Particle Physics and the Standard Model

QCD Ona Cray: the masses of elementaryparticles

by Gerald Guralnik, Tony Warnock, and Charles Zemach

ow ears we extract answers from We believe that a successful computer The calculations, which have two input QCD at energies below 1 GeV? simulation must combine the following (1) parameters (the pion mass and the long- H As noted in the text, the confine- physical and mathematical ingenuity to range quark-quark force constant in units of ment of quarks suggests that weak-coupling search out the best formulations of problems the lattice spacing), provide estimates of perturbative methods are not going to be still unsolved in principle; (2) sophisticated many measurable quantities. The accompa- successful at these energies. Nevertheless, if numerical analysis and computer program- nying table shows some of our results on QCD is a valid theory it must explain the ming, and (3) a computer with the speed, elementary particle masses and certain multiplicities, masses, and couplings of the memory, and input/output rate of the Cray meson coupling strengths. These results rep- experimentally observed strongly interacting XMP with a solid-state disk (or better). We resent several hundred hours of Cray time. particles. These would emerge from the the- have done calculations of particle masses on The quoted relative errors derive from the ory as bound states and resonances of quarks a lattice of 55,296 space-time points using the statistical analysis of the Monte Carlo calcu- and gluons. A valid theory must also account Cray XMP. Using new methods developed lation itself rather than from a comparison for the apparent absence of isolated quark with coworkers R. Gupta, J. Mandula, and with experimental data. Significantly more states and might predict the existence and A. Patel, we are examining glueball masses, computer time would significantly reduce properties of particles (such as glueballs) that renormalization group behavior, and the the errors in the calculated masses and coupl- have not yet been seen. behavior of the theory on much larger lat- ings. The most promising nonperturbative for- tices. The results to date support the belief Our work would not have been possible mulation of QCD exploits the Feynman path that QCD describes interactions of the without the support of C Division and many integral. Physical quantities are expressed as elementary particles and that these numeri- of its staff. We have received generous sup- integrals of the quark and gluon fields over cal methods are currently the most powerful port from Cray Research and are particularly the space-time continuum with the QCD means for extracting the predictive content indebted to Bill Dissly and George Spix for Lagrangian appearing in an exponential as a of QCD. contribution of their skills and their time. 9 kind of Gibbs weight factor. This is directly analogous to the partition function formula- tion of statistical machanics. The path inte- gral prescription for strong interaction dynamics becomes well defined mathe- matically when the space-time continuum is Calculated and experimental values for the masses and coupling approximated by a discrete four-dimensional strengths of some mesons and baryons. lattice of finite size and the integrals are evaluated by Monte Carlo sampling, Calculated Relative Experimental The original Monte Carlo ideas of Metrop- Value Error Value olis and Ulam have now been applied to (MeV/c2) (v.) (MeY”/c’) QCD by many researchers. These efforts Masses have given credibility, but not confirmation, to the hope that computer simulations might p meson 767 18 769 indeed provide critical tests of QCD and ExciIcd p 416 27 I 300’? significant numerical results. With consider- 6 meson I54 15 983 able patience (on the order of many months ..1I meson 413 17 1275 of computer time) a VAX 11/780 can be used Prolon 989 23 940 10 study universes of about 3000 space-time A baryon I99 17 1210 points. Such a universe is barely large enough to contain a proton and not really adequate Couplings for a quantitative calculation. Consequently, with these methods, any result from a com- f, 21 93 puter of VAX power is, at best, only an fp Is I44 indication of what a well-done numerical simulation might produce.

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