165 research outputs found
Banks-Zaks fixed point analysis in momentum subtraction schemes
We analyse the critical exponents relating to the quark mass anomalous
dimension and beta-function at the Banks-Zaks fixed point in Quantum
Chromodynamics (QCD) in a variety of representations for the quark in the
momentum subtraction (MOM) schemes of Celmaster and Gonsalves. For a specific
range of values of the number of quark flavours, estimates of the exponents
appear to be scheme independent. Using the recent five loop modified minimal
subtraction (MSbar) scheme quark mass anomalous dimension and estimates of the
fixed point location we estimate the associated exponent as 0.263-0.268 for the
SU(3) colour group and 12 flavours when the quarks are in the fundamental
representation.Comment: 33 latex pages, 25 tables, anc directory contains txt file with
electronic version of renormalization group function
and channels of decay at the physical point with periodic boundary conditions
We present a lattice calculation of the matrix elements and
amplitudes with both the and 1/2 channels and ,
the measure of direct violation. We use periodic boundary conditions
(PBC), where the correct kinematics of can be achieved via an
excited two-pion final state. To overcome the difficulty associated with the
extraction of excited states, our previous work \cite{Bai:2015nea,RBC:2020kdj}
successfully employed G-parity boundary conditions, where pions are forced to
have non-zero momentum enabling the two-pion ground state to express the
on-shell kinematics of the decay. Here instead we overcome the
problem using the variational method which allows us to resolve the two-pion
spectrum and matrix elements up to the relevant energy where the decay
amplitude is on-shell.
In this paper we report an exploratory calculation of decay
amplitudes and using PBC on a coarser lattice size of
with inverse lattice spacing GeV and the physical
pion and kaon masses. The results are promising enough to motivate us to
continue our measurements on finer lattice ensembles in order to improve the
precision in the near future
Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD
A study of two-pion scattering for the isospin channels, and ,
using lattice QCD is presented. M\"obius domain wall fermions on top of the
Iwasaki-DSDR gauge action for gluons with periodic boundary conditions are used
for the lattice computations which are carried out on two ensembles of gauge
field configurations generated by the RBC and UKQCD collaborations with
physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial
extents of and 4.58 fm, respectively. The all-to-all propagator method
is employed to compute a matrix of correlation functions of two-pion operators.
The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation
functions to extract phase shifts with multiple states, two pions with a
non-zero relative momentum as well as two pions at rest. Our results for phase
shifts for both and channels are consistent with and the Roy
Equation and chiral perturbation theory, though at this preliminary stage our
errors for are large. An important finding of this work is that GEVP is
useful to obtain signals and matrix elements from multiple states
AAindex: amino acid index database, progress report 2008
AAindex is a database of numerical indices representing various physicochemical and biochemical properties of amino acids and pairs of amino acids. We have added a collection of protein contact potentials to the AAindex as a new section. Accordingly AAindex consists of three sections now: AAindex1 for the amino acid index of 20 numerical values, AAindex2 for the amino acid substitution matrix and AAindex3 for the statistical protein contact potentials. All data are derived from published literature. The database can be accessed through the DBGET/LinkDB system at GenomeNet (http://www.genome.jp/dbget-bin/www_bfind?aaindex) or downloaded by anonymous FTP (ftp://ftp.genome.jp/pub/db/community/aaindex/)
Direct CP violation and the ΔI=1/2 rule in K→ππ decay from the standard model
We present a lattice QCD calculation of the ΔI=1/2, K→ππ decay amplitude A0 and ϵ′, the measure of direct CP violation in K→ππ decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a 323×64 lattice with an inverse lattice spacing of a-1=1.3784(68) GeV. However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the ππ ground state and more accurately relate the lattice operators to those defined in the standard model. We find Re(A0)=2.99(0.32)(0.59)×10-7 GeV and Im(A0)=-6.98(0.62)(1.44)×10-11 GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result Re(A0)=3.3201(18)×10-7 GeV. These results for A0 can be combined with our earlier lattice calculation of A2 [2] to obtain Re(ϵ′/ϵ)=21.7(2.6)(6.2)(5.0)×10-4, where the third error represents omitted isospin breaking effects, and Re(A0)/Re(A2)=19.9(2.3)(4.4). The first agrees well with the experimental result of Re(ϵ′/ϵ)=16.6(2.3)×10-4. A comparison of the second with the observed ratio Re(A0)/Re(A2)=22.45(6), demonstrates the standard model origin of this “ΔI=1/2 rule” enhancement.We present a lattice QCD calculation of the , decay amplitude and , the measure of direct CP-violation in decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a lattice with an inverse lattice spacing of GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find GeV and GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result GeV. These results for can be combined with our earlier lattice calculation of to obtain , where the third error represents omitted isospin breaking effects, and Re/Re. The first agrees well with the experimental result of . A comparison of the second with the observed ratio ReRe, demonstrates the Standard Model origin of this " rule" enhancement
Amino acid "little Big Bang": Representing amino acid substitution matrices as dot products of Euclidian vectors
<p>Abstract</p> <p>Background</p> <p>Sequence comparisons make use of a one-letter representation for amino acids, the necessary quantitative information being supplied by the substitution matrices. This paper deals with the problem of finding a representation that provides a comprehensive description of amino acid intrinsic properties consistent with the substitution matrices.</p> <p>Results</p> <p>We present a Euclidian vector representation of the amino acids, obtained by the singular value decomposition of the substitution matrices. The substitution matrix entries correspond to the dot product of amino acid vectors. We apply this vector encoding to the study of the relative importance of various amino acid physicochemical properties upon the substitution matrices. We also characterize and compare the PAM and BLOSUM series substitution matrices.</p> <p>Conclusions</p> <p>This vector encoding introduces a Euclidian metric in the amino acid space, consistent with substitution matrices. Such a numerical description of the amino acid is useful when intrinsic properties of amino acids are necessary, for instance, building sequence profiles or finding consensus sequences, using machine learning algorithms such as Support Vector Machine and Neural Networks algorithms.</p
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