1

Trend in Charm Spectroscopy

• A Recap of particles

• An Intro

• DsJ Spectroscopy

• X,Y,Z states

• Charmed baryons

• Measurement of Spins

• D0-D0 Mixing

• Summary and Conclusion

byUsha Mallik (The University of Iowa)

2

3 generations of quarks, & leptons

e+ e- hadronse+ e- μ+ μ-R

=

Quarks, leptons spin 1/2

These quarks immediately ‘Dress-up’ as Hadrons by strong interactions (QCD)

e+e- qq , l+l-

3

Continuum and Resonance Production

R

cc

Hidden charm

bb

4

What happens at BABAR

b

b

b

q

q

b

(4S)

B

B

(10580) MeV

e- beam energy 9.1 GeV, e+ beam energy 3 GeV, E(cm) = 10.58 GeV

e+e- 4S) BB , also cc, ss, uu, dd

e+e- bb) 1.05 nb

(cc) 1.30 nb

(uds) 2.09 nb

time

(5279MeV)

5

b

b

(1S) (9460) MeV

q

q

q

q

X

X

time

Since (1S) is below B meson pair production threshold,

the original b quarks can not be present in the final state:

causing the decay rate slower, ie, the lifetime of (1S) longer,

and the resonance narrow.

OZI Suppression in Decays

6

The “Periodic Table” of Hadrons

Originally in the 1960’s with only u, d, s quarks:

meson qq {q u, d, s ; q u, d, s }

JP = 0- , Pseudoscalar nonet with '

JP = 1- , Vector nonet

J = ½ + ½ = 0

J = ½ + ½ = 1

Gell-Mann’s Eight-fold Way :

3 3 = 1 8

7

JP = 0- , Pseudoscalar nonet and c

JP = 1- , Vector nonet and J/

With u, d, s, c quarks, the picture gets richer

8

The BABAR Detector at PEP-II and the Dataset

BBSee )4(Ecm = 10.58 GeVAnd Much More

Peak luminosity > 1.2 x 1034 cm-2 s-1; Delivered luminosity > 425 fb-1

9

Charm-strange mesons (cs) : Ds, DsJ

With 400 fb-1 data, over 1 billion charmed hadrons produced

10

Expected spectroscopy

3P0

11

DSJ(2317)+ and DSJ(2460)+ observed in

States prior to 2003

But for 2573: 2+ not established

DSJ(2317)+ = 2319.6 ± 0.2 ± 1.4 MeV/c2

DSJ(2460)+ = 2460.2 ± 0.2 ± 0.8 MeV/c2

Also observed in B-decays

Ground State DS(1969)+: JP=0-, c and s spins opposite, in S-wave

Observed States

Spin-Parity Established

12

(2006)

x 103 x 103 x 103

1

(fits better with a Gaussian, rather than BW)

13

Yield =182 30 Mass ( MeV/c2): 2715 +11

-14

Width (MeV/c2): 11520+36-32

14

Preliminary (New)

15

A Very Rich Spectroscopy in cs is emerging

16

NEXT:

The New Charmonia ! The Alphabet Soup !

17

The Charmonium(-like) States

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

18

Confirmed by BABAR, CDF, D0

19

Properties of X(3872)

20

Preliminary (New)

21

22

While searching for BABAR finds new state Y(4260)

Not seen in DD

23

24

NEXT

The Status of Charmed Baryons

25

Baryons

baryon qqq, anti-baryon qqq

(uud)(udd)

(uds)(dds)

(uus)

(uss)(dss)

J = ½ + ½ + ½ = ½

Baryon Octet

(uuu)

J = ½ + ½ + ½ = 3/2

(ddd)

(sss)

Baryon Decuplet

333 = 188’10

26

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 with JP = ½ observed

27

The singly charmed u,d,c sub-multiplets from the 20’ 9 members; JP = 1/2

(2698)

(2285)

(2472)(2466)

(2574)(2579)

36

About charmed baryons

c+ -+ + c

0 - +0K-

-+0 -+-+ -K-++

c0 -

p-

-K+

-+0

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)

Example Decays:

28

Charm Baryon production

Charm baryon or anti charm baryon + X

b c, and c s are weak decays, ~10-13 s lifetime

Charm baryon lifetimes are small, even though weak decays

e+e- BB

e+e- cc

Weak Decays of -, - and 0 take ~ 1,000 times longer

29

30

Observation of Λc(2880)+ and Λc(2940)+ decaying to D0p

New Decay mode: Λc(2880)+ D0p First observation of charm baryon charm meson

Nsig=2280310

Λc(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

31

cx(3077)+

cx(2970)+

New charm strange baryons BaBar confirms these states

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

32

c0 Production and Decay

PDG values

c0 Decay

33

From B decays

Continnum 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

34

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 may results from

c* production, but uncertainty is large.

