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3900 ) : experiment xperiment, the theory ory, lattic lattice Z c - - PowerPoint PPT Presentation

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Miguel Albaladejo (IFIC, Valencia) In collaboration with: P. Fern andez-Soler, F. K. Guo, C. Hidalgo-Duque, J. Nieves 3900 ) : experiment xperiment, the theory ory, lattic lattice Z c ( 3900 Based on: [arXiv:1512.03638,Phys.Lett.B 755 ,337

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SLIDE 1

Miguel Albaladejo (IFIC, Valencia)

In collaboration with:

  • P. Fern´

andez-Soler, F. K. Guo, C. Hidalgo-Duque, J. Nieves

Zc(3900 3900): experiment xperiment, the theory

  • ry, lattic

lattice

Based on:

[arXiv:1512.03638,Phys.Lett.B 755,337 (2016)] [arXiv:1606.03008,Eur.Phys.J.C (under review)]

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 2

Outline

1

Experiment

2

Theory

3

Lattice

4

Conclusions

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SLIDE 3

Outline

1

Experiment

2

Theory

3

Lattice

4

Conclusions

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SLIDE 4

Experiment Theory Lattice Conclusions Charmonium-like sector

Charmonium-like sector

(Taken from: [Olsen, Front. Phys. 10, 121(’15)]) Recent reviews (2015-2016):

[Olsen, Front. Phys. 10, 121(’15)] [Chen et al.,Phys. Rept. 639, 1(’16)] [Hosaka et al.,PTEP 2016, 062C01(’16)]

All the c¯ c states predicted by QM below D¯ D threshold have been found In 2003, X(3872) is discovered

[Belle Collab., PRL,91,262001]

Very close to D0¯ D0 threshold. Close to (but lower) χc1(23P1).

Lattice QCD:

[Prelovsek, Leskovec, PRL,111,192001]

candidate for X(3872) only if c¯ c + D¯ D∗ components are considered together

1 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Experimental information on Zc(3885)/Zc(3900)

Experimental information on Zc(3885)/Zc(3900)

Zc(3900) first seen by BESIII and Belle Collabs. in J/ψπ± invariant mass spectrum in e+e− → Y(4260) → J/ψπ+π−

[PRL,110,252001(’13)][PRL,110,252002(’13)]

Later on, CLEO-c data confirmed Zc(3900) in e+e− → ψ(4160) → J/ψπ+π−

[PL,B727,366(’13)]

BESIII analyses e+e− → Y(4260) → ¯ D∗Dπ, and sees Zc(3885) in ¯ D∗D invariant mass spectrum. JP = 1+ favoured.

[PRL,112,022001(’14)]

BESIII confirms Zc(3885) in ¯ D∗D spectrum at different e+e− c.m. energies

[PR,D92,092006(’15)]

If they are the same object, Ratio:

Γ(Zc→D¯ D∗) Γ(Zc→J/ψπ) = 6.2 ± 2.9

Events / 20 MeV/c2 MJ/ψπ− (MeV)

Y(4260) → J/ψππ

10 20 30 40 50 60 70 80 90 100 110 3200 3400 3600 3800 4000

2 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 6

Experiment Theory Lattice Conclusions Experimental information on Zc(3885)/Zc(3900)

Experimental information on Zc(3885)/Zc(3900)

Zc(3900) first seen by BESIII and Belle Collabs. in J/ψπ± invariant mass spectrum in e+e− → Y(4260) → J/ψπ+π−

[PRL,110,252001(’13)][PRL,110,252002(’13)]

Later on, CLEO-c data confirmed Zc(3900) in e+e− → ψ(4160) → J/ψπ+π−

[PL,B727,366(’13)]

BESIII analyses e+e− → Y(4260) → ¯ D∗Dπ, and sees Zc(3885) in ¯ D∗D invariant mass spectrum. JP = 1+ favoured.

[PRL,112,022001(’14)]

BESIII confirms Zc(3885) in ¯ D∗D spectrum at different e+e− c.m. energies

[PR,D92,092006(’15)]

If they are the same object, Ratio:

Γ(Zc→D¯ D∗) Γ(Zc→J/ψπ) = 6.2 ± 2.9

Events / 20 MeV/c2 MJ/ψπ− (MeV)

Y(4260) → J/ψππ

10 20 30 40 50 60 70 80 90 100 110 3200 3400 3600 3800 4000

2 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Experimental information on Zc(3885)/Zc(3900)

Experimental information on Zc(3885)/Zc(3900)

Zc(3900) first seen by BESIII and Belle Collabs. in J/ψπ± invariant mass spectrum in e+e− → Y(4260) → J/ψπ+π−

[PRL,110,252001(’13)][PRL,110,252002(’13)]

Later on, CLEO-c data confirmed Zc(3900) in e+e− → ψ(4160) → J/ψπ+π−

[PL,B727,366(’13)]

BESIII analyses e+e− → Y(4260) → ¯ D∗Dπ, and sees Zc(3885) in ¯ D∗D invariant mass spectrum. JP = 1+ favoured.

