Two-Photon-Exchange Effects in Nucleon EM Form Factors

Transcription

1 Two-Photon-Exchange Effects in Nucleon EM Form Factors Introduction Radiative Corrections TPE Extraction TPE Calculations Future Experiments Summary Kees de Jager Jefferson Lab MAMI & Beyond March 3 - April 3, 29 Thomas Jefferson National Accelerator Facility Mainz, March 31, 29, 1

2 World Data Set on G E p by mid 199s p 2. p M µ G /G E p General assumption that G Ep /G M p 1 Although data showed large scatter Relied on Rosenbluth separation Q [GeV ] ( ) = ε τ σ R Q 2,ε E E ' σ ( E,θ) σ Mott = (G p M ) 2 ( Q 2 ) + ε τ (G p E ) 2 ( Q 2 ) Q 2 = 4EE'sin 2 ( θ 2 ) 1 ε = 1+ 2(1+ τ )tan 2 (θ / 2) Mainz, March 31, 29, 2

3 World Data Set on G E p ten years later p µ G /G E p 1.2 p M Large new data set based on polarization transfer showed linear decrease of G Ep /G M p with Q 2 In contrast with Rosenbluth data [GeV ] John Arrington (PRC 68, (23)) performed detailed reanalysis of SLAC data resulting in acceptable scatter of data Hall C Rosenbluth data (PRC 7, 1526 (24)) in agreement with SLAC data No reason to doubt quality of either Rosenbluth or polarization transfer data Investigate possible theoretical sources for discrepancy 2 Q Mainz, March 31, 29, 3

4 Speculation : missing radiative corrections Speculation : there are radiative corrections to Rosenbluth experiments that are important and are not included in the analysis missing correction : linear in ε, not strongly Q 2 -dependent G E term is proportionally smaller at large Q 2 Q 2 = 6 GeV 2 John Arrington effect more visible at large Q 2 if both FF scale in same way Mainz, March 31, 29, 4

5 Radiative correction diagrams γ µ Radiative corrections dσ = dσ (1 + δ RC ) Γ µ elastic electron scattering electron vertex correction electron self-energy diagrams vacuum polarization two-photon exchange box diagrams proton vertex correction proton self-energy diagrams box and crossedbox diagrams Different in Super-Rosenbluth (proton detection) emission of soft real photons Mainz, March 31, 29, 5

6 Status of radiative corrections Tsai (1961), Mo & Tsai (RMP 41, 25 (1969)) box diagram calculated using only nucleon intermediate state and using q 1 ~ or q 2 ~ in both numerator and denominator (calculate 3-point function) -> gives correct IR divergent terms Maximon & Tjon (PRC 62, 5432 (2)) same as above, but make the above approximation only in numerator (calculate 4-point function) + use on-shell nucleon form factors in loop integral Blunden, Melnitchouk, Tjon (PRC 72, (25)) further improvement by keeping the full numerator Afanasev (hep-ph/ ) including hard-photon emission in bremsstrahlung can account for ~2% of discrepancy between Rosenbluth and polarization transfer Bystritskiy, Kuraev, Tomasi-Gustaffson (PRC 75, 1527 (27)) claim that leading and next-to-leading logarithmic approximation for hardphoton emission can explain full discrepancy, but this can not be substantiated because of use of incorrect cut-off energies and implausible size of resulting radiative corrections Mainz, March 31, 29, 6

7 First Estimate of Two-photon Contributions Guichon and Vanderhaeghen (PRL 91, (23)) estimated the size of two-photon corrections (TPE) necessary to reconcile the Rosenbluth and polarization transfer data, introducing three ~ ~ generalized form factors Y 2γ, G E and G M 2 d! d" # G M $ P t P l 5 6 2% $(1 + %) 2. G E & / $ +% 2 + 2% $ + G ( 1 M '. / 1 G E G M G E & G % G E ( M ' 1 +% G M ) 2 + Y 2, (-,Q 2 ) 3 * 4 ) 2 + Y 2, (-,Q 2 ) 3 * 4 Need ~3% value for Y 2γ (6% correction to ε- slope), independent of Q 2, which yields minor correction to polarization transfer, to bring the two data sets into agreement. However, these corrections are not supported by the e + /e - cross-section ratio data Mainz, March 31, 29, 7

8 Experimental Verification of TPE contributions Initially, the ratio of e + p and e - p cross section was the only available direct measurement of two-photon contributions However, existing data were limited in statistics, Q 2 -range and ε-range Arrington (PRC 69, 3221 (24)) demonstrated that TPE effects were non-zero with a 3σ-significance He also extracted a TPE correction consistent with the e + /e - ratio (PRC 71, 1522 (25)) 18 Mainz, March 31, 29, 8

