LHCb pentaquarks in a constituent quark model Pablo G. Ortega ,D.R. - - PowerPoint PPT Presentation

LHCb pentaquarks in a constituent quark model

Pablo G. Ortega,D.R. Entem, F. Fern´ andez

Outline

1

Motivation

2

The model

3

Results

4

Conclusions

Outline

1

Motivation

2

The model

3

Results

4

Conclusions

Motivation 0 / 28

Quark model

Motivation Multiquarks, molecules and baryon and meson spectra 1 / 28

Discoveries at B-factories

Exotic Mesons: X(3872), Ds0(2317), Zc(3900), Zb(10600),. . . Exotic baryons: Λc(2940), Pc(4380), Pc(4450),. . . Signals of exotic structures? Possibility to study the coupling with higher Fock spaces. Some of them may be naive q¯ q or qqq structures. Others are more elusive: X(3872) ֌

Motivation Multiquarks, molecules and baryon and meson spectra 2 / 28

X(3872) state

Quantum numbers compatible with JPC = 1++ Width : Γ < 1.2 (90% C.L.) Mass : MX = 3871.63 ± 0.19 MeV /c2 ֌ Close to D0 ¯ D∗0 threshold: δm = −0.9 ± 0.34 MeV. R1 = B(X→J/ψπ+π−π0)

B(X→J/ψπ+π−)

= 1.0 ± 0.4 ± 0.3 (Belle) 0.8 ± 0.3 (BaBar) , R2 =

B(X→J/ψγ) B(X→J/ψπ+π−) =

0.33 ± 0.12 (BaBar) 0.14 ± 0.05 (Belle) , R3 = B(X→ψ(2S)γ)

B(X→J/ψγ) ≤ 2.1 ( at 90% C.L.) (Belle).

Experimental data suggest a weakly-bound D0D∗0 molecule coupled to 2P c¯ c states.

Motivation Multiquarks, molecules and baryon and meson spectra 3 / 28

Λc(2940)+ baryon

Discovered in D0p and Σc(2455)0,++π± channels Mass: 2939.8 ± 1.3 ± 1.0 MeV /c2 Width: 17.5 ± 5.2 ± 5.9 MeV (BaBar) Mass: 2938.0 ± 1.3+2.0

−4.0 MeV /c2

Width: 13+8 +27

−5 −7 MeV (Belle)

D∗0p molecule in S-wave? ֌ Quantum numbers:

JP

2S+1LJ 1 2 − 2S 1

2

4D 1

2

1 2 + 2P 1

2

4P 1

2

3 2 − 4S 3

2

2D 3

2

4D 3

2

3 2 + 2P 3

2

4P 3

2

4F 3

2

JP = 3

2 − ֌ Similar to X(3872) state

Motivation Multiquarks, molecules and baryon and meson spectra 4 / 28

LHCb Pentaquarks: Pc(4380) and Pc(4450)

• R. Aaij et al, Phys. Rev. Lett. 115, 072001 (2015).

Discovered in 2015 in Λ0

b → J/ψK −p

decay. Preferred quantum numbers: ( 3

2 ∓, 5 2 ±)

But other combinations such as ( 3

2 −, 3 2 −)

not excluded (L. Roca, arxiv:1602.06791) Masses close to DΣ∗

c and D∗Σc channel

thresholds. MPc(4380) = 4380 ± 8 ± 29 MeV , MPc(4450) = 4449.8 ± 1.7 ± 2.5 MeV , ΓPc(4380) = 205 ± 18 ± 86 MeV , ΓPc(4450) = 39 ± 5 ± 19 MeV .

Motivation Multiquarks, molecules and baryon and meson spectra 5 / 28

LHCb Resonances: X(4140), X(4274), X(4500), X(4700)

Motivation Multiquarks, molecules and baryon and meson spectra 6 / 28

Outline

1

Motivation

2

The model

3

Results

4

Conclusions

The model 6 / 28

Ingredients of constituent quark model

The model includes: Spontaneous breaking of chiral symmetry ֌ Constituent mass and Pseudo-Goldstone bosons.

• C. D. Roberts, arxiv:1109.6325v1 [nucl-th]

QCD perturbative effects ֌ Gluon exchange. Confinement ֌ Screened potential.

The model Constituent quark model 7 / 28

Constituent quark model

Nucleon-Nucleon interaction:

• D. R. Entem, F. Fern´

andez, A. Valcarce, PRC62, 034002 (2000).

• A. Valcarce, A. Faessler, F. Fern´

andez, PLB345, 367 (1995).

• F. Fern´

andez, A. Valcarce, U. Straub, A. Faessler, JPG19, 2013 (1993).

