Baryon Electroproduction

Transcription

1 Baryon Electroproduction Cole Smith University of Virginia JLAB Users Group Meeting June 18, 2004

2 N* Program at JLAB e e γ v N*, π,2 πηρω,,, N N, Primary Goals Extract photocoupling amplitudes for known,n* resonances Partial wave and isospin decomposition of hadronic decay Assume EM and strong interaction vertices factorize Helicity amplitudes A 3/2 A 1/2 S 1/2 and their Q 2 dependence Study quark wave function and symmetries Quark models: relativity, gluons vs. mesons. Identify missing resonances expected from SU(6)xO(3) More selective hadronic decays: 2 π, ηρω,,,kλ

3 JLAB N* Electroproduction Experiments Experiment E E E E E E E E E E E E E E Reaction ep e p π 0 PRL88, (2002) ep e n π + Pub. in preparation ep e n π + γpn * Pub. in preparation ed e p π - γnn * Analysis starting this year ep e p η γns 11 PRL86, 1702 (2001) e p e p π 0 σ LT/ N PRC68, (2003) e p e n π + σ LT/ N CLAS Collaboration review e p e p π 0 e p e n π + ep e p π 0 ep e p π 0 ep e p ω ep e p π + π - e p e p π + π - e p e p π 0 A A ET T PRC68, (2003) e p e n π + PRL88, (2002) ep e K + Λ Physics Status R EM R EM σ LT/ NN * Analysis starting this year σ LT/ NN * Analysis starting this year R EM high Q 2 Pub. in preparation R EM high Q 2 Analysis ongoing Missing N * Analysis ongoing Missing N * PRL91, (2003) Missing N * A ET R SM R SM N *, Missing N * PRL90, (2003) ep ep π + π - Axial FF Analysis ongoing

4 JLAB N* Electroproduction Experiments (cont d) Experiment Reaction Physics Status E E E ep e X e p e K + Λ e p e p π 0 A ET Missing N * R EM R SM PRL91, (2003) PRL90, (2003) Pub. in Preparation E E ep e p γ π 0 ep e p π 0 N * R EM R SM high Q 2 PRC69, (2004) Analysis ongoing E ep e p π 0 N (1232) PRD82, 45 (1999) ep e p η S 11 (1535) PRD60, (1999) Other electroproduction experiments with impact on N* program Local duality studies (Hall C) Inclusive Rosenbluth separations (Hall C) Spin structure functions (Hall A,B,C)

5 π resolution of probe Resonance excitation mechanism may depend on distance scale probed. N low Constituent quark model only justified at photon point. Lattice QCD: Quark mass vs. Q 2 high

6 No shortage of hadron models π π Constituent quark Diquark Flux tube Chiral quark soliton π But, there are complications

7 Complications Resonances exist in presence of Q 2 dependent backgrounds. Simplest assumption: smoothly varying

8 Complications L. Tiator, N*2004 Use reaction models (e.g- MAID, DMT, Sato-Lee) Quark models need to get dressed

9 Pion contributions to photoexcitation of (1232) Yang, Kamalov nucl-th/ (DMT model) Born (K-matrix) Born+rescattering γ p π π p Rescattering contributes 40% of resonant M1 excitation and nearly 100% of E2!

10 What does empirical E2/M1 ratio measure? e / γ * e Deformation of N, quark core? Answer may depend on wavelength of probe e / γ * π + π 0 Shape of pion cloud? e

11 Q 2 Evolution: Chiral Bag Models D.H. Lu, A.W Thomas, A.G. Williams PRC 55, 3108 (1997) Quark-pion coupling consistent π with PCAC and chiral symmetry breaking R = 0.8 fm PT projection 0 N (a) A 3/2 (10 3 GeV 1/2 ) Real Imag Bare Fig.1a (bare) Real Fig.1b Imag Fig.1b Real Fig.1c Imag Fig.1c Pion Cloud N B N N B B B N B (b) (c) Q 2 (GeV 2 ) Pion cloud contribution to A 3/2 comparable to bare (1232) at low Q 2

12 Pion Electroproduction Structure Functions e e peep (, ) π γ * / 0 p θ * φ * π o Longitudinal sensitivity w/o Rosenbluth separation. Measurement requires out-of-plane detection of hadronic decay. Structure functions extracted from fits to φ * distributions for each (Q 2,W, cosθ * ) point. LT and TT interference sensitive to weak quadrupole and longitudinal multipoles. d d 2 σ p ( sin cos2 2 ( 1) sin cos ) * * Ω π * π 2 * * * * = σt + εlσl + εσtt θπ φπ + εl ε + σlt θπ φπ k γ * M * Re( E M ) Re( S1+ M1+ )

