Transcript Hadron structure and hadronic matter M.Giannini Cortona,13

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
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
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
(*)
(*)
(*)
(*)
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)
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
PDG
4* & 3*
    
   
   
M
2
(GeV)
F37
P33''
F35
P31
1.8
+
+
(56,2 )
(70,0 )
P13
F15
P11''
P33'
1.6
S11
D13
+
(56,0 )'
P11'
1.4
P33
1.2
(56,0+)
1
0.8
(70,1-)
D33 D13'
D15
S11'
S31
P11
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
x - / x
x =  + 
hyperradius
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
Goldstone Boson Exchange
x =  
hyperradius
Quark-antiquark lattice potential
G.S. Bali Phys. Rep. 343, 1 (2001)
V = - b/r + c r
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
- 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 (!)
Rome group
CQM: CI
LF WF
full curve: with
quark ff
dotted curve: without quark ff
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
M.G., E. Santopinto, M. Traini, A. Vassallo, to be published
V(x) = - /x + x
 and  not much different
from the NR case
•Boosts to initial and final states
Calculated values!
•Expansion of current to any order
•Conserved current
GEp
GMp
GEn
GMn
M. De Sanctis, M. G., E. Santopinto, A. Vassallo, nucl-th/0506033
G Mp
Fit with quark form factors
G En
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)
Results for the Interacting quark-diquark model
Quark-diquark interaction: linear + coulomb-like
exchange (spin and isospin dependent
Charge form factor of the proton
Time-like Nucleon form factors
Observable in
Motivations:
-Dispersion relations require: GM(q2<0)  GM(q2>0) q2  ∞
- Neutron data from FENICE
data are obtained after integration over
Angles (low statistics) and assuming
|GE| = |GM|
TL data fit
SL data fit
 GE unknown
 phases of GE & GM unknown
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
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
Various authors + Radici,
hep-ex/0603056
submitted a E.P.J C
Electromagnetic transitions
-> helicity amplitudes for e.m. excitation of nucleon resonances
Virtual photon
N*, 
N
NR
LF
Pace et al.
hCQM, J. Phys. G (1998)
m = 3/2
m = 1/2
Green curves H.O.
Blue curves hCQM
N
 helicity amplitudes
red fit by MAID
blue hCQM
dashed π cloud contribution (Mainz)
GE-MZ coll., EPJA 2004 (Trieste 2003)
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
Interlude
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
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
mq Kabc / m=0(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 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
Inclusive and semi inclusive reactions
• Nucleon structure functions
• Generalized Parton Distributions (GPD)
• Drell-Yan
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:
 

CN moments: M nCN  Q2   dx x n2 F2 x,Q2
1
0
( Nacht .)
Nachtmann moments: M n
1
 n1
0
x3
Q   dx
2

3  3n 1r  n n  2 r 2
F2 x,Q
n  2 n  3

2

  2x 1 r , r  1 1 4m 2 x 2 Q 2
Main difference: Nachtmann moments are free from target-mass corrections
(which depend on the x-shape of the leading twist)
CN 
Mn
Q  M
2
Nacht .
n
 
m2
m4
Q  a 2  b 4  ...
Q
Q
2
m = nucleon mass
twist analysis
M
( Nacht .)
n
 n4 
 n6 
an4 
an6
2
2
Q  n Q  2  s Q   4  s Q 
Q
Q
2
2
 
 
 n Q 2 : leading twist
an4 ,  n4  and an6,  n6: effective strenghts and anomalous dimensions of HT
[free parameters]
proton
• LT important at all Q2
• LT dominant for n=2
n=2
n=4
• HT<~0 at low Q2
• HT>0 at large Q2
• HT comes from partial
cancellation of twists
with opposite signs
Similar results for the
deuteron
n=6
n=8
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):


F2D x,Q 2 IA
  d 4 p Tr Wˆ  p, q  gAˆ p, pD 
pD = deuteron 4-momentum
Relativistic deuteron spectral function
off shell nucleon structure function



usual convolution formula: on-shell nucleon F2
and light-cone momentum distribution in D
the decomposition is not unique
 


