Results on charmonium(-like) states from Belle

V. ZhukovaBelle Collaboration

“Quarkonium Working Group”, Beijing, 6-10 November 2017

1 / 21

New measurement and angular analysis of thee+e− → D

(∗)+D

∗− process near the open charmthreshold with initial state radiation

2 / 21

Introduction and motivation

Spectrum of charmonium

Vector states above open-charmthreshold are not fully understood

Parameters of ψ states obtainedfrom σtot(e

+e− → hadrons)

are model-dependenthave large uncertainties

Data collected should allow forcoupled-channel analysis

3 / 21

Introduction and motivation

Spectrum of charmonium

Vector states above open-charmthreshold are not fully understood

Parameters of ψ states obtainedfrom σtot(e

+e− → hadrons)

are model-dependenthave large uncertainties

Data collected should allow forcoupled-channel analysis

Solution =⇒ Measure exclusive cross sections

3 / 21

Introduction and motivation

Comparison with previous results

Belle and BaBar resultsagree with each other

Statistics is too low tostudy the structure of thecross sections

Sum of all measuredexcusive cross-section toopen-charm channelssaturates the total crosssection

4 / 21

Introduction and motivation

Comparison with previous results

Belle and BaBar resultsagree with each other

Statistics is too low tostudy the structure of thecross sections

Sum of all measuredexcusive cross-section toopen-charm channelssaturates the total crosssection

Goals:

To improve accuracy of cross section measurements

To measure separately cross sections for all 3 possible helicity combinations(TT, LT, LL) for the D∗D̄∗ final state

4 / 21

Introduction and motivation

MethodPartial reconstruction

Reconstruct D∗, γISR

e+

e−

γISR

γ

D(∗)

D∗ πslow

D

Mrecoil(D(∗)γ) =

√

(Ec.m. −ED(∗)γ)

2 − p2

D(∗)γ

Mrec(D*+γisr) GeV/c2

Eve

nts/

0.1

GeV

/c2

0

1

2

3

×104

1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

D+D∗−

ց

D∗+D∗−

ւ

5 / 21

Introduction and motivation

MethodPartial reconstruction

Reconstruct D∗, γISR

e+

e−

γISR

γ

D(∗)

D∗ πslow

D

Mrecoil(D(∗)γ) =

√

(Ec.m. −ED(∗)γ)

2 − p2

D(∗)γ

Mrec(D*+γisr) GeV/c2

Eve

nts/

0.1

GeV

/c2

0

1

2

3

×104

1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

D+D∗−

ց

D∗+D∗−

ւ

Problem: Cannot distinguish between D, D∗ and D∗∗ in the final state

5 / 21

Introduction and motivation

MethodPartial reconstruction

Reconstruct D∗, γISR and πslow

e+

e−

γISR

γ

D(∗)

D∗ πslow

D

∆Mrecoil = Mrecoil(D(∗)γISR)−Mrecoil(D

(∗)πslowγ)

e+e− → D+D∗−

∆Mrec Gev/c2

N /0

.5 G

eV/c

2

01000200030004000500060007000

0.14 0.145 0.15 0.155 0.16

Recoil mass difference∆Mrecoil

ւ ց

cut:

±3MeV/c2

e+e− → D∗+D∗−

∆ Mrec Gev/c2

N /0

.5

M

eV/c

2

0

5000

10000

15000

20000

25000

0.14 0.145 0.15 0.155 0.16

6 / 21

Introduction and motivation

MethodPartial reconstruction

Reconstruct D∗, γISR and πslow

M(D(∗)+D∗−) ≡ Mrecoil(γISR)

e+

e−

γISR

γ

D(∗)

D∗ πslow

D

Mrecoil(γISR) =√

(E2c.m. − 2Ec.m. ·EγISR

)

Refit Mrecoil(D(∗)γISR) to D∗ mass to improve the Mrecoil(γISR) resolution

M(D*+ D*– ) resolution Gev/c2

Eve

nts/

5 M

eV/c

2

0

5000

10000

15000

-0.2 -0.1 0 0.1 0.2

Mrecoil(γISR) resolution:

Before re-fit — hatched histogramAfter re-fit — solid line

7 / 21

Analysis

Comparison with previous analysis

Increased data sample: 547 fb−1 =⇒ 951 fb−1

Additional modes for D reconstruction =⇒

Extended signal region for Mrecoil(D(∗)γISR)

|(Mrecoil(D(∗)+γISR)−M(D∗−))| <

300✟✟200 MeV/c2

σ[e+e− → D(∗)+D∗−] =dN/dM

ηtot(M) · dL/dM

dL/dM up to second-order QED corrections(Kuraev & Fadin (1985))

D0 decay channels:

1 K−π+

2 K−K+

3 K−π−π+π+

4 K0Sπ

+π−

5 K−π+π0

6 K0SK

+K−

7 K0Sπ

0

8 K−K+π−π+

9 K0Sπ

+π−π0

8 / 21

Analysis

Backgrounds

1 Combinatorial background under the reconstructed D(∗)+ peak

2 Real D(∗)+ mesons and a combinatorial πslow

3 Both the D(∗)+ meson and πslow are combinatorial

4 Reflections from the processes e+e− → D(∗)+D∗−π0γISR

where the π0 is lost

5 Contribution of the e+e− → D(∗)+D∗−π0fastwhere the hard π0fast is misidentified as γISR

Background contribution estimated from the data

9 / 21

Cross sections

√s GeV

σ (n

b)

0

1

2

3

4

4 4.5 5 5.5 6

0

2

4

4 4.2 4.4

√s GeV

σ (n

b)

0

1

2

3

4 4.5 5 5.5 6

0

1

2

3

4 4.2 4.4

D+D∗− D+D∗−

√s GeV

σ (n

b)

0

1

2

3

4

5

3.8 4 4.2 4.4 4.6 4.8 5√s GeV

σ (n

b)

01234567

4 4.2 4.4 4.6 4.8 5

PRL 98, 092001 (2007)

Belle 2007Belle 2017

PRL 98, 092001 (2007)

Belle 2007Belle 2017

10 / 21

Angular analysis

Angular analysis of the process e+e− → D

+D

∗−

Study D∗ helicity angle distributionin each bin of M(D+D∗−)

D∗ are transversely polarized=⇒ Check method

4.05 < M(D+D∗−) < 4.3GeV/c2

0

50

100

150

200

-1 -0.5 0 0.5 1

F (cos θ) = η(cos θ)·dM/dL·(fL + fT )

0

2

4 D+ D*-T

σ (n

b)

D+ D*-L

√s GeV

0

2

4

4 4.5 5 5.5 6

fL = σL · cos2 θfT = σT · (1− cos2 θ)

11 / 21

Angular analysis

Angular analysis of the process e+e− → D

∗+D

∗−

Study of the D∗ helicity angle distribution in each bin of M(D∗+D∗−)Helicity composition of the D∗+D∗− final state:

D∗+T D∗−

T , D∗+T D∗−

L and D∗+L D∗−

L

D∗

T ≡ transversely polarized D∗ mesonD∗

L ≡ longitudinally polarized D∗ meson

Total cross sectionσ = σTT + σTL + σLL

f = η(c1, c2)· dL/dM ·(fLL+fTL+fTT )+fbg

c1 ≡ cos θf c2 ≡ cos θp

θ’s are D∗’s helicity angles

fTT = σTT · (1− c21) · (1− c22)

fTL = σTL ·(

(1− c21) · c22 + c21 · (1− c22))

fLL = σLL · c21 · c22

cosθ fcosθ

p -1-0.5

00.5

1

-1-0.5

00.5

1050

100150

12 / 21

Angular analysis

Fit results

0

0.5

1

1.5

4 4.5 5 5.5 6√s GeV

σ (n

b) D*+T D*-

T

0

0.5

1

1.5

4 4.1 4.2 4.3 4.4 4.5

0

0.5

1

1.5

4 4.5 5 5.5 6√s GeV

σ (n

b) D*+T D*-

L

0

0.5

1

1.5

2

4 4.1 4.2 4.3 4.4 4.5

0

0.5

1

4 4.5 5 5.5 6√s GeV

σ (n

b)

