Meson Form Factors and Reaction Mechanism

Tanja Horn

Hall C Summer Meeting

4 August 2008

The Fundamental IssueThe Fundamental Issue

• Confinement occurs at an intermediate distance scale

– Lattice QCD and phenomenological models give insight into the hadron structure at the confinement scale

• Need experimental observables of the fundamental degrees of freedom of QCD in coordinate space– Forward parton distributions do not resolve partons in space

– Form Factors measure spatial distributions, but the resolution cannot be selected independent of momentum transfer

– Need a combination of both

Exclusive Processes and GPDsExclusive Processes and GPDs

• Increasing the virtuality of the photon (Q2) allows one to probe short distances

• Sensitivity to partonic degrees of freedom

• At sufficiently high Q2, the process should be understandable in terms of the “handbag” diagram– Incoming virtual photon scatters off one

quark– interaction can be calculated in perturbative

QCD

– The non-perturbative (soft) physics is represented by the GPDs

• Shown to factorize from QCD perturbative processes for longitudinal photons [Collins, Frankfurt, Strikman, 1997]

t-channel process

handbag

GPDs fromGPDs from Exclusive Meson Exclusive Meson ProductionProduction

• Interest: spin/flavor structure of quark GPDs – mesons select spin– Requires L/T separation to facilitate interpretation, which is complicated

by convolution with meson distribution amplitude (DA)– Vector mesons () allow for transverse imaging of the nucleon

From: Diehl, Kugler, Schaefer, CW 2005

Q2 dependence of σL and σT

• The Q-6 QCD scaling prediction is reasonably consistent with recent JLab π+ σL data

T. Horn et al., arXiv:0707.1794 (2007)

Hall C data at 6 GeV

Q2=1.4-2.2 GeV2

Q2=2.7-3.9 GeV2

σL

σT

• To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies

T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001.

FFππ - a factorization puzzle? - a factorization puzzle?

T. Horn et al., arXiv:0707.1794 (2007).• Fπ has a simple prediction in perturbative QCD

• The Q2 dependence of Fπ is also consistent with hard-soft factorization prediction (Q-2) already at values Q2>1 GeV2

• But the observed magnitude of Fπ is larger than the hard QCD prediction

– Could be due to QCD factorization not being applicable in this regime

– Or insufficient knowledge about additional soft contributions from the meson wave function

H.J. Kwee and R.F. Lebed, arXiv:0708:4054 (2007) H.R.Grigoryan and A.V.Radyushkin, arXiv:0709.0500 (2007)

A.P. Bakulev et al, Phys. Rev. D70 (2004)]

Strangeness in GPDs and exclusive processes

• Kaon production probes polarized GPDs analogous to pions

• High –t meson production to learn about the reaction mechanism

– QCD factorization

• Kaon pole term is expected to be prominent

– Kaon form factor measurements

• Relatively model independent pole dominance test through

Q2 dependence of σKaon

• Many measurements of exclusive p(e,e’K+)Λ(Σ°) exist, but contribution of σT unknown at higher energies

• Difficult to draw a conclusion about the reaction mechanism– Limited Q2 range

– Significant uncertainty due to scaling in xB and -t

W=1.84 GeV W=1.84 GeV

p(e,e’K+)Λ p(e,e’K+)Σ°

KK++ Form Factor at 6 GeV Form Factor at 6 GeV

-t dependence shows some “pole-like” behavior

)()()(

2 22222

2

QFegkmt

tQKNK

KL

• JLAB experiment E93-018 extracted –t dependence of σL

K+ near Q2=1 GeV2

– Trial Kaon FF extraction was attempted using a simple Chew-Low extrapolation technique

Q2=1.0 GeV2

Q2=0.75 GeV2

gKLN poorly known

W=1.84 GeV

t=mK2 (kaon pole)

Motivation Summary

• Studies of kaon electroproduction provide a way to determine if scaling behavior observed in Fπ would manifest itself in a similar system

• Direct comparison of the scaling properties of σL provides another important tool in the search of the onset of factorization

– σL is expected to evolve towards Q-6 scaling at sufficiently large Q2

– Transverse contributions are suppressed by an additional factor of Q-2

• xB dependence of σL in Σ° production could provide information about pole and non-pole contributions

Experiment GoalsExperiment Goals

• To meet motivation requirements perform the measurement above the resonance region – first time for W>2.5 GeV• Allows for meaningful studies of the Q2 dependence of σL and better

extraction of the kaon form factor

• Measure the Q2 dependence of the p(e,e’K+)Λ(Σ°) cross section at fixed xB and –t to search for evidence of hard-soft factorization– Separate the cross section components: L, T, LT, TT

– The highest Q2 for any L/T separation in K+ electroproduction

• Also measure the Q2 dependence of the kaon form factor to shed new light on the apparent pion form factor scaling puzzle

Experiment Overview

x Q2

(GeV2)

W

(GeV)

-t

(GeV/c)2

0.25 1.6-3.5 2.4-3.4 0.2

0.40 3.0-6.0 2.3-3.1 0.5

• Measure separated cross sections for the p(e,e’K+)Λ(Σ°) reaction at two values of xB

– Near parallel kinematics to separate L,T,LT,TT

• Measure the separated cross sections at varying –t allows for extraction of kaon ff (W>2.5 GeV)

• Planned proposal for PAC34 – T. Horn, P. Markowitz, G. Huber

• The virtual photon cross section can be written in terms of contributions from transversely and longitudinally polarized photons.

