1. Hadronic Structure Function from Perturbative Dressing
Firooz Arash
Physics Department, Tafresh University, Tafresh, Iran
And
Fatimeh Taghavi
Phydics Department, Iranian Science and Technology University, Tehran, Iran
XI International Conference on Elastic and diffractive Scattering, Blois, France, May 15-20, 2005

2. INTRODUCTION Our knowledge of hadron structure :
Spectroscopy: quarks are massive and particles are their bound states.
DIS data: Interpretation relies upon the quarks of LQCD with small quark mass .
In this picture :
large number of partons
Color charge of quark field in LQCD is
ill-defined :
In an interacting theory it is not GAUGE INVARIENT  reflecting gluon color.

3. Introduction-2
In contrast, color associated with the constituent (Valon) quark is well-defined .
Perturbative dressing of a LQCD field to all orders is possible, hence, constructing a valon In conformity with the color confinement {see: M. Lavelle and D. McMullen, Phys. Lett. B 371, 83 (1996); Phys. Rep. 279, 1 (1997).}

4. Introduction-3
Measurment of Natchmann moments of proton structure function of proton at Jlab {Osipenko, et al. PRD 67 (2003) & pertonzo, Simula, hep-ph/ }
 existence of a new type of scaling which can be interpreted as constituent form factor, consistent with the elastic nucleon data:
Proton structure originates from the elastic coupling with the extended objects inside proton.

5. Purpose and Motivation
Evaluate the structure of a valon ( constituent quark) in the NLO
Verify its conformity with the Structure Function (SF) data on NUCLEON and PION., refinements (GSR)
Polarization Structure Function of Nucleon

6. FORMALISM
By definition: Valon is the universal building block for every hadron.
Its internal structure is generated perturbatively. at high enough Q2 in a DIS experiment it is the structure of a valon that is being probed. At sufficiently low Q2 it behaves as a valence quark and hadrons are viewed as bound states of valons.

7. Formalism-2 Structure of a U-type valon:
G’s are probability. functions . Their moments as a function
of Q2 are completely known in QCD.

8. Parton Distribution In a Valon
Use Inverse Mellin Transformation. The parametric form is given by:
Parameters a, b, c, etc are functions of Q2 and are given in the appendix of
F. Arash, and A. N. Khorramian, Phys. Rev. C 67, (2003)

9. Parton distribution in a valon at a typical value of Q2=20 GeV2

10. Hadron Structure Proton
Gvalon/h (y) is the valon distribution in a hadron and is independent of Q2 Their form are already known.(R. C. Hwa, and C. B. Yang, Phys. Rev. C 66, (2002). They satisf the following sum rules:

11. Gvalon/h (y) Is not known theoretically
Use a phenomenological form:
Exclusicve valon distribution:
GUUD(y1,y2,y3)=(y1y2)m y3n d(y1+y2+y3-1),
Integrate out the unwanted y’s. you get the individual valon distribution.
Gj(y)=b[a,b] ya (1-y)b.

12. Note that once F2v(x/y, Q2) is calculated from pQCD, the only free parameters in the model are m,and n (in the case of nucleon) in
GUUD(y1,y2,y3)=(y1y2)m y3n d(y1+y2+y3-1),
Since Gj(y) is independent of Q2, they can be fixed at one Q2 values for all.

14. Gluon distribution in Proton

15. SU(2) Asymmetry (GSR)
In our model there is no room in the valon structure for the breaking of SU(2) symmetry of the sea.
But there exists soft gluons that bind valons in a proton. Taking that into considerations with a mechanism depicted bellow:

16. a u-bar couples to a D-type valon forming a p- while a d-quark combines with a U-type to form a D++ . This is the lowest fluctuation for uu-bar. Similarly a dd(bar) fluctuates into p+ n .
D++ is more massive than n, the probability of dd(-bar) fluctuation will dominate over uu-bar, resulting in SU(2) breaking: Results are as follows:
Exp.
0.068 ( )
0.1 (
At Q=7.35 GeV
GSR=0.264

