Logarithmic link smearing for full QCD

A Lie-algebra based recipe for smoothing gauge links in lattice field theory is presented, building on the matrix logarithm. With or without hypercubic nesting, this LOG/HYL smearing yields fat links which are differentiable with respect to the original ones. This is essential for defining UV-filtered (“fat link”) fermion actions which may be simulated with a HMC-type algorithm. The effect of this smearing on the distribution of plaquettes and on the residual mass of tree-level O(a)-improved clover fermions in quenched QCD is studied.     

格点QCD基础求解器及其异构计算实现的性能优化

格点量子色动力学(格点QCD)是研究夸克、胶子等微观粒子间相互作用的重要理论和方法.通过将时空离散化为四维结构网格,并将量子色动力学的基本场量定义在网格上,让研究人员可以使用数值模拟方法,从第一性原理出发研究强子间相互作用和性质,但这个过程中的计算量极大,需要进行大规模并行计算.格点QCD计算的核心基础为格点QCD求解器,是程序运行主要的计算热点模块.本文研究在国产异构计算平台下格点QCD求解器的实现与优化,提出一套格点QCD求解器的设计实现,实现了BiCGSTAB求解器,显著降低了迭代次数;通过对奇偶预处理技术,降低了所求问题的计算规模;针对国产异构加速卡的特点,优化了Dslash模块的访存操作.实验测试表明,相比优化前的求解器获得了约30倍的加速比,为国产异构超算下格点QCD软件性能优化提供了有益的参考价值.     

WTO — a deterministic approach to 4-fermion physics

The program WTO, which is designed for computing cross sections and other relevant observables in the e⁺e⁻ annihilation into four fermions, is described. The various quantities are computed over both a completely inclusive experimental set-up and a realistic one, i.e. with cuts on the final state energies, final state angles, scattering angles and final state invariant masses. Initial state QED corrections are included by means of the structure function approach while final state QCD corrections are applicable in their naive formulation. A gauge restoring mechanism is included according to the Fermion-Loop scheme. The program structure is highly modular and particular care has been devoted to computing efficiency and speed.     

Valence and sea quark mixing in meson states

A meson model with qq and (qq)^2 mixing has been developed.The 0^- meson state has been studied within this model space.Considerable qq and (qq)^2 mixing has been found.The first excited state is in the energy range-1.5GeV,This state may be relevant to the new discovered exotic meson states.     

QCDNUM: Fast QCD evolution and convolution

The qcdnum program numerically solves the evolution equations for parton densities and fragmentation functions in perturbative QCD. Un-polarised parton densities can be evolved up to next-to-next-to-leading order in powers of the strong coupling constant, while polarised densities or fragmentation functions can be evolved up to next-to-leading order. Other types of evolution can be accessed by feeding alternative sets of evolution kernels into the program. A versatile convolution engine provides tools to compute parton luminosities, cross-sections in hadron–hadron scattering, and deep inelastic structure functions in the zero-mass scheme or in generalised mass schemes. Input to these calculations are either the qcdnum evolved densities, or those read in from an external parton density repository. Included in the software distribution are packages to calculate zero-mass structure functions in un-polarised deep inelastic scattering, and heavy flavour contributions to these structure functions in the fixed flavour number scheme.

Program summary

Program title: QCDNUM version: 17.00Catalogue identifier: AEHV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHV_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU Public LicenceNo. of lines in distributed program, including test data, etc.: 45 736No. of bytes in distributed program, including test data, etc.: 911 569Distribution format: tar.gzProgramming language: Fortran-77Computer: AllOperating system: AllRAM: Typically 3 MbytesClassification: 11.5Nature of problem: Evolution of the strong coupling constant and parton densities, up to next-to-next-to-leading order in perturbative QCD. Computation of observable quantities by Mellin convolution of the evolved densities with partonic cross-sections.Solution method: Parametrisation of the parton densities as linear or quadratic splines on a discrete grid, and evolution of the spline coefficients by solving (coupled) triangular matrix equations with a forward substitution algorithm. Fast computation of convolution integrals as weighted sums of spline coefficients, with weights derived from user-given convolution kernels.Restrictions: Accuracy and speed are determined by the density of the evolution grid.Running time: Less than 10 ms on a 2 GHz Intel Core 2 Duo processor to evolve the gluon density and 12 quark densities at next-to-next-to-leading order over a large kinematic range.     

MathQCDSR: A Mathematica package for QCD sum rules calculations

We present a software package written in Mathematica for standard QCD sum rules calculations. Two examples are given to demonstrate how to use the package. One is for the mass spectrum of octet baryons from two-point correlation functions; the other for the magnetic moments of octet baryons in the external-field method. The free package FeynCalc is used to handle the gamma-matrix algebra. In addition to two notebooks for the construction of the QCD sum rules, two corresponding notebooks are provided for a Monte Carlo-based numerical analysis, complete with in-line graphical display of sum rule matching, error distributions, and scatter plots for correlations.

