Transcript Some Results from BAbAR BY Usha Mallik (University of Iowa

New States in Charm Spectroscopy
from Babar and Belle: a review
by
Usha Mallik (The University of Iowa)
International Conference on Relativistic Hadronic and
Nuclear Physics – LC2007, Columbus, OH, May 14-18
• An Intro
• DsJ Spectroscopy
• X,Y,Z states
• Charmed baryons
• News flash from
– Measurement of Spins
– D0-D0 Mixing
• Summary and Conclusion
1
What happens at e+e- B-factory
e- beam energy 9.1 GeV, e+ beam energy 3 GeV, E(cm) = 10.58 GeV
e- beam energy 8.0 GeV, e+ beam energy 3.5 GeV, E(cm) = 10.58 GeV
e+e-   (4S)  BB
 also cc, ss, uu, dd
b
b
B (5279MeV)
q
(4S)
(10580) MeV
q
B
b
e+e-  (bb) 1.05 nb
 (cc)
1.30 nb
b
time
Also a charm factory
 (uds) 2.09 nb
2
BELLE AND BABAR: B AND c-FACTORIES
Asymmetric e+e- collisions at 10.58 GeV
Peak luminosity 17 x 1033 cm-2 s-1
Belle
710 fb-1
recorded
Babar
422 fb-1
recorded
3
Charm-strange mesons (cs) : Ds, DsJ
 Ds0*(2317) and Ds1(2460): surprising states
 DsJ*(2860): another new state
 X(2690) and DsJ(2700): even more new states, or are they the same ?
4
Expected spectroscopy
5
Observed States
States prior to 2003
Even for 2573: 2+ not established
DSJ(2317)+ and DSJ(2460)+ observed in e+e-  cc
Also observed in B-decays
Well-established experimentally
- Masses and width
- Natural JP: 0+ for Ds0*(2317) and 1+ for Ds1(2460)
- Decay modes and Branching fractions
Interpretation of these new states still unclear!
Ground State DS(1969)+: JP=0-,
c and s spins opposite, in S-wave
Belle: Phys. Rev. Lett. 91 (2003) 262001
BaBar: Phys. Rev. D74 (2006) 032007
Belle: Belle-Conf-0461 (2006)
BaBar: Phys. Rev. D74 (2006) 031103
One possibility : identify these 2 states as the
0+ and 1+ cs states
However strong difficulties within the
potential model
Semi-relativistic model
Other possibilities:
4 quark states? DK molecule? D atom?
6
Chiral symmetry?
DsJ*(2860): ANOTHER NEW STATE
• Looking in cc continuum:
• e+e-  D0(K-+,K-+0)K+X and e+e-  D+(K-++)K0sX
D0(K-+)K+
Ds1(2536)
D+(K-+ +)K0s
D0(K-+ 0)K+
Ds1(2536)
Ds2(2573)
Ds2(2573)
240 fb-1
Ds2(2573)
Ds1(2536)
New state at 2860 MeV/c2!
Bump at 2690 MeV/c2?
BaBar: Phys. Rev. Lett. 97 (2006) 222001
7
DsJ*(2860) AND… X(2690)?
• Combining the 3 modes
Sum of 3 modes
– M = (2856.6 ± 1.5 ± 5.0) MeV/c2
–  = (47 ± 7 ± 10) MeV
– J P = 0 + , 1 -, 2 + , …
• Final state is DK, i.e. two pseudoscalars
X(2690)
240 fb-1
Bkg subtracted
DsJ*(2860)
• Interpretation?
– Radial excitation of Ds0*(2317)?
hep-ph/0606110
– cs with JP = 0+?
hep-ph/0608139
– cs with JP = 3-?
hep-ph/0607245
• Another structure at 2690 MeV/c2?
– M = (2688 ± 4 ± 3) MeV/c2
–  = (112 ± 7 ± 36) MeV
• Need confirmation by other experiments…
BaBar: Phys. Rev. Lett. 97 (2006) 222001
8
EVEN MORE STATES: DsJ(2700)
• Study of B+  D0D0K+
Dalitz plot
– Looking at the Dalitz plot and
the D0K+ projection
•
B+  D0DsJ, DsJ  D0K+
M = (2715 ± 11 +11-14) MeV/c2
 = (115 ± 20 +36-32) MeV
JP = 1- favored
Same resonance as seen by BaBar
