Charmonium Spectroscopy on the Lattice Gunnar Bali Universitt - PowerPoint PPT Presentation

Charmonium Spectroscopy on the Lattice Gunnar Bali Universität Regensburg Charm 2009 Leimen, 20 May 2009

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook The new Charmonia Lattice spectroscopy Fine structure Disconnected quark lines Outlook Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 2 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook 1974 – 1977: 10 c ¯ c resonances, 1978 – 2001: 0 c ¯ c ’s 2002 – 2008: ≤ 12 new c ¯ c ’s found by BaBar, Belle, CLEO-c, CDF, D0 new detectors 4.6 Y(4660) standard ψ (4415) ????? - 4.4 higher luminosity Z + (4430) DD ** Y(4350) - - 4.2 Y(4260) new channels: * D s * D s * D s D s X(4160) ψ (4160) - - 4.0 B decays ψ (4040) Z(3934) D s D s D * D * Y(3940) - X(3943) m/GeV 3.8 DD * X(3871/3875) γγ - ψ (3770) DD ψψ -production 3.6 ψ (2S) η c (2S) h c χ c gg in p ¯ p collisions. 3.4 3.2 c ¯ qq ¯ c in c ¯ c ? J/ ψ 3.0 η c cg ¯ c hybrids ? L = 0 L = 1 L = 2 Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 3 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook Possible QCD phase diagram: diquarks ? Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 4 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook Hybrid mesons m c ≫ Λ QCD − → Adiabatic and non-relativistic approximations: H = 2 m c + p 2 H ψ nlm = E nl ψ nlm , m c + V ( r ) 1.5 1 hybrid potential: 0.5 V(r)/GeV 0 Lattice: -0.5 - Σ u Π u -1 + Σ g -1.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 r/fm Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 5 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook 1 Input: L QCD = − 16 πα L FF + ¯ q f ( D / + m f ) q f = m phys m latt − → a N N m latt π / m latt = m phys / m phys − → m u ≈ m d N π N · · · Output: hadron masses, matrix elements, decay constants, etc... Extrapolations: 1 a → 0: functional form known. 2 L → ∞ : harmless but often computationally expensive. → m phys 3 m latt : chiral perturbation theory ( χ PT) but m latt must be q q q sufficiently small to start with. ( m latt = m phys has only very recently been realized.) π π Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 6 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook Quenched Lattice: glueballs, charmonia and hybrids (No “disconnected diagrams” and no sea quarks → no mixing G , c ¯ c , no decay !) c , c ¯ qq ¯ 2S+1 L J 1 S 0 3 S 1 1 P 1 3 P 0 3 P 1 3 P 2 1 D 2 3 D 2 3 D 3 1 F 3 3 F 3 n.a. 5 0 +- 12 0 +- 4.5 1 -+ ψ (4415) 11 Y(4350) Y(4260) ψ (4160) 2 +- 4 ψ (4040) 10 Y(3940) X(3943) Z(3930) ψ (3770) X(3872) 9 3.5 χ c 1 χ c 2 h c m/GeV χ c 0 m r 0 8 3 η c J/ Ψ 7 experiment DD ** 2.5 6 DD CP-PACS Columbia 2 5 hybrids glueballs 4 1.5 J PC 0 -+ 1 -- 1 +- 0 ++ 1 ++ 2 ++ 2 -+ 2 -- 3 -- 3 +- 3 ++ exotic Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 7 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook ? First result with sea quarks 04 FNAL+MILC ( n f ≈ 2 + 1) a − 1 ≈ 1 . 1 , 1 . 6 , 2 . 3 GeV Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 8 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook C Ehmann, GB ( n f = 2, a − 1 ≈ 1 . 73 GeV from m N ) 1 S 0 3 S 1 1 P 1 3 P 0 3 P 1 3 P 2 1 D 2 3 D 2 3 D 3 1 F 3 3 F 3 5.5 5.0 Y(4660) 4.5 ψ (4415) Y(4350) m/GeV Y(4260) ψ (4160) X(4160) 4.0 ψ (4040) Y(3940) X(3943) Z(3934) ψ (3770) X(3872) ψ ’ χ c 2 η c ’ h c χ c 1 3.5 χ c 0 lattice exotic DD ** J/ ψ 3.0 DD η c experiment 0 -+ 1 -- 1 +- 0 ++ 1 ++ 2 ++ 2 -+ 2 -- 3 -- 3 +- 3 ++ 1 -+ 2 +- Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 9 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook J PC name O h repr. state operator 0 ++ a 0 A 1 χ c 0 1 0 − + π A 1 η c γ 5 ρ T 1 1 −− J /ψ γ i Lattice operators 1 ++ χ c 1 γ 5 γ i a 1 T 1 1 + − b 1 T 1 h c γ i γ j 1 + − π × ∇ γ 5 ∇ i T 1 h c a 0 × ∇ T 1 1 −− J /ψ ∇ i A 1 → J = 0 , 4 , · · · 1 − + a ′ γ 4 ∇ i 0 × ∇ T 1 exotic 0 ++ ( ρ × ∇ ) A 1 A 1 χ c 0 γ i ∇ i → J = 3 , 6 , · · · A 2 1 ++ ( ρ × ∇ ) T 1 χ c 1 ǫ ijk γ j ∇ k T 1 2 ++ ( ρ × ∇ ) T 2 T 2 χ c 2 s ijk γ j ∇ k E → J = 2 , 4 , · · · ( a 1 × ∇ ) A 1 0 −− s ijk γ j ∇ k A 1 exotic T 1 → J = 1 , 3 , 4 , · · · ( a 1 × ∇ ) T 2 T 2 2 −− γ 5 s ijk γ j ∇ k 1 − + ( b 1 × ∇ ) T 1 γ 4 γ 5 ǫ ijk γ j ∇ k T 1 exotic T 2 → J = 2 , 3 , 4 , · · · 2 + − a ′ 0 × D T 2 γ 4 D i exotic 3 ++ ( a 1 × D ) A 2 γ 5 γ i D i A 2 1 ++ ( a 1 × D ) T 1 T 1 χ c 1 γ 5 s ijk γ j D k 2 ++ ( a 1 × D ) T 2 T 2 γ 5 ǫ ijk γ j D k 3 + − ( b 1 × D ) A 2 A 2 γ 4 γ 5 γ i D i · · · · · · · · · · · · · · · Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 10 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook J -assignment for PC = −− J Dudek et al. 5124±71 6103±93 4956±46 5000 4899±84 4928±43 4803±42 4848±53 4721±40 4813±42 4472±78 4598±42 4500 mass / MeV 4441±49 4000 3899±36 3856±10 3902±31 3844±19 3862±24 3859±16 3723±27 3500 3108±2 3000 A1 T1 T2 E A2 0, 4 ... 1, 3, 4 ... 2, 3, 4 ... 2, 4 ... 3 ... Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 11 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook Wavefunctions after variational optimization (Coulomb gauge). CE, GB S1 2S 3S Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 12 / 21