13 CEBAF Large Acceptance Spectrometer (CLAS) e / p q = e e /

14 N (1232) Quadrupole Transition: Sensitive to chiral dynamics? Dynamical pion cloud models describe trend of recent data. Strong model dependence at low Q 2. New data from CLAS (e1e) and Mainz now being analyzed. (Joo, 2002) CLAS e1e

15 CLAS e1e Run (Nov-Dec 2002) Beam energy GeV Q 2 = GeV 2 W<1.4 GeV Beam polarization ~70% Current 10 na LH2 target thickness 2.0 cm Torus 1500 A (38%) DAQ rate 2800 Hz Livetime 89% Trigger Threshold 0.3 GeV Cerenkov threshold 1 p.e Q 2 (GeV 2 ) Elastic (1232) Trigger Threshold Elastic and inelastic data taken simultaneously providing normalization check. Fiducial Cut W (GeV)

16 New results from CLAS e1e run cos θ* φ* Q 2 = 0.2 GeV 2 W=1.22 GeV Unconstrained fits to φ* only Constrained fits to both cos θ* and φ* MAID03 fitted to all previous π o electroproduction data

17 Structure Functions Invariant Mass W

18 Structure Functions cos θ *

19 Legendre Coefficients Partial Wave Fit σ T LσL σtt σ + ε = A + AP + AP LT = C = D + D P (M 1+ dominance) Resonant Multipoles Result 2 M1 + = A o /2 ( ) Re( E M ) = A 2 C / 3 / 8 * Re( S M ) = D / 6 * Non-Resonant Multipoles Re( E M ) = A / 2 * Re( S M ) = D * ( ( )) Re( M M ) = A + 2 A + C / 8 *

20 Preliminary Low Q 2 Results for E2/M1 and C2/M1 Initial indications are data favor Sato-Lee dynamical model CLAS E1E

21 Preliminary R EM and R SM for Q 2 > 2 GeV 2 Maurizio Ungaro, (UConn and JLAB) Hadron helicity conservation requires E2=M1 Transverse quadrupole may be vanishing around Q 2 =5-6 GeV 2 Scalar quadrupole growing stronger with Q 2 relative to M1

22 E CLAS Electroproduction of (1232) Recent quark models still fall short at low Q 2 Missing qq strength? Sea quarks? p Large N c : F * 2 GPD G M

23 Amplification Through Interference Unpolarized Structure Function * σlt Re( LT ) = Re( L) Re( T ) + Im( L) Im( T ) Im( S ) Im( M ) Polarized Structure Function / * σ LT Im( L T ) = Re( L) Im( T ) Im( L) Re( T ) Re( S ) Im( M ) Im( S ) Re( E ) 1 0,1+

24 CLAS: Testing Dynamical Models w/ Polarized Response Functions Joo et al., Phys.Rev. C, 68, (2003) A e dσ k dσ dσ dσ dσ = + h + P hp dω k dω dω dω dω dσ dω dσ dω dσ dω dσ dω 0 * e * t * et * 0 e t et * cm * * * * γ = R + ε R + 2 ε (1 + ε) R cosφ + εr cos2φ * 0 * T L L L LT TT = 2 ε (1 ε) R sinφ = = Polarized beam ± h Polarized target ± P L 0 * / LT xyz,, xyz,, ( θγ, LT, TT ) f R R xyz,, xz, ( θγ, /, /) LT TT f R R beam target double-polarization A A e t A et σ e = σ 0 σ t = σ 0 σ et = σ 0 A et MAID SL DMT cosθ* Polarized target asymmetries A t 0.6 MAID φ * [deg] SL DMT

25 σ / : LT Fifth structure function at (1232) Resonance π / 0 peep (, ) p e e / π + (, ) n Strong resonant-background interference Opposite peaking behavior in π + and π 0 Model dependence stronger in π 0 channel.

26 Unitary Isobar Model : Sensitivity to Born terms in / / / * σlt = D0 + D1P1 (cos θπ ) +... σ / : LT UIM fit (Aznauryan) Pion pole = 0 Electric Born = 0 Magnetic Born = 0 Note complete set of Born terms necessary to describe data. Almost no free parameters in Delta(1232) region.

27 Sato-Lee dynamical model: t-channel pion pole term π 0 p π + n Turning off pion pole term affects neutral pion channel, despite being absent at tree level. p * γ n π + p * γ π + 0 π n p Evidence of importance of rescattering in neutral pion channel (already seen at threshold).

