1 New States in Charm Spectroscopy from Babar and Belle: a review An Intro D sJ Spectroscopy X,Y,Z states Charmed baryons News flash from –Measurement.
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1
New States in Charm Spectroscopy from Babar and Belle: a review
• An Intro
• DsJ Spectroscopy
• X,Y,Z states
• Charmed baryons
• News flash from– Measurement of Spins
– D0-D0 Mixing
• Summary and Conclusion
byUsha Mallik (The University of Iowa)
International Conference on Relativistic Hadronic and Nuclear Physics – LC2007, Columbus, OH, May 14-18
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What happens at e+e- B-factory
e- beam energy 9.1 GeV, e+ beam energy 3 GeV, E(cm) = 10.58 GeVe- beam energy 8.0 GeV, e+ beam energy 3.5 GeV, E(cm) = 10.58 GeV
b
b
b
q
q
b
(4S)
B
B
(10580) MeV
e+e- 4S) BB also cc, ss, uu, dd
(5279MeV)
e+e- bb) 1.05 nb (cc) 1.30 nb (uds) 2.09 nb
timeAlso a charm factory
3
BELLE AND BABAR: B AND c-FACTORIES
710 fb-1
recordedBelle
Asymmetric e+e- collisions at 10.58 GeV
Babar 422 fb-1
recorded
Peak luminosity 17 x 1033 cm-2 s-1
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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 ?
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Expected spectroscopy
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DSJ(2317)+ and DSJ(2460)+ observed in e+e- cc
States prior to 2003
Even for 2573: 2+ not established
Also observed in B-decaysWell-established experimentally - Masses and width
- Natural JP: 0+ for Ds0*(2317) and 1+ for Ds1(2460)
- Decay modes and Branching fractions
Ground State DS(1969)+: JP=0-, c and s spins opposite, in S-wave
Observed States
Interpretation of these new states still unclear!One possibility : identify these 2 states as the 0+ and 1+ cs states
However strong difficulties within the potential modelSemi-relativistic model
Other possibilities:4 quark states? DK molecule? D atom? Chiral symmetry?
Belle: Phys. Rev. Lett. 91 (2003) 262001 BaBar: Phys. Rev. D74 (2006) 032007Belle: Belle-Conf-0461 (2006)BaBar: Phys. Rev. D74 (2006) 031103
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DsJ*(2860): ANOTHER NEW STATE • Looking in cc continuum:
• e+e- D0(K-+,K-+0)K+X and e+e- D+(K-++)K0sX
BaBar: Phys. Rev. Lett. 97 (2006) 222001
D0(K-+)K+ D0(K-+ 0)K+ D+(K-+ +)K0s
Ds1(2536)
Ds1(2536) Ds2(2573) Ds2(2573)
240 fb-1 Ds1(2536) Ds2(2573)
New state at 2860 MeV/c2!Bump at 2690 MeV/c2?
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DsJ*(2860) AND… X(2690)?
Sum of 3 modes
BaBar: Phys. Rev. Lett. 97 (2006) 222001
DsJ*(2860)
X(2690) 240 fb-1
• Combining the 3 modes– M = (2856.6 ± 1.5 ± 5.0) MeV/c2
= (47 ± 7 ± 10) MeV– JP = 0+, 1-, 2+, …
• Final state is DK, i.e. two pseudoscalars• 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…
Bkg subtracted
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EVEN MORE STATES: DsJ(2700)
Belle: hep-ex/0608031
bkgsubtracted
Dalitz plot D0K+ projection
DsJ(2700)
DsJ(2700)
DsJ(2700)
D0K+ projection
J=1
J=0
J=2
Background
• Study of B+ D0D0K+
– Looking at the Dalitz plot and the D0K+ projection
• New resonance decaying to D0K+
– 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
• Interpretation?– cs state 23S1?
• expected mass at 2720 MeV/c2
– Chiral symmetry: 1+ - 1- doubletpaired with Ds1(2536)?