Baryon spectra:

• A. Valcarce, H. Garcilazo, and J. Vijande, PRC72, 025206 (2005).
• H. Garcilazo, A. Valcarce, F. Fern´

andez, PRC64, 058201 (2001).

Meson spectrum:

• J. Vijande, F. Fern´

andez y A. Valcarce, JPG31, 481 (2005).

• J. Segovia, A. M. Yasser, D. R. Entem, F. Fern´

andez, PRD78, 114033 (2008).

• J. Segovia, P. G. Ortega, D. R. Entem, F. Fern´

andez, PRD90, 074027 (2016).

The model Constituent quark model 8 / 28

Solving the two body problem

Meson wave function ֌ Gaussian Expansion Method:

ψlm( p) = nmax

n=1 CnlYlm(ˆ

p)φnl(p), with φnl(p) = (−i)l

Nnl (2ηn)l+3/2 ple− p2

4ηn

GEM free parameters: {nmax, r1, a} Rayleigh-Ritz variational principle:

nmax

n′=1

• (T α

nn′ − ENα nn′)cα n′l + no chnl α′

V αα′

nn′ cα′ n′l

• = 0

Baryon wave functions ֌ Gaussian with scaled range. Resonating Group Method:

Interaction at quark level ֌ Interaction between clusters Direct and exchange potentials:

q1 ¯ q2 q3 ¯ q4 q1 ¯ q2 q3 ¯ q4 q1 ¯ q2 q3 ¯ q4 q1 ¯ q2 q3 ¯ q4

The model Solving the two body problem 9 / 28

3P0 interaction Pair creation hamiltonian: H = g

• d3x ¯

ψ(x)ψ(x)

q¯ q A B

Non relativistic reduction:

T = −3 √ 2γ′

µ

• d3pd3p′ δ(3)(p + p′)
• Y1
• p−p′

2

• b†

µ(p)d† ν(p′)

C=1,I=0,S=1,J=0

with γ′ = 25/2π1/2γ and γ =

g 2m

Running of the 3P0 strength γ

γ(µ) = γ0 log(µ/µγ ) γ0 = 0.81 ± 0.02 µγ = 49.84 ± 2.58 MeV Solid line is the fit Shaded area → 90% C.L. The model 3P0 Model 10 / 28

Coupling between q¯ q and q¯ q − q¯ q sectors

Effect of q¯ q on meson-meson states ֌ Molecular states Mixed states: |Ψ =

α cα |ψ + β χβ(P) |φM1φM2β

Solving the coupling with the q¯ q meson spectrum ֌ Schr¨

• dinger-type equation:
• β

HM1M2

β′β

(P′, P) + V eff

β′β(E; P′, P)

• χβ(P)P2dP = Eχβ′(P′)

with V eff

β′β(E; P′, P):

q¯ q A B A′ B′ The model Coupled channel formalism 11 / 28

Coupling formalism with T matrix

Resonances → Poles of the Scattering Matrix:

Sα′

α = 1 − 2πi√µαµα′kαkα′T α′ α (E + i0; kα′, kα)

T matrix obtained with Lippmann-Schwinger:

T β′β(E; P′, P) = V β′β

T

(P′, P) +

β′′

• dP′′P′′2V β′β′′

T

(P′, P′′)

1 E−Eβ′′(P′′)T β′′β(E; P′′, P)

With V β′β

T

(P′, P) = V β′β(P′, P) + V β′β

eff (P′, P)

where V β′β

eff (P′, P) = α hβ′α(P′)hαβ(P) E−Mα

q¯ q A B A′ B′

The complete T matrix factorizes like VT:

T β′β(E; P′, P) = T β′β

V

(E; P′, P) +

α,α′ φβ′α′(E; P′)∆α′α(E)−1 ¯

φαβ(E; P)

The model Coupled channel formalism 12 / 28

Coupling elements

From T β′β(E; P′, P) = T β′β

V

(E; P′, P) +

α,α′ φβ′α′(E; P′)∆α′α(E)−1 ¯

φαβ(E; P):

Modified vertex:

φαβ′(E; P) = hαβ′(P) −

β

T β′β

V

(E; P, q)hαβ(q) q2/2µ − E q2 dq, ¯ φαβ(E; P) = hαβ(P) −

β′

hαβ′(q)T β′β

V

(q, P, E) q2/2µ − E q2 dq

−

|q¯ q >α |AB >β |q¯ q >α |AB >β |AB >β′

Complete propagator: ∆α′α(E) =

• (E − Mα)δα′α + Gα′α(E)
• Exact mass-shift of the

state:

