The Proton at Low Q 2 Ron Gilman*, Rutgers, The State University of New Jersey

1. The Proton at Low Q2Ron Gilman*, Rutgers, The State University of New Jersey Outline • Introduction & Motivation • Scattering Experiment Techniques • Jefferson Lab Program • Proton Radius Puzzle • Summary *Supported by NSF PHY 09-69239

2. Basics: Charge Distributions A standard problem in classical electromagnetic physics is calculating electric fields resulting from charge distributions. Concepts like the root mean square (rms) radius are well defined:〈rE2〉 = ∫d3r r2 ρE(r), where ρE(r) is the normalized charge distribution. When we start studying scattering theory in quantum mechanics, we learn that the scattering cross section from a charge distribution is the scattering cross section from a point particle times a form factor squared. The form factor is the Fourier transform of the charge distribution. Polarization

3. Basics: Form Factors Experiments measure the form factors as functions of q2. These are observables that theories can calculate, and a basic property of proton, neutron, and nuclear structure, so interesting to measure. In NRQM, we can calculate the density from the FF. Polarization

4. Basics: Small q expansion For small qR, and spherically symmetric distributions, one can expand the sin(qR) term in the Fourier transform to obtain: F(q2) = 1 - q2<r>2/3! + q4<r>4/5! ... to determine the rms radius, and higher moments of the charge distribution. But there are two issues with this: 1) How well can the parameters be determined by a finite set of data? 2) Due to relativity, the rest frame charge distribution is not an observable. So - we have a useful parameter commonly called the charge radius, that is not the charge radius. Polarization

5. The Proton Radius For hadronic physicists, the proton (electric) radius is a fairly simple aspect of the structure of the proton, but it has not been one of the most interesting quantities to study. There has been much greater interest in the high q2 / short range structure of the nucleon, to compare with quark models. Also the radius has been considered relatively well known - the precision is already better than the theory - until recently. This was thanks largely to the work of Ingo Sick, atomic physics and electron scattering measurements had been brought into agreement: Polarization

6. The Jefferson Lab Program With the development of CEBAF in the 1980s and 1990s, it was recognized that major improvements could be made in our knowledge of the nucleon form factors, due to the high current, polarized electron beam - the accelerator physicists deserve much of the credit. Major advances were also due to experiments fully utilizing polarization techniques developed by theorists in the 1960s, along with a new generation of polarimeters, advances in polarized targets, and improved implementation of ratio techniques. This has allowed us to push the precise knowledge of proton and neutron structure of to "large" q2, several GeV2. Polarization

7. ep Scattering Formulas: 1 currents algebra cross sections with form factors: and kinematic factors:

8. The Procedure • Measure cross sections • Perform radiative corrections • Do Rosenbluth separations - or - fit world data with form factor parameterization The EM interaction is too strong!

9. The Procedure • Measure cross sections • Perform radiative corrections • Do Rosenbluth separations - or - fit world data with form factor parameterization The electron is too light!

10. Polarizations: 1 Use polarizations for form factor ratios Sensitive to spin transport, insensitive to almost everything else ... but needs large statistics

11. Polarizations: 2 Measuring two angles at the same time allows a ratio to be made, reducing sensitivity to PbPt, which can vary by 20% or more over time.

12. The High Q2 Program at JLab? • With the proton polarimeter in Hall A: we learned • the proton electric and magnetic structures are not the same shape, the dipole, as was generally believed • the ratio GE/GM falls nearly linearly with Q2 • 2γ exchange effects are important, leading to a series of experiments in Halls A, B, C, OLYMPUS@DESY, Novosibirsk • With the polarized 3He target in Hall A, the neutron electric and magnetic form factors were much better determined at modest Q2 • With the ratio technique in Hall B, the neutron magnetic form factor was determined to large Q2 to closely (10%) follow the dipole formula, with unprecedented precision

13. The Proton Data • Red: old Rosenbluth data • Blue: JLab Hall A FPP data: Jones et al. PRL, Punjabi et al. PRC, Gayou et al. PRC, Gayou et al. PRL (Does not include recent results from Hall C by Meziane and by Puckett) • Black: "super-Rosenbluth" • Models of 2γ-exchange largely resolve the difference, moving the Rosenbluth results towards the polarization results.