Phys.Polon. B 35, 2377 (2004)
414 fb-1
420 fb-1
449 x 106 BB pairs produced
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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
• Enhancement observed around 2700 MeV/c2 in DK and D*K• 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
BaBar: preliminary
New result
preliminary
Summing all 8 DK modes Summing all 8 D*K modes Ds1(2536)
Background(generic MC)
Phase space
347 fb-1
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• Ds0*(2317)+, Apr. 2003: unexpected observation of a narrow resonance in BaBar
Ds0*(2317)
Ds1(2460)
DsJ*(2860)
X(2690)
• Ds1(2460)+, May 2003: CLEO, BaBar observed a new narrow resonance
• DsJ*(2860)+, Jul. 2006: new state discovered by BaBar
• DsJ(2700)+, Jul. 2006: new state discovered by Belle ( X(2690)?)
• X(2690)+, Jul. 2006: broad enhancement seen in BaBar
DsJ(2700)
S wave P wave D wave
CURRENT SITUATION A Very Rich Spectroscopy in cs is emerging
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NEXT: The New Charmonia(-like) States !
The Alphabet Soup !
■ X(3872)■ X(3940), Y(3940) and Z(3930)■ Y(4260)
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The Charmonium(-like) States
Below DD threshold states well understood. The X,Y,Z states are all above the threshold
hc
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X(3872)
Belle: Phys. Rev. Lett. 91 (2003) 262001Belle: hep-ex/0505038BaBar: Phys. Rev. D73 (2006) 011101Belle: hep-ex/0505037BaBar: Phys. Rev. D74 (2006) 071101
250 fb-1
260 fb-1
X(3872) J/+-
X(3872) J/
• 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/ – Implies: CX(3872)=+1
• Belle, CDF: +- inv. mass distribution + angular analyses – L(+-) = odd, I = 1 J/00 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/+-
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X(3872): STILL SOME SURPRISES
• Belle: looking at B D0D00K
• Excess in the D0D00 invariant mass
– M = 3875.4 ± 0.7 +1.2-2.0 MeV/c2
Belle: Phys. Rev. Lett. 97 (2006) 162002BaBar: preliminary
• 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
414 fb-1
• BaBar: looking at B D0D*0K (D*0 D00/)
• Excess in the D0D*0 invariant mass
– M = 3875.6 ± 0.7 +1.4-1.5 MeV/c2
347 fb-1
New result
preliminary
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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/+- BaBar: Phys. Rev. D73 (2006) 011101• R(B0/B+) = 2.23 ± 0.93 ± 0.55 in B D0D*0K 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/+- BaBar: Phys. Rev. D73 (2006) 011101 m = (0.2 ± 1.6) MeV/c2 in B D0D*0K BaBar: Preliminary
• Glueball? Hybrid? …
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X(3940), Y(3940) AND Z(3930)
New state seen in e+e- J/ X
Also, obs erv ed X DD*, but not X DD
M = (3943 ± 6 ± 6) MeV/c2 = (15.4 ± 10.1) MeV
cc state c(3S) [31S0]?
357 fb-1
Belle: hep-ex/0507019Belle: Phys. Rev. Lett. 94 (2005) 182002Belle: Phys. Rev. Lett. 96 (2006) 082003
253 fb-1
Near threshold enhancement in B J/ K
M = (3943 ± 11 ± 13) MeV/c2
= (87 ± 22 ± 26) MeVcc state ’c1 [23P1]?
New resonance state in DD
M = (3929 ± 5 ± 2) MeV/c2
= (29 ± 10 ± 2) MeVcc state ’c2 [23P2]?
395 fb-1
X(3940) Y(3940)
Z(3930)
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Y(4260): ANOTHER MYSTERY
• New resonance discovered in e+e- ISR(J/+-) by BaBar
• 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-, YJ/+-
– Needs confirmation
JPC=1--
BaBar: Phys. Rev. Lett. 95 (2005) 142001Belle: hep-ex/0612006BaBar: hep-ex/0607083BaBar: PRD 73, 011101 (2006)Cleo-c : PRD 74, 091104 (2006)
553 fb-1
233 fb-1
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Y(4260)... AND Y(4325)?
• Study of Y(4260) (2S) in ISR production
• Incompatible – with BaBar Y(4260), (4415) or 3-body phase space
• Compatible – with Belle Y(“4295”)
BaBar: hep-ex/0610057
M= (4324 ± 24) MeV/c2
= (172 ± 33) MeV298 fb-1
Preliminary
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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
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– 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”)
CC Summary
Y(3940) = ’c1?X(3940) = c(3S)?
