two-photon physics in hadronic processes marc vanderhaeghen college of william & mary /...
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Two-photon physics Two-photon physics in in
hadronic processeshadronic processes
Marc VanderhaeghenCollege of William & Mary / Jefferson Lab
PPP7 workshop, Taipei, June 7 - 10, 2007
OutlineOutline 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 GEarly Measurements of GEEpp
• relied on Rosenbluth separation• measure d/d at constant Q2
• GEp inversely weighted with Q2, increasing the systematic error
above Q2 ~ 1 GeV2
At 6 GeV2 R changes by only 8% from =0 to =1 if GE
p=GMp/µp
Hence, measurement of GEp with 10% accuracy
requires 1.6% cross-section measurement
Method : at fixed Q2, vary angle (or equivalently ) and plot reduced cross section versus
Spin Transfer Reaction Spin Transfer Reaction 11H(e,e’p)H(e,e’p)
Pn 0
hPt h2 (1 )GEpGM
p tane
2
/ I0
hPl h Ee Ee' GMp 2
(1 )tan2 e
2
/ M / I0
I0 GEp Q2 2
GMp Q2 2
1 2(1 )tan2 e
2
GEp
GMp
Pt
Pl
Ee Ee'
2Mtan
e
2
No error contributions from• analyzing power• beam polarimetry
Rosenbluth vs polarization transfer measurements of GE/GM of proton
Jlab/Hall A Polarization
data
Jones et al. (2000)
Gayou et al. (2002)
SLAC, Jlab
Rosenbluth data
Puzzle Puzzle : two methods, : two methods, two different results !two different results !
Speculation : missing radiative Speculation : missing radiative correctionscorrections
Speculation : there are radiative corrections to Rosenbluth
experiments that are important and are not included missing correction : linear in not strongly Q
2 dependent
GE term is proportionally smaller at large Q2
if both FF scale in same wayeffect more visible at large Q2
Q2 = 6 GeV2
Radiative correction diagramsRadiative correction diagrams
bremsstrahlung
vertex
corrections
2 photon
exchange box
diagrams
Status of radiative correctionsStatus of radiative corrections
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
N
Elastic eN scattering Elastic eN scattering beyond beyond one-photonone-photon exchange exchange
approximationapproximation
equivalently, introduce
Kinematical invariants :
(me = 0)
Observables including two-photon exchangeObservables including two-photon exchange
Real parts Real parts of two-photon amplitudesof two-photon amplitudes
Phenomenological analysisPhenomenological 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 : Two-photon exchange calculation : elastic contributionelastic contribution
Blunden, Tjon, Melnitchouk (2003, 2005)
N
world Rosenbluth data
Polarization Transfer
hard scattering
amplitude
electron helicity quark helicity
Calculation for eecan 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
Two-photon exchange : Two-photon exchange : partonic partonic calculationcalculation
kinematics partonic subprocess :
Separation soft-hard parts in electron-quark Separation soft-hard parts in electron-quark boxbox
Follow the decomposition of Grammer and Yennie (1973) :
soft part calculated as 3-point function
reproduces Low Energy Theorem
hard scattering
amplitude
Two-photon exchange : Two-photon exchange : partonic partonic calculationcalculation
GPD integrals
“magnetic” GPD
“electric” GPD
“axial” GPD
Two-photon exchange : Two-photon exchange : partonic calculationpartonic calculation
GPDs
Chen, Afanasev, Brodsky, Carlson, Vdh
(2004)
Experimental Experimental verification verification
of TPE contributionsof TPE contributionsExperimental 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
εε - - dependence of TPE contributions (I)dependence of TPE contributions (I)
Chen, Kao, Yang (2007)
Polynomial fit
“log” fit
1γ only : Rosenbluth1γ + 2γ : log fit
1γ + 2γ : polynomial fit
Q2 (GeV2)
ε
0 10.2 0.4 0.6 0.8
1.75
3.25
5.00
e+ p / e- p
1.00
1.10
1.12
ε
0 0.4 10.2 0.80.6
e+ p / e- p
1.02
1.10
1.14
Chen, Kao, Yang (2007)
polynomial fit
log fit
εε - - dependence of TPE contributions (II)dependence of TPE contributions (II)
Polarization transfer observablesPolarization transfer observables
12
2 correction
on is small
2 correction on
can be tested at small
proton proton Dirac & Pauli Dirac & Pauli FFs :FFs :
modified Regge GPD model
PQCD
Belitsky, Ji, Yuan (2003)
GPD framework
Guidal, Polyakov, Radyushkin, Vdh (2005)
data : SLAC
data : JLab/HallAdata : JLab/HallA
Normal spin asymmetries in Normal spin asymmetries in elastic eN scatteringelastic eN scattering
on-shell intermediate state
spin of beam OR target
NORMAL to scattering
plane
directly proportional to the imaginary part of 2-photon exchange amplitudes
OR
order of magnitude estimates :
target :
beam :
time reversed states
momenta and spins reversed
rotation over 180o around axis ? to plane
phase
SSA in elastic eN scatteringSSA in elastic eN scattering
Unitarity
with
Time reversal invariance :
Perturbation theory in em
to
to
1 exchange gives no contribution to spin asymmetries
spin asymmetries arise from interference between
1 exchange and absorptive part of 2 exchange
2 exchange
1 exchange
function of elastic nucleon form factors
absorptive part of double
virtual Compton scattering
toDe Rujula et al.
(1971)
elastic contribution
on-shell nucleon intermediate nucleon
inelastic contribution
resonant and non-resonant N intermediate states calculated with MAID2003 : unitary isobar model
X= N
all 13 **** resonances below 2 GeV included
Drechsel, Hanstein, Kamalov, Tiator (1999)
Beam Beam normal spin normal spin asymmetryasymmetry
N (elastic)
N (inelastic)
total (N + N)
MAMI dataF. Maas et al., PRL 94 (2005)
New measurements at MAMI at backward angles :
Pasquini & Vdh (2004)
for E Eee = 0.570 GeV = 0.570 GeV
Bn = -8.59±0.89 ppm measurement of resonance
form factors over range in Q2
no suppression of Bn with energy at fixed
Q2
x10-6
ps (GeV)
QQ2 2 = 0.05 GeV= 0.05 GeV22
BBn n in in
diffractive regiondiffractive region
Afanasev & Merenkov
BBn n
σγp
E158 : Bn = -3.5 -> -2.5 ppm (K. Kumar, prelim.)
Note on SLAC E158 :
30% inelastic events included
Expt. E(GeV) θe Q2 GeV2 Bn(ppm)
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
HAPPEX 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
Beam Beam normal spin asymmetry : normal spin asymmetry : experimentsexperiments
Elastic electron-nucleon amplitudes Elastic electron-nucleon amplitudes with electron helicity flipwith electron helicity flip
In Born approximation :
Elastic electron-quark amplitudes Elastic electron-quark amplitudes
with electron helicity flipwith electron helicity flip
lepton mass new amplitude
BeamBeam normal spin asymmetry : partonic normal spin asymmetry : partonic calculationcalculation
“magnetic” GPD
“magnetic” GPD
“electric” GPD
“electric” GPD
Beam normal spin asymmetry : Beam normal spin asymmetry : protonproton resultsresults
Future PV experimental set-ups (0.1 ppm precision) :
challenge to measure this asymmetry
Results of GPD
calculation
Note : elastic contribution to
Bn is negligibly small
SummarySummary
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
difference Rosenbluth vs polarization data-> GE
p /GMp : now mainly understood as due to two-photon exchange
effects -> quantitative theoretical calculations needed-> precision test : several new expt. planned