Developments in the measurement of G n E. , the neutron electric form factor

Transcription

1 Developments in the measurement of G n E, the neutron electric form factor Donal Day University of Virginia October 14, 23 -

2 Outline Introduction: Formalism, Interpretation, Motivation Models Experimental Techniques Traditional (unpolarized beams) Modern (polarized beams, targets, polarimeters) Experiments using polarized electrons at Jefferson Lab Recoil polarization Beam-target asymmetry Outlook

3 Formalism dσ dω = σ E n Mott (F 1 ) 2 + τ E h2 (F 1 + F 2 ) 2 tan 2 (θ e ) + (F 2 ) 2io E, k E R, P R F p 1 = 1 F n 1 = F p 2 = 1.79 F n 2 = 1.91 electron γ G E,M nucleon In Breit frame F 1 and F 2 related to charge and spatial curent densities: E, k M ρ = J = 2eM[F 1 τf 2 ] J i = eūγ i u[f 1 + F 2 ] i=1,2,3 G E `Q2 = F 1 (Q 2 ) τf 2 `Q2 G M `Q2 = F 1 `Q2 + F 2 `Q2 For a point like probe G E and G M are the FT of the charge and magnetizations distributions in the nucleon, with the following normalizations Q 2 = limit: G p E = 1 Gn E = Gp M = 2.79 Gn M = 1.91

4 G n E Interpretation In the NR limit (Breit Frame), G E is FT of the charge distribution ρ(r): G n E `q2 = 1 Z (2π) 3 d 3 rρ(r)e (iq r) = q2 r2 ne Experimental: Mean square charge radius r 2 ne is negative. Theory has intuitive explanation: Charge Distribution 4πr 2 ρ(r) r (fm) pion-nucleon theory: valence quark model: n = p + π cloud n = ddu & spin-spin force d periphery

5 Charge radius, Foldy term dg r2 ne n = 6 E() = 6 df 1 n () + 3 dq 2 dq 2 2M F n 2 2 () = rin 2 + r2 Foldy Foldy term, 3µ n 2m n = (.126)fm 2, has nothing to do with the rest frame charge distribution. r2 ne is measured through neutron-electron scattering r2 ne = 3m e a m n b ne =.113 ±.3 ±.4fm 2. r2 in = suggesting that the spatial charge extension seen in F 1 is about or very small. Recent Work: N. Isgur, Phys. Rev. Lett. 83, 272 (1999) M. Bawin & A.A. Coon, Phys. Rev. C. 6, 2527 (1999) G n E arises from the neutron s rest frame charge distribution. A. Glozman & D. Riska, Phys. Lett. B 459 (1999) 49. Pionic loop fluctuations make minute contribution to r 2 in.

6 Why measure G n E? FF are fundamental quantities Test of QCD description of the nucleon Symmetric quark model, with all valence quarks with same wf: G n E G n E details of the wavefunctions G E n CI (valence) CI+DI (valence+sea) Galster Q 2 (GeV/c) 2 Sensitive to sea quark contributions Soliton model: ρ(r) at large r due to sea quarks Dong, Liu, Williams, PRD Necessary for study of nuclear structure. Few body structure functions

7 Proton Form Factor Data Rosenbluth separation dσ dω = σ Mott (1 + τ) E E " G 2 E + τ(1 + (1 + τ)2tan2 (θ/2))g 2 M {z } # G p M well measured via Rosenbluth, but not Gp E hence Recoil Polarization G E p/g D Dipole Parametrization: Good description of early G p E,M data G p E = Gp M µ p = G D = 1 + Q Andivahis Walker Hohler Price JLAB ! 2 G D = 1 + Q2 k 2 2 implies an exponential charge distribution: ρ (r) e kr Q (GeV/c) Q 2 (GeV/c) 2 G M p/µ p G D Andivahis Walker Sill Hohler Price Q 2 (GeV/c) 2

