The Electric and Magnetic Form Factor of the Neutron with Super Bigbite

Transcription

1 The Electric and Magnetic Form Factor of the Neutron with Super Bigbite Seamus Riordan University of Virginia Gordon Cates, University of Virginia Bogdan Wojtsekhowski, Jefferson Lab for the Super Bigbite, E , and E Collaborations May 19, 20 Seamus Riordan Exclusive 20 GE n and Gn M with SBB 1/32

2 Outline Form Factor Models and Interpretations G n E to Q2 = 10 GeV 2 : E G n M to Q2 = 13.5 GeV 2 : E Seamus Riordan Exclusive 20 GE n and Gn M with SBB 2/32

3 Motivation Form factors are a fundamental property of the nucleon Provide excellent testing ground for QCD and QCD-inspired models Gives constraints on models of nucleon structure Are not yet calculable from first principles Seamus Riordan Exclusive 20 GE n and Gn M with SBB 3/32

4 Nucleon Currents Scattering matrix element, M j µj µ Q 2 Generalizing to spin 1/2 with arbitrary structure, one-photon exchange, using parity conservation, current conservation the current parameterized by two form factors J µ = eū(p ) [ F 1 (q 2 )γ ν + i 2M q νσ µν F 2 (q 2 ) ] u(p) κ j µ Form Factors Dirac - F 1, chirality non-flip Pauli - F 2, chirality flip µ p µ J µ q µ p Seamus Riordan Exclusive 20 GE n and Gn M with SBB 4/32

5 Sachs Form Factors Replace with Sachs Form Factors G E = F 1 κτf 2 G M = F 1 + κf 2 lim Q2 0 G p E (Q2 = 0) = 1, G p M (Q2 = 0) = µ p = 2.79 G n E(Q 2 = 0) = 0, G n M (Q2 = 0) = µ n = 1.91 Rosenbluth Formula [ ] dσ dω = dσ E GE 2 + τg2 M + 2τG 2 θ M dω E 1+τ tan2,τ = Q2 2 4M 2 Mott Seamus Riordan Exclusive 20 GE n and Gn M with SBB 5/32

6 Neutron Form Factors Typically lag behind proton counterparts Neutron studies require nuclear corrections G n E is small /µ n G D n G M VMD - Lomon (2002) CQM - Miller (2002) Rock Lung Markowitz Anklin(1994) Bruins Anklin(1998) Kubon Lachniet Q [GeV ] n G E VMD - E. Lomon (2002) q(qq) DSE - C. Roberts, ANL (2008) RCQM - G. Miller (2005) d(e,e d) T - Schiavilla & Sick F 2 /F 1 ln (Q /Λ )/Q, Λ = 300 MeV Galster fit (1971) Passchier Herberg Ostrick Madey Glazier Zhu Warren Meyerhoff Becker Bermuth Rohe Geis E Q [GeV ] Seamus Riordan Exclusive 20 GE n and Gn M with SBB 6/32

7 Nucleon Structure Information in Form Factors Constituent quark models q(qq) Dyson-Schiwinger equations approach Charge distributions in the IMF QCD motivated fits - VMDs, GPDs With proton and neutron form factors - quark flavor and isoscalar/vector decomposition Seamus Riordan Exclusive 20 GE n and Gn M with SBB 7/32

8 Constituent Quark Light-Front Cloudy Bag Model Constituent quark model - successful for calculation of baryon magnetic moments Construct wavefunction for 3 massive quarks, relate current matrix elements to form factors Light front dynamics makes boosts to wavefunction easy so relating initial and final states for current matrix element is much easier, but rotations are more difficult Form allows for quark orbital angular momentum Form is assumed for spatial distribution, confinement size is a free parameter Miller includes additional pion cloud effects for low Q 2 behavior Seamus Riordan Exclusive 20 GE n and Gn M with SBB 8/32

9 Constituent Quark Light-Front Cloudy Bag Model Results match present G p E at higher Q2 p /G M p µ p G E GEp(1) GEp(2) RCQM - G. Miller (2005) Q [GeV ] n G E RCQM - G. Miller (2005) Passchier Herberg Ostrick Madey Glazier Zhu Warren Meyerhoff Becker Bermuth Rohe Geis E Q [GeV ] G p E suppression at higher Q2 due to inclusion of quark orbital angular momentum Seamus Riordan Exclusive 20 GE n and Gn M with SBB 9/32

