dispersion relations for DVCS

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dispersion relations for DVCS

• Marc Vanderhaeghen
• Johannes Gutenberg Universität, Mainz

DVCS meeting, JLab, August 6-7, 2008
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Dispersion relations for DVCS amplitudes (in
terms of GPDs)
Anikin, Teryaev (2007) Diehl, Ivanov
(2007) Polyakov, Vdh (2008) Kumericki-Passek,
Mueller, Passek (2008)
Dispersion relations for 12 VCS amplitudes
Drechsel, Gorchtein, Metz, Pasquini, Vdh (2000)
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helicity averaged twist-2 DVCS amplitude
twist-2 DVCS amplitude for GPD H convolution
integral
involves singlet GPD
SSA measures Im part
Re part involves convolution integral
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Dispersion Relation for helicity averaged
(twist-2) DVCS amplitude
energy variables
helicity averaged ampl even in ?
once subtracted fixed-t dispersion relation
(analyticity, crossing)
subtraction at ? 0
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DR for DVCS amplitude (contd)
once subtracted fixed-t dispersion relation in
variable x
subtraction constant
link with twist-2 GPD
numerically stable implementation
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subtraction constant in DR
difference between convolution and DR integrals
subtraction constant is independent of ?
formally put ? 0
time reversal GPD even in ? (2nd argument)

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subtraction constant in DR relation with D-term
Lorentz invariance polynomiality of
Mellin moments of GPDs
highest moment generated by Polyakov-Weiss
D-term contribution to GPD
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subtraction constant in DR relation with D-term
(contd)
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subtraction constant in DR relation with D-term
(contd)
Gegenbauer expansion of D-term
Gegenbauer polynomials
in ?QSM at t 0 d1 -4.0, d3 -1.2, d5
-0.4
(GPV 01)
also calculable in lattice QCD
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DR evaluation of DVCS amplitude (GPD H)
Double Distribution model
bv bs 1
bv bs 20
Dual model
based on same forward distr.
result for real part shown for ? 0
Polyakov, Vdh (2008)
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DR for axial vector DVCS amplitude (GPD Htilde)
Under crossing amplitude odd in ?
assume unsubtracted dispersion relation
(cfr. Bjorken sum rule, GDH sum rule, in forward
case)
link with GPD
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DR for amplitudes involving GPDs E and Etilde
GPD E once-subtracted DR
GPD (H E) is unsubtracted subtraction constant
for GPD E is (cfr. - D-term )
- ?(t)
GPD Etilde once-subtracted DR
sum of pseudoscalar meson poles ( p0, ?, )
subtraction constant for GPD Etilde
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DR evaluation (dual model for GPDs) Polyakov,
Vdh (2008)
data JLab/Hall A
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Bethe-Heitler
DR evaluation (dual model for GPDs) Polyakov,
Vdh (2008)
data JLab/Hall A
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Conclusions
Dispersion relations for DVCS amplitudes
constraint from analyticity, crossing built in
subtraction constants for H and E D-term
for Htilde no subtraction (?) for
Etilde PS meson poles
Experimental Strategy measurement of imaginary
parts single polarization observables over
sufficiently broad range in ? real parts fix
the subtraction constants, cross check by
extracting constants at same t for different
values of ?