Meson spectrum in the large N limit

Abstract

We present the result of our computation of the lowest lying meson masses for SU(N) gauge theory in the large N limit (with Nf /N → 0). The final values are given in units of the square root of the string tension, and with errors which account for both statistical and systematic errors. By using 4 different values of the lattice spacing we have seen that our results scale properly. We have studied various values of N (169, 289 and 361) to monitor the N-dependence of the most sensitive quantities. Our methodology is based upon a first principles approach (lattice gauge theory) combined with large N volume independence. We employed both Wilson fermions and twisted mass fermions with maximal twist. In addition to masses in the pseudoscalar, vector, scalar and axial vector channels, we also give results on the pseudoscalar decay constant and various remormalization factors.

SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

“…In the few cases labelled by * in table 15 the fits are very poor with χ 2 /n df ≥ 3, and so we quadruple the stated error in those cases in the hope that this encodes the increased uncertainty. Referring to tables 1-8 we see that the number of values used within a given fit varies from 6 in SU(3) to 4 in SU (10) and SU (12). Since we have 2 parameters in our fit, 4 points is a very small number for a fit.…”

“…; l √ σ ∼ 2.6 for SU (8), SU (10), SU (12). We will exhibit a finite volume analysis for a representative of each of these three groups.…”

“…It is convenient to use a 2 σ(a) since its calculated value has very small errors. The results of these continuum extrapolations are listed in tables 23-30 for the gauge groups ranging from SU 2) to SU (12). (As always, each E doublet, and each T 2 or T 1 triplet appears as a single state in our tables and discussions.)…”

“…A few entries are accompanied by a star denoting a poor fit, 2.5 < χ 2 /n df < 3.5, or a double star denoting a very poor fit, χ 2 /n df ≥ 3.5. For SU (10) and SU (12) we have only 5 values of β and since the masses at the coarsest value of β often have to be discarded from the fit (not surprisingly) and JHEP12(2021)082 since we are fitting 2 parameters, we often have only 2 degrees of freedom. For lower N we usually have 3 and sometimes 4 degrees of freedom, which gives much more confidence in the extrapolations.…”

“…The computational cost of performing calculations at larger N means that further improvement to our work is still desirable. (It would also be very interesting to see the existing calculations at very large N using space-time reduction [12] extended to calculations of the glueball spectrum, just as they have been in 2 + 1 dimensions [13].) Nonetheless we are able in this paper to provide the first calculation of the masses of the ground states in all the R P C channels of the continuum SU(N → ∞) gauge theory, as well as some excited states in most channels.…”