )( )X in the Belle experiment (KEK) pp collisions possible at RHIC-II Radici et al. Problem change of sign? (Jaffe) s-p interf. from elastic phase shifts spectator model calculation of from Im [ interf. of two channels ] Bacchetta-Radici Dihadron fragm Function DiFF confronto con Hermes e Compass

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DRELL - YAN

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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) + less important terms transversity h 1 can be extracted Boer-Mulders function Sivers effect Collins-Soper frame

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Monte Carlo Simulations and measurability of the various effects (Sivers, Boer Mulders, transversity h 1 ) 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 In a series of papers by Bianconi and Radici: x 2 is the parton momentum in p ↑

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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 choice (normalization) for nucleon momentum The asymmetry turns out to be That is proportional to 1/Q 2 valid also after Evolution (Polyakov)

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PAX: M 2 ~10-100 GeV 2, s~45-200 GeV 2, =x 1 x 2 =M 2 /s~0.05-0.6 → Exploration of valence quarks (h 1 q (x,Q 2 ) large) A TT for PAX kinematic conditions A TT /a TT > 0.2 Models predict |h 1 u |>>|h 1 d | Drago

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Sivers function usual parton distribution Direct access to Sivers function test QCD basic result: J. Collins usual fragmentation function process dominated by no Collins contribution Measuring the Sivers function Sivers function non-vanishing in gauge theories. Chiral models with vector mesons as gauge bosons can be used Drago, PRD71(2005) (Sivers) u = -(Sivers) d in chiral models at leading order in 1/N c.

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Quark-antiquark and/or meson cloud effects (at the hadron scale) Exotic states (Genova) Meson cloud contributions in various processes GPD (Pavia) elastic and inelastic nucleon form factors (Genova-Pechino) pion and nucleon form factors (Roma) Unquenching the CQM (Genova) From valence quarks to the next Fock-state component

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Exotic states 1)Pentaquark: four quarks + antiquark (example S=1 baryon) no theoretical reason against their existence presently no convincing experimental evidence Why? - not bound - not observable (too large width and/or too low cross section 2)Tetraquark: There seems to be phenomenological evidence Theoretical description in agreement with the observed spectrum

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Complete classification of states in terms of O(3) SU sf (6) SU c (3) (useful for both model builders and experimentalists) The explicit have been explicitly constructed Mass formula (encoding the symmetries) gives predictions for the scalar nonets in agreement with the KLOE results. E. Santopinto, G. Galatà Tetraquark spectroscopy talk by Galatà

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Meson-Cloud Model for GPD Boffi-Pasquini the physical nucleon N is made of a bare nucleon dressed by a surrounding meson cloud One-meson approximation Light cone hamiltonian (with meson-baryon coupling) Baryon-Meson fluctuation probability amplitude for a nucleon to fluctuate into a (BM) system Z: probability of finding the bare N in the Physical N

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during the interaction with the hard photon, there is no interaction between the partons in a multiparticle Fock state the photon can scatter either on the bare nucleon (N) or one of the constituent in the higher Fock state component (BM) valence quark baryon-meson substate GPDs in the region - < x < : Describe the emission of a Quark-antiquark pair From the initial nucleon

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active meson bare proton active baryon totale dependence at fixed t= -0.5 t=-0.5 =0.1 t=-0.5 =0.3 u + d u - d H u+d H u-d E u+d E u-d B. Pasquini, S. Boffi, PRD73 (2006) 094029 Convolution formalism LCWF hCQM (rel KE, no OGE) for the baryon h.o. wave funtion for the pion

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Similar approach with the hCQM D. Y. Chen, Y. B. Dong, M. G., E. Santopinto, Trieste Conf., May 2006 Vertex (Thomas) similar to Boffi-Pasquini Used for elastic for factors and helicity amplitudes

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Some results: Proton electric ff Proton magnetic ff a)bare nucleon b)active nucleon c)meson

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De Melo, Frederico, Pace, Pisano, Salme’ Photon vertex Quark-pion amplitude (BS) Pion absorption by a quark valence pair production Unified description of TL and SL ff Importance of instantaneous terms Model meson wf Some free parameters Vector meson dominance Rome group

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Blue and red curve: different values of the relative weight of the instantaneous terms

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Similarly for the nucleon Quark-nucleon amplitude from an effective lagrangian density Araujo et al. PL b (2000) triangle (or elastic)non valence Talk by Pisano Dotted curve: triangle contribution Full curve: total contribution

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