Transcript Two-photon

Normal spin asymmetries
and
two-photon processes :
theory
Marc Vanderhaeghen
College of William & Mary / Jefferson Lab
PAVI06 workshop, Milos, Greece, May 16 - 20, 2006
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

Z box processes to PV 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
Two-photon exchange effects
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)
Two methods, two different results !
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
GPD integrals
“magnetic” GPD
“electric” GPD
“axial” GPD
Two-photon exchange : partonic calculation
GPDs
Chen, Afanasev, Brodsky,
Carlson, Vdh (2004)
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  exchange gives no contribution to spin asymmetries
to
spin asymmetries arise from interference between
1 exchange and absorptive part of 2 exchange
to
De Rujula et al. (1971)
1 exchange
function of elastic nucleon form
factors
2 exchange
absorptive part of double
virtual Compton scattering
Hadronic Tensor: Absorptive part of Doubly Virtual Compton Tensor
q
P n
q
X
P n
on-shell intermediate states (MX
2
2
=W )
Transverse spin asymmetries
lepton
hadron
 Beam normal spin asymm.
 Target normal spin asymm.
sum over spins unpolarized particles
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)
(near) collinear singularities
Q21 ' 0, Q22  0
Quasi - VCS
'
k // k1
Q21  0, Q22 ' 0
'
Quasi - VCS
k1 // k’
Q21 ' 0, Q22 ' 0
Quasi - RCS
k1 = 0, W = ps – me
'
Kinematical bounds for Q12 and Q22
Elastic contribution
Inelastic contribution
Phase space integration

2-dim integration (Q12, Q22) for the elastic intermediate state

3-dim integration (Q12, Q22,W2) for inelastic excitations
‘Soft’ intermediate electron;
Both photons are hard collinear
One photon is
Hard collinear
MAMI A4
E = 855 MeV
Θcm= 57 deg
SAMPLE
E =200 MeV
Beam normal spin
asymmetry
 N (inelastic)
tot (N +  N)
Ee = 0.2 GeV
N (elastic)
Integrand [ppm GeV-1]
SAMPLE data
Wells et al., PRC (2001)
0 p
+ n
tot
Pasquini & Vdh (2004)
 inelastic contribution dominated by
the region of threshold pion production
 MAID in the threshold region is
consistent with chiral predictions
Quasi-RCS peak
Beam normal spin asymmetry : Ee = 0.2 GeV
EFT calculation :
Diaconescu & Ramsey-Musolf (2004)
to second order in Ee /MN
Pions are integrated out
NLO
calculation includes :
LO



Recoil corrections to
scattering from point
charge
Nucleon charge radius
Nucleon isovector magnetic
moment
SAMPLE data
S. Wells et al. (2001)
Beam normal spin asymmetry:
energy dependence at fixed cm=120o
+ n
full calculation
0 p
quasi-RCS approximation
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 :
talk : L. Capozza
Integrand : beam normal spin asymmetry
Ee = 0.855 GeV
D13 (1520)
 (1232)
0 p
+ n
tot
Quasi-RCS peak
Beam normal spin asymmetry
Ee = 0.570 GeV
Proton
 N
(inelastic)
N (elastic)
total
Neutron
N -> Δ transition form factors
in large Nc limit
modified Regge model
Regge model
measurement of
NΔ magnetic
form factor over
range of Q2
Bn at high energy & forward angle
forward region (q -> 0) :
dominated by near collinear
singularity
Q21 ' 0, Q22 ' 0, W = ps – me
Quasi RCS
p total cross section
'
Log enhancement
Afanasev & Merenkov : PRD 70 (2004) 073002
corrected result given by :
Gorchtein : PRC 73 (2006) 035213
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
Bn in diffractive region
Ee ( in GeV )
E158 : Bn = -3.5 -> -2.5 ppm
(K. Kumar, prelim.)
45 : SLAC E158
12
6
3
Gorchtein
intermediate energies & forward angles


dominance of collinear-photon exchange =>
replace 3-dim integral over (Q12,Q22,W) with 1-dim integral along
the line : Q12 ≈ 0 ; Q22 = Q2 (s-W2) / (s-M2)
Afanasev & Merenkov
used σγp from
parameterization by
N. Bianchi at al. (1996)
for resonance region
and Block&Halzen
(2004) for high energy
(Regge fit)
Beam normal spin asymmetry : Ee = 3 GeV
Afanasev & Merenkov
approximate hadronic
tensor by forward limit
and use fit to
experimental data on σγp
data also
expected from G0
HAPPEX
talk : L. Kaufmann
Bn : resonance contribution
( no forward approx. )
HAPPEX
Ee = 3 GeV
Integrand [ppm
 (1232)
Wmax= 2. GeV
(MAID2000)
integration up to Wmax= 2.5 GeV
(MAID2003)
GeV-1]
F15 (1680)
D13 (1520)
0 p
+ n
Pasquini & Vdh
tot
Additional contributions
like 2-pion intermediates states
become important
Quasi-RCS peak
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 - 37
0.13 – 0.6
E-158(ep)
46.0
~3.0
0.06
E-158(ee)
46.0
~100
0.03
HAPPEX
Bn(ppm)
-3.5 -> -2.5
Target normal spin asymmetry
Ee = 0.570 GeV
Proton
%
N
(inelastic)
N (elastic)
total
Neutron
Integrand : target normal spin asymmetry
Ee = 0.855 GeV
 N loops
 N loops
(1232)
0 p
+ n
tot
Ee = 2 GeV
(1232)
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
Z box diagram processes
to
PV elastic eN scattering
in coll. with
C. Carlson, Y.C. Chen, V. Pascalutsa, B. Pasquini
PV electron scattering
polarized electrons, unpolarized target
e
e

V
V
e
e
V, A
A, V
Z
p
p
e
p
e
p
2

p
p
Strange Electric and Magnetic
form factors,
+ Axial form factor
At a given Q2,
ranges from 1 (forward angle) to 0 (backward angle)
Rosenbluth separation of strange form factors
elastic eN scattering : general PV amplitude
Kinematical invariants :
VA
e- helicity conservation
Parity + Time reversal (or charge conjugation)
3 structures
contains 3 independent Invariant Amplitudes function of Q2, 
leading order contribution to MPV
e
p
e
e
e
V
A
V
A
p
p
p
beyond the leading order
e
p
V
A
V
A
e
p
e
p
V
A
V
A
e
p
Hadronic corrections at backward angles
( intermediate Q2 )

Z0
+ 2 diagrams with  and Z interchanged
calculation in forward kinematics (APV) exists :
Marciano & Sirlin (1984)
in non-forward kinematics :
more tensor structures & form factors effects
check results with quark-parton model calculation :
Bohm & Spiesberger (1986, 1987)
lepton
tensors
hadron
tensors
Summary
Normal spin asymmetries (NSA) in elastic electron-nucleon scattering :
unique new tool to access the imaginary part of 2 exchange amplitudes
Imaginary part of 2 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