Proton Form Factor Puzzle and the CLAS Two-Photon Exchange Experiment

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1 Proton Form Factor Puzzle and the CLAS Two-Photon Exchange Experiment Dipak Rimal Florida International University April 15, 2014 University of Virginia Nuclear Physics Seminar, 2014 TPE in CLAS D. Rimal 1

2 Outline Motivation Proton Electromagnetic Form Factors and Measurements Rosenbluth Separation and Polarization Transfer Methods Proton Form Factor Puzzle Puzzle Solver: Two-Photon Exchange Correction? The CLAS Two-Photon Exchange Experiment Experimental Details Data Analysis Methods Results and Discussions Conclusions and Outlook TPE in CLAS D. Rimal 2

3 Proton Form Factors Proton 2 up and 1 down valence quarks + strong interaction (gluons) Sea of quark anti-quark pairs Charge and magnetization distributed over the volume! Form Factors Proton Form Factors Fundamental observables that provide information about the composite nature of the proton Measure the deviation of the proton from a point-like particle In the non-relativistic limit, they are related to the Fourier transform of charge distribution inside proton Have been studied for several decades! Not yet completely understood Elastic electron scattering is the tool to study form factors TPE in CLAS D. Rimal 3

4 Elastic Electromagnetic Form Factors The invariant electron-proton scattering amplitude in OPE approximation: M 1 = i e2 q j 2 µj µ, where j µ = ū e(l 0 µ ) µue(lµ) J µ = ū p(p 0 µ ) µ (q)u p(p µ). The hadronic current operator: µ F 1(Q 2 ) µ + iapple µ q 2M F2(Q2 ), F 1 and F 2 are Dirac and Pauli form factors, Q 2 = q 2 =4EE 0 sin 2 2 The di erential cross section in the lab frame: "! # d d = F 2 1 d lab d + Q 2 apple2 Mott 4M F Q2 2M 2 (F1 + applef2)2 tan 2 2 ( d d ) Mott = 2 E 0 cos 2 2 4E 3 sin 4 is the Mott cross section for scattering o point like 2 particles TPE in CLAS D. Rimal 4

5 Elastic Electromagnetic Form Factors Sach s electric and magnetic form factors: G E (Q 2 )=F 1 apple F 2 G M (Q 2 )=F 1 + applef 2 where = Q2 4M 2 is the kinematic factor. As Q 2! 0:G E (0) = 1 and G M (0) = µ p (proton magnetic moment) The di erential cross section: d d lab d = d Mott R = "G 2 E (Q2 ) + G 2 M (Q2 ) where: 1 "(1 + ) " # d "(1 + ) R = d d lab d Mott h i "G 2 E (Q2 )+ G 2 M (Q2 ), " =(1+2(1+ Q2 4M 2 )tan2 2 ) 1. TPE in CLAS D. Rimal 5

6 Proton Form Factor Measurements Rosenbluth separation method R = "G 2 E(Q 2 ) + G 2 M (Q 2 ) Qattan et al., Phys. Rev. Lett. 94 (2005) Unpolarized electron beam is scattered o unpolarized proton target Measure reduced cross section ( R )asthefunctionof" at fixed Q 2 Extract G E and G M contributions from the slope and intercept respectively At high Q 2,contributionsfromG M dominates over G E TPE in CLAS D. Rimal 6

7 Proton Form Factor Measurements Polarization transfer method: p(~e, e 0 ~p ) Longitudinally polarized electron transfers its polarization to recoil proton. Transverse (P t)andlongitudinal(p l )polarizationoftherecoiledprotonare measured (Jones et al. Phys. Rev. Lett. 84, 1398 (2000) G E G = P t Ee+Ee 0 M P tan( /2) l 2Mp Polarization transfer is a ratio measurement and has smaller systematic uncertainties Qattan et al. Phys. Rev. Lett 94 (2005) Puzzle Arrington et al. Phys. Rev. C76 (2007) Huge discrepancy!! Increases with Q 2 Two methods! Two di erent answers! Both methods assume an exchange of a single virtual photon in the process Rosenbluth has large statistical and systematic uncertainties Possible explanation: Two Photon Exchange (TPE) beyond the Born Approximation TPE contribution expected to be 5 8% at high Q 2 TPE in CLAS D. Rimal 7

8 TPE Contribution Use G M from Rosenbluth separation and G E from polarization transfer measurement Additional slope must come from TPE ) 5-8 % TPE in CLAS D. Rimal 8

9 TPE Formalism The general 1- and 2- exchange amplitude: apple 1: ū(p 0 µ ) G M P µ F 2 M u(p) apple 2: ū(p 0 µ P ) G µ M F2 M = e2 Q 2 ū(l0 ) µu(l) M + F KP µ 3 M 2 u(p) with P = p+p0 and K = l+l0 2 2 and the cross section becomes: 1: d d 2: d d h / G 2 i M + "G2 E / h G 2 M + " G 2 E + 2"( G M + G i E GM )Y 2 Y 2 / Re F 3 G M! Guichon and Vanderhaeghen, PRL, 91, Thus we have: Another " dependent term G E and G M are modified TPE in CLAS D. Rimal 9

