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

2. (*)Ph.D. Thesis: SLAC-R-868
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, (2006)]
Motivation for quasi-two-body approach to Cascade Resonance study
Application to Lc+ → 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 to Lc+ → 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 Decay4

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)
> 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, (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. Reconstructed Lc+ → X- p+ K+, X- → L p- Events
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) x
Lc+ p- L0 p X- K+ p+
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+ 8
PDG mass

9. Resonant Structures in the Lc+ → X- p+ K+ Signal Region
Only obvious structure:
X (1530)0 → X- p+
Lc+ signal region
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
 X(1530)0
wj = (7/ √2) P4(cosq)
from Lc+ signal region
Spin 5/2 Test
PL moments (L ≥ 6) give no signal
Efficiency-corrected
P2 Moment Dist.
 spin 3/2 clearly established
 spin 5/2 ruled out
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] 10
Other interesting aspects of Dalitz plot – not as simple as it first appears !

11. Further Investigation of X0(1530) Spin
Efficiency-corrected, Lc+ Mass-sideband-subtracted
cosθX Spectrum
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+3cos2θ structure
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, (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. Partial wave amplitude description of the (X-p+) system
produced in the decay Lc+ →→ X- p+ K+
Amplitudes of the (X- p+) system: (X(1530)) & (non-resonant)
Angular distribution of the X- produced in the decay of the (X- p+) system:
 Total Intensity I =

14.  Helicity Formalism AJl in terms of S-P interf. P-D interf.
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 
S-P interf.
P-D interf.
J=1/2
J=3/2
Interference
(Assuming
r1/2= r-1/2)
Cannot distinguish
between (S1/2 + P3/2)
nor between (P3/2 + D3/2)
~ however strong P3/2 wave suggests term containing S1/2, P3/2 amplitudes dominates
[ Minami ambiguity ]
Try simple model assuming only S1/2 and P3/2 amplitudes

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

16. Or (K+p+) I=3/2 amplitude
Implication of Fits to the X(1530)0 Lineshape
Efficiency-corrected P2(cosq) moment
Efficiency-corrected P0(cosq) moment
p.q S ai mi 4
i = 1
P-wave BW
PDG ( m, G )
Residuals
Residuals
Data - Fit
Data - Fit
Data - Fit
Data - Fit
Poor fit
due to interference
with other waves?
Expected improvement
in fit quality not realized
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. Does a small X(1690)0 → X- p+ decay rate make sense?
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(1530)0
X(1690)0
Im A
S-wave accelerates & catches up on the P-wave
Dip (~1680 MeV/c2) may be due to resonant X(1690) 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 G = 10 ± 6 MeV
M.I. Adamovich et al. Eur.Phys.J. C5, 621 (1998)
M = 1686 ± 4 MeV/c2
G = ± 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
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. Reconstructed Lc+ → L KS K+ Eventsπ- Λ0 K+ p
Ks0 x
Λc+ π+
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:
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
dE/dx &
Cherenkov info (DIRC)

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

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

23. Dalitz plot for Lc+ → L KS K+
Accumulation of events in KSK+
near threshold  evidence of
a0(980)+
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)
a0(980)+ 23
X(1690)0

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

25. Isobar Model Description of the Lc+ → L K0 K+ Dalitz Plot
relative strength
Under the assumption of spin 1/2 for the X(1690):
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) < GeV/c2
Excellent reproduction of skewed lineshape and of cosqL distribution
Background-subtracted, efficiency-corrected data
― Integrated signal function smeared by mass
resolution [Histogram]
― Signal function with no resolution 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 X(1690)0 signal region 27 For J(X[1690]) = 1/2
Actual X(1690) signal significantly smaller
(~25%) than apparent signal because of interference effects 27

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

29. X(1690)0 Spin 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: 1st W- event in BC was W- → X0 p-]
Large acceptance, multi-pupose detector
Acceptance: < cosq* < (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. Excellent Vertex Reconstruction Capability (1)
233 fb-1 e+ e- data
SVT e- e+
SVT support tube
DCH inner wall
beampipe
z profile e- side Ta Be
-0.2 < y < 0.7 cm
-3.1< x < -2.2 cm Fe p KS
pKS0
Vertex + -
DOCA < 3 mm
KS0 FL > 2 mm

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

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

35. Very uniform Lc+ → L K0 K+ Dalitz Plot Acceptance
Efficiency Parametrization as a Function of m(LKS)
E0 = Average Efficiency E1 E2 E3
Smooth efficiency as a
fcn of ( m, cosq ) E4 E5 E6
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. Q: How do BaBar and GlueX Compare ?
Multiple purpose Yes
Acceptance > 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
Good (?)
Inclusive AND Exclusive Production; constrained kinematic fits improve substantially; multiple production mechanisms; polarization information.
For X
Studies
A: Very well Overall !

39. LASS-GlueX: A More Direct Comparison [ SLAC-R– 298, (1986) ]
11 GeV/c
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 :
E processors built
by Paul Kunz + 1 Tech.
E processors later for
MC and kinematic fitting
First use of a Solenoidal Vertex
magnet + detector in a fixed target
experiment.

40. Example of Data Quality K- p  K0S p- 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 )
X = p+p-
K- p → X L ( 11 GeV/c )
g p → X p ( 9 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. Peyrou Plot for p+ in K- p → K- p+ n pT (GeV/c) pz (GeV/c)
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. Q: How do LASS and GlueX Compare ?
Multiple purpose Somewhat
Acceptance ~4p; dipole covers low q
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
[no g detection]
Yes
~4p; problem with low polar angle charged tracks?
Very good
Good (?)
Inclusive AND Exclusive Production; constrained kinematic fits improve substantially; multiple production mechanisms; polarization information.
[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. 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.
p → K+ X
X = X-K+

47. 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 (L K0) 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+ (L K-) 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*
p → K0 X
X = X- p+ K+
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 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

51. MIGRAD FIT PARAMETER VALUES
Fit c2/NDF = 188.4/192
Prob.. = 56.4%
SLAC-R-868

52. Fit Results: (K+ KS) & (L KS) Mass Projections
m(L KS) mass cut-off
[1.62 < m(L KS) <1.765 GeV/c2]
introduces a kink
because of restricted
range of (L K+) helicity
cosine 52

53. Comparison of Max. Likelihood Fit Result to the Signal Projections
Under the assumption of spin 3/2 for the X(1690):
c2/NDF = 234.3/192
C. L. = 1.9 %
1.615 < m(LKs) < GeV/c2
Interference term very small
 Equiv. to incoherent superposition of amplitudes
Lineshape skewing not reproduced!

54. Comparison of Max. Likelihood Fit Result to the Signal Projections
Under the assumption of spin 5/2 for the X(1690):
c2/NDF = 210.3/192
C. L. = 17.4 %
1.615 < m(LKs) < GeV/c2
Net interference term very small
 Equiv. to incoherent superposition of amplitudes
Lineshape skewing not reproduced!

55. Summary of Results & Systematic Uncertainties
Spin 1/2
Spin 1/2
favored
Poor
C.L.
Accept.
C.L.
Fail to reproduce skewed lineshape; fit mass value moves higher in attempt to compensate 55