Cascade Physics at BaBar and GlueX with Selected LASS-GlueX Comparisons Veronique Ziegler (SLAC) GlueX Workshop Jeffer

1. Cascade Physics at BaBar and GlueX with Selected LASS-GlueX Comparisons Veronique Ziegler (SLAC) GlueX Workshop Jefferson Lab, March 6-8, 2008

2. Overview • Relevance of Cascades to Baryon Spectroscopy • 2. Cascade Physics from Charm Baryon Decay (*) • BaBar as a Charm Baryon Factory • Measurement of the W- spin [PRL 97, 112001 (2006)] • Motivation for quasi-two-body approach to Cascade Resonance study • Application toLc+ → K+ X(1530)0, X(1530)0 →X-p+ • Measure X(1530) spin; shortcomings of quasi-two-body approach; need for understanding of entire Dalitz plot [to be submitted to Phys.Rev.D] • Application toLc+ → K+ X(1690)0, X(1690)0→L K0 • Quasi-two-body approach again inadequate; performed full Dalitz plot analysis [Proceedings of MENU & NSTAR conferences; Phys.Rev.D article in preparation] • Comparison of Detector Characteristics Relevant to Cascade Physics • BaBar − GlueX • LASS − GlueX • Possible Cascade Studies with GlueX • Summary • ======================================================================================================================================== • Note: The inclusion of charge conjugate states is implied for BaBar analyses. (*)Ph.D. Thesis: SLAC-R-868

3. Relevance of Cascades to Baryon Spectroscopy • Quark content ( u or d, s, s )  QCD calculations easier to handle  Developments in fast algorithms raised expectations from Lattice QCD • Narrow widths  reduces potential overlap with neighboring states • Predictions of mass, width, spin/parity rely on model-based calculations  Experimental validations are essential  Very little known about X states which might populate the [70, 1-]1 and [56, 2+]2 of SU(6) X O(3)  Properties of X(1690) are crucial: first excited state not used as input in predictions X(1530) 3

4. Cascade Physics from Charm Baryon Decay 4

5. BaBar as a Charm Baryon Factory Present data sample contains: (N = s L) > 490 M U(4S) → BB events (s = 1.05 nb) > 1500 M e+e- → qq events (s = 3.39 nb) > 600 M e+e- → cc events (s = 1.30 nb) Charm Baryon (& Meson) Factory Excellent resolution High statistics charm baryon production  Large Samples of Charm Baryon Two-body & Quasi-two-body Decays Rare Decay Modes Accessible with Reasonable Statistics  Can Study Hyperon & Hyperon Resonance properties with high precision e.g. W- Spin [PRL 97, 112001(2006)]]  Hyperon & Hyperon Resonance Cottage Industry  5

6. Spin measurement of W- from Xc0 → W- K+, W- → L K- decays • Helicity Formalism • Examine implications of W- spin hypotheses for angular distribution of L from W- decay [density matrix element for W- spin projection li = density matrix element for charm baryon parent ] 6

7. The X(1530)0 From Lc+ → X-p+ K+ Decay

8. PID Information • →Proton • →Kaon • →p+, p- • 3-σ mass cut on intermediate states • intermd. states mass-constrained [L, X-] • p* > 2.0 GeV/c [reduces background]. • LL > 2.0 mm rX > +1.5 mm [outgoing]. dE/dx & Cherenkov info (DIRC) p- p K+ p+ L0 p- x Lc+ X- Reconstructed Lc+ → X-p+K+, X- → Lp- Events ct = 7.9 cm ct = 4.9 cm m(X-p+) ↔Lc+ mass-signal region  m(X-p+) ↔Lc+ mass-sideband region .. m(X-p+) ↔ (Lc+) mass-sideband-subtracted ct = 60 μm Data ~230 fb-1 (Lc+)Mass-sideband-subtracted Uncorrected dominant N ~13800 events  X(1530)0 → X-p+ HWHM ~ 6 MeV/c2  Lc+ → X-p+ K+ PDG mass 8

9. Lc+ signal region Resonant Structures in the Lc+ → X-p+ K+ Signal Region Only obvious structure: X(1530)0 → X-p+ Rectangular Dalitz plot Note: m2(X- K+) depends linearly on cosqX

