modelling hadron form factors · 2013. 2. 20. · eduard a. kuraev 32 hadron electromagnetic form...

Eduard A. KURAEV JINR-BLTP

Dubna-Russia

Modelling Hadron Form

Factors

Eduard A. KURAEV Trento, 19-II-2013 1

Trento, 20/II/2013

E.A.K., E. Tomasi-Gustafsson, A. Dbeyssi Phys.Lett. B712 (2012) 240-244

Eduard A. KURAEV 2

Proton Form Factors ...before

Rosenbluth separation/ Polarization observables

Dipole approximation: GD=(1+Q2/0.71 GeV2)-2

Trento, 19-II-2013

Eduard A. KURAEV 3

Dipole Approximation

• Classical approach –  Nucleon FF (in non relativistic

approximation or in the Breit system) are Fourier transform of the charge or magnetic distribution.

• The dipole approximation corresponds to an exponential density distribution.

–  ρ = ρ0 exp(-r/r0), –  r0

2= (0.24 fm)2, <r2> ~(0.81 fm) 2 m2D =0.71 GeV2

GD=(1+Q2/0.71 GeV2)-2

Trento, 19-II-2013

Breit system

Fourier Transform


Root mean square radius

Polarization experiments - Jlab A.I. Akhiezer and M.P. Rekalo, 1967 GEp collaboration 1)  "standard" dipole function for

the nucleon magnetic FFs GMp and GMn

2) linear deviation from the dipole function for the electric proton FF Gep

3) QCD scaling not reached 3) Zero crossing of Gep? 4) contradiction between

polarized and unpolarized measurements

Trento, 19-II-2013 5 Eduard A. KURAEV

A.J.R. Puckett et al, PRL (2010), PRC (2012)

Eduard A. KURAEV 6

Issues • Some models (IJL 73, Di-quark, soliton..) predicted such behavior before the data appeared

•  Simultaneous description of the four nucleon form factors : GE, GM, proton and neutron

•  ...in the space-like and in the time-like regions

BUT

Kolomna, 11-VI-2010 Trento, 19-II-2013

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Time-like observables: | GE| 2 and | GM| 2 .

As in SL region: - Dependence on q2 contained in FFs - Even dependence on cos2q (1g exchange) - No dependence on sign of FFs - Enhancement of magnetic term but TL form factors are complex!

A. Zichichi, S. M. Berman, N. Cabibbo, R. Gatto, Il Nuovo Cimento XXIV, 170 (1962) B. Bilenkii, C. Giunti, V. Wataghin, Z. Phys. C 59, 475 (1993). S. Bilenki, S. Ryndin, (1965). G. Gakh, E.T-G., Nucl. Phys. A761,120 (2005).

Eduard A. KURAEV

Trento, 19-II-2013

Individual determination of GE and GM up to large Q2

Expected Results

R=GE/GM

BaBAR

PS170 PANDA sim

M. Sudol et al, EPJA 2010

Eduard A. KURAEV 8

L = 2 10 32 cm-2 s-1

100 days

The nucleon: homogenous, symmetric sphere?


r~0.7 fm → Q= 0.29 GeV

works for the SCALAR part, NOT for the VECTOR part of A=(Φ, A)

→

•  Spherical symmetric distributed mass density,

•  A point at a distance r<R from the center feels only the matter inside

Analogy with Gravitation Coulomb Potential ~ Gravitational Potential Mass~charge

1/r

R~1/Q3 is NOT the experimental behavior

R=

The nucleon


antisymmetric state of colored quarks

3 valence quarks and a neutral sea of qq pairs

Does not hold in the spatial center of the nucleon: the center of the nucleon is electrically neutral, due to strong gluonic field

Main assumption

The nucleon


In the internal region of strong chromo-magnetic field, the color quantum number of quarks does not play any role, due to stochastic averaging

Intensity of the gluon field in vacuum:

Inner region: gluonic condensate of clusters with randomly oriented chromo-magnetic field (Vainshtein, 1982):

didj proton neutron

Colorless quarks: Pauli principle

Model


1) uu (dd) quarks are repulsed from the inner region 2) The 3rd quark is attracted by one of the identical quarks, forming a compact di-quark 3) The color state is restored Formation of di-quark: competition between attraction force and stochastic force of the gluon field

Antisymmetric state of colored quarks

Colorless quarks: Pauli principle

attraction force >stochastic force of the gluon field

proton: (u) Qq=-1/3 neutron: (d) Qq=2/3


Proton: r0=0.22 fm, p02 = 1.21 GeV2

Neutron: r0=0.31 fm, p02 = 2.43 GeV2

Model

attraction force > stochastic force of the gluon field

Applies to the scalar part of the potential


Quark counting rules apply to the vector part of the potential

Model


Nature does not like empty place: Additional suppression for the scalar part due to colorless internal region: “charge screening in a plasma”:

Additional suppression (Fourier transform)

fitting parameter

Model

Neutrality condition: Boltzmann constant

Fourier Transform


Root mean square radius

space-time distribution of the electric charge in the space-time volume

Model: generalized form factors


Definition:

In SL- Breit frame (zero energy transfer):

In TL-(CMS): : time evolution of the charge distribution in the domain

2) The vacuum state transfers all the released energy to a state of matter consisting of:

•  6 massless valence quarks •  Set of gluons •  Sea of current qq pairs of quarks with energy q0>2Mp, J=1, dimensions

The annihilation channel:


3) Pair of p and p formed by three bare quarks: • Structureless • Colorless pointlike FFs !!!

1) Creation of a pp state through intermediate state with



•  The point-like hadron pair expands and cools down: the current quarks and antiquarks absorb gluon and transform into constituent quarks •  The residual energy turns into kinetic energy of the motion with relative velocity

•  The strong chromo-EM field leads to an effective loss of color. Fermi statistics: identical quarks are

repulsed. The remaining quark of different flavor is attracted to one of the identical quarks, creating a compact diquark (du-state)



The neutral plasma acts on the distribution of the electric charge (not magnetic).

Prediction: additional suppression due to the neutral plasma similar behavior in SL and TL regions

•  Implicit normalization at q2=4Mp2: |GE|=|GM| =1

•  No poles in unphysical region


•  The long range color forces create a stable colorless state of proton and antiproton •  The initial energy is dissipated from current to constituent quarks originating on shell separated by R.


The repulsion of p and p with kinetic energy is balanced by the confinement potential

At larger distances, the inertial force exceeds the confinement force: p and p start to move apart with relative velocity



For very small values of the velocity FSI lead to the creation of a bound NN system .

p and p leave the interaction region: at large distances the integral of Q(t) must vanish.


Space-Like region

GEn

GEp polarization

GEp dipole


Proton Form Factors

GMp

GEp Akhiezer-Rekalo

GEp Rosenbluth |GMp|=|GEp|


Neutron TL region


Time-Like region

R=|GEp|/|GMp|

Not a fit Ps178 BaBar Dafne E835


Point-like form factors?

S. Pacetti


Hadron Form Factors: Conclusions

New, interesting results in Space-like and Time-like regions

IHEP VEPP-Novosibirsk

Unified model in SL and TlL regions •  pointlike behavior at threshold •  complex FFs due to to FSI , vanishing at asymptotics •  spin one intermediate state dynamical polarization of p and p?



S. Pacetti

Antiprotons at FAIR

Eduard A. KURAEV

HESR

SIS 100/300

SIS18

RESR/CR

30 GeV Protons 50 MeV

p-Linac

Cu Target 107 p/s @ 3 GeV

Collecting Accumulating

Precooling

Accelerating Cooling

100m

PANDA

pbar production • proton Linac 50 MeV • accelerate p in SIS18/SIS100 • produce pbar on target • collect pbar in CR, • cooling in RESR

http://www-panda.gsi.de/ http://www.fair-center.eu/

Parameters of HESR •  Injection of pbar at 3.7 GeV •  Slow synchrotron (1.5-14.5 GeV/c) •  Storage ring for internal target operation •  Luminosity up to L~ 2x1032 cm-2s-1

•  Beam cooling (stochastic & electron) Trento, 19-II-2013 31

Eduard A. KURAEV 32

Hadron Electromagnetic Form factors Characterize the internal structure of

a particle ( point-like) Elastic form factors contain

information on the hadron ground state.