Z(3930) = ’c2?
X(3872)
Y(4260)
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NEXT
The Status of Charmed Baryons
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Baryons with 4 flavors (u,d,s,c)
3/2+1/2+
1/2-u,d,s, decuplet
u,d,s, octet
Ground states
Ground state
= 4 20’20’20
Anti-symmetric
*
5 ground states with JP = 3/2 observed: only c* was missing
All 9 ground states c=1, JP = ½ + observed
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The singly charmed u,d,c sub-multiplets from the 20’ 9 members; JP = 1/2
(2698)
(2285)
(2472)(2466)
(2574)(2579)
3 6
About charmed baryons
Anti-symm under the interchange of the two light quarks (u,d,s)
symm. under the interchange of the two light quarks (u,d,s)
Charm baryon + X
e+e- BB
e+e- cc
Charmed baryons can be produced from continuum or from B-decays
Characteristics: momentum of charmed baryon in e+e- rest frame, p*: high when produced in cc, low when produced in B decays
25
c(2800)
Charmed Baryon States
Belle
Babar
Cleo
Most of the JP’s assigned none measured
26
Observation of Λc(2880)+ and Λc(2940)+ decaying to D0p
New Decay mode: Λc(2880)+ D0p First observation of charm baryon charm meson
Nsig=2280310Λc(2940)
Λc(2880)
Wrong sign D0P
D0 mass sidebands
Λc(2765)Λc(2880)
Λc(2940)
Belle confirms in c (c)
BaBar PRL 98:012001(2007)
M(ΛC + -) GeV/c25410 1.8
0.4-1.02937.9 1007060-40-210 )2940(c
4.00.70.3-5.5 0.4
0.3-0.22881.2 4050880 )2880(c
5.95.217.5 1.01.32939.8 3102280 )2940(c
1.11.55.8 0.50l.2881.9 190 2800 )2880(c
[MeV] ]2M[MeV/c Yield sonanceRe
D0p invariant mass GeV/c2
Belle Hep-ex/0608043
Excellent agreement in mass and width
27
414 fb-1
preliminary
hep-ex/0608012
Observation of c(2815) & c(2980)
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cx(3077)+
cx(2970)+
New charm strange baryons BaBar confirms these states
Belle, PRL97:162001(2006) BaBar hep-ex/0607042
preliminary
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c0 Production and Decay
PDG values
c0 Decay
hep-ex/0703030, submitted to PRL
30
From B decays:first observation
Continuum production
Off-peak data: Below B-pair thres-hold, no peak
c0 Production in B decays
p* distribution, momentum in the e+e- rest frame
hep-ex/0703030, submitted to PRL
-410 Few )0( XcBB
31
Discovery of the C*
Combined
BaBar PRL 231 fb-1
97:232001(2006)
)2GeV/c(pdgMMM 0c
0c
*c
Data from all four c0
decay modes are combined and fit yields: 105 21 6 5.2 signal significance
m ( mc* - mc0)= (70.8 1.0 1.1) MeV/c2
Theory range: m = 50 – 94 MeV/c2
= 1.01 0.23 0.11
For XP > 0.5, most/all the c0 might result from
c* production, but uncertainty is large.