8 Neutron Form Factors without Polarization No neutron target, G n M dominates Gn E, proton dominates neutron Traditional techniques used to measure G n M and Gn E have been: Elastic scattering 2 H(e, e ) 2 H Inclusive quasielastic scattering: 2 H(e, e )X Neutron in coincidence with electron: 2 H(e, e n)p Neutron in anti-coincidence with electron: 2 H(e, e p)p Ratio techniques d(e,e n)p d(e,e p)n FSI. minimizes roles of g.s. wavefunction and Quasielastic kinematics and simplest nucleus

9 Measurements of the Neutron Form Factors Target Type Q 2 (GeV/c) 2 Deduced quantities Reference 2 H elastic G En F.A. Bumiller et al., PRL 25, 1774 (197) 2 H elastic G En Drickey & Hand, PRL 9, 1774 (1962) 2 H elastic G En G.G. Simon, et al., NP A364, 285 (1981) 2 H ratio.11 G Mn H.A. Anklin et al., PL B336, 313 (1994) 2 H quasielastic G En, G Mn B. Grossette et al., PR 141, 1435 (1966) 2 H elastic G En, G Mn P. Benaksas et al., PRL 13, 1774 (1964) 2 H coincidence G Mn P. Markowitz et al. PR C48, R5 (1993) 2 H quasielastic.6-.3 G En, G Mn E.B. Hughes et al. PR 146, 973 (1966) 2 H elastic G Mn J.I. Friedman et al. PR 12, 992 (196) 2 H elastic G En S. Galster et al. NP B32, 221 (1971) 2 H ratio G En, G Mn P. Stein et al. PRl 16, 592 (1966) 2 H ratio G Mn E.E. Bruins et al. PRL 75, 21 (1995) 2 H ratio.2-.9 G Mn H.A. Anklin et al., PL B428, 248 (1998).2-.9 G Mn G. Kubon et al., PL B524, 26 (22) 2 H elastic G En S. Platchov et al. NP A51, 74 (199) 2 H ratio G En, G Mn W. Bartel et al. PL 3B, 285 (1969) 2 H quasielastic G Mn A.S. Esaulov et al. Sov. J. NP 45, 258 (1987) 2 H quasielastic G En, G Mn E.B. Hughes et al. PR 139, B458 (1965) 2 H quasielastic.4-.2 G Mn D. Braess et al. Zeit Phys. 198, 527 (1967)reanalysis of Hughes 2 H quasielastic G En, G Mn W. Bartel et al. NP B58, 429 (1973) 2 H ratio G En, G Mn W. Bartel et al. PL 39B, 47(1972) 2 H anticoincidence G En, G Mn K.M. Hanson et al. PR D8, 753 (1973) 2 H quasielastic G Mn R.G. Arnold et al. PRL 61, 86 (1988) 2 H quasielastic G En, G Mn A. Lung et al. PRL 7, 718 (1993) 2 H anticoincidence G En, G Mn R.J. Budnitz et al. PR 173, 1357 (1968) 2 H quasielastic G Mn S. Rock et al. PRL 49, 1139 (1982)

10 G n M unpolarized G M n /µn G D Kubon (2) Anklin (98+94) Bruins (95) Lung (93) Markowitz (93) Kubon Anklin Bruins ratio ratio ratio Lung D(e, e )X Markowitz ratio D(e, e n)p D(e, e p)n D(e, e n)p Q 2 (GeV/c) 2

11 G n M unpolarized and polarized 1.2 G M n /µn G D Xu (2+) Kubon (2) Anklin (98+94) Bruins (95) Lung (93) Markowitz (93) Kubon Anklin Bruins ratio ratio ratio Lung D(e, e )X Markowitz Xu ratio D(e, e n)p D(e, e p)n D(e, e n)p 3 He( e, e )X Q 2 (GeV/c) 2

