Transcript Two-photon

Hadron
Form Factors :
theory
Marc Vanderhaeghen
College of William & Mary / JLab
EINN 2005, Milos (Greece), September 20-24, 2005
Outline
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Nucleon electromagnetic form factors :
theoretical approaches
NΔ form factors
two-photon exchange effects
nucleon FF : Rosenbluth vs polarization data
extension to N -> Δ FF
For weak form factors/parity violation :
see talks -> D. L’Huillier, K. Paschke
Recent review on “electromagnetic form factors of the nucleon and
Compton scattering”
Ch. Hyde-Wright and K. de Jager : Ann. Rev. Nucl. Part. Sci. 2004, 54
Nucleon electromagnetic form factors :
theoretical approaches
i) Dispersion theory
ii) Mapping out pion cloud,
chiral perturbation theory
iii) lattice QCD :
recent results & chiral extrapolation
iv) link to Generalized Parton Distributions :
nucleon “tomography”
v) other
disclaimer : v) will not be discussed in this talk
nucleon FF : dispersion theory
*
q
N
V
q2 > 0 : timelike
Hoehler et al. (1976)
q2 = - Q2 < 0 :
spacelike
Mergell, Meißner, Drechsel (1995)
N
Hammer, Meißner (2004)
Hammer, Meißner, Drechsel (1996)
general principles : analyticity in q2 , unitarity
FF -> dispersion relation in q2
branch cuts for q2 > 4 mπ2 : vector meson poles + continua (ππ,… )
basic dipole behavior : explained by 2 nearby poles with residua of
equal size but opposite sign
analysis of Hammer & Meißner (2004)
isovector channel : 2π continuum + 4 poles : ρ, ρ’(1050), ρ’’(1465), ρ’’’(1700)
isoscalar channel : 4 poles : ω, φ(1019), S’(1650) S’’(1680)
masses & 16 residua (V, T) fitted + PQCD scaling behavior parametrized
nucleon FF : dispersion theory
Hammer, Meißner (2004)
Hammer, Meißner, Drechsel
(1996)
phenomenological fit by
Friedrich, Walcher (2003)
DR : good description, except for GEp / GMp
nucleon form factors : pion cloud
Friedrich, Walcher
(2003)
phenomenological fit :
“smooth” part
(sum of 2 dipoles)
+ “bump”
(gaussian)
6 parameter fit for
each FF
pion cloud
pronounced structure in all FF around Q  0.5 GeV/c
extending out
to  2 fm
nucleon FF : Chiral Perturbation Theory
Kubis, Meißner
(2001)
Goldstone boson Baryon loops
(relativistic ChPT,
4th order, IR reg.)
+ vector mesons
SU(3)
SU(2) : πN
DR
see also Schindler et al.
(2005)
(EOM renorm. scheme)
nucleon FF : lattice QCD
QCDSF Coll. : Goeckeler et al. (2003)
Lattice results fitted by dipoles -> for isovector channel : masses MeV , MmV
lattice
lattice
Expt.
Expt.
quenched approximation :
qq loops neglected
Expt.
linear extrapolation in mπ
lattice
reasonable good description of
GEp / GMp at larger Q2
(where role of pion cloud is
diminished)
nucleon FF : lattice & chiral extrapolation
Leinweber, Lu, Thomas (1999)
Hemmert and Weise (2002)
lattice : QCDSF
(r1V )2
+…
lattice : QCDSF
4 LEC fit
κV
3 LEC fit
lattice : QCDSF
(r2V )2
Hemmert : chiral extrapolation
using SSE at O(ε3) -> fit LEC
to available lattice points
qualitative description obtained,
not clear for (r1V )2
nucleon FF : lattice & chiral extrapolation
Pascalutsa, Holstein, Vdh (2004)
For κ : resummation of higher order terms by using a new sum rule (SR)
(linearized version of GDH) -> analyticity is built in
Relativistic chiral loops (SR) give smoother behavior than the
heavy-baryon expansion (HB) or Infrared-Regularized ChPT (IR)
lattice : Adelaide group
(Zanotti)
red curve is the 2-parameter fit to lattice data
based on sum rule (SR) result
chiral loops
LHP Collaboration (R. Edwards)
nucleon FF : lattice
prospects
F1V
state of art : employ full QCD lattices
(e.g. MILC Coll.) using “staggered”
fermions for sea quarks
employ domain wall fermions for
valence quarks
Pion masses down to less than 300 MeV
As the pion mass approaches the
(r2)1 physical value, the calculated
nucleon size approaches the
V
correct value
√
next step : fully consistent treatment of
chiral symmetry for both valence &
sea quarks
FF : link to Generalized Parton Distributions
Q2 large
Ji , Radyushkin
(1996)
*
t = Δ2
x+
ξ
P - Δ/2
low –t process :
x-ξ
GPD (x, ξ ,t)
-t << Q2
P + Δ/2
(x + ξ) and (x - ξ) : longitudinal momentum fractions of quarks
at large Q2 : QCD factorization theorem
hard exclusive
process can be described by 4 transitions (GPDs) :
~
Vector : H (x, ξ ,t)
Axial-Vector : H (x, ξ ,t)
Tensor : E (x, ξ ,t)
Pseudoscalar : E (x, ξ ,t)
see talks -> Diehl, Camacho, Hadjidakis
~
known information on GPDs
forward limit : ordinary parton distributions
unpolarized quark distr
polarized quark distr
: do NOT appear in DIS
new information
