Measurement of the Charged Pion Form Factor at Large Q2

1
Measurement of the Charged Pion Form Factor at
Large Q2

• Dave Gaskell
• Jefferson Lab
• ECT Workshop on Hadron Electromagnetic Form
  Factors
• May 22, 2008

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Outline

• Motivation and techniques for measuring Fp(Q2)
• Data
• ?Pre-JLab data
• ?JLab Fp program
• Consistency checks for electroproduction data
• Future measurements
• Speculation
• Credits
• ? Henk Blok, Garth Huber, Dave Mack
• ? Jochen Volmer, Vardan Tadevosyan, Tanja Horn

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pQCD and the Pion Form Factor
At large Q2, pion form factor (Fp) can be
calculated using perturbative QCD (pQCD) at
asymptotically high Q2, only the hardest portion
of the wave function remains and Fp takes
the very simple form G.P. Lepage, S.J.
Brodsky, Phys.Lett. 87B(1979)359.
fp
where f?93 MeV is the ???? decay constant.
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Pion Form Factor at Finite Q2
At finite momentum transfer, higher order terms
contribute ? Calculation of higher order, hard
(short distance) processes difficult, but
tractable

• There remain so-called soft (long distance)
  contributions that cannot be calculated in the
  perturbative expansion
• Understanding the interplay of these hard and
  soft processes is a key goal!

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Measurement of p Form Factor Low Q2

• At low Q2, Fp can be measured directly via high
  energy elastic p- scattering from atomic
  electrons
• CERN SPS used 300 GeV pions to measure form
  factor up to Q2 0.25 GeV2
• Amendolia et al, NPB277, 168 (1986)
• These data used to extract the pion charge radius
  
• rp 0.657 0.012 fm
• Maximum accessible Q2
• roughly proportional to pion
• beam energy
• Q21 GeV2 requires
• 1000 GeV pion beam

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Measurement of p Form Factor Larger Q2

• At larger Q2, Fp must be measured indirectly
  using the pion cloud of the proton via
  p(e,ep)n
• At small t, the pion pole process dominates the
  longitudinal cross section, sL
• In Born term model, Fp2 appears as,
• Drawbacks of the this technique
• Isolating sL experimentally
• challenging
• Theoretical uncertainty in
• form factor extraction

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Extraction of p Form Factor in p(e,ep)n

• p electroproduction can only access tlt0 (away
  from pole)
• Early experiments used Chew-Low technique
• Measured t dependence
• Extrapolated to physical pole
• This method is unreliable different fit forms
  consistent with data yet yield very different FF

• Cross section model incorporating FF is
  required!
• ? t-pole extrapolation is implicit, but one is
  only fitting data in physical region

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Fp(Q2) Measurements before 1997
Data above Q21 GeV2 questionable ? Extracted Fp
from unseparated cross sections, no experimental
isolation of sL ?Used extrapolation of sT fit at
low Q2 to calculate sL ?Largest Q2 points also
taken at large tmin
?

• Theoretical guidance suggests non-pole
  contributions grow dramatically for -tmingt0.2
  GeV2 Carlson and Milana PRL 65, 1717(1990)
• Pole term may not dominate!

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Fp Program at Jefferson Lab

• Two Fp experiments have been carried out (so
  far!) at JLab
• Fp-1 Q20.6-1.6 GeV2
• Fp-2 Q21.6, 2.45 GeV2

• Second experiment took advantage of higher beam
  energy to access larger W, smaller -t
• Full deconvolution of L/T/TT/LT terms in cross
  section
• Ancillary measurement of p-/p (separated) ratios
  to test reaction mechanism
• Both experiments ran in experimental Hall C Fp-1
  in 1997 and Fp-2 in 2003