9 Calculations of TPE effects dσ = dσ (1 + δ) { }! = 2 f (Q 2,") + 2# M M 1 M 2 f(q 2, ε) is the standard Mo & Tsai correction (soft photon exchange), which has some ε-dependence and is IR divergent IR divergent terms are canceled by soft-photon emission terms Two methods of calculating δ 2γ : Hadronic Use nucleon-pole diagrams with on-shell form factors in photon-nucleon vertices Partonic Factorize TPE amplitude into hard process of e-q scattering and a soft process described by GPDs Mainz, March 31, 29, 9

10 Calculation by Blunden, Melnitchouk, and Tjon (PRC 72, (25)) resolves the discrepancy up to 2-3 GeV 2 Only elastic contribution Linear ε-approximation Note: TPE effect on cross section and polarizations are of same size Effect on G E amplified in high- Q 2 Rosenbluth measurements Most polarization measurements at large ε, smaller TPE Hadronic TPE Calculations M G / G E µ p p p M G / G E µ p PT LT LT LT ε =.5.8 ε = Q PT PT corrected LT (GeV ) Q 2 2 (GeV ) Mainz, March 31, 29, 1

11 TPE in Rosenbluth vs. Polarization Transfer (ε, Q ) Rosenbluth ε P L 1γ+2γ / PL 1γ Polarization Transfer ε 2 Q = 6 GeV TPE corrections on σ as large as on P T in polarization transfer Effect on Form Factor strongly enhanced by Rosenbluth separation P T 1γ+2γ / PT 1γ Q = 6 GeV ε 2 Mainz, March 31, 29, 11

12 Generalized Form Factors In the BMT calculations the largest TPE contributions come from δg M (and at large Q 2 from δg E ) R=.84 GeV Q 2 =2.64 GeV Q 2 2 = 1 GeV 9. Q 2 =4 GeV 2.1 Y 2γ δ G / G E E /G D δ M G / G M Q 2 =5 GeV 2 Q 2 =6 GeV 2 Born Born + 2 [N + P33] Born + 2 [N + P33 + D13 + D33 + P11 + S11 + S31] Q 2 2 = 3 GeV Kondratyuk and Blunden (PRC 75, 3821 (27)) have studied the nucleon resonance contributions, found large contribution from Δ ε Q 2 2 = 6 GeV Mainz, March 31, 29, 12

13 Dispersion Analysis Fit to EMFF Belushkin, Hammer and Meissner (PLB 658, 138 (28)) performed separate dispersion analysis fits to EMFF data with only Rosenbluth and with only polarization transfer SC (Superconvergence) and pqcd denote the different constraints used for the dispersion relations Difference was then attributed to TPE and compared to BMT results 2γ Q 2 =.5 GeV 2 Q 2 =2 GeV 2 Ref. [15] Q 2 =4 GeV 2 Ref. [15] ε Q 2 =3 GeV Q 2 =1 GeV 2 Ref. [15] Ref. [15] Q 2 =5 GeV ε Solid: Δ 2γ SC approach Dashed: 1σ error bands Dotted: Δ 2γ pqcd approach Dash-dotted: BMT calculation Mainz, March 31, 29, 13

14 Arrington, Melnitchouk, Tjon PRC 76, 3525 (27) Effect on L-T Extractions full reanalysis of data, incorporating BMT calculations, but adding extra (small) phenomenological correction above Q 2 = 1 GeV 2 #! 2" =.1 [ $ % 1] lnq2 ln 2.2 LT + BMT* PT ~1% at 2 GeV 2, 2% at 5 GeV 2 Apply 1% of the extra correction as an uncertainty (affects G M p uncertainty) Corrections hardly visible in e + /e - ratio Mainz, March 31, 29, 14

15 Partonic TPE Calculations Afanasev et al. (PRC 93, (24)) Model schematics: Assume factorization Hard eq-interaction GPDs describe quark emission/ absorption Soft/hard separation 1.2 Rosenbluth w/2-γ corrections vs. Polarization data σ R / (µ p G dipole ) γ+2γ, m.reg. GPD, G M Brash.991 1γ+2γ, gauss. GPD, G M Brash.993 1γ data Polarization transfer 1γ+2γ (hard) 1γ+2γ (hard+soft) σ R / (µ p G dipole ) γ+2γ, m.reg. GPD, G M Brash.996 1γ+2γ, gauss. GPD, G M Brash.998 1γ data Q 2 = 3.25 GeV 2 Q 2 = 4 GeV 2 G E p / (GM p /µp ) Pol.: Jones et al. Pol.: Gayou et al..2 Pol.: Gayou et al. fit Rosenbluth, Mo-Tsai corr. only Rosenbluth, incl. 2γ corr. w/gauss. GPD Q 2 (GeV 2 ) σ R / (µ p G dipole ) ε 1γ+2γ, m.reg. GPD, G M Brash 1. 1γ+2γ, gauss. GPD, G M Brash 1.2 1γ data ε σ R / (µ p G dipole ) Q 2 = 5 GeV ε 1γ+2γ, m.reg. GPD, G M Brash.995 1γ+2γ, gauss. GPD, G M Brash.998 1γ data ε Mainz, March 31, 29, 15 Q 2 = 6 GeV 2

