Excited light meson spectroscopy from lattice QCD · Excited light meson spectroscopy from lattice QCD With Jo ... ’, , Probe annihilation dynamics in QCD. 11 Isoscalars m s

Excited light meson spectroscopy from lattice QCD

With Jo Dudek, Robert Edwards, Mike Peardon, Bálint Joó, David Richards and the Hadron Spectrum Collaboration

Christopher Thomas, Jefferson Lab

[email protected]

PANIC11, MIT, Cambridge, MA, July 2011

Outline

1

• Introduction and motivation

• Excited isoscalar mesons

• Energy-dependent I=2 phase shift

• Summary and outlook

PR D83, 071504 (2011)PR D83, 111502 (2011)

Motivation

Upcoming experimental efforts in light meson sector (and charmonium)

2

GlueX and CLAS12 (JLab), BESIII, COMPASS, PANDA, ...

Motivation


Quark-antiquark pair:

Parity: P = (-1)(L+1)

Charge Conj Sym: C = (-1)(L+S)

JPC = 0- + , 0+ + , 1- - , 1+ + , 1+ - , 2- - , 2+ + , 2- +, …

L

L2S+1LJ

½½

J = L S

3


Probe low energy d.o.f. of QCD

Motivation



Parity: P = (-1)(L+1)


JPC = 0- + , 0+ + , 1- - , 1+ + , 1+ - , 2- - , 2+ + , 2- +, …

L

L2S+1LJ

Exotics (JPC = 1 - +, 2 + -, ...)? – can’t just be a pair

e.g. hybrids, multi-mesons

½½

J = L S

4


Probe low energy d.o.f. of QCD

Motivation



Parity: P = (-1)(L+1)


JPC = 0- + , 0+ + , 1- - , 1+ + , 1+ - , 2- - , 2+ + , 2- +, …

L

L2S+1LJ

Exotics (JPC = 1 - +, 2 + -, ...)? – can’t just be a pair

e.g. hybrids, multi-mesons

½½

J = L S

5


Motivation

Photoproduction at GlueX/CLAS12 (JLab @ 12 GeV)– systematic study of light mesons, particular interest in exotics

JLab

6

Motivation

Photoproduction at GlueX/CLAS12 (JLab @ 12 GeV)– systematic study of light mesons, particular interest in exotics

JLab

7

Use Lattice QCD to extract excited spectrum and photocouplings

8

Isoscalars

Isoscalars (I = 0) e.g. , ’, ,

9

Isoscalars

Isoscalars (I = 0) e.g. , ’, , Probe annihilation dynamics in QCD

10

Isoscalars

ms = mu = md [SU(3) sym]– eigenstates are octet, singlet


11

Isoscalars


ms ≠ mu = md – physical states are a mixture

‘Ideal mixing’


12

Isoscalars



‘Ideal mixing’

In general


13

Isoscalars



‘Ideal mixing’

Experimentally , (1--) and f2(1270), f2’(1525) (2++) – close to ‘ideal’

, ’ (0-+) – closer to octet-singlet

In general


14

Isoscalars



‘Ideal mixing’

Experimentally , (1--) and f2(1270), f2’(1525) (2++) – close to ‘ideal’

, ’ (0-+) – closer to octet-singlet

In general Can also mix with glueballs


Calculate energies and matrix elements (“overlaps”, Z’s) from correlation functions of meson interpolating fields

Spectroscopy on the lattice

15



16

Construct operators which only overlap with one spin in the continuum limit

Here up to 3 derivs and p = 0

definite JPC

‘Distillation’ technology for constructing on lattice PR D80 054506 (2009)



17

Construct operators which only overlap with one spin in the continuum limit

Here up to 3 derivs and p = 0

definite JPC

‘Distillation’ technology for constructing on lattice PR D80 054506 (2009)

Variational Method

18

Large basis of operators matrix of correlators

Generalised eigenvector problem:

Variational Method

19



Eigenvalues energies (t >> t0)

Variational Method

20



Eigenvalues energies

Also optimal linear combination of operators to overlap on to a state

Z(n) related to eigenvectors

(t >> t0)

Variational Method

21



Eigenvalues energies

Also optimal linear combination of operators to overlap on to a state

Z(n) related to eigenvectors

(t >> t0)

Var. method uses orthog of eigenvectors; don’t just rely on separating energies

22

Isoscalars in LQCD

Use variational method with large basis of operators

23

Isoscalars in LQCD


Basis doubled in size c.f. isovectors:

No glueball ops for now

24

Isoscalars in LQCD

Disconnected Wick contractionsq

q

q

q

q

q




JLab

25

Isoscalars in LQCD


q

q

q

q

q




Use GPUs for some parts of the computations

JLab

26

Isoscalars in LQCD


q

q

q

q

q




Use GPUs for some parts of the computations

Anisotropic lattices (as/at = 3.5), as 0.12 fm; 163 (2.0 fm)

Dynamical, Nf = 2+1, M 400 MeV

Lattice details in: PR D78, 054501; PR D79, 034502

27

Isoscalars

163 (Ls 2.0 fm)

PR D82, 034508 (2010)