10 Accessing the TPE Contribution Invariant amplitude for lepton-proton elastic scattering: M total = q l q p[m 1 + q 2 l M l.vertex + q 2 p Mp.vertex + q2 l M loop + q l q pm 2 ], And the cross section (to the order 2 ) = born(1 + even + q l q p 2 ) even is the lepton-charge-even radiative correction Additional lepton charge dependent contribution from lepton proton bremsstrahlung interference = born(1 + even + q l q p 2 + q l q p e.p.br. ), (e + p) (e p) 1+ even 2 e.p.br. ' 1+ even e.p.br. 2( 2 + e.p.br. ) ' 1. (1 + even) The ratio after applying charge odd radiative corrections R 2 = even R 2 provides a model-independent measurement of the real part of the TPE contribution TPE in CLAS D. Rimal 10

11 Previous World Data TPE e ect was measured in early 1960s ) Small e ect (ignored) World data is not enough to resolve the discrepancy Can not draw any conclusion because of the size of the error bars Need precise measurement with wide kinematic coverage ) CEBAF Large Acceptance Spectrometer (CLAS) Other experiments measuring the ratio! DESY, VEPP-3 TPE in CLAS D. Rimal 11

12 The CLAS Two-Photon Exchange Experiment TPE in CLAS D. Rimal 12

13 CEBAF Large Acceptance Spectrometer (CLAS) 4 hermetic detector, divided into six independent sectors Six Superconducting Coils! toroidal magnetic field! bends particle towards or away from the beamline depending upon charge 3regionsofDriftChambers! for charged particle tracking Time of Flight Scintillators! for timing measurements EM Calorimeters! for energy measurements/trigger ) only used in trigger by TPE Čerenkov Counters! electron/pion separation! optimized for in-benders! not used by TPE TPE in CLAS D. Rimal 13

14 Producing a Mixed Electron Positron Beam in Hall-B Primary electron beam: 5.5 GeV and na Radiator: 0.9% of primary electrons radiate high energy photons Tagger magnet: sweep the primary electrons to the tagger dump Converter: 9% of photons convert to electron/positron pairs Chicane: separate the lepton beams, stop photons and recombine the e + and e beams Target: 30 cm liquid hydrogen Detector: CEBAF Large Acceptance Spectrometer (CLAS) TPE in CLAS D. Rimal 14

15 Chicane Field Optimization Figure: Sparse Fiber Monitor (built at FIU) Block one lepton beam Record the position of the beam at SFM varying chicane current Repeat for the other beam Repeated after each chicane flip Chicane current was reproducible TPE in CLAS D. Rimal 15

16 TPE Calorimeter 30 module shashlik (Pb/scint) calorimeter Positioned downstream of the target just outside CLAS Used for beam profile measurements Not used during regular production data taking TPE in CLAS D. Rimal 16

17 Experimental Features Continuous incident energy distribution from 0-5GeV Coincidence detection of lepton and proton at the opposite CLAS sectors Match acceptance Select regions of CLAS with 100% acceptance for both e + and e Systematic controls Reverse torus and chicane magnetic fields periodically to cancel artificial charge asymmetries Non-standard particle identification: Use elastic scattering kinematics for event selection TPE in CLAS D. Rimal 17

18 Elastic Event Selection Selected negative/positive or positive/positive charged pair in the opposite CLAS sectors Target vertex cut: 45 <v z < 15 cm Co-planarity cut: = l p Vertex distribution along Z-axis TPE in CLAS D. Rimal 18

19 Elastic Event Selection Use elastic scattering kinematics to reconstruct beam energy: Using final lepton and proton polar angles: " # 1 E( l, p)=m tan 1 l 2 tan p Using momenta of lepton and proton: E(p l,p p)=p l cos l + p p cos p Reconstructed beam energy di erence E beam = E( l, p) E(p l,p p) Calculate the di erence between measured and calculated momentum of the scattered lepton E 0 l = Emeas l E calc l ( l, p) E( l, p ) Identical e + /e beam energy TPE in CLAS D. Rimal 19

20 Elastic Event Selection E beam and E 0 l are correlated Cut on E beam + E 0 l and E beam E 0 l Cut on the di erence between measured and calculated momentum of the recoil proton p 0 p = pmeas p p calc p ( l, p) TPE in CLAS D. Rimal 20