Gα′α(E) =

β

• dqq2 φαβ(q, E)hβα′(q)

q2/2µ − E

−

|q¯ q >α |AB >β |q¯ q >α′ |q¯ q >α |AB >β |AB >β′ |q¯ q >α′

The model Coupled channel formalism 13 / 28

Outline

1

Motivation

2

The model

3

Results

4

Conclusions

Results 13 / 28

Results for the X(3872) coupled calculation

D0D∗0 and D±D∗∓ molecular states are included Coupled to c¯ c(23P1) meson state ֌ Theoretical bare mass= 3947.4 MeV Inclusion of J/ψρ y J/ψω channels, needed for describing the strong decays ֌ Rearrangement diagrams Small contribution to the mass The value of γ is fine-tuned to obtain the X(3872) experimental mass γ Ebind c¯ c(23P1) D0D∗0 D±D∗∓ J/ψρ J/ψω 0.231 −0.60 12.40 79.24 7.46 0.49 0.40 0.226 −0.25 8.00 86.61 4.58 0.53 0.29

Results X(3872) 14 / 28

X(3872) Decay results

Results for strong decays Experimental results: R1 = B(X→J/ψπ+π−π0)

B(X→J/ψπ+π−)

= 1.0 ± 0.4 ± 0.3 0.8 ± 0.3 Theoretical results: Ebind(MeV) Γπ+π−J/ψ(KeV ) Γπ+π−π0J/ψ(KeV ) R1 −0.60 27.61 14.40 0.52 −0.25 24.18 10.64 0.44

Results X(3872) 15 / 28

X(3872) Decay results

Results for radiative decays Experimental results: R2 =

B(X→J/ψγ) B(X→J/ψπ+π−) =

0.33 ± 0.12 0.14 ± 0.05 Theoretical results: Ebind(MeV) ΓVMD

J/ψγ

ΓANN

J/ψγ

RM

2

Γc¯

c J/ψγ

Rc¯

c 2

R2 −0.60 0.014 0.056 2.5 10−3 8.15 0.29 0.30 −0.25 0.011 0.045 2.3 10−3 5.25 0.22 0.22

Table : Decays in KeV. Molecular component ֌ Vector Meson Dominance (VMD) mechanism and Annihilation (ANN). RM

2 is the ratio including only contributions from the molecular component,

Rc¯

c 2

• nly contributions from the c¯

c component and R2 is the complete result.

Results X(3872) 15 / 28

X(3872) Decay results

Results for radiative decays Experimental results: R3 = B(X→ψ(2S)γ)

B(X→J/ψγ) ≤ 2.1 ( at 90% C.L.)

Theoretical results: Ebind(MeV) Γc¯

c J/ψγ

Γc¯

c Ψ(2S)γ

R3 −0.60 8.15 9.80 1.20 −0.25 5.25 6.31 1.20

Table : Decays in KeV. Molecular component ֌ Negligible. Only radiative decays from the c¯ c component are considered.

Results X(3872) 15 / 28

Λc(2940)+ baryon: D∗N in JP = 3

2 − sector Only quark-quark interaction D∗N molecule in S-wave Results including charged molecular states:

Mass P4S3/2 P2D3/2 P4D3/2 PD0∗p PD+∗n PI=0 PI=1 2938.80 96.22 0.86 2.92 63.93 36.07 97.52 2.48

Decays:

Decay channel Width (MeV ) decay channel Width (keV ) Λ+

c → D0p

9.42 Λ+

c → Σ++ c

π− 4.19 Λ+

c → D+n

10.74 Λ+

c → Σ+ c π0

4.35 Λ+

c → Σ0 cπ+

4.51 Γ(total) 20.2 Γ(experimental) 17+8

−6

Results Λc (2940)+ charm baryon as a pentaquark molecule 16 / 28

Partner in b sector: Λb(6248)0

Possibility existence of a partner of Λb(2940)+ in b sector Description as a B∗N molecule in JP = 3

2 − sector.