10. Using Legendre Polynomial Moments to Obtain X(1530) Spin Information Lc+ signal region Efficiency-corrected P4 Moment Dist. efficiency-corrected unweighted m(X-p+) distribution in data wj = (7/ √2) P4(cosq) from Lc+ signal region  X(1530)0 Spin 5/2 Test • PL moments (L ≥ 6) give no signal  spin 3/2 clearly established  spin 5/2 ruled out Efficiency-corrected P2 Moment Dist. wj = √10 P2(cosq) from Lc+ signal region Schlein et al. showed JP =3/2+ or JP=5/2-, and claimed J>3/2 not required. [Phys.Rev.Lett.11, 167 (1963), Phys.Rev.142,883 (1966)] “ Spin-parity 3/2+ is favored by the data” [PDG (2006)] Spin 3/2 Test  Present analysis by establishing J=3/2 will also establish positive parity by implication [i.e. P-wave resonance] • Other interesting aspects of Dalitz plot – not as simple as it first appears ! 10

11. Further Investigation of X0(1530) Spin Efficiency-corrected, Lc+ Mass-sideband-subtracted cosθXSpectrum 1.51 < m(X-p+) < 1.56 GeV/c2 a (1 + 3 cos2θ) for J=3/2 hypothesis • Assumption of single wave • quadratic nature of • distribution •  rule out spin 1/2 • Also rule out spin ≥ 5/2 • Best fit by far is with • a (1 + 3 cos2θ) but it is not a good fit! • Strong interactions in the (X – p+) system possible X(1530) interference with other (X-p+) amplitudes Dominant 1+3cos2θstructure J=5/2 hypothesis

12. Evidence for S-P wave interference in the (X-p+)system produced in the decay Lc+ → X-p+ K+ Efficiency-corrected m(X-p+) distributions weighted by P1(cosq): Classic S-P wave interference pattern as a function of m(X-p+) X(1530)0 • Oscillation due to rapid • Breit-Wigner P-wave phase • motion & slowly varying • S-wave phase. • Eg. Kp scattering, • [D. Aston et al., Nucl.Phys.B296, 493 (1998)] • & D0→K0 K+ K- for similar behaviour in f region [Phys.Rev.D72, 052008(2005), BABAR] Lc+ signal region Lc+ high mass sidebands little evidence of structure • First clear evidence of X(1530)0 Breit-Wigner phase motion Lc+ low mass sidebands

13. Amplitudes of the (X- p+) system: (X(1530)) & (non-resonant) Partial wave amplitude description of the (X-p+) system produced in the decay Lc+→→ X- p+K+ Angular distribution of the X- produced in the decay of the (X- p+) system:  Total IntensityI =

14. S-P interf. P-D interf. Helicity Formalism Relationship between |L, S> states & helicity states [M. Jacob & C.G. Wick On the General Theory of Collisions for Particles with Spin Annals of Physics 7, 401 (1959)] AJl in terms of S, P, D waves  J=1/2 Interference J=3/2 (Assuming r1/2= r-1/2) Cannot distinguish between (S1/2 + P3/2) nor between (P3/2 + D3/2) ~ however strongP3/2 wave suggests term containing S1/2, P3/2 amplitudes dominates [ Minami ambiguity ] Try simple model assuming only S1/2 and P3/2 amplitudes

15. √2 P0(cosq) moment √10 P2(cosq) moment Amplitude Analysis Assuming S and P Waves - = Unphysical • √10 P2(cosq) moment projects too much signal!! • need more than S and P waves

16. 4 4 p.q S ai mi p.q S ai mi i = 1 i = 1 P-wave BW P-wave BW Efficiency-corrected P2(cosq) moment Efficiency-corrected P0(cosq) moment P-wave BW P-wave BW PDG ( m, G ) PDG ( m, G ) Implication of Fits to the X(1530)0 Lineshape Residuals Residuals Data- Fit Data- Fit Data- Fit Data- Fit Expected improvement in fit quality not realized • Poor fit • due to interference with other waves? Effect should disappear in P0(cosq) moment distribution Structure in X- K+ i.e. another isobar ? Or (K+p+) I=3/2 amplitude contribution?

