881 research outputs found
The GL_2 main conjecture for elliptic curves without complex multiplication
The main conjectures of Iwasawa theory provide the only general method known
at present for studying the mysterious relationship between purely arithmetic
problems and the special values of complex L-functions, typified by the
conjecture of Birch and Swinnerton-Dyer and its generalizations. Our goal in
the present paper is to develop algebraic techniques which enable us to
formulate a precise version of such a main conjecture for motives over a large
class of p-adic Lie extensions of number fields. The paper ends by formulating
and briefly discussing the main conjecture for an elliptic curve E over the
rationals Q over the field generated by the coordinates of its p-power division
points, where p is a prime greater than 3 of good ordinary reduction for E.Comment: 39 page
Overlap/Domain-wall reweighting
We investigate the eigenvalues of nearly chiral lattice Dirac operators
constructed with five-dimensional implementations. Allowing small violation of
the Ginsparg-Wilson relation, the HMC simulation is made much faster while the
eigenvalues are not significantly affected. We discuss the possibility of
reweighting the gauge configurations generated with domain-wall fermions to
those of exactly chiral lattice fermions.Comment: 7 pages, 3 figures, presented at the 31st International Symposium on
Lattice Field Theory (Lattice 2013), 29 July-3 August 2013, Mainz, German
Lattice study of meson correlators in the epsilon-regime of two-flavor QCD
We calculate mesonic two-point functions in the epsilon-regime of two-flavor
QCD on the lattice with exact chiral symmetry. We use gauge configurations of
size 16^3 32 at the lattice spacing a \sim 0.11 fm generated with dynamical
overlap fermions. The sea quark mass is fixed at \sim 3 MeV and the valence
quark mass is varied in the range 1-4 MeV, both of which are in the
epsilon-regime. We find a good consistency with the expectations from the
next-to-leading order calculation in the epsilon-expansion of (partially
quenched) chiral perturbation theory. From a fit we obtain the pion decay
constant F=87.3(5.6) MeV and the chiral condensate Sigma^{MS}=[239.8(4.0) MeV
]^3 up to next-to-next-to-leading order contributions.Comment: 20 pages, 12 figures, final version to appear in PR
B_K with two flavors of dynamical overlap fermions
We present a two-flavor QCD calculation of on a
lattice at fm (or equivalently 1.67 GeV). Both valence
and sea quarks are described by the overlap fermion formulation. The matching
factor is calculated non-perturbatively with the so-called RI/MOM scheme. We
find that the lattice data are well described by the next-to-leading order
(NLO) partially quenched chiral perturbation theory (PQChPT) up to around a
half of the strange quark mass (). The data at quark masses
heavier than are fitted including a part of
next-to-next-to-leading order terms. We obtain , where the first error is statistical and the second is an
estimate of systematic uncertainties from finite volume, fixing topology, the
matching factor, and the scale setting.Comment: 36 pages, 14 figures, comments and references added, analysis and
systematic error revised, minor change in the final result. version to appear
in PRD, reference correcte
Determination of the chiral condensate from 2+1-flavor lattice QCD
We perform a precise calculation of the chiral condensate in QCD using
lattice QCD with 2+1 flavors of dynamical overlap quarks. Up and down quark
masses cover a range between 3 and 100 MeV on a 16^3x48 lattice at a lattice
spacing around 0.11 fm. At the lightest sea quark mass, the finite volume
system on the lattice is in the epsilon-regime. By matching the low-lying
eigenvalue spectrum of the Dirac operator with the prediction of chiral
perturbation theory at the next-to-leading order, we determine the chiral
condensate in 2+1-flavor QCD with strange quark mass fixed at its physical
value as Sigma (MS-bar at 2 GeV) = [242(04)(^+19_-18}) MeV}]^3, where the
errors are statistical and systematic, respectively.Comment: 4 pages, 3 figures, errors in table 1 and fig.3 corrected. Published
in PR
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