Results including charged molecular states:

M (MeV ) P4S3/2 P2D3/2 P4D3/2 PB∗−p PB∗0n PI=0 PI=1 6248.34 95.15 1.08 3.77 52.56 47.44 99.91 0.09

Decays:

Decay channel Width (MeV ) Decay channel Width (keV ) Λ0

b → B−p

3.69 Λ0

b → Σ+ b π−

6.30 Λ0

b → B0n

3.75 Λ0

b → Σ0 bπ0

6.34 Λ0

b → Σ− b π+

6.38

More details at:

• P. G. Ortega et al., Physics Letters B 718, 1381-1384 (2013)

Results Λc (2940)+ charm baryon as a pentaquark molecule 17 / 28

Exotic baryon spectroscopy (I)

Low kinetic energy and diagram multiplicity creates a rich spectroscopy in D(∗)N, B(∗)N, D(∗)∆ and B(∗)∆ systems. Masses, quantum numbers and main channel of predicted baryonic molecules:

JP Isospin Molecule Mass(MeV ) Eb(MeV ) Pmax(Channel)

1 2 −

DN 2805.24 −1.70 98.08(2S1/2)

1 2 −

1 D∗N 2947.61 −0.48 99.93(2S1/2)

3 2 −

D∗N 2940.06 −8.02 96.05(4S3/2)

1 2 −

BN 6206.11 −12.09 87.61(2S1/2)

1 2 −

1 BN 6217.83 −0.36 99.05(2S1/2)

1 2 −

1 B∗N 6260.58 −3.43 99.86(2S1/2)

3 2 −

B∗N 6248.87 −15.15 95.07(4S3/2)

Results Baryon-Meson molecules 18 / 28

Exotic baryon spectroscopy (II)

Continuation:

JP Isospin Molecule Mass(MeV ) Eb(MeV ) Pmax(Channel)

1 2 −

2 D∗∆ 3232.70 −6.47 99.71(2S1/2)

3 2 −

1 D∆ 3097.14 −0.88 99.13(4S3/2)

3 2 −

2 D∗∆ 3238.19 −0.98 99.69(2S1/2)

5 2 −

1 D∗∆ 3226.05 −13.12 97.25(6S5/2)

1 2 −

2 B∗∆ 6540.88 −14.21 99.69(2S1/2)

3 2 −

1 B∆ 6498.56 −10.72 88.14(4S3/2)

3 2 −

2 B∆ 6505.61 −3.67 94.72(4S3/2)

3 2 −

1 B∗∆ 6554.71 −0.39 97.10(4S3/2)

3 2 −

2 B∗∆ 6550.25 −4.85 99.48(4S3/2)

5 2 −

1 B∗∆ 6531.94 −23.16 96.76(6S5/2)

Results Baryon-Meson molecules 19 / 28

Decays of D(∗)N and B(∗)N molecules

Strong decays to allowed channels, accesible through quark rearrangement diagrams. Decays through inestable D∗ → Dπ and ∆ → Nπ included. All decays expresed in MeV.

JP Isospin Molecule ΓDN ΓΣcπ ΓDπN

1 2 −

1 D∗N 2.54 0.054

3 2 −

D∗N 20.76 0.014 JP Isospin Molecule ΓBN ΓΣbπ ΓBπN

1 2 −

1 B∗N 7.81 0.002

3 2 −

B∗N 7.44 0.018

Results Baryon-Meson molecules 20 / 28

Decays of D(∗)∆ and B(∗)∆ molecules

JP Isospin Molecule ΓD∆ ΓΣcη ΓD∗N ΓDN ΓDπ∆ ΓD∗Nπ ΓDNπ

1 2 −

2 D∗∆ 0.005 110.89

3 2 −

1 D∆ 1.31 0.001 0.049 112.89

3 2 −

2 D∗∆ 6.18 0.038 114.04

5 2 −

1 D∗∆ 0.003 0.02 0.64 107.50 ΓΣcρ = ΓΣcω = ΓΛcρ = ΓΣcπ = ΓΛcπ = 0 JP Isospin Molecule ΓB∆ ΓΣbη ΓB∗N ΓBN ΓBπ∆ ΓB∗Nπ ΓBNπ

1 2 −

2 B∗∆ 0.002 111.07

3 2 −

1 B∆ 0.01 3.91 0.02 98.49

3 2 −

2 B∆ − 107.87

3 2 −

1 B∗∆ 12.47 0.06 0.224 0.019 0.076 114.75

3 2 −

2 B∗∆ 19.84 113.70

5 2 −

1 B∗∆ 0.001 0.09 0.90 108.41 ΓΛbρ = ΓΣbπ = ΓΛbπ = 0

Results Baryon-Meson molecules 21 / 28

LHCb Pentaquarks: Pc(4380) and Pc(4450)

• R. Aaij et al, Phys. Rev. Lett. 115, 072001 (2015).

Discovered in 2015 in Λ0

b → J/ψK −p

decay. Preferred quantum numbers: ( 3

2 ∓, 5 2 ±)

But other combinations such as ( 3

2 −, 3 2 −)

not excluded (L. Roca, arxiv:1602.06791) Masses close to DΣ∗

c and D∗Σc channel

thresholds. MPc(4380) = 4380 ± 8 ± 29 MeV , MPc(4450) = 4449.8 ± 1.7 ± 2.5 MeV , ΓPc(4380) = 205 ± 18 ± 86 MeV , ΓPc(4450) = 39 ± 5 ± 19 MeV .