12 G n E Before Polarization No free neutron extract from e D elastic scattering: small θ e approximation dσ dω = σ NS dσ dω = (Gp E + Gn E) 2» A `Q 2 + B `Q 2 tan 2 θe 2 «C E (q) z } { Z ˆu(r) 2 + w(r) 2 j ( qr 2 )dr Galster Parametrization: G n E = τµ n 1+5.6τ G D

13 G n E from Elastic Scattering D(e, e d) Components of the tensor polarization give useful combinations of the form factors, t 2 = 1 j 8 2S 3 τ dg C G Q τ2 d G2 Q + 1 ff 3 τ d ˆ1 + 2(1 + τd )tan 2 (θ/2) G 2 M G Q (Q 2 ) = (G p E + Gn E )C Q(q) suffers less from theoretical uncertainties than A(Q 2 ). G n E can be extracted to larger momentum transfers.

14 G n E at large Q2 through 2 H(e, e )X PWIA model σ is incoherent sum of p and n cross section folded with deuteron structure. σ = (σ p + σ n )I (u, w) = εr L + R T (G En / G D ) Galster Extraction of G n E : Rosenbluth Separation R L Subtraction of proton contribution Problems: Unfavorable error propagation Sensitivity to deuteron structure SLAC: A. Lung et al, PRL. 7, 718 (1993) No indication of non-zero G n E Lung et al.(1993) Hanson et al.(1973) Q 2 (GeV/c) 2 If G n E is small at large Q2 then F n 1 must cancel τf n 2, begging the question, how does F1 n evolve from at Q 2 = to cancel τf n 2 at large Q2?

15 Models of Nucleon Form Factors VMD F(Q 2 ) = P i C γvi Q 2 +M 2 V i F Vi N(Q 2 ) breaks down at large Q 2 CBM Lu, Thomas, Williams (1998) M pqcd F 2 F 1 helicity conservation Q 2 Hybrid VMD-pQCD Counting rules: F 1 α2 s (Q2 ) Q 4 Q 2 F 2 /F 1 constant JLAB proton data: QF 2 /F 1 constant GK, Lomon Lattice Dong.. (1998) RCQM Soliton LFCBM Helicity non-conservation point form (Wagenbrunn..) light front (Cardarelli..) Holzwarth Miller pqcd (Ralston..) LF (Miller..)

16 Theoretical Models Vector Meson Dominance e' γ C γ i V ρ,ω N' F V i Interaction in terms of coupling strengths of virtual photon and vector mesons and vector mesons and nucleon. Success at low and moderate Q 2 offset by failure to accomodate pqcd. e m 2 m +Q 2 2 pqcd High Q 2 helicity conservation requires that Q 2 F 1 /F 2 constant as F 2 helicity flip arises from second order corrections and are suppressed by an additional factor of 1/Q 2. Furthermore for Q 2 Λ QCD counting rules find F 1 α s (Q 2 ) 2 /Q 4. Thus F 1 1 Q 4 and F 2 1 Q 6 Q2 F 2 F constant. 1 Lattice calculations of form form factors Fundamental but limited in stat. accuracy Dong et al PRD58, 7454 (1998) QCD based Models Try to capture aspects of QCD RCQM, Di-quark model, CBM N Hybrid Models Failure to follow the high Q 2 behavior suggested by pqcd led GK to incorporate pqcd at high Q 2 with the low VMD behavior. Inclusion of φ by GK had significant effect on G n E. Lomon has updated with new fits to selected data. Helicity non-conservation shows up in the light front dynamics analysis of Miller which predicted Q F 2 F constant and the violation of helicity conservation. Ralston s 1 pqcd model also predicts that Q F 2 F constant. 1 Both models include quark orbital angular momentum.