[PRL,112,022001(’14)]

BESIII confirms Zc(3885) in ¯ D∗D spectrum at different e+e− c.m. energies

[PR,D92,092006(’15)]

If they are the same object, Ratio:

Γ(Zc→D¯ D∗) Γ(Zc→J/ψπ) = 6.2 ± 2.9

Events / 20 MeV/c2 MJ/ψπ− (MeV)

Y(4260) → J/ψππ

10 20 30 40 50 60 70 80 90 100 110 3200 3400 3600 3800 4000 Events / 4 MeV/c2 MD∗−D0 (MeV)

Y(4260) → ¯ D∗Dπ

10 20 30 40 50 60 70 80 90 100 3900 3950 4000 4050 4100

2 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Experimental information on Zc(3885)/Zc(3900)

Experimental information on Zc(3885)/Zc(3900)

Zc(3900) first seen by BESIII and Belle Collabs. in J/ψπ± invariant mass spectrum in e+e− → Y(4260) → J/ψπ+π−

[PRL,110,252001(’13)][PRL,110,252002(’13)]

Later on, CLEO-c data confirmed Zc(3900) in e+e− → ψ(4160) → J/ψπ+π−

[PL,B727,366(’13)]

BESIII analyses e+e− → Y(4260) → ¯ D∗Dπ, and sees Zc(3885) in ¯ D∗D invariant mass spectrum. JP = 1+ favoured.

[PRL,112,022001(’14)]

BESIII confirms Zc(3885) in ¯ D∗D spectrum at different e+e− c.m. energies

[PR,D92,092006(’15)]

If they are the same object, Ratio:

Γ(Zc→D¯ D∗) Γ(Zc→J/ψπ) = 6.2 ± 2.9

Events / 20 MeV/c2 MJ/ψπ− (MeV)

Y(4260) → J/ψππ

10 20 30 40 50 60 70 80 90 100 110 3200 3400 3600 3800 4000 Events / 4 MeV/c2 MD∗−D0 (MeV)

Y(4260) → ¯ D∗Dπ

10 20 30 40 50 60 70 80 90 100 3900 3950 4000 4050 4100 Events / 4 MeV/c2 MD∗−D0 (MeV)

Y(4260) → ¯ D∗Dπ (updated data)

5 10 15 20 25 30 35 3900 3950 4000 4050 4100

2 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Experimental information on Zc(3885)/Zc(3900)

Experimental information on Zc(3885)/Zc(3900)

Zc(3900) first seen by BESIII and Belle Collabs. in J/ψπ± invariant mass spectrum in e+e− → Y(4260) → J/ψπ+π−

[PRL,110,252001(’13)][PRL,110,252002(’13)]

Later on, CLEO-c data confirmed Zc(3900) in e+e− → ψ(4160) → J/ψπ+π−

[PL,B727,366(’13)]

BESIII analyses e+e− → Y(4260) → ¯ D∗Dπ, and sees Zc(3885) in ¯ D∗D invariant mass spectrum. JP = 1+ favoured.

[PRL,112,022001(’14)]

BESIII confirms Zc(3885) in ¯ D∗D spectrum at different e+e− c.m. energies

[PR,D92,092006(’15)]

If they are the same object, Ratio:

Γ(Zc→D¯ D∗) Γ(Zc→J/ψπ) = 6.2 ± 2.9

Events / 20 MeV/c2 MJ/ψπ− (MeV)

Y(4260) → J/ψππ

10 20 30 40 50 60 70 80 90 100 110 3200 3400 3600 3800 4000 Events / 4 MeV/c2 MD∗−D0 (MeV)

Y(4260) → ¯ D∗Dπ

10 20 30 40 50 60 70 80 90 100 3900 3950 4000 4050 4100 Events / 4 MeV/c2 MD∗−D0 (MeV)

Y(4260) → ¯ D∗Dπ (updated data)

5 10 15 20 25 30 35 3900 3950 4000 4050 4100

2 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Introduction: theoretical speculation

Introduction: theoretical speculation

“One of the most interesting resonances”: couples strongly to charmonium (∼ ¯ cc) and yet it has charge (∼ ¯ ud). Minimal quark constituent is four [¯ cc¯ ud]. Many different interpretations have been given (see reviews mentioned before): Tetraquark ¯ D∗D molecular state Simply a kinematical effect Hadrocharmonium It has also been searched for in lattice QCD

D∗− D0

¯ c d c ¯ u

“Tetraquark”

c d ¯ c ¯ u What is still missing? A joint study of both reactions in which the Zc structure has been seen

3 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Introduction: theoretical speculation

Introduction: theoretical speculation

“One of the most interesting resonances”: couples strongly to charmonium (∼ ¯ cc) and yet it has charge (∼ ¯ ud). Minimal quark constituent is four [¯ cc¯ ud]. Many different interpretations have been given (see reviews mentioned before): Tetraquark ¯ D∗D molecular state Simply a kinematical effect (ruled out) Hadrocharmonium It has also been searched for in lattice QCD

D∗− D0

¯ c d c ¯ u

“Tetraquark”

c d ¯ c ¯ u What is still missing? A joint study of both reactions in which the Zc structure has been seen

