Precision Charmed Meson Spectroscopy and Decay Constants from Chiral Fermions Overlap Fermion on 2+1 flavor Domain Wall Fermion Configurations Overlap Fermion on 2+1 flavor Domain Wall Fermion Configurations Charmonium and Charmed-strange Meson Spectrum and f Ds Charmonium and Charmed-strange Meson Spectrum and f Ds χ QCD 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

f D and f Ds

Some desirable features: –O(a 2 ) error are small (e.g. spectrum). –O(m 2 a 2 ) errors are small (dispersion relation, hyperfine splitting) can include charm quark – The effective propagator is –D c = D/(1 – D/2) is chirally symmetric, i.e. {γ 5, D c } = 0. –D c + 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

2+1 Flavor DWF Configurations (RBC and UKQCD) 16 3 x 32 x 16, a -1 =1.73 GeV (a = fm), m l a=0.01, 0.02, 0.03, m s a= x 64 x 16, a -1 =1.73 GeV (a = fm), m l a=0.005, 0.01, 0.02, 0.03, m s a= x 64 x 16, a -1 =2.42 GeV (a = fm), m l a=0.004, 0.006, 0.008, m s a=0.03

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

Determination of ρ (24 3 x 64 lattice) from Hyperfine Splitting ρ=1.62ρ=1.50

Overlap with Deflation

Speed up with deflation and HYP smearing No critical slowing down Can calculate for any mass except zero Multi-mass inversion (30 masses) 16^3 x 3224^3 x 6432^3 x 64 w/o DDD+Sresw/o DDD+Sw/o DDD+S lowmode Inner iter Outer iter Overhead5 pro 6pro speedup235179

16 3 x x 64

D S Spectrum

32 3 x 64, m l a = 0.006, a = fm S.J. Dong talk

Hyperfine Splitting of Charmonium (50 config.) Expt: 116.5(1) MeV

Sharpe and Zhang, ‘95

f Ds on 32 3 x 64 lattice at chiral limit

f Ds f Ds = (9.5) MeV

fDfD

C. Aubin, Lattice ‘09

Z 3 Grid Source with Low-Mode Substitution H+L L HHHH HLHL L + Mesons Z 3 Grid: noise on 64 grid points separated by 8 lattice spacings on a time slice of 32 3 x 64 lattice

H+L H L L L L L HHHHHH HHLHHL ++ Low-mode substitution for Baryons

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

2+1 flavor DWF+Overlap 0 flavor Overlap Is a tetraquark mesonium?

0 ¯ ¯ (1) 1 ¯ + (1) 0 ++ (0)0 + ¯ (1) 1 + ¯ (1) π (137) 0 + (1/2) ρ (770) σ (600) f 0 (980) f 0 (1370) f 0 (1500) a 0 (980) a 0 (1450) a 1 (1230) K 0 * (1430) J PG (I)) M (MeV) a 2 (1320) 2 + ¯ (1) f 0 (1710) K 0 * (800)

Beijing, 2004, page 28 Why a 0 (980) is not a state? The corresponding K 0 would be ~ 1100 MeV which is 300 MeV away from both and. The corresponding K 0 would be ~ 1100 MeV which is 300 MeV away from both and. Cannot explain why a 0 (980) and f 0 (980) are narrow while σ(600) and κ(800) are broad. Cannot explain why a 0 (980) and f 0 (980) are narrow while σ(600) and κ(800) are broad. γ γ width of a 0 (980) and f 0 (980) are much smaller than expected of states. γ γ width of a 0 (980) and f 0 (980) are much smaller than expected of states. Large indicates Large indicates in f 0 (980), but cannot be in I=1 a 0 (980). How to explain the mass degeneracy then? in f 0 (980), but cannot be in I=1 a 0 (980). How to explain the mass degeneracy then?

Our results shows scalar mass around MeV, suggesting Our results shows scalar mass around MeV, suggesting a 0 (1450) is a two quark state. a 0 (1450) is a two quark state. msmsmsms

KYIS , page 30 Further study is needed to check the volume dependence of the observed states. Scattering states Scattering states (Negative scattering length) length) Scattering states Scattering states Possible BOUND state σ(600)? σ(600)?

Volume dependence of spectral weights Volume independence suggests the observed state is an one particle state Volume independence suggests the observed state is an one particle state W0W0W0W0 W1W1W1W1

0 ¯ ¯ (1) 1 ¯ + (1) 0 ++ (0)0 + ¯ (1) 1 + ¯ (1) π (137) 0 + (1/2) ρ (770) σ (600) f 0 (980) f 0 (1370) f 0 (1500) a 0 (980) a 0 (1450) a 1 (1230) K 0 * (1430) J PG (I)) M (MeV) a 2 (1320) 2 + ¯ (1) f 0 (1710) K 0 * (800) Kπ Mesonium ππ Mesonium

Beijing, 2004, page 33 Scalar Mesons and Glueball glueball

Summary Chiral fermions (Overlap valence on 2+1 flavor DWF configurations) Preliminary results on D S spectrum at one sea mass and one lattice spacing. Preliminary results on hyperfine splitting of charmonium, and f Ds 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.