Hadronic Structure Function from Perturbative Dressing

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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

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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.

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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).

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Introduction-3

• Measurment of Natchmann moments of proton
  structure function of proton at Jlab Osipenko,
  et al. PRD 67 (2003) 092991 pertonzo, Simula,
  hep-ph/0301206
• ? 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.

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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

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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.

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Formalism-2

• Structure of a U-type valon

Gs are probability. functions . Their moments as
a function of Q2 are completely known in QCD.
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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, 045201 (2003)
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Parton distribution in a valon at a typical value
of Q220 GeV2
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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, 025205 (2002). They satisf the
following sum rules
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• Gvalon/h (y) Is not known theoretically
• ?Use a phenomenological form
• Exclusicve valon distribution
• GUUD(y1,y2,y3)(y1y2)m y3n d(y1y2y3-1),
• Integrate out the unwanted ys. you get the
  individual valon distribution.
• Gj(y)ba,b ya (1-y)b.

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• 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(y1y2y3-1),
• Since Gj(y) is independent of Q2, they can be
  fixed at one Q2 values for all.

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Gluon distribution in Proton
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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

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• 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

GSR0.264 At Q7.35 GeV
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Gottfried
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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

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Pion and Kaon

• For Proton

For Pion
Integrate over unwanted momenta. For Pion ??
For D ,
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Pion and kaon

• The two valons in pion cannot be distinguished
  (apart from flavor). U and D-bar have the same
  masses-gt their average momentum also must be the
  same.? ? mn
• ?Only one parameter to determine Pion
• structure. Used xuv data at Q225 GeV2
• To fix mn0.1

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Pion and kaon

• GU/pb10.01,10.01-1 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.

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Pion and kaon
Q27 GeV2
ZEUS, Nucl. B 637 , (2002)3
----- SMRS
_____ Model
.. GRV
Data E615 Phys Rev. D 39, 92 (1989) F. Arash,
PRD 69, (2004)
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Pion and kaon
Q215 GeV2
data ZEUS col. NuclD.Phys. B 637 (2002) 3.
Sea F. Arash, PRD 69 (2004)
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Q260 GeV2
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• F2p(x, Q2)kF2p(x,Q2) (for one meson exchange
  data call.)
• K0.37

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F2p(x, Q2)kF2p(x,Q2)
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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/kb1mk,1nk-1 ymk(1-y)nk.
• Need two parameters, but can be reduced into only
  one unknown parameter.

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• The average momentum fraction of light valon lty1gt
  and the heavy valon
• lty2gt in the kaon are
• lty1gt(mk1)/(mknk)
• lty2gt(mk1)/(mknk)
• Let the ratio of moments to be equal to the ratio
  of masses

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kaon

• lty1gt/lty2gtmU/mS300/500(mk1)/(nk1)
• So only one parameter

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Parton dist in k- and p- at Q225 GeV2
valence
Valence quark dist. Xu(bar) in p- (solid
line) and in k- (dashed line)
sea
Strange quark in K-
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Spin Structure of Hadron

For ghgp1 then gvalon gU1 and gD1 DGj(y)dFj
Gj(y) dFjNj yaj (1-y)bj(1gjyhjy0.5)
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Polarization
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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

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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
  0.08-0.2 for Q2 2-10 GeV2
• D. DGU (Q2) fairly large and grows rapidly.
• At Q210 it is about 4.4
• ??Impossible to build a spin ½ valon just out of
  quarks and gluons.

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Spin of a valon

• So, need an additional element
• Orbital angular momentum
• SUM RULE
• SUz1/2 (Sval. Ssea)Uz (Sgluon)U z LUz1/2

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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.