3 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 12

Outline

1

Experiment

2

Theory

3

Lattice

4

Conclusions

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SLIDE 13

Experiment Theory Lattice Conclusions Coupling ¯ D∗D and J/ψπ channels

Coupling ¯ D∗D and J/ψπ channels

Coupled channel formalism is needed, because Zc(3900): is expected to be dynamically generated in ¯ D∗D channel (#2), but it is also seen in J/ψπ channel (#1). T = (I − V · G)−1 · V , Vij = 4√mi1mi2 √mj1mj2 e−q2

i /Λ2 i e−q2 j /Λ2Cij ,

G(E) are loop functions (Regularized with standard gaussian regulator) J/ψπ → J/ψπ: known to be tiny, C11 = 0. ¯ D∗D → J/ψπ: we make the simplest possible assumption, C12 ≡ C (constant) ¯ D∗D → ¯ D∗D: In a momentum expansion (HQSS), simply a constant, C22 ≡ C1Z. Problem: no resonance in the complex plane above threshold with only constant potentials (even with coupled channels). We introduce some energy dependence, C22(E) = C1Z + b (E − mD − mD∗) .

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  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Amplitudes: Y(4260) → (J/ψπ−)π+, (D∗−D0)π+

Amplitudes: Y(4260) → (J/ψπ−)π+, (D∗−D0)π+

π+ D∗− D0 Y(4260) ¯ D0 1 D∗− D0 Y(4260) D0 ¯ D0 1 D∗− π+ D∗− D0 Y(4260) D− D+ 1 D∗0 π+

  • M2(s, t)
  • 2 =
  • 1

t − m2

D1

+ I3(s)T22(s)

  • 2

q4

π(s) + |β (1 + T22(s)G22(s))|2

s (Mandelstam) ¯ D∗D invariant mass squared I3(s): three meson loop propagator ¯ D∗D rescattering enters through T22(s) qπ

2(s) = λ(M2 Y, s, m2 π)/(4M2 Y)

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  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Amplitudes: Y(4260) → (J/ψπ−)π+, (D∗−D0)π+

Amplitudes: Y(4260) → (J/ψπ−)π+, (D∗−D0)π+

J/ψ π+ π− Y(4260) π− J/ψ Y(4260) D0 ¯ D0 1 D∗− π− π− J/ψ Y(4260) D− D+ 1 D∗0 π− π+ J/ψ Y(4260) ¯ D0 D0 1 D∗+ π+ π+ J/ψ Y(4260) D+ D− 1 ¯ D∗0 π+

The decay proceeds mainly through [T12(s)] Y → (¯ D∗D)π → (J/ψπ)π Some direct production included through α s, t (Mandelstam) J/ψπ−, J/ψπ+ invariant mass squared

  • M1(s, t)
  • 2 = |τ(s)|2 q4

π(s) + |τ(t)|2 q4 π(t) + 3 cos2 θ − 1

4

  • τ(s)τ(t)∗ + τ(s)∗τ(t)
  • q2

π(s)q2 π(t) ,

τ(s) = √ 2I3(s)T12(s) + α

6 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Events distributions and Experimental data

Events distributions and Experimental data

Events distributions Ni: Ni(s) = Ki (Ai(s) + Bi(s)) Ai(s) = ti,+

ti,−

dt

  • Mi(s, t)
  • 2

Ki (unknown) global normalization constants Bi are background functions (parametrized as in the experimental analyses) (B2 = 0) “Branching ratio”:

Rexp = Γ

  • Zc → D¯

D∗ Γ (Zc → J/ψπ) = 6.2 ± 2.9

Theoretically estimated as the (physical) ratio of areas around Zc(3900) mass

Rth =

  • dsA2(s)
  • dsA1(s)

Events / 20 MeV/c2 MJ/ψπ− (MeV)

Y(4260) → J/ψππ

10 20 30 40 50 60 70 80 90 100 110 3200 3400 3600 3800 4000 Events / 4 MeV/c2 MD∗−D0 (MeV)

Y(4260) → ¯ D∗Dπ (updated data)

5 10 15 20 25 30 35 3900 3950 4000 4050 4100 7/ 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Results: comparison with experiment(s)

Results: comparison with experiment(s)

Events / 4 MeV/c2 MD∗−D0 (MeV) Stat.+Sys. Stat. Fit Data 5 10 15 20 25 30 35 3900 3950 4000 4050 4100 Events / 20 MeV/c2 MJ/ψπ− (MeV) Stat.+Sys. Stat. Fit Data 10 20 30 40 50 60 70 80 90 100 110 3200 3400 3600 3800 4000

Λ2 (GeV) C1Z (fm2) b (fm3)

  • C (fm2)

χ2/dof Rth 1.0 −0.19 ± 0.08 ± 0.01 −2.0 ± 0.7 ± 0.4 0.39 ± 0.10 ± 0.02 1.02 6.0 ± 3.5 ± 0.5 0.5 +0.01 ± 0.21 ± 0.03 −7.0 ± 0.4 ± 1.4 0.64 ± 0.16 ± 0.02 1.09 6.5 ± 3.6 ± 0.2 1.0 −0.27 ± 0.08 ± 0.07 0 (fixed) 0.34 ± 0.14 ± 0.01 1.31 10.3 ± 9.0 ± 1.1 0.5 −0.27 ± 0.16 ± 0.13 0 (fixed) 0.54 ± 0.16 ± 0.02 1.36 10.9 ± 9.0 ± 2.5

Four different fits: b = {free, 0}, Λ2 = {0.5, 1.0} GeV Only the T-matrix parameters are shown (not shown: normalization, ...) All fits have ˆ χ2 ≃ 1 (≃ 1.4 for b = 0), and are within the error band of the best

  • ne

Reproduction of the data is excellent

8 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 18

Experiment Theory Lattice Conclusions Results: comparison with experiment(s)

Results: comparison with experiment(s)

Events / 4 MeV/c2 MD∗−D0 (MeV) Stat.+Sys. Stat. Fit Data 5 10 15 20 25 30 35 3900 3950 4000 4050 4100 Events / 20 MeV/c2 MJ/ψπ− (MeV) Stat.+Sys. Stat. Fit Data 10 20 30 40 50 60 70 80 90 100 110 3200 3400 3600 3800 4000

Zc(3900)− (above thr.)