17. Evidence for S-P wave interference in the (X-p+)system produced in the decay Lc+ → X-p+ K+ Efficiency-corrected P1(cosq) moment Background-subtracted Efficiency-corrected P0(cosq) moment X(1690)0 X(1530)0 Im A S-wave accelerates & catches up on the P-wave Dip (~1680 MeV/c2) may be due to resonantX(1690)0 S-wave negative parity for X(1690)0 Speculation: non-resonant S-wave Coherent superposition of resonant S-wave i.e. slowly-varying amplitudes & phase X(1690)0 Does a small X(1690)0 → X-p+ decay rate make sense? Re A 17

18. X(1690)0 Decay to X-p+ 345 GeV/c S- beam on Cu and C • M = 1686 ± 4 MeV/c2 G= 10 ± 6 MeV • This X(1690) decay mode exists • Product of the production cross section and branching fraction, s.BF, is small compared to that for X(1530)0: consistent with BaBar values M.I. Adamovich et al. Eur.Phys.J. C5, 621 (1998) X(1530)0 X(1690)0 X(1690)0 • Interesting to pursue the X-p+ S-P wave amplitude analysis • Evidence for negative parity would • contradict present theoretical • expectations, except for:

19. The X(1690)0 From Lc+ → L K0 K+ Decay

20. π- π+ π- p Λ0 Ks0 x Λc+ K+ • PID Information • →Proton • →Kaon • →p+, p- • 3-σ mass cut on intermediate states • intermd. states mass-constrained [L , KS] • p*(Lc+) > 1.5 GeV/c (reduces background) • LL, LKs > +2.0, +1.0 mm [sign  outgoing]. Likelihood Selectors Reconstructed Lc+ → L KS K+ Events Data ~200 fb-1 N ~2900 events HWHM ~ (3.1 ± 0.5) MeV/c2 ct = 7.9 cm ct = 2.7 cm ct = 60 μm Selection Criteria: dE/dx & Cherenkov info (DIRC)

21. m(L KS) ↔Lc+ mass-signal region  m(L KS) ↔Lc+ mass-sideband region .. m(L KS) ↔ (Lc+) mass-sideband-subtracted The X(1690)0 from Lc+ → (L KS) K+ Decay Uncorrected (Lc+)Mass-sideband-subtracted Uncorrected N ~2900 events  X(1690)0 → L KS HWHM ~ (3.1 ± 0.5) MeV/c2 Lc+ Low-mass sideband limit Note skewing

22. wj = (7/ √2) P4(cosq) from Lc+ signal region ▬ efficiency-corrected, background-subtracted unweighted m(L KS) distribution in data X(1690)0 → wj = √10 P2(cosq) from Lc+ signal region Using Legendre Polynomial Moments to Obtain X(1690) Spin Information Efficiency-corrected P4 Moment Dist. Spin 5/2 Test Suggest J(X[1690]) =1/2 efficiency-corrected, bckgr.-subtracted dist. in data for 1.665<m(L KS)<1.705 GeV/c2 Efficiency-corrected P2 Moment Dist. Spin 3/2 Test …however cosqL clearly not flat as expected for J = 1/2 WHY? 22

23. Rectangular Dalitz plot • Easy background (Lc+ mass sidebands) parametrization • Same kinematic variables used for efficiency parametrization • Phase-space is: where p = momentum of K+ in • Lc+ rest-frame; • and q = momentum of L in • (L KS) rest-frame. cosqL m(L KS) (GeV/c2) Dalitz plot for Lc+ → L KS K+ Accumulation of events in KSK+ near threshold  evidence of a0(980)+ a0(980)+ 23 X(1690)0

24. 2l+1 ma = 999 MeV/c2 rj(m) = 2qj/m r = gKK/ghp Fit for gKK & r with mafixed ghp = 324 ± 15 MeV [Crystal Barrel Exp.] Isobar Model Description of the Lc+ → L K0 K+ Dalitz Plot pL. ql 2l+1 Fit for m0 & G(m0) with L=0, l=0 gKK = 473 ± 49 MeV [BaBar Exp.]

25. Isobar Model Description of the Lc+ → L K0 K+ Dalitz Plot Under the assumption of spin 1/2 for the X(1690): relative strength La0(980)+ - X(1690)0K+ Interference Weak decay yields 4 terms with same structure but different amplitude and phase Hence define: effective scale effective phase ‘ where p’= momentum of K+ in (L KS) rest-frame. Individual Breit-Wigner Intensity Contributions

26. Comparison of Max. Likelihood Fit Result to the Signal Projections For J(X[1690]) = 1/2 1.615 < m(LKs)< 1.765 GeV/c2 • Excellent reproduction of skewed lineshape and of cosqL distribution • Background-subtracted, efficiency-corrected data ―Integrated signal functionsmearedby mass resolution [Histogram] ― Signal function with noresolution smearing • ―|A(a0(980)|2 contribution • ―|A(X(1690)|2 contribution • ― Interference term contribution c2/NDF = 188.4/192 C. L. = 56.4 %