D*+L D*-

L

0

0.5

1

4 4.1 4.2 4.3 4.4 4.5

13 / 21

Summary

Conclusions

We measured the exclusive cross sections of thee+e− → D+D∗− and e+e− → D∗+D∗− processes

The accuracy of the cross section measurements is increased

The systematic uncertainties are significantly reduced

For the e+e− → D∗+D∗− process we measured separatelythe cross sections for all three possible helicity final states(TT, LT and LL)

14 / 21

2

Observation of an alternative χc0(2P ) candidatein e

+e− → J/ψDD̄

15 / 21

Introduction

Motivation

X(3915)րց

Observed by Belle, confirmed by BaBar in B → (J/ψ ω)KPRL 94, 182002 (2005), PRD 82, 011101 (2010)

Observed by both Belle and BaBar in γγ → J/ψ ωPRL 104, 092001 (2010), PRD 86, 072002 (2012)

BaBar: JP = 0+ =⇒ χc0(2P ) candidate

PRD 86, 072002(2012)

Difficulties (see, e.g., S. L. Olsen (2015), F.-K.Guo et al. (2012)):Too narrow: 20 MeV (measured) versus ∼100 MeV (expected)

Not seen in DD̄ (expected as dominating mode!)

Unnaturally small 23P2-23P1 mass splitting

Strong OZI violation: large BF in OZI-suppressed J/ψ ω mode

16 / 21

Introduction

Motivation

X(3915)րց

Observed by Belle, confirmed by BaBar in B → (J/ψ ω)KPRL 94, 182002 (2005), PRD 82, 011101 (2010)

Observed by both Belle and BaBar in γγ → J/ψ ωPRL 104, 092001 (2010), PRD 86, 072002 (2012)

BaBar: JP = 0+ =⇒ χc0(2P ) candidate

PRD 86, 072002(2012)

Difficulties (see, e.g., S. L. Olsen (2015), F.-K.Guo et al. (2012)):Too narrow: 20 MeV (measured) versus ∼100 MeV (expected)

Not seen in DD̄ (expected as dominating mode!)

Unnaturally small 23P2-23P1 mass splitting

Strong OZI violation: large BF in OZI-suppressed J/ψ ω mode

Search for alternative χc0(2P ) candidate in e+e− → J/ψDD̄ annihilation

16 / 21

Analisys

Method

e+e− → J/ψDD̄, D ≡ D0 or D+

Mrec(J/ψ,D) =√

(pe+e− − p J/ψ − pD)2

J/ψ → {e+e−, µ+µ−}Both D0 and D+ used:

D0 → {K−π+,K0sπ

+π−,K−π+π0,K−π+π+π−} (4 channels)

D+ → {K0sπ

+,K−π+π+,K0sπ

+π0,K−π+π+π0,K0sπ

+π+π−}(5 channels)

Signal and background separated using the MLP neural network

Global optimization of the selection requirements: 4 variables per Dchannel (signal regions in M J/ψ, MD, Mrec(J/ψ,D) and MLP outputcutoff value)

Resulting sample: 103 events with 24.9 ± 1.1± 1.6 background events

17 / 21

Analisys

Signal fitAmplitude analysis in 6D phase space: {MDD̄, θprod, θ J/ψ, θX∗ , φl− , φD}

S(Φ) =∑

λbeam=−1,1λℓℓ=−1,1

∣

∣

∣

∑

X∗

Aλbeam λℓℓ(Φ)AX∗(MDD̄)∣

∣

∣

2

Resonance: AX∗ — relativistic BW,Non-resonant amplitude:AX∗ =

√

FDD̄(MDD̄),FDD̄(MDD̄) - non-resonant form factor,default model: FDD̄ = 1Model: X∗ + non-resonant contribution