28 Q 2 Dependence of σ LT at (1232) Resonance σlt = D + D P(cos θπ ) +... D / / / * Im ( M S ) / * Large model dependence S 0+ multipole sensitive to pion loop corrections in pizero electroproduction at threshold D Im (( M M ) S ) / * Sensitive to phase difference of S 1+ and M 1+ multipoles arising from interference with Born terms. Larger model dependence in π 0 p channel. Large sensitivity to model details in partial wave data

29 Global Fit to CLAS Single Pion Electroproduction Data I. Aznauryan, V. Burkert, H. Egiyan, K. Joo, C. Smith (to be submitted PRC) Data from published and soon to be published experiments: E E E (V. Burkert, R. Minehart). E (S. Dytman). Publications: PRL, 86, 1702(2001), PRL, 88, (2002), PRC, 68R, (2003). Beam energies E=1.515, GeV at luminosity ~ 3 x cm -2 s -1. Measured absolute diff. cross section and beam single spin asymmetry. Channels (pπ 0 ), (nπ + ) and (pη) measured with near complete C.M. acceptance. Data corrected for geometric acceptance, detector efficiency, binning effects (migration, resolution) using high fidelity CLAS simulation. Radiative corrections extensively studied. Radiated physics model used in Monte Carlo event generator required several iterations at higher W. Global fit (pπ 0, nπ + ) performed for W= GeV and Q 2 =0.40 and 0.65 GeV 2.

30 Jlab Analysis of Nucleon Resonances (JANR) Based on Unitary Isobar Model. Includes all resonances seen in photoproduction PWA. Breit-Wigner resonant amplitudes: qr k ΓΓ r π γ MΓ Al± ( W) = al± 2 2 q k η π Γ M W imγ 1/2 Fixed background from nucleon pole diagrams, t-channel pion, ρ- and ω-meson exchange. Regge behavior for W 2 > 2 GeV 2 with a smooth transition from UIM to Regge background: total 1 ( W W ) B B B 1 + ( W W ) 1 + ( W W ) 2 0 tot = born + 2 regge 2 Ad-hoc phase modifications to resonant 0P33 amplitudes to satisfy Watson s 0 theorem below 2-pion threshold.

31 Jlab Analysis of Nucleon Resonances (JANR) (cont d) Unitarized nonresonant amplitudes using K-matrix formalism: g πnn ( 1 ) B = + ih B unit l± nonunit pv ps transition with increasing W. BORN: Nucleon and meson form factors: Proton FF: Bosted parameterization Neutron magnetic: Brash parameterization. Neutron electric: fitted Important for simultaneous fits to π 0 p and π + n data Biggest effect on E 0+ multipole, which contributes strongly to π + n. Best fit: GeN(Q 2 =0.4) = 0.05 Pion FF: monopole: 1/(1+Q2/0.54). Vector mesons: fitted (20% variations from nominal). References I.G. Aznauryan, Phys. Rev. C67, (2003) I.G. Aznauryan, Phys. Rev. C68, (2003) I.G. Aznauryan, to be submitted to PRC (2004)

32 Dispersion Relations Causality, analyticity constrain real and imaginary amplitudes: ( ±,0) 2 P ( ±,0) / / i (,, ) = Born + i (,, / / π ± s s s u thr Re B s t Q Im B s t Q ) ds Born term is nucleon pole in s- and u-channels and meson-exchange in t-channel. Dispersion integrals summed over 3 energy regions: 2 2.2GeV 3GeV / / / / ds = ds + ds + ds Integrals over resonance region saturated by known resonances (Breit-Wigner). P33(1232) amplitudes found by solving integral equations. For integrals over intermediate energy region small (±0.1 mfm) contributions introduced to obtain better description of data. Integrals over high energy region were calculated through π,ρ,ω,b 1,a 1 Regge poles. However these contributions were negligible in Regions 1 and 2. For η channel, contributions of Roper P11(1440) and S11(1535) to unphysical region s<(m η +m N ) 2 of dispersion integral included thr thr 2.2GeV 3GeV

33 Fit Summary Observable dσ π 0 dω dσ π + dω ( ) ( ) 2 Q Data points χ 2 data UIM χ 2 data DR ALT / 0 ( π ) A ( π + ) LT / dσ ( η ) dω

34 P 33 (1232) JANR Global Fit pπ 0 Structure Functions

35 P 33 (1232) JANR Global Fit nπ + Structure Functions

36 P 33 (1232) JANR Global Fit pπ 0 Structure Functions

37 P 33 (1232) JANR Global Fit nπ + Structure Functions

38 P 33 (1232) Multipoles JANR Global Fit Results δ 3/2 1 + = π /2 Fits prefer at W=1.229 GeV Strong non-resonant interference evident. Differences with MAID and SAID for Re(S 1+ )