16 Reanalysis of SLAC data on G M p E. Brash et al. (PRC 65, 511 (22)) have reanalyzed SLAC data with JLab G Ep /G M p results as constraint, using a similar fit function as Bosted Reanalysis results in ~3% increase of G M p data Arrington (PRC 71, 1522 (25) obtained similar results by implementing the TPE effects extracted from a comparison of Rosenbluth and polarization transfer data Mainz, March 31, 29, 16

17 !"#$%&'$&(&)*+,-./,.1*+,-. VEPP-3 positron-electron :.;! "! ~65 *+144&+!.)1-*1((3*,+. <&+*&=$)832>&+. ~25 Use VEPP-3 ring (5 ma) e + /e - energy 1.6 GeV θ 25 and 65 Q 2.3 and 1.5 GeV 2 Internal gas target Luminosity (cm 2 s) -1.*,+34&$)&((.23(($3-4(&.)1-*1((3*, ) ?*$)832>&+. J. Arrington, D. Nikolenko, spokespersons, nucl-ex/4-82 Mainz, March 31, 29, 17

18 VEPP-3 positron-electron comparison Expected to run Summer/fall 29 Measurements at two ε-values Projected slope based on TPE amplitudes from global extraction 1.4 ± 2.2 % at 1.6 GeV 2 Mainz, March 31, 29, 18

19 Positron-electron comparison in Use 5% radiator to generate photon beam, dump electron beam into tagger dump Put photon beam through 2% converter to generate positron/electron pairs Steer positron (electron) beam above (below) photon blocker with 4-dipole chicane system Overlapping positron and electron beams incident on hydrogen target Detect scattered lepton and recoiling proton in coincidence in CLAS reconstruct initial lepton energy Mainz, March 31, 29, 19

20 Preliminary CLAS results First engineering run successful Good agreement with SLAC data. <Q 2 >=.18 GeV 2 (CLAS). Q 2 <.3 GeV 2 (SLAC) Brian Raue (FIU) CLAS Collaboration Meeting, November 28 ε Mainz, March 31, 29, 2

21 Positron-electron comparison in E5-7 Scheduled to run in late 211 Will provide e + /e - cross-section ratios over large range of Q 2 and ε 1% Novosibirsk Mainz, March 31, 29, 21

22 in DORIS positron-proton and electron-proton elastic scatt hypothesis of Multi- Photon exchange DoriS Max. energy 4.45 GeV Stored current 12 ma Mainz, March 31, 29, 22

23 BLAST Left-right symmetric Large acceptance:.1 < Q 2 /GeV 2 <.8 2 o < θ < 8 o, -15 o < φ < 15 o COILS B max = 3.8 kg DRIFT CHAMBERS Tracking, PID (charge) δp/p=3%, δθ =.5 CERENKOV COUNTERS e/π separation SCINTILLATORS Trigger, ToF, PID (π/p) NEUTRON COUNTERS Neutron tracking (ToF) BEAM COILS TARGET DRIFT CHAMBERS CERENKOV COUNTERS All the advantages of VEPP-3 expt. Pure beam, well-defined energy (Q 2, ε) coverage close to CLAS Coincidence measurement Could do (e,e n), other reactions NEUTRON COUNTERS SCINTILLATORS BEAM Mainz, March 31, 29, 23

24 Projected results for OLYMPUS 1 hours each for e+ and e- at luminosity = 6 x 1 32 cm -2 s -1 1 hours each for e + and e - Lumi = 6 x 1 32 cm -2 s Full proposal submtted and approved 29/1 Transfer of BLAST 211/12 OLYMPUS Running Mainz, March 31, 29, 24

25 Benefits of improved LT separations Compare precise LT and PT to constrain linear part of TPE corrections. At high Q 2, almost all ε-dependence comes from TPE Mainz, March 31, 29, 25