in continuum, X(2690)?
– Mass and width not inconsistent,
same decay mode
•
DsJ(2700)
New resonance decaying to D0K+
–
–
–
–
•
D0K+ projection
Interpretation?
DsJ(2700)
Background
D0K+ projection
DsJ(2700)
420 fb-1
bkg
subtracted
414 fb-1
J=1
J=0
– cs state 23S1?
• expected mass at 2720 MeV/c2
– Chiral symmetry: 1+ - 1- doublet
paired with Ds1(2536)?
J=2
Phys.Polon. B 35, 2377 (2004)
9
449 x 106 BB pairs produced
Belle: hep-ex/0608031
EVEN MORE STATES: DsJ(2700)
• Study of B  D(*)D(*)K decays in BaBar (22 modes)
– Looking at 8 DK + 8 D*K invariant masses, adding 15 decay modes wrt Belle
Summing all 8 D*K modes
Summing all 8 DK modes
Ds1(2536)
347 fb-1
Phase space
Background
(generic MC)
• Enhancement observed around 2700 MeV/c2 in DK and D*K
BaBar: preliminary
• Additional cs surprise? Maybe!
– One or two resonances around 2.6-2.7 GeV/c2 in D*K?
• Need to perform a full Dalitz plot analysis
– Takes into account interferences
10
CURRENT SITUATION
A Very Rich Spectroscopy in cs is emerging
• Ds0*(2317)+, Apr. 2003:
unexpected observation of a
narrow resonance in BaBar
DsJ*(2860)
• Ds1(2460)+, May 2003: CLEO,
BaBar observed a new
narrow resonance
X(2690)
DsJ(2700)
• DsJ*(2860)+, Jul. 2006:
new state discovered by
BaBar
Ds1(2460)
Ds0*(2317)
• X(2690)+, Jul. 2006: broad
enhancement seen in
BaBar
• DsJ(2700)+, Jul. 2006: new
state discovered by Belle
( X(2690)?)
S wave
P wave
D wave
11
NEXT:
The New Charmonia(-like) States !
The Alphabet Soup !
■ X(3872)
■ X(3940), Y(3940) and Z(3930)
■ Y(4260)
12
The Charmonium(-like) States
hc
Below DD
threshold states
well understood.
The X,Y,Z states
are all above the
threshold
13
X(3872)
• First observation by BELLE in B decays:
B± X(3872)K± with X(3872)  J/+– Confirmed by BaBar, CDF, D0
– M = (3871.2 ± 0.5) MeV/c2
–  < 2.3 MeV at 90% CL
• Observation of B  X(3872)K,
X(3872)  J/ 
–
•
•
X(3872)  J/+-
250 fb-1
X(3872)  J/ 
260 fb-1
Implies: CX(3872)=+1
Belle, CDF: +- inv. mass distribution + angular analyses
– L(+-) = odd, I = 1  J/00 should not be observed
– JPC = 1++ favored
BaBar: search for a charged partner (decaying to J/0-)
– No signal  I = 0  I violated in J/+-
Belle: Phys. Rev. Lett. 91 (2003) 262001
Belle: hep-ex/0505038
BaBar: Phys. Rev. D73 (2006) 011101
Belle: hep-ex/0505037
BaBar: Phys. Rev. D74 (2006) 071101
14
X(3872): STILL SOME SURPRISES
•
Belle: looking at B  D0D00K
•
BaBar: looking at B  D0D*0K (D*0 
D00/)
414 fb-1
347 fb-1
•
Excess in the D0D00 invariant
mass
– M = 3875.4 ± 0.7
+1.2
-2.0
MeV/c2
•
Excess in the D0D*0 invariant mass
– M = 3875.6 ± 0.7 +1.4-1.5 MeV/c2
•
•
Masses between Belle and BaBar in good agreement
2.5 away from the X(3872) world average!
•
If X(3872), JP = 2+ disfavored
hep-ex/0606055
15
Belle: Phys. Rev. Lett. 97 (2006) 162002
BaBar: preliminary
X(3872): INTERPRETATION
• X(3872) likely not a charmonium state
– Radial excitation of c1 (JPC = 1++) expected at 3950 MeV/c2
– If 3D1 or 3D2, radiative decays to  states, not observed