39 P 33 (1232) JANR Global Fit Results DR and UIM fits consistent Extraction of R EM R SM agrees with truncated multipole analysis JLAB Fit

40 Early evidence of Roper in photoproduction Devenish et al, PL, 36B, 394 (1971) P33+born All resonances excluding P11 All resonances including P11 θ π = 180 o θ π = 6 o γ p π + n Dip in cross section due to Born interference with Re(M1-) γ p π 0 p Dip in cross section due to cancellation in Born + Delta(1232)

41 Comparison of MAID98 with 1978 (e,e π + ) data from Bonn 2 Q = Q = 0.30 Roper off Roper on Hint of Roper sensitivity in pi+ channel. Possibly strong decrease with Q 2 for A 1/2.

42 JANR Global Fit Results Sensitivity to P 11 (1440) Shift in S 1/2 Shift in A 1/2 Polarized structure function σ / LT sensitive to imaginary part of P 11 (1440) through interference with real Born background. Joo et al., to be published

43 JANR Global Fit Results P 11 (1440) Photocoupling Amplitudes 3 qg q 3 π Li Cano Zero crossing around Q 2 =0.5 GeV 2 RQM-Capstick RQM-Simula Strong longitudinal strength! Hybrid model excluded?

44 JANR Global Fit Results S 11 (1535) Photocoupling Amplitudes JANR and dispersion fits consistent Consistency between Nπ and pη Non-zero Longitudinal couplings

45 JANR Global Fit Results D 13 (1520) Photocoupling Amplitudes Non-zero Longitudinal couplings

46 E Hall A VCS and π 0 Electroproduction LH2 target vessel (6.35 x 15 cm) G. Laveisssiere, PRC69 (2004) HRSE Q Q D Q Dump Collimators e- Q 2 =1.0 GeV 2 d 2 σ/dω * (µb/sr) a) b) W=1230 c) d) W=1410 W=1550 W=1810 Q Q D Q HRSH p+ d 2 σ/dω * (µb/sr) * π cosθ = φ (degrees) π 0 Models disagree up to 50%! Large discrepancies with data. MAID2000 SAID NF18K W (GeV)

47 E Hall A VCS and π 0 Electroproduction d 2 σ (µb/sr) σ + T σ T +εσ L G. Laveisssiere, PRC69 (2004) εσ L Refits improve agreement, but still some differences between SAID and MAID σ LT TL Still some disagreement in Q2 evolution σσ TT b (GeV -2 ) W (GeV) W (GeV)

48 D 13 (1520) Transition Form Factor hcqm model: Difficulties for A 3/2 at low Q 2 similar to (1232)

49 S 11 (1535) Transition Form Factor Models overpredict strength at low Q 2

50 Dynamical model fits: S 11 (1535) S. Kamalov, N*2004 SAID02 R.A. Arndt et al. PRC 66, (2002) Resonant background interferes destructively

51 Unitary corrections important for π and ρn channels M. Ripani, V. Mokeev et al., Nucl.Phys. A672 (2000) 220 γp π ++ vertex dressing

52 Single Quark Transition Model EM transitions between all members of two SU(6)xO(3) multiplets expressed as 4 reduced matrix elements A,B,C,D J = AL + Bσ L + Cσ L + Dσ L L z z A 3/2, A 1/2 SU(6) Clebsch- Gordon A,B,C,D Lz = 1 S z =1 L z = 1 = 1 S z L z = 2 = 1 S z orbit flip Example: + 56,0 70,1 (D=0) Fit A,B,C to D 13 (1535) and S 11 (1520) spin flip Predicts 16 amplitudes of same supermultiplet spin-orbit V. Burkert et al. Phys. Rev. C67 (2003)

53 Single Quark Transition Model Predictions for [56,0 + ] [70,1 - ] Transitions Proton

54 Single Quark Transition Model Predictions for [56,0 + ] [70,1 - ] Transitions Neutron

55 Future N* Plans E1 data taking is finished, BUT Enormous backlog of E1 data to be analyzed 3-4 years of hard work. Low and High Q 2 : Delta and Roper Transition form factors in 2 nd resonance region up to Q 2 =6.0 More data for polarization observables to help constrain fits (E ) linearly polarized photons transverse/longitudinally polarized hydrogen and deuterium targets Analysis of deuterium (neutron) target data and new data from BONUS Test SQTM γn pπ -, γn nπ 0 to isolate isoscalar amplitudes For 3 rd resonance region definitely full coupled channel analysis All final states All isospin channels JLAB initiatives: Lattice QCD, Excited Baryon Analysis Center CLAS database (Moscow State University)