Zc(3900)−

“Zc(3900)+”

Λ2 (GeV) C1Z (fm2) b (fm3)

  • C (fm2)

χ2/dof Rth 1.0 −0.19 ± 0.08 ± 0.01 −2.0 ± 0.7 ± 0.4 0.39 ± 0.10 ± 0.02 1.02 6.0 ± 3.5 ± 0.5 0.5 +0.01 ± 0.21 ± 0.03 −7.0 ± 0.4 ± 1.4 0.64 ± 0.16 ± 0.02 1.09 6.5 ± 3.6 ± 0.2 1.0 −0.27 ± 0.08 ± 0.07 0 (fixed) 0.34 ± 0.14 ± 0.01 1.31 10.3 ± 9.0 ± 1.1 0.5 −0.27 ± 0.16 ± 0.13 0 (fixed) 0.54 ± 0.16 ± 0.02 1.36 10.9 ± 9.0 ± 2.5

Four different fits: b = {free, 0}, Λ2 = {0.5, 1.0} GeV Only the T-matrix parameters are shown (not shown: normalization, ...) All fits have ˆ χ2 ≃ 1 (≃ 1.4 for b = 0), and are within the error band of the best

  • ne

Reproduction of the data is excellent

8 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 19

Experiment Theory Lattice Conclusions Results: comparison with experiment(s)

Reflection of threshold and Zc(3900) in J/ψπ+π− spectrum

√t = MJ/ψπ+ (MeV) 3400 3600 3800 4000 Events / 20 MeV/c2 √s = MJ/ψπ− (MeV) 10 20 30 40 50 60 70 80 90 100 110 3200 3400 3600 3800 4000

When MJψπ− ≡ √s ∈ (3.40, 3.55) GeV

⇓

MJψπ+ ≡ √ t can be at √ t = 3.9 GeV (D¯ D∗ threshold, Zc(3900) mass) This explains the enhancement (reflection)

9 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 20

Experiment Theory Lattice Conclusions Results: Spectroscopy

Results: Spectroscopy

ΓZc/2 (MeV) MZc (MeV) BESIII Cleo-c Belle 0.5 GeV 1.0 GeV 10 20 30 40 50 3880 3890 3900 3910

MZc (MeV) ΓZc /2 (MeV) Ref. Final state 3899 ± 6 23 ± 11 (BESIII) J/ψ π 3895 ± 8 32 ± 18 (Belle) J/ψ π 3886 ± 5 19 ± 5 (CLEO-c) J/ψ π 3884 ± 5 12 ± 6 (BESIII) ¯ D∗D 3882 ± 3 13 ± 5 (BESIII) ¯ D∗D 3894 ± 6 ± 1 30 ± 12 ± 6 (Λ = 1.0 GeV) both 3886 ± 4 ± 1 22 ± 6 ± 4 (Λ = 0.5 GeV) both 3831 ± 26+ 7

−28

virtual state (Λ = 1.0 GeV) both 3844 ± 19+12

−21

virtual state (Λ = 0.5 GeV) both

Two different scenarios:

1

(b = 0) Zc is a ¯ D∗D resonance very close to threshold

(Differences with experiments are related to Breit-Wigner parametrizations)

2

(b = 0) Zc is a virtual state In both scenarios, Data are very well reproduced A single structure (not two) Zc(3885)/Zc(3900) is needed

10 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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Experiment Theory Lattice Conclusions Results: Spectroscopy

Bound state, resonance, virtual ...

Well known example: NN scattering and the deuteron Triplet (3S1–3D1): at ≃ 5 fm. In this wave there is a bound

  • state. The deuteron is a well

known, really physical particle. Singlet (1S0): as ≃ −24 fm. In this wave there is a virtual state. A virtual state does not correspond to a real particle. (Wavefunction not localized.) It produces effects at the threshold similar to those of a bound state or a nearby resonance.

Events / 20 MeV/c2 MJ/ψπ− (MeV) Data

b = 0 (resonance) b = 0 (virtual)

30 40 50 60 70 80 90 100 110 120 130 3800 3830 3860 3890 3920 3950 11 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 22

Experiment Theory Lattice Conclusions Results: Spectroscopy

Complex plane & poles: First scenario (resonance)

3850 3875 3900 3925 3950 ReE (MeV) 5 10 15 20 25 30 ImE (MeV) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 |T|2

Pole located at 3894 − i30 MeV Plot: unphysical Riemann sheet connected to the physical one above D∗¯ D Shift of the pole towards higher energies (interference!)

