Charmed Bottom Mesons from Lattice QCD

Transcription

1 Charmed Bottom Mesons from Lattice QCD Nilmani Mathur Department of Theoretical Physics Tata Institute of Fundamental Research, India Collaborators : ILGTI, M. Padmanath, R. Lewis Lattice 2016, University of Southampton

2 Why Charmed-bottom

3 Set up Gauge Configurations: HISQ Valence quark propagators : -- Light to charm : Overlap -- Bottom : NRQCD with improved coefficients

4 Some desirable features: Overlap Fermions No O(a) error. The effective propagator : (1 D) D( m) ( D ma c ) 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 (more than 20 masses 10-15% overhead Renormalization may be relatively simple (e.g. with chiral Ward identity). Undesirable feature: -- Cost

5 Overlap fermions on Flavors HISQ Configurations Lattices used for this study : HISQ gauge configurations from MILC 24 3 x 64, a = 0.12 fm, m l /m s = 1/5, m π L = 4.54, m π = 305 MeV 32 3 x 96, a = fm, m l /m s = 1/5, m π L = 4.5, m π = 312 MeV 48 3 x 144, a = fm, m l /m s = 1/5, m π L = 4.51, m π = 319 MeV PHYSICAL REVIEW D 87, (2013) (MILC) HYP smearing on gauge fields Both point source and coulomb gauge fixed wall source are used No of eigenvectors projected : 350 (a = fm) : 350 (a = 0.09 fm) : 75 (a = fm)

6 Rest mass Vs Kinetic mass Charm mass is tuned by meson kinetic mass and not from rest mass a la FermiLab formulation El-khadra et al, PRD55, 3933(1997) Expanding the energy momentum relation in powers of pa = M 12 + c 2 p 2 Rest mass : Kinetic mass : M 2 = M 1 /c 2

7 Dispersion relation (at charm mass) E ( p) E ( p 0) p c Finite momentum wall source is used to project to particular momentum state which reduce errorbars substantially.

8 Lattice spacings and tuning of charm and strange masses Lattice spacings are calculated by Omega(sss) mass = 1672 GeV 48 3 x 144 : (5) fm 32 3 x 96 : (10) fm 24 3 x 64 : (14) fm which are quite consistent with lattice spacings determined by MILC Strange mass is tuned by setting pseudoscalar ss mass at 685 MeV m s a = (a = fm) = (a = fm) = (a = fm) Taking m s = 100 MeV m s a = (a = fm), = (a = fm) Charm mass is tuned by 1 (m 4 η c 3m J/ψ ) m c a = (a = fm) = (a = fm), = 0.29 (a = fm) Considering kinetic masses of mesons (a la Fermilab formulation)

9 Omega(sss) effective mass

10 Lattice spacings and tuning of charm and strange masses Lattice spacings are calculated by Omega(sss) mass = 1672 GeV 48 3 x 144 : (5) fm 32 3 x 96 : (10) fm 24 3 x 64 : (14) fm which are quite consistent with lattice spacings determined by MILC Strange mass is tuned by setting pseudoscalar ss mass at 685 MeV m s a = (a = fm) = (a = fm) = (a = fm) Taking m s = 100 MeV m s a = (a = fm), = (a = fm) Charm mass is tuned by 1 (m 4 η c 3m J/ψ ) m c a = (a = fm) = (a = fm), = 0.29 (a = fm) Considering kinetic masses of mesons (a la Fermilab formulation)

11 Dowdall et all, PRD 85,054509,2012 A. Hart et all, PRD 79, (2009) NRQCD Action Tadpole improvement. Coefficients are improved

12

13 b-quark mass tunning

14 We have calculated ground state energy spectra of mesons and baryons for all possible quantum numbers with l, s, c and b quarks Decay constants from two points functions are also being evaluated Results for charmed-bottom mesons and baryons will be presented

15 Pseudoscalar meson mass

16 Pseudoscalar meson mass Pseudoscalar meson mass from physical to about 6 GeV

17 Hyperfine splitting in charmonia

18 Hyperfine splitting in bottomonia

19 Hyperfine splitting : Bs

20 B c (0 - )

21 Prediction : B c * Only pseudoscalar B c is known experimentally (also possibly B c (2s)?) Hyperfine splittings (MeV) bu : 45 bs : 48 bb : 62 cc : 113 bc :?

22 B c Onium or B meson type? b u b b b s c c b c b c

23 Prediction : B c *

24 Mass-splittings

25 Hyperfine splittings in bottom mesons

26 Triply bottom baryon

27 Hyperfine splittings in charmed-bottomed baryons cbb ccb

28 Conclusions and Outlooks Ground state hadron spectra including all flavors are calculated using NRQCD (b) and overlap (l, s, and c) valence quarks on HISQ gauge configurations. Basic mass spectra for charmed-bottom mesons and baryons are presented here. Proper chiral and continuum limits need to be taken Decay constants are under study