first moments : nucleon electroweak form factors
Δ
P - Δ/2
Dirac
P + Δ/2
Pauli
axial
ξ independence :
Lorentz invariance
pseudo-scalar
GPDs : 3D quark/gluon imaging
of nucleon
Fourier transform of GPDs :
simultaneous distributions of quarks w.r.t. longitudinal
momentum x P and transverse position b
theoretical parametrization needed
GPDs : t dependence
modified Regge parametrization : Guidal, Polyakov, Radyushkin, Vdh (2004)
Input : forward parton distributions at m2 = 1 GeV2 (MRST2002 NNLO)
Drell-Yan-West relation : exp(- α΄ t ) -> exp(- α΄ (1 – x) t) : Burkardt (2001)
parameters :
regge slopes : α’1 = α’2 determined from rms radii
determined from F2 / F1 at large -t
future constraints : moments from lattice QCD
electromagnetic form factors
PROTON
NEUTRON
modified Regge parametrization
Regge parametrization
GPDs : transverse image of the nucleon
Hu(x, b? )
(tomography)
x
b? (GeV-1)
proton Dirac & Pauli form factors
modified Regge model
Regge model
PQCD
Belitsky, Ji, Yuan (2003)
timelike proton FF : GM = F1 + F2
PQCD
Fermilab
p p -> e+ e-
q2
timelike
(q2 > 0)
spacelike (q2 < 0)
analytic function in q2
(Phragmen-Lindelöf theorem)
around |q2| = 10 GeV2 timelike FF twice as large as spacelike FF
HESR@GSI can measure timelike FF up to q2 ≈ 25 GeV2
timelike proton FF : F2 / F1
VMD
Iachello et al. (1973, 2004)
q2
JLab
JLab
PQCD
12 GeV (2005)
4 M2
VMD
PQCD
REAL part
IMAG part
REAL part
IMAG part
Belitsky, Ji, Yuan (2003)
measurement of timelike F2 / F1
Brodsky et al. (2003)
Polarization Py normal to
elastic scattering plane
(polarized beam OR target)
e+
VMD
p
PQCD
p
e-
N -> Δ transition form factors
in large Nc limit
modified Regge
model
Regge model
electromagnetic N -> Δ(1232) transition in
chiral effective field theory
J P=3/2+ (P33),
M ' 1232 MeV,  ' 115 MeV
N !  transition:
 N !  (99%),  N !  (<1%)
non-zero values for E2 and C2 : measure of
non-spherical distribution of charges
Sphere: Q20=0
Oblate Q20/R2 < 0
:
spin 3/2
Prolate:
Role of quark core (quark spin flip) versus pion cloud
Q20/R2 > 0
Effective field theory calculation of the
e p -> e p π0 process in Δ(1232) region
Pascalutsa, Vdh ( hep-ph/0508060 )
Power counting : in Δ region, treat parameters δ = (MΔ – MN)/MN
and mπ on different footing ( mπ ~ δ2 )
in threshold region : momentum p ~ mπ / in Δ region : p ~ MΔ - MN
calculation to NLO in δ expansion (powers of δ)
LO
vertex corrections : unitarity & gauge
invariance exactly preserved to NLO
e p -> e p π0 in Δ(1232) region : observables
W = 1.232 GeV , Q2 = 0.127 GeV2
EFT calculation
error bands due
to NNLO,
estimated as :
Δσ ~ |σ| δ2
data : MIT-BATES (2001, 2003, 2005)
Q2 dependence of E2/M1 and C2/M1 ratios
REM = E2/M1
data points :
MIT-Bates (2005)
see talk -> Sparveris
MAMI :
RSM = C2/M1
REM (Beck et al., 2000)
RSM (Pospischil et al., 2001;
Elsner et al., 2005)
EFT calculation
error bands due to NNLO,
estimated as :
ΔR ~ |R| δ2 + |Rav| Q2/MN2
EFT calculation predicts the Q2 dependence
mπ dependence of E2/M1 and C2/M1 ratios
Q2 = 0.1 GeV2
quenched lattice QCD
results :
at mπ = 0.37, 0.45, 0.51 GeV
Alexandrou et al., (2005)
linear
extrapolation
in mq ~ mπ2
see talk -> Tsapalis
EFT calculation
discrepancy
with lattice
explained by
chiral loops
(pion cloud) !
Pascalutsa, Vdh
(2005)
see also talk
data points : MAMI, MIT-Bates
-> Gail
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 !
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)
Two-photon exchange in N -> Δ transition
Pascalutsa, Carlson, Vdh ( hep-ph/0509055 )
General formalism for eN -> e Δ
has been worked out
N
Δ
Model calculation for large Q2
in terms of N -> Δ GPDs
1 result
1 + 2 result
REM little affected < 1 %
RSM mainly affected when
extracted through
Rosenbluth method
Summary
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Nucleon electromagnetic form factors :
-> dispersion theory, chiral EFT : map out pion cloud of nucleon
-> lattice QCD : state-of-art calculations go down to mπ ~ 300 MeV, into the
regime where chiral effects are important / ChPT regime
-> link with GPD : provide a tomographic view of nucleon
NΔ form factors :
-> chiral EFT ( δ-expansion) is used in dual role :
describe both observables and use in lattice extrapolations,
-> resolve a standing discrepancy : strong non-analytic behavior in quark mass
due to opening of πN decay channel
difference Rosenbluth vs polarization data
-> GEp /GMp : understood as due to two-photon exchange effects
-> precision test : new expt. planned
-> NΔ transition : effect on RSM when using Rosenbluth method