14. Why were we interested in low Q2 at JLab? • Friedrich & Walcher fit, EPJA 17, 607, (2003) • 2-dipole fit of the form factors leaves residual bumps, interpreted as evidence for meson-cloud effects • Not in agreement with newest data. • Articles appear studying the Zemach radius and corrections to Hydrogen hyperfine splitting - most sensitive to low Q2 FF • Friar and Sick, PLB 579 (2004) • Brodsky, Carlson, Hiller, and Hwang, PRL 96 (2005) • Friar and Payne, PRC 72 (2005) • Nazaryan, Carlson, and Griffioen, PRL 96 (2006)

15. Four experiments • BLAST - long planned program for low Q2 nucleon and deuteron structure with polarized beam - internal polarized target • Mainz A1 - unpolarized cross sections, 0.01 - 1 GeV2 • E05-103 run 2006 • FPP calibrations for low energy deuteron photodisintegration used to determine proton GE/GM • E08-007 run 2008 • Dedicated FPP experiment to more systematically cover the 0.3 - 0.7 GeV2 range with higher statistics • E08-007 part II to run Nov 2011 Feb 2012 - May 2012 (along with g2p) • Dedicated polarized beam - polarized target measurements to cover the range about 0.015 - 0.16 GeV2 with high precision

16. BLAST Low Q2 Data C.B. Crawford et al., Phys. Rev. Lett. 98, 052301 (2007) • BLAST FF ratio consistent with unity, within ≈2% uncertainties • Consistent with earlier fits / analyses / theory calculations

17. E05-103 Low Q2 Data G. Ron et al., Phys. Rev. Lett. 99, 202002 (2007) • Our initial FPP results indicate the FF ratio is lower than previously believed, around 0.4 GeV2

18. E05-103 Low Q2 Data G. Ron et al., Phys. Rev. Lett. 99, 202002 (2007) Note that the fits ... have a range of slopes near the origin, not well constrained with data • Our initial FPP results indicate the FF ratio is lower than previously believed, around 0.4 GeV2

19. E05-103 Low Q2 Data G. Ron et al., Phys. Rev. Lett. 99, 202002 (2007) • Combining Berger at al. PLB 35, 1971 dσ/dΩ with new FPP data in G. Ron et al PRL 98, we showed fits tend to get GM about right, but tend to over predict GE

20. Mainz A1 Data J. Bernauer et al., Phys. Rev. Lett. 105, 242001 (2010) • The figure is from J. Bernauer’s Ph.D. thesis: Rosenbluth separation results compared to spline fit.

21. E08-007 Data X. Zhan et al., PLB 705, 59 (2011). M. Paolone et al., Phys Rev Lett 105, 072001, 2010 (Q2 = 0.8 GeV2) • Results essentially unchanged since online data. • About 1% total uncertainty on FF ratio. • Decreased ratio compared to earlier measurements prompted 2 years of thorough systematics studies: cuts, spin transport, backgrounds, ... • Major finding: with very high statistics here one sees changes in ratio as cuts are made very tight. • Reanalyzed G Ron data in very good agreement.

22. Large Improvement in FF Ratio Rosenbluth Polarization E08007E03104

23. E08-007 Impact AMT Fit of world data except Mainz A1 data. w/ E08007 • GE reduced up to ≈2% from 0.3 - 1 GeV2 • GM increased ≈0.5% from 0.1 - 0.8 GeV2 • FF ratio smaller by up to ≈2.5% from 0.3 - 0.8 GeV2 • Slopes changed at Q2 = 0 changing ``radii’’.

24. But some tension between Mainz and JLab Note that the FF ratio agrees better than the individual form factors ... so the difference must arise from Mainz vs. world cross sections. Is there an issue in the FF ratio at the low Q2 limit, or is it an end-point problem / statistics? We will know better once we have the polarized target results. Polarization

25. E08-007 Phase II

26. g2p + E08-007 part IIMajor New Installation in Hall ALast run before 12 GeV shutdown Strong Support from DOE and an additional ≈$200K of User Contributions Septa New Beam Diagnostics (BPM,BCM,Harps,Tungsten Calo) Chicane Local Dump Polarized Target

27. g2p: Camsonne, Crabb, Chen, Slifer et al.Fundamental spin observable never measured at low or moderate Q2 • BC Sum Rule : violation suggested for proton at large Q2,but found satisfied for the neutron & 3He. • Spin Polarizability: Major failure (>8σ) of χPT for neutron δLT. Need g2 isospinseparation to solve. • Hydrogen HyperFine Splitting : Lack of knowledge of g2 at low Q2 is one of the leading uncertainties. • Proton Charge Radius : one of the leading uncertainties in extraction of <Rp> from μ−H Lamb shift. BC Sum Rule Spin Polarizability δLT