Cross Section Separation

πcos2φdφdt

dσεπcosφdφdt

dσ1)(εε2εdφdtσ2d TTLT dφdt

dσL

dtddσT

• Separate σL, σT, σLT, and σTT by simultaneous fit using measured azimuthal angle (φK) and knowledge of photon polarization (ε)

Separation in a Multi-Separation in a Multi-Dimensional Phase SpaceDimensional Phase Space

• Multiple SHMS settings (±2° left and right of the q vector) are used to obtain good φ coverage over a range of –t

– Measuring 0<φ<2π allows to determine L, T, LT and TT

• Determine LT, TT for xB=0.25 only– For xB=0.40 apply a “parallel” cut on θK

Radial coordinate (-t),

Azimuthal coordinate (φ)

SHMS+2°

High ε

• Cuts are placed on the data to equalize the Q2-W range measured at the different ε-settings

SHMS-2°

Low ε

High ε

Kaon PIDKaon PID

• Aerogel Cerenkov is essential for proper kaon identification at lower momenta as time-of-flight alone is not sufficient

TOF

Aerogel Cerenkov

Heavy Gas Cerenkov

Momentum (GeV/c)

Dis

cri

min

atio

n p

ow

er

E93-108 Kaon PID

Kaon 12 GeV Kinematics

Expected Missing Mass Expected Missing Mass ResolutionResolution

Simulation at Q2=2.0 GeV2 , W=3.0 and high ε

• Missing mass resolution is very good

• Acceptance allows for simultaneous studies of both Λ and Σ° channels

• Kinematic dependences of the ratio

Λ

Σ°

Predictions for the Q2 dependence of R=σL/σT

• VGL/Regge parameterization was used for the L/T ratio– Projected Δ(L/T)=30-50% for

typical kinematics

• Future predictions may indicate larger values of R, and thus lower uncertainties– Reaching Q2=8 possible (still

under study)

VGL/Regge

Fπ param

• QCD scaling predicts σL~Q-6 and σT~Q-8

• Projected uncertainties use R as determined from VGL/Regge

Projected Uncertainties for Q-n scaling

• Data will provide important information about the onset of factorization in 12 GeV kinematics and may provide a way to study effects related to SU(3)

x Q2

(GeV2)

W

(GeV)

-t

(GeV/c)2

0.25 1.6-3.5 2.4-3.4 0.2

0.40 3.0-6.0 2.0-3.0 0.5

p(e,e’K+)Λ

xB=0.25

1/Q61/Q4

1/Q8

• Limited by t<0.2 GeV2 requirement to minimize non-pole contributions

Projected Uncertainties for the Kaon FF Q-2 dependence

• Data will provide important information the apparent scaling puzzle observed in the pion ff

• Measure form factor to Q2=3 GeV2 with good overlap with elastic scattering data

For VGL/Regge calculation, assume Λ2K=0.67 GeV2,

and Λ2K*=1.5 GeV2,

p(e,e’K+)Λ

W>2.5 GeV

• First measurement of FK well above the resonance region

Summary

• First measurement of kaon electroproduction above the resonance region• Meaningful studies of the Q2 dependence of the cross section and kaon ff

extractions

• L/T separated K+ cross sections will be essential for our understanding of the reaction mechanism at 12 GeV

• determine if scaling behavior observed in pion production would manifest itself in a similar system

• Direct comparison of the scaling properties of σL over a wide kinematic range provides another important tool in the search of the onset of factorization

– σL is expected to evolve towards Q-6 scaling at sufficiently large Q2

– Transverse contributions are suppressed by an additional factor of Q-2

Projected Uncertainties for σL at constant Q2

• xB scan at Q2=3 GeV2

• Expect significant x-dependence is non-pole contributes

– Provides information about non-pole contributions

Axial only

Pion pole only

Axial and pole

Uncertainty in σL

22

-121

-1εε

dσL )ε(R)ε(Rdσ

21

• Assuming equal correlated sytematic uncertainties at each ε

T

L

σσR

• Due to amplification by 1/Δε, uncertainty in σL is dominated by uncorrelated systematic uncertainty

• If R more favorable, precision in σL improves even for small Δε

• QCD scaling predicts σL~Q-6 and σT~Q-8

• Projected uncertainties for σL are improved by a factor of more than two compared to 6 GeV

Q-n scaling after the Jlab Upgrade

Fit: 1/Qn

• Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics

x Q2

(GeV2)

W

(GeV)

-t

(GeV/c)2

0.31 1.5-4.0 2.0-3.1 0.1

0.40 2.1-5.5 2.0-3.0 0.2

0.55 4.0-9.1 2.0-2.9 0.5

• E12-07-105 (T. Horn et al) approved for 42 days in Hall C

• Experiment (E12-06-101) approved for 55 days in Hall C

• The 11 GeV electron beam and the SHMS in Hall C with θ=5.5º allows for precision data up to Q2=6 GeV2

• May expect to see the onset of perturbative regime

FFππ after the JLab Upgrade after the JLab Upgrade

Tests of the Handbag Tests of the Handbag DominanceDominance

• To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies

– No single criterion for the applicability, but tests of necessary conditions can provide evidence that the Q2 scaling regime (partonic picture) has been reached

• One of the most stringent tests of factorization is the Q2 dependence of the π electroproduction cross section– σL scales to leading order as Q-6

– σT scales as Q-8

– As Q2 becomes large: σL >> σT

Factorization

H H~E E

~

• Factorization theorems for meson electroproduction have been proven rigorously only for longitudinal photons [Collins, Frankfurt, Strikman, 1997]

Q2 ?

Pion/Kaon ratio studiesPion/Kaon ratio studies

• Overlap with Fpi-3 at Q2=6 GeV2

• Additional info about reaction mechanism through π+/K+ ratios• QCD Factorization