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Onset of Scaling in Exclusive Processes

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. Outline.

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Onset of Scaling in Exclusive Processes

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  1. 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

  2. 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

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

  4. 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) S l i = S lf • HHC has many implication on exclusive processes • For example, in one-photon-exchange approximation: • ds/dW(e+e-→BB)  1+cos2q • ds/dW(e+e-→MM)  sin2q • Form Factors in ep → ep: • GE(Q2)/QGM(Q2)→0 for large Q2→0 Polarization in exclusive reactions

  5. 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 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 gd  pn

  6. The simplest hard scale: 4-momentum transfer per target nucleon qCM=90o Hard regime in gd → pn Already with E~1 GeV |tN| exceeds the nucleon mass in more realistic pQCD (light-front) calculations the relevant scale is transverse momentum pT

  7. n =1+6+3+3= 13 ds/dt ≈ s2-n s11ds/dt = cost onset of scalinggoverned by proton transverse momentum PT2 = 1/2 Eg Md sin2(qcm) J. Napolitano et al., P.R.L. 61, (1988) 2530 • CCR scaling for • pT> 1.1 GeV • power law fit • n =10.5  0.7 0.0 0.5 1.0 1.5 Eg (GeV) PT~1.1 GeV/c g d → p n at SLAC New extensive studies at SLAC and JLab

  8. g d → p n: experimental data

  9. All ds/dt data grouped in 10o bins for Jpcm=30o-150o • no relative normalization between different data sets • statistical and systematic errors added in quadrature • Fit to s-11 of partial samples of data over ΔEg≈1.2 GeV wide windows (ΔPT≈200400 MeV/c, depending on Jpcm ) ds/dt Jpcm • Egwindow shifted by 100 MeV for each subsequent fit up to the highest Eg window. 100 MeV 1200 MeV Eg(or PT ) Check of CCR: adopted procedure

  10. An example qCM = 65o

  11. Study of the c2 as a function of the minimum PT of the fit interval • Statistical criterion: • fix a 90% CL for the fit •  c2(90%) = 1.41.6 • PTth set at c2< c2(90%) Determination of pT threshold • for central angles: • PTth = 1.00  1.27 GeV/c • <PTth> = 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

  12. P.Rossi et al, P.R.L. 94, 012301 (2005) Data consistent with CCR Check of CCR Fit of ds/dt data for the central angles and PT≥1.1 GeV/cwith A s-11 For all but two of the fits c2£ 1.34 • Better c2at 55o and 75o if different data • sets are renormalized to each other • No data at PT≥1.1GeV/c at forward and • backward angles • Clear s-11 behaviour for last 3 points at 35o

  13. With circ. polarized photons • proton polarizations: • With lin. polarized photons • photon pol. asymmetry 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

  14. Py’ Cx’ Cz’ 0 1 2 Eg (GeV) HHC limit PTth1.7 from CCR Indications for HHC violations? More data needed g d → p n: polarization data Data at 90o (CM) only

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

  16. Abbott et al., EPJ A7,421 (2000) Combined analysis of cross section and polarization (t20) data FC • some systematic discrepancy in A measurements • FM 1 order of magnitude smaller than FC and FQ FM • cross section largely dominated by A • B measured at backward scattering angles FQ Deuteron FFs

  17. Alexa et al., PRL 82,1374 (1999) CCR in elastic scattering leading term: the “deuteron FF”: For Q2 above 4 GeV2 data are consistent with CCR Scaling of deuteron FFs

  18. HHC limit (Brodsky-Hiller) HHC limit (Kobushkin-Syamtomov) Q2 > 0.8-1 GeV2 Trend of t20 data not consistent with HHC Polarization in ed → ed Deuteron tensor polarization tij depend on the scattering angle Data at 70° (LAB)

  19. 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→p-p, K+p→K+p, …) • Detailed analysis of experimental data shows that gd→pn cross section agrees with CCR for central CM angles and pT > 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

  20. JLab Hall A, PRL 88,092301-1 Data violates CCR (but not HHC) Proton Form Factors Asymptotic scaling: Dirac F1 Q-4 Pauli F2 Q-6 Q2F2/F1= const pQCD + quark orbital angular momentum: (Ralston, CIPANP 2000, Quebec City) Q F2/F1= const in agreement with data

  21. HHC can be checked in many other exclusive processes, not necessarily involving polarization, like • e+ e-→ M M e+ e-→ B B 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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