Onset of Scaling in Exclusive Processes

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Onset of Scaling in Exclusive Processes
Marco Mirazita Istituto Nazionale di Fisica
Nucleare Laboratori Nazionali di Frascati
First Workshop on Quark-Hadron Duality and the
Transition to pQCD Laboratori Nazionali di
Frascati, June 6-8 2005
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Outline

• Asymptotics in exclusive processes counting
  rule and helicity conservation
• Experimental test of asymptotic predictions in
  em reactions
• -cross section and polarization data in g d ? p
  n
• -Form Factors and tensor polarization in e d ? e
  d
• Comments and outlooks

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Scaling laws for exclusive processes
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Polarization in exclusive reactions
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The counting rule

• There are a large number of measured exclusive
  reactions in which the empirical power law
  fall-off predicted by dimensional counting pQCD
  appear to be accurate over a large range of
  momentum transfer
• pp?pp p-p?p-p Kp?Kp
• A critical question is the momentum transfer
  required such that leading-twist pQCD
  contributions dominate.
• An efficient way for reaching the hard regime is
  the deuteron photodisintegration reaction gd ? pn

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Hard regime in gd ? pn
Already with E1 GeV tN exceeds the nucleon mass
in more realistic pQCD (light-front) calculations
the relevant scale is transverse momentum pT
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g d ? p n at SLAC
New extensive studies at SLAC and JLab
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g d ? p n experimental data
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Check of CCR adopted procedure
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An example
qCM 65o
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Determination of pT threshold

• for central angles
• PTth 1.00 ? 1.27 GeV/c
• ltPTthgt 1.13 GeV/c
• for forward and backward angles
• PTth 0.6 ? 0.7 GeV/c
• PTth uncert. ?100 MeV/c

SCALING THRESHOLD pT 1.1 GeV/c
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Check of CCR
Fit of ds/dt data for the central angles and
PT1.1 GeV/c with A s-11
For all but two of the fits c2? 1.34

• Better c2 at 55o and 75o if different data
• sets are renormalized to each other
• No data at PT1.1 GeV/c at forward and
• backward angles
• Clear s-11 behaviour for last 3 points at 35o

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HHC in gd ?pn
Py 0 (?
t-1) HHC PREDICTIONS Cx 0 (? t-1)
Cz 0 (? t-2)
at 90o
HHC PREDICTION S 1 (? t-2) at 90o
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g d ? p n polarization data
Data at 90o (CM) only
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Elastic ed scattering
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Deuteron FFs
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Scaling of deuteron FFs
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Polarization in ed ? ed
Deuteron tensor polarization tij depend on the
scattering angle
Data at 70 (LAB)
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Comments and Outlook - 1

• CCR is based on dimensional arguments only,
  provided that
• - energy is high enough
• - partons are free
• Details of QCD strong interactions dont play
  any role

• CCR reproduces the general behaviour of the
  cross section for several exclusive hadronic
  reactions (pp?pp, p-p?p-p, Kp?Kp, )

• Detailed analysis of experimental data shows
  that gd?pn cross section agrees with CCR for
  central CM angles and pT gt 1.1 GeV

• Deuteron em Form Factors are consistent with CCR
  predictions

• More realistic QCD calculations could give non
  negligible corrections to the expected scaling.
  For example
• - oscillations in fixed angle cross sections
• - proton em Form Factors scaling

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Proton Form Factors
Asymptotic scaling Dirac F1 ? Q-4
Pauli F2 ? Q-6 Q2 F2/F1 const
pQCD quark orbital angular momentum (Ralston,
CIPANP 2000, Quebec City) Q F2/F1 const in
agreement with data
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Comments and Outlook - 2

• HHC is less successful in describing
  polarization data, even in hadron-hadron reactions

• Polarization observables are more sensitive to
  QCD details, corrections could be large

• Experimental data on em reactions seem to
  indicate violation of HHC, but the situation is
  not sufficiently clear

• More polarization data are needed
• - deuteron photodisintegration at other angles
  than 90o
• - tensor polarization in ed elastic scattering at
  higher Q2

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Hadronic reactions with deuteron
Uzikov, hep-ph/0503185
dd?3He n dd?3H p
pd?pd
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Polarization in pd elastic scattering
Azhgirey et al., PL 391B,22
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From Hadrons to Partons
The challenge is to look for some experimentally
accessible phenomena naturally predicted by pQCD
Scaling in some physics observables is one of the
simplest signatures of pQCD
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