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  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 23

Experiment Theory Lattice Conclusions Results: Spectroscopy

Complex plane & poles: First scenario (resonance)

3850 3875 3900 3925 3950 ReE (MeV) 5 10 15 20 25 30 ImE (MeV) |T|2 Pole located at 3894 − i30 MeV Plot: unphysical Riemann sheet connected to the physical one above D∗¯ D Shift of the pole towards higher energies (interference!)

12 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 24

Outline

1

Experiment

2

Theory

3

Lattice

4

Conclusions

slide-25
SLIDE 25

Experiment Theory Lattice Conclusions Zc(3900) on the lattice

Zc(3900) on the lattice

LQCD simulations on Zc(3900) still scarce:

[Prelovsek et al., PR,D91,014504(’15)] (mπ = 266 MeV)

“no additional candidate”

[Y. Ikeda et al. [HAL QCD], arXiv:1602.03465]

(mπ 410 MeV) Virtual poles with very low masses and deep in the complex plane.

[Y. Chen et al., PR,D89,094506(’14)] [L. Liu et al., PoS LATTICE 2014, 117(’14)] [S. H. Lee et al., arXiv:1411.1389]

Results are not conclusive (large pion masses, etc...) We can predict energy levels in a finite box. Cooperation between (unitary) EFTs and LQCD simulations is useful to understand the hadron spectrum.

[M. Doring, U. G. Meissner, E. Oset and A. Rusetsky, EPJ,A47,139(’11)]

3650 3700 3750 3800 3850 3900 3950 4000 4050 1.5 2 2.5 3 3.5 4 E (MeV) Lmπ I = 1 0++ D+ ¯ D0 1+− D∗ ¯ D 0++ D∗ ¯ D∗ 1+− D∗ ¯ D∗

D+ ¯ D0 D∗+ ¯ D0 D+ ¯ D∗0 D∗+ ¯ D∗0

[M.A., C. Hidalgo-Duque, J. Nieves,

  • E. Oset, PR,D88,014510(’13)]

13 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 26

Experiment Theory Lattice Conclusions Formalism for finite volume

Formalism for finite volume [M.A., P. Fern´

andez-Soler, J. Nieves, arXiv:1606.03008]

Periodic boundary conditions: discrete momenta infinite volume finite volume

  • q continuous
  • q = 2π

L n,

  • n ∈ Z3
  • R3

d3q (2π)3 e−2(q2−k2

2)/Λ2

E − ωD¯

D∗(q)

1 L3

  • n∈Z3

e−2(q2−k2

2)/Λ2

E − ωD¯

D∗(q)

T−1(E) = V−1(E) − G(E) ˜ T−1(E, L) = V−1(E) − ˜ G(E, L)

ωthe

D¯ D∗(q) = mD + mD∗ + mD+mD∗ 2mDmD∗ q2 (non relativistic)

Finite volume → box of edge L: it is an infinite square well potential (like QM) Energy levels: bound states in the box. Given by: ˜ T−1(Em(L), L) = 0 (Interacting energy levels) In particular, if the interaction is zero (V(E) = 0), then the energy levels are given by the poles of the ˜ G function: Em(L) = ωD¯

D∗(2π n/L)

(Free energy levels)

14 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 27

Experiment Theory Lattice Conclusions Formalism for finite volume

Formalism for finite volume [M.A., P. Fern´

andez-Soler, J. Nieves, arXiv:1606.03008]

Periodic boundary conditions: discrete momenta infinite volume finite volume

  • q continuous
  • q = 2π

L n,

  • n ∈ Z3
  • R3

d3q (2π)3 e−2(q2−k2

2)/Λ2

E − ωD¯

D∗(q)

1 L3

  • n∈Z3

e−2(q2−k2

2)/Λ2

E − ωD¯

D∗(q)

T−1(E) = V−1(E) − G(E) ˜ T−1(E, L) = V−1(E) − ˜ G(E, L)

Energy-momentum dispersion relation on the lattice

[Prelovsek et al., PR,D91,014504(’15)]

ωthe

D¯ D∗(q) = mD + mD∗ + mD + mD∗

2mDmD∗ q2 ωlat

D¯ D∗(q) = mD,1 + mD∗,1 + mD,2 + mD∗,2

2mD,2mD∗,2 q2 − m3

D,4 + m3 D∗,4

8m3

D,4m3 D∗,4

q4 .

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  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 28

Experiment Theory Lattice Conclusions Results

Results

E∗ (MeV) L (fm)

Resonance, Λ2 = 1 GeV

D∗ ¯ D J/ψπ–D∗ ¯ D E(l)

D∗ ¯ D

E(l)

J/ψπ

3850 3900 3950 4000 4050 4100 1.5 1.75 2 2.25 2.5 E∗ (MeV) L (fm)

Virtual state, Λ2 = 1 GeV

3850 3900 3950 4000 4050 4100 1.5 1.75 2 2.25 2.5

Results for the discrete energy levels as a function of box size (L) J/ψπ channel not essential:

Always a level close to a free J/ψπ one. Coupled channels case levels follow single channel case levels (except near the free J/ψπ levels).

Level below threshold (attractive interaction) goes to threshold for L → ∞: no bound state Relevant energy level: the one above threshold. Shift w.r.t. free levels is larger for the resonance case. No “additional/extra” energy level.