Results LHCb Pentaquarks 22 / 28

LHCb pentaquarks: Pc(4380) and Pc(4450)

¯ D(∗)Σ(∗)

c

molecules in S-wave and P-wave. We obtain the following candidates:

Molecule JP I Mass(MeV /c2) BE(MeV /c2) Width J/ψp Width ¯ D∗Λc ¯ DΣc

1 2 − 1 2

4320.8 0.8 2.4 1.1 ¯ DΣ∗

c 3 2 − 1 2

4385.0 1.0 10.0 14.7 ¯ D∗Σc

1 2 − 1 2

4458.9 3.8 5.3 63.6 ¯ D∗Σc

3 2 − 1 2

4461.3 1.4 0.8 21.2 ¯ D∗Σc

3 2 + 1 2

4462.7 0.01 0.2 6.3 ¯ D∗Σ∗

c 1 2 − 1 2

4519.8 7.3 0.9 9.9 ¯ D∗Σ∗

c 3 2 − 1 2

4523.3 3.9 22.9 4.0 ¯ D∗Σ∗

c 5 2 − 1 2

4524.5 2.6 0.05 3.0 ¯ D∗Σ∗

c 5 2 + 1 2

4526.2 1.0 0.05 0.8

• P. G. Ortega et al., arxiv:1606.06148v1

Results LHCb Pentaquarks 23 / 28

LHCb Resonances

Results LHCb resonances 24 / 28

LHCb Resonances

Quark model predictions:

State JPC nL Mass (MeV/c2) Width (MeV)

• Exp. (MeV/c2)

χc0 0++ 3P 4261.7 4P 4497.7 115.40 4506 ± 11+12

−15

5P 4697.6 112.02 4704 ± 10+14

−24

6P 4855.6 χc1 1++ 3P 4271.5 29.80 4273.3 ± 8.3 4P 4520.8

LHCb results:

Results LHCb resonances 25 / 28

LHCb Resonances: Searching for X(4140)

Coupling channel calculation for the JPC = 1++ sector: D(∗)

s

D(∗)

s

and J/ψφ channels. Any signal of X(4140) neither bound nor virtual ֌ Analysis of line shapes of J/ψφ channel

Fh |ABβ |ABβ T ββ′(E; k, P) − Fh

(a)

|q¯ qα tβα

qh (E; k)

|ABβ −Fq

(b)

The X(4140) appears as a threshold cusp

10 20 30 40 50 60 70 80 4100 4120 4140 4160 4180 4200 4220 4240 Events mJ/ψ φ [MeV]

More details at:

• P. G. Ortega et al., arxiv:1608.01325v1

Results LHCb resonances 26 / 28

Outline

1

Motivation

2

The model

3

Results

4

Conclusions

Conclusions 26 / 28

Conclusions

Heavy quark sector shows a rich phenomenology, including two, three, four and five body problems depending on the dynamics. Use of Constituent Quark Model plus a coupled channels calculation can account for this phenomenology from naive meson and baryon spectrum to the recently pentaquark signals (and beyond). Rich spectroscopy predicted for charmonium and bottomonium exotic baryons.

Conclusions 27 / 28

Thanks for your attention.

Pablo Garc´ ıa Ortega (IFIC) portega@ific.uv.es

Conclusions 28 / 28

Lineshapes

Molecular contribution ֌

dBrh ((AB)β) dE

= const × k|Mβ

h (E)|2Θ(E)

with Mβ

h (E) = Fh

• 1 −

β′

• dP T ββ′(E; kβ, P)

2µβ′P2 P2−k2

β′

• n shell

Mesonic contribution ֌

dBrq ((AB)β) dE

= const × k

• Mβ

q (E)

• 2 Θ(E)

with Mβ

q = −Fq

• α,α′ φα′β(E; k)∆α′α(E)−1

Fh |ABβ |ABβ T ββ′(E; k, P) − Fh

(a)

|q¯ qα tβα

qh (E; k)

|ABβ −Fq

(b)

Lineshapes 29 / 28

Lineshapes for X(3872) with Eb = −0.25 MeV

c¯ c Production D ¯ D∗ Production

2 4 6 8 10 12 14 3870 3875 3880 3885 3890

Number of events/2 MeV M(D0 D0π0) (MeV)

(a)

2 4 6 8 10 12 14 3870 3875 3880 3885 3890

Number of events/2 MeV M(D0 D0π0) (MeV)

