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PPT – Hadron structure and hadronic matter M.Giannini Cortona,13 october 2006 PowerPoint presentation | free to view - id: 127fda-OTk4Y

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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)
- 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

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 -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

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

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 -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

- - 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 t not much different from the NR case

- 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

GMp

Fit with quark form factors

GEn

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)

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(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

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

Electromagnetic transitions -gt helicity

amplitudes for e.m. excitation of nucleon

resonances

Virtual photon

N, ?

NR

N

LF

Pace et al.

hCQM, J. Phys. G (1998)

m 3/2

m 1/2

Blue curves hCQM

Green curves H.O.

N ?? helicity amplitudes

red fit by MAID blue hCQM dashed p 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 (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

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

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

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

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

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

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)

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

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Generalized Parton Distributions (GPD)

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

Parton interpretation of GPD

Quark-antiquark

DGLAP ERLB DGLAP

ERLB Efremov-Radyshkin-Brodsky

-Lepage

DGLAP Dokschitzer-Gribov-Lipa

tov-Altarelli-Parisi

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

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

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)

HT

HT

Scopetta-Vento PR D71 (2005)

Scopetta PR D72 (2005)

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

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

less important terms

transversity h1 can be extracted

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

valid also after Evolution (Polyakov)

choice

(normalization)

nucleon momentum

for

The asymmetry ??turns out to be

That is proportional to 1/Q2

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)

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 .

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

- 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

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

probability amplitude for a nucleon to fluctuate

into a (BM) system

Z 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 quark

baryon-meson substate

GPDs in the region -? lt x lt? Describe the

emission of a Quark-antiquark pair From the

initial nucleon

?-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

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

- bare nucleon
- active nucleon
- c) 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

Vector meson dominance

De Melo, Frederico, Pace, Pisano, Salme

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

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