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

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Charmonium Spectroscopy on the Lattice Gunnar Bali Universitt Regensburg Charm 2009 Leimen, 20 May 2009 Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook The new Charmonia Lattice spectroscopy

SLIDE 1

Charmonium Spectroscopy on the Lattice

Gunnar Bali

Universität Regensburg

Charm 2009 Leimen, 20 May 2009

SLIDE 2

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

SLIDE 3

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 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 *

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) Charmonium Spectroscopy on the Lattice 3 / 21

SLIDE 4

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

SLIDE 5

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

Hybrid mesons

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

mc + V (r)

Lattice:

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

Σg

hybrid potential:

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 5 / 21

SLIDE 6

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

Input: LQCD = −

1 16παL FF + ¯

qf (D / + mf )qf mlatt

= mphys

− → a mlatt

π /mlatt N

= mphys

/mphys

− → 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

→ mphys

: chiral perturbation theory (χPT) but mlatt

must be sufficiently small to start with. (mlatt

= mphys

has only very recently been realized.)

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 6 / 21

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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, c¯ qq¯ c, no decay !)

12 11 10 9 8 7 6 5 4 exotic 3++ 3+- 3-- 2-- 2-+ 2++ 1++ 0++ 1+- 1-- 0-+ JPC 5 4.5 4 3.5 3 2.5 2 1.5 n.a.

3F3 1F3 3D3 3D2 1D2 3P2 3P1 3P0 1P1 3S1 1S0 2S+1LJ

m r0 m/GeV DD** DD glueballs experiment CP-PACS Columbia hybrids

X(3943) ψ(3770) Y(4260) Y(4350) ψ(4160) ψ(4040) ψ(4415) Y(3940) Z(3930) X(3872)

1-+ ηc J/Ψ hc χc0 χc1 χc2 0+- 2+- 0+-

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 7 / 21

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Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

First result with sea quarks 04

FNAL+MILC (nf

≈ 2 + 1) a−1 ≈ 1.1, 1.6, 2.3 GeV

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 8 / 21

SLIDE 9

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

C Ehmann, GB (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)

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 9 / 21

SLIDE 10

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

Lattice operators

A1 → J = 0, 4, · · · A2 → J = 3, 6, · · · E → J = 2, 4, · · · T1 → J = 1, 3, 4, · · · T2 → J = 2, 3, 4, · · ·

name Oh repr. JPC state

perator

a0 A1 0++ χc0 1 π A1 0−+ ηc γ5 ρ T1 1−− J/ψ γi a1 T1 1++ χc1 γ5γi b1 T1 1+− hc γiγj π × ∇ T1 1+− hc γ5∇i a0 × ∇ T1 1−− J/ψ ∇i a′

0 × ∇

T1 1−+

exotic

γ4∇i (ρ × ∇)A1 A1 0++ χc0 γi∇i (ρ × ∇)T1 T1 1++ χc1 ǫĳkγj∇k (ρ × ∇)T2 T2 2++ χc2 sĳkγj∇k (a1 × ∇)A1 A1 0−−

exotic

sĳkγj∇k (a1 × ∇)T2 T2 2−− γ5sĳkγj∇k (b1 × ∇)T1 T1 1−+

exotic

γ4γ5ǫĳkγj∇k a′

0 × D

T2 2+−

exotic

γ4Di (a1 × D)A2 A2 3++ γ5γiDi (a1 × D)T1 T1 1++ χc1 γ5sĳkγjDk (a1 × D)T2 T2 2++ γ5ǫĳkγjDk (b1 × D)A2 A2 3+− γ4γ5γiDi · · · · · · · · · · · · · · ·

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 10 / 21

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Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

J-assignment for PC = −− J Dudek et al.

3000 3500 4000 4500 5000

mass / MeV

A1 0, 4 ... T1 1, 3, 4 ... T2 2, 3, 4 ... E 2, 4 ... A2 3 ...

