Precision Charmed Meson Spectroscopy and Decay Constants

from Chiral Fermions

• Overlap Fermion on 2+1 flavor Domain Wall Fermion

Configurations• Charmonium and Charmed-strange Meson Spectrum and fDs

χQCD Collaboration: A. Alexandru, S.J. Dong, T. Draper, T. Doi, I. Horvath, B. Joo, F.

Lee, A. Li, KFL, R. Lewis, N. Mathur, X. Meng, T. Streuer, H. Thacker, and J.B. Zhang

YITP, Feb. 5, 2010

fD and fDs

Some desirable features:

– O(a2) error are small (e.g. spectrum).– O(m2a2) errors are small (dispersion relation, hyperfine

splitting) can include charm quark– The effective propagator is – Dc = D/(1 – D/2) is chirally symmetric, i.e. {γ5, Dc} = 0.– Dc + m is like in the continuum formalism. – Multi-mass algorithm (30 masses)– Renormalization is relatively simple (e.g. with chiral Ward

identity).

Undesirable feature:

– Numerically intensive (can be tamed with eigenmode deflation)

Overlap Fermion

1121 )()()1( maDmDD c

2+1 Flavor DWF Configurations(RBC and UKQCD)

163 x 32 x 16, a-1 =1.73 GeV (a = 0.114 fm), ml a=0.01, 0.02, 0.03, ms a=0.04

243 x 64 x 16, a-1 =1.73 GeV (a = 0.114 fm), ml a=0.005, 0.01, 0.02, 0.03, ms a=0.04

323 x 64 x 16, a-1 =2.42 GeV (a = 0.085 fm), ml a=0.004, 0.006, 0.008, ms a=0.03

Overlap on 2+1 Flavor DWF configurations with HYP SmearingMixed actionFor chirally symmetric valence, it is like partial quenching with one extra parameter in valence-sea mass (Chen, O’Connell, Walker-Loud, arXiv:0706.0035)

1 2 1 2

1 2 1 2

2

2 2

2 2

( ),

( ) ,

( ) ,

v v v v

vs v s mix

s s s s sea

sea res

m B m m

m B m m a

m B m m a

m

Determination of ρ (243 x 64 lattice) from Hyperfine Splitting

ρ=1.62 ρ=1.50

Overlap with Deflation

, , 5 ,1

*5 5

1, , ,

, 5 ,, * *

1

( , ) (1 ) | |

(0, ) | | ; (0, ) | |

( , )

|

where,

Therefore,

where,

a

| | |

(1 / 2) (1 / 2)

X =

d

( )

n

X

nHL R L R L R

i

i i

H LL R L R L R

nL R L RL

L Ri i i i i

H HL R

D m X i i

D i i D i i

X D m X

i i i iX

m m

X

except for the zero mod s.(X ) eL LL RX

Speed up with deflation and HYP smearing

No critical slowing downCan calculate for any mass except zeroMulti-mass inversion (30 masses)

16^3 x 32 24^3 x 64 32^3 x 64

w/o D D D+S res w/o D D D+S w/o D D D+S

lowmode 0 200 200 10-8 0 200 200 0 400 400

Inner iter 340 321 108 10-11 344 341 107 309 281 101

Outer iter 627 72 85 10-8 2931 147 184 4028 132 156

Overhead 5 pro 5 pro 6pro

speedup 23 51 79

5 5 5 221

( )(0, ) 1 1 1( )

nW i

Wi W iW

H bD HH cH

163 x 32 243 x 64

DS Spectrum

323 x 64, mla = 0.006, a = 0.0814 fmS.J. Dong talk

H.F. 119.4 (13) MeVm

Hyperfine Splitting of Charmonium (50 config.)