F2D x,Q 2  F2D(conv.) x,Q 2   F2D x,Q 2
- traditional decomposition:
f
D
n

all the rest: relativistic,
off-shell effects, …
two models
  M 
1 noff  Q 2
 
M nneutron Q 2  2M ndeuteron Q 2
p (q) = virtual nucleon (photon)
4-momentum
n
proton 
Q 
2
Kulagin-Petti
Melnitchouk
Differ in n(off)
neutron leading twist
good statistical and
systematic precision
n=2
n=6
n=4
n=8
at large Q2 good
agreement with neutron
moments obtained from
existing NLO PDF’s
at low Q2 the extracted
LT runs faster than the
PDF prediction @ NLO
Generalized Parton Distributions
(GPD)
Generalized Parton Distributions in Exclusive Virtual Photoproduction
*(q)
Q2 =
-q2
>>
, *, , ,...
hard
x+
soft
x-
t = (P-P’)2 <<
GPDs
P,S
P’,S’
P,S
t
GPDs
P’,S’
+
G
+5
unpol.
long. pol.
is+5

GPDs depend on two momentum fractions
(chiral odd) transv. pol.
and
average fraction of the longitudinal skewness parameter: fraction of
momentum carried by partons
longitudinal momentum transfer
t-channel momentum
transfer squared
Parton interpretation of GPD
Quark-antiquark
DGLAP
ERLB
DGLAP
Dokschitzer-Gribov-Lipatov-Altarelli-Parisi
DGLAP
ERLB
Efremov-Radyshkin-Brodsky-Lepage
Non pol GPD for u,d quarks
(similar results for helicity GPD)
GBE model
Light cone wave functions
Fixed t = -0.5 GeV2
 = 0
(solid)
0.1 (dashed)
0.2 (dotted)
Boffi, Pasquini, Traini
NP B, 2003 & 2004
hCQM with relat. KE
no OGE
f1q (unpolarized distribution)
g1q (longitudinal polarization or helicity distribution)
h1q (transverse polarization or transversity distribution)
In the forward limit
- Assuming that the calculated GPQ correspond to the hadronic scale 02 ≈ 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
Chiral-odd GPD
Pavia group: overlap representation
instant form wf
rel hCQM (no OGE)
See talk by
Pincetti
Fixed t = -0.5 GeV2
 = 0
(solid)
0.1 (dashed)
0.2 (dotted)
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)
HT
HT
Scopetta-Vento
PR D71 (2005)
Scopetta
PR D72 (2005)
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
Problem
(Jaffe)
from e+e()()X in the Belle experiment (KEK)
pp collisions possible at RHIC-II
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
DRELL - YAN
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
transversity h1 can be extracted
+ less important terms
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↑
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)
nucleon momentum
for
The asymmetry turns out to be
That is proportional to 1/Q2
valid also after
Evolution
(Polyakov)
Drago
ATT for PAX kinematic conditions
PAX: M2~10-100 GeV2, s~45-200 GeV2, =x1x2=M2/s~0.05-0.6
→ Exploration of valence quarks (h1q(x,Q2) large)
ATT/aTT > 0.2
Models predict |h1u|>>|h1d|
ATT  aˆ TT
h1u (x1 , M 2 )h1u ( x1 , M 2 )
u(x1 , M 2 )u( x1 , M 2 )
(where q p  q p  q)
Measuring the Sivers function
AND-Y  f1T ( x1, k1 )  f ( x2 )
Sivers function
Direct access to Sivers function
usual parton distribution
test QCD basic result:
ANpp DX  ( f1T )q  Dq
( f1T )D- Y  ( f1T )DIS
process dominated by
no Collins contribution
J. Collins
qq  cc
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 .
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)
Exotic states
1)
Pentaquark: four quarks + antiquark (example S=1 baryon)
no theoretical reason against their existence
presently no convincing experimental evidence
Why?
2)
- 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
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
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
Z: probability of finding the bare N in the
Physical N
probability amplitude for
a nucleon to fluctuate
into a (BM) system
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
GPDs in the region - < x <:
Describe the emission of a
Quark-antiquark pair
From the initial nucleon
baryon-meson substate
dependence at fixed t= -0.5
u+d
t=-0.5 =0.1
Hu+d
Hu-d
Eu+d
Eu-d
u-d
Convolution formalism
LCWF
hCQM (rel KE, no OGE) for the baryon
h.o. wave funtion for the pion
u+d
Hu+d
t=-0.5 =0.3
Hu-d
active meson
bare proton
active baryon
totale
B. Pasquini, S. Boffi, PRD73 (2006) 094029
Eu+d
Eu-d
u-d
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
Some results:
Proton electric ff
Proton magnetic ff
a)
b)
c)
bare nucleon
active nucleon
meson
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
De Melo, Frederico, Pace, Pisano, Salme’
Vector meson dominance
Blue and red curve: different values of the relative weight of the instantaneous terms
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