27. Fit Results For J(X[1690]) = 1/2 X(1690)0 signal region • Actual X(1690) signal significantly smaller (~25%) than apparent signal because of interference effects 27

28. ‡ no smearing Signal function |A(a0(980)|2 contribution |A(X(1690)|2 contribution Interference term contribution Fit Results‡ (different relative intensity scale) Region of destructive interference 28

29. X(1690)0Spin Study Conclusions • Model based on coherent superposition of amplitudes describing Lc+ isobar modes • J[X(1690)] = 1/2 favored by the data (C.L. 56.4%) • J[X(1690)] = 3/2 (C.L. 1.9%)& 5/2 (C.L. 17.4%) yield poorer fits and systematically fail to reproduce the skewed X(1690)0 lineshape • Discrimination should be improved with final BaBar statistics

30. Comparison of Detector Characteristics Relevant to Cascade Physics

31. BaBar-GlueX Comparisons Reminder: X topology Diagram (*) Would also like to reconstruct X0. [Note: 1stW- event in BC was W-→ X0 p-] • Large acceptance, multi-pupose detector • Acceptance: -0.92 < cosq* < 0.85 (q* : c.m.s. polar angle w.r.t. collision axis) • Excellent charged particle tracking (SVT & Drift Chamber) and P.I.D. (& DIRC) • Excellent g measurement (i.e. p0→ g g, h → g g, etc.) in EMC

32. SVT e+ e- DOCA < 3 mm KS0 FL > 2 mm - -0.2 < y < 0.7 cm -3.1< x < -2.2 cm Ta + KS pKS0 Vertex Fe Be Ta p z profile e- side Excellent Vertex Reconstruction Capability (1) 233 fb-1 e+ e- data SVT support tube DCH inner wall beampipe

33. y (mm) x (mm) Excellent Vertex Reconstruction Capability (2) SVT Layer 1 Inner SVT r.f. shield Ta foils Beampipe

34. ○ measured + fit Excellent Vertex Reconstruction Capability (3) (10 mm) (10 mm) Radial Vertex Resolution ~ 90 mm

35. Very uniform Lc+ → L K0 K+ Dalitz Plot Acceptance Efficiency Parametrization as a Function of m(LKS) E1 E2 E3 E0 = Average Efficiency Smooth efficiency as a fcn of ( m, cosq ) E5 E6 E4 Ei = fcn(mass) = 2nd order polynomial Weak dependence on cosqL

36. Very Good Invariant Mass Resolution e.g. for L K0 in Lc+ → L K0 K+

37. Very Good Particle I.D. 37

38. Multiple purpose Yes Acceptance 0.85 > cosq* > -0.92 Charged-particle tracking Excellent Photon detection Excellent Vertex resolution Excellent Mass resolution Excellent Particle ID Excellent Use Inclusive charm baryon production; high multiplicity environment  select large p* events; single production mechanism; no initial polarization, etc… Yes ~4p; problem with low polar angle charged tracks? Very good Very good Good (?) Very good Very good Inclusive AND Exclusive Production; constrained kinematic fits improve substantially; multiple production mechanisms; polarization information. Q: How do BaBar and GlueX Compare ? BaBar GlueX For X Studies A: Very well Overall !

39. K- @ 11 GeV/c LASS-GlueX: A More Direct Comparison[ SLAC-R– 298, (1986) ] Innovations: Solenoid (2.2 T) + Dipole (30 kG m) ~ 4p Acceptance and Trigger Run in "Interaction Mode“ ; ~ Electronic Bubble Chamber First use of microprocessor farm in HEP : 9 370 -168E processors built by Paul Kunz + 1 Tech. 2 3081E processors later for MC and kinematic fitting First use of a Solenoidal Vertex magnet + detector in a fixed target experiment.