17. Gottfried

18. Pion and Kaon
Having determined the structure of a valon, it is straight forward for other Hadrons.
Need to calculate the valon distribution Gvalon/h (y) in the particular hadron:
 Take a simple phenomenological form for exclusive valon distribution:

19. Pion and Kaon For Proton: For Pion:
Integrate over unwanted momenta. For Pion 
For D ,

20. Pion and kaon
The two valons in pion cannot be distinguished (apart from flavor). U and D-bar have the same masses-> their average momentum also must be the same.  m=n
Only one parameter to determine Pion
structure. Used xuv data at Q2=25 GeV2
To fix m=n=0.1

21. Pion and kaon GU/p=b[1+0.01,1+0.01]-1 y0.01(1-y)0.01
Is a very broad curve, can be replces by 1.
Indicating that valons in a pion are tightly bound.
 valons are heavier than the hosting pion.
{sea F. Arash, PLB 557 (2003) 38.}

22. Pion and kaon Q2=7 GeV2 ----- SMRS _____ Model ….. GRV
ZEUS, Nucl. B 637 , (2002)3
----- SMRS
_____ Model
….. GRV
Data: E615 Phys Rev. D 39, 92 (1989)
F. Arash, PRD 69, (2004)

23. Pion and kaon Sea F. Arash, PRD 69 (2004) Q2=15 GeV2
data: ZEUS col. NuclD.Phys. B 637 (2002) 3.
Sea F. Arash, PRD 69 (2004)

24. Q2=60 GeV2

25. F2p(x, Q2)=kF2p(x,Q2) (for one meson exchange data call.)

26. F2p(x, Q2)=kF2p(x,Q2)

27. Pion and kaon
Kaon:
There are a few data points on the ratio xu(bar) K-/ xu(bar) p- at large x canbe used to find mk and nk in
Gj/k=b[1+mk,1+nk]-1 ymk(1-y)nk.
Need two parameters, but can be reduced into only one unknown parameter.

28. The average momentum fraction of light valon <y1> and the heavy valon
<y2> in the kaon are
<y1>=(mk+1)/(mk+nk)
<y2>=(mk+1)/(mk+nk)
Let the ratio of moments to be equal to the ratio of masses:

29. kaon <y1>/<y2>=mU/mS=300/500=(mk+1)/(nk+1)
So only one parameter

31. Parton dist in k- and p- at Q2=25 GeV2
valence
Valence quark dist. Xu(bar) in p- (solid line)
and in k- (dashed line)
sea
Strange quark in K-

32. Spin Structure of Hadron
For gh=gp1 then gvalon= gU1 and gD1
DGj(y)=dFj Gj(y)
dFj=Nj yaj (1-y)bj(1+gjy+hjy0.5)

37. Polarization

39. Spin of a valon
We see that the model describes the experimental data on hadronic level.
We also know that those data do not account for the spin of nucleon
 Dos the sum of the spins of the valons produce the nucleon spin?
NEED to know the contributions of different components of a valon to its spin

40. Spin of a Valon It turns out that for a U-type valon
A. Dqvalence/U =1 for all Q2.
B. Dqsea/U varying with Q2 but remains small: for Q2= 2-10 GeV2
D. DGU (Q2) fairly large and grows rapidly.
At Q2=10 it is about 4.4
Impossible to build a spin ½ valon just out of quarks and gluons.

41. Spin of a valon So, need an additional element
Orbital angular momentum
SUM RULE:
SUz=1/2 (Sval. +Ssea)Uz +(Sgluon)U z +LUz=1/2

43. Ummary and comclusion
Structure of a valon produced perturbatively in QCD. It is universal, independent of the hosting hadron. The structure is evaluated.
Structure of any hadron can be determined with minimum (1 or 2) unknown parameters.
Polarized structure of nucleon can be obtaine form the valon model.
Wile experimental data is reproduced but need the orbital angular momentum even at the valon level.