In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors.

Neutron and proton form factors are different.

Deuteron: 2 structure functions, but 3 form factors.

Playground for theory and experiment at low q2 probe the size of the

nucleus, at high q2 test QCD scaling

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The proton vertex is parametrized in terms of FFs: Pauli and Dirac F1,F2

Electromagnetic Interaction

q2<0

e- e-

p p

)2q(2FM2qi

)2q(1Fνµνσ

µγµΓ +=

or in terms of Sachs FFs: GE=F1-t F2, GM=F1+F2, t=-q2/4M2

The electron vertex is known,gm The interaction is carried by a virtual photon of mass q2

What about high order

radiative corrections?

Eduard A. KURAEV


Crossing Symmetry Scattering and annihilation channels:

- Described by the same amplitude :

- function of two kinematical variables, s and t

k2 → – k2 - which scan different kinematical regions

p2 → – p2

Trento, 19-II-2013 35

Analyticity

_ _

q2<0

e- e-

p p

q2>0

e-

e+ p

p

q2 q2=4mp2

FFs are complex FFs are real Unp

hysi

cal r

egio

n

GE=GM

Space-like

Time-like GE(0)=1

GM(0)=mp

Asymptotics - QCD - analyticity

p+p ↔ e++e- e+p e+p

p+p ↔

e++

e- +p

Eduard A. KURAEV

Eduard A. KURAEV 36

Dipole Approximation and pQCD

V. A. Matveev, R. M. Muradian, and A. N. Tavkhelidze (1973), Brodsky and Farrar (1973), Politzer (1974), Chernyak & Zhitnisky (1984), Efremov & Radyuskin (1980)…

Dimensional scaling

–  Fn (Q2)= Cn [1/( 1+Q2/mn) n-1], • mn=n2 , <quark momentum squared> • n is the number of constituent quarks

–  Setting 2 =(0.471±.010) GeV2 (fitting pion data)

•  pion: F (Q2)= C [1/ (1+Q2/0.471 GeV2)1],

•  nucleon: FN (Q2)= CN [1/( 1+Q2/0.71 GeV2)2], •  deuteron: Fd (Q2)= Cd [1/( 1+Q2/1.41GeV2)5]

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Eduard A. KURAEV 37

The Rosenbluth separation

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞⎜⎜

⎝

⎛++Ω

=Ω )2(2)2(2)1(1 QMGQEG

Mottdd

dd

ετ

τσσ

2M4

2Q,1

2e2)tan1(21 =

−++=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎠⎞⎜

⎝⎛ τθ

τε

® Holds for 1g exchange only

Linearity of the reduced cross section

PRL 94, 142301 (2005)

® tan2qe dependence e

Q2 f

ixed

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Eduard A. KURAEV 38

The polarization induces a term in the cross section proportional to GE GM Polarized beam and target or polarized beam and recoil proton polarization

The polarization method (1967)

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Eduard A. KURAEV 39

The simultaneous measurement of Pt and Pl reduces the systematic errors

The polarization method (exp)

Trento, 19-II-2013

C. Perdrisat et al, JLab-GEp collaboration

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Proton form factors at large q2

E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)

Applies to NN and NN Interaction (Pomeranchuk theorem) t=0 : not a QCD regime!

Connection with QCD asymptotics?

Eduard A. KURAEV

E. T-G. e-Print: arXiv:0907.4442 [nucl-th]

L = 2 10 32 cm-2 s-1

100 days

modelling hadron form factors · 2013. 2. 20. · eduard a. kuraev 32 hadron electromagnetic form...

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