Hadron form factor measurements at large momentum transfer Egle Tomasi-Gustafsson IRFU, SPhN-...
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Transcript of Hadron form factor measurements at large momentum transfer Egle Tomasi-Gustafsson IRFU, SPhN-...
Hadron form factor measurements at large momentum transfer
Egle Tomasi-GustafssonIRFU, SPhN-Saclay, and
IN2P3- IPN Orsay France
Kolomna, 11-VI-2010 1Egle Tomasi-Gustafsson
Egle Tomasi-Gustafsson 2
PLAN
•Introduction
•What is new?•Space-like region : new data at JLab
• Rosenbluth separation (unpolarized scattering)•Recoil proton polarization
(A.I. Akhiezer and M.P. Rekalo in 1968)•Time-like region
•Plans at PANDA
•Global description in a wide kinematical region• Asymptotics• Counting rules• Two photon exchange
Kolomna, 11-VI-2010
Egle Tomasi-Gustafsson 3
Hadron Electromagnetic Form factors
Characterize the internal structure of a particle ( point-like)
Elastic form factors contain information on the hadron ground state.
In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors.
Neutron and proton form factors are different.
Deuteron: 2 structure functions, but 3 form factors.
Playground for theory and experiment at low q2 probe the size of the
nucleus, at high q2 test QCD scaling
Kolomna, 11-VI-2010
4Kolomna, 11-VI-2010
The proton vertex is parametrized in terms of FFs: Pauli and Dirac F1,F2
Electromagnetic Interaction
q2<0
e-e-
p p
)2q(2FM2
qi)2q(1F
or in terms of Sachs FFs:GE=F1- t F2, GM=F1+F2, t=-q2/4M2
The electron vertex is known,gm
The interaction is carried by a virtual photon of mass q2
What about high order
radiative corrections?
Egle Tomasi-Gustafsson
Egle Tomasi-Gustafsson Kolomna, 11-VI-20105
Crossing Symmetry
Scattering and annihilation channels:
- Described by the same amplitude :
- function of two kinematical variables, s and t
k2 → – k2
- which scan different kinematical regions
p2 → – p2
6Kolomna, 11-VI-2010
Analyticity
__
q2<0
e-e-
p p
q2>0
e-
e+ p
p
q2q2=4mp2
FFs are complexFFs are real
Unp
hysi
cal r
egio
n
GE=GM
Space-like
Time-likeGE(0)=1
GM(0)=mp
Asymptotics- QCD- analyticity
p+p ↔ e++e-e+p e+p
p+p
↔ e
++
e- +
p
Egle Tomasi-Gustafsson
Egle Tomasi-Gustafsson 7
Proton Form Factors ...before
Rosenbluth separation/ Polarization observables
Dipole approximation: GD=(1+Q2/0.71 GeV2)-2
Kolomna, 11-VI-2010
Egle Tomasi-Gustafsson 8
Dipole Approximation
• Classical approach– Nucleon FF (in the Breit
system) are Fourier transform of the charge or magnetic distribution.
•The dipole approximation corresponds to an exponential density distribution.
– ρ = ρ0 exp(-r/r0),
– r02= (0.24 fm)2, <r2> ~(0.81 fm) 2
m2D =0.71 GeV2
Dipole approximation: GD=(1+Q2/0.71 GeV2)-2
Kolomna, 11-VI-2010
Egle Tomasi-Gustafsson 9
Dipole Approximation and pQCD
V. A. Matveev, R. M. Muradian, and A. N. Tavkhelidze (1973), Brodsky and Farrar (1973), Politzer (1974), Chernyak & Zhitnisky (1984), Efremov & Radyuskin (1980)…
Dimensional scaling
– Fn (Q2)= Cn [1/( 1+Q2/mn) n-1],• mn=n2 , <quark momentum squared>• n is the number of constituent quarks
