The Y (4260) and Y (4360) enhancements within coupled-channels - - PowerPoint PPT Presentation

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the y 4260 and y 4360 enhancements within coupled channels
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The Y (4260) and Y (4360) enhancements within coupled-channels - - PowerPoint PPT Presentation

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Meson 2018, Krakow - Poland, June 7, 2018 The Y (4260) and Y (4360) enhancements within coupled-channels Susana Coito Collaborator: Francesco Giacosa Jan Kochanowski University, Kielce, Poland Introduction Ideas about dynamical poles:

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SLIDE 1

“Meson 2018”, Krakow - Poland, June 7, 2018

The Y (4260) and Y (4360) enhancements within coupled-channels

Susana Coito

Collaborator: Francesco Giacosa

Jan Kochanowski University, Kielce, Poland

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SLIDE 2

Introduction

Ideas about dynamical poles: scalar mesons

Boglione, Penington, PRD 65, 114010 (2002) van Beveren, Rijken, Metzger, Dullemond, Rupp, Ribeiro, ZPC 30, 615 (1986) van Beveren, Rupp, IJTPGTNO 11, 179 (2006) [arXiv:hep-ph/0605317]

  • pen-charm axial mesons

van Beveren, Rupp, PRL 91, 012003 (2003)

charmonium scalar

Gamermann, Oset, Strottman, and Vacas, PRD 76, 074016 (2007)

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SLIDE 3

Within similar models to the one we present here a0(980)

Wolkanowski, Giacosa, Rischke, PRD 93, 014002 (2016)

K ∗

0 (800)

Wolkanowski, So ltysiak, Giacosa, NPB 909, 418 (2016)

0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.5 1.0 1.5 2.0 2.5

m GeV

dK0

m GeV1

Kπ

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SLIDE 4

Concerning the Y (4260) A signal that has 1st been detected in

)

2

) (GeV/c ψ J/

  • π

+

π m(

3.8 4 4.2 4.4 4.6 4.8 5

2

Events / 20 MeV/c

10 20 30 40

)

2

) (GeV/c ψ J/

  • π

+

π m(

3.8 4 4.2 4.4 4.6 4.8 5

2

Events / 20 MeV/c

10 20 30 40

)

2

) (GeV/c ψ J/

  • π

+

π m(

3.8 4 4.2 4.4 4.6 4.8 5

2

Events / 20 MeV/c

10 20 30 40

)

2

) (GeV/c ψ J/

  • π

+

π m(

3.8 4 4.2 4.4 4.6 4.8 5

2

Events / 20 MeV/c

10 20 30 40

3.6 3.8 4 4.2 4.4 4.6 4.8 5 1 10

2

10

3

10

4

10

PRL95,142001 (2005) BABAR, e+e− → J/ψπ+π−.

M ∼ 4.26 GeV, Γ = 50 − 90 MeV yet showing no decays to any of the open OZI-allowed decay channels!

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SLIDE 5

There is the idea that such enhancement might not be a true resonance

4.0 4.5 5.0 5.5 20 40 60 80 mπ+π−J/ψ(GeV) X-sect(events/20 MeV/c2)

  • D∗

s D∗ s

(a)

van Beveren, Rupp, PRL 105, 102001 (2010) van Beveren, Rupp, PRD 79, 111501(R) (2009)

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SLIDE 6

DsDs, D∗D∗, DsD∗

s , D∗ s D∗ s , DD1, D∗D1, DsD1s 4.0 4.2 4.4 4.6 50 100 E(GeV) σ(pb) 100 200 σ(pb)

  • ⋆

⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆⋆ ⋆⋆⋆ ⋆ ⋆ ⋆ ⋆ ⋆ J/ψπ+π− hcπ+π−

ψ(4040), ψ(4160), ψ(4415) Data: BESIII PRL118,092001(2017); PRL118,092002(2017)

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SLIDE 7

Recent ideas about the Y (4260) and the Y (4390)

  • Possible identification of Y states with ψ states through

coupling to decay channels in a “molecular” manner

  • Interference between ψ(4160) and ψ(4415) states

Lu, Anwar, Zou, PRD 96, 114022 (2017) Chen, Liu, Matsuki, EPJC 78, 136 (2018) Zhang, Zhang, PRD 96, 054008 (2017) He, Chen, EPJC 77, 398 (2017) Wang, CPC 41, 083103 (2017)

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SLIDE 8

On the other hand, the determination of the ψ masses is not always easy to disentagle... ψ(3770), ψ(4040), ψ(4160), ψ(4415)

5 0.5 5 0.5 10 3.7 3.8 3.9 4 σ(nb) (a) (a) (b) (b) (c) (c) M(D D

– ), GeV/c2

1 3.8 4 4.2 4.4 4.6 4.8 5

BELLE, PRD77,011103(R)(2008) e+e− → D ¯ D

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SLIDE 9

An effective Lagrangian model

production experiment → interaction region → final hadrons anihilation and production vertex meson-meson loops ⇔ coupled-channels

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SLIDE 10

The case of the ψ(3770) with D0 ¯ D0 and D+D− loops

  • S. Coito, F. Giacosa, arXiv:1712.00969

a Lagrangian density for a V → PP LψDi ¯

Di = igψD ¯ Dψµ 2

  • i
  • ∂µDi ¯

Di − ∂µ ¯ DiDi

  • Vertex decay width and amplitude

Γψ→Di ¯

Di(s) = ki(s, mDi)

8πs |Mψ→Di ¯

Di|2

|Mψ→Di ¯

Di|2 = g 2 ψD ¯ D

4 3k2

i (s, mDi)f 2 Λ (s)