Morningstar and Peardon PR D60, 034509 (1999)

PR D83, 111502 (2011)

28

Isoscalars

163 (Ls 2.0 fm)

PR D82, 034508 (2010)


PR D83, 111502 (2011)

29

Isoscalars

163 (Ls 2.0 fm)

First light isoscalar exotics in LQCD

PR D82, 034508 (2010)


PR D83, 111502 (2011)

30

Isoscalars

163 (Ls 2.0 fm)


PR D82, 034508 (2010)


PR D83, 111502 (2011)

S-wave

L

L½

½

J = L S

31

Isoscalars

163 (Ls 2.0 fm)


PR D82, 034508 (2010)


PR D83, 111502 (2011)

S-wave

L

L½

½

J = L S

- mass splitting = 21(5) MeV

32

Isoscalars

163 (Ls 2.0 fm)


PR D82, 034508 (2010)


PR D83, 111502 (2011)

S-wave

P-wave

L

L½

½

J = L S


33

Isoscalars

163 (Ls 2.0 fm)


PR D82, 034508 (2010)


PR D83, 111502 (2011)

S-wave

P-wave

D-wave

L

L½

½

J = L S


34

Isoscalars

163 (Ls 2.0 fm)


PR D82, 034508 (2010)


PR D83, 111502 (2011)

S-wave

P-wave

D-wave

Large overlap with op [Di, Dj] F

L

L½

½

J = L S


35

Isoscalars

163 (Ls 2.0 fm)


PR D82, 034508 (2010)


PR D83, 111502 (2011)More interpretation of isovector and isoscalar results:“lowest hybrid meson supermultiplet” arXiv:1106.5515

S-wave

P-wave

D-wave

Large overlap with op [Di, Dj] F

L

L½

½

J = L S


Isoscalars

PR D82, 034508 (2010)


PR D83, 111502 (2011)

36

163 (Ls 2.0 fm)

Isoscalars

PR D82, 034508 (2010)


PR D83, 111502 (2011)

37

Most close to ideally mixed

163 (Ls 2.0 fm)

Isoscalars

PR D82, 034508 (2010)


PR D83, 111502 (2011)

38

Most close to ideally mixed

But - ’ = 42(1) , f1 – f1’ = 31(2) , 1-+ exotics

163 (Ls 2.0 fm)

What about multi-particle states?

39


40

Continuous spectrum

Infinite Volume

2m E

Infinite Volume


41

Cubic box with periodic boundary conditions

Continuous spectrum

Infinite Volume

2m E

2m E

Finite Volume

Quantised momenta

Discrete spectrum

Infinite Volume

Finite Volume


42

Boxes – extracted meson levels (I=1)

Nf = 3, M 700 MeV


43


Dashed lines – non-interacting two-meson levels

Nf = 3, M 700 MeV


44


No clear evidence for two-meson states

Dashed lines – non-interacting two-meson levels

Need ops that ‘look like’ two-mesons

Nf = 3, M 700 MeV

Scattering in a box

45

Euclidean time: can’t directly study dynamical properties like widths

Lüscher: (elastic) energy shifts in finite volume phase shift

Scattering in a box

46

2m E



Scattering in a box

47

Map out phase shift resonance parameters (mass, width)2m E



Extract phase shift at discrete E

I=2 spectrum

48

M 400 MeV

PR D83, 071504 (2011)

+ similar diagrams

‘Distillation’ for efficient computation

PR D80 054506 (2009)

I=2 spectrum

49

M 400 MeV

PR D83, 071504 (2011)

+ similar diagrams


PR D80 054506 (2009)

I=2 spectrum

50

M 400 MeV

PR D83, 071504 (2011)

+ similar diagrams


PR D80 054506 (2009)

I=2 spectrum

51

M 400 MeV

PR D83, 071504 (2011)

I=2 phase shift

52

N N’PR D83, 071504 (2011)

I=2 phase shift

53

N N’PR D83, 071504 (2011)

I=2 scattering length

54PR D83, 071504 (2011)

Summary and Outlook

55

• Extensive isoscalar meson spectrum

• Exotics and non-exotic hybrids, high spin, excited states

• Flavour mixing angles

• Multi-meson operators – I=2 phase shift mapped out

Summary

Summary and Outlook

56

• Extensive isoscalar meson spectrum

• Exotics and non-exotic hybrids, high spin, excited states

• Flavour mixing angles

• Multi-meson operators – I=2 phase shift mapped out

Summary

• Include glueball operators; A1++ (0++) channel

• Other scattering channels – map out resonances

• Lighter pion masses, larger volumes, ...

Outlook

57

Extra Slides

58

59

Prin. Corr. Meff

t = 3

PR D83, 111502 (2011)

60

Flavour Mixings

Determine mixing of physical states by looking at overlaps

61

Mixing AnglePR D83, 111502 (2011)

62

CorrelatorsPR D83, 111502 (2011)

63

Documents

Excited light meson spectroscopy from lattice QCD · Excited light meson spectroscopy from lattice QCD With Jo ... ’, , Probe annihilation dynamics in QCD. 11 Isoscalars m s