qqQ charmonium threshold states and QQq Q potentials Gunnar Bali - - PowerPoint PPT Presentation

Q¯ qqQ charmonium threshold states and QQq 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) Q¯ qqQ and QQq 2 / 24

Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

Input: LQCD = −

1 16παL FF + ¯

qf (D / + mf )qf mlatt

N

= mphys

N

− → a mlatt

π /mlatt N

= mphys

π

/mphys

N

− → mu ≈ md · · · Output: hadron masses, matrix elements, decay constants, etc... Extrapolations:

1 a → 0: functional form known. 2 L → ∞: harmless but often computationally expensive. 3 mlatt

q

→ mphys

q

: chiral perturbation theory (χPT) but mlatt

q

must be sufficiently small to start with. (mlatt

PS = mphys π

has only very recently been realized.)

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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 4.6 4.4 4.2 4.0 3.8 3.6 3.4 3.2 3.0 L = 2 L = 1 L = 0 m/GeV

ηc J/ψ ψ(2S) ψ(4040) ψ(4415) χc ψ(3770) ψ(4160) ηc(2S) hc Y(4260) X(3871/3875) X(3943) Y(3940) Z(3934) Y(4660) Y(4350) X(4160) DD DD* D*D* DD** DsDs DsDs

*

Ds

*Ds *

• Z+(4430)

standard ????? new detectors higher luminosity new channels: B decays γγ ψψ-production gg in p¯ p collisions. c¯ qq¯ c in c¯ c ? cg¯ c hybrids ?

Gunnar Bali (Regensburg) Q¯ qqQ and QQq 4 / 24

Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

Hybrid mesons

mc ≫ ΛQCD − → Adiabatic and non-relativistic approximations: Hψnlm = Enlψnlm , H = 2mc + p2

mc + V (r)

Lattice:

• 1.5
• 1
• 0.5

0.5 1 1.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 V(r)/GeV r/fm Σu

• Πu

Σg

+

hybrid potential:

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

C Ehmann, GB 07 (nf = 2, a−1 ≈ 1.73 GeV from mN)

3.0 3.5 4.0 4.5 5.0 5.5 0-+ 1-- 1+- 0++ 1++ 2++ 2-+ 2-- 3-- 3+- 3++ 1-+ 2+-

1S0 3S1 1P1 3P0 3P1 3P2 1D2 3D2 3D3 1F3 3F3

m/GeV lattice exotic DD** DD experiment

ηc ηc’ X(3943) X(4160) J/ψ ψ’ ψ(3770) ψ(4040) ψ(4160) ψ(4415) Y(4260) Y(4350) Y(4660) hc χc0 χc1 χc2 Z(3934) Y(3940) X(3872)

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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 0.2

• 0.2
• 0.4
• 0.6

1.6 1.4 1.2 1.0 0.8 [E(r) - 2 mB]/GeV r/fm nf = 2 + 1 2mB 2mBs state |1> state |2>

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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. Correlation matrix:

           

√nf √nf − nf

           

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

Mixing angle: BB content of the ground state 0.125 0.25 0.375 0.5 2 4 6 8 10 12 14 16 18

θ/π

r/a a ≈ 0.083 fm

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

Coupled channel potential model for threshold effects ?

Many channels (DD, D∗D, DsDs, D∗D

∗, · · · ) ⇒ many parameters!

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

• perators and good statistics.

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

c¯ c ↔ DD mixing (for nf = 2) GB, C Ehmann 09/10 :

2 2 2 2

_

+ 4 _ 4

(c¯ c annihilation diagrams negelected.)

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

nf = 2, a−1 ≈ 2.59 GeV, La ≈ 1.83 fm, mPS ≈ 290 MeV

• + 1
• - 1

++

3000 3500 4000 4500 5000 M[MeV] ηc ηc’ D1D

*

D1D ψ’ J/ψ D

*D

χc1’ χc1

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

Eigenvector components of the J/ψ.

2 4 6 8 10 12

• 1
• 0,75
• 0,5
• 0,25

0,25 0,5 0,75 1 φi(J/ψ) (cc)l (cc)n (cu cu)l (cu cu)n

Components of the D1D.

