Transcript Two-photon

Two-photon physics
in
hadronic processes
Marc Vanderhaeghen
College of William & Mary / Jefferson Lab
PPP7 workshop, Taipei, June 7 - 10, 2007
Outline

Elastic eN scattering beyond the one-photon exchange approximation
puzzle of different results extracted for GE/GM
in Rosenbluth vs polarization experiments
two-photon exchange processes

Beam (target) normal spin asymmetry in elastic eN scattering
new observable :
absorptive part of double Virtual Compton Scattering (VCS) amplitude
resonance region, diffractive region, partonic estimate (GPDs)
in coll. with A.Afanasev, S. Brodsky, C. Carlson, Y.C. Chen, M. Gorchtein,
P.A.M. Guichon, V. Pascalutsa, B. Pasquini
Carlson, Vdh : Ann. Rev. Nucl. Part. Sci. 57 (2007) 171-204
Early Measurements of GEp
• relied on Rosenbluth separation
• measure d/d at constant Q2
• GEp inversely weighted with Q2, increasing the systematic error
above Q2 ~ 1 GeV2
Method : at fixed Q2, vary angle q
(or equivalently ) and plot
reduced cross section versus 
At 6 GeV2 R changes by only 8% from =0 to =1 if
GEp=GMp/µp
Hence, measurement of GEp with 10% accuracy
requires 1.6% cross-section measurement
Spin Transfer Reaction 1H(e,e’p)
Pn  0
q 
p
p
hPt  h2  (1  )GE GM tan e / I 0
2
hPl   hE e  E e' GM   (1  )tan
p
2
2
 qe 
/ M / I0
 2
2
2
q 
I0  GEp Q2    GMp Q2  1 2(1  )tan2 e 
 2 

GEp
Pt E e  E e' q e 
t an
p 
2
GM
Pl 2M
No error contributions from
• analyzing power
• beam polarimetry
Puzzle : two methods,
two different results !
Rosenbluth vs polarization transfer measurements of GE/GM of proton
SLAC, Jlab
Rosenbluth data
Jlab/Hall A
Polarization data
Jones et al. (2000)
Gayou et al. (2002)
Speculation : missing radiative corrections
Speculation : there are radiative corrections to Rosenbluth
experiments that are important and are not included
2
missing correction : linear in , not strongly Q dependent
Q2 = 6 GeV2
GE term is proportionally smaller at large Q
effect more visible at large Q2
2
if both FF scale in same way
Radiative correction diagrams
bremsstrahlung
vertex
corrections
2 photon
exchange box
diagrams
Status of radiative corrections
N

Tsai (1961), Mo & Tsai (1968)

box diagram calculated using only nucleon intermediate state and
using q1 ¼ 0 or q2 ¼ 0 in both numerator and denominator
(calculate 3-point function) -> gives correct IR divergent terms
Maximon & Tjon (2000)

