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

Outline Asymptotics in exclusive processes: counting rule and helicity conservation Experimental test of asymptotic predictions in em reactions -cross section and polarization data in  d → p n -Form Factors and tensor polarization in e d → e d Comments and outlooks

Scaling laws for exclusive processes FF in elastic scattering Cross section n=n A +n B +n C +n D total number of elementary constituents Scaling is a manifestation of asymptotically free hadron interactions Brodsky and Farrar, Phys. Rev. Lett. 31 (1973) 1153 Matveev et al., Lett. Nuovo Cimento, 7 (1973) 719 A B C D From dimensional arguments at high energies in binary reactions: CONSTITUENT COUNTING RULE

Polarization in exclusive reactions Lepage and Brodsky, Phys. Rev. D22 (1980) 2157 Brodsky and Lepage, Phys. Rev. D24 (1981) 2848 For high energy and momentum transfer the total helicity is conserved (HHC)  i  f HHC has many implication on exclusive processes For example, in one-photon-exchange approximation: d  d  (e + e - → BB)  1+cos 2  d  d  (e + e - → MM)  sin 2  Form Factors in ep → ep: G E (Q 2 )/QG M (Q 2 ) → 0 for large Q 2 → 0

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 K + p → K + p 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  d  pn

Hard regime in  d → pn in more realistic pQCD (light-front) calculations the relevant scale is transverse momentum p T Already with E~1 GeV |t N | exceeds the nucleon mass The simplest hard scale: 4-momentum transfer per target nucleon  CM =90 o

 d → p n at SLAC E  (GeV) J. Napolitano et al., P.R.L. 61, (1988) 2530 New extensive studies at SLAC and JLab CCR scaling for p T > 1.1 GeV power law fit n =10.5  0.7 n = = 13 d  /dt ≈ s 2-n s 11 d  /dt = cost P T ~1.1 GeV/c onset of scaling governed by proton transverse momentum P T 2 = 1/2 E  M d sin 2 (  cm )

 d → p n: experimental data

All ds/dt data grouped in 10 o bins for p cm =30 o -150 o no relative normalization between different data sets statistical and systematic errors added in quadrature d  /dt E  (or P T ) p cm E  window shifted by 100 MeV for each subsequent fit up to the highest E  window. 100 MeV Fit to s -11 of partial samples of data over Δ E  ≈ 1.2 GeV wide windows (ΔP T ≈200  400 MeV/c, depending on p cm ) 1200 MeV Check of CCR: adopted procedure

An example  CM = 65 o

Determination of p T threshold Study of the  2 as a function of the minimum P T of the fit interval Statistical criterion: fix a 90% CL for the fit   2 (90%) = 1.4  1.6 P T th set at  2 <  2 (90%) for central angles: P T th = 1.00  1.27 GeV/c = 1.13 GeV/c for forward and backward angles: P T th = 0.6  0.7 GeV/c P T th uncert.  100 MeV/c SCALING THRESHOLD: p T = 1.1 GeV/c

Check of CCR Fit of d  /dt data for the central angles and P T ≥1.1 GeV/c with A s -11 For all but two of the fits  2  1.34 Data consistent with CCR P.Rossi et al, P.R.L. 94, (2005) Better  2 at 55 o and 75 o if different data sets are renormalized to each other No data at P T ≥1.1 GeV/c at forward and backward angles Clear s -11 behaviour for last 3 points at 35 o

HHC in  d → pn With circ. polarized photons proton polarizations: P y’ = 0(  t -1 ) HHC PREDICTIONS C x’ = 0(  t -1 ) C z’ = 0(  t -2 ) at 90 o With lin. polarized photons photon pol. asymmetry HHC PREDICTION  = +1(  t -2 ) at 90 o

 d → p n: polarization data Data at 90 o (CM) only P y’ C x’ C z’ HHC limit E  (GeV) P T th  1.7 from CCR Indications for HHC violations? More data needed

Elastic ed scattering A and B are functions of 3 FFs: charge (F C ), magnetic dipole (F M ) and electric quadrupole (F Q ) Cross section alone does not allow extraction of all FFs POLARIZATION For example: Tensor polarization of the outgoing deuteron Cross section expressed in terms of 2 structure functions e e’ d d’

Deuteron FFs Abbott et al., EPJ A7,421 (2000) Combined analysis of cross section and polarization (t 20 ) data FQFQ FCFC FMFM F M  1 order of magnitude smaller than F C and F Q cross section largely dominated by A B measured at backward scattering angles some systematic discrepancy in A measurements

Scaling of deuteron FFs CCR in elastic scattering leading term: the “deuteron FF”: Alexa et al., PRL 82,1374 (1999) For Q 2 above  4 GeV 2 data are consistent with CCR

Polarization in ed → ed Deuteron tensor polarization t ij depend on the scattering angle Data at 70 ° (LAB) HHC limit (Brodsky-Hiller) HHC limit (Kobushkin-Syamtomov) Q 2 > GeV 2 Trend of t 20 data not consistent with HHC

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 don’t play any role CCR reproduces the general behaviour of the cross section for several exclusive hadronic reactions (pp → pp,   p →   p, K + p → K + p, …) Detailed analysis of experimental data shows that  d → pn cross section agrees with CCR for central CM angles and p T > 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

JLab Hall A, PRL 88, Proton Form Factors Asymptotic scaling: Dirac F 1  Q -4 Pauli F 2  Q -6 Q 2 F 2 /F 1 = const pQCD + quark orbital angular momentum: (Ralston, CIPANP 2000, Quebec City) Q F 2 /F 1 = const in agreement with data Data violates CCR (but not HHC)

Comments and Outlook - 2 Polarization observables are more sensitive to QCD details, corrections could be large HHC is less successful in describing polarization data, even in hadron-hadron reactions 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 90 o - tensor polarization in ed elastic scattering at higher Q 2 HHC can be checked in many other exclusive processes, not necessarily involving polarization, like e + e - → M M e + e - → B B

Hadronic reactions with deuteron Uzikov, hep-ph/ dd → 3 He n + dd → 3 H p pd → pd

Polarization in pd elastic scattering Azhgirey et al., PL 391B,22

From Hadrons to Partons The challenge is to look for some experimentally accessible phenomena naturally predicted by pQCD Low energyHigh energy Transition Region Few GeV ? Energy Scaling in some physics observables is one of the simplest signatures of pQCD

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