1. Exploring the Electromagnetic Structure of the Charged Pion and Kaon
Garth Huber
CAP Congress, Ottawa, ON. June 14, 2016.
FRN: SAPIN

2. Charged Pion Form Factor
The pion is attractive as a QCD laboratory:
Simple, 2 quark system
Electromagnetic form factor can be calculated exactly at very large momentum transfer (small distances).
For moderate Q2, it remains a theoretical challenge.
“the positronium atom of QCD”
Pion’s structure is determined by two valence quarks, and the quark-gluon sea.
Downside for experimentalists:
No “free” pion targets.
Measurements at large momentum transfer difficult. 2

3. Measurement of Fπ via Electroproduction
Above Q2>0.3 GeV2, Fπ is measured indirectly using the “pion cloud” of the proton via pion electroproduction p(e,e’π+)n
At small –t, the pion pole process dominates the longitudinal cross section, σL
In Born term model, Fπ2 appears as
Drawbacks of this technique:
Isolating σL experimentally challenging.
The Fπ values are in principle dependent upon the model used, but this dependence is expected to be reduced at sufficiently small −t. 3

4. Fp Program at JLab Hall C
SOS: 1.7 GeV/c
HMS: 7 GeV/c
2 Fp experiments have been carried out at JLab
(spokespersons H. Blok, G. Huber, D.Mack)
Fp-1: Q2= GeV2 with 4 GeV beam,
Fp-2: Q2=1.6, 2.45 GeV2 with 6 GeV beam, 4

5. L-T separation required to separate σL from σT.
Need to take data at smallest available –t, so L has maximum contribution from the + pole.

6. Fp Extraction from JLab data
Model is required to extract Fp from sL
JLab Fp experiments used the VGL Regge model [Vanderhaeghen, Guidal, Laget, PRC 57, 1454 (1998)]
Propagator replaced by p and r Regge trajectories
Most parameters fixed by photoproduction data
2 free parameters: Lp, Lr
At small –t, sL only sensitive to Lp
Horn et al, PRL97, ,2006
The model of: T.K. Choi, K.J. Kong, B.G. Yu [arXiv: ] may soon become available as a second way to extract Fp from data. 6

7. Fπ-2 VGL p(e,e’π+)n model check
To check whether VGL Regge model
properly accounts for:
π+ production mechanism.
spectator nucleon.
other off-shell (t-dependent)
effects.
extract Fπ values for each t-bin
separately, instead of one value from
fit to all t-bins.
Deficiencies in model may show up as t-dependence in extracted Fπ(Q2) values.
Resulting Fπ values are insensitive (<2%) to t-bin used.
Lends confidence in applicability of VGL model to the kinematical regime of the JLab data, and the validity of the extracted Fπ(Q2) values.
G.M. Huber et al., PRC 78(2008)
Error band based on fit to all t-bins.
Only statistical and t-uncorrelated systematic uncertainties shown.

8. π-/π+ data to check t-channel dominance
+ t-channel diagram is purely isovector (G-parity conservation).
Isoscalar backgrounds (such as b1(1235) contributions to t-channel) will dilute ratio.
Qualitatively in agreement with our Fπ-1 analysis:
We found evidence for small additional contribution to σL at W=1.95 GeV not taken into account by the VGL model.
We found no evidence for this contribution at W=2.2 GeV.
Vrancx-Ryckebusch Model:
VR extend VGL with hard DIS process of virtual photons off nucleons.
[PRC 89(2014)025203]
RL=0.8 consistent with |AS/AV|<6%.
G.M. Huber, et al., PRL 112, (2014)

9. Current Experimental Status
JLab results in a region of Q2 where model calculations begin to diverge.
Bethe-Salpeter/Dyson-Schwinger:
[P. Maris and P. Tandy, Phys.Rev.C 62(2000)055204]
B-S equation is conventional formalism for relativistic bound states.
D-S expansion in terms of dressed quark propagators, consistent w/ confinement.
Model parameters fixed from f and m, then r and F predicted.
Constituent Quark Model:
[C-W. Hwang, Phys.Rev.D 64(2001)034001]
Relativistic constituent quarks and effective interaction on the light front
Consistent treatment of quark spins.
Wave function parameters determined from f and 0→ decay width, then charge and transition FF’s and 0 branching ratios predicted.
Disperson Relation with QCD Constraint:
[B.V. Geshkenbein, Phys.Rev.D 61(2000)033009]
Uses constraints posed by causality and analyticity to relate the timelike and spacelike domains of the pion form factor on the complex plane.
Additional constraints, such as behavior of F in asymptotic region, imposed.
For details see: G.M. Huber et al., PRC 78(2008)

10. 12 GeV era – Hall C with SHMS and HMS
11 GeV/c Spectrometer
Partner of existing 7 GeV/c HMS
MAGNETIC OPTICS:
Point-to Point QQQD for easy calibration and wide acceptance.
Horizontal bend magnet allows acceptance at forward angles (5.5°)
Detector Package:
Drift Chambers
Hodoscopes
Cerenkovs
Calorimeter
All derived from existing HMS/SOS detector designs
Well-Shielded Detector Enclosure
Rigid Support Structure
Rapid & Remote Rotation
Provides Pointing Accuracy & Reproducibility demonstrated in HMS
SHMS (New)
SHMS: dQQQD
HMS (Exists)
HMS: QQQD
SHMS = Super High Momentum Spectrometer
HMS = High Momentum Spectrometer

