qqQ charmonium threshold states and QQq Q ¯ potentials Gunnar Bali Universität Regensburg QWG7 Fermilab, 18 May 2010
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II Lattice QCD Threshold charmonia Outlook I QQq baryonic potentials Outlook II Charmonium results from GB & Christian Ehmann, arXiv:0710.0256, arXiv:0903.2947, arXiv:0911.1238, in prep. QQq potentials from GB & Johannes Najjar, arXiv:0910.2824, in prep. Q ¯ qqQ potentials (not discussed): GB & Martin Hetzenegger, in prep. Gunnar Bali (Regensburg) qqQ and QQq 2 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II 1 Input: L QCD = − 16 πα L FF + ¯ q f ( D / + m f ) q f = m phys m latt − → a N N / m phys m latt π / m latt = m phys − → m u ≈ m d N N π · · · 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 PS = m phys has only very recently been realized.) π Gunnar Bali (Regensburg) qqQ and QQq 3 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II 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) qqQ and QQq 4 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II 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 0.5 hybrid potential: 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) qqQ and QQq 5 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II C Ehmann, GB 07 ( 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) qqQ and QQq 6 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II Two state potentials GB, H Neff, T Düssel, T Lippert, Z Prkacin, K Schilling 04/05 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) qqQ and QQq 7 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II Two state system: Eigenstates: | 1 � cos θ | QQ � + sin θ | BB � = | 2 � − sin θ | QQ � + cos θ | BB � = with B = Qq . √ n f Correlation matrix: √ n f − n f Gunnar Bali (Regensburg) qqQ and QQq 8 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II Mixing angle: BB content of the ground state 0.5 0.375 θ/π 0.25 a ≈ 0 . 083 fm 0.125 0 2 4 6 8 10 12 14 16 18 r/a Gunnar Bali (Regensburg) qqQ and QQq 9 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II Coupled channel potential model for threshold effects ? ∗ , · · · ) ⇒ many parameters! Many channels ( DD , D ∗ D , D s D s , D ∗ D However, very good to address qualitative questions: For what I , S and radial excitation do we get attraction/repulsion ? Are Z + s possible and/or likely ? “Direct” calculation of the spectrum ? We have to be able to resolve radial excitations! (remember e.g. the very dense 1 −− sector.) Required: large basis of test wavefunctions including c ¯ c , c ¯ qq ¯ c and cg ¯ c operators and good statistics. Gunnar Bali (Regensburg) qqQ and QQq 10 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II c ¯ c ↔ DD mixing (for n f = 2) GB, C Ehmann 09/10 : 2 2 _ 2 2 _ 4 + 4 ( c ¯ c annihilation diagrams negelected.) Gunnar Bali (Regensburg) qqQ and QQq 11 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II n f = 2, a − 1 ≈ 2 . 59 GeV, La ≈ 1 . 83 fm, m PS ≈ 290 MeV χ c1 ’ 5000 * D 1 D D 1 D 4500 ψ ’ M[MeV] * D D η c ’ 4000 χ c1 3500 J/ ψ η c 3000 -+ 1 -- 1 ++ 0 Gunnar Bali (Regensburg) qqQ and QQq 12 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II Eigenvector components of the J /ψ . Components of the D 1 D . 1 1 0,8 0,75 0,6 0,5 0,4 0,25 0,2 φ i (D 1 D ) φ i (J/ ψ) 0 0 -0,2 -0,25 (cc) l (cc) l -0,4 -0,5 (cc) n (cc) n (cu cu) l -0,6 (cu cu) l (cu cu) n -0,75 (cu cu) n -0,8 -1 -1 2 4 6 8 10 12 2 4 6 8 10 12 Gunnar Bali (Regensburg) qqQ and QQq 13 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II Components of the D ∗ D . Eigenvector components of the χ c 1 . 1 1 0,8 0,8 0,6 0,6 0,4 0,4 (cc) l 0,2 (cc) n 0,2 φ i ( χ c1 ) (cq cq) l * ) φ i (D 0 D 0 0 (cq cq) n -0,2 -0,2 (cc) l -0,4 -0,4 (cc) n -0,6 -0,6 (cq cq) l (cq cq) n -0,8 -0,8 -1 -1 2 4 6 8 10 12 2 4 6 8 10 12 Gunnar Bali (Regensburg) qqQ and QQq 14 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II Outlook I ∃ first simulations near the physical m π at a − 1 ≈ 2 GeV. ∃ first precision calculations of annihilation and mixing diagrams. Study of c ¯ c ↔ c ¯ qq ¯ c is well on its way. The continuum limit is important, in particular for the fine structure. There will be a lot of progress in charmonium spectroscopy below and above decay thresholds in the next years. Forces between pairs of static-light mesons for different S and I are being studied, to qualitatively understand 4-quark binding ( X ( 3872 ) , Z + ( 4430 ) etc.). Gunnar Bali (Regensburg) qqQ and QQq 15 / 24 Q ¯
Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II QQq : factorization Distance r between Q and Q in static-static-light baryon ( QQq ). In the limit r → 0 this becomes a Qq static-light meson. For small r , the factorization � − 1 exp − ∝ exp − 2 t should hold: V QQq ( r ) ≃ m Qq + 1 ( r ≪ Λ − 1 ) 2 V QQ ( r ) (NB: the 1 / m corrections to the static limit are different, even at r = 0.) Minimal string picture with QQ tension = 1 2 QQ string tension: ( r ≫ Λ − 1 ) V QQq ( r ) ≃ const + V QQ ( r ) Gunnar Bali (Regensburg) qqQ and QQq 16 / 24 Q ¯
Recommend
More recommend