10 Novel DSE/Fadeev q(qq) ANL Calculation Poincare covariant model based on QCD s Dyson-Schwinger equations to describe dressed quark propagator Uses model where two of three quarks are in diquark state Bethe-Salpeter equation describes diquark boundstate Fadeev amplitudes describe quark interchanges Few free parameters tuned to nucleon properties such as mass and magnetic moments n G E q(qq) DSE - C. Roberts, ANL (2008) Passchier Herberg Ostrick Madey Glazier Zhu Warren Meyerhoff Becker Bermuth Rohe Geis E Bhagwat et. al. arxiv:nucl-th/ Cloët et. al. arxiv:nucl-th/ Q [GeV ] Seamus Riordan Exclusive 20 GE n and Gn M with SBB 10/32

11 pqcd Can treat with pqcd for large Q 2 Log order calculations for F 1, F 2 by Belitsky et al. (including hadron helicity non-conservation through quark OAM) makes prediction that as Q 2 Q 2 F 2 = const. log 2 (Q 2 /Λ 2 ) F 1 Λ parameter related to size of the nucleon Published proton data fits very well at early Q 2 (Q 2 /Log 2 (Q 2 /Λ 2 ))F 2 /F Q 2 (GeV 2 ) Λ=400MeV Λ=300MeV Λ=200MeV [2] [3] Seamus Riordan Exclusive 20 GE n and Gn M with SBB 11/32

12 pqcd Can treat with pqcd for large Q 2 Log order calculations for F 1, F 2 by Belitsky et al. (including hadron helicity non-conservation through quark OAM) makes prediction that as Q 2 Q 2 F 2 = const. log 2 (Q 2 /Λ 2 ) F 1 Λ parameter related to size of the nucleon (Q 2 /ln 2 [Q 2 /Λ 2 ]) (F 2N / κ N F 1N ) From DSE approach: Proton Neutron Published proton data fits very well at early Q Q 2 [GeV 2 ] Seamus Riordan Exclusive 20 GE n and Gn M with SBB 11/32

13 pqcd Can treat with pqcd for large Q 2 Log order calculations for F 1, F 2 by Belitsky et al. (including hadron helicity non-conservation through quark OAM) makes prediction that as Q Q 2 F 2 = const. log 2 (Q 2 /Λ 2 ) F 1 Λ parameter related to size of the nucleon n /G M n µ n G E F 2 /F 1, Λ = 150 MeV F 2 /F 1, Λ = 300 MeV Q [GeV ] Published proton data fits very well at early Q 2 Seamus Riordan Exclusive 20 GE n and Gn M with SBB 11/32

14 Form Factor Interpretations and Models Impact parameter densities in infinite momentum frame i bi x i = 0 Unpolarized and Transversely Polarized: Z ρ N dq 0 (b) = 0 2π QJ 0(bQ)F 1 (Q 2 ) ρ N T (b) = ρ N 0 (b) sin(φ b φ S ) Z 0 dq 2π Q 2 2M N J 1 (bq)f 2 (Q 2 ) q y b φ x S Carlson and Vanderhaeghen, Phys. Rev. Lett. 100, , (2008) G. Miller, Phys. Rev. C 78, 0322(R) (2008) Seamus Riordan Exclusive 20 GE n and Gn M with SBB 12/32

15 b is NOT radial quantity, is taken wrt momentum weighted distribution of all partons in IMF Unpolarized, polarized φ = 90 Ρ0 n,ρt n 1 fm 2 Ρ0 p,ρt p 1 fm Neutron Proton by fm by fm Seamus Riordan Exclusive 20 GE n and Gn M with SBB 13/32

16 b is NOT radial quantity, is taken wrt momentum weighted distribution of all partons in IMF Unpolarized, polarized φ = 90 Ρ0 n,ρt n 1 fm 2 Ρ0 p,ρt p 1 fm Neutron Proton by fm by fm Neutron has negative density at b = 0 Large x, d quarks dominate in neutron Neutron u/d Neutron u/d PDF Ratio x Seamus Riordan Exclusive 20 GE n and Gn M with SBB 13/32

17 Transversely Polarized Transverse Density Transversely Polarized Spin Orientation bx fm Momentum Direction In IMF quarks which are rotating towards/away from photon are enhanced across polarization-q plane Suggestive of orbital angular momentum (M. Burkardt) Seamus Riordan Exclusive 20 GE n and Gn M with SBB 14/32

