Light meson decay constants beyond the quenched approximatio(2)

by making a global four parameters t which includes the excited states, the values of the mass and of the decay constant of the lightest state do not change beyond the statistical errors we quote. The extrapolated value for f=(m ZA ) at R2= 0:7 can be compared with the one obtained from the direct unquenched fermion simulation described in ref. 8], at nearly matched values of the pion and rho masses (m ' 0:57 and m ' 0:67): mf ZA= 0:226(11). The size of the statistical errors and the general avour dependence allow to conclude that the inclusion of sea quarks tends to increase, especially for the case, the values of the (raw) decay constants. By comparing the large and small volume results, one can conclude that the e ect, which is visible only for moderately light quark masses, is stable against nite size corrections. Physical values of the light meson decay constants can be obtained only after extrapolating to zero lattice spacing and to the chiral limit, a scope beyond this work. The extrapolation from negative avour numbers appears smooth after matching a number of physical quantities corresponding to the renormalized parameters of the theory, agrees with the results obtained from direct fermion simulations and gives strong support for visible unquenching corrections for light meson decay constants.

We calculate the effects of including dynamical fermion loops in the lattice QCD estimates of meson decay constants, by extrapolating the results from negative flavour numbers after a suitable matching of the pion and rho mass. For moderately light quarks,

run label nf (f ZV ) 1

a f=ZA f=(m ZA) (a) 4 0.322(8) 0.166(4) 0.235(6) (b) 2 0.324(7) 0.168(4) 0.238(6) (c) 0 0.328(8) 0.166(4) 0.234(6) extrap. 2 0.331(12) 0.234(9) (d) 4 0.373(9) 0.160(5) 0.243(8) (e) 2 0.394(6) 0.166(5) 0.251(8) (f) 0 0.418(9) 0.173(5) 0.263(8) extrap. 2 0.440(13) 0.271(13) (g) 4 0.371(7) 0.157(3) 0.234(5) (h) 2 0.405(8) 0.168(5) 0.255(8) (i) 0 0.424(9) 0.172(6) 0.264(10) extrap. 2 0.454(13) 0.283(13) Table 1: The values of the meson decay constants.

run label nf Volume (a) 4 163 32 6.4 (b) 2 163 32 6.1 (c) 0 163 32 5.767 (d) 4 163 32 6.463 (e) 2 163 32 6.1 (f) 0 163 32 5.7 (g) 4 243 32 6.463 (h) 2 243 32 6.1 (i) 0 243 32 5.7 Table 2: The details of each run of Table 1. In runs (e) and (f) f respectively.

K nconf a m am m2=m2 0.155 26 0.577(4) 0.705(6) 0.670(10) 0.1557 20 0.586(3) 0.706(7) 0.689(11) 0.1582 20 0.591(5) 0.710(7) 0.693(11) 0.158 47 0.464(4) 0.658(8) 0.497(9) 0.161 89 0.467(2) 0.662(5) 0.498(5) 0.165 92 0.457(3) 0.659(8) 0.481(7) 0.158 60 0.467(3) 0.671(6) 0.484(6) 0.161 34 0.465(3) 0.660(8) 0.496(6) 0.165 36 0.455(3) 0.651(6) 0.488(7) used to determine the decay constants values is measured only on 47 and 45 con gurations

We calculate the effects of including dynamical fermion loops in the lattice QCD estimates of meson decay constants, by extrapolating the results from negative flavour numbers after a suitable matching of the pion and rho mass. For moderately light quarks,

References1] F. Butler, H. Chen, J. Sexton, A. Vaccarino, D. Weingarten,\Meson Decay Constants from the Valence Approximation to Lattice QCD", preprint hep-lat 9302012. 2] R. Petronzio, Nucl. Phys. B (Proc. Suppl.) 42 (1995) 942 3] G. M. de Divitiis, R. Frezzotti, M. Guagnelli, M. Masetti, R. Petronzio,\The bermions: an approach to lattice QCD dynamical fermions from negative avour numbers", preprint ROM2F-95-15, hep-lat 9507020, accepted for publication in Nucl. Phys. B. 4] E. Witten, Nucl. Phys. B 156 (1979) 269; G. Veneziano, Nucl. Phys. B 159 (1979) 213. 5] R. Frezzotti, M. Masetti, R. Petronzio, work in preparation. 6] N. Cabibbo, E. Marinari, Ph. Lett. B 119 (1982) 387. 7] M. Luscher, Nucl. Phys. B 418 (1994) 637; B. Bunk, K. Jansen, B. Jegerlenner, M. Luscher, H. Simma, R. Sommer, Nucl. Phys. B (Proc. Suppl.) 42 (1995) 49. 8] D. Daniel, R. Gupta, D. G. Richards, Phys. Rev. D 43 (1991) 3715.

We calculate the effects of including dynamical fermion loops in the lattice QCD estimates of meson decay constants, by extrapolating the results from negative flavour numbers after a suitable matching of the pion and rho mass. For moderately light quarks,

0.341 (

= f ZV )

0.32 0.3 0.28 0.26

3

3

3

3

f=(m ZA)

0.24 0.22 0.2

3

3

3

3

-6

-4

-2

nf

0

2

4

Figure 1: The avour dependence of f=(m ZA ) and 1=(f ZV ) decay constants for (m=m )2= 0:7 8

We calculate the effects of including dynamical fermion loops in the lattice QCD estimates of meson decay constants, by extrapolating the results from negative flavour numbers after a suitable matching of the pion and rho mass. For moderately light quarks,

0.5

0.45

3 3 3 3

1 (

= f ZV )

0.4

0.35

0.3

f=(m ZA)0.25

3

3

3

3

0.2

-6

-4

-2

nf

0

2

4

Figure 2: The avour dependence of f=(m ZA ) and 1=(f ZV ) decay constants for the (m=m )2= 0:5. Crosses refer to the 243 32 lattice and diamonds to the 163 32. 9