(c)

Belle B → KD0 ¯ D0π0

2 4 6 8 10 12 14 3870 3875 3880 3885 3890

Number of events/2 MeV M(D0 D*0) (MeV)

(b)

2 4 6 8 10 12 14 3870 3875 3880 3885 3890

Number of events/2 MeV M(D0 D*0) (MeV)

(d)

BaBar B → KD0 ¯ D∗0

Lineshapes 30 / 28

Results for the X(3940) coupled calculation

X(3940) ֌ Seen on the J/ψ invariant mass spectrum Mass: 3943 ± 6 ± 6 MeV Width: 52 MeV to 90%C.L. Decays to DD∗ channel ֌ Good candidate for χc1(2P) Masses and probabilities: γ Masa Γ c¯ c(23P1) D0D∗0 D±D∗∓ J/ψρ J/ψω 0.231 3942.5 93.8 61.02 18.57 16.86 0.01 3.54 0.226 3941.8 89.9 61.09 18.53 16.85 0.01 3.52 Partial widths γ D0D∗0 D±D∗∓ J/ψρ J/ψω 0.231 41.82 41.91 0.04 10.01 0.226 40.15 40.28 0.03 9.45

Lineshapes 31 / 28

Strong decay description

Described with the wave function of the channel J/ψρ (J/ψω) Improved if we include the width of the ρ (ω) state: Γπ+π−J/ψ =

• J,L

kmax dk Γρ (MX − Eρ − EJ/ψ)2 +

Γ2

ρ

4

• MρJ/ψ(k)
• 2 .

where MρJ/ψ =

• d3PχD ¯

D∗(P)hD ¯ D∗→ρJ/ψ(P, P′).

Lineshapes 32 / 28

Radiative decay description

Decay through the molecular component:

ΓANN =

4 27α qEΨ MX e − q2

2β2 D

η00 − 1

2η+−

2 ΓVMD =

4 27α qEΨ MX

• 3|φρ(r = 0)|χρJ/Ψ(q) + |φω(r = 0)|χωJ/Ψ(q)

2

J/ψ γ D D∗ X X J/ψ ω J/ψ γ

(a) (b)

Decay through the c¯ c component:

ΓE1

• n2S+1LJ → n′2S′+1L′

J′

• = 4αe2

c q3

3

(2J′ + 1)SE

fi δSS′ |Efi|2 Ef Mi

Lineshapes 33 / 28

More XYZ state results in c sector

JPC = 0++ sector: Description of X(3915) and Y (3940) as c¯ c(23P0) + D ¯ D coupled states. Effect of incorporate the DsDs threshold ֌ New state X(3915) and Y (3940) can be two different resonances as suggested by Belle Collaboration. JPC = 1−− sector: Description of G(3900) as c¯ c(33S1) + D ¯ D∗ state ψ(4040) − ψ(4160) states inversion due to Ds ¯ D∗

s threshold

Improvement branching ratio description. More details at:

• P. G. Ortega et al., Jour.
• f Phys.

G: 40 (2013) 065107

Lineshapes 34 / 28

JPC = 0++ sector: X(3915) and Y (3940)

Y (3940) ֌ Discovered at Belle in B → KπππJ/ψ Mass: 3943 ± 11 ± 13 MeV Width: 87 ± 22 ± 26 MeV X(3915) ֌ Discovered at Belle in γγ → J/ψω Mass: 3914 ± 3 ± 2 MeV Width: 17 ± 10 ± 5 MeV Two resonances or only one? Close meson state c¯ c(23P0) ֌ Mass= 3908.984 MeV Close thresholds: D ¯ D − → M = 3736.050 MeV J/ψω − → M = 3879.566 MeV Ds ¯ Ds − → M = 3936.970 MeV J/ψφ − → M = 4116.371 MeV

JPC = 0++ sector: X(3915) and Y (3940) 35 / 28

Coupled channel calculation of JPC = 0++

Effect of the thresholds over the theoretical bare state? Pole masses, widths and probabilities of the channels:

Masa (MeV ) P(23P0) P(DD) P(J/ψω) P(DsDs) P(J/ψφ) Γ(DD) Γ(J/ψω) Γ(DsDs) Threshold DD. 3920.81 − i 5.33 40.37 59.63 − − − 10.65 − − Threshold DD + J/ψω. 3919.50 − i 4.95 40.60 54.73 4.67 − − 8.85 1.04 − Threshold DD + J/ψω + DsDs. 3896.29 − i 2.18 34.39 47.05 9.07 9.49 − 3.52 0.84 − 3966.21 − i 98.18 59.51 34.65 0.18 5.67 − 36.54 4.08 155.74 Threshold DD + J/ψω + DsDs + J/ψφ. 3896.05 − i 2.10 34.22 46.67 9.41 9.67 0.03 3.37 0.83 − 3970.07 − i 94.67 57.27 35.32 0.15 5.72 1.54 38.69 2.89 147.76

Effect of incorporate the DsDs threshold ֌ New state X(3915) and Y (3940) can be two different resonances as suggested by Belle Collaboration.

