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

“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: 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] open-charm axial mesons van Beveren, Rupp, PRL 91 , 012003 (2003) charmonium scalar Gamermann, Oset, Strottman, and Vacas, PRD 76 , 074016 (2007)

Within similar models to the one we present here a 0 (980) Wolkanowski, Giacosa, Rischke, PRD 93 , 014002 (2016) K ∗ 0 (800) Wolkanowski, So� ltysiak, Giacosa, NPB 909 , 418 (2016) 2.5 2.0 � � m � � GeV � 1 � 1.5 1.0 d K 0 0.5 0.0 0.8 1.0 1.2 1.4 1.6 1.8 2.0 m � GeV � K π

Concerning the Y (4260) A signal that has 1st been detected in 40 40 40 40 2 2 2 2 Events / 20 MeV/c Events / 20 MeV/c Events / 20 MeV/c Events / 20 MeV/c 4 10 3 10 30 30 30 30 2 10 10 1 3.6 3.8 4 4.2 4.4 4.6 4.8 5 20 20 20 20 10 10 10 10 0 0 0 0 3.8 3.8 3.8 3.8 4 4 4 4 4.2 4.2 4.2 4.2 4.4 4.4 4.4 4.4 4.6 4.6 4.6 4.6 4.8 4.8 4.8 4.8 5 5 5 5 - - - - 2 2 2 2 m( m( m( m( + + + + J/ J/ J/ J/ ) (GeV/c ) (GeV/c ) (GeV/c ) (GeV/c ) ) ) ) π π π π π π π π ψ ψ ψ ψ PRL 95 ,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!

There is the idea that such enhancement might not be a true resonance D ∗ s D ∗ s X-sect(events/20 MeV/c 2 ) (a) 80 • 60 • • • 40 • • • • • • • • • • • • • • • • • • 20 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 4.0 4.5 5.0 5.5 m π + π − J/ψ (GeV) van Beveren, Rupp, PRL 105 , 102001 (2010) van Beveren, Rupp, PRD 79 , 111501(R) (2009)

D s D s , D ∗ D ∗ , D s D ∗ s , D ∗ s D ∗ s , DD 1 , D ∗ D 1 , D s D 1 s σ (pb) h c π + π − 200 ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ 100 ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ 0 ⋆ ⋆⋆⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ σ (pb) J/ψπ + π − • 100 • • • • • • • • • • • • • • • 50 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • ••••• • • • • • • • • • • • • • • • • • • • • • • • • 0 • • • 4.0 4.2 4.4 4.6 E (GeV) ψ (4040), ψ (4160), ψ (4415) Data: BESIII PRL 118 ,092001(2017); PRL 118 ,092002(2017)

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)

On the other hand, the determination of the ψ masses is not always easy to disentagle... ψ (3770), ψ (4040), ψ (4160), ψ (4415) σ (nb) (a) 5 (a) 0.5 0 0 (b) (b) 5 0.5 0 0 10 (c) (c) 1 0 0 3.7 3.8 3.9 4 3.8 4 4.2 4.4 4.6 4.8 5 – ), GeV/c 2 M(D D BELLE, PRD 77 ,011103(R)(2008) e + e − → D ¯ D

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

The case of the ψ (3770) with D 0 ¯ D 0 and D + D − loops S. Coito, F. Giacosa, arXiv:1712.00969 a Lagrangian density for a V → PP 2 � D i − ∂ µ ¯ � � ∂ µ D i ¯ L ψ D i ¯ D i = ig ψ D ¯ D ψ µ D i D i i Vertex decay width and amplitude D i ( s ) = k i ( s , m D i ) D i | 2 Γ ψ → D i ¯ |M ψ → D i ¯ 8 π s 4 D i | 2 = g 2 3 k 2 i ( s , m D i ) f 2 |M ψ → D i ¯ Λ ( s ) ψ D ¯ D Form-factor 2 / Λ 2 f Λ ( q i ) = e − q i

Building a propagator 1 − g µν + p µ p ν � � G µν ( p ) = p 2 − m 2 ψ + i ε m 2 ψ ∆ µν ( p ) = G µν ( p ) + G µµ ′ ( p )Π µ ′ ν ′ ( p ) G ν ′ ν ( p ) + · · · , � Π µν ( p ) = g 2 Π i µν ( p , m D i ) ψ D ¯ D i − g µν + p µ p ν Π( s ) = 1 � � � Π µν ( p ) = g 2 Π i ( s , m D i ) ψ D ¯ p 2 D 3 i

