372 research outputs found
Massive photons: an infrared regularization scheme for lattice QCD+QED
Standard methods for including electromagnetic interactions in lattice
quantum chromodynamics calculations result in power-law finite-volume
corrections to physical quantities. Removing these by extrapolation requires
costly computations at multiple volumes. We introduce a photon mass to
alternatively regulate the infrared, and rely on effective field theory to
remove its unphysical effects. Electromagnetic modifications to the hadron
spectrum are reliably estimated with a precision and cost comparable to
conventional approaches that utilize multiple larger volumes. A significant
overall cost advantage emerges when accounting for ensemble generation. The
proposed method may benefit lattice calculations involving multiple charged
hadrons, as well as quantum many-body computations with long-range Coulomb
interactions.Comment: 6 pages, 4 figures, 2 tables; significant revisions to abstract and
main text; revised presentation of results for clarity (results unchanged);
acknowledgements updated; matches published versio
Universality of Mixed Action Extrapolation Formulae
Mixed action theories with chirally symmetric valence fermions exhibit very
desirable features both at the level of the lattice calculations as well as in
the construction and implementation of the low energy mixed action effective
field theory. In this work we show that when such a mixed action effective
field theory is projected onto the valence sector, both the Lagrangian and the
extrapolation formulae become universal in form through next to leading order,
for all variants of discretization methods used for the sea fermions. Our
conclusion relies on the chiral nature of the valence quarks. The result
implies that for all sea quark methods which are in the same universality class
as QCD, the numerical values of the physical coefficients in the various mixed
action chiral Lagrangians will be the same up to lattice spacing dependent
corrections. This allows us to construct a prescription to determine the mixed
action extrapolation formulae for a large class of hadronic correlation
functions computed in partially quenched chiral perturbation theory at the
one-loop level. For specific examples, we apply this prescription to the
nucleon twist--2 matrix elements and the nucleon--nucleon system. In addition,
we determine the mixed action extrapolation formula for the neutron EDM as this
provides a nice example of a theta-dependent observable; these observables are
exceptions to our prescription.Comment: 36 pages, appendix on twisted mass sea fermions added, expanded
discussion of NLO operators, version published in JHEP; typographical errors
corrected in Eqs. (68) and (69
Estoire d’ Eracles: the Old French Continuation of William of Tyre
This translation relates to The Crusades
Mixed Meson Masses with Domain-Wall Valence and Staggered Sea Fermions
Mixed action lattice calculations allow for an additive lattice spacing
dependent mass renormalization of mesons composed of one sea and one valence
quark, regardless of the type of fermion discretization methods used in the
valence and sea sectors. The value of the mass renormalization depends upon the
lattice actions used. This mixed meson mass shift is an important lattice
artifact to determine for mixed action calculations; because it modifies the
pion mass, it plays a central role in the low energy dynamics of all hadronic
correlation functions. We determine the leading order, , and
next to leading order, , additive mass shift of
\textit{valence-sea} mesons for a mixed lattice action with domain-wall valence
fermions and rooted staggered sea fermions, relevant to the majority of current
large scale mixed action lattice efforts. We find that on the asqtad improved
coarse MILC lattices, this additive mass shift is well parameterized in lattice
units by , which in physical
units, using fm, corresponds to . In terms of the mixed action effective field
theory parameters, the corresponding mass shift is given by at leading order plus
next-to-leading order corrections including the necessary chiral logarithms for
this mixed action calculation, determined in this work. Within the precision of
our calculation, one can not distinguish between the full next-to-leading order
effective field theory analysis of this additive mixed meson mass shift and the
parameterization given above.Comment: 28 pages, 3 figures, 5 table
Massive Photons: An Infrared Regularization Scheme for Lattice QCD plus QED
Standard methods for including electromagnetic interactions in lattice quantum chromodynamics calculations result in power-law finite-volume corrections to physical quantities. Removing these by extrapolation requires costly computations at multiple volumes. We introduce a photon mass to alternatively regulate the infrared, and rely on effective field theory to remove its unphysical effects. Electromagnetic modifications to the hadron spectrum are reliably estimated with a precision and cost comparable to conventional approaches that utilize multiple larger volumes. A significant overall cost advantage emerges when accounting for ensemble generation. The proposed method may benefit lattice calculations involving multiple charged hadrons, as well as quantum many-body computations with long-range Coulomb interactions