2 4 6 8 10 12

• 1
• 0,8
• 0,6
• 0,4
• 0,2

0,2 0,4 0,6 0,8 1 φi(D1D ) (cc)l (cc)n (cu cu)l (cu cu)n

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

Eigenvector components of the χc1.

2 4 6 8 10 12

• 1
• 0,8
• 0,6
• 0,4
• 0,2

0,2 0,4 0,6 0,8 1 φi(χc1) (cc)l (cc)n (cq cq)l (cq cq)n

Components of the D∗D.

2 4 6 8 10 12

• 1
• 0,8
• 0,6
• 0,4
• 0,2

0,2 0,4 0,6 0,8 1 φi(D0D

*)

(cc)l (cc)n (cq cq)l (cq cq)n

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

Outlook I

∃ first simulations near the physical mπ 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) Q¯ qqQ and QQq 15 / 24

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 exp

   −    ∝ exp    −

− 1 2

  

• 

    

t

should hold: VQQq(r) ≃ mQq + 1

2VQQ(r)

(r ≪ Λ−1) (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:

VQQq(r) ≃ const + VQQ(r) (r ≫ Λ−1)

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

How does the light quark see the two static quarks?

• Λ

−1

Q Q

r

Figure: This is the HQET picture for r ≪ Λ−1.

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

How does the light quark see the two static quarks?

r

Q Q

Λ

−1

Figure: r ≫ Λ: light quark is near static source.

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

How does the light quark see the two static quarks?

r

Q Q

−1

Λ

Figure: r ≫ Λ: light quark is in the centre.

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

Construction of the states

r = 0 r > 0 Wave Operator O′(3),O′

h

D′

∞h,D′ 4h

S γ5

1 2 +,G+ 1 1 2 g,G1g

P− 1

1 2 −,G− 1 1 2u,G1u

P+ γ1∆1 − γ2∆2 ⊕ cyclic

3 2 −,H− 3 2u , G2u 1 2 u ⊥, G1u

D− γ5(γ1∆1 − γ2∆2) ⊕ cyclic

3 2 +,H+ 3 2g , G2g 1 2g ⊥, G1g

D+ γ1∆2∆3 + γ2∆3∆1 + γ3∆1∆2

5 2 +,G+ 2 1 2g/5 2 g,G1g

F− γ5(γ1∆2∆3 + γ2∆3∆1 + γ3∆1∆2)

5 2 −,G− 2 1 2u/5 2 u, G1u

Table: ΓD Dirac structure.

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

r = 0: Regge trajectories

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

r > 0: overview

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

The degeneracy problem understood

Lattice with lighter mπ ≈ 430 MeV and a ≈ 0.08 fm P−(1/2u), P+,⊥(1/2u) and P+,(3/2u) fit results (one exponential).

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

QQq potentials in the γ5 ≡ 1

2g channel

Red, green and blue crosses are QQq potentials.

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

QQq potentials in the γ5 ≡ 1

2g channel

Orange triangles are the factorization mQq + 1

2VQQ(r).

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

QQq potentials in the γ5 ≡ 1

2g channel

Pink and light line are ground state points, shifted by the respective static- light energy splittings.

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

QQq potentials in the γ5 ≡ 1

2g channel

The red band is the Nambu-Goto expectation for the first gluonic hybrid excitation: E2 − E0 + GS, where En(r) = σGSr

• 1 +
• 2n − d−2

12

• π

σr2 .

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

The groundstate potentials in comparison

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Outline Lattice QCD Threshold charmonia Outlook I QQq potentials Outlook II

Outlook II

The HQET factorization applies to r ≪ Λ−1. The scale where this factorization breaks down depends on the state. Light quark excitations are more important than gluonic ones. Not shown: correlators with the light quark in the centre mostly have a better ground state overlaps → no evidence for Qq diquark formation. Ongoing: decreasing the light quark mass to increase Λ−1. See also the work on the ground state QQq potential by Yamamoto and Suganuma 08.

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