204 research outputs found
Dyson instability for 2D nonlinear O(N) sigma models
For lattice models with compact field integration (nonlinear sigma models
over compact manifolds and gauge theories with compact groups) and satisfying
some discrete symmetry, the change of sign of the bare coupling g_0^2 at zero
results in a mere discontinuity in the average energy rather than the
catastrophic instability occurring in theories with integration over
arbitrarily large fields. This indicates that the large order of perturbative
series and the non-perturbative contributions should have unexpected features.
Using the large-N limit of 2-dimensional nonlinear O(N) sigma model, we discuss
the complex singularities of the average energy for complex 't Hooft coupling
lambda= g_0^2N. A striking difference with the usual situation is the absence
of cut along the negative real axis. We show that the zeros of the partition
function can only be inside a clover shape region of the complex lambda plane.
We calculate the density of states and use the result to verify numerically the
statement about the zeros. We propose dispersive representations of the
derivatives of the average energy for an approximate expression of the
discontinuity. The discontinuity is purely non-perturbative and contributions
at small negative coupling in one dispersive representation are essential to
guarantee that the derivatives become exponentially small when lambda -> 0^+ We
discuss the implications for gauge theories.Comment: 10 pages, 10 figures uses revte
Asymptotically Universal Crossover in Perturbation Theory with a Field Cutoff
We discuss the crossover between the small and large field cutoff (denoted
x_{max}) limits of the perturbative coefficients for a simple integral and the
anharmonic oscillator. We show that in the limit where the order k of the
perturbative coefficient a_k(x_{max}) becomes large and for x_{max} in the
crossover region, a_k(x_{max}) is proportional to the integral from -infinity
to x_{max} of e^{-A(x-x_0(k))^2}dx. The constant A and the function x_0(k) are
determined empirically and compared with exact (for the integral) and
approximate (for the anharmonic oscillator) calculations. We discuss how this
approach could be relevant for the question of interpolation between
renormalization group fixed points.Comment: 15 pages, 11 figs., improved and expanded version of hep-th/050304
The non-perturbative part of the plaquette in quenched QCD
We define the non-perturbative part of a quantity as the difference between
its numerical value and the perturbative series truncated by dropping the order
of minimal contribution and the higher orders. For the anharmonic oscillator,
the double-well potential and the single plaquette gauge theory, the
non-perturbative part can be parametrized as A (lambda)^B exp{-C/lambda} and
the coefficients can be calculated analytically. For lattice QCD in the
quenched approximation, the perturbative series for the average plaquette is
dominated at low order by a singularity in the complex coupling plane and the
asymptotic behavior can only be reached by using extrapolations of the existing
series. We discuss two extrapolations that provide a consistent description of
the series up to order 20-25. These extrapolations favor the idea that the
non-perturbative part scales like (a/r_0)^4 with a/r_0 defined with the force
method. We discuss the large uncertainties associated with this statement. We
propose a parametrization of ln((a/r_0)) as the two-loop universal terms plus a
constant and exponential corrections. These corrections are consistent with
a_{1-loop}^2 and play an important role when beta<6. We briefly discuss the
possibility of calculating them semi-classically at large beta.Comment: 13 pages, 16 figures, uses revtex, contains a new section with the
uncertainties on the extrapolations, refs. adde
A Numerical Study of the Hierarchical Ising Model: High Temperature Versus Epsilon Expansion
We study numerically the magnetic susceptibility of the hierarchical model
with Ising spins () above the critical temperature and for two
values of the epsilon parameter. The integrations are performed exactly, using
recursive methods which exploit the symmetries of the model. Lattices with up
to sites have been used. Surprisingly, the numerical data can be fitted
very well with a simple power law of the form for the {\it whole} temperature range. The numerical values for
agree within a few percent with the values calculated with a high-temperature
expansion but show significant discrepancies with the epsilon-expansion. We
would appreciate comments about these results.Comment: 15 Pages, 12 Figures not included (hard copies available on request),
uses phyzzx.te
New Optimization Methods for Converging Perturbative Series with a Field Cutoff
We take advantage of the fact that in lambda phi ^4 problems a large field
cutoff phi_max makes perturbative series converge toward values exponentially
close to the exact values, to make optimal choices of phi_max. For perturbative
series terminated at even order, it is in principle possible to adjust phi_max
in order to obtain the exact result. For perturbative series terminated at odd
order, the error can only be minimized. It is however possible to introduce a
mass shift in order to obtain the exact result. We discuss weak and strong
coupling methods to determine the unknown parameters. The numerical
calculations in this article have been performed with a simple integral with
one variable. We give arguments indicating that the qualitative features
observed should extend to quantum mechanics and quantum field theory. We found
that optimization at even order is more efficient that at odd order. We compare
our methods with the linear delta-expansion (LDE) (combined with the principle
of minimal sensitivity) which provides an upper envelope of for the accuracy
curves of various Pade and Pade-Borel approximants. Our optimization method
performs better than the LDE at strong and intermediate coupling, but not at
weak coupling where it appears less robust and subject to further improvements.