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  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 29

Experiment Theory Lattice Conclusions Results

Results

E∗ (MeV) L (fm)

Resonance, Λ2 = 1 GeV

D∗ ¯ D J/ψπ–D∗ ¯ D E(l)

D∗ ¯ D

E(l)

J/ψπ

3850 3900 3950 4000 4050 4100 1.5 1.75 2 2.25 2.5 E∗ (MeV) L (fm)

Virtual state, Λ2 = 1 GeV

3850 3900 3950 4000 4050 4100 1.5 1.75 2 2.25 2.5

Results for the discrete energy levels as a function of box size (L) J/ψπ channel not essential:

Always a level close to a free J/ψπ one. Coupled channels case levels follow single channel case levels (except near the free J/ψπ levels).

Level below threshold (attractive interaction) goes to threshold for L → ∞: no bound state Relevant energy level: the one above threshold. Shift w.r.t. free levels is larger for the resonance case. No “additional/extra” energy level.

15 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 30

Experiment Theory Lattice Conclusions Results

Results

E∗ (MeV) L (fm)

Resonance, Λ2 = 1 GeV

D∗ ¯ D J/ψπ–D∗ ¯ D E(l)

D∗ ¯ D

E(l)

J/ψπ

3850 3900 3950 4000 4050 4100 1.5 1.75 2 2.25 2.5 E∗ (MeV) L (fm)

Virtual state, Λ2 = 1 GeV

3850 3900 3950 4000 4050 4100 1.5 1.75 2 2.25 2.5

Results for the discrete energy levels as a function of box size (L) J/ψπ channel not essential:

Always a level close to a free J/ψπ one. Coupled channels case levels follow single channel case levels (except near the free J/ψπ levels).

Level below threshold (attractive interaction) goes to threshold for L → ∞: no bound state Relevant energy level: the one above threshold. Shift w.r.t. free levels is larger for the resonance case. No “additional/extra” energy level.

15 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 31

Experiment Theory Lattice Conclusions Results

Results

E∗ (MeV) L (fm)

Resonance, Λ2 = 1 GeV

D∗ ¯ D J/ψπ–D∗ ¯ D E(l)

D∗ ¯ D

E(l)

J/ψπ

3850 3900 3950 4000 4050 4100 1.5 1.75 2 2.25 2.5 E∗ (MeV) L (fm)

Virtual state, Λ2 = 1 GeV

3850 3900 3950 4000 4050 4100 1.5 1.75 2 2.25 2.5

Results for the discrete energy levels as a function of box size (L) J/ψπ channel not essential:

Always a level close to a free J/ψπ one. Coupled channels case levels follow single channel case levels (except near the free J/ψπ levels).

Level below threshold (attractive interaction) goes to threshold for L → ∞: no bound state Relevant energy level: the one above threshold. Shift w.r.t. free levels is larger for the resonance case. No “additional/extra” energy level.

15 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-32
SLIDE 32

Experiment Theory Lattice Conclusions Results

Results

E∗ (MeV) L (fm)

Resonance, Λ2 = 1 GeV

D∗ ¯ D J/ψπ–D∗ ¯ D E(l)

D∗ ¯ D

E(l)

J/ψπ

3850 3900 3950 4000 4050 4100 1.5 1.75 2 2.25 2.5 E∗ (MeV) L (fm)

Virtual state, Λ2 = 1 GeV

3850 3900 3950 4000 4050 4100 1.5 1.75 2 2.25 2.5

Results for the discrete energy levels as a function of box size (L) J/ψπ channel not essential:

Always a level close to a free J/ψπ one. Coupled channels case levels follow single channel case levels (except near the free J/ψπ levels).

Level below threshold (attractive interaction) goes to threshold for L → ∞: no bound state Relevant energy level: the one above threshold. Shift w.r.t. free levels is larger for the resonance case. No “additional/extra” energy level.

15 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-33
SLIDE 33

Experiment Theory Lattice Conclusions Comparison with LQCD simulations

Comparison with LQCD simulations

E∗ (MeV) E(0)

D∗ ¯ D

E(1)

D∗ ¯ D

E(1)

J/ψπ

Res. Lat. Vir. 3820 3860 3900 3940 3980 4020 4060 4100

R scenario (left) vs. VS scenario (right) Lattice energy levels: center Λ2 = 0.5 GeV: ( , ) Λ2 = 1.0 GeV: ( , )

Our aim is to compare with an actual LQCD simulation

[Prelovsek et al., PR,D91,014504(’15) [arXiv:1405.7623]]

Calculations done at L = 1.98 fm, mπ = 266 MeV. Three separate regions, all theoretical predictions in good agreement with LQCD Except for this point? Eth = 4000+24

−13 MeV

Elat = 4070 ± 30 MeV ∆E = 70 ± 40 MeV (< 2σ dev.) Summary: both scenarios (resonance and virtual) agree with LQCD

16 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 34

Experiment Theory Lattice Conclusions Comparison with LQCD simulations

Comparison with LQCD simulations

E∗ (MeV) E(0)

D∗ ¯ D

E(1)

D∗ ¯ D

E(1)

J/ψπ

Res. Lat. Vir. 3820 3860 3900 3940 3980 4020 4060 4100

R scenario (left) vs. VS scenario (right) Lattice energy levels: center Λ2 = 0.5 GeV: ( , ) Λ2 = 1.0 GeV: ( , )

