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

OutlineOutline

• 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 Scaling laws for exclusive processesprocesses

2

B

Q

F

d

dσ

2

FF in elastic scattering

Bn

B QF

12

2)(n-

2ncm ss

1θf

dt

dσ

Cross section

n=nA+nB+nC+nD 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 Polarization in exclusive reactionsreactions

Lepage and Brodsky, Phys. Rev. D22 (1980) 2157Brodsky and Lepage, Phys. Rev. D24 (1981) 2848

For high energy and momentum transfer the total helicity is conserved (HHC)

if

HHC has many implication on exclusive processes

For example, in one-photon-exchange approximation:

• dd(e+e-→BB) 1+cos2

• dd(e+e-→MM) sin2

• Form Factors in ep → ep: GE(Q2)/QGM(Q2)→0 for large Q2→0

The counting ruleThe 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 Hard regime in d d → → pnpn

in more realistic pQCD (light-front) calculations the relevant scale is

transverse momentum pT

Already with E~1 GeV |tN| exceeds the nucleon mass

The simplest hard scale: 4-momentum transfer per target nucleon

CM=90o

d d → → p n at SLACp n at SLAC

0.0 0.5 1.0 1.5 E (GeV)

J. Napolitano et al., P.R.L. 61, (1988) 2530

New extensive studies at SLAC and JLab

• CCR scaling for pT> 1.1 GeV • power law fit n =10.5 0.7

n =1+6+3+3= 13 d/dt ≈ s2-n s11d/dt = cost

PT~1.1 GeV/c

onset of scaling governed by proton transverse momentum

PT2 = 1/2 E Md

sin2(cm)

d d → → p n: experimental datap n: experimental data

• All ds/dt data grouped in 10o bins for pcm=30o-

150o

• no relative normalization between different data sets• statistical and systematic errors added in quadrature d/dt

E (or PT )

pcm

•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 ΔE≈1.2 GeV wide windows (ΔPT≈200400 MeV/c, depending on p

cm )

1200 MeV

Check of CCR: adopted Check of CCR: adopted procedureprocedure

An exampleAn example

CM = 65o

Determination of pDetermination of pTT thresholdthreshold

Study of the 2 as a function of the minimum PT of the fit interval

Statistical criterion:• fix a 90% CL for the fit 2(90%) = 1.41.6 • PT

th set at 2< 2(90%)

• for central angles: PT

th = 1.00 1.27 GeV/c <PT

th> = 1.13 GeV/c• for forward and backward angles: PT

th = 0.6 0.7 GeV/c• PT

th uncert. 100 MeV/cSCALING

THRESHOLD:pT = 1.1 GeV/c

Check of CCRCheck of CCRFit of d/dt data for the central angles and PT≥1.1 GeV/c with

A s-11For all but two of the fits 21.34

Data consistent with CCR

P.Rossi et al, P.R.L. 94, 012301 (2005)

•Better2 at 55o and 75o if different data sets are renormalized to each other

•No data at PT≥1.1 GeV/c at forward and backward angles

•Clear s-11 behaviour for last 3 points at 35o

HHC in HHC in d d →→pnpn

'yP

• With circ. polarized photons

proton polarizations: Py’ = 0 ( t-1)HHC PREDICTIONS Cx’ = 0 ( t-1) Cz’ = 0 ( t-2) at 90o

• With lin. polarized photons

photon pol. asymmetry

||

||

HHC PREDICTION = +1 ( t-2) at 90o

d d → → p n: polarization p n: polarization datadata

Data at 90o (CM) only

Py’

Cx’

Cz’

HHC limit

0 1 2E (GeV)

PTth1.7 from CCR

Indications for HHC violations?More data needed

Elastic ed Elastic ed scatteringscattering

2

2222

22222222

41

3

4

3

2

9

8

d

M

MQC

M

QQFQB

QFQFQFQA

A and B are functions of 3 FFs:charge (FC), magnetic dipole (FM) and electric quadrupole (FQ)Cross section alone

does not allow extraction of all FFs

POLARIZATION

For example:

Tensor polarization of the outgoing deuteron

2222

1212221

222220

2

13

2223

21213

1

9

8

3

82

QFSt

FFSt

FFFFSt

M

QM

MQQC

/sin/sin

/tan

/

Cross section expressed in terms of 2 structure functions

2222

0

tanQBQA

d

d

e

e’

d

d’

Deuteron FFsDeuteron FFs Abbott et al., EPJ A7,421 (2000)

Combined analysis of cross section and polarization (t20) data

FQ

FC

FM

• FM 1 order of magnitude smaller than FC and FQ • cross section largely dominated by A• B measured at backward scattering angles

• some systematic discrepancy in A measurements

Scaling of deuteron Scaling of deuteron FFsFFs

CCR in elastic scattering

leading term:

the “deuteron FF”:

dnQFF

12

10 QAFd

Alexa et al., PRL 82,1374 (1999)

For Q2 above 4 GeV2 data are consistent with CCR

Polarization in ed Polarization in ed → → ededDeuteron tensor polarization tij depend on the scattering angle

Data at 70° (LAB)

HHC limit(Brodsky-Hiller)

HHC limit (Kobushkin-Syamtomov)

Q2 > 0.8-1 GeV2

Trend of t20 data not consistent with HHC

Comments and Outlook Comments and Outlook - 1- 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 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

JLab Hall A, PRL 88,092301-1Proton Form FactorsProton Form FactorsAsymptotic 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 = constin agreement with data

Data violates CCR (but not

HHC)

Comments and Outlook Comments and Outlook - 2- 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 90o - tensor polarization in ed elastic scattering at higher Q2 • HHC can be checked in many other exclusive processes,

not necessarily involving polarization, like

e+ e- → M M e+ e- → B B