1 ∆( s ) = s − m 2 ψ + Π( s ) For N channels N Ω j ( s ) + i √ s Γ j ( s ) � � � Π( s ) = , Ω , Γ ∈ ℜ , j √ s Γ j ( s ′ , m 1 , m 2 ) � ∞ Ω j ( s , m 1 , m 2 ) = PP d s ′ s ′ − s π s th The unitarized spectral function is given by d ψ ( E ) = − 2 E π Im ∆( E ) � j Γ j ( E 2 ) = 2 E 2 [ E 2 − m 2 ψ + Re Π( E 2 )] 2 + [Im Π( E 2 )] 2 π

The ψ (3770) cross section σ (nb) 8 D ¯ D ∗ ⋆ ∗ ∗∗ ••• ∗ 6 ∗ ∗ ∗ ••• • ∗ •• 4 ∗ • ∗ ∗ ⋆ ∗ ⋆ • • 2 • • ∗ ⋆ ⋆ 3.74 3.76 3.78 3.80 E (GeV) Data: BES PLB 668 ,263 (2008); BES PRL 97 ,121801 (2006) Fit parameters: m ψ : 3773 . 05 ± 0 . 95 MeV Λ: 272 . 55 ± 1 . 17 MeV χ 2 / d . o . f - 0 . 86

Pole trajectories Re E (GeV) 3.72 3.74 3.76 3.78 3.80 ↓ ◦ ⋄ -0.01 • ↑ ⋄ • -0.02 Im E (GeV) ◦ 0 . 7 g g • -0.03 ⋄ 1 . 3 g • 3741 . 2 − i 18 . 5 MeV 3776 . 8 − i 12 . 3 MeV ◦ - 3773 . 5 − i 5 . 5 MeV ⋄ 3741 . 0 − i 9 . 5 MeV 3784 . 9 − i 17 . 2 MeV

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 ∗ 8 Our model Breit � Wigner 6 d � m � � GeV � 1 � 4 2 0 3.7 3.8 3.9 4.0 4.1 4.2 4.3 m � GeV � Poles around: ψ (4040) : 4053 − i 39 MeV Y (4008) : 3934 − i 30 MeV

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 ∗ D s D s D s D ∗ s above ψ (4160) threshold: D ∗ s D ∗ s DD 1 DD ′ 1 (not seen yet) suppressed channel, but seen in the experiment: J /ψ f 0 (980) ... and the ψ (4415) and Y (4390) below ψ (4415) threshold: DD DD ∗ D ∗ D ∗ D s D s D s D ∗ s D ∗ s D ∗ s DD 1 DD ′ 1 above ψ (4415) threshold: D ∗ D 1 D ∗ D ′ 1 D s D s 1 D s D ′ s 1 suppressed channel, but see in the experiment: J /ψ f 0 (980)

Interactions: V → PP , PV , VV , PA , VS � D 2 − ∂ µ ¯ � ∂ µ D 1 ¯ PP : L I = ig VPP ψ µ D 2 D 1 + h . c . D ∗ µν + h . c . , PV : L I = ig VPV ˜ Ψ µν D ¯ Ψ µν = 1 2 ǫ µναβ Ψ αβ , Ψ αβ = ∂ α ψ β − ∂ β ψ α , D ∗ µν = ∂ µ D ∗ ν − ∂ ν D ∗ µ ˜ VV : L I = i � � D ∗ µ ¯ D ∗ µ ¯ D ∗ ν 2 − D ∗ ν 2 g VVV Ψ µν + h . c ., Ψ µν = ∂ µ ψ ν − ∂ ν ψ µ . 1 1 2 PA : L I = ig ψ DD 1 ψ µ D ¯ D µ 1 + h . c . SV : L I = g ψ µ J /ψ µ f 0 (980)

Line-Shape for the ψ (4160) d s (GeV − 1 ) 8 6 4 2 4.10 4.20 4.30 E (GeV) 5 channels: DD DD ∗ D ∗ D ∗ D s D s D s D ∗ s

d S (GeV − 1 ) 10 8 6 4 2 4.10 4.20 4.30 E (GeV) 5 channels, + D ∗ s D ∗ s , and + DD 1 DD ′ 1 (with an arbitrary coupling)

0.15 σ (nb) • 0.10 • • • • • • • • • • • • • • • 0.05 • • • • • •• • • • • •• • • • • • • • • • • • • •• ••••••• • • • • • • • • • • • 4.10 4.20 4.30 E (GeV) Channel J /ψ f 0(980) compared to J /ψππ data

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. ∴