Program summary

Program title: MathQCDSRCatalogue identifier: AEJA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 93 897No. of bytes in distributed program, including test data, etc.: 631 481Distribution format: tar.gzProgramming language: MathematicaComputer: PCs and WorkstationsOperating system: Any OS that supports Mathematica. The package has been tested under Windows XP, Macintosh OS X, and LinuxClassification: 11.5External routines: FeynCalc (http://www.feyncalc.org/). It is a freely available Mathematica package for high-energy physics calculations. Here it is used primarily to handle gamma-matrix algebra.Nature of problem: The QCD sum rule method is a nonperturbative approach to solving quantum chromodynamics (QCD), the fundamental theory of the strong force. The approach establishes a direct link between hadron phenomenology and the QCD vacuum structure via a few QCD parameters called vacuum condensates and susceptibilities. It has been widely applied in nuclear and particle physics to gain insight into various aspects of strong-interaction physics.Solution method: First, QCD sum rules are constructed by evaluating correlation functions from two perspectives. On the quark level, it leads to a function of QCD parameters and the Borel mass parameter M. On the hadronic level, it leads to a function of phenomenological parameters and the same M. By numerically matching the two sides over a range in M, the phenomenological parameters can be extracted. The construction involves a large amount of gamma-matrix algebra, Fourier transform, and Borel transform. The matching usually involves searching for minimum χ². We employ a Monte Carlo-based procedure to perform the analysis which allows for realistic error estimates.Restrictions: The package deals with only standard (SVZ) QCD sum rule calculations. It can be easily adapted to handle other variants of the method (like finite-energy sum rules). Due to the use of FeynCalc, two of the notebooks (qcdsr2pt-construction.nb and qcdsr3pt-construction.nb) only run on version 6.0 of Mathematica. The other two can run on any version.Additional comments: The package consists of the following 4 notebooks:

• • 

  qcdsr2pt-construction.nb – This notebook constructs the QCD sum rules for octet baryon masses and outputs them, one particle at a time, to disk in plain text for analysis. For reference, we include all the output files (named Mass-*.txt) as part of the package, totaling 8 files in about 20 lines. The user should generate the outputs on their own computer and check against the supplied ones.

• • 

  qcdsr2pt-analysis.nb – This notebook reads and analyzes the QCD sum rules produced by qcdsr2pt-construction.nb. The user can save the graphics in the analysis to disk in a variety of formats.

• • 

  qcdsr3pt-construction.nb – This notebook constructs the QCD sum rules for the octet baryon magnetic moments and outputs them, one particle at a time, to disk in plain text for analysis. Again, for reference, we include all the output files (named Mag-*.txt), totaling 24 files in about 400 lines. The user should generate the outputs on their own computer and check against the supplied ones to make sure the program is running properly.

• • 

  qcdsr3pt-analysis.nb – This notebook reads and analyzes the QCD sum rules produced by qcdsr3pt-construction.nb. The user can save the graphics in the analysis to disk in a variety of formats.

Each notebook can be run separately, apart from the simple interface between the construction and analysis programs via plain text files written to disk.Running time: For mass calculations, qcdsr2ptconstruction.nb and qcdsr2pt-analysis.nb take about a minute each to run on a laptop. For magnetic moment calculations, qcdsr3pt-construction.nb can take up to 10 minutes for a given particle, and qcdsr3pt-analysis.nb typically a few minutes, depending on the number of Monte Carlo samples.     

A nested Krylov subspace method to compute the sign function of large complex matrices

We present an acceleration of the well-established Krylov–Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon density. Krylov–Ritz methods approximate the sign function using a projection on a Krylov subspace. To achieve a high accuracy this subspace must be taken quite large, which makes the method too costly. The new idea is to make a further projection on an even smaller, nested Krylov subspace. If additionally an intermediate preconditioning step is applied, this projection can be performed without affecting the accuracy of the approximation, and a substantial gain in efficiency is achieved for both Hermitian and non-Hermitian matrices. The numerical efficiency of the method is demonstrated on lattice configurations of sizes ranging from 4⁴ to 10⁴, and the new results are compared with those obtained with rational approximation methods.     

Ntuples for NLO events at hadron colliders

We present an event-file format for the dissemination of next-to-leading-order (NLO) predictions for QCD processes at hadron colliders. The files contain all information required to compute generic jet-based infrared-safe observables at fixed order (without showering or hadronization), and to recompute observables with different factorization and renormalization scales. The files also make it possible to evaluate cross sections and distributions with different parton distribution functions. This in turn makes it possible to estimate uncertainties in NLO predictions of a wide variety of observables without recomputing the short-distance matrix elements. The event files allow a user to choose among a wide range of commonly-used jet algorithms and jet-size parameters.     

Lattice QCD thermodynamics on the Grid

We describe how we have used simultaneously O(¹⁰³) nodes of the EGEE Grid, accumulating ca. 300 CPU-years in 2-3 months, to determine an important property of Quantum Chromodynamics. We explain how Grid resources were exploited efficiently and with ease, using user-level overlay based on Ganga and DIANE tools above standard Grid software stack. Application-specific scheduling and resource selection based on simple but powerful heuristics allowed to improve efficiency of the processing to obtain desired scientific results by a specified deadline. This is also a demonstration of combined use of supercomputers, to calculate the initial state of the QCD system, and Grids, to perform the subsequent massively distributed simulations. The QCD simulation was performed on a ¹⁶³×4 lattice. Keeping the strange quark mass at its physical value, we reduced the masses of the up and down quarks until, under an increase of temperature, the system underwent a second-order phase transition to a quark-gluon plasma. Then we measured the response of this system to an increase in the quark density. We find that the transition is smoothened rather than sharpened. If confirmed on a finer lattice, this finding makes it unlikely for ongoing experimental searches to find a QCD critical point at small chemical potential.