– Setting 2 =(0.471±.010) GeV2 (fitting pion data)
• pion: F (Q2)= C [1/ (1+Q2/0.471 GeV2)1],
• nucleon: FN (Q2)= CN [1/( 1+Q2/0.71 GeV2)2],• deuteron: Fd (Q2)= Cd [1/( 1+Q2/1.41GeV2)5]
Kolomna, 11-VI-2010
Egle Tomasi-Gustafsson 10
The Rosenbluth separation
)2(2)2(2
)1(1 QMGQEG
Mottd
ddd
2M4
2Q,1
2e2)tan1(21
2MG2
EGR
®Holds for 1 g exchange only
Linearity of the reduced cross section
PRL 94, 142301 (2005)
®tan2qe dependencee
Q2 f
ixed
Kolomna, 11-VI-2010
Egle Tomasi-Gustafsson 11
Rosenbluth separation
=0.5=0.2
=0.8
Contribution of the electric term
…to be compared to the absolute value of the error on s and to the size and e dependence of RC
Kolomna, 11-VI-2010
Egle Tomasi-Gustafsson 12
The polarization induces a term in the cross section proportional to GE GM
Polarized beam and target or
polarized beam and recoil proton polarization
The polarization method (1967)
Kolomna, 11-VI-2010
Egle Tomasi-Gustafsson 13
The simultaneous measurement of Pt and Pl reduces the systematic errors
The polarization method (exp)
Kolomna, 11-VI-2010
C. Perdrisat et al, JLab-GEp collaboration
Polarization experiments - JlabA.I. Akhiezer and M.P. Rekalo, 1967
GEp collaboration1) "standard" dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep?4) contradiction between
polarized and unpolarized measurements
Kolomna, 11-VI-2010 14Egle Tomasi-Gustafsson
A.J.R. Puckett et al, PRL (2010)
Egle Tomasi-Gustafsson 15
Issues•Some models (IJL 73, Di-quark, soliton..) predicted such behavior before the data appeared
•Simultaneous description of the four nucleon form factors...•...in the space-like and in the time-
like regions•Consequences for the light ions
description•When pQCD starts to apply?•Source of the discrepancy
BUT
Kolomna, 11-VI-2010
Egle Tomasi-GustafssonGDR 25/XI/2010 16
Neutron/proton form factors ratio GEn (Hall A)
Egle Tomasi-Gustafsson17
The IA deuteron structure: S=1, T=0
2) The S (u) and D (w) deuteron wave function
1) The nucleon form factors:
GDR 25/XI/2010
Egle Tomasi-Gustafsson18
GEn from the deuteron
E. T-G. and M. P. Rekalo, Europhys. Lett. 55, 188 (2001)
GDR 25/XI/2010
•GEn > GEp starting from 2-3 GeV2 !
Egle Tomasi-Gustafsson 19Kolomna, 11-VI-2010
Iachello, Jakson and Landé (1973)
Isoscalar and isovector FFs* ,ρ,
Egle Tomasi-Gustafsson 20
The nucleon form factors
VDM : IJLF. Iachello..PLB 43, 191 (1973)
Extended VDM (G.-K. 92): E.L.Lomon PRC 66, 045501 2002)
HohlerNPB 114, 505 (1976)
BostedPRC 51, 409 (1995)
Electric Magneticne
utro
npr
oton
E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh, EPJA (2005)
Kolomna, 11-VI-2010
21Kolomna, 11-VI-2010
Time-like observables: | GE| 2 and | GM| 2 .
As in SL region:- Dependence on q2 contained in FFs- Even dependence on cos2 q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex!
A. Zichichi, S. M. Berman, N. Cabibbo, R. Gatto, Il Nuovo Cimento XXIV, 170 (1962)B. Bilenkii, C. Giunti, V. Wataghin, Z. Phys. C 59, 475 (1993).G. Gakh, E.T-G., Nucl. Phys. A761,120 (2005).