No signal found in the c0 mass
Sidebands (hatched area)
32
Also observed the charged partner c’+
33
Measurement of Absolute Branching Fraction of c
34
Measurement of B cp
35
Study of b → ccs decay
Inconsistency in the MC and data p* distribution: MC only has b → cud
Search B decays into charm-baryon-anti-charm-baryon pair
B → cc and B → c c K
BABAR, PRL. 95 142003, 2005 PRD 75 012003, 2007
36
B decays to cc and c cK
E = energy difference between reconstructed B and Ecm
mES : beam momentum substituted reconstructed B mass: e+e- BB
An example
37
B decays to cc
PRD 74 (2006) 111105
38
B decays to c cK PRL 97 (2006) 202003
39
NEXT
Spin Measurements
40
- inherits the spin projections of the c0
Examine implications of - spin hypotheses for angular distribution of from - decay
Initial helicity, λi = λ ()= ± 1/2 Final state helicity, λf = λ () - λ(pseudoscalar) = ± 1/2
Decay amplitude for Ω- → Λ K-: ffifiADA JJ
)0,,(*
λ() = ± 1/2
λ(K) = 0
λ(K) = 0J = 1/2m = + 1/2m = - 1/2
) = + 1/2() = - 1/2
quantization axis
K-
-K+(+) c
0 = 0 c
- = 0
since, no orbital angular momentum projection w.r.t. quantization axis in Ξc0 decay
41
)cos5cos21(
)cos31(
1
42
2
I
I
I
Spin measurement of - from c0 → - K+, -
→ K- decays
→ Fit Prob = 10 -17
→ Fit Prob = 0.64→ Fit Prob = 10 -7
Background-SubtractedEfficiency-Corrected
J = 1/2
J = 5/2
J = 3/2
Data
~ 116 fb-1
Similar conclusion from c
0 → -+, - → K- decays
[assumingJ(c0) = 1/2]
PRL 97 (2006) 112001
Conclusion:J(-) = 3/2
Extending the Spin Formalism to 3-body Decays
The (1530)0 Spin from c+ → (- +) K+
also mass, width info. amplitude analysis (in progress)
The (1690)0 Spin from c+ → (0KS
0) K+
also mass, width info. amplitude analysis (to be done) (-p+)/(K0) Branching Ratio Limit
(to be done)
12
Study of and
43
NEXT
D0 – D0 Mixing
44
45
Time-Evolution of D0 DecaysD0 can reach the K+ - final state in two ways:1) Doubly-Cabibbo-Suppressed decay2) Mixing to D0bar, followed by Cabibbo-Favoured decay... and interference between them.
Q: How can we distinguish these?A: By the time evolution.
46
• Mixing contours from 2006 PDG– K decay the dominant
mode in the search for mixing
– CP lifetimes sensitive to measuring y
– Semileptonic sensitive to RM= (x2+y2)/2
95% CL allowed
CPV allowed
K=0 assumed
yCP=(0.900.42)%
Summary PDG 2006
~ 0: measured by CLEO
47
Summary
K=0 assumed
~ 0: measured by CLEO
95% CL allowed
CPV allowed
BaBar K
Belle ycp (1)
Updated with new results for this talk
(HFAG plots will be available soon)
• Assuming CP conservation BaBar has found evidence for mixing at 3.9 CL using D0Kdecay mode (384 fb-1)
• ycp by Belle also evidence for mixing at 3.2CL (540 fb-1)– Clear Evidence of Mixing
• Most sensitive measurement of x by Belle (D0Ks)
• A precision measurement of cosneeded to express mixing in x and y– CLEO-c quantum correlation– BaBar and Belle B-factories
• Are also charm factories• Searches for CP violation
– Improved techniques– More data
Belle ycp
hep-ex/0703036 Submitted To PRL(Belle)hep-ex/0703020 Submitted To PRL (BaBar)0704.1000v1 [hep-ex], Moriond EW/QCD 2007(Belle)
Belle Ks
48
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 D0-D0bar 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
49
SummaryExperimental 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
50
Example: Mixing
One of the main HEP discoveries in 2006: Bs Oscillations
x=24.8y~0.1?Bs
0 oscillate very rapidly
Rate first measured in 2006 by CDF and D0
Toy MC
51
52
Best fit
No mixing
1σ
2σ
3σ4σ5σ
Contours include statistical & systematic errors
Fit is inconsistentwith no-mixing at 3.9
Fit Results
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)x10-3x'2, y' correlation: -0.94
WS decay time, signal region
data - no mix PDFmix - no mix PDF
Fit to signal & sideband regionsPlot above shows just signal region:
1.843<m<1.883 GeV/c2
0.1445<m< 0.1465 GeV/c2
Evidence for D0-D0 mixing!
53Ratio of WS/RS events clearly increase with time. Mixing signal!
