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: - PowerPoint PPT Presentation
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Hadron structure and hadronic matter M.Giannini Cortona,13 october 2006
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*
0.8
1
1.2
1.4
1.6
1.8
2
P11
P11'
P33
P33'
P11''
P31
F15P13
P33''F37
M
(GeV)
π = 1π = 1 π = −1
35F
13D11S
31S11S '15D33 13D D '
(70,1 -)
(56,0+)
(56,0+)'
(56,2+)(70,0+)
3 Constituent quark models for baryons
• Isgur-Karl (IK) => Capstick-Isgur (CI) relat. KE, linear three-body confinement + OGE
• 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 = 2 + 2 hyperradius x - / x
Goldstone Boson Exchange
x = 2 2
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 , Gp
M , GnE , Gn
M
Renewed experimental interest Jefferson Lab (Hall A) data on Gp
E/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 Gp
E/GpM
- discrepancy with Rosenbluth data (?)
- linear and strong decrease
- pointing towards a zero (!)
Rome group
CQM: CI
LF WF
full curve: with quark ffdotted curve: without quark ff
Graz-Pavia:Point Form Spectator Approximation (PFSA)CQM: GBE
Boffi et al., EPJ A14, 17 (2002)
Neutron electric ff: SU(6) violationDash-dotted confinement only
M.G., E. Santopinto, M. Traini, A. Vassallo, to be published
GEp
GEn GM
n
GMp
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
Fit with quark form factors
GMp
GEn
-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)
Results for the Interacting quark-diquark model
Quark-diquark interaction: linear + coulomb-like exchange (spin and isospin dependent
-> helicity amplitudes for e.m. excitation of nucleon resonances
Pace et al.
NR
LFN
Virtual photon
N*,
hCQM, J. Phys. G (1998)
Blue curves hCQMGreen curves H.O.
m = 3/2
m = 1/2
N helicity amplitudes
red fit by MAIDblue hCQMdashed 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 working3) 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 tointerpret and eventually guide LQCD results
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 IILMInteracting Instanton Liquid Model
Why IILM?- instanton appear to be the dynamical mechanism responsible for the chiralsymmetry 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 theeigenvalue 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
PT predicts it is a constant as a function of the quark mass
It can be calculated independently with IILM
mq Kabc / m=0(0) Kabc 3-point correlator
With IILM one can calculate the nucleon mass for different values of mπ
The results agree with the lattice calculationsBy 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: Mn
CN( ) Q2( )≡ dx0
1
∫ xn−2 F2 xQ2( )
Nachtmann moments: Mn
(Nacht .) Q2( )≡ dx0
1
∫ξn1
x3 F2 xQ2( )3 3 n1( )r n n2( )r2
n2( ) n 3( )
ξ =2x 1+ r( ), r = 1 1+ 4m2x2 Q2
Main difference: Nachtmann moments are free from target-mass corrections (which depend on the x-shape of the leading twist)
• HT comes from partial cancellation of twists with opposite signs
n=4n=2
n=6 n=8
Similar results for the deuteron
leading twist moments of the neutron F2
[NPA 766 (2006), in collaboration with S. Kulagin and W. Melnitchouk]
F2D x,Q2( ) IA⏐ →⏐ d4 p∫ T W pq( )A p pD( )⎡⎣ ⎤⎦
p (q) = virtual nucleon (photon) 4-momentum
pD = deuteron 4-momentum
nuclear effects in deuteron at moderate and large x (x > 0.1):
F2D x,Q2( )=F2
D(conv.) xQ2( )dF2D xQ2( )
all the rest: relativistic, off-shell effects, …
usual convolution formula: on-shell nucleon F2 and light-cone momentum distribution in D
- traditional decomposition:
the decomposition is not unique two models
M nneutron( ) Q2( )=2Mn
deuteron( ) Q2( )1−n
off( ) Q2( )fn
D −Mnproton( ) Q2( )
off shell nucleon structure function Relativistic deuteron spectral function
Kulagin-PettiMelnitchouk
Differ in n(off)
neutron leading twist
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
n=4n=2
n=6 n=8
good statistical and systematic precision
Generalized Parton Distributions
(GPD)
*(q), *, , . . .