– No satisfactory cc assignment
• D0D*0 molecule?
Prediction: Phys. Rev. D71 (2005) 074005
– B0  X(3872)K0 suppressed by a factor 10 compared to B+  X(3872)K+
– Measurements:
• R(B0/B+) = 0.50 ± 0.30 ± 0.05 in B  J/+• R(B0/B+) = 2.23 ± 0.93 ± 0.55 in B  D0D*0K
BaBar: Phys. Rev. D73 (2006) 011101
BaBar: Preliminary
• 4 quark state?
Prediction: Phys. Rev. D71 (2005) 014028
– Predict 2 neutral states and 2 charged states
• Neutral states produced in B0 and B+ decays: m  (7 ± 2) MeV/c2
– Measurements:
• m = (2.7 ± 1.3 ± 0.2) MeV/c2 in B  J/+• m = (0.2 ± 1.6) MeV/c2 in B  D0D*0K
• Glueball? Hybrid? …
BaBar: Phys. Rev. D73 (2006) 011101
BaBar: Preliminary
16
X(3940), Y(3940) AND Z(3930)
X(3940)
New state seen in e+e-  J/ X
357 fb-1
Y(3940)
Near threshold enhancement in B  J/ K
253 fb-1
M = (3943 ± 11 ± 13) MeV/c2
 = (87 ± 22 ± 26) MeV
cc state ’c1 [23P1]?
Also, observed X  DD*,
but not X  DD
M = (3943 ± 6 ± 6) MeV/c2
 = (15.4 ± 10.1) MeV
cc state c(3S) [31S0]?
Z(3930)
New resonance state in   DD
395 fb-1
Belle: hep-ex/0507019
Belle: Phys. Rev. Lett. 94 (2005) 182002
Belle: Phys. Rev. Lett. 96 (2006) 082003
M = (3929 ± 5 ± 2) MeV/c2
 = (29 ± 10 ± 2) MeV
cc state ’c2 [23P2]?
17
Y(4260): ANOTHER MYSTERY
• New resonance discovered in e+e-  ISR(J/+-) by BaBar
233 fb-1
JPC=1-553 fb-1
•
•
•
•
•
BaBar measures: M = (4259 ± 8) MeV/c2,  = (88 ± 23) MeV
Belle measures: M = (4295 ± 10 +10-3) MeV/c2,  = (133 +26-22+13-6) MeV
Confirmed by CLEO: M = (4284 +17-16 ± 4) MeV/c2,  = (73+39-25± 5) MeV
No evidence for:
– e+e-  ISR(DD), e+e-  ISR(+-), e+e-  ISR(pp), e+e-  ISR(J/)
3 enhancement in B decays
– B-YK-, YJ/+– Needs confirmation
BaBar: Phys. Rev. Lett. 95 (2005) 142001
Belle: hep-ex/0612006
BaBar: hep-ex/0607083
BaBar: PRD 73, 011101 (2006)
Cleo-c : PRD 74, 091104 (2006)
18
Y(4260)... AND Y(4325)?
• Study of Y(4260)  (2S) in ISR production
Preliminary
M= (4324 ± 24) MeV/c2
 = (172 ± 33) MeV
298 fb-1
• Incompatible
– with BaBar Y(4260), (4415) or 3-body phase space
• Compatible
– with Belle Y(“4295”)
19
BaBar: hep-ex/0610057
Y(4260): INTERPRETATION
• No cc assignment for 1-- state
• Probably not a glueball
Phys. Lett. B625 (2005) 212
– No evidence for Y(4260)  
• 4 quark state [cs][cs]?
Phys. Rev. D72 (2005) 031502
– Should decay dominantly to DsDs
• Hybrid meson?
– DD, D*D*, DD* decays suppressed
– DD1(2420) decays should dominate
• c1 molecule?
Phys. Lett. B634 (2006) 399
• hybrid + quenched lattice QCD predicts, for 1-– M = 4380 ± 150 MeV/c2
Phys. Rev. D74 (2006) 034502
20
CC Summary
– Possibly charmonium states
• X(3940) = c(3S)? Y(3940) = ’c1? Z(3930) = ’c2?
– Probably NOT charmonium states (what are they?)
• X(3872), Y(4260), Y(“4325”)
Y(4260)
X(3940) = c(3S)?
Y(3940) = ’c1?
Z(3930) = ’c2?
X(3872)
21
NEXT
The Status of Charmed Baryons
22
Baryons with 4 flavors (u,d,s,c)
444 = 4 20’20’20
1/2+
3/2+
Ground states
*
u,d,s, octet
Ground state
u,d,s, decuplet
Anti-symmetric