28. Issues Major Challenges 149 days lost to mechanical failures and design issues. Polarized target magnet repair Septa magnet redesign and later deterioration (was used in previous high dose experiment) Chicane structural support failure Local Dump Cooling redesign Major Achievements 8 PhD students and 4 Post-Docs DAQ rate is Hall A record : 7-8 kHz/HRS with <30% deadtime Entire new suite of beamline diagnostics for operation at 50nA Polarized target performance has been outstanding : <PT>=31%@2.5T and 85%@5T Normalized Yield (Arb units) Transverse Asymmetry Nitrogen Elastic VERY VERY PRELIMINARY! Proton Elastic/Nitrogen Q.E. Δ-Resonance

29. μGE/GM Projected Uncertainties

30. μGE/GM Projected Uncertainties Lost to Septum magnet Already taken Lost to target magnet

31. Hyperfine Splitting and Zemach radius • EHFS = (1+∆QED+∆pR+∆phvp+∆pμvp+∆pWEAK+∆S) EFp = 1420.405 751 766 7(9) MHz • Structure term ∆S = ∆Z +∆POL, with ∆Z = -2amerZ(1+dradZ), and ∆POL an inelastic structure correction dependent on g2p. • The Zemach radius is Uncertainty from Q2 ≈ 0.01 - 1 GeV2 Parameterizations vary by ≈2 ppm

32. Note on PV Experiments • For a given experimental asymmetry, with an oversimplified assumption of electric or magnetic dominance, A ≈ GpZ/Gpγ, so a reduced GEp leads to a reduced GpZ and a reduced GEs.

33. While Low Q2 seemed important • Nucleon Structure • Impact on hyperfine splitting • Impact on parity violation • But it seemed that the differences were not all that large and the measurement not very important, until the proton radius puzzle arose in 2010.

34. Proton Radius Puzzle Muonic hydrogen disagrees with atomic physics and electron scattering determinations of slope of FF at Q2 = 0. Polarization ``Slope’’ of GEp at Q2 = 0 (fm)

35. Possible Resolutions to the Puzzle / Critiques • The μp result is wrong.No doubts about the experiment, but some discussion about the theory and proton structure for extracting the proton radius. • The ep (scattering) results are wrong.The fit procedures are not good enough. Perhaps the data do not go to low enough Q2, and there are structures in the form factors. • Proton structure issues in theory.Theory critique of theory - off-shell proton in two-photon exchange leads to enhanced effects differing between μ and e, or leads to theoretically unjustified sticking-in-form-factor models. • Novel beyond-Standard-Model Physics differentiates μ and e.But constraints on novel physics exist, and there seems to be no generally accepted solution at present.

36. PSI Muonic Hydrogen Measurements R. Pohl et al., Nature 466, 09259 (2010): 2S➭2P Lamb shift ΔE (meV) = 209.9779(49) - 5.2262 rp2 + 0.0347 rp3 ➮ rp = 0.842 ± 0.001. Possible issues: atomic theory & proton structure Polarization

37. PSI Muonic Hydrogen Measurements R. Pohl et al., Nature 466, 09259 (2010): 2S➭2P Lamb shift ΔE (meV) = 209.9779(49) - 5.2262 rp2 + 0.0347 rp3 ➮ rp = 0.842 ± 0.001. Possible issues: atomic theory & proton structure Proton structure: De Rujula suggested rp3 could be anomalously large. Miller & Cloet and Distler, Bernauer & Walcher showed that this is inconsistent with modern form factor fits. Wu & Kao showed if you add narrow peaks in unmeasured low-Q2 regions you can get different results. There is no reason at present to believe such structures exist - and we would also expect them to affect the ep atom and scattering determinations of the radii. Polarization

38. Examples of Atomic Physics Calculations Carlson & Vanderhaeghen (2011): box diagram corrections essentially agree with Pachucki and with Martynenko, although individual terms within the evaluation vary. Hill & Paz (2011): Elastic contribution of C&V and others from SIFF model. Real part of inelastic not under good theoretical control and have nonphysical limiting behaviors in existing models. Numerical values given not all that different from others. The SIFF criticism has also been made by Miller, Thomas, Carroll, & Rafelski, who point out that it has been made for many years. But the issue remains under dispute.

39. Mainz A1 ep Elastic Scattering Data Simulate radiation J. Bernauer et al., PRL 105, 242001 (2010) Simulate background Fit cross sections directly • Cross sections ➭corrections form factors ➭fits radius • Figures from J. Bernauer’s Ph.D. thesis. • 0.5% absolute uncertainty proposed, few % achieved, data normalized to GE = 1 at Q2 = 0.

40. Mainz A1 Data • From J. Bernauer’s Ph.D. thesis: spline fits tend to give r ≈ 0.875 fm, vs polynomial fits with r ≈ 0.883 fm. Uncertainties are statistics + linearly added systematics. • Reported r is an average of these, with statistical, systematic, and model uncertainties.