18 GPD Parameterization - Diehl et al. Non-skewed moments of GPDs yield form factors F p 1 = F p 2 = Z 1 1 Z 1 1 ( 2 dx 3 Hu (x,ξ = 0,t,µ 2 ) 1 ) 3 Hd (x,ξ = 0,t,µ 2 ) ( 2 dx 3 E u (x,ξ = 0,t,µ 2 ) 1 ) 3 E d (x,ξ = 0,t,µ 2 ) Form factors can be used to constrain GPD models Parameterization from Diehl et al: ( H q x0 ) α(0) [( v (x,t) = exp α log x ) ] 0 x x + b 0 t E q v (x,t) = N q κ q x α (1 x) β q [tα (1 x) 3 log 1x ] + D q(1 x) 3 + C q x(1 x) 2 exp Seamus Riordan Exclusive 20 GE n and Gn M with SBB 15/32

19 Quark Flavor Decomposition From E02-3: u /F 1 d F GPD VMD Faddeev&DSE Lattice F p 1,2 = 2 3 F u 1,2 1 3 F d 1,2 F n 1,2 = 1 3 F u 1, F d 1,2 u uf 2 d /κ -1 d F 2 κ Q [GeV ] Lattice: Bratt et al., arxiv: , m π = 140 MeV High Q 2 for GE n data allows for quark decomposition GPDs formulated for quark flavors Lattice is better suited for isovector FF, scaling behavior Seamus Riordan Exclusive 20 GE n and Gn M with SBB 16/32

20 Quark Flavor Decomposition 0.5 Up and down quark F2/F1 distributions do not appear to follow 1/Q u /F 1 u κ ū 1 F d /F 1 d d F 2 κ Q [GeV ] G n E Q [GeV ] data with Kelly paramterization for remaining FFs Curve - Kelly parameterization Seamus Riordan Exclusive 20 GE n and Gn M with SBB 17/32

21 Extending G n E to Q2 = 10 GeV 2 - Spin Observables Akhiezer and Rekalo (1968) - Polarization experiments offer a better way to obtain G E than Rosenbluth separation Polarization observable measurements generally have fewer systematic contributions from nuclear structure and radiative effects Polarization Transfer G E = P t (E e + E e )tanθ e /2 G M P l 2M Seamus Riordan Exclusive 20 GE n and Gn M with SBB 18/32

22 Polarized Target Measurements Long. polarized beam/polarized target transverse to q in scattering plane polarization axis e e θe ω, q θ φ momentum transfer Helicity-dependent asymmetry roughly proportional to G E /G M σ + σ 2 τ(τ+1)tan(θ/2)g E /G M A = σ + + σ (G E /G M ) 2 +(τ+2τ(1+τ)tan 2 (θ/2)) Seamus Riordan Exclusive 20 GE n and Gn M with SBB 19/32

23 G n E Measurements at JLab G n E least well measured range of Q2 More difficult to measure relative to other FFs since G n E is intrinsically small compared to Gn M Neutron is not stable outside nucleus, use targets 2 H and 3 He Four experiments done at JLab: Hall C - E Zhu et al., Warren et al. - d( e,e n)p, Q 2 = 0.5,1.0 GeV 2 Hall C - E Madey et al. - d( e,e n)p, Q 2 = GeV 2 Hall A - E He( e,e n)pp, Q 2 = GeV 2 Hall A - E He( e,e n)pp, Q 2 = GeV 2 Seamus Riordan Exclusive 20 GE n and Gn M with SBB 20/32

24 Goals Bring G n E up to similar range as Gp E Challenges: Strategy: Cross section falls with Q 2, factor of 100 Q 2 = GeV 2 Polarization transfer difficult with high nucleon momentum Measure polarized target asymmetry Increase luminosity - upgrade detectors/target Increase target polarization - narrow width laser, hybrid alkalai Improve PID from electron and nucleon arm Seamus Riordan Exclusive 20 GE n and Gn M with SBB 21/32

25 High Q 2 GE n Experimental Layout (Not to scale) 48D48 Magnet GEM Veto Polarized 3 He Target n 17m Path HCAL e BigBite w/ upgraded detectors Upgraded Bigbite detector stack for higher rates, better PID Hadron calorimeter at 17 m, additional GEM veto Place magnet B dl = 1.7 T m in front to deflect protons - reduces background by factor of 5 Seamus Riordan Exclusive 20 GE n and Gn M with SBB 22/32

26 Upgraded 3 He Target Simulations show sustainable polarization of 62% with I = 60 µa Overall effective luminosity gain of 15 Seamus Riordan Exclusive 20 GE n and Gn M with SBB 23/32