26 ! red = P "[1 + P 1 (# $.5) + P 2 (# $.5) 2 ] Non-linearity Tests Born approx σ R linear in ε, TPE can have non-linearity SLAC NE11, JLab E1-1: quadratic terms consistent with zero Global fit, averaged over all Q 2 yields P 2 =.19±.27 Project δp 2 ±.2 for both linearity scans, with global δp 2 ±.11 E5-17 will set meaningful limits over a wide Q 2 -range Global linearity limits: V.Tvaskis et al., PRC 73, 2526 (26) Mainz, March 31, 29, 26

27 E5-17: Return of Super-Rosenbluth E5-17: Ran in Hall C, Summer 27 Increase precision of LT separations; better measure of LT- PT difference Nearly all ε dependence is TPE for Q 2 > 5 GeV 2 Precise linearity tests at Q 2 =.983, GeV 2 12 Kinematics points Q GeV 2 13 points at Q 2 = points at Q 2 =2.284 Mainz, March 31, 29, 27

28 TPE Study Using Recoil Polarization ε-independent TPE amplitudes yield linear effect on cross section However, so do G M = and Y 2γ = A + B/ε Indistinguishable in σ, but very different in polarization transfer Experiment E4-19 measured polarization of recoil proton as function of ε, ρan in Hall C late 27 GPD: Afanasev Hadronic: Blunden Predict different sign of TPE in PT Mainz, March 31, 29, 28

29 SSA in elastic en scattering spin of beam OR target OR recoil proton NORMAL to scattering plane on-shell intermediate state (M X = W) involves the imaginary part of two-photon exchange amplitudes Target: general formula of order e 2 GPD model allows connection of real and imaginary amplitudes Hadronic models sensitive to intermediate state contributions, no reliable theoretical calculations at present Beam: general formula of order m e e 2 (few ppm) Measured in PV experiments (longitudinally polarized electrons) at SAMPLE, A4 (Mainz), G and HAPPEx (JLab) Only non-zero result so far for TPEX Peter Blunden Mainz, March 31, 29, 29

30 Available data on SSA Transverse Asymmetry [1-6 ] A4 (MAMI) Beam Energy [GeV] (ppm) Transverse Beam Asymmetry A n G (JLab) Center-of-Mass Angle θ CM (degrees) 1 6 B n SAMPLE E = 2 MeV More recent calculations by Borisyuk&Kobushkin (arxiv: ) θ (deg) 1 6 B n θ (deg) A4 E = 855 MeV Mainz, March 31, 29, 3

31 HAPPEX 24 Hydrogen Transverse E e = 3 GeV, θ CM ~16 o, Q 2 =.99 GeV 2 A T = ppm ± 1.47 ppm (stat) ±.24 ppm (syst) Total corrections ~2 ppb Dominant systematic errors: Polarimetry (19 ppb) Beam asymmetry (1 ppb) Al background dilution (7 ppb, assumed A T Al = ) Afanasev HAPPEX 24 (preliminary) Mainz, March 31, 29, 31

32 HAPPEX 25 Helium Transverse E e = 2.75 GeV, θ lab ~6 o, Q 2 =.77 GeV 2 A T = ppm ± 1.34 ppm (stat) ±.37 ppm (syst) Dominant systematic errors: Polarimetry (3 ppb) Linearity (14 ppb) Beam asymmetry (1 ppb) Al background dilution (12 ppb) Afanasev Curve for E b =3 GeV Without inelastic states, 1-9 HAPPEX 25 (preliminary) Mainz, March 31, 29, 32

33 TPE Beyond the Elastic Cross Section Important direct and indirect consequences on other experiments High-precision quasi-elastic experiments Proton charge radius, hyperfine splitting Strangeness from parity violation Neutron & Nuclear form factors Transition form factors Bethe-Heitler, Coulomb Distortion, Mainz, March 31, 29, 33

34 Summary and Outlook General agreement that at least most of the discrepancy in the G Ep /G M p data determined by Rosenbluth separation and by recoil polarization transfer is due to two-photon exchange effects However, there is so far no quantitative proof of this Beam Single-Spin Asymmetry data have indeed proven the existence of TPE effects and data on the e + p/e - p cross-section ratio indicate the existence of non-zero TPE effects Various theoretical models also support the resolution of the above discrepancy through TPE effects The three scheduled experiments that will provide accurate data on the e + p/e - p cross-section ratio are anxiously awaited, but these will only cover a Q 2 -range up to 3 GeV 2 Thus, a continuous dedicated theoretical effort is required to complement such experimental studies Mainz, March 31, 29, 34

35 THANK YOU! Mainz, March 31, 29, 35