Inconsistentwith no-mixinghypothesis2=24
Consistent withprediction fromfull likelihood fit2=1.5(stat. only)
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:
54
55 27
Production in continuum s1/2 ≤ 10.58 GeV
- Two photons production
- Double charmonium production
- Initial State radiation
Production in B decay s1/2 ≈ 5.28 GeV
bc color suppressed transition
charmonium and open-charm
B-Factories: production processes
56
57
58
Legendre Polynomial Moments in Spin Determination
s)polynomial Legendre normalized( ,cos coscos and
0 odd is if and ,12 where
ij
1
1
max
dPP
PlJl
ji
l
For - spin J, the previous angular distributions can be written
N
jjlll PPNdP
ddN
1
1
1coscoscos
cos that So
)( where,coscos
max
0
l
lll PPN
ddN
Each assumption for J defines lmax
if J is correct calculable is and
, if ,0 max
l
l
P
llP
NP
PN
j l
jl 1
max
max)(cos
that So
max
max)(cos
l
jlj P
Pw
i.e. projects the complete signal by giving each event weight:
9
59
c0 →
[loose cuts]
Illustration of the Use of Legendre Polynomial Moments in Spin Determination
(will prove useful later)
efficiency-corrected * √10 P2 (cos) weighted
wj = √10 P2(cos)from c
0 signal region
▬ efficiency-corrected *, mass-sideband-subtracted unweighted m( K-) distribution in data
- →signal
For example, for c0 → - K+ and J()=3/2:
20
202
)(cos101)(cos
21cos31
4cosPP
PPNNd
dN
lmaxlmax = 2, < P > =1/√10
efficiency-corrected * (7/ √2) P4 (cos) weighted
wj = (7/ √2) P4(cos) [for J=5/2, lmax=4, < Pl > = √2/7 ] from c
0 signal region
max
- →signal
60
61
62
Observation of b ccs cw- (W- cs)
W- W-
Charm baryon pair production in B Decays
63
List of Decay Modes (pair production)
2*4/ BES psm 2/* sEE B
2*4/ BES psm
2/* sEE B
Reconstruct the B mesonUse energy momentum conservation between e+e- cm and BB in cm
(also : )
Look for signal events in the mes, 2D distribution
64
Fit to SignalAnalysis ongoing
B- cc K-
p
65
Study of c0 (css)
Production Process and Ratio of Branching Fractions of C0
(css) cc or B C
0 + X C0 - +
- + - +
-K- + +Preliminary results shown at 2005 summer conferencesImproved analysis using likelihood selection in progress
66
Helicity Formalism, Spin Determination
Suited to two-body (successive) decays Can be extended to intermediate resonances
(ie, quasi-twobody decays using Dalitz plots)
67
quantization axis
Charm baryon rest-frame Hyperon rest-frame
HyperonPseudoscalar
Hyperon daughter
Pseudoscalar
J(Ξc0) = 1/2 in Ξc
0 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- → Λ0 K- :
Total Intensity:
ffifiADA JJ
)0,,(*
c0 → K+ - → 0 K-
J = 1/2m = + 1/2m = - 1/2
λi = + 1/2λi = - 1/2
λf = ± 1/2λK = 0
λK = 0
2*
,
2
,
)0,,(21
21
ffi
fi
fi
fi
ADAI Ji
Ji
density matrix element for - spin projection i = density matrix element for charm baryon parent
Does not depend on i
[Wigner-Eckart theorem]
c0 -K+
K-
Helicity angle of Angle made by p() in rest frame with p(-) in c
0
rest frame
68 )cos5cos21(
)cos31(
1
42
2
I
I
I
Spin measurement of -
→ Fit Prob = 10 -17
→ Fit Prob = 0.64
→ Fit Prob = 10 -7
Background-SubtractedEfficiency-Corrected
J = 1/2
J = 5/2
J = 3/2
5cos9coscos3141 I
cos3141 I
22
2
Spin measurement of - from c0 → - K+, -
→ K- decaysAngular Distribution Parametrizations for JΩ=3/2 hypothesis
No Asymmetry
Asymmetry
Negligible Decay Asymmetry Parameter
Fit for→ = 0.04 ± 0.06
= 0.04 ± 0.06
Background-SubtractedEfficiency-Corrected
9
70
Spin measurement of c0 from c
0 → - +, - → 0 K- decaysFit parametrization α(1 + 3 cos2θ) for JΩ = 3/2 hypothesis→ Fit Prob = 0.69; J(-) = 3/2, consistent with results from c
0 → - +
Background-subtractedEfficiency-corrected
Conclusion: J(-) = 3/2 [Assuming J(c0) , J(c
0) <5/2]
PRL version ready for review comm
71
Reconstructed c+
→ - + K+, - → 0 - Events
Data~230 fb-1
m(- +) ↔ c+ mass-signal region
m(- +) ↔ c+ mass-sideband region
. . m(- +) ↔ (c
+) mass-sideband-subtracted
Uncorrected
xc
+
-
0
-
p
-
K++
PID Information →Proton →Kaon →+, -
3-σ mass cut on intermediate states intermd. states mass-constrained [, -]
L > +1.5 mm [sign outgoing].