1/2All 9 ground states c=1, JP = ½ + observed
5 ground states with JP = 3/2 observed: only c* was missing
23
About charmed baryons
The singly charmed u,d,c sub-multiplets from the 20’  9 members; JP = 1/2
3
(2285)
6
Anti-symm under the
interchange of the two
light quarks (u,d,s)
(2472)
(2574)
(2466) (2579)
symm. under the
interchange of the two
light quarks (u,d,s)
(2698)
Charmed baryons can be produced
from continuum or from B-decays
e+e-  cc
Charm baryon + X
Characteristics: momentum of charmed baryon in e+erest frame, p*: high when produced in cc, low when
produced in B decays
e+e-  BB
24
Charmed Baryon States
c(2800)
Belle
Babar
Cleo
Most of the JP’s assigned
none measured
25
Observation of Λc(2880)+ and Λc(2940)+ decaying to D0p
BaBar PRL 98:012001(2007)
New Decay mode: Λc(2880)+ 
D0p First observation of charm
baryon  charm meson
Λc(2940)
Λc(2880)
Nsig=2280310
Belle confirms in c  (c)
Λc(2765)
Belle Hep-ex/0608043
Λc(2880)
Wrong sign D0P
Λc(2940)
D0p invariant mass GeV/c2
0
2]
sidebands
Yield D mass
M[MeV/c
[MeV]
M(ΛC + -) GeV/c2
Excellent agreement in mass and width
Re sonance
 c (2880) 2800  190
2881.9  0l.  0.5
 c (2940)
2280  310
2939.8  1.3  1.0 17.5  5.2  5.9
 c (2880)
0.4
880  50  40 2881.2  0.2-0.3
70 100
 c (2940) 210 -40
-60
1.8
2937.9  1.0-0.4
5.8  1.5  1.1
0.7  0.4
5.5-0.3
10  4  5
26
Observation of c(2815) & c(2980)
414 fb-1
preliminary
hep-ex/0608012
27
New charm strange baryons
BaBar confirms these states
preliminary
cx(3077)+
cx(2970)+
Belle, PRL97:162001(2006)
BaBar hep-ex/0607042
28
c0 Production and Decay
c0 Decay
PDG values
hep-ex/0703030,
submitted to PRL
29
c0 Production in B decays
From B decays:
first observation
hep-ex/0703030,
submitted to PRL
Continuum production
p* distribution,
momentum in the
e+e- rest frame
Off-peak data:
Below B-pair
thres-hold, no
peak
-4
B( B   0
c X )  Few  10
30
BaBar PRL 231 fb-1
97:232001(2006)
Discovery of the C*
Data from all four c0 decay modes are
combined and fit yields: 105  21  6
5.2 signal significance
No signal found in the c0 mass
Sidebands (hatched area)
m ( mc* - mc0)= (70.8  1.0  1.1) MeV/c2
Theory range: m = 50 – 94 MeV/c2
= 1.01 0.23 0.11
Combined
For XP > 0.5, most/all the c0 might result from
c* production, but uncertainty is large.
M*  M0  M
c
c
pdg
2)
0 (GeV/c
31
c
Also observed the
charged partner c’+
32
Measurement of Absolute Branching Fraction of c
33
Measurement of B  cp
34
Study of b → ccs decay
BABAR, PRL. 95 142003, 2005
PRD 75 012003, 2007
Inconsistency in
the MC and data
p* distribution: MC
only has b → cud
Search B decays
into charm-baryonanti-charm-baryon
pair
B → cc and B → c c K
35
B decays to cc and c cK
An example
E = energy difference between
reconstructed B and Ecm
mES : beam momentum substituted
reconstructed B mass: e+eBB
36
B decays to cc
PRD 74 (2006) 111105
37
B decays to c cK
PRL 97 (2006) 202003
38
NEXT
Spin Measurements
39
Examine implications of - spin hypotheses
for angular distribution of  from - decay