Our aim is to compare with an actual LQCD simulation

[Prelovsek et al., PR,D91,014504(’15) [arXiv:1405.7623]]

Calculations done at L = 1.98 fm, mπ = 266 MeV. Three separate regions, all theoretical predictions in good agreement with LQCD Except for this point? Eth = 4000+24

−13 MeV

Elat = 4070 ± 30 MeV ∆E = 70 ± 40 MeV (< 2σ dev.) Summary: both scenarios (resonance and virtual) agree with LQCD

16 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

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SLIDE 35

Experiment Theory Lattice Conclusions Comparison with LQCD simulations

Comparison with LQCD simulations

E∗ (MeV) E(0)

D∗ ¯ D

E(1)

D∗ ¯ D

E(1)

J/ψπ

Res. Lat. Vir. 3820 3860 3900 3940 3980 4020 4060 4100

✗?

R scenario (left) vs. VS scenario (right) Lattice energy levels: center Λ2 = 0.5 GeV: ( , ) Λ2 = 1.0 GeV: ( , )

Our aim is to compare with an actual LQCD simulation

[Prelovsek et al., PR,D91,014504(’15) [arXiv:1405.7623]]

Calculations done at L = 1.98 fm, mπ = 266 MeV. Three separate regions, all theoretical predictions in good agreement with LQCD Except for this point? Eth = 4000+24

−13 MeV

Elat = 4070 ± 30 MeV ∆E = 70 ± 40 MeV (< 2σ dev.) Summary: both scenarios (resonance and virtual) agree with LQCD

16 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-36
SLIDE 36

Experiment Theory Lattice Conclusions Comparison with LQCD simulations

Comparison with LQCD simulations

E∗ (MeV) E(0)

D∗ ¯ D

E(1)

D∗ ¯ D

E(1)

J/ψπ

Res. Lat. Vir. 3820 3860 3900 3940 3980 4020 4060 4100

✓!

R scenario (left) vs. VS scenario (right) Lattice energy levels: center Λ2 = 0.5 GeV: ( , ) Λ2 = 1.0 GeV: ( , )

Our aim is to compare with an actual LQCD simulation

[Prelovsek et al., PR,D91,014504(’15) [arXiv:1405.7623]]

Calculations done at L = 1.98 fm, mπ = 266 MeV. Three separate regions, all theoretical predictions in good agreement with LQCD Except for this point? Eth = 4000+24

−13 MeV

Elat = 4070 ± 30 MeV ∆E = 70 ± 40 MeV (< 2σ dev.) Summary: both scenarios (resonance and virtual) agree with LQCD

16 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-37
SLIDE 37

Experiment Theory Lattice Conclusions Comparison with LQCD simulations: what’s next?

Comparison with LQCD simulations: what’s next?

Both scenarios (resonance and virtual) agree with both cutoffs (Λ2 = 0.5 GeV and 1 GeV). What to do? One possibility is to study volume dependence (several volumes) We compare here two predictions:

Resonance scenario with Λ2 = 0.5 GeV (blue bands) Virtual scenario with Λ2 = 1.0 GeV (orange bands)

E∗ (MeV) L (fm) Vir., Λ2 = 1.0 GeV Res., Λ2 = 0.5 GeV E(1)

D∗ ¯ D

E(2)

J/ψπ

3980 4000 4020 4040 4060 4080 4100 1.9 2 2.1 2.2 2.3 2.4 2.5

Both are indistinguishable around L ≃ 2 fm (say 1.9 fm < L < 2.2 fm) But they are clearly different at L ≃ 2.4 fm (say 2.3 fm < L < 2.5 fm)

17/ 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-38
SLIDE 38

Experiment Theory Lattice Conclusions Comparison with LQCD simulations: what’s next?

Comparison with LQCD simulations: what’s next?

Both scenarios (resonance and virtual) agree with both cutoffs (Λ2 = 0.5 GeV and 1 GeV). What to do? One possibility is to study volume dependence (several volumes) We compare here two predictions:

Resonance scenario with Λ2 = 0.5 GeV (blue bands) Virtual scenario with Λ2 = 1.0 GeV (orange bands)

E∗ (MeV) L (fm) Vir., Λ2 = 1.0 GeV Res., Λ2 = 0.5 GeV E(1)

D∗ ¯ D

E(2)

J/ψπ

3980 4000 4020 4040 4060 4080 4100 1.9 2 2.1 2.2 2.3 2.4 2.5

Both are indistinguishable around L ≃ 2 fm (say 1.9 fm < L < 2.2 fm) But they are clearly different at L ≃ 2.4 fm (say 2.3 fm < L < 2.5 fm)

17/ 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-39
SLIDE 39

Outline

1

Experiment

2

Theory

3

Lattice

4

Conclusions

slide-40
SLIDE 40

Experiment Theory Lattice Conclusions Conclusions (this work)

Conclusions (this work)

Zc(3900) is a most-interesting, exotic, structure. A candidate for “tetraquark”, or a D∗¯ D molecule...

