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

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The description of the spectrum is the first task of a model builder: ... the calculated proton radius is about 0.5 fm ... By CP-PACS if the instanton size is 0.32 fm ... – PowerPoint PPT presentation

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


1
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

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 -gt 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

7
3 Constituent quark models for baryons
  • Isgur-Karl (IK) gt 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 ?? ??
hyperradius
??x - ??/ x
8
Goldstone Boson Exchange
9
x
???? ?????
hyperradius
10
Quark-antiquark lattice potential
G.S. Bali Phys. Rep. 343, 1 (2001)
V - b/r c r
11
Nucleon form factors -gt 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

12
  • - 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 (!)

13
Rome group CQM CI LF WF
full curve with quark ff dotted
curve without quark ff
14
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
15
M.G., E. Santopinto, M. Traini, A. Vassallo, to
be published
V(x) - ?/x ??x
? and t not much different from the NR case
16
  • 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
17
GMp
Fit with quark form factors
GEn
18
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-gt 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)
19
Results for the Interacting quark-diquark model
Quark-diquark interaction linear coulomb-like

exchange (spin and isospin dependent
20
Charge form factor of the proton
21
Time-like Nucleon form factors Observable in
Motivations
  • Dispersion relations require GM(q2lt0) ? GM(q2gt0)
    q2 ? 8

TL data fit
  • Neutron data from FENICE

data are obtained after integration over Angles
(low statistics) and assuming
SL data fit
GE GM
? GE unknown
? phases of GE GM unknown
22
Exp reactions
PANDA
Recent interest of DAFNE for upgrade at q2 lt
(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
23
Electromagnetic transitions -gt helicity
amplitudes for e.m. excitation of nucleon
resonances
Virtual photon
N, ?
NR
N
LF
Pace et al.
24
hCQM, J. Phys. G (1998)
25
m 3/2
m 1/2
Blue curves hCQM
Green curves H.O.
26
N ?? helicity amplitudes
red fit by MAID blue hCQM dashed p cloud
contribution (Mainz)
GE-MZ coll., EPJA 2004 (Trieste 2003)
27
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

28
Interlude
29
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 (gt 100 MeV for u,d
quarks) hence mp gt 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 mp -gt 0 the dependence on
quark mass determined by the chiral Perturbation
Theory (?PT) Quark model large masses (mp
m? ) hadron masses scale with quark masses
30
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 lt m chiral effects dominates
Cristoforetti, Faccioli, Traini, Negele,
hep-ph/0605256
31
mq Kabc / rm0(0)
Kabc 3-point correlator
?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 mp
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
32
Inclusive and semi inclusive reactions
  • Nucleon structure functions
  • Generalized Parton Distributions (GPD)
  • Drell-Yan

33
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
34
proton
  • LT important at all Q2
  • LT dominant for n2
  • HTlt0 at low Q2
  • HTgt0 at large Q2
  • HT comes from partial cancellation of twists
    with opposite signs

n4
n2
Similar results for the deuteron
n6
n8
35
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 gt 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)
36
neutron leading twist
good statistical and systematic precision
n4
n2
at large Q2 good agreement with neutron moments
obtained from existing NLO PDFs
n6
n8
at low Q2 the extracted LT runs faster than the
PDF prediction _at_ NLO
37
(No Transcript)
38
Generalized Parton Distributions (GPD)
39
Generalized Parton Distributions in Exclusive
Virtual Photoproduction

?(q)
?, ?, ?, ??, . . .
hard
Q2 -q2 gtgt t (P-P)2 ltlt
x - ?
x ?
soft
GPDs
P,S
P,S
P,S
P,S
t
?
??5
G
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
40
Parton interpretation of GPD
Quark-antiquark
DGLAP ERLB DGLAP
ERLB Efremov-Radyshkin-Brodsky
-Lepage
DGLAP Dokschitzer-Gribov-Lipa
tov-Altarelli-Parisi
41
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
42
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 x0.3 (valence quarks only)
Dashed curves no evolution
43
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)
44
HT
HT
Scopetta-Vento PR D71 (2005)
Scopetta PR D72 (2005)
45
SIDIS spin asymmetry
Motivations for
Radici et al.
Goal - integrate over PhT(P1P2)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 ee- (??)(??)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
46
DRELL - YAN
47
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
48
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?
49
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
50
Drago
ATT for PAX kinematic conditions
PAX M210-100 GeV2, s45-200 GeV2,
tx1x2M2/s0.05-0.6 ? Exploration of valence
quarks (h1q(x,Q2) large)
51
Measuring the Sivers function
Direct access to Sivers function
Sivers function
usual parton distribution
test QCD basic result
J. Collins
process dominated by no Collins contribution
usual fragmentation 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/Nc .
52
Quark-antiquark and/or meson cloud effects
From valence quarks to the next Fock-state
component
(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)

53
Exotic states
  • Pentaquark four quarks antiquark (example
    S1 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
  • Tetraquark
  • There seems to be phenomenological evidence
  • Theoretical description in agreement with the
    observed spectrum

54
Tetraquark spectroscopy
Complete classification of states in terms of
O(3) ?SUsf(6) ? SUc(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.
talk by Galatà
E. Santopinto, G. Galatà
55
Meson-Cloud Model for GPD
Boffi-Pasquini
the physical nucleon N is made of a bare
nucleon dressed by a surrounding
meson cloud
Light cone hamiltonian (with meson-baryon
coupling)
One-meson approximation
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
56
  • 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 -? lt x lt? Describe the
emission of a Quark-antiquark pair From the
initial nucleon
57
?-dependence at fixed t -0.5
t-0.5 ?0.1
Convolution formalism LCWF hCQM (rel KE, no OGE)
for the baryon h.o. wave funtion for the pion
t-0.5 ?0.3
B. Pasquini, S. Boffi, PRD73 (2006) 094029
58
Similar approach with the hCQM
Vertex (Thomas) similar to Boffi-Pasquini Used
for elastic for factors and helicity amplitudes
D. Y. Chen, Y. B. Dong, M. G., E. Santopinto,
Trieste Conf., May 2006
59
Some results
Proton electric ff
Proton magnetic ff
  • bare nucleon
  • active nucleon
  • c) meson

60
Rome group
valence pair production
Photon vertex
Quark-pion amplitude (BS)
Pion absorption by a quark
Unified description of TL and SL ff Importance of
instantaneous terms Model meson wf Some free
parameters
Vector meson dominance
De Melo, Frederico, Pace, Pisano, Salme
61
Blue and red curve different values of the
relative weight of the instantaneous terms
62
Similarly for the nucleon
triangle (or elastic)
non valence
Talk by Pisano
Quark-nucleon amplitude from an effective
lagrangian density Araujo et al. PL b (2000)
Dotted curve triangle contribution Full
curve total contribution
63
(No Transcript)
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