λ() = ± 1/2

K+
(+)
λ(K) = 0
c0 = 0
quantization axis
-
- = 0
(c0  0)
J = 1/2
m = + 1/2
m = - 1/2
K() = + 1/2
() = - 1/2

λ(K) = 0
- inherits the spin projections of the c0
since, no orbital angular momentum projection w.r.t. quantization axis in Ξc0 decay
 Initial helicity, λi = λ ()= ± 1/2
 Final state helicity, λf = λ () - λ(pseudoscalar) = ± 1/2
J
J*
 Decay amplitude for Ω- → Λ K-: Ai  f  Di  f ( , ,0) A f
40
Spin measurement of - from c0 → - K+, - →  K- decays
Data
~ 116 fb-1
Background-Subtracted
Efficiency-Corrected
Conclusion:J(-) = 3/2
PRL 97 (2006) 112001
Similar conclusion
from c0 → -+,
- → K- decays
[assumingJ(c0) = 1/2]
J = 1/2
J = 3/2
J = 5/2
 I 1
→ Fit Prob = 10 -17
 I  (1  3 cos2  )
→ Fit Prob = 0.64
→ Fit Prob = 10 -7
 I  (1  2 cos2   5 cos4  )
41
Extending the Spin Formalism to 3-body Decays
Study of  (1530)0 and  (1690)0
The  (1530)0 Spin from c+ → (- +) K+
 also mass, width info.
 amplitude analysis (in progress)
 The  (1690)0 Spin from c+ → (0KS0) K+
 also mass, width info.
 amplitude analysis (to be done)
 (-p+)/(K0) Branching Ratio Limit
(to be done)
12
NEXT
D0 – D0 Mixing
43
44
Time-Evolution of D0 Decays
D0 can reach the K+ - final state in two ways:
1) Doubly-Cabibbo-Suppressed decay
2) Mixing to D0bar, followed by Cabibbo-Favoured
decay
... and interference between them.
Q: How can we distinguish these?
A: By the time evolution.
45
Summary
PDG 2006
• Mixing contours from
2006 PDG
95% CL allowed
CPV allowed
– K decay the dominant
mode in the search for
mixing
– CP lifetimes sensitive to
measuring y
– Semileptonic sensitive to
RM= (x2+y2)/2
yCP=(0.900.42)%
K=0 assumed
K~ 0: measured
by CLEO
46
Summary
hep-ex/0703036 Submitted To PRL(Belle)
hep-ex/0703020 Submitted To PRL (BaBar)
0704.1000v1 [hep-ex],
Moriond
EW/QCD
2007(Belle)
Updated
with
new results
for this talk
• Assuming CP conservation BaBar has
found evidence for mixing at 3.9 CL
using D0K decay mode (384 fb-1)
• ycp by Belle also evidence for mixing at
3.2 CL (540 fb-1)
(HFAG plots will be available soon)
95% CL allowed
CPV allowed
– Clear Evidence of Mixing
• Most sensitive measurement of x by
Belle (D0Ks)
• A precision measurement of cos
needed to express mixing in x and y
Belle ycp (1)
Belle ycp
BaBar K
– CLEO-c quantum correlation
– BaBar and Belle B-factories
• Are also charm factories
Belle Ks
• Searches for CP violation
K=0 assumed
– Improved techniques
– More data
K~ 0: measured
by CLEO
47
Some Recent Theoretical Work
• D-Dbar Mixing And New Physics: General
Considerations and Constraints on the MSSN (M.
Ciuchini et al)
– hep-ph/0703204v1
• Lessons from BaBar and Belle measurements of D0D0bar mixing parameters, (Y. Nir)
– hep-ph/0703235v1
• Littlest Higgs Model with T-Parity Confronting the New
Data on D0-D0bar Mixing,(M. Blanke et al)
– hep-ph/0703254v1
• Basics of D0-D0bar Mixing, (P. Ball)
– hep-ph/0703245v1
48
Summary
Experimental status:
• A new landscape in many areas including spectroscopy
has opened up with high luminosity and precision
–
–
–
–
New DsJ Spectroscopy
X, Y, Z States
Charmed Baryon Spectroscopy
Spin Measurements (necessary to identify levels, complex
analysis for multi-body states: c (1530), c (1690), in Charmed
Baryon decays )
– Evidence for D0-D0 Mixing
• Lots of on-going analyses with the current dataset
– More decay modes investigated to understand these
resonances
• Lots of new data to analyse!
Expecting ~three/four times more data than shown in analyses
A race to find Beyond Standard Model Physics
49
Example: Mixing
One of the main HEP discoveries in 2006: Bs Oscillations
Bs0 oscillate very rapidly
Rate first measured in 2006 by
CDF and D0
x=24.8
y~0.1?
Toy MC
50
51
Fit Results
WS decay time, signal region
RD: (3.03±0.16±0.10)x10-3
x’2: (-0.22±0.30±0.21)x10-3
y’: (9.7±4.4±3.1)x10-3
x'2, y' correlation: -0.94
Best fit
data - no mix PDF
mix - no mix PDF
1σ
Fit is inconsistent
with no-mixing at 3.9 
2σ
No mixing
Contours include statistical & systematic errors
3σ
4σ
5σ
Fit to signal & sideband regions
Plot above shows just signal region:
1.843<m<1.883 GeV/c2
0.1445<m< 0.1465 GeV/c2
Evidence for D0-D0 mixing!
52
Many validation tests done
Most powerful is performing a time-independent fit of the
Wrong-Sign and Right-Sign yields in slices of proper lifetime:
(stat. only)
Consistent with
prediction from
full likelihood fit
||2=1.5
Inconsistent
with no-mixing
hypothesis
||2=24
Ratio of WS/RS events clearly increase with time. Mixing signal!
53
54
B-Factories: production processes
Production in continuum s1/2 ≤ 10.58 GeV
Production in B decay s1/2 ≈ 5.28 GeV
- Two photons production
bc color suppressed transition
- Double charmonium production
charmonium and open-charm
- Initial State radiation
55 27
56
57
Legendre Polynomial Moments in Spin Determination
For - spin J, the previous angular distributions can be written
 lmax

dN
 N  Pl Pl (cos ), where   ()
d cos
 l 0

where lmax  2 J  1, and if l is odd Pl  0
and
 P (cos )P (cos ) d cos   ,
1
1
i
j
ij
(normalizedLegendrepolynomial
s)
N
dN
So that 
Pl (cos )d cos  N Pl   Pl (cos j )
1 d cos
j 1
1
Each assumption for J defines lmax
 Pl  0, if l  lmax , if J is correct
and
Pl
So t hat
9
is calculable
N
Plmax (cos j )
j 1
Plmax

N
i.e. projects the complete
signal by giving
Pl (cos j )
w

each event weight:
j
58
max
Plmax
Illustration of the Use of Legendre Polynomial Moments in Spin Determination
(will prove useful later)
c0 →
[loose cuts]
For example, for c0 → - K+ and J()=3/2:
dN
N
1
 1


