Onset of Scaling in Exclusive Processes Marco Mirazita Istituto Nazionale di Fisica Nucleare...
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Transcript of Onset of Scaling in Exclusive Processes Marco Mirazita Istituto Nazionale di Fisica Nucleare...
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