3108±2 3723±27 3856±10 4472±78 3862±24 3902±31 3899±36 3859±16 4598±42 4928±43 4813±42 4848±53 3844±19 4441±49 4721±40 4956±46 4899±84 5124±71 4803±42 6103±93

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 11 / 21

SLIDE 12

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

SLIDE 13

Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

S Choe et al (QCD-TARO 03): fine splitting ∆M = mJ/ψ − mηc (nF = 0)

Clo v er non-p ert. Clo v er Wilson Con tin uum Exp erimen t M (M eV ) 0.25 0.2 0.15 0.1 0.05 120 100 80 60 40 20 Clo v er non-p ert. Clo v er Wilson Con tin uum Exp erimen t a 2 (GeV 2 ) M (M eV ) 0.25 0.2 0.15 0.1 0.05 120 100 80 60 40 20

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 13 / 21

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Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

NRQCD: ∆M = 1 6m2

ψ|V4|ψ + · · · Leading order perturbation theory: V4(r) = 8πCFαsδ3(r). ∆M scale from r0 = 0.5 fm scale from 1P − 1S Columbia 72(2) MeV 83(??) MeV CP-PACS 73(1)(4) MeV 85(4)(6) MeV QCD-TARO 77(2)(6) MeV 89(??) MeV χQCD 88(4) MeV 121(6) MeV JLAB 97(6) MeV ??? JLAB (Dudek et al): mc ≈ 5 % too small ! χQCD (Tamhankar et al) + JLAB: only one lattice spacing a. χQCD: La < 0.9 fm → 1P − 1S underestimated ?

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 14 / 21

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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 mΩ, 310 MeV > mπ ≥ 165 MeV, Na ≈ 2.9 fm.

60 80 100 120 140 mJ / ψ - mηc[MeV] Experiment Nf=2+1,NP ν Nf=2,kinetic Nf=2,pole Nf=0,kinetic Nf=0,NP ν Nf=0,pole

∆M → 117 MeV as a → 0 ? “I = 0” vs. “I = 1” ???

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 15 / 21

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Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

Disconnected quark lines ? (nf = 0: P de Forcrand et al (QCD-TARO 04))

0.5 1.0 1.5 2.0 2.5 3.0 3.5

vector meson mass/GeV

−40 40 80 120

∆M/MeV

PS : mfull(t=1)−mcon(t=1) PS : mfull(t=2)−mcon(t=2)

∆M = m“η” − m“π”

η η η η

connected disconnected

t

Disconnected diagrams mη > mπ

mω − mη < mρ − mπ

C McNeile & C Michael 04: sign change for heavy quarks ?? L Levkova & C DeTar 08: ∆M ≈ 3 − 4 MeV (nf = 0). Obviously, disconnected diagrams are important, e.g.: ψ′(′) ↔ DD.

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 16 / 21

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Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

What about mixing with other I = 0 states? C Ehmann, GB: ηc ↔ η mixing (nf = 2): t 2 4 2 2

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 17 / 21

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Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

Mixing vs. no mixing:

1 2 3 4 5 6 7 8 9 10 t/a 0,5 1 1,5 2 2,5 3 ameff η η’ ηc

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 18 / 21

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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 0.2

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>

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 19 / 21

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Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

Coupled channel potential model for threshold effects ?

Many channels (DD, D∗D, DsDs, D∗D∗, · · · ) ⇒ many parameters!

“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.

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 20 / 21

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Outline The new charmonia Lattice spectroscopy Fine structure Disconnected diagrams Outlook

Outlook

First nf = 2 + 1 simulations near physical mπ at a−1 ≈ 2 GeV. First precision calculations of annihilation and mixing diagrams. The continuum limit is important, in particular for the fine structure. There will be a lot of progress in sub-threshold charmonium spectroscopy in the next two years. Calculation of forces between pairs of static-light mesons for different S and I is on its way, to qualitatively understand 4-quark binding. Study of c¯ c ↔ c¯ qq¯ c, initially for JPC = 1−−.

Gunnar Bali (Regensburg) Charmonium Spectroscopy on the Lattice 21 / 21