17 Theoretical Models

18 Spin Correlations in elastic scattering Dombey, Rev. Mod. Phys (1968): p( e, e ) Akheizer and Rekalo, Sov. Phys. Doklady (1968): p( e, e, p) Arnold, Carlson and Gross, Phys. Rev. C (1981): 2 H( e, e n)p Essential statement Exploit spin degrees of freedom O G E G M instead of O G 2 E + G2 M Early work at Bates, Mainz 2 H( e, e n)p, Eden et al. (1994) 1 H( e, e p), Milbrath et al. (1998) 3 He(e,e ), Woodward, Jones, Thompson, Gao ( ) 3 He(e,e n), Meyerhoff, (1994)

19 Neutron Form Factors Polarized Beam Unpolarized Beam Spin Correlations Cross Section Measurements Recoil Polarimetry Beam-Target Asymmetry Ratio Method Quasielastic ed Elastic ed D( e,e n)p D( e,e n)p 3 He( e,e n)pp 3 He( e,e )X D(e, e n)p D(e, e p)n D(e,e )X D(e,e ) D(e,e d ) G n M G n M G n M G n M G n E G n E G n E G n E G n E

20 G n E from spin observables No free neutron targets scattering from 2 H or 3 He can not avoid engaging the details of the nuclear physics. Minimize sensitivity to the how the reaction is treated and maximize the sensitivity to the neutron form factors by working in quasifree kinematics. Detect neutron. Indirect measurements: The experimental asymmetries (ξ s, A ed A qe exp) are compared to theoretical calculations. Theoretical calculations are generated for scaled values of the form factor. Form factor is extracted by comparison of the experimental asymmetry to acceptance averaged theory. Monte Carlo Polarized targets The deuteron and 3 He only approximate a polarized neutron Scattering from other unpolarized materials, f dilution factor V,

21 Recoil Polarization Electron scattering plane e e' θ e n t Secondary scattering plane n(p) l θ φ I P t = 2 p τ(1 + τ)g E G M tan(θ e /2) I P l = 1 M N (E e + E e ) p τ(1 + τ)g 2 M tan2 (θ e /2) G E G M = P t P l (E e +E e ) 2M N tan( θ e 2 ) Direct measurement of form factor ratio by measuring the ratio of the transfered polarization P t and P l

22 Recoil Polarization Principle and Practice Interested in transfered polarization, P l and P t, at the target Polarimeters are sensitive to the perpendicular components only, Pn pol and P pol t Measuring the ratio P t /P l requires the precession of P l by angle χ before the polarimeter. If polarization precesses χ (e.g. in a dipole with B normal to scattering plane): P pol t = sinχ P l + cosχ P t For χ = 9 o, P pol t For χ = o, P pol t = P l and is related to G 2 M = P t and is related to G E G M G n E /Gn M via 2 H( e, e n)p in JLAB s Hall C - Charybdis and N-Pol

23 Quality of polarimeter data optimized by taking advantage of proper flips (helicity reversals). L 1 = N o [1 + pa y (θ + α)] R 2 = N o [1 pa y (θ + β)] R 1 = N o [1 pa y (θ + α)] L 2 = N o [1 + pa y (θ + β)] Using the geometric means, L L 1 L 2 and R R 1 R 2, the false (instrumental) asymmetries, α and β, cancel. ξ = pa y = L R L + R

24 G n E in Hall C, E93-38 Recoil polarization, 2 H( e, e n)p In quasifree kinematics, P s is sensitive to G n E nuclear physics and insensitive to Up down asymmetry ξ transverse (sideways) polarization P s = ξ s /P e A pol. Requires knowledge of P e and A pol Rotate the polarization vector in the scattering plane (with Charybdis) and measure the longitudinal polarization, P l = ξ l /P e A pol Take ratio, P s P l. P e and A pol cancel Three momentum transfers, Q 2 =.45, 1.13, and 1.45(GeV/c) 2. Data taking 2/21.