JPC Mass, MeV/c2 Width, MeV Significance

0++ 3862+26−32

201+154−67

9.1σ

2++ 3879+20−17

171+129−62

8.0σ

2++ 3879+17−17

148+108−50

8.0σ

2++ 3883+26−24

227+201−125

8.0σ 2, GeV/cDD

M4 4.5 5 5.5 6

2E

vent

s / 5

0 M

eV/c

0

2

4

6

8

10

12

14

16

18

X∗ + NR + bg

NR amplitude and

background

18 / 21

Analisys

JPC = 0++ versus JPC = 2++

Approach: Toy MC pseudoexperiments generated in accordance with fitresults for JPC = 0++ and 2++ and fitted for both hypotheses

(-2 ln L)∆40− 20− 0 20 40

Pse

udoe

xper

imen

ts

0

10

20

30

40

50

60

70

80Value in data

++0++2

Result:

JPC = 2++ excluded at the level 2.5σ including systematics

JPC = 0++ with CL=77% (default model)

19 / 21

Analisys

X∗(3860) versus X(3915) — the fight for χc0(2P )

Theory X(3915) X∗(3860)

JPC 0++ ± +

Mass3854 MeV/c2 (Ebert et al.)

± +3916 MeV/c2 (Godfrey et al.)

Width Broad (Γ ∼ 100 MeV) − +

mχc2(2P )−mχc0(2P )

mχc2(1P )−mχc0(1P )0.6..0.9 − +

BF(DD̄) Large − +

BF(J/ψ ω) Small − +

In addition, X∗(3860)

is produced similarly to χc0(1P ) (Belle (2004))

agrees with the peak in γγ data with M = 3837.6 ± 11.5 MeV/c2 andΓ = 221± 19 MeV

20 / 21

Analisys

X∗(3860) versus X(3915) — the fight for χc0(2P )

Theory X(3915) X∗(3860)

JPC 0++ ± +

Mass3854 MeV/c2 (Ebert et al.)

± +3916 MeV/c2 (Godfrey et al.)

Width Broad (Γ ∼ 100 MeV) − +

mχc2(2P )−mχc0(2P )

mχc2(1P )−mχc0(1P )0.6..0.9 − +

BF(DD̄) Large − +

BF(J/ψ ω) Small − +

In addition, X∗(3860)

is produced similarly to χc0(1P ) (Belle (2004))

agrees with the peak in γγ data with M = 3837.6 ± 11.5 MeV/c2 andΓ = 221± 19 MeV

Conclusion:X∗(3860) wins!

20 / 21

Summary

Conclusions

A new charmoniumlike state X(3860) is observed

M = 3862+26 +40−32 −13 MeV/c2

Γ = 201+154 +88−67 −82 MeV

JPC = 0++ favoured

X(3860) =⇒ good χc0(2P ) candidate

21 / 21

Summary

Conclusions

A new charmoniumlike state X(3860) is observed

M = 3862+26 +40−32 −13 MeV/c2

Γ = 201+154 +88−67 −82 MeV

JPC = 0++ favoured

X(3860) =⇒ good χc0(2P ) candidate

Thank you for your attention!

21 / 21

Event selection

Criteria|dr|< 2 cm and |dz|< 4 cm

PK/π = LK/(LK + Lπ) > 0.6

KS candidates:

|Minv(π+π−)−MK0

S

| < 15 MeV/c2

the distance between the two piontracks < 1 cm

the transverse flight distance from IP> 0.1 cm

the angle between the KS momentumdirection and decay path in x− yplane < 0.1 rad

π0 candidates:

|Minv(γγ)−Mπ0| < 15 MeV/c2

D0 decaychannels:

1 K−π+

2 K−K+

3 K−π−π+π+

4 K0Sπ

+π−

5 K−π+π0

6 K0SK

+K−

7 K0Sπ

0

8 K−K+π−π+

9 K0Sπ

+π−π0

D+ decaychannels:

1 K+π−π−

2 K0Sπ

−

3 K0SK

+

D∗ decaychannels:

1 D0π+

1 / 14

Calibration of γISR energy

Analysis of the process e+e− → D

(∗)+D

∗−

Method:

partial reconstruction;

reconstruction D∗, πslow and

γISR;

e+

e−

γISR

γ

D(∗)

