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

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*

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

• Glozman-Riska-Plessas (GBE)

relat. KE, linear two-body confinement + flavour dependent Goldstone Boson (π 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 = 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

Dashed curve: NRIA(Non relativistic impulse approximation)

See also the talk by Melde

and not much different from the NR case

V(x) = - /x + x

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

Charge form factor of the proton

Time-like Nucleon form factorsObservable in

TL data fit

SL data fit

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|

GE unknown

phases of GE & GM unknown

Exp reactions:

Recent interest of DAFNE for upgrade at q2 < (2.5)2 GeV2

working groups of Gr.1 and Gr.3 for triennal INFN planVarious authors + Radici,hep-ex/0603056 submitted a E.P.J C

PANDA

The cross section can be written as the sum of a Born (|GE/GM|) and a non Born (2 exchange) term

Bianconi, Pasquini, Radici, P.R. D74 (06); hep-ph/0607277

unpolarized

polarized :

Born: contains sin(GM-GE)

Electromagnetic transitions

-> 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

Talk by Cristoforetti

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 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)

M nCN( ) Q2( )=Mn

Nacht.( ) Q2( )am2

Q2 bm4

Q4 ... m = nucleon mass

M n(Nacht .) Q2( )=μn Q2( )

an4( )

Q2 s Q2( )⎡⎣ ⎤⎦n

4( )

an

6( )

Q4 s Q2( )⎡⎣ ⎤⎦n

6( )

twist analysis

μn Q2

( ) : leading twist

an4( ) n

4( ) nd an6( ) n

6( ): effeive senhs nd noμ ous diμ ensions of HT [fee πμ ees]

proton

• LT important at all Q2

• LT dominant for n=2

• HT<~0 at low Q2

• HT>0 at large Q2

• 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)

simple relations

choice (normalization)

for

nucleon momentum

The asymmetry n turns out to be

That is proportional to 1/Q2

valid also afterEvolution(Polyakov)

PAX: M2~10-100 GeV2, s~45-200 GeV2, =x1x2=M2/s~0.05-0.6

→ Exploration of valence quarks (h1q(x,Q2) large)

AATTTT for PAX kinematic conditions for PAX kinematic conditions

ATT/aTT > 0.2Models predict |h1

u|>>|h1d|

)M,x(u)M,x(u

)M,x(h)M,x(haA

21

21

21

u1

21

u1

TTTT =

)qqqwhere( pp ==

Drago

)(),( 2111Y-D xfkxfA TN ⊗∝ ⊥

⊥

Sivers function usual parton distribution

Direct access to Sivers function

test QCD basic result: DIS1Y-D1 )()( ⊥⊥ −= TT ff J. Collins

qqTDXpp

N DfA ⊗∝ ⊥→ )( 1

usual fragmentation function

process dominated by no Collins contribution

€

qq → cc

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/Nc .

Quark-antiquark and/or meson cloud effects

(at the hadron scale)

• Exotic states (Genova)

• Meson cloud contributions in various processesGPD (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 componentFrom valence quarks to the next Fock-state component

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 evidenceTheoretical description in agreement with the observed spectrum

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 constructedMass 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

Meson-Cloud Model for Meson-Cloud Model for GPDGPD

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 fluctuationprobability amplitude for a nucleon to fluctuate into a (BM) systemZ: probability of finding the bare N in the

Physical N

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 quarkvalence quark baryon-meson baryon-meson substatesubstate

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