Form-factor fΛ(qi) = e−qi

2/Λ2

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SLIDE 11

Building a propagator Gµν(p) = 1 p2 − m2

ψ + iε

  • − gµν + pµpν

m2

ψ

  • ∆µν(p) = Gµν(p) + Gµµ′(p)Πµ′ν′(p)Gν′ν(p) + · · · ,

Πµν(p) = g 2

ψD ¯ D

  • i

Πiµν(p, mDi) Π(s) = 1 3

  • −g µν + pµpν

p2

  • Πµν(p) = g 2

ψD ¯ D

  • i

Πi(s, mDi)

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SLIDE 12

∆(s) = 1 s − m2

ψ + Π(s)

For N channels Π(s) =

N

  • j
  • Ωj(s) + i√sΓj(s)
  • ,

Ω, Γ ∈ ℜ, Ωj(s, m1, m2) = PP π ∞

sth

√sΓj(s′, m1, m2) s′ − s ds′ The unitarized spectral function is given by dψ(E) = −2E π Im ∆(E) = 2E 2 π

  • j Γj(E 2)

[E 2 − m2

ψ + Re Π(E 2)]2 + [Im Π(E 2)]2

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SLIDE 13

The ψ(3770) cross section

3.74 3.76 3.78 3.80 2 4 6 8 E(GeV) σ(nb)

  • ⋆

⋆ ⋆ ⋆ ⋆ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗∗ ∗ ∗ ∗ D ¯ D

Data: BES PLB 668,263 (2008); BES PRL 97,121801 (2006) Fit parameters: mψ: 3773.05 ± 0.95 MeV Λ: 272.55 ± 1.17 MeV χ2/d.o.f - 0.86

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SLIDE 14

Pole trajectories

3.72 3.74 3.76 3.78 3.80

  • 0.03
  • 0.02
  • 0.01

ReE(GeV) ImE(GeV)

  • ⋄

⋄

  • 0.7g
  • g

⋄ 1.3g ↑ ↓

  • 3741.2 − i18.5 MeV

3776.8 − i12.3 MeV

  • 3773.5 − i5.5 MeV

⋄ 3741.0 − i9.5 MeV 3784.9 − i17.2 MeV

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SLIDE 15

The ψ(4040) and the Y (4008)

  • cf. poster of M. Piotrowska (collab. with F. Giacosa and P. Kovacs)

Total spectral function with channels DD, DD∗, and D∗D∗

3.7 3.8 3.9 4.0 4.1 4.2 4.3 2 4 6 8 m GeV dm GeV1 BreitWigner Our model

Poles around: ψ(4040) : 4053 − i39 MeV Y (4008) : 3934 − i30 MeV

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SLIDE 16

The ψ(4160) and the Y (4260)...

  • cf. S. Coito, PoS Hadron2017 (2018) 030.

Coupled-channels (through the loops): below ψ(4160) threshold: DD DD∗ D∗D∗ DsDs DsD∗

s

above ψ(4160) threshold: D∗

s D∗ s DD1 DD′ 1 (not seen yet)

suppressed channel, but seen in the experiment: J/ψf0(980)

... and the ψ(4415) and Y (4390)

below ψ(4415) threshold: DD DD∗ D∗D∗ DsDs DsD∗

s D∗ s D∗ s DD1 DD′ 1

above ψ(4415) threshold: D∗D1 D∗D′

1 DsDs1 DsD′ s1

suppressed channel, but see in the experiment: J/ψf0(980)

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SLIDE 17

Interactions: V → PP, PV , VV , PA, VS PP : LI = igVPP ψµ

  • ∂µD1 ¯

D2 − ∂µ ¯ D2D1

  • + h.c.

PV : LI = igVPV ˜ ΨµνD ¯ D∗µν + h.c. , ˜ Ψµν = 1 2ǫµναβΨαβ , Ψαβ = ∂αψβ − ∂βψα, D∗µν = ∂µD∗ν − ∂νD∗µ VV : LI = i 2gVVV Ψµν

  • D∗µ

1

¯ D∗ν

2 −D∗ν 1

¯ D∗µ

2

  • +h.c., Ψµν = ∂µψν−∂νψµ .

PA : LI = igψDD1ψµD ¯ Dµ

1 + h.c.

SV : LI = gψµJ/ψµf0(980)

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SLIDE 18

Line-Shape for the ψ(4160)

4.10 4.20 4.30 2 4 6 8 E(GeV) ds(GeV−1)

5 channels: DD DD∗ D∗D∗ DsDs DsD∗

s

slide-19
SLIDE 19

4.10 4.20 4.30 2 4 6 8 10 E(GeV) dS(GeV−1)

5 channels, +D∗

s D∗ s , and +DD1 DD′ 1 (with an arbitrary coupling)

slide-20
SLIDE 20

4.10 4.20 4.30 0.05 0.10 0.15 E(GeV) σ(nb)

  • •
  • Channel J/ψf 0(980) compared to J/ψππ data
slide-21
SLIDE 21

Summary and Conclusions

  • The ψ and Y spectra above D ¯

D threshold are very intriguing as there is a big quantum mixing

  • Loops ⇔ coupled-channels are important and simple Breit-Wigner fits

are too naive

  • We show results of an effective Lagrangian approach for the ψ(3770),

ψ(4040) and ψ(4160) interfering with their respective open-decay channels.

  • In the presented results the Y (4260) do not emerge as a companion

pole of the ψ(4160), but a full study of the interferences including closed-channels and mixing among the different ψ is still undergoing. ∴