11. Fπ(Q2) after JLab 12 GeV Upgrade
JLab 12 GeV upgrade will allow measurement of Fπ
up to Q2 = 6 → 8.5 GeV2
No other facility worldwide can perform this measurement.
New overlap point at Q2=1.6 will be closer to pole to constrain -tmin dependence.
New low Q2 point will provide best comparison of the electroproduction extraction of
Fπ vs elastic π+e data.
Approved with “A” scientific rating and identified by JLab PAC41 as “high impact”.
(E : GH, D. Gaskell, spokespersons)
Extension to Q2=8.5 GeV2 submitted to PAC44 (GH, D. Gaskell, T. Horn, spokespersons) 11 11

12. The Charged Kaon – a second QCD test caseπ+ K+
In the hard scattering limit, pQCD predicts that the π+ and K+ form factors will behave similarly
It is important to compare the magnitudes and Q2-dependences of both form factors. 12

13. Measurement of K+ Form Factor
Similar to p+ form factor, elastic K+ scattering from electrons used to measure charged kaon for factor at low Q2
[Amendolia et al, PLB 178, 435 (1986)]
Can “kaon cloud” of the proton be used in the same way as the pion to extract kaon form factor via p(e,e’K+)L ?
Kaon pole further from kinematically allowed region.
Can we demonstrate that the “pole” term dominates the reaction mechanism? 13

14. Isolate Exclusive Final States via Missing Mass
SHMS+HMS missing mass resolution expected to be very good.
Spectrometer coincidence acceptance allows for simultaneous studies of Λ and Σ° channels.
Kaon-pole dominance test through
Should be similar to ratio of g2pKΛ/g2pKΣ coupling constants if t-channel exchange dominates.
Simulation at Q2=2.0 GeV2 , W=3.0 and high ε
p(e,e’K+)Λ
p(e,e’K+)Σ° 14

15. Projected Uncertainties for K+ Form Factor
p(e,e’K+)Λ
First measurement of FK well above the resonance region.
Measure form factor to Q2=3 GeV2 with good overlap with elastic scattering data.
W>2.5 GeV
Limited by -t<0.2 GeV2 requirement to minimize non-pole contributions.
Data will provide an important second system for theoretical models, this time involving a strange quark.
For VGL/Regge calculation, assume Λ2K=0.67 GeV2, and Λ2K*=1.5 GeV2,
Scheduled as an early SHMS commissioning experiment: LT-separation.
(E : T. Horn, G. Huber and P. Markowitz, spokespersons) 15

16. Hall C Meson Form Factors Timeline
SHMS superconducting magnet installation and testing
Until Sept, 2016
SHMS front detector installation
July – Aug, 2016
Hall C Experimental Readiness Review
Aug 22 – 23, 2016
SHMS commissioning with beam
Dec 6 – 21, 2016
First physics-quality runs in Hall C
Feb 11 – May 7, 2017
First p(e,e’K+) run
May 31 – June 20, 2017
Data Reconstruction Software (hcana)
Z. Ahmed (PDF), completed
SHMS Detector Checkout & Commissioning
W. Li (Ph.D.), S. Basnet (M.Sc.), work underway
p(e,e’K+)Λ Kaon Form Factor
L/T commissioning experiment (2017 – 2018)
Pion Form Factor and π+ QCD-Scaling Experiments
Interleaved run-plans (2018 – 2020)
Regina Efforts 16

17. 17 17 17

18. pQCD and the Charged Pion Form Factor
At very large Q2, pion form factor (Fp) can be calculated using perturbative QCD (pQCD)
at asymptotically high Q2,
the pion wave function becomes
and Fπ takes the very simple form
G.P. Lepage, S.J. Brodsky, Phys.Lett. 87B(1979)359. fp
f=93 MeV is the p+→+ decay constant. 18 18

19. 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 are “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 19 19

20. Extraction of form factor from L data
p(e,e’+)n data are obtained some distance from the t=m2 pole.
No reliable phenomenological extrapolation possible.
A more reliable approach is to use a model incorporating the + production mechanism and the `spectator’ nucleon to extract F from L.
Our philosophy is to publish our experimentally measured dL/dt, so that updated values of F(Q2) can be extracted as better models become available. 20

21. Check of Pion Electroproduction Technique
Directly compare F(Q2) values extracted from very low -t electroproduction with the
exact values measured in elastic e- scattering.
METHOD PASSES CHECKS:
Q2=0.35 GeV2 data from DESY
consistent with limit of elastic scattering data within uncertainties.
[H. Ackermann, et al., NP B137(1978)294]
A much better check is planned in E12–06–101 by taking Q2=0.30 GeV2 data at
50% lower -t (0.005 GeV2).
E Proposal:
G.M. Huber, D. Gaskell, spokespersons