Egle Tomasi-Gustafsson
Egle Tomasi-Gustafsson 22
Models in T.L. region
E. T-G., F. Lacroix, C. Duterte, G.I. Gakh EPJA 2005
VDM : IJLF. Iachello..PLB43 191 (1973)
Extended VDM (G.-K. 92): E.L.Lomon PRC66 045501(2002)
‘QCD inspired’
proton
neutron
Kolomna, 11-VI-2010
Egle Tomasi-Gustafsson 23
Spin Observables
Analyzing power, A
Double spin observables
Kolomna, 11-VI-2010
Egle Tomasi-Gustafsson 24
Kolomna, 11-VI-2010
Angular Distributions
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section:
is equivalent to:
Egle Tomasi-Gustafsson 25
Models in T.L. Region (polarization)
VDM : IJL
Ext. VDM
‘QCD inspired’
AngularAsymmetry
Ay Axx Ayy
AxzAzz
E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 2005
Kolomna, 11-VI-2010
Egle Tomasi-Gustafsson 26
SIS
HESR
PANDA
http://www-panda.gsi.de/Parameters of HESR
• Injection of p at 3.7 GeV• Slow synchrotron (1.5-14.5 GeV/c)• Storage ring for internal target operation• Luminosity up to L~ 2x1032 cm-2s-1• Beam cooling (stochastic & electron)
need of • highest rates• good resolution• Good Particle
Identification
Proton-Antiproton Annihilation
Kolomna, 11-VI-2010
27Kolomna, 11-VI-2010 27
• 3 body reactions kinematical constraints
PID
• 2 body reactions (hadrons)
π+π-, K+K-
610~
ee
It is possible to discriminate e+e- from π+ π-
High statistics GEANT4 simulations • < few 0/00 misidentified events / cosCM bin
• < 1% on the total cross section up to 16 GeV2
Physical BackgroundM. Sudol et al, arXiv:0907.4478 [nucl-ex]
Egle Tomasi-Gustafsson
28Kolomna, 11-VI-2010
Individual determination of GE and GM up to large Q2
Expected Results
R=GE/GM
BaBAR
PS170 PANDA sim
L = 2 10 32 cm-2 s-1
100 jours
M. Sudol et al, EPJA 2010, arXiv:0907.4478 [nucl-ex]
Egle Tomasi-Gustafsson
29Kolomna, 11-VI-2010
Phragmèn-Lindelöf theorem
Asymptotic properties for analytical functions
E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265 (2005)
D=0.05, 0.1
If f(z) a as z along a straight line, and f(z) b as zalong another straight line, and f(z) is regular and bounded in the angle between, then a=b and f(z) a
uniformly in the angle.
Egle Tomasi-Gustafsson
30Kolomna, 11-VI-2010
Phragmèn-Lindelöf theorem
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)
Applies to NN and NNInteraction (Pomeranchuk theorem)t=0 : not a QCD regime!
Connection with QCD asymptotics?
Egle Tomasi-Gustafsson
E. T-G. e-Print: arXiv:0907.4442 [nucl-th]
Egle Tomasi-Gustafsson31GSI 1/XII/2010
Radiative Corrections (ep)
RC to the cross section:- large (may reach 40%)- e and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign !!!)
Q2=5 GeV2
Q2=3.75 GeV2
Q2=1.75 GeV2
E. T.-G., G. Gakh, PRC 72, 015209 (2005)
Andivahis et al., PRD50, 5491 (1994)
2MG2
EGR
Egle Tomasi-GustafssonGSI 1/XII/2010 32
Scattered electron energy
All orders of PT needed beyond Mo & Tsai approximation!
Initial state emission
final state emission
Quasi-elastic scattering
3%
Y0
Not so small!
Shift to LOWER Q2
Egle Tomasi-GustafssonGSI 1/XII/2010 33
Short history (I)
Schwinger: corrections to cross section for electron scattering in external field
s=s0(1+d) (1)
Yennie, Frauchi, Suura: cross section of any pure process (without real photon emission) is zero.
Kessler, Ericsson, Baier, Fadin, Khoze, Y. Tsai : quasi real electron method. Emission of hard photon is described in terms of a convolution of a radiative function with Born cross section.
(1) Not adequate
Egle Tomasi-GustafssonGSI 1/XII/2010 34
The Structure Function Method
Distinguish: -leading contributions of higher order
-non leading ones
E. A. K. and V.S. FADIN, Sov. J. of Nucl. Phys. 41, 466 (1985)
The SF method is based on: • Renormalization group evolution equation• Drell-Yan parton picture of the cross section in QCD
Electron SF: probability to ‘find’ electron in the initial electron, with energy fraction x and virtuality up to Q2
Egle Tomasi-GustafssonGSI 1/XII/2010 35
LSF: ‰ precision
2e
2
m
QlnL,1L
%2.0400
1L
E. A. K. and V.S. FADIN, Sov. J. of Nucl. Phys. 41, 466 (1985)
LLA (Leading Logarithm Approximation)
Precision of LLA
%01.0L2
Even when corrections in first order PT are d~100%, the accuracy of higher order RC (LSF) is / a p d1% !
Including K-factor
Egle Tomasi-GustafssonGSI 1/XII/2010 36
The LSF cross section (for ep )
•If the electron is detected in a calorimeter: the cross section is integrated over the scattered electron energy fraction:
•The K-factor includes all non leading contributions:
1),z(Ddz1
0
QED Radiative Corrections and DVCS
Egle Tomasi-GustafssonGSI 1/XII/2010 38
V.V. Bytev, E.A. Kuraev, E.T.G., Phys.Rev.C77:055205,2008.
