Download - Hadron Form Factors : theory
Hadron Hadron Form FactorsForm Factors : :
theory theory
Marc Vanderhaeghen
College of William & Mary / JLab
EINN 2005, Milos (Greece), September 20-24, 2005
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
OutlineOutline
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
NucleonNucleon electromagneticelectromagnetic form factors : form factors : theoretical approachestheoretical approaches
i) Dispersion theoryii) Mapping out pion cloud, chiral perturbation theory iii) lattice QCD : recent results & chiral extrapolationiv) link to Generalized Parton Distributions : nucleon “tomography” v) other
disclaimer : v) will not be discussed in this talk
nucleon FF : nucleon FF : dispersion theorydispersion theory **
NN NN VV
qq Hoehler et al. (1976)
Mergell, Meißner, Drechsel (1995)
Hammer, Meißner, Drechsel (1996)
Hammer, Meißner (2004)
general principles : analyticity in q2 , unitarity
FF -> dispersion relation in q2
branch cuts for q2 > 4 mπ2 : vector meson poles + continua
(ππ,… )
q2 > 0 : timelike
q2 = - Q2 < 0 : spacelike
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 : nucleon FF : dispersion theorydispersion theory
Hammer, Meißner (2004)
Hammer, Meißner, Drechsel (1996)
phenomenological fit by
Friedrich, Walcher (2003)
DR : good description, except for GEp / GM
p
nucleon form factors : nucleon form factors : pion cloudpion cloudFriedrich, Walcher
(2003)
phenomenological fit :
“smooth” part
(sum of 2 dipoles)
+ “bump”
(gaussian)
6 parameter fit for each FF
pronounced structure in all FF around Q 0.5 GeV/c
pion cloudpion cloud extending out to 2
fm
nucleon FF : nucleon FF : Chiral Perturbation Chiral Perturbation TheoryTheory Kubis,
Meißner (2001)
SU(3)
SU(2) : πN
DR
Goldstone boson -Baryon loops
(relativistic ChPT, 4th order, IR reg.)
+ vector mesons
see also Schindler et al. (2005)
(EOM renorm. scheme)
nucleon FF : nucleon FF : lattice QCDlattice QCDQCDSF Coll. : Goeckeler et al.
(2003)Lattice results fitted by dipoles -> for isovector channel : masses Me
V , Mm
V
lattice
Expt. Expt.
lattice
Expt.
lattice
quenched approximation : qq loops neglected
linear extrapolation in mπreasonable good description of GE
p / GMp at larger Q2
(where role of pion cloud is diminished)
nucleon FF : nucleon FF : lattice & chiral lattice & chiral extrapolationextrapolationLeinweber, Lu, Thomas (1999)
Hemmert and Weise (2002)
+ …
4 LEC fit
3 LEC fit
lattice : QCDSF
lattice : QCDSF
lattice : QCDSF
Hemmert : chiral extrapolation using SSE at O(ε3) -> fit LEC to available lattice points
κV
(r1V )2
(r2V )2
qualitative description obtained, not clear for (r1
V )2
Relativistic chiral loops (SR) give smoother behavior than the heavy-baryon expansion (HB) or Infrared-Regularized
ChPT (IR)
red curve is the 2-parameter fit to lattice data based on sum rule (SR) result
Pascalutsa, Holstein, Vdh (2004)
nucleon FF : nucleon FF : lattice & chiral lattice & chiral extrapolationextrapolation
For κ : resummation of higher order terms by using a new sum rule (SR) (linearized version of GDH) -> analyticity is built in
chiral loops
lattice : Adelaide group (Zanotti)
nucleon FF :nucleon FF : lattice prospectslattice prospects
LHP Collaboration (R. Edwards)
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 physical value, the calculated nucleon size approaches the correct value
next step : fully consistent treatment of chiral symmetry for both valence & sea quarks
F1V
√(r2)1V
FF : link toFF : link to G Generalizedeneralized P Partonarton DDistributionsistributions
x + ξ
x - ξ
P - Δ/2 P + Δ/2
*Q2 large t = Δ2 low –t process :
-t << Q2
GPD (x, ξ ,t)
Ji , Radyushkin (1996)
at large Q2 : QCD factorization theorem hard exclusive process can be described by 4 transitions (GPDs) :
(x + ξ) and (x - ξ) : longitudinal momentum fractions of quarks
VectorVector : : H (x, ξ ,t)
TensorTensor : : E (x, ξ ,t)
Axial-VectorAxial-Vector : : H (x, ξ ,t)
PseudoscalarPseudoscalar : : E (x, ξ ,t)
~
~
see talks -> Diehl, Camacho, Hadjidakis
known information onknown information on GPDs GPDs
first moments : nucleon electroweak form factors
ξ independence : Lorentz invariance
P - Δ/2 P + Δ/2
Δ
Pauli
Dirac
axial
pseudo-scalar
forward limit : ordinary parton distributions unpolarized quark distr
polarized quark distr
: do NOT appear in DIS new information