21 Kinematic Cuts Summary E + E 0 E E 0 p p TPE in CLAS D. Rimal 21

22 Dead Detector Cuts (Acceptance) Fiducial cuts to select regions in (p,, )with same detection e ciency for both e + and e Remove ine cient TOF paddles Several dead regions in sector 3 forward region! Removed if lepton/proton hits sector 3 forward region Employ swimming algorithm: For each detected elastic e ± p event, generate aconjugateleptonwiththesamevertexand momentum Swim both original and the conjugate lepton through CLAS Accept the event only if the original lepton and its conjugate both hit the active region of the detector TPE in CLAS D. Rimal 22

23 Kinematic coverage (Q 2 vs. ") Trigger requires at least one particle in the forward ( <45 ) region of CLAS TPE in CLAS D. Rimal 23

24 Background Subtraction Sample background from the E E 0 tails, plot on Fit Sampled = Fit distributions with Gaussian Use fit background for all kinematics since sampling fails at other kinematics due to peak width Subtract background from the peak TPE in CLAS D. Rimal 24

25 Cross section Ratio The number of detected elastic events: N l t / (el p)a l t Ap t, where l is the sign of lepton charge, A l t and Ap t acceptance in torus polarity t are the lepton and proton Take a ratio of e + p to e p elastic events for the given torus and chicane ) Proton acceptance cancels R c t = Nt(e+ p) N t(e p) = (e+ p)a + t Ap t (e p)a t A p t Take the square root of the product of individual torus ratios for the given chicane polarity to form a double ratio ) Lepton acceptance cancels s v q R c = (R+ c N +(e + p) N (e + p) Rc )= N +(e p) N (e p) = u t (e+ p)a + + (e+ + p)a (e p)a + (e p)a By charge-symmetry A + + = A and A + = A+ Take the square root of the product of individual chicane double ratios to form a quadruple ratio ) Beam asymmetry cancels q R q = (R + R ) TPE in CLAS D. Rimal 25

26 electron/positron Luminosity e + /e pair-production is inherently charge-symmetric e + -left is the same as e -left! periodically flipping the chicane leads to symmetric luminosities Calorimeter data before and after each chicane flip to measure relative left/right e + /e flux Any remaining e ects are estimated in systematic uncertainties TPE in CLAS D. Rimal 26

27 RESULTS TPE in CLAS D. Rimal 27

28 Results (high Q 2 ) Average Q 2 of the bins 1.5 GeV/c 2 Background subtracted Dead detector cuts applied With charge-odd bremsstrahlung radiative corrections D. Adikaram, Ph.D. Thesis, Old Dominian University (2014). TPE in CLAS D. Rimal 28

29 Results (high ") Average " 0.88 Negligible background at high " Background subtracted Dead detector cuts applied With charge-odd bremsstrahlung radiative corrections TPE in CLAS D. Rimal 29

30 Results (low Q 2 ) Average Q 2 of the bins 0.85 GeV 2 Background subtracted Dead detector cuts applied With charge-odd bremsstrahlung radiative corrections TPE in CLAS D. Rimal 30

31 Systematic Uncertainties electron/positron Luminosity Estimated from the ratio variance with di erent magnet cycles CLAS imperfections Estimated from the ratio variance with CLAS sectors Background subtraction Elastic event selection cuts Fiducial cuts Target vertex cuts TPE in CLAS D. Rimal 31

32 Comparison to the world data at Q 2 > 1 GeV/c 2 D. Adikaram, Ph.D. Thesis, Old Dominian University (2014). TPE in CLAS D. Rimal 32

33 Comparison to the world data at " 0.9 h"i 0.88 Blunden et al., Phys. Rev. C 91, (2003). Blunden et al., Phys. Rev. C 72, (2005). TPE in CLAS D. Rimal 33

34 Comparison to the world data at Q GeV 2 Blunden et al., Phys. Rev. C 72, (2005). Blunden et al., Phys. Rev. C 91, (2003). TPE in CLAS D. Rimal 34

35 Summary Significant discrepancy exists between Rosenbluth and polarization transfer measurements of the proton electric to magnetic form factor ratio ( G E G M ) The proposed explanation is the e ect of the two-photon exchange beyond the Born approximation (e + p) provides a model independent measurement of the TPE e ect (e p) CLAS TPE experiment measured (e+ p) (e p) over a wide range of Q2 and " with significantly better precision than previous measurements In the kinematics of the experiment, our results are in agreement with the hadronic TPE calculations by Blunden, Melnitchouk, and Tjon Analysis note is under review by the CLAS Collaboration Other experiments (OLYMPUS, Novosibirsk) are also analyzing their data to extract the ratio at Q 2 < 2.5 GeV 2 Results from the CLAS TPE and other experiments provide vital information required to reconcile Rosenbluth and polarization transfer measurements Measurements at higher Q 2,wherethediscrepancyislarger,arenecessaryto completely resolve the form factor discrepancy TPE in CLAS D. Rimal 35

36 Thank You TPE in CLAS D. Rimal 36

37 Back up slides Backup slides TPE in CLAS D. Rimal 37