41. Mainz A1 Data GE(Q2) = 1 - Q2r2/6 + ... • Low Q2 Mainz data: left - raw data, right- rebinned GE • Conclusion: in principle, the differences between r = 0.84 and 0.88 fm are large, but higher order terms obscure this

42. e-μ Universality In the 1970s / 1980s, there were several experiments that tested whether the ep and μp interactions are equal. They found no convincing differences, once the μp data are renormalized up about 10%. In light of the proton ``radius’’ puzzle, the experiments are not as good as one would like. Ellsworth et al.: form factors from elastic μp Kostoulas et al. parameterization of μp vs. ep elastic differences no difference Entenberg et al DIS: σμp/σep ≈ 1.0±0.04 (±8.6% systematics)

43. e-μ Universality The 12C radius was determined with ep scattering and μC atoms. The results agree: Cardman et al. eC: 2.472 ± 0.015 fm Offermann et al. eC: 2.478 ± 0.009 fm Schaller et al. μC X rays: 2.4715 ± 0.016 fm Ruckstuhl et al. μC X rays: 2.483 ± 0.002 fm Sanford et al. μC elastic: 2.32 +0.13-0.18 fm Perhaps carbon is right, e’s and μ’s are the same. Perhaps hydrogen is right, e’s and μ’s are different. Perhaps both are right - opposite effects for proton and neutron cancel with carbon. But perhaps the carbon radius is insensitive to the nucleon radius, and μd or μHe would be a better choice.

44. Example of Beyond Standard Model Batell, McKeen, Pospelov propose new e/μ differentiating force with ≈ 100 MeV force carriers (guage boson V + complex scalar field), leading to large PV μp scattering. Two forces are needed to keep consistency with gμ-2 data. Barger, Chiang, Keung, Marfatia indicate that the K → μν decay which could radiate V, and constrains its parameters.

45. Possible Way to Resolve Puzzle:New ep Experiments • Obvious 1st guess: high energy proton beam (FNAL?) on atomic electrons, akin to low Q2 pion form factor measurements - difficult - only goes to 0.01 GeV2. • With MEIC/EIC, etc., obvious alternative in the longer term: use a ring with bending magnets to provide access to near 0 degree scattering - perhaps in several years • Very low Q2 JLab experiment, near 0o using ``PRIMEX’’ setup: A. Gasparian, D. Dutta, H. Gao et al.

46. The ``PrimEx’’ Proposal • Low intensity beam in Hall B into windowless gas target. • Scattered ep and Moller electrons into HYCAL at 0o. • Lower Q2 than Mainz. Very forward angle, insensitive to 2γ, GM. • Conditionally approved by August 2011 PAC: ``Testing of this result is among the most timely and important measurements in physics.’’ Unlikely to run until 2016 or so (my estimate).

47. "Our" proposal: μp Scattering at PSIArrington, Gilad, Gilman, Kohl, Meziani, Piasetzky, Ron, Strauch • Directly test the most interesting possibility, that μp and ep scattering are different: • to higher precision than previously, • in the low Q2 region (same as Mainz and a JLab experiment now starting) for sensitivity to radius • with μ± to study possible 2γ mechanisms, but with improved sensitivity from low energy and large angle • measuring both μ±p and e±p to have direct comparison and a robust, convincing result.

48. The Results! projected μ+p • πM1 channel, with pin = 115, 153, and 210 MeV/c: PID reasons. • Choose θscatter = 20 - 100o: rates, backgrounds, systematics. • ΔR = 4% ➭ ΔG’ = 8% ➭ Δσ’ = 16%. • Statistics shown with estimated systematics lead to ΔR ≈ 0.01 fm for μ+, e±, but about 0.015 fm for μ-. • Un-answered question: if radius differences are real, are cross section differences really this large?

49. More Results • Left: pseudo-random data (10o bins) showing effect of a large angle offset. • Right: Estimate of uncertainties on extracted radius - systematic uncertainties dominate • Relative e-μ radius has decreased uncertainties, estimated to be a factor of 2 or more.

50. Experimental Issues Studied • Backgrounds: Moller & Bhabha scattering, π elastic scattering, π and μ decay in flight, scattering from cell walls • Rate issues: determining event by event properties of 10 MHz of beam particles, singles rates in detectors, trigger rates • Systematic uncertainties: angle determination, beam momentum determination, multiple scattering effects, determining flux and efficiency • Detectors: GEMs, Sci-Fis, beam Cerenkov, wire chambers, threshold Cerenkov, scintillators, certain issues in triggering and DAQ • Management: cost, time line, possible funding