We also show that it is possible to fix the arbitrary parameter appearing in
the LDE using the strong coupling expansion, in order to get accuracies
comparable to ours.Comment: 10 pages, 16 figures, uses revtex; minor typos corrected, refs. adde
Fisher's zeros as boundary of renormalization group flows in complex coupling spaces
We propose new methods to extend the renormalization group transformation to
complex coupling spaces. We argue that the Fisher's zeros are located at the
boundary of the complex basin of attraction of infra-red fixed points. We
support this picture with numerical calculations at finite volume for
two-dimensional O(N) models in the large-N limit and the hierarchical Ising
model. We present numerical evidence that, as the volume increases, the
Fisher's zeros of 4-dimensional pure gauge SU(2) lattice gauge theory with a
Wilson action, stabilize at a distance larger than 0.15 from the real axis in
the complex beta=4/g^2 plane. We discuss the implications for proofs of
confinement and searches for nontrivial infra-red fixed points in models beyond
the standard model.Comment: 4 pages, 3 fig
form factors with 2+1 flavors
Using the MILC 2+1 flavor asqtad quark action ensembles, we are calculating
the form factors and for the semileptonic decay. A total of six ensembles with lattice spacing from
to 0.06 fm are being used. At the coarsest and finest lattice
spacings, the light quark mass is one-tenth the strange quark mass
. At the intermediate lattice spacing, the ratio ranges from
0.05 to 0.2. The valence quark is treated using the Sheikholeslami-Wohlert
Wilson-clover action with the Fermilab interpretation. The other valence quarks
use the asqtad action. When combined with (future) measurements from the LHCb
and Belle II experiments, these calculations will provide an alternate
determination of the CKM matrix element .Comment: 8 pages, 6 figures, to appear in the Proceedings of Lattice 2017,
June 18-24, Granada, Spai
form factors for new-physics searches from lattice QCD
The rare decay arises from flavor-changing
neutral currents and could be sensitive to physics beyond the Standard Model.
Here, we present the first - QCD calculation of the
tensor form factor . Together with the vector and scalar form factors
and from our companion work [J. A. Bailey , Phys. Rev. D
92, 014024 (2015)], these parameterize the hadronic contribution to
semileptonic decays in any extension of the Standard Model. We obtain the total
branching ratio in
the Standard Model, which is the most precise theoretical determination to
date, and agrees with the recent measurement from the LHCb experiment [R. Aaij
, JHEP 1212, 125 (2012)]. Note added: after this paper was submitted
for publication, LHCb announced a new measurement of the differential decay
rate for this process [T. Tekampe, talk at DPF 2015], which we now compare to
the shape and normalization of the Standard-Model prediction.Comment: V3: Corrected errors in results for Standard-Model differential and
total decay rates in abstract, Fig. 3, Table IV, and outlook. Added new
preliminary LHCb data to Fig. 3 and brief discussion after outlook. Replaced
outdated correlation matrix in Table III with correct final version. Other
minor wording changes and references added. 7 pages, 4 tables, 3 figure
decay form factors from three-flavor lattice QCD
We compute the form factors for the semileptonic decay
process in lattice QCD using gauge-field ensembles with 2+1 flavors of sea
quark, generated by the MILC Collaboration. The ensembles span lattice spacings
from 0.12 to 0.045 fm and have multiple sea-quark masses to help control the
chiral extrapolation. The asqtad improved staggered action is used for the
light valence and sea quarks, and the clover action with the Fermilab
interpretation is used for the heavy quark. We present results for the form
factors , , and , where is the momentum
transfer, together with a comprehensive examination of systematic errors.
Lattice QCD determines the form factors for a limited range of , and we
use the model-independent expansion to cover the whole kinematically
allowed range. We present our final form-factor results as coefficients of the
expansion and the correlations between them, where the errors on the
coefficients include statistical and all systematic uncertainties. We use this
complete description of the form factors to test QCD predictions of the form
factors at high and low . We also compare a Standard-Model calculation of
the branching ratio for with experimental data.Comment: V2: Fig.7 added. Typos text corrected. Reference added. Version
published in Phys. Rev.
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