40. Example of Data QualityK- p  K0Sp- p at 11 GeV/c: ~ 100 k evts Presented to Prof. Dalitz on his retirement (1990) First use of colored scatter plots in HEP (?) (Very primitive) No printer;35 mm slide of IBM 5080 monitor + off-site creation of transparencies and prints

41. Chew-Low Plot Acceptance K- p → X L ( 11 GeV/c ) g p → X p( 9 GeV/c ) X = p+p- K- p → X L ( 11 GeV/c ) X = p+p- -u≤2(GeV/c)2 (~34 k events) SLAC-R-421 Baryon exchange Meson exchange -t=2(GeV/c)2 41

42. The Need to Reconstruct Tracks Backward-going in the Lab Peyrou Plot for p+ in K- p → K- p+ n pz = 0 pT (GeV/c) Backward in Lab Frame pz (GeV/c)

43. Multiple purpose Somewhat Acceptance ~4p; dipole covers lowq Charged-particle tracking O.K. (2mm wire-spacings P.C.’s) Photon detection Non-existent Vertex resolution O.K. Mass resolution O.K Particle ID Very Limited Inclusive: large flight length required (>2 cm) Exclusive: substantial gains from overall fits to topology and kinematics; multiple production mechanisms; polarization information Yes ~4p; problem with low polar angle charged tracks? Very good Very good Good (?) Very good Very good Inclusive AND Exclusive Production; constrained kinematic fits improve substantially; multiple production mechanisms; polarization information. Q: How do LASS and GlueX Compare ? LASS GlueX [no g detection] [p0 from missing mass] For X Studies A: GlueX should do much better than LASS ! 43

44. Effect of Constrained Kinematic Fits LASS: K- p → L KS KS Inclusive L and KS studies required flight length > 2 cm. For this exclusive reaction, after kinematic and topological fit, no flight length requirements necessary. [Nucl.Phys.B 301, 525 (1988)] ←f2’(1525) Low statistics, but very clean ! f0(980) a2(1320)

45. Possible X Studies with GlueX • Survey Processes to Provide an Overview of X(*) Photoproduction • Inclusive X- (X0 ?) Production • Feynman x and pT2 distributions • Chew-Low plot(s) • Polarization measurements • Etc… • Similar Studies for Cascade Resonance Production (e.g. X(1530)→X-p+) and Associated Spectra • Note: In the LASS search for W*- states, the inclusive mass distribution for (X-p+K-) showed nothing; however when the (X-p+) was selected to correspond to the X(1530)0, a signal for the W(2250)- was observed.

46. p → K+ X X = X-K+ Possible X Studies with GlueX (ctd.) • Exclusive t-channel (i.e. meson exchange) Processes • Production of two-body systems with a X • e.g. g p.→ K+(X- K+) • → K+(X0 K0) • → K0(X0 K+) • would enable the study • of high mass L* and S* • states decaying via these • X modes.

47. p → K0 X X = X- p+ K+ Possible X Studies with GlueX (ctd.) • Production of three-body systems with a X, or a X* system with two-body decay: with a forward K0: • e.g. g p.→ K0(X- p+) K+,K0(X0 p0) K+,K0(X0 K0) p+ • → K0(LK0) K+ with a forward K+: • e.g. g p.→ K+(X- p+) K0,K+(X- p0) K+ • → K+(X0 p-) K+,K+(X0 p0) K0 • → K+(LK-) K+ • Interesting four-body possibilities • when add pion • e.g. g p.→ K+(L K- p+) K+, • accessible at BaBar via Xc0→ LK-p+, complicated Dalitz plot S*, L* States analyzed in Lc+ decay - can observe in a totally different context m(Lc+)

48. Possible X Studies with GlueX (ctd.) • Exclusive u-channel (i.e. baryon exchange) Processes • All of the t-channel processes discussed have corresponding u-channel counterparts in which the bachelor K+ or K0 is attached to the proton vertex • At 9 GeV/c, such processes should have small cross section values; however with very large statistics and an interaction trigger, interesting results may be obtained. E.g. in LASS, the forward-produced K+K- system in K-p → L(K+K-) was studied, but when K-p →(L K-)fwd K+ was examined, a nice X(1820) signal was observed. So in g p→ (X- K+)fwd K+may see some interesting L*/S* distributions! K-p → (L K-)fwd K+@ 11GeV/c (4c fits) ←X(1820)

49. SUMMARY • Three-body systems involving two-body Cascade resonance decays require analysis of the entire Dalitz plot when the statistical level is such that the shortcomings of a quasi-two-body approach become apparent. GlueX should be in this statistical situation. • In terms of acceptance, track and vertex reconstruction (after kinematic fits), and particle identification capability, GlueX should be able to perform Cascade studies of the kind suggested in section 4) provided the relevant cross section values are large enough.

50. BACKUP SLIDES