D∗ πslow

DMrecoil(D(∗)γ) =

√

(Ec.m. − ED(∗)γ)2 − p2

D(∗)γ

∆Mrecoil =Mrecoil(D(∗)γISR)−Mrecoil(D

(∗)πslowγ)

Mrec(D* γ) Gev/c2

N /0

.05

GeV

/c2

0

200

400

600

800

1000

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Spectrum of Mrecoil(D∗γISR)

Mrecoil(D(∗)γ) =

√

(Ec.m. −ED(∗)γ)2 − p2

D(∗)γ

2 / 14

Calibration of γISR energy

Correction of γISR energyreference channel

e+e− → ψ(2S)γISR

ցψ(2S) → J/ψπ+π−

Conclusions:

phokhara generator describes thesecond radiation correction correctly

The same process on the other

side

The recoil mass Mrecoil(J/ψπ+π−)

0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5

0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5

3 / 14

Analysis

The recoil mass Mrecoil(D∗γISR)

before correction γISR energy

Mrec(D* γ) Gev/c2

N /0

.05

GeV

/c2

0

200

400

600

800

1000

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

after correction γISR energy

Mrec(D* γ) Gev/c2

N /0

.05

GeV

/c2

0

200

400

600

800

1000

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

cut:

|Mrecoil(D∗γISR)−M(D∗)| < 300MeV/c2

4 / 14

Analysis

Backgrounds1 Combinatorial background under the reconstructed D(∗)+ peak2 Real D(∗)+ mesons and a combinatorial πslow

3 Both the D(∗)+ meson and πslow are combinatorial4 Reflections from the processes e+e− → D(∗)+D∗−π0γISR

where the π0 is lost5 Contribution of the e+e− → D(∗)+D∗−π0fast

where the hard π0fast is misidentified as γISR

e+e− → D+D∗−

∆Mfitrec GeV/c2

M(D

)

G

eV/c

2

A

B

B

C

C

D

1.82

1.84

1.86

1.88

1.9

1.92

0.14 0.15 0.16

e+e− → D∗+D∗−

∆Mfitrec Gev/c2

M(D

* )

G

eV/c

2

A

B2

B1

C1 C2

D

2.01

2.02

2.03

0.14 0.15 0.165 / 14

Analysis

Mass spectra

M(D+D*– ) GeV/c2

Eve

nts/

20 M

eV/c

2

951 fb-1

0

100

200

300

400

4 4.5 5 5.5 6 M(D*+D*– ) GeV/c2

Eve

nts/

20 M

eV/c

2

951 fb-1

0

100

200

300

400

4 4.5 5 5.5 6

e+e− → D+D∗− e+e− → D∗+D∗−

PRL 98, 092001(2007)

547 fb−1

PRL 98, 092001(2007)

547 fb−1

6 / 14

Analysis

Reflection from the processes e+e− → D

(∗)+D

∗−π0γISR

e+e− → D+D∗− e+e− → D∗+D∗−

M(D+ D*– ) GeV/c2

Eve

nts/

20 M

eV/c

2

0

100

200

300

4 4.5 5 5.5 6M(D*+ D*– ) GeV/c2

Eve

nts/

20 M

eV/c

2

0

100

200

300

4 4.5 5 5.5 6

Background (blue points) from

e+e− → D(∗)+D∗−π0missγISR

is evaluated from the isospin-conjugated process

e+e− → D(∗)0D∗−π+missγISR

with the reconstruction of D(∗)0, π−slow and γISR7 / 14

Analysis

Backgrounds

e+e− → D∗+D∗−

a)

M(D*) GeV/c2

Eve

nts

/0.2

M

eV/c

2

0

200

400

2.01 2.02 2.03

∆Mrec GeV/c2

Eve

nts

/0.2

MeV

/c2

b)

0

200

400

600

0.14 0.15 0.16 0.17

x ≡ M(D∗) x ≡ ∆Mrec

f = fsignal + fbackground

fbackground = α ·√x · (1 + β · x+ γ · x2)

Mbg (1)-(3) = 0.58 ·Msb B + 0.53 ·Msb C − 0.307 ·Msb D

8 / 14

Analysis

Backgrounds

e+e− → D+D∗−

a)

