#### Transcript GDR-PH-QCD, IPNO 7/XII/2012

Modelling Hadron Form Factors Egle Tomasi-Gustafsson IRFU, SPhN-Saclay, and IN2P3- IPN Orsay GDR-PH-QCD, IPNO 7/XII/2012 IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 1 IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 2 Polarization experiments - Jlab A.I. Akhiezer and M.P. Rekalo, 1967 GEp collaboration 1) "standard" dipole function for the nucleon magnetic FFs GMp and GMn 2) linear deviation from the dipole function for the electric proton FF Gep 3) QCD scaling not reached 3) Zero crossing of Gep? 4) contradiction between polarized and unpolarized measurements A.J.R. Puckett et al, PRL (2010) IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 3 Issues • Some models (IJL 73, Diquark, soliton..) predicted such behavior before the data appeared BUT • Simultaneous description of the four nucleon form factors... • ...in the space-like and in the time-like regions • Consequences for the light ions description • When pQCD starts to apply? • Source of the discrepancy IPNO, Kolomna, 7-XII-201211-VI-2010 Egle TOMASI-GUSTAFSSON 4 Proton form factors at large q2 L = 2 10 32 cm-2 s-1 Connection with QCD asymptotics? 100 days Applies to NN and NN Interaction (Pomeranchuk theorem) t=0 : not a QCD regime! E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) IPNO, 7-XII-2012 E. T-G. e-Print: arXiv:0907.4442 [nucl-th] Egle TOMASI-GUSTAFSSON 5 The nucleon: homogenous, symmetric sphere? Analogy with Gravitation Coulomb Potential ~ Gravitational Potential Mass~charge 1/r • Spherical symmetric distributed mass density, • A point at a distance r<R from the center feels only the matter inside works for the SCALAR part, NOT for the → VECTOR part of A=(Φ, A) R= r~0.7 fm → Q= 0.29 GeV R~1/Q3 is NOT the experimental behavior IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 6 The nucleon 3 valence quarks and a neutral sea of qq pairs antisymmetric state of colored quarks Main assumption Does not hold in the spatial center of the nucleon: the center of the nucleon is electrically neutral, due to strong gluonic field IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 7 The nucleon Inner region: gluonic condensate of clusters with randomly oriented chromo-magnetic field (Vainshtein, 1982): Intensity of the gluon field in vacuum: In the internal region of strong chromo-magnetic field, the color quantum number of quarks does not play any role, due to stochastic averaging didj IPNO, 7-XII-2012 proton neutron Egle TOMASI-GUSTAFSSON 8 Model Antisymmetric state of colored quarks Colorless quarks: Pauli principle 1) uu (dd) quarks are repulsed from the inner region 2) The 3rd quark is attracted by one of the identical quarks, forming a compact di-quark 3) The color state is restored Formation of di-quark: competition between attraction force and stochastic force of the gluon field proton: (u) Qq=-1/3 neutron: (d) Qq=2/3 attraction force >stochastic force of the gluon field IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 9 Model attraction force > stochastic force of the gluon field Proton: r0=0.22 fm, p02 = 1.21 GeV2 Neutron: r0=0.31 fm, p02 = 2.43 GeV2 Applies to the scalar part of the potential IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 10 Model Quark counting rules apply to the vector part of the potential IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 11 Model Additional suppression for the scalar part due to colorless internal region: “charge screening in a plasma”: Neutrality condition: Additional suppression (Fourier transform) IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON Boltzmann constant fitting parameter 12 Fourier Transform Root mean square radius Perugia, 18-XII-2012 Egle TOMASI-GUSTAFSSON 13 Model: generalized form factors Definition: space-time distribution of the electric charge in the space-time volume In SL- Breit frame (zero energy transfer): In TL-(CMS): : time evolution of the charge distribution in the domain IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 14 The annihilation channel: 1) Creation of a pp state through intermediate state with 2) The vacuum state transfers all the released energy to a state of matter consisting of: • 6 massless valence quarks • Set of gluons • Sea of current qq pairs of quarks with energy q0>2Mp, J=1, dimensions 3) Pair of p and p formed by three bare quarks: •Structureless •Colorless pointlike FFs !!! IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 15 The annihilation channel: • The point-like hadron pair expands and cools down: the current quarks and antiquarks absorb gluon and transform into constituent quarks • The residual energy turns into kinetic energy of the motion with relative velocity • The strong chromo-EM field leads to an effective loss of color. Fermi statistics: identical quarks are repulsed. The remaining quark of different flavor is attracted to one of the identical quarks, creating a compact diquark (du-state) IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 16 The annihilation channel: The neutral plasma acts on the distribution of the electric charge (not magnetic). Prediction: additional suppression due to the neutral plasma similar behavior in SL and TL regions • Implicit normalization at q2=4Mp2: |GE|=|GM| =1 • No poles in unphysical region IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 17 The annihilation channel: The repulsion of p and p with kinetic energy is balanced by the confinement potential • • The long range color forces create a stable colorless state of proton and antiproton The initial energy is dissipated from current to constituent quarks originating on shell separated by R. IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 18 The annihilation channel: At larger distances, the inertial force exceeds the confinement force: p and p start to move apart with relative velocity p and p leave the interaction region: at large distances the integral of Q(t) must vanish. For very small values of the velocity FSI lead to the creation of a bound NN system . IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 19 Space-Like region GEp polarization GEp dipole GEn IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 20 Proton Form Factors GEp polarization GEp dipole |GMp|=|GEp| GMp IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 21 Neutron TL region IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 22 Time-Like region R=|GEp|/|GMp| Not a fit Ps178 BaBar Dafne E835 IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 23 Point-like form factors? S. Pacetti IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 24 Point-like form factors? S. Pacetti IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 25 Point-like form factors? S. Pacetti IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 26 Hadron Form Factors: Conclusions New, interesting results in Space-like and Timelike regions VEPP-Novosibirsk IHEP Unified model in SL and TlL regions • pointlike behavior at threshold • complex FFs due to to FSI , vanishing at asymptotics • spin one intermediate state dynamical polarization of p and p? IPNO, 7-XII-2012 Egle TOMASI-GUSTAFSSON 27