1  3 cos2   N 
P0 (cos ) 
P2 (cos ) 
d cos 4
10
 2

(
)
P0
P2
lmax = 2, < lP > =1/√10
max
wj = (7/ √2) P4(cos) [for J=5/2, lmax=4, < Pl
wj = √10 P2(cos)
from c0 signal region
▬
from c0 signal region
- →
- →
signal
signal
> = √2/7 ]
max
efficiency-corrected *, mass-sideband-subtracted unweighted m( K-) distribution in data
efficiency-corrected * √10 P2 (cos) weighted
efficiency-corrected * (7/ √2) P4 (cos) weighted
59
60
61
Observation of b  ccs
 cw- (W-  cs)
Charm baryon pair production in B Decays
W-
W-
62
List of Decay Modes (pair production)
mES 
(s / 4)  pB*2
E  EB*  s / 2
Reconstruct the B meson
Use energy momentum conservation
between e+e- cm and BB in cm
E  EB*  s / 2
Look for signal events in the mes, E: 2D distribution
mES 
(s / 4)  pB*2
)
(also :
63
B -   c  c KpK
Fit to Signal
Analysis ongoing
64
Study of c0 (css)
Production Process and Ratio of Branching Fractions of C0 (css)
cc or B  C0 + X
C0  - +
 - + - +
-K- + +
Preliminary results shown at 2005 summer conferences
Improved analysis using likelihood selection in progress
65
Helicity Formalism, Spin Determination
Suited to two-body (successive) decays
Can be extended to intermediate resonances
(ie, quasi-twobody decays using Dalitz plots)
66
Helicity angle of  : Angle made by p() in
 rest frame with p(-) in c0 rest frame
c0
K+


-
Pseudoscalar
Hyperon daughter
Hyperon
quantization axis
Hyperon rest-frame
Charm baryon rest-frame
KPseudoscalar
c0 → K+ -
→
λK = 0
J = 1/2
m = + 1/2
m = - 1/2
0 K λf = ± 1/2 λK = 0
λi = + 1/2
λi = - 1/2
 J(Ξc0) = 1/2  in Ξc0 rest-frame m = ± 1/2 along z (quantization) axis
 no angular momentum projection w.r.t. quantization axis  Ω- helicity, λi = ± 1/2
 final state helicity λf = λf (Λ0) - λf (pseudoscalar) = ± 1/2
 Decay amplitude for
Ω-
Total Intensity:
→
Λ0
K- :
Ai  f  Di  f ( , ,0) A f
J
J*
1
I   i AJi  f
2 i , f
2
Does not depend on i
[Wigner-Eckart theorem]
1
  i DJi* f ( , ,0) A f
2 i , f
2
density matrix element for - spin projection i
= density matrix element for charm baryon parent
67
Spin measurement of -
Background-Subtracted
Efficiency-Corrected
J = 1/2
 I 1
→ Fit Prob = 10 -17
J = 3/2
 I  (1  3 cos2  )
→ Fit Prob = 0.64
J = 5/2
 I  (1  2 cos2   5 cos4  )
→ Fit Prob = 10 -7
68
Spin measurement of - from c0 → - K+, - → 0 K- decays
Angular Distribution Parametrizations for JΩ=3/2 hypothesis
Background-Subtracted
Efficiency-Corrected
Negligible Decay
Asymmetry Parameter
 = 0.04 ± 0.06
9
(
)
No Asymmetry
I
1
1  3 cos2 
4
I
1
1  3 cos2    cos 9 cos2   5
4
(
0
(
))
Asymmetry
Fit for  →  = 0.04 ± 0.06
Spin measurement of c0 from c0 → - +, - → 0 K- decays
Fit parametrization α(1 + 3 cos2θ) for JΩ = 3/2 hypothesis
→ Fit Prob = 0.69; J(-) = 3/2, consistent with
results from c0 → - +
Background-subtracted
Efficiency-corrected
PRL version ready
for review comm
Conclusion: J(-) = 3/2 [Assuming J(c0) , J(c0) <5/2]
70
Reconstructed c+ → - + K+, - → 0 - Events
p
K+
+
x
c+
 PID Information
→Proton
→Kaon
→+, -
dE/dx &
Cherenkov info (DIRC)
 3-σ mass cut on intermediate states
 intermd. states mass-constrained [, -]
0
-
 L > +1.5 mm [sign  outgoing].
 r > +1.5 mm [sign  outgoing].
-
m(- +) ↔ c+ mass-signal region
m(- +) ↔ c+ mass-sideband region
.
.
m(- +) ↔ (c+) mass-sideband-subtracted
Uncorrected
Data
~230 fb-1
 c+ → - + K+
Uncorrected
(c+)Mass-sideband-subtracted
 (1530)0 → - +
71
13
PDG mass
Resonant Structures in c+ → - + K+, - → 0 Events
Only obvious structure:
 (1530)0 → - +
c+ signal region
72
Spin measurement of 0(1530) from c+ → 0(1530) K+, 0(1530) →  + decays
Uncorrected cosθ Spectrum
Clear
1+3cos2θ
structure
α(1 + 3 cos2θ) for J=3/2 hypothesis
0(1530) Signal Region
[Not mass-sideband-subtrated]
0(1530) Mass-Sideband Regions
Skewed distribution due to:
• Efficiency loss at small angles  Not big effect
• ( ) system decay asymmetry  S-P wave interference (next slides)
73
Using the angular structure of (1530)0 →  + candidates to project
away background events
c+ →  + K+ Signal Region
Uncorrected
sidebands
For pure spin 3/2:
dN/dcos = α(1 + 3 cos2)
Use of angular structure
to project away the bkgr.
c+ Signal Region