JPC = 0++ sector: X(3915) and Y (3940) 36 / 28

Coupled calculation of JPC = 1−− around 4 GeV

G(3900) ֌ Discovered at BaBar in e+e− → DD Mass: 3943 ± 17 ± 12 MeV Width: 52 ± 8 ± 7 MeV Close to the threshold D∗ ¯ D∗ and ψ(4040) and ψ(4160) states Calculation with theoretical states: c¯ c(33S1) (Mass: 4097.615 MeV ) c¯ c(23D1) (Mass: 4152.715 MeV ) Description of partial waves ֌ Thresholds D ¯ D, D ¯ D∗, D∗ ¯ D∗, Ds ¯ Ds, Ds ¯ D∗

s and D∗ s ¯

D∗

s

Mass and probabilities of coupled channel calculation

M (MeV ) P(33S1) P(23D1) P(DD) P(DD∗) P(D∗D∗) P(DsDs) P(DsD∗

s )

P(D∗

s D∗ s )

3994.6 − i 11.60 31.56 3.00 2.49 36.44 17.75 7.53 0.52 0.71 4048.4 − i 7.54 0.92 36.15 2.99 23.49 25.81 8.86 0.92 0.85 4123.9 − i 71.11 59.01 0.98 2.13 6.84 19.19 0.75 3.37 7.73

JPC = 1−− sector: ψ(4040) − G(3900) − ψ(4160) 37 / 28

Partial waves and branching ratios

State inversion due to Ds ¯ D∗

s

Study of partial waves and branching ratios Partial waves:

M Γ Γ(DD) Γ(DD∗) Γ(D∗D∗) Γ(DsDs) Γ(DsD∗

s )

3994.6 23.37 0.12 19.09 − 4.16 − 4048.4 15.09 0.51 7.24 4.42 2.92 − 4123.9 142.23 4.73 7.51 100.03 3.82 26.15

Branching ratios:

Ratio C 3 (Eichten)

3P0 (Segovia) 3P0 (Barnes)

This work Experimental value

B(ψ(4040)→D ¯ D) B(ψ(4040)→D ¯ D∗)

0.0003 0.21 0.003 0.07 0.24 ± 0.05 ± 0.12

B(ψ(4040)→D∗ ¯ D∗) B(ψ(4040)→D ¯ D∗)

1.0 3.70 1.0 0.61 0.18 ± 0.14 ± 0.03

B(ψ(4160)→D ¯ D) B(ψ(4160)→D∗ ¯ D∗)

0.008 0.27 0.46 0.05 0.02 ± 0.03 ± 0.02

B(ψ(4160)→D ¯ D∗) B(ψ(4160)→D∗ ¯ D∗)

0.16 0.03 0.011 0.08 0.34 ± 0.14 ± 0.05

JPC = 1−− sector: ψ(4040) − G(3900) − ψ(4160) 38 / 28

The 1-loop corrections to OGE potential

Addition of the one-loop QCD corrections to the spin-dependent terms of the potential

S.N. Gupta and S.F. Radford, Phys. Rev. D 24, 2309 (1981)

☞ There is a spin-dependent term which affects only to mesons with different flavor quarks.

• O. Lakhina and E.S. Swanson, Phys. Lett. B 650, 159 (2007)

☞ The 0+ state is more sensitive to the inclusion of the one-loop corrections.

jP

q = 1/2−

jP

q = 1/2+

jP

q = 3/2+

0− 1− 0+ 1+ 1+ 2+ This work (αs) 1984 2110 2510 2593 2554 2591 This work (α2

s )

1984 2104 2383 2570 2560 2609 Exp. 1969.0 ± 1.4 2112.3 ± 0.5 2318.0 ± 1.0 2459.6 ± 0.9 2535.12 ± 0.25 2572.6 ± 0.9

☞ The potentially generated mass shifts depend only on the energy difference between the bare c¯ s state and the open-flavored threshold.

DK D∗K

D∗

s0(2317)

Ds1(2460)

0+ 1+ weak strong

☞ The states should be degenerated. ☞ They should couple equally to DK and D∗K.