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Hall C at Jefferson Lab
Accelerator 2 cold superconducting linacs Ee up
to 6 GeV Continuous polarized electron beam
(P85)
Hall C 2 magnetic focusing spectrometers High
Momentum Spectrometer superconducting Short
Orbit Spectrometer - resistive
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JLab Fp Experiment Details
Short Orbit Spectrometer e- High Momentum
Spectrometer p ?Relatively small acceptance
easily understood ?Pointing, kinematics well
constrained Cryogenic targets, high currents
yield relatively fast measurement
Easy to isolate exclusive channel ?Excellent
particle identification ?CW beam minimizes
accidental coincidences ?Missing mass
resolution easily excludes 2-pion contributions
Fp-1 missing mass distribution
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Measuring sL
Rosenbluth separation required to isolate
sL ?Measure cross section at fixed (W,Q2,-t) at 2
beam energies ?Simultaneous fit at 2 e values to
determine sL, sT, and interference terms Control
of point-to-point systematic uncertainties
crucial due to 1/e error amplification in sL
Careful attention must be paid to spectrometer
acceptance, kinematics, efficiencies,
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Model for Fp Extraction
After ?L is determined, a model is required to
extract F?(Q2) ? Model incorporates ?
production mechanism
JLab Fp measurements use the Vanderhaeghen-Guidal-
Laget (VGL) Regge model Vanderhaeghen, Guidal,
Laget, PRC 57, 1454 (1998) Additional
calculations would be nice to check model
dependence and there is some recent activity on
that front ?Obukhovsky, Fedorov, Faessler,
Gutsche, and Lyubovitskij PLB 634, 220 (2006),
PRC 76, 025213 (2007) ?Kaskulov, Gallmeister,
and Mosel, arXiv0804.1834 (hep-ph) ? T. Mart,
arXiv0805.1800 (hep-ph) Although we extract
the form factor in the context of a particular
model, the separated cross sections will always
be available to any future, alternate models that
come along
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Fp Extraction from JLab data
Horn et al, PRL97, 192001,2006
VGL Regge Model

• Feynman propagator
• replaced by p and ? Regge propagators.
• Represents the exchange of a series of particles,
  compared to a single particle.
• Model parameters fixed from pion photoproduction.
• Free parameters ??, ?? (trajectory cutoff).

?p20.513, 0.491 GeV2, ??21.7 GeV2
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Model Check of Fp Extraction

• Test VGL model by extracting form factor for each
  t bin
• If calculation appropriately models reaction
  mechanism, should get same result independent of
  t
• Fp-2 results almost totally insensitive to t bin
  used

Published Fp error band based on fit to all
t-bins.
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VGL Fit to Fp-1 Data
F?-1 data V. Tadevosyan et al., PRC 75,
055205(2007)

• Fp-1 data taken at W1.95 GeV (constrained by
  max. beam energy of 4 GeV)
• VGL model fits data fairly well at larger Q2, but
  shape disagrees significantly at lower Q2
• Disagreement possibly due to lack of resonances
  in VGL
• Extraction of form factor performed assuming any
  backgrounds in data minimized at tmin

?p20.393, 0.373, 0.412, 0.458 GeV2 ??21.5 GeV2.
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Form Factor Extraction from Fp-1 Data

• 1. Fit Lp2 in each t bin
• 2. Extrapolate to t-tmin
• ?NOT tmp2
• This method assumes backgrounds are minimized (or
  zero) at tmin
• Model uncertainty evaluated assuming particular
  forms for the background
• see Henk Bloks talk last week for more details
• This method was not needed for Fp-2 data

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Fp(Q2) in 1997
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Fp(Q2) in 2008
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Fp(Q2) in 2008
Only true L-T separated data shown
Trend suggested by extractions from unseparated
cross sections still holds ?far from asymptotic
limit 1 sigma deviation from monopole at Q22.5
GeV2
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Fp(Q2) Models
Maris and Tandy, Phys. Rev. C62, 055204 (2000)
? relativistic treatment of bound quarks
(Bethe-Salpether equation Dyson-Schwinger
expansion)
Nesterenko and Radyushkin, Phys. Lett. B115,
410(1982) ? Greens function analyticity used to
extract form factor
Brodsky and de Teramond,
hep-th/0702205 Phys.Rev.D77, 056007 (2008) ?
Anti-de Sitter/Conformal Field Theory approach