Legendre polynomials orthogonality condition

Weight = N x P2(cos)
Projects mass distribution
having cos2 component
100
c+ Low Mass-Sideband Region
100
c+ High Mass-Sideband Region
 No cos2 component
in sideband distributions
74
Evidence of S-P wave interference in the (- p+) system produced in the
decay c+ → - p+ K+
m( +) distribution weighted by P1(cos):
75
S-P wave description of the (-+) system
produced in the decay c+ →  + K+
l
- -
…….

quantization axis
K+
( - +) rest-frame
c+
Amplitudes describing the (- +) system:
S  f  l  0, j  1 / 2
 S  (1)
Pf  l  1, j  l  1 / 2  1 / 2
 P  (1) l 1  1
Pf  l  1, j  l  1 / 2  3 / 2
 P  (1)l 1  1
l 1
+ ………….
 1



 Total Intensity ~
i  1 / 2 ,
i D1/ 2* ( , ,0) S  D1/ 2* ( , ,0) P  D3 / 2* ( , ,0) P
i
f
f
i
f
f
i
f
2
f
 f  1/ 2
i (i  1/2)  density matrixelementsdescribing thespin populationof thec
(
)
where, i  helicit y of     system  i (c )
 f   -   



76
Helicity Formalism (3)
I
i

 1 / 2 ,
i D1 / 2* ( , ,0) S  D1 / 2* ( , ,0) P  D3 / 2* ( , ,0) P
i
f
f
i
f
f
i
f
f
2
where f   
 f  1 / 2
2
2
 1 / 2  d11//221 / 2 ( ) S1 / 2  d11// 221 / 2 ( ) P1/ 2  d13//221 / 2 ( ) P1/ 2  d11// 221 / 2 ( ) S 1 / 2  d11// 221 / 2 ( ) P1 / 2  d13//221 / 2 ( ) P1 / 2 


2
2
  1 / 2  d 11/ 2/ 2 1 / 2 ( ) S1 / 2  d 11/ 2/ 2 1 / 2 ( ) P1/ 2  d 31/ /22 1 / 2 ( ) P1/ 2  d 11/ 2/ 2 1 / 2 ( ) S 1 / 2  d 11/ 2/ 2 1 / 2 ( ) P1 / 2  d 31/ /22 1 / 2 ( ) P1 / 2 


Parityconservation :
S  f  S (  1 ) j  S Ξ  S π S f  S f (  1,   1; j  1/2, S  1 / 2, S  0)
S-1/2 = S1/2
P f  P (  1 ) j  S Ξ  S π Pλf  -Pf ( j  1 / 2); P f  P (  1 ) j  S Ξ  S π Pλf  Pf ( j  3 / 2)
P--1/2 = -P--1/2
P+-1/2 = P+1/2
2
2
1
1 / 2  d11//221 / 2 ( ) S1 / 2  d11//221 / 2 ( ) P1/ 2  d13//221 / 2 ( ) P1/ 2  d11//221 / 2 ( ) S1 / 2  d11//221 / 2 ( ) P1/ 2  d13//221 / 2 ( ) P1/ 2 


2
2
2
1
  1 / 2  d 11/ 2/ 2 1 / 2 ( ) S1 / 2  d 11/ 2/ 2 1 / 2 ( ) P1/ 2  d 31/ /22 1 / 2 ( ) P1/ 2  d 11/ 2/ 2 1 / 2 ( ) S1 / 2  d 11/ 2/ 2 1 / 2 ( ) P1/ 2  d 31/ /22 1 / 2 ( ) P1/ 2 


2

Assume ~0 to extract cos
2


2
 2
 2  1  3 cos  
  2 Re S1 / 2 P1/ *2 cos 
 I  ( 1 / 2   1 / 2 ) S1 / 2  P1 / 2  P1 / 2 
4