r > +1.5 mm [sign outgoing].
dE/dx & Cherenkov info (DIRC)
(c+)Mass-sideband-
subtractedUncorrected
c+
→ - + K+
PDG mass
0 → - +
13
72
Resonant Structures in c+
→ - + K+, - → 0 -
Events Only obvious structure:
(1530) → - +
c+ signal region
73
Spin measurement of 0(1530) from c+
→ 0(1530) K+, 0(1530) → + decays
α(1 + 3 cos2θ) for J=3/2 hypothesisUncorrected cosθ Spectrum
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)
Clear 1+3cos2θ structure
74
For pure spin 3/2: dN/dcos = α(1 + 3 cos2)
c+ → + K+ Signal Region
Uncorrected
Legendre polynomials orthogonality condition
Weight = N x P2(cos)
Using the angular structure of (1530)0 → + candidates to project
away background events
Use of angular structure to project away the bkgr.
100
100
c+ Signal Region
c+ Low Mass-Sideband Region
c+ High Mass-Sideband Region
Projects mass distributionhaving cos2 component
No cos2 component in sideband distributions
sidebands
75
Evidence of S-P wave interference in the (- p+) system produced in the
decay c+ → - p+ K+
m( +) distribution weighted by P1(cos):
76
K +
Amplitudes describing the (- +) system:
quantization axis
c+ (- +) rest-frame
- - …….
+ ………….
l
S-P wave description of the (-+) system produced in the decay c
+ → + K+
1)1( 2/32/1 ,1
1)1( 2/12/1 ,1
1)1( 2/1 ,0
1
1
1
lP
lP
lS
ljlP
ljlP
jlS
f
f
f
)0,,()0,,()0,,(2/1,2/1
2*2/3
*2/1
*2/1
fi
ffiffiffiPDPDSDi
)( system ofhelicity where,
theof populationspin thedescribing elementsmatrix density 1/2)(i
c
c
-f
ii
i
Total Intensity ~
77
.2
1cos3RecosRe2
cosRe24cos31 I
)()()()()()(21
)()()()()()(21
)()()()()()(
)()()()()()(
where)0,,()0,,()0,,( I
2*2/12/1
*2/12/12/12/1
*2/12/1
22
2/1
2
2/12
2/12/12/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/12/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/12/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/12/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/1
2
2/12/3
2/1 2/12/12/1
2/1 2/12/12/1
2/1 2/12/1
2/1,2/1
2*2/3
*2/1
*2/1
PSPS
PSPPS
PdPdSdPdPdSd
PdPdSdPdPdSd
PdPdSdPdPdSd
PdPdSdPdPdSd
PDPDSD fi
fi
ffiffiffi
Helicity Formalism (3)
)2/3( 1 );2/1( 1
0) ,2/1 1/2, ;1 ,1( 1
:onconservatiParity
j PP)(Pj -PP)(P
SSjSS)(S
ff
πΞ
fff
πΞ
f
ff
πΞ
f
λSSj
PλSSj
P
SSjS
0(Assume 1/2= -1/2)
Assume ~0 to extract cos
S-P interference
S-1/2 = S1/2
P--1/2 = -P-
-1/2P+
-1/2 = P+1/2
78
c+
J=1/2
0(1530)J=3/2
p
qK+ (1530)
-
L = 2, 1
l = 1 [(+) parity]
…towards a measurement of the mass & width of 0(1530)
Fit Params:
M: 1531.6 ± 0.1 (stat.)
