# Hadron Form Factors : theory

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### Transcript of 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