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Staggered Heavy Baryon Chiral Perturbation Theory
Although taste violations significantly affect the results of staggered
calculations of pseudoscalar and heavy-light mesonic quantities, those entering
staggered calculations of baryonic quantities have not been quantified. Here I
develop staggered chiral perturbation theory in the light-quark baryon sector
by mapping the Symanzik action into heavy baryon chiral perturbation theory.
For 2+1 dynamical quark flavors, the masses of flavor-symmetric nucleons are
calculated to third order in partially quenched and fully dynamical staggered
chiral perturbation theory. To this order the expansion includes the leading
chiral logarithms, which come from loops with virtual decuplet-like states, as
well as terms the order of the cubed pion mass, which come from loops with
virtual octet-like states. Taste violations enter through the meson propagators
in loops and tree-level terms the order of the squared lattice spacing. The
pattern of taste symmetry breaking and the resulting degeneracies and mixings
are discussed in detail. The resulting chiral forms are appropriate to lattice
results obtained with operators already in use and could be used to study the
restoration of taste symmetry in the continuum limit. I assume that the fourth
root of the fermion determinant can be incorporated in staggered chiral
perturbation theory using the replica method.Comment: 54 pages; v2: corrected discussion in Sec. III.C, conclusions
unchange
Kaon mixing matrix elements from beyond-the-Standard-Model operators in staggered chiral perturbation theory
Models of new physics induce K-Kbar mixing operators having Dirac structures
other than the "left-left" form of the Standard Model. We calculate the
functional form of the corresponding B-parameters at next-to-leading order in
both SU(3) and SU(2) staggered chiral perturbation theory (SChPT). Numerical
results for these matrix elements are being generated using improved staggered
fermions; our results can be used to extrapolate these matrix elements to the
physical light and strange quark masses. The SU(3) SChPT results turn out to be
much simpler than that for the Standard Model B_K operator, due to the absence
of chiral suppression in the new operators. The SU(2) SChPT result is of
similar simplicity to that for B_K. In fact, in the latter case, the chiral
logarithms for two of the new B-parameters are identical to those for B_K,
while those for the other two new B-parameters are of opposite sign. In
addition to providing results for the 2+1 flavor theory in SU(3) SChPT and the
1+1+1 flavor theory in SU(2) SChPT, we present the corresponding continuum
partially quenched results, as these are not available in the literature.Comment: 16 pages, 3 figures. Typos corrected--published versio
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