Helicity asymmetry Q2=2.3 GeV2
xBj=0.36
Charge asymmetry
RCBorn
39Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
Unpolarized cross section
• Induces four new terms• Odd function of : q• Does not contribute at q =90°
Two Photon Exchange:
M.P. Rekalo and E. T.-G., EPJA 22, 331 (2004)G.I. Gakh and E. T.-G., NPA761, 120 (2005)
40Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
•Properties of the TPE amplitudes with respect to the transformation: cos = - cos i.e., -
(equivalent to non-linearity in Rosenbluth fit)
•Based on these properties one can remove or single out TPE contribution
Symmetry relations
E. T.-G., G. Gakh, NPA (2007)
Egle Tomasi-Gustafsson Kolomna, 11-VI-2010 41
•Differential cross section at complementary angles:
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2 contribution:
The SUM cancels the 2 contribution:
42Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
Simulations
Approximations:• Neglect contributions to GE,GM• Consider only real part
Main effect: odd cos -qdistribution
20.0/3 MGF
02.0/3 MGF
0/3 MGF
05.0/3 MGF
q2=5.4,8.2,13.8 GeV2
43Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
Fitting the angular distributions...
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section:
is equivalent to:
44Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
Fitting the angular distributions...
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)
1 g exchange:
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
45Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
q2=5.4 GeV2
2 g 0
Fitting the angular distributions...
46Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
q2=5.4 GeV2
2 g 0.02
Fitting the angular distributions...
47Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
q2=5.4 GeV2
2 g 0.05
Fitting the angular distributions...
48Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
q2=5.4 GeV2
2 g 0.20
Fitting the angular distributions…
49Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
0.02
q2=5.4 GeV2
q2= 8.2 GeV2
q2=13.8 GeV2
0.05 0.201g 2g
50Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
N=a0+a2cos q sinq +a1 cos2q, a2~2g
Gep III results (2010)
Egle Tomasi-GustafssonGSI 1/XII/2010 51
Bystritskiy SF
No radiative corrections applied to the data
No evidence of two photon effects
52Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
Radiative Return (ISR)
.s
m,
x
sin
xx
x),x,s(W
,s
m
s
Ex),m)(ppee(),x,s(W
s
m
cosddm
)ppee(d
e
2
22
122
2
2
2
2
e+ +e- p + p +
B. Aubert ( BABAR Collaboration) Phys Rev. D73, 012005 (2006)
53Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
1.877÷1.950
Angular distribution
Eve
nts
/0.2
vs.
cos
q
2.400÷3.0002.200÷2.4002.100÷2.200
2.025÷2.1001.950÷2.025
2 -g exchange?
54Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO
12-XII-2008
Angular Asymmetry
Mpp=1.877-1.9
A=0.01±0.02
Mpp=2.4-3
E. T.-G., E.A. Kuraev, S. Bakmaev, S. Pacetti, Phys. Lett. B (2008)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 55GSI, 8-XII-2009
Structure Function method
e+ +e- p + p + DE=0.05
• Virtual and soft photon emission
• Hard photon emission
• LLA- Structure Functions Kuraev,Fadin (1985) Egle Tomasi-GustafssonGSI 1/XII/2010 56
Differential cross section (SF)
Egle Tomasi-GustafssonGSI 1/XII/2010 57
• The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Egle Tomasi-GustafssonGSI 1/XII/2010 58
K-factor (hard)
1. of the order of one2. from the even part of the cross section
cos q
Charge Asymmetry
Egle Tomasi-GustafssonGSI 1/XII/2010 59
Radiative correction factor
Egle Tomasi-GustafssonGSI 1/XII/2010 60
s=10 GeV2
cos q
Ncorr=Nraw(1+ )d
d
Integrated in all phase space for gProton structureless
Dalitz-plot p+p →e++e- (+ )g
Egle Tomasi-GustafssonGSI 1/XII/2010 61
x+=Ee+
x-=Ee-
s=10 GeV2
Conclusions Comparison of scattering and annihilation channels:
model independent statements
Study of the validity of one photon exchange approximation: basic question for deriving information on the hadron structure : in annihilation processes all FFs information is contained in a precise measurement of the angular distribution.
Determination of time-like form factors up to large q2 Tests of validity of pQCD and analiticity. Polarization
observables?basic program with anti-proton beams: Panda Physics Performance Report e-Print: arXiv:0903.3905 [hep-ex] Kolomna, 11-VI-2010 62
Egle Tomasi-Gustafsson