27 Upgraded BigBite Components Estimated rates are 60 khz/cm 2 - current drift chambers replaced by GEM chambers GEM detectors shown to work up to 2500 khz/cm 2 at CERN Momentum resolution of σ p /p 0.5% for e of 3 4 GeV BigBite Cerenkov+preshower pushes pion contributions < 0.1% 440 GEM 400x1500 GEM GEM 500x x2000 Gas C Lead Glass Calorimeter Scintillator 3He Target o o Seamus Riordan Exclusive 20 GE n and Gn M with SBB 24/32

28 Hadron Calorimeter, HCAL HCAL based on COMPASS design Threshold can be set dramatically higher than original neutron arm, 50 khz with 50 MeV threshold High detection efficiency, > 95% Acceptance can be configured to match QE nucleon profile Time-of-flight resolution comparable to neutron arm with optimized readout scheme (300 ps was achieved with E864 calorimeter at AGS) Seamus Riordan Exclusive 20 GE n and Gn M with SBB 25/32

29 Quasielastic Selection and Backgrounds Cuts on missing momenta, invariant mass allow for suppression of inelastic events Inelastics can be corrected using Monte Carlo with MAID or sideband subtraction 0.1 E beam =8.8 GeV E beam = 8.8 GeV 3 He(e,e n(p)π) n σ/ W cm 2 /GeV BigBite & BigHAND p < 0.15 GeV/c per one inelastic event γ cuts: W GeV 2 TOF = ± 1 ns q 0.1 GeV/c p π + π W 2 GeV 2 particle ID With bending magnet and GEM veto, proton contamination will be negligable Seamus Riordan Exclusive 20 GE n and Gn M with SBB 26/32

30 FSI Contributions Nuclear effects evaluated through GEA by M. Sargsian Effective polarization highly dependent on missing momentum cuts Different from 86% inclusive assumption For our detector acceptances and cuts, effective polarization neutron polarization % p max, GeV/c Seamus Riordan Exclusive 20 GE n and Gn M with SBB 27/32

31 Anticipated Results Brings GE n up to similar level as other form factors in 50 days beamtime 1.0 /G D 0.5 Madey E02-3 VMD - E. Lomon (2002) RCQM - G. Miller (2006) DSE - C. Roberts (2009) d(e,e d) T - Schiavilla & Sick F /Λ 2 2 /F ln (Q )/Q, Λ = 300 MeV 1 Galster fit (1971) n G E 0.0 E , SBS Q [GeV ] Strong divergence between different model predictions DSE predicts zero crossing Seamus Riordan Exclusive 20 GE n and Gn M with SBB 28/32

32 Extending G n M to Q2 = 14 GeV 2 Ratio technique to extract GM n from relative differential cross section to G p M R = dσ dω d(e,e n) dσ dω d(e,e p) ησ Mott τ/ε 1+τ (Gn M )2 dσ dω = R p(e,e ) dσ dω η σ Mott n(e,e ) 1+τ dσ dω = p(e,e ) ((G ne )2 + τ (GnM ε )2) dσ dω p(e,e ) η = E /E,ε = ( 1+ q 2 /Q 2 tan 2 (θ/2) ) 1 Not as sensitive for corrections for nuclear structure (< 1%) Not very sensitive to GE n Need to know nucleon detection efficiencies, calibrate on H 2 Need for extracting GE n from measured ratio Gn E /Gn M Seamus Riordan Exclusive 20 GE n and Gn M with SBB 29/32

33 G n M Setup 7 Q 2 points ranging from 3.5 GeV 2 to 13.5 GeV 2 Setup similar to G n E with LD 2 target (Not to scale) 48D48 Magnet GEM Veto LD 2 Target n 17m Path HCAL e BigBite w/ upgraded detectors Seamus Riordan Exclusive 20 GE n and Gn M with SBB 30/32

34 Antipated Results Approved beam of 25 days Total error on GM n 4% at Q2 = 13.5 GeV 2 G n M calculated using conservative Bodek parameterization /µ n G D n G M VMD - Lomon (2002) CQM - Miller (2002) Rock Lung Markowitz Anklin(1994) Bruins Anklin(1998) Kubon Lachniet E , CLAS12 E (Super BigBite) Q [GeV ] CLAS12 GM n points shown for 56 days proposed (30 approved) Seamus Riordan Exclusive 20 GE n and Gn M with SBB 31/32

35 Conclusion Measuring the electric and magnetic form factors of the neutron to high Q 2 helps complete our picture of the nucleon Super Bigbite allows us to take form factor measurements to very high Q 2 with relative errors comparable to previous measurements Will allow for differentiation between several popular form factor models Seamus Riordan Exclusive 20 GE n and Gn M with SBB 32/32