22. One way to understand non-pole to σL
Data–driven approach to better understand non–pole backgrounds at higher –t.
Exclusive 2H(e,e’π+)nn and 2H(e,e’π-)pp L/T-separations.
+ t–channel diagram is purely isovector (G-parity conservation).
Isoscalar backgrounds would distort ratio (e.g. b1(1235) in t–channel).
Significant RL deviation predicted
E RL≈1.0 at -tmin
Deviation of data from RL=1.0 could confirm large non-pole contributions estimated by model.
RL=1.0

23. Another way to understand non-pole to σL
Test by extracting Fπ at different distances from pole.
Expt: Fπ-2, -tmin=0.093 GeV2
W=2.22 GeV.
Fπ-1, -tmin=0.15 GeV2
W=1.95 GeV.
W=2.22 point 30% closer to pole.
→ Agreement ~4%.
We plan further tests:
Q2=1.6 GeV2
-tmin =0.029 GeV2
W=3.00 GeV
Q2=2.45 GeV2
-tmin =0.048 GeV2
W=3.20 GeV
Q2=3.85 GeV2
-tmin =0.12, 0.21, 0.49 GeV2
W=3.07, 2.62, 2.02 GeV
Q2=6.0 GeV2
-tmin =0.21, 0.53 GeV2
W=3.19, 2.40 GeV

24. π-/π+ Separated Response Function Ratios
Transverse Ratios tend to ¼ as –t increases:
→ Is this an indication of Nachtmann’s quark charge scaling?
-t=0.3 GeV2 seems too low for this to apply. Might indicate the partial cancellation of soft QCD corrections in the formation of the ratio.
A. Nachtmann, Nucl.Phys.B115 (1976) 61.
Another prediction of quark-parton mechanism is the suppression of σTT/σT due to s-channel helicity conservation.
Data qualitatively consistent with this, since σTT decreases more rapidly than σT with increasing Q2.
2H(e,e’π+)nn
1H(e,e’π+)n
2H(e,e’π-)pp
G.M. Huber, et al., PRC 92, (2015)

25. Kaon Form Factor
Measure the –t dependence of the p(e,e’K+)Λ,Σ° cross section at fixed Q2 and W>2.5 GeV to search for evidence of K+ pole dominance in σL
Separate the cross section components: L, T, LT, TT
First L/T measurement above the resonance region in K+ production
If warranted by the data, extract the Q2 dependence of the kaon form factor to shed new light on QCD’s transition to quark-gluon degrees of freedom.
Even if we cannot extract the kaon form factor, the measurements are important.
K+Λ and K+Σ˚ reaction mechanisms provide valuable information in our study of hadron structure
Flavor degrees of freedom provide important information for QCD model building and understanding of basic coupling constants 25

26. p0 →g*g Transition Form Factor
Recent data from BaBar on the p0 →g*g transition form factor have deepened the mystery of how QCD transitions from the soft to the hard regime.
For real photons, Fπγγ determines rate of π0→γγ decay, deeply related to axial anomaly.
For virtual photons, since only one hadron is involved, π0→γ*γ has the simplest structure for pQCD analysis.
In lowest order pQCD, the π0→γ*γ transition form factor is given by 26

27. BaBar p0 →g*g Data [B. Aubert et al., PRD 80(2009)052002]
SLAC e+e- collider with asymmetric beams (3.1 GeV e+, 9 GeV e-) designed for time-like studies.
e+e-→e+e-π0 reaction utilized for space-like π0 production.
One e± scattered at large angle (detected) yielding virtual photon with large Q2.
Second e± (undetected) scattered at small angle yielding “nearly real” photon.
Data analysis is challenging:
Dominant background, Virtual Compton Scattering, exceeds π0 production cross section by >103.
Because of high π0 lab frame energy, most π0→γγ decays resolved as only single γ cluster in calorimeter.
Very different energy, angular distributions, and trigger corrections, for e- tag and e+ tag events. 27

28. Fg*gp0(Q2) Experimental Results
Unlike older data, new BaBar results show no tendency to converge to the pQCD asymptotic limit.
“After the release of the BaBar data for Fγ*γπ0, our community is in deep shock, as the conventional approach to the gold-plated exclusive process at very high Q2, based on 1) factorization and ) leading-twist pQCD evolution seems to be invalid.”
- Bronlowski & Arriola, arXiv:
CELLO [Z.Phys. C49 (1991) 401]
CLEO [Phys. Rev. D57 (1998) 33]
BABAR [Phys. Rev. D80 (2009) ] 28

29. What do the p0 →g*g data imply?
If the BaBar data are correct, they have broad implications.
e.g. does soft-hard factorization apply at experimentally accessible Q2?
Various authors advocate the non-vanishing of the pion DA at high and low x, together with essentially switched-off pQCD evolution.
Obtain
where the log indicates the breaking of factorization.
Li and Mishima, PRD 80(2009) 29

30. Very Important to see if other Deep Exclusive observables behave in a consistent fashion
New η,η’ data from BaBar utilizing same technique are consistent with pQCD evolution!
Charged pion data can have smaller systematic uncertainties.
P. del Amo Sanchez et al., arXiv: 30