soft
P,S P’,S’
Q2 = -q2 >>
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 - ξ
Generalized Parton Distributions in Exclusive Virtual Generalized Parton Distributions in Exclusive Virtual PhotoproductionPhotoproduction
x + ξ
GPDs
P,S P’,S’
GPDs
+
+5 =
is+5
unpol.
long. pol.
transv. pol.
t
hard
(chiral odd)
Parton interpretation of GPD
DGLAP ERLB DGLAP
DGLAPDokschitzer-Gribov-Lipatov-Altarelli-Parisi
ERLBEfremov-Radyshkin-Brodsky-Lepage
Quark-antiquark
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 GeV2
ξ = 0 (solid) 0.1 (dashed) 0.2 (dotted)
In the forward limit f1q (unpolarized distribution)
- Assuming that the calculated GPQ correspond to the hadronic scale μ02 ≈ 0.1 GeV2
- Performing a NLO evolutionup to Q2 = 3 GeV2
Beyond x=0.3 (valence quarks only)
one can calculate the measuredasymmetries
Dashed curves: no evolution
g1q (longitudinal polarization or helicity distribution)
h1q (transverse polarization or transversity distribution)
Chiral-odd GPD
Pavia group: overlap representation instant form wf rel hCQM (no OGE)
Fixed t = -0.5 GeV2
ξ = 0 (solid) 0.1 (dashed) 0.2 (dotted)
See talk by Pincetti
ScopettaVento
Quarks are complex systems containing partons of any typeConvolution of the quark GPD with the NR IK CQM wfRespect of: forward condition, integral of , polynomial condition
Scopetta Simple MIT bag model (only HT is non vanishing)
Scopetta-VentoPR D71 (2005)
ScopettaPR D72 (2005)
HT
HT
SIDIS spin asymmetry
Goal: - integrate over PhT=(P1+P2)T; asimmetry in RT=(P1-P2)T, that is in fR ; - extract transversity h1 through coming from the interference of the hadron pair (h1h2) produced in s or in p wave
Motivations for
from e+e- (ππ)(ππ)X in the Belle experiment (KEK) pp collisions possible at RHIC-II
Radici et al.
Problem change of sign?(Jaffe)
s-p interf. from ππ elastic phase shifts
spectator model calculation of from Im [ interf. of two channels ]
Bacchetta-Radici
Dihadron fragmFunction DiFF
confronto con Hermes e Compass
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)
+ less important termstransversity h1 can be extracted
Boer-Mulders function
Sivers effect Collins-Soper frame
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 π- events (black triangles) 25.000 π+ 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:
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)
GPDs in the region GPDs in the region --ξξ < x << x <ξξ::Describe the emission of a Describe the emission of a Quark-antiquark pairQuark-antiquark pairFrom the initial nucleonFrom the initial nucleon
active mesonbare proton
active baryon
totale
ξξdependence at fixed t= -0.5 dependence at fixed t= -0.5 t=-0.5 ξ=0.1
t=-0.5 ξ=0.3
u + d u - d
Hu+d Hu-d
Eu+d Eu-d
u + d u - d
Hu+d Hu-d
Eu+d Eu-d
B. Pasquini, S. Boffi, PRD73 (2006) 094029
Convolution formalismLCWFhCQM (rel KE, no OGE) for the baryonh.o. wave funtion for the pion
Similar approach with the hCQM
D. Y. Chen, Y. B. Dong, M. G., E. Santopinto, Trieste Conf., May 2006
Vertex (Thomas) similar to Boffi-PasquiniUsed for elastic for factors and
helicity amplitudes
Some results:
Proton electric ff
Proton magnetic ff
a) bare nucleonb) active nucleonc) meson
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 ffImportance of instantaneous termsModel meson wf Some free parameters
Vector meson dominance
Rome group
Blue and red curve: different values of the relative weight of the instantaneous terms
Similarly for the nucleon
Quark-nucleon amplitude from an effective lagrangian densityAraujo et al. PL b (2000)
triangle (or elastic) non valenceTalk by Pisano
Dotted curve: triangle contribution Full curve: total contribution