Con tin uum 120 Exp erimen t Wilson 100 Clo v er Clo v er non-p ert. 80 � M ( M eV ) 60 40 20 0 0 0.05 0.1 0.15 0.2 0.25 Con tin uum 120 Exp erimen t Wilson 100 Clo v er Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook Clo v er non-p ert. 80 � M S Choe et al (QCD-TARO 03) : fine splitting ∆ M = m J /ψ − m η c ( n F = 0) ( M eV ) 60 40 20 0 0 0.05 0.1 0.15 0.2 0.25 2 � 2 a ( GeV ) Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 13 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook 1 NRQCD: ∆ M = � ψ | V 4 | ψ � + · · · 6 m 2 c Leading order perturbation theory: V 4 ( r ) = 8 π C F α s δ 3 ( r ) . ∆ M scale from r 0 = 0 . 5 fm scale from 1 P − 1 S Columbia 72(2) MeV 83(??) MeV CP-PACS 73(1)(4) MeV 85(4)(6) MeV QCD-TARO 77(2)(6) MeV 89(??) MeV χ QCD 88(4) MeV 121(6) MeV JLAB 97(6) MeV ??? JLAB (Dudek et al): m c ≈ 5 % too small ! χ QCD (Tamhankar et al) + JLAB: only one lattice spacing a . χ QCD: La < 0 . 9 fm → 1 P − 1 S underestimated ? Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 14 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook Y Namekawa et al (PACS-CS, arXiv:0810.2364) a − 1 ≈ 2 . 2 GeV from m Ω , 310 MeV > m π ≥ 165 MeV, Na ≈ 2 . 9 fm. Experiment N f =2+1 ,NP ν N f =2 ,kinetic N f =2 ,pole N f =0 ,kinetic N f =0 ,NP ν N f =0 ,pole 60 80 100 120 140 m J / ψ - m η c [MeV] ∆ M → 117 MeV as a → 0 ? “ I = 0” vs. “ I = 1” ??? Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 15 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook Disconnected quark lines ? ( n f = 0: P de Forcrand et al (QCD-TARO 04) ) 120 PS : m full (t=1)−m con (t=1) PS : m full (t=2)−m con (t=2) ∆ M = m “ η ” − m “ π ” 80 ∆ M/MeV η η 40 disconnected η η connected 0 t −40 0.5 1.0 1.5 2.0 2.5 3.0 3.5 vector meson mass/GeV Disconnected diagrams � m η > m π m ω − m η < m ρ − m π � C McNeile & C Michael 04: sign change for heavy quarks ?? L Levkova & C DeTar 08: ∆ M ≈ 3 − 4 MeV ( n f = 0). Obviously, disconnected diagrams are important, e.g.: ψ ′ ( ′ ) ↔ DD . Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 16 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook What about mixing with other I = 0 states? C Ehmann, GB: η c ↔ η mixing ( n f = 2): 2 2 4 2 t Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 17 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook Mixing vs. no mixing: 3 η η ’ η c 2,5 2 am eff 1,5 1 0,5 0 7 0 1 2 3 4 5 6 8 9 10 t/a Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 18 / 21

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook Two state potentials GB, H Neff, T Düssel, T Lippert, Z Prkacin, K Schilling 0.6 0.4 [E(r) - 2 m B ]/GeV 0.2 2m B s 0 2m B -0.2 state |1> -0.4 state |2> n f = 2 + 1 -0.6 0.8 1.0 1.2 1.4 1.6 r/fm Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 19 / 21