Jorge Segovia (jorge.segovia@tum.de) Molecular components in D∗ s0(2317) and Ds1(2460) mesons 9/19

The D∗

s0(2317) meson

100 200 300 400 500 600 q- q (αs) q- q (αs

2) q-

q + DK

m-m-

1- S (MeV) Quark Model q- q q- q + DK V → ∞ LQCD Ensemble (1) q- q q- q + DK V → ∞ LQCD Ensemble (2) 100 200 300 400 500 600 Experiment

P.G. Ortega et al., arXiv: 1603.07000 [hep-ph]

☞ Observations: The mass is much higher using the naive quark model and without the 1-loop spin corrections to the OGE potential. The mass-shift due to the α2

s -corrections allows that the 0+ state be close to the

DK threshold. This makes the DK coupling a relevant dynamical mechanism. When we couple the 0+ c¯ s ground state with the DK threshold, the splitting mD∗

s0(2317) − m1S = 249.6 MeV is in good agreement with experiment.

Probabilities of the different Fock components: State Mass P[q¯ q (3P0)] P[DK(S − wave)] D∗

s0(2317)

2323.7 66.3% 33.7%

Jorge Segovia (jorge.segovia@tum.de) Molecular components in D∗ s0(2317) and Ds1(2460) mesons 13/19

The Ds1(2460) and Ds1(2536) mesons (I)

200 300 400 500 600 q- q (αs) q- q (αs

2)

+D*K(S) +D*K(S+D)

m-m-

1- S (MeV) Quark Model q- q q- q + D*K V → ∞ LQCD Ensemble (1) q- q q- q + D*K V → ∞ LQCD Ensemble (2) 200 300 400 500 600 Experiment

P.G. Ortega et al., arXiv: 1603.07000 [hep-ph]

☞ Observations: The naive quark model predicts states almost degenerated, with masses close to the experimentally observed mass of the Ds1(2536). The inclusion of the 1-loop corrections to the OGE potential does not improve the situation, making the splitting between the two states even smaller.

Jorge Segovia (jorge.segovia@tum.de) Molecular components in D∗ s0(2317) and Ds1(2460) mesons 14/19

The Ds1(2460) and Ds1(2536) mesons (II)

☞ Probabilities of the different Fock components: State Mass Width P[q¯ q (1P1)] P[q¯ q (3P1)] P[D∗K(S)] P[D∗K(D)] Ds1(2460) 2484.0 0.00 12.9% 32.8% 54.3%

• Ds1(2536)

2562.1 0.22 34.4% 15.8% 49.8%

• Ds1(2460)

2484.0 0.00 12.1% 33.6% 54.1% 0.2% Ds1(2536) 2535.2 0.56 31.9% 14.5% 16.8% 36.8% The quark-antiquark component in the wave function of the Ds1(2536) meson holds quite well the 1P1 and 3P1 composition predicted by HQS. Crucial in order to have a very narrow state and describe well its decay properties Γ(Ds1(2536)+) = Γ(D∗0K +) + Γ(D∗+K 0) R1 = Γ(Ds1(2536)+ → D∗0K +) Γ(Ds1(2536)+ → D∗+K 0) R2 = ΓS(Ds1(2536)+ → D∗+K 0) Γ(Ds1(2536)+ → D∗+K 0) R3 = Γ(Ds1(2536)+ → D+π−K +) Γ(Ds1(2536)+ → D∗+K 0) This work Experiment Γ (MeV) 0.56 0.92 ± 0.03 ± 0.04 R1 1.15 1.18 ± 0.16 R2 0.52 0.72 ± 0.05 ± 0.01 R3(%) 14.5 3.27 ± 0.18 ± 0.37

Jorge Segovia (jorge.segovia@tum.de) Molecular components in D∗ s0(2317) and Ds1(2460) mesons 16/19

Low-lying charmed-strange mesons

Overall agreement between quark model, lattice QCD and experimental data

• 200
• 100

100 200 300 400 500 600 Ds Ds

*

Ds0

*

Ds1 Ds1

’

Ds2

*

m-m-

1- S (MeV) Quark Model Ds Ds

*

Ds0

*

Ds1 Ds1

’

Ds2

*

LQCD Ensemble (1) Ds Ds

*

Ds0

*

Ds1 Ds1

’

Ds2

*

• 200
• 100

100 200 300 400 500 600 LQCD Ensemble (2)

☞ Theoretical results on D∗

s1(2700), the D∗ sJ(2860) and the DsJ(3040)

• J. Segovia et al., Phys. Rev. D 91, 094020 (2015).

Jorge Segovia (jorge.segovia@tum.de) Molecular components in D∗ s0(2317) and Ds1(2460) mesons 18/19