Two Meson Systems with Ginsparg-Wilson Valence Quarks
Unphysical effects associated with finite lattice spacing and partial
quenching may lead to the presence of unphysical terms in chiral extrapolation
formulae. These unphysical terms must then be removed during data analysis
before physical predictions can be made. In this work, we show that through
next-to-leading order, there are no unphysical counterterms in the
extrapolation formulae, expressed in lattice-physical parameters, for meson
scattering lengths in theories with Ginsparg-Wilson valence quarks. Our work
applies to most sea quark discretization, provided that chiral perturbation
theory is a valid approximation. We demonstrate our results with explicit
computations and show that, in favorable circumstances, the extrapolation
formulae do not depend on the unknown constant C_Mix appearing at lowest order
in the mixed action chiral Lagrangian. We show that the I=1 KK scattering
length does not depend on C_Mix in contrast to the I=3/2 K-pi scattering
length. In addition, we show that these observables combined with f_K / f_pi
and the I=2 pi-pi scattering length share only two linearly independent sets of
counterterms, providing a means to test the mixed action theory at one lattice
spacing. We therefore make a prediction for the I=1 KK scattering length.Comment: 21 pages, 2 figures, 2 tables. Version to be published in PRD.
Improved discussion in Sec. III B. Added reference
The K+K+ Scattering Length from Lattice QCD
The K+K+ scattering length is calculated in fully-dynamical lattice QCD with
domain-wall valence quarks on the MILC asqtad-improved gauge configurations
with rooted staggered sea quarks. Three-flavor mixed-action chiral perturbation
theory at next-to-leading order, which includes the leading effects of the
finite lattice spacing, is used to extrapolate the results of the lattice
calculation to the physical value of m_{K+}/f_{K+}. We find m_{K+} a_{K+K+} =
-0.352 +- 0.016, where the statistical and systematic errors have been combined
in quadrature.Comment: 17 pages, 12 figures. NPLQCD collaboratio
Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
The I=2 pipi scattering length is calculated in fully-dynamical lattice QCD
with domain-wall valence quarks on the asqtad-improved coarse MILC
configurations (with fourth-rooted staggered sea quarks) at four light-quark
masses. Two- and three-flavor mixed-action chiral perturbation theory at
next-to-leading order is used to perform the chiral and continuum
extrapolations. At the physical charged pion mass, we find m_pi a_pipi(I=2) =
-0.04330 +- 0.00042, where the error bar combines the statistical and
systematic uncertainties in quadrature.Comment: 20 pages, 7 figure
Meson and baryon spectrum for QCD with two light dynamical quarks
We present results of meson and baryon spectroscopy using the Chirally
Improved Dirac operator on lattices of size 16**3 x 32 with two mass-degenerate
light sea quarks. Three ensembles with pion masses of 322(5), 470(4) and 525(7)
MeV and lattice spacings close to 0.15 fm are investigated. Results on ground
and excited states for several channels are given, including spin two mesons
and hadrons with strange valence quarks. The analysis of the states is done
with the variational method, including two kinds of Gaussian sources and
derivative sources. We obtain several ground states fairly precisely and find
radial excitations in various channels. Excited baryon results seem to suffer
from finite size effects, in particular at small pion masses. We discuss the
possible appearance of scattering states in various channels, considering
masses and eigenvectors. Partially quenched results in the scalar channel
suggest the presence of a 2-particle state, however, in most channels we cannot
identify them. Where available, we compare our results to results of quenched
simulations using the same action.Comment: 27 pages, 29 figures, 11 table
Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems
We consider solution operators of linear ordinary boundary problems with "too
many" boundary conditions, which are not always solvable. These generalized
Green's operators are a certain kind of generalized inverses of differential
operators. We answer the question when the product of two generalized Green's
operators is again a generalized Green's operator for the product of the
corresponding differential operators and which boundary problem it solves.
Moreover, we show that---provided a factorization of the underlying
differential operator---a generalized boundary problem can be factored into
lower order problems corresponding to a factorization of the respective Green's
operators. We illustrate our results by examples using the Maple package
IntDiffOp, where the presented algorithms are implemented.Comment: 19 page
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