No signal found in the c0 mass

Sidebands (hatched area)

35

Also observed the charged partner c’+

36

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

37

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

38

B decays to cc

PRD 74 (2006) 111105

39

B decays to c cK PRL 97 (2006) 202003

40

NEXT

Spin Measurements

41

- 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

density matrix element for - spin projection i

= density matrix element for charm baryon parent

Transition matrix element does not depend on i

[Wigner-Eckart theorem]

quantization axis

K-

-K+

(+) c0 = 0

c

- = 0

since, no orbital angular momentum projection w.r.t. quantization axis in Ξc0 decay

diagonal density matrix element for - spin projection i = () is i

Total Intensity:

2*

,

2

,

)0,,(2

1

2

1ffi

fi

fii

fi

ADAI Ji

J

42

)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

J ≥ 7/2 also excluded: angular distribution increases more steeply near cos ~ ±1 and has (2 J -2) turning points.8

Similar conclusion from c

0 → -+, - → K- decays

Conclusion:J(-) = 3/2 [assumingJ(c

0) = 1/2]

PRL 97 (2006) 112001

43

NEXT

D0 – D0 Mixing

44

45

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

46

47

Time-Evolution of D0 → K+ π−

D0 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.

48

Best fit

No mixing

1σ

2σ

3σ

4σ

5σ

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!

49Ratio 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:

50

Summary

• 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 )

– D0-D0 Mixing Observed

Expecting ~three/four times more data than shown in analyses

A race to find Beyond Standard Model Physics

51

52

53

54

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

d

dN

1

1

1coscoscos

cos that So

)( where,coscos

max

0

l

lll PPN

d

dN

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

55

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

)(cos10

1)(cos

2

1cos31

4cos

PP

PPNN

d

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 c0 signal region

max

- →signal

56

57

58

59

Observation of b ccs cw- (W- cs)

W- W-

Charm baryon pair production in B Decays

60

List of Decay Modes (pair production)

2*4/ BES psm 2/* sEE B

2*4/ BES psm

2/* sEE B

Reconstruct the B meson

Use energy momentum conservation between e+e- cm and BB in cm

(also : )

Look for signal events in the mes, 2D distribution

61

Fit to SignalAnalysis ongoing

B- cc K-

p

62

Study of c0 (css)

Production Process and Ratio of Branching Fractions of C0

(css)

cc or B C0 + X C

0 - +

- + - +

-K- + +Preliminary results shown at 2005 summer conferencesImproved analysis using likelihood selection in progress

63

Inclusive c0 Studies

Branching Fractions and Production Mechanism from p* Spectrum

Decay Modes of C0 Studied -+, -+- +, and -K- + +

C0-+

P* > 2.8 GeV/c

225 fb -1

Results:

BABAR

SLAC-PUB-11323, hep-ex/0507011

64

Helicity Formalism, Spin Determination

Suited to two-body (successive) decays

Can be extended to intermediate resonances

(ie, quasi-twobody decays using Dalitz plots)

65

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,,(2

1

2

1ffi

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

66 )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

5cos9coscos314

1 I

cos314

1 I

22

2

Spin measurement of - from c0 → - K+, -

→ K- decays

Angular 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

68

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 c0 → - +

Background-subtractedEfficiency-corrected

Conclusion: J(-) = 3/2 [Assuming J(c0) , J(c

0) <5/2]

PRL version ready for review comm

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)

“…nothing of significance on resonances has been added since our 1988 edition.” [PDG(2004), p 967]

12

Study of and

70

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

x

c+

-

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

71

Resonant Structures in c+

→ - + K+, - → 0 -

Events Only obvious structure:

(1530) → - +

c+ signal region

72

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

73

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

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

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

l

P

l

P

lS

ljlP

ljlP

jlS

f

f

f

)0,,()0,,()0,,(

2/1,2/1

2*2/3

*2/1

*2/1

f

i

ffiffiffiPDPDSDi

)( system ofhelicity where,

theof populationspin thedescribing elementsmatrix density 1/2)(i

c

c

-f

ii

i

Total Intensity ~

76

.2

1cos3RecosRe2

cosRe24

cos31 I

)()()()()()(2

1

)()()()()()(2

1

)()()()()()(

)()()()()()(

where)0,,()0,,()0,,( I

2*2/12/1

*2/12/12/12/1

*2/12/1

22

2/1

2

2/1

2

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

f

i

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-

-1/2

P+-1/2 = P+

1/2

77

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

pm

q

m

pm

dm

dN

c

2

220

2220

2

)(

1.

pp

qq

P2(cos) weighted

Uncorrected

PDG:

M: 1531.80 ± 0.32

: 9.1 ± 0.5 MeV(Very preliminary)

In progress

78

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 KS0) ↔ c

+ mass-sideband region . .

m(0 KS0) ↔ (c

+) mass-sideband-subtracted

c+

→ 0 KS0 K+

c+

→ 0KS0K+

Low-mass sideband limit

79

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

80

[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

81

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+

82

*0 Production in c+ & c

Decays

cancel

83

Investigation of c+,0 Decays

to 3-body Final States

c+ → - + +

c+ → 0 KS

0 + c

0 → 0 K- +

84

… Reconstructing c+ → 0 KS

0 + Events

Data

~200 fb-1

S = 0 S = -1

Cabbibo-suppressed c+ → 0 K0 +

85

“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*(

892)

Yie

ld/ 1

0 M

eV/c

2

Evidence for the decay c+ → 0 K*(892)+

K(892)+→ KS0+

→ 0 +

Mass-sideband-subtracted

Mass-sideband-subtracted

86

Excited Charm Baryons

87

Excited

c States

L=0 straightforward

88

89

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

90Detector Tomography with pKS0 vertices

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