• A.P. Bakulev et al, Phys. Rev. D70, 033014 (2004)

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Interpretation Issues

• A common criticism of electroproduction technique
  is that its difficult to be certain that one is
  measuring the physical form factor
• What tests/studies can we perform to give us
  confidence in the result?
• Check consistency of model with data (see
  earlier)
• Verify that electroproduction technique yields
  results consistent with p-e elastic scattering at
  same Q2
• Extract form factor at several values of tmin
  for fixed Q2
• Test that the pole diagram is really the dominant
  contribution to the reaction mechanism

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Comparison of pe to H(e,ep)

• Does electroproduction really measure the
  physical form-factor since we are starting with
  an off-shell pion?
• This can be tested making p(e,ep) measurements
  at same kinematics as pe elastics
• Looks good so far
• Electroproduction data at Q2 0.35 GeV2
  consistent with extrapolation of SPS elastic data

An improved test will be carried out after the
JLAB 12 GeV upgrade ?smaller Q2 (0.30
GeV2) ?-t closer to pole (0.005 GeV2)
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Form Factor Extraction at different -tmin
Is the model used to extract the form factor
sensitive to the distance from the pion
pole? ?Test by extracting FF at different
distances from t pole ?Ex Fp-2, -tmin0.093
GeV2 Fp-1, -tmin0.15 GeV2 Additional data
at JLab at 12 GeV will provide further tests
Q21.6 GeV2, -tmin0.029 GeV2 Q22.45
GeV2,-tmin0.048 GeV2
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Pole Dominance Tests

• Extraction of Fp relies on dominance of pole
  diagram
• t-channel diagram pure isovector
• Other Born diagrams both isovector and isoscalar
• Measure (separated) p-/p ratios to test pole
  dominance

p
g
p
N
N
Ratio 1 suggests no isoscalar backgrounds
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p-/p Ratios from Fp-1
Q20.6 GeV2
Globally, RL(p-/p) close to 1.0
Q21.0 GeV2
Q21.6 GeV2
Preliminary
W1.95 GeV
Agreement with simple pole dominance expectation
better as Q2 increases
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Fp Program at 6 GeV

• JLab Fp program has built on pioneering H(e,ep)
  measurements of the 1970s
• ? Facilities at JLab (beam, spectrometers)
  improved precision of cross sections
• Improved reliability of Fp extraction by
  isolating sL
• Where possible, tested the electroproduction
  technique as a valid method for extracting Fp
• At 6 GeV, Q22.5 GeV2 is the ultimate reach of
  the Fp program
• Larger Q2 requires the 12 GeV upgrade

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Jefferson Lab 12 GeV Upgrade
CD-2 approved Nov. 2007
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Experimental Hall C
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Super-HMS
Properties Min. Angle 5.5 deg. Max. Angle 40
deg. Momentum range 2-11 GeV/c Solid angle 5
msr Momentum acceptance -10-22
Design modeled on HMS ?Excellent control of
acceptance and point-to-point systematics
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Fp(Q2) after JLAB 12 GeV Upgrade

• JLab 12 GeV upgrade will allow measurement of Fp
  up to 6 GeV2
• Will we see the beginning of the transition to
  the perturbative regime?
• Additional point at Q21.6 GeV2 will be closer to
  pole will provide another constraint on -tmin
  dependence
• Q20.3 GeV2 point will be best direct test of
  agreement with elastic pe data

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Fp beyond 12 GeV JLab

• 12 GeV JLab will yield the ultimate reach for the
  electroproduction technique for measuring Fp
  (until EIC?)
• Can we extend measurements to larger Q2 without a
  major investment in a new accelerator?
• Maybe!
• Beyond nucleon pole backgrounds, an additional
  concern has been pQCD backgrounds to the pion
  pole process
• Keeping pQCD backgrounds small (in addition to
  the general philosophical goal of staying close
  to pion pole) partially dictates maximum Q2
  available at JLab
• Relaxing this constraint would allow us to access
  significantly larger Q2