[M. A., C. Hidalgo-Duque, F. K. Guo and J. Nieves, arXiv:1512.03638, Phys. Lett. B 755, 337 (2016)]

We have presented the first simultaneous study of the two decays (Y(4260) → J/ψππ, ¯ D∗Dπ) in which Zc(3900) is seen Data are well reproduced in all fits (ˆ χ2 ≃ 1) Two different scenarios are found:

1

(b = 0) Zc(3900) is a ¯ D∗D resonance

2

(b = 0) Zc(3900) is a virtual state

In any case, a single structure for Zc(3885)/Zc(3900) is needed. Improved data on J/ψπ invariant mass spectrum are necessary

[M. A., P. Fern´ andez-Soler and J. Nieves, arXiv:1606.03008, Eur. Phys. J. C (under review)]

We have used our T-matrix to compute energy levels in a finite volume Good agreement is found for both scenarios (resonance and virtual state) with the energy levels reported in a LQCD simulation [Prelovsek et al., PR,D91,014504(’15)] To discriminate both scenarios, we suggest to perform LQCD simulations at several different volumes

18 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-41
SLIDE 41

Experiment Theory Lattice Conclusions Conclusions (this work)

Conclusions (this work)

Zc(3900) is a most-interesting, exotic, structure. A candidate for “tetraquark”, or a D∗¯ D molecule...

[M. A., C. Hidalgo-Duque, F. K. Guo and J. Nieves, arXiv:1512.03638, Phys. Lett. B 755, 337 (2016)]

We have presented the first simultaneous study of the two decays (Y(4260) → J/ψππ, ¯ D∗Dπ) in which Zc(3900) is seen Data are well reproduced in all fits (ˆ χ2 ≃ 1) Two different scenarios are found:

1

(b = 0) Zc(3900) is a ¯ D∗D resonance

2

(b = 0) Zc(3900) is a virtual state

In any case, a single structure for Zc(3885)/Zc(3900) is needed. Improved data on J/ψπ invariant mass spectrum are necessary

[M. A., P. Fern´ andez-Soler and J. Nieves, arXiv:1606.03008, Eur. Phys. J. C (under review)]

We have used our T-matrix to compute energy levels in a finite volume Good agreement is found for both scenarios (resonance and virtual state) with the energy levels reported in a LQCD simulation [Prelovsek et al., PR,D91,014504(’15)] To discriminate both scenarios, we suggest to perform LQCD simulations at several different volumes

18 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-42
SLIDE 42

Experiment Theory Lattice Conclusions Conclusions (this work)

Conclusions (this work)

Zc(3900) is a most-interesting, exotic, structure. A candidate for “tetraquark”, or a D∗¯ D molecule...

[M. A., C. Hidalgo-Duque, F. K. Guo and J. Nieves, arXiv:1512.03638, Phys. Lett. B 755, 337 (2016)]

We have presented the first simultaneous study of the two decays (Y(4260) → J/ψππ, ¯ D∗Dπ) in which Zc(3900) is seen Data are well reproduced in all fits (ˆ χ2 ≃ 1) Two different scenarios are found:

1

(b = 0) Zc(3900) is a ¯ D∗D resonance

2

(b = 0) Zc(3900) is a virtual state

In any case, a single structure for Zc(3885)/Zc(3900) is needed. Improved data on J/ψπ invariant mass spectrum are necessary

[M. A., P. Fern´ andez-Soler and J. Nieves, arXiv:1606.03008, Eur. Phys. J. C (under review)]

We have used our T-matrix to compute energy levels in a finite volume Good agreement is found for both scenarios (resonance and virtual state) with the energy levels reported in a LQCD simulation [Prelovsek et al., PR,D91,014504(’15)] To discriminate both scenarios, we suggest to perform LQCD simulations at several different volumes

18 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-43
SLIDE 43

Experiment Theory Lattice Conclusions Conclusions (general)

Conclusions (general)

Charmonium spectrum, well known below D¯ D threshold. Since 2003, the charmonium(-like) spectrum increases continuously (≃ 1 state/year), but we do not fully understand: there are c¯ c, there are meson-meson molecules, there are tetraquarks, and many others. They must be mixing, specially around thresholds. Lattice still must go down to physical masses. We shall all be studying Heavy Quark Physics...

19 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-44
SLIDE 44

Experiment Theory Lattice Conclusions Conclusions (general)

Conclusions (general)

Charmonium spectrum, well known below D¯ D threshold. Since 2003, the charmonium(-like) spectrum increases continuously (≃ 1 state/year), but we do not fully understand: there are c¯ c, there are meson-meson molecules, there are tetraquarks, and many others. They must be mixing, specially around thresholds. Lattice still must go down to physical masses. We shall all be studying Heavy Quark Physics...

19 / 19

  • M. Albaladejo (IFIC, Valencia): Zc(3900): experiment, theory, lattice

2nd Hadron Spanish Network Days, Sept. 8-9, 2016

slide-45
SLIDE 45

Miguel Albaladejo (IFIC, Valencia)

In collaboration with:

  • P. Fern´

andez-Soler, F. K. Guo, C. Hidalgo-Duque, J. Nieves

Zc(3900 3900): experiment xperiment, the theory

  • ry, lattic

lattice

Based on:

[arXiv:1512.03638,Phys.Lett.B 755,337 (2016)] [arXiv:1606.03008,Eur.Phys.J.C (under review)]

2nd Hadron Spanish Network Days, Sept. 8-9, 2016