2


*
 *  3 cos   1 
.
 2( 1 / 2   1 / 2 )Re S1 / 2 P1 / 2 cos  Re S1 / 2 P1 / 2 
2



(
(
)
(
)
)
S-P interference
0
77
(Assume 1/2= -1/2)
…towards a measurement of the mass & width of 0(1530)

L = 2, 1
K+
0(1530)
c+
0(1530)
J=1/2
p
J=3/2
-
q
l=1
[(+) parity]
Fit with relativistic Breit-Wigner Function with L=2 & l =1
[incorporating a Blatt-Weisskopf barrier factor (R~ 5 (GeV)-1) and resolution “smearing”]
 p qq  2 L
dN
1
2l
( p )
(
 m.
qq )
2
2
 m m 
dm
m02  m 2  m02 tot
(m)
c


(
Uncorrected
P2(cos) weighted
)
Fit Params:
PDG:
M: 1531.6 ± 0.1 (stat.)
M: 1531.80 ± 0.32
: 11.9 ± 0.2 MeV
(Very preliminary)
: 9.1 ± 0.5 MeV
In progress
78
Reconstructed c+ → 0 KS0 K+ Events
m(0 KS0) ↔ c+ mass-signal region
m(0 KS0) ↔ c+ mass-sideband region
.
.
m(0
KS0)
↔ (c mass-sideband-subtracted
+)
Data
~200 fb-1
Uncorrected
 c+ → 0 KS0 K+
 c+ →
0KS0K+
Uncorrected
(c+)Mass-sideband-subtracted
 (1690)0 → 0 KS0
Low-mass sideband limit
79
…towards a measurement of the mass & width of  (1690)0 → 0 KS0
Only “obvious” structure:
 (1690)0 → 0 KS0
 c+
S-Wave Breit-Wigner Function (& Linear bkgr.)
with resolution “smearing”
Uncorrected
Fit Params:
M: 1684.7 +- 0.9 (stat.)
Background-subtracted
Uncorrected
: 12.0 +- 0.2 MeV
(Very preliminary)
Stop fit at 1.76
80
23
Spin measurement of (1690)0 from c+ → (1690)0 K+, 0(1690) → 0KS0 decays
[Uncorrected] Background-Subtracted cosθ Spectrum
~Flat  consistent with J=1/2 hypothesis
Direct Method:
- Extract signal cos distribution
- Requires large sideband
subtraction
α(1 + 3 cos2θ) for J=3/2 hypothesis
[prob = 0.2]
α(1) for J=1/2 hypothesis
[prob = 0.9]
Inconclusive
Spin 1/2 favored
Indirect Method:
c+ signal region
Uncorrected

Uncorrected
m( KS) distribution weighted by P2(cos)
 c+ signal events
 No cos2 component anywhere  Spin 1/2
24
 Spin hypothesis:
Weight signal events
by P2(cos)
81
…towards an U.L. on BR( (1690)0 → - + )/BR( (1690)0 → 0 KS0 )
c+ → 0 KS0 K+
Background-subtracted
Uncorrected (0 KS0) invariant mass
[c+ → 0 KS0 K+ ]
Clear signal for  (1690)0 → 0 KS0
c+ → - + K+
Background-subtracted
Uncorrected (- +) invariant mass
[ c+ → - + K+ ]
No signal for  (1690)0 → - +
82
*0 Production in c+ & c0,  Decays
cancel
83
Investigation of c+,0 Decays
to 3-body Final States
  c+ →  -  +  +
 c+ → 0 KS0 +
 c0 → 0 K- +
84
… Reconstructing c+ → 0 KS0 + Events
Data
~200 fb-1
 S = 0
 S = -1
Cabbibo-suppressed c+ → 0 K0 +
85
c+ → 0 K0 + Dalitz Plot Analysis
“Obvious” resonant structures
Mass-sideband-subtracted

K(892)+→ KS0+
Uncorrected
K*(892) Yield/ 10 MeV/c2
(1385)+
Mass-sideband-subtracted
Uncorrected
 (1385) → 0 +
Evidence for the decay c+ → 0 K*(892)+
86
● Previously observed C.S. mode: c
+
→
+
K*(892)0
Excited Charm Baryons
87
Excited
c
States
L=0 straightforward
88
89
X(3872): BELLE Finds Data Disfavors 0++ and 2++, Leaving 1++
M[Ge
3872
DDThreshold
cc ? 1++ is c1’
X(3872) is
too light
Solid lines: Experiment
Left: NR model, Barnes, Godfrey, Swanson
Right: “Relativized” model, Godfrey, Isgur
(Spin) Singlets: dotted, Triplets: dashed
90
BABAR 230 fb -1
e-
Detector Tomography with pKS0 vertices
e+
91
92
93
94