: 11.9 ± 0.2 MeV
Fit with relativistic Breit-Wigner Function with L=2 & l =1[incorporating a Blatt-Weisskopf barrier factor (R~ 5 (GeV)-1) and resolution “smearing”]
l
tot
L qmmmm
pmq
mpm
dmdN
c
2
220
2220
2
)(1.
p pq q
P2(cos) weighted
UncorrectedPDG:
M: 1531.80 ± 0.32
: 9.1 ± 0.5 MeV(Very preliminary)
In progress
79
Uncorrected
Reconstructed c+ → 0 KS
0 K+ Events
(c+)Mass-sideband-
subtracted0 → 0 KS
0
Data~200 fb-1 Uncorrected
m(0 KS0) ↔ c
+ mass-signal region m(0 KS
0) ↔ c+ mass-sideband region
. . m(0 KS
0) ↔ (c+) mass-sideband-subtracted
c+
→ 0 KS0 K+
c+
→ 0KS0K+
Low-mass sideband limit
80
S-Wave Breit-Wigner Function (& Linear bkgr.)with resolution “smearing”
…towards a measurement of the mass & width of (1690) → 0 KS0
Background-subtractedUncorrected
Fit Params:
M: 1684.7 +- 0.9 (stat.)
: 12.0 +- 0.2 MeV
Only “obvious” structure: (1690) → 0 KS
0
c+
Uncorrected
Stop fit at 1.76
(Very preliminary)
23
81
[Uncorrected] Background-Subtracted cosθ Spectrum~Flat consistent with J=1/2 hypothesis
Spin measurement of (1690)0 from c+ → (1690)0 K+, 0(1690) → 0KS
0 decays
Spin hypothesis:Weight signal events
by P2(cos)
c+ signal region
Uncorrected
α(1 + 3 cos2θ) for J=3/2 hypothesis [prob = 0.2]α(1) for J=1/2 hypothesis [prob = 0.9]
m(KS) distribution weighted by P2(cos)
c+ signal events
Uncorrected
No cos2 component anywhere Spin 1/2
Spin 1/2 favored
Direct Method: - Extract signal cos distribution - Requires large sideband subtraction
Inconclusive
Indirect Method:
24
82
Uncorrected (- +) invariant mass[ c
+ → - + K+ ]
No signal for (1690)0 → - +
Uncorrected (0 KS0) invariant mass
c+
→ 0 KS0 K+ ]
Clear signal for (1690)0 → 0 KS0
…towards an U.L. on BR( (1690)0 → - + )/BR (1690)0 → 0 KS0 )
Background-subtracted
Background-subtracted
c+
→ 0 KS0 K+
c+
→ - + K+
83
*0 Production in c+ & c
Decays
cancel
84
Investigation of c+,0 Decays
to 3-body Final States
c+ → - + +
c+ → 0 KS
0 + c
0 → 0 K- +
85
… Reconstructing c+ → 0 KS
0 + Events
Data
~200 fb-1
S = 0 S = -1
Cabbibo-suppressed c+ → 0 K0 +
86
“Obvious” resonant structures
(1385)+
Large K*(892) contrib.
c+ → 0 K0 + Dalitz Plot Analysis
Uncorrected
Uncorrected
● Previously observed C.S. mode: c+ → + K*(892)0
K*(8
92) Y
ield
/ 10
MeV
/c2
Evidence for the decay c+ → 0 K*(892)+
K(892)+→ KS0+
→ 0 +
Mass-sideband-subtracted
Mass-sideband-subtracted
87
Excited Charm Baryons
88
Excitedc
States
L=0 straightforward
89
90
X(3872): BELLE Finds Data Disfavors 0++ and 2++, Leaving 1++
cc ? 1++ is c1’
X(3872) is too light
M[Ge
DDThreshold
3872
Solid lines: ExperimentLeft: NR model, Barnes, Godfrey, SwansonRight: “Relativized” model, Godfrey, Isgur(Spin) Singlets: dotted, Triplets: dashed
91Detector Tomography with pKS0 vertices
230 fb -1BABAR
e- e+
92
93
94
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