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pQCD Contributions to H(e,ep)

• In addition to Born terms, pQCD processes can
  also contribute to p production
• Carlson and Milana PRL 65, 1717 (1990)
  calculated these contributions for Cornell
  kinematics
• Asymptotic form for Fp
• ?King-Sachrajda nucleon distribution
• For tgt0.2 GeV2, pQCD contributions grow rapidly
• This helps set the constraint on maximum
  accessible Q2
• (fixed W, -tmin grows w/Q2)

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H(e,ep) in GPD framework

• Non-pole backgrounds can also be calculated in a
  GPD framework
• Mp proportional to linear combination of

pole term
VGG model PRD 60, 094017 (1990) calculation of
non-pole backgrounds shows different t
dependence than CM calculation
Not authorized or endorsed by V,G, or G
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H(e,ep0) and H(e,ep)
Same diagrams/GPDs that contribute to p
production also contribute to p0 Measurement of
sL for p0 could shed some light on non-pole
contributions at large -t
p0
p
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Transverse Target Asymmetry
Non-pole contribution can also be constrained
using the transverse target asymmetry
Asymmetry measures interference between pole and
non-pole contributions
Experimentally difficult ? need double
Rosenbluth separation to eliminate contributions
from transverse photons
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Fp at Even Larger Q2?

• If larger tmin were useable, we could measure Fp
  up to Q29 GeV2 at 12 GeV
• Even at 6 GeV, data at Q24 GeV2 already exist!
• Needed L/T separated p0 cross sections
• Will be attempted by approved Hall A DVCS
  experiment at 6 GeV (L/T ratio favorable?)
• Could be extended to larger Q2 at 12 GeV

Separated p cross sections at Q24 GeV2
-tmin 0.45 GeV2
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Measurement of K Form Factor
Similar to p form factor, elastic K scattering
from electrons used to measure charged kaon form
factor at low Q2 Amendolia et al, PLB 178, 435
(1986) Can the kaon cloud of the proton be
used in the same way as the pion to extract kaon
form factor via p(e,eK)L ? Kaon pole further
from kinematically allowed region Can we
demonstrate that the pole term dominates the
reaction mechanism?
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Kaon Form Factor at Large Q2

• JLAB experiment E93-018 (1996) extracted t
  dependence of K longitudinal cross section near
  Q21 GeV2
• A trial Kaon FF extraction was attempted using a
  simple Chew-Low extrapolation technique
• gKLN poorly known
• Assume form factor follows monopole form
• Used measurements at Q20.75 and 1 GeV2 to
  constrain gKLN and FK simultaneously
• Improved extraction possible using VGL model?

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Test Extraction of K Form Factor
-t dependence shows some pole-like behavior
G. Niculescu, PhD. Thesis, Hampton U.
Extraction shows power of the data, but should
not be interpreted (yet?) as real extraction of
kaon FF!
Chew-Low type extraction
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Kaon Form Factor at 12 GeV

• At 12 GeV JLab, will be able to make measurements
  down to Q2 0.2 GeV2
• Test form factor extraction in region of overlap
  with elastic Ke data
• A program of measurements in Hall C could attempt
  form factor extraction to Q22 GeV2, and measure
  L/T cross sections to Q26 GeV2

Figure courtesy of T. Horn
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Summary

• Measurement of the charged pion form factor at
  large Q2 requires use of the H(e,ep) reaction
• New Jefferson Lab data has improved the
  reliability of Fp measurements up to Q22.5 GeV2
• The JLab 12 GeV upgrade will allow us to extend
  these measurements to at least Q26 GeV2
• The JLab 6 GeV data has already provided useful
  tests of the validity of the electroproduction
  technique
• 12 GeV will allow even more checks
• p0 electroproduction (and transverse target
  asymmetry?) may help us understand the role of
  non-pole backgrounds in the H(e,ep) reaction
• This may allow us to extend Fp measurements to
  even larger Q2
• Measurements of the kaon form factor can also be
  attempted at JLab at 12 GeV