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

2

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

4

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 ?

5

Expected spectroscopy

6

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

7

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?

8

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

9

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

10

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

11

• 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

12

NEXT: The New Charmonia(-like) States !

The Alphabet Soup !

■ X(3872)■ X(3940), Y(3940) and Z(3930)■ Y(4260)

13

The Charmonium(-like) States

Below DD threshold states well understood. The X,Y,Z states are all above the threshold

hc

14

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/+-

15

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

16

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? …

17

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)

18

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

19

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

20

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

21

– 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)

22

NEXT

The Status of Charmed Baryons

23

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

24

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)

28

cx(3077)+

cx(2970)+

New charm strange baryons BaBar confirms these states

Belle, PRL97:162001(2006) BaBar hep-ex/0607042

preliminary

29

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