GPDs : GPDs : 3D quark/gluon 3D quark/gluon imaging of nucleonimaging of nucleon
Fourier transform of GPDs :
simultaneous distributions of quarks w.r.t. longitudinal momentum x P and transverse position b
theoretical parametrization needed
modified Regge parametrization : Guidal, Polyakov, Radyushkin, Vdh (2004)
Input : forward parton distributions at = 1 GeV2 (MRST2002 NNLO)
regge slopes : α’1 = α’2 determined from rms radii
determined from F2 / F1 at large -t
Drell-Yan-West relation : exp(- α΄ t ) -> exp(- α΄ (1 – x) t) : Burkardt (2001)
parameters :
future constraints : moments from lattice QCD
GPDsGPDs : : tt dependence dependence
electromagnetic form factorselectromagnetic form factors
modified Regge parametrization
Regge parametrization
PROTONPROTON NEUTRONNEUTRON
GPDs GPDs : : transverse transverse image of the image of the nucleon (tomography) nucleon (tomography) Hu(x, b? )
b? (GeV-1)
x
proton proton Dirac & Pauli form factorsDirac & Pauli form factors
modified Regge model
Regge model
PQCD
Belitsky, Ji, Yuan (2003)
timelike timelike proton FF :proton FF : GGM M = F= F11 + F + F22
PQCD
analytic function in q2
(Phragmen-Lindelöf theorem)
around |q2| = 10 GeV2 timelike FF twice as large as spacelike FF
Fermilab
p p -> e+ e- timelike
(q2 > 0)
spacelike (q2 < 0)
HESR@GSI can measure timelike FF up to q2 ≈ 25 GeV2
q2
timelike timelike proton FF :proton FF : FF22 / F / F11
4 M2
JLab
(2005)
JLab
12 GeV PQCD
VMD
Belitsky, Ji, Yuan (2003)
Iachello et al. (1973, 2004)
q2
REAL part
IMAG part
VMD
REAL partIMAG part
PQCD
measurement of measurement of timelike Ftimelike F22 / F / F11
Polarization Py normal to elastic scattering plane
(polarized beam OR target)
pp
e+
e-
VMD
PQCD
Brodsky et al. (2003)
N -> N -> ΔΔ transition form factorstransition form factors
modified Regge
model
Regge model
in large Nc limit
electromagnetic electromagnetic N -> N -> ΔΔ(1232)(1232) transition in transition in chiral chiral effective field theoryeffective field theory
Role of quark core (quark spin flip) versus pion cloud
non-zero values for E2 and C2 : measure of non-spherical distribution of charges
Sphere: Q20=0 Oblate:
Q20/R2 < 0 Prolate: Q20/R2 > 0
spin 3/2
J P=3/2+ (P33),
M ' 1232 MeV, ' 115 MeV
N ! transition:
N ! (99%), N ! (<1%)
Effective field theory calculation of the Effective field theory calculation of the e p -> e p e p -> e p ππ00 process in process in ΔΔ(1232)(1232) region region
calculation to NLO in δ expansion (powers of δ)
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
Pascalutsa, Vdh ( hep-ph/0508060 )
LO
vertex corrections : unitarity & gauge invariance exactly preserved to NLO
data : MIT-BATES (2001, 2003, 2005)
e p -> e p e p -> e p ππ00 in in ΔΔ(1232)(1232) region : region : observablesobservables
EFT calculation
error bands due to NNLO,
estimated as :
Δσ ~ |σ| δ2
W = 1.232 GeV , Q2 = 0.127 GeV2
QQ22 dependence of dependence of E2/M1 E2/M1 andand C2/M1 C2/M1 ratiosratios
EFT calculation predicts the Q2 dependence
data points :
MIT-Bates (2005)
see talk -> Sparveris
MAMI :
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
REM = E2/M1
RSM = C2/M1
mmππ dependence of dependence of E2/M1 E2/M1 andand C2/M1 C2/M1 ratiosratios
quenched lattice QCD results :
at mπ = 0.37, 0.45, 0.51 GeV
linear extrapolatio
n in mq ~ mπ
2
discrepancy with lattice explained by chiral
loops (pion cloud) !
Alexandrou et al., (2005)
data points : MAMI, MIT-Bates
EFT calculation
Pascalutsa, Vdh (2005)
Q2 = 0.1 GeV2
see also talk
-> Gail
see talk -> Tsapalis
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
Two methods, two different results !
Two-photon Two-photon exchange effectsexchange effects
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
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)
1 result
1 + 2 result
Two-photon exchange inTwo-photon exchange in N -> N -> ΔΔ transitiontransition
General formalism for eN -> e Δ has been worked out
Model calculation for large Q2 in terms of N -> Δ GPDs
Pascalutsa, Carlson, Vdh ( hep-ph/0509055 )
NN ΔΔ
REM little affected < 1 %
RSM mainly affected when extracted through
Rosenbluth method
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 -> GE
p /GMp : understood as due to two-photon exchange effects
-> precision test : new expt. planned -> NΔ transition : effect on RSM when using Rosenbluth method
SummarySummary