25 G n E in Hall C via 2 H( e, e n)p P X P Y P Z E e =.884 GeV; E e =.643 GeV; Θ e = ; Q 2 =.45 (GeV/c) 2 ; Galster Parameterization Quasifree Emission φ c.m. = np Quasifree Emission φ c.m. = np Quasifree Emission φ c.m. = np φ c.m. = 18 np PWBA (RC) FULL (RC): FSI+MEC+IC φ c.m. = 18 np φ c.m. = 18 np c.m. [deg] Θ np

26 G n E in Hall C via 2 H( e, e n)p Top Rear Array Z (Momentum Direction) Rear Veto/Tagger Front Array P L, δ Polarization Vector Bottom Rear Array Front Veto/Tagger Lead Curtain Charybdis To HMS e e Target LD2, LH2 9 deg. P X = PL, P, S + 9 deg. P + X = P, L X Taking the ratio eliminates the dependence on the analyzing power and the beam polarization greatly reduced systematics G n E G n M = K tan δ where tanδ = P s P l = ξ s ξ l

27 Counts ns Counts ctof-ctof calc (ns) TOF- TOF calc (ns) Left: Coincidence TOF for neutrons. Difference between measured TOF and calculated TOF assuming quasi-elastic neutron. Right: TOF for neutron in front array and neutron in rear array. TOF is kept as the four combinations of (-,+) helicity, and (Upper,Lower) detector and cross ratios formed. False asymmetries cancel. r = N + U N D N U N+ D «1/2 ξ = (r 1)/(r + 1)

28 G n E in Hall C via 2 H( e, e n)p ξ S (%) ξ L (%) χ = Q 2 = 1.14 (GeV/c) 2 (n,n) In Front p/p = -3/+5% ξ S χ 2 /ndf =.9 = ±.13 % χ = -9 χ 2 /ndf = ξ L = 6.21 ±.33 % Runs ξ L (%) 2.5 χ = +9 χ 2 /ndf = ξ L = ±.36 % Runs

29 G n E in Hall C via 2 H( e, e n)p 2 2 Fit to Data for Q = 1.15 (GeV/c) Asymmetry, ξ (%) (nn) δ ξ = A P sin( χ + δ ) Y (np) Precession Angle, χ (deg)

30 Results through 2 H( e, e n)p Systematic Errors (included): Precession θ 1% CEX <.2% Depolarization.5% G n M 2.% P beam 1-2% other 2% total 3%

31 Beam Target Asymmetry - Principle Polarized Cross Section: u y normal σ = Σ + h Beam Helicity h ± 1 A = σ + σ σ + + σ = Σ e h = ±1 xz plane e' θ e (q, ω) polarization axis (θ, φ ) θ φ u x u z along q A = A T {}}{ a cosθ (G M ) 2 + A T L {}}{ b sinθ cosφ G E G M c (G M ) 2 + d (G E ) 2 ; ε = N N N + N = P B P T A Θ = 9 Φ = Θ = Φ = = A = bg E G M c (G M ) 2 + d (G E ) 2 = A = ag 2 M c (G M ) 2 + d (G E ) 2

32 Experimental Asymmetry Quasi-Elastic Scattering off Polarized Deuteron ɛ = P e (1 β)a e + (1 + αβ)p V t A V ed + (1 βγ)p T t A T ed (1 + β) + (1 αβ)p V t A V d + (1 + βγ)p T t A T d P V t, P T t = vector, tensor polarization α, β, γ = normalization ratios Deuteron supports a tensor polarization, P T t, in addition to the usual vector polarization, P V t - This can lead to both helicity dependent and helicity independent contributions After (symmetric) acceptance averaging and ignoring small P T t ɛ = 1+αβ 1+β P e P V t A V ed or A V ed = 1+β (1+αβ) P e P V t ɛ G n E extracted via AV ed from data and MC simulation

33 Beam Target Asymmetry in E H( e, e n)p ( ) σ(h, P) σ 1 + hpa V ed h: Beam Helicity P : Vector Target Polarization T : Tensor Target Polarization T = 2 4 3P 2 A T d is suppressed by T 3% Theoretical Calculations of electrodisintegration of the deuteron by H. Arenhövel and co-workers