M(D+) GeV/c2

Eve

nts

/2.0

MeV

/c2

0

500

1000

1.8 1.85 1.9 1.95

b)

∆Mfitrec GeV/c2

Eve

nts

/0.0

5 M

eV/c

2

0

500

1000

1500

0.14 0.15 0.16

x ≡ M(D+) x ≡ ∆Mrec

f = fsignal + fbackground

fbackground = α ·√x · (1 + β · x+ γ · x2)

Mbg (1)-(3) = 0.5 ·Msb B + 0.5 ·Msb C − 0.25 ·Msb D

9 / 14

Analysis

Cross sections calculation

e+e− → D+D∗−

M(D+ D*-) Gev/c2

N /2

0

MeV

/c2

0

0.0025

0.005

0.0075

0.01

4 4.2 4.4 4.6 4.8 5

total efficiency

e+e− → D∗+D∗−

M(D*+ D*-) Gev/c2

N /2

0

MeV

/c2

0

0.002

0.004

0.0060.008

0.01

4 4.25 4.5 4.75 5

total efficiency

σe+e−→D(∗)+D∗− = dN/dM

ηtot(M)·dL/dM

dN/dM - mass spectrum,

ηtot - total efficiency,

dL/dM - differential luminosity;

10 / 14

Analysis

4.0 < M(D∗+D∗−) < 4.1GeV/c2

cosθ fcosθ

p

a)

-1-0.5

00.5

1

-1-0.5

00.5

10255075

4.25 < M(D∗+D∗−) < 4.6GeV/c2

cosθ fcosθ

p

c)

-1-0.5

00.5

1

-1-0.5

00.5

1050

100

4.1 < M(D∗+D∗−) < 4.25GeV/c2

cosθ fcosθ

p -1-0.5

00.5

1

-1-0.5

00.5

1050

100150

M(D∗+D∗−) > 4.6GeV/c2

cosθ fcosθ

p

d)

-1-0.5

00.5

1

-1-0.5

00.5

1050

100150

11 / 14

Analysis

The summary of the systematic errors in the cross section calculation.

Source D+D∗− D∗+D∗−

Background subtraction 2% 2%Reconstruction 3% 4%Selection 1% 1%Angular distribution − 2%Cross section calculation 1.5% 1.5%

B(D(∗)) 2% 3%MC statistics 1% 2%

Total 5% 7%

12 / 14

Analysis

Signal fit

S(Φ) =∑

λbeam=−1,1λℓℓ=−1,1

∣

∣

∣

∑

X∗

Aλbeam λℓℓ(Φ)AX∗(MDD̄)

∣

∣

∣

2

, (1)

Here, Aλbeam λℓℓ(Φ) is the signal amplitude calculated using the helicity formalizm

(the phase space Φ is 6-dimensional). For resonance, AX∗ = relativisticBreit-Wigner. For nonresonant amplitude, AX∗ =

√

FDD̄(MDD̄), whereFDD̄(MDD̄) is the nonresonant amplitude form factor (FDD̄ = 1 by default).Alternatives: mass dependence of NRQCD prediction for e+e− → ψχc [PRD 77,014002 (2008)], FDD̄ =M−4

DD̄[Victor Chernyak, based on PLB 612, 215 (2005)].

4 4.5 5 5.5 6 6.5 72, GeV/c

DDm

0

0.2

0.4

0.6

0.8

1

1.2

ConstantNRQCD

-4DD

M

13 / 14

Analysis

Signal fit resultsFit results in the default model. For the 2++ hypothesis, there are three solutions(fit is started 1000 times from random initial values in order to check for that).

JPC Mass, MeV/c2 Width, MeV Significance

0++ 3862+26−32 201+154

−67 9.1σ2++ 3879+20

−17 171+129−62 8.0σ

2++ 3879+17−17 148+108

−50 8.0σ2++ 3883+26

−24 227+201−125 8.0σ

Red dashed line - only background and nonresonant amplitudes, blue solid line -X∗, JPC = 0++.

2, GeV/cDD

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