same as above, but make the above approximation only in
numerator (calculate 4-point function)
+ use on-shell nucleon form factors in loop integral
Blunden, Melnitchouk, Tjon (2003)
further improvement by keeping the full numerator
Elastic eN scattering beyond
one-photon exchange approximation
Kinematical invariants :
(me = 0)
equivalently, introduce
Observables including two-photon exchange
Real parts of two-photon amplitudes
Phenomenological analysis
Guichon, Vdh (2003)
2-photon exchange corrections
can become large on the
Rosenbluth extraction,and
are of different size for
both observables
relevance when extracting
form factors at large Q2
Two-photon exchange calculation :
elastic contribution
world Rosenbluth data
N
Polarization Transfer
Blunden, Tjon, Melnitchouk (2003, 2005)
Two-photon exchange : partonic calculation
hard
scattering
amplitude
electron helicity
quark helicity
Calculation for em > em can be found in literature
(e.g. van Nieuwenhuizen (1971) ), which we verified explicitly
IR divergences of boxes must disappear or cancel in the end,
regularize through photon mass l
Separation soft-hard parts in electron-quark box
Follow the decomposition of Grammer and Yennie (1973) :
soft part calculated as 3-point function
reproduces Low Energy Theorem
kinematics partonic subprocess :
Two-photon exchange : partonic calculation
hard
scattering
amplitude
GPD integrals
“magnetic” GPD
“electric” GPD
“axial” GPD
Two-photon exchange : partonic calculation
GPDs
Chen, Afanasev, Brodsky,
Carlson, Vdh (2004)
Experimental verification
of TPE contributions
Experimental verification (will be
performed in next couple of years ! )
• non-linearity in -dependence
(test of model calculations)
• transverse single-spin asymmetry
(imaginary part of two-photon
amplitude)
• ratio of e+p and e-p cross section
(direct measurement of two-photon
contributions)
• CLAS experiment E04-116 aims at a
measurement of the -dependence of the
e+/e- ratio for Q2-values up to 2.0 GeV2
• At the VEPP-3 ring that ratio will be
measured at two  and Q2-values
ε - dependence of TPE contributions (I)
Chen, Kao, Yang (2007)
Polynomial fit
“log” fit
1γ only : Rosenbluth
1γ + 2γ : log fit
1γ + 2γ : polynomial fit
ε - dependence of TPE contributions (II)
e+ p / e- p
e+ p / e- p
Q2 (GeV2)
1.12
3.25
1.10
1.00
1.14
1.75
5.00
0
0.2
0.4
0.6
1.10
0.8
1
1.02
0
0.2
0.4
0.6
ε
polynomial fit
1
ε
log fit
Chen, Kao, Yang (2007)
0.8
Polarization transfer observables
1g  2g
1g
2 g correction
on
is small
2 g correction on
can be tested at small  !
proton Dirac & Pauli FFs :
GPD framework
PQCD
modified Regge GPD model
data : SLAC
data : JLab/HallA
Belitsky, Ji, Yuan (2003)
data : JLab/HallA
Guidal, Polyakov, Radyushkin, Vdh (2005)
Normal spin asymmetries in elastic
eN scattering
directly proportional to the imaginary part of 2-photon
exchange amplitudes
spin of beam OR target
NORMAL to scattering
plane
OR
on-shell intermediate state
order of magnitude estimates :
target :
beam :
SSA in elastic eN scattering
time reversed states
momenta and spins reversed
phase
rotation over 180o
around axis ? to plane
Unitarity
with
Time reversal invariance :
Perturbation theory in em
to
1 g exchange gives no contribution to spin asymmetries
to
spin asymmetries arise from interference between
1g exchange and absorptive part of 2g exchange
to
De Rujula et al. (1971)
1g exchange
function of elastic nucleon form
factors
2g exchange
absorptive part of double
virtual Compton scattering
elastic contribution
on-shell nucleon intermediate nucleon
inelastic contribution
X=  N
resonant and non-resonant  N intermediate states
calculated with MAID2003 : unitary isobar model
all 13 **** resonances below 2 GeV included
Drechsel, Hanstein, Kamalov, Tiator (1999)
Beam normal spin asymmetry
N (elastic)
 N (inelastic)
total (N +  N)
Pasquini & Vdh (2004)
MAMI data
F. Maas et al., PRL 94 (2005)
for Ee = 0.570 GeV
Bn = -8.59±0.89 ppm
New measurements at MAMI at backward angles :
measurement of resonance form
factors over range in Q2
Bn in
x10-6
Bn
diffractive region
Q2 = 0.05 GeV2
no suppression of Bn with
energy at fixed Q2
Afanasev & Merenkov
Note on SLAC E158 :
30% inelastic events included
E158 : Bn = -3.5 -> -2.5 ppm
(K. Kumar, prelim.)
ps (GeV)
σγp
Beam normal spin asymmetry : experiments
Expt.
E(GeV)
θe
Q2 GeV2
SAMPLE
0.192
146
0.10
-16.4±5.9
A4
0.570
35
0.11
-8.59±0.89
A4
0.855
35
0.23
-8.52±2.31
3.0
16
0.11
-6.7 ± 1.5
G0
3.0
19
0.15
-4.06± 1.62
G0
3.0
37
0.25
-4.82 ± 2.85
E-158(ep)
46.0
~3.0
0.06
-3.5 -> -2.5
E-158(ee)
46.0
~100
0.03
HAPPEX
Bn(ppm)
Elastic electron-nucleon amplitudes
with electron helicity flip
In Born approximation :
Elastic electron-quark amplitudes
with electron helicity flip
lepton mass
new amplitude
Beam normal spin asymmetry : partonic calculation
“magnetic” GPD
“electric” GPD
“magnetic” GPD
“electric” GPD
Beam normal spin asymmetry : proton results
Results of GPD
calculation
Note : elastic contribution to
Bn is negligibly small
Future PV experimental set-ups (0.1 ppm precision) :
challenge to measure this asymmetry
Summary
difference Rosenbluth vs polarization data
-> GEp /GMp : now mainly understood as due to two-photon exchange effects
-> quantitative theoretical calculations needed
-> precision test : several new expt. planned
Normal spin asymmetries (NSA) in elastic electron-nucleon scattering :
unique new tool to access the imaginary part of 2g exchange amplitudes
-> Imaginary part of 2g amplitude
absorptive part of non-forward doubly VCS tensor
-> Unitarity to relate the absorptive part of doubly VCS tensor to
pion-electroproduction amplitudes
beam NSA in the resonance region as a new tool to extract
resonance transition form factors
-> In hard scattering region : use handbag approach to relate beam and
target NSA to moments of GPDs