$B$ Meson Matrix Elements from Various Heavy Quark Effective

Various properties of heavy-light mesons are determined, including decay constants, the $B_{B}$-parameter, and the Isgur-Wise function. The heavy (bottom) quark is simulated with the static, NRQCD and/or (fixed-velocity) lattice-HQET effective theories, us

hep-lat/9509060 18 Sep 1995

Various properties of heavy-light mesons are determined, including decay constants, the $B_{B}$-parameter, and the Isgur-Wise function. The heavy (bottom) quark is simulated with the static, NRQCD and/or (fixed-velocity) lattice-HQET effective theories, us

1.4Static B-parameter for O_L operator

t1=2

1.320^3 * 30, beta=6.0, 32 cfg.

Kappa = 0.156

1.2Z[1S;n#=5;t_0=2,t=3])

2

t

(2

C

)1.11

t

(

2C

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)

21t

,1

t(

3

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8

/

3

0.8

0.7

0.601234Time (t2)56789

Various properties of heavy-light mesons are determined, including decay constants, the $B_{B}$-parameter, and the Isgur-Wise function. The heavy (bottom) quark is simulated with the static, NRQCD and/or (fixed-velocity) lattice-HQET effective theories, us

0.8

0.75

0.7

0.65

Meff

0.6

0.55

0.5

0.45

0.4HQET-light, LS, Z-source20^3 * 30, beta=6.0, 32 cfg.HQET: v = (0.25,0,0) + (0,0.25,0) + (0,0,0.25); u_0=1.0Kappa = 0.154Z[1S;n#=5;t_0=2,t=3]02468101214Time

Various properties of heavy-light mesons are determined, including decay constants, the $B_{B}$-parameter, and the Isgur-Wise function. The heavy (bottom) quark is simulated with the static, NRQCD and/or (fixed-velocity) lattice-HQET effective theories, us

4f 0 aMQ ZL0]( c ) ZL( c ) ZL0]( s ) ZL( s ) f+5 0:110+4 0:148+4 0:127+4 1:15+2 2:0 0:128 6 4 1 5 4+5 0:103+4 0:143+4 0:120+3 1:15+2 1:7 0:124 5 4 4 3 1Bs B

0]

Table 4 p The (UN-renormalized) ZL= (fB mB=2)latt for Qs and Qd pseudoscalar mesons with Wilson light quarks and NRQCD heavy quarks (with tadpole improvement). The presence (absence) of the superscript 0] indicates that the O(1=M ) correction is not (is) included in the matrix element of the current.APE-litude for O(1/M) corrected current

1:15+2 1+2 1:15 1

f f

Bs B

0 aMQ

m

(static) 1 78+4 MeV 0 4 2:0 76+8 MeV 30+4 MeV 6 5+7 MeV+5 MeV 1:7 77 6 35 5 Table 3 Bs{B and B{B mass splittings.NRQCD-light Pseudoscalar, LS, Z-source 0.6 0.58 0.56 0.54 0.52 Meff 0.5 0.48 0.46 0.44 0.42 0.4 0 2 4 6 Time 8 10 12 14 20^3 * 30, beta=6.0, 32 cfg. NRQCD: (collab.) K.E.+ sigma.B, symm. update n=2, Ma=1.7, u_0=0.88 Kappa=0.154 Z[1S;n#=3;t_0=2,t=3]

Bs B a 1 2:1 GeV

m

m

B B a 1 2:1 GeV

m

0.2"t1=0""t1=1""t1=2""t1=3""t1=4"

0.15

ZL

0.1

0.05

20^3 * 30, beta=6.0, 32 cfg. NRQCD: (collab.) K.E.+ sigma.B, symm. update n=2, Ma=1.7, u_0=0.88 Kappa= 0.154 Z[n#=3;t_0=2,t=3]

0 0 2 4 6 Time (t2) 8 10 12 14

Figure 6.\APE" ratio of LS and SS correlation functions for the axial current.

REFERENCES1. J. Mandula and M. Ogilvie, Nucl. Phys. B (Proc. Suppl. ) 34, 480 (1994). 2. T. Draper and C. McNeile, Nucl. Phys. B (Proc. Suppl. ) 34, 453 (1994). 3. T. Draper, C. McNeile and C. Nenkov, Nucl. Phys. B (Proc. Suppl. ) 42, 325 (1995). 4. S. Collins et al., Nucl. Phys. B (Proc. Suppl. ) 42, 395 (1995). 5. A. Ali Khan et al., Nucl. Phys. B (Proc. Suppl. ) 42, 382 (1995). 6. J. Flynn, O. Hernandez and B. Hill, Phys. Rev. D 43, 3709 (1991). 7. P. Lepage and P. Mackenzie, Phys. Rev. D 48, 2250 (1993). 8. V. Gimenez, Nucl. Phys. B401, 116 (1993). 9. J. Christensen, T. Draper and C. McNeile, in preparation. 10. (MILC collaboration) C. Bernard et al., Nucl. Phys. B (Proc. Suppl. ) 42, 388 (1995).

Figure 5. E ective mass plot for the pseudoscalar. But this ratio uses unnecessarily large times, and our results, presented in table 4, are from simultaneous ts to local-smeared and smearedsmeared two-point correlation functions. Our ratio fB=fB= 1:15+2 compares with the following 1 quenched= 6:0 results: 1:18(1) 10] (extrapolated Wilson heavy quark) and 1:12 5] (NRQCD heavy and clover light). We got 1:22+1 3] for 1 static-heavy{Wilson-light (without tadpole improvement).s