Expt: 116.5(1) MeV

2 2 22 2 2

2 2 2 2

1 2

1 3 1 1 3 log ( ) log 32 3

+ ( ) ( )

sv vvcv sv vv ss

cv

v s

g m mf m m mfm

c m c m

Sharpe and Zhang, ‘95

4 /2( , )lim ,

( , )

2

DS

S

S

m tA A PD t

D PP

A m P

Z G p tf e

m G p t

Z A Z mZ P

fDs on 323 x 64 lattice at chiral limit

fDs

fDs = 266.0 (9.5) MeV

fD

C. Aubin, Lattice ‘09

Z3 Grid Source with Low-Mode Substitution

t

H+L L

t0

i†j

t0

i†j

0H+L

HH

HL

L

+

†i j ij

Mesons

Z3 Grid: noise on 64 grid points separated by 8 lattice spacings on a time slice of 323 x 64 lattice

t t

0 t

ijk

0

i

0

H+L

H+L

H+L

†j

H

L

L

L

L

L

0 t

ijk

HHH

HHL

++†i j ij

i j k ij jk

Low-mode substitution for Baryons

Proton Correlator and Relative Errors with Low-mode Substituion (12 configurations)

3

3.5

4

1+-1++0++1 - -0 -+

3

3.5

4

Mas

s(Ge

V)

c

J /

c0c1 hc

2+1 Q C DExp .

2+1 flavorDWF+Overlap

0 flavorOverla

p

Is a tetraquark mesonium?

*0(2317)SD

0¯ ¯(1)1¯+(1)

0++(0)0+ ¯(1)1+ ¯(1)

π(137)

0+ (1/2)

ρ(770)

σ(600)

f0(980)

f0(1370)

f0(1500)

a0(980)

a0(1450)

a1(1230)

K0*(1430)

JPG(I))

M (M

eV)

a2(1320)

2+ ¯(1)

f0(1710)

K0*(800)

Beijing, 2004, page 28

Why a0(980) is not a state?

• The corresponding K0 would be ~ 1100 MeV which is 300 MeV away from both and .

• Cannot explain why a0(980) and f0(980) are narrow while σ(600) and κ(800) are broad.

• γ γ width of a0(980) and f0(980) are much smaller than expected of states.

• Large indicates

in f0(980), but cannot be in I=1 a0(980). How to explain the mass degeneracy then?

*0 (1430)K (800)

qq

0 0(980) , (980) sf D f

ss

qq

Our results shows scalar mass around 1400-1500 MeV, suggesting

a0(1450) is a two quark state.

)(JI PCG ),0(1 )1(1

ms

KYIS06 2006, page 30

)]0(0 )(JI ,[ PCG55

Further study is needed to check the volume dependence of the observed states.

Scattering states(Negative scattering length)

)0()0( pEpE

)1()1( pEpE

Scattering states

Possible BOUND state σ(600)?

Volume dependence of spectral weights

Volume independence suggests the observed state is an one particle state

W0

W1

0¯ ¯(1)1¯+(1)

0++(0)0+ ¯(1)1+ ¯(1)

π(137)

0+ (1/2)

ρ(770)

σ(600)

f0(980)

f0(1370)

f0(1500)

a0(980)

a0(1450)

a1(1230)

K0*(1430)

JPG(I))

M (M

eV)

a2(1320)

2+ ¯(1)

f0(1710)

K0*(800)

MesoniumsKK Kπ Mesoniumππ Mesonium

qq

Beijing, 2004, page 33

Scalar Mesons and Glueball

0(1500)f

00 (1470)a

*0 (1430)K*

0 (1430)K

*0 (1430)K*

0 (1430)K

0 (1470)a 0 (1470)a

(800)

0(980)f0 (980)a 0 (980)a00 (980)a

(800)

(800) (800)

)( KK

)( K

0(1370)f

(600)

0(1710)fglueball

qq

2 2q q

SummaryChiral fermions (Overlap valence on 2+1 flavor DWF configurations)Preliminary results on DS spectrum at one sea mass and one lattice spacing.Preliminary results on hyperfine splitting of charmonium, and fDs at chiral and continuum limits. Systematic errors (NLO MAPQ PT fitting)Noise grid source can reduce errors by a factor of 3 to 4. Need to observe all members of multiplets in addition to to discern tetraquark mesoniums.

qq