34 E93-26 A V ed D( e, e n)p is sensitive to G n E ( ) σ(h, P) = σ 1 + hpa V ed has low sensitivity to potential models has low sensitivity to subnuclear degrees of freedom (MEC, IC) in quasielastic kinematics Sensitivity to G n E Insensitivity to Reaction A ed V.1.5 G E n =.5 Galster G E n =1. Galster G E n =1.5 Galster A ed V.1.5 Born N N+MEC N+MEC+IC N+MEC+IC+REL θ cm np (deg) θ cm np (deg)

35 Gen1 neutron detector High Momentum Spectrometer polarized target incoming beam line, chicane magnet

36 Polarized Target Chicane to compensate for beam deflection of 4 degrees Scattering Plane Tilted Protons deflected 17 deg at Q 2 =.5 Raster to distribute beam over 3 cm 2 face of target Electrons detected in HMS (right) Neutrons and Protons detected in scintillator array (left) Beam Polarization measured in coincidence Möller polarimeter

37 LN 2 Microwave Input To Pumps Liquid Helium NMR Signal Out Refrigerator To Pumps Liquid Helium Signal LN 2 Frequency Solid Polarized Targets frozen(doped) 15 ND 3 4 He evaporation refrigerator 5T polarizing field remotely movable insert dynamic nuclear polarization 5 Gen Target Performance, 1Sep1 e Beam Magnet Target (inside coil) 1 K NMR Coil B 5T Deuteron Polarization(%) A Time(min)

38 Neutron Detector Highly segmented scintillator Rates: 5-2 khz per detector Pb shielding in front to reduce background 2 thin planes for particle ID (VETO) 6 thick conversion planes 142 elements total, >28 channels Extended front section for symmetric proton coverage PMTs on both ends of scintillator Spatial resolution 1 cm Time resolution 4 ps Provides 3 space coordinates, time and energy 14 Protons 12 1 Beam Height Neutrons cm 1 cm 1. cm 1 cm (length:16cm) Coincidence Time (ns)

39 n Detector Single Event Display Sample Neutron Track Sample Proton Track majority of protons in upper half of detector

40 Experimental Technique for D( e, e n)p For different orientations of h and P : N hp σ (h,p) Beam-target Asymmetry: ɛ = N N + N N N + N + N + N = hpfav ed.1.5 Burger Plot v4 neutron-std neutron-alt proton-std proton-alt std W cm θ np lab E ypos θ pq special

41 Data and MC Comparison W [MeV] Q 2 [(GeV/c) 2 ] θ nq [radian] cm [degree] θ np

42 Extracting G n E.1 data A ed V A ed V A ed V E, MeV A ed V y pos, cm χ cm E y pos θ nq θ np 2σ θ nq, radian cm, deg θ np Scale Factor ( Galster)

43 Results through D( e, e n)p Systematic Errors (included): P target 3-5% f 3% cuts 2% kinematics 2% G n M 1.7% P beam 1-3% other 1% total 6-8%

44 Relevant Theories

45 Laboratory Collaboration Q 2 (GeV/c) 2 Reaction Reported MIT-Bates E H(ẽ, e ñ) 1994 <.8 2 H(ẽ, e n) Planned <.8 3 He(ẽ, e n) Planned Mainz-MAMI A He(ẽ, e n) 1994 A3.15,.34 2 H(ẽ, e ñ) 1999 A He(ẽ, e n) 1999 A He(ẽ, e n) 1999/23 A1.3,.6,.8 2 H(ẽ, e ñ) Analysis NIKHEF.21 2 H(ẽ, e n) 1999 Jefferson Lab E9326.5, 1. 2 H(ẽ, e n) 21/23 E , 1.15, H(ẽ, e ñ) 23 E , 2.4, He(ẽ, e n) Approved

46 Conclusions G n E G n E remains the poorest known of the four nucleon form factors. is a fundamental quantity of continued interest. Significant progress has been made at several laboratories by exploiting spin correlations G n E can be described by the Galster parametrization (surprisingly) and data under analysis is of sufficient quality to test QCD inspired models. Future progress likely with new experiments and better theory.