Flavor symmetry breaking and improved quark actions

This page summarizes, in terse graphical form, some of the results of our tests of flavor symmetry breaking with various improved actions for Kogut-Susskind quarks.

For more details on this project, you can jump to the following papers: (PostScript files)
First Phys. Rev. paper on testing actions
Second Phys. Rev. paper on testing actions
Lattice-98 conference proceedings

The graphs below show the spectrum of pseudoscalar masses for several different quark actions. To make a fair comparison, we have computed the spectrum at two quark masses for each action, and interpolated to the point where the ratio of the Goldstone pion mass to the rho mass is 0.55. Then, we plot all of the pseudoscalar masses in units of the rho mass. Thus, in each of the plots, the Goldstone pion mass is at 0.55. Then, all of the other pion masses lie above it. Of course, the object is to get all of the pion masses as close to the Goldstone pion mass as possible.

First, just to get the pattern straight, we plot the pseudoscalar masses for one quark action, and label all of the pions. The pions are labelled by their "spin $\otimes$ flavor" structure, where the first factor is the spin and the second factor acts in the four-component flavor space

We see that the local non-Goldstone pion, the flavor $\gamma_0\gamma_5$pion, is one of the best behaved, with the nonlocal pions much worse. The worst case is the three link "flavor unit matrix" pion. The pattern of near degeneracies is predicted by the analysis of Lee and Sharpe.


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The first graph shows the pseudoscalar spectrum for several actions at a fairly coarse lattice, generated with a Symanzik improved gauge action at 10/g2=7.3, using to flavors of dynamical quarks with the Naik term plus three link fattening in the dynamical action.

The actions used for the spectrum computation were:
OneLink: The conventional Kogut-Susskind action, with nearest neighbor coupling
FatNaik: Including simplest three-link fattening paths, as well as the Naik term to correct rotational symmetry
Fat5tad: Includes paths up to five links long, with "minimax" setting of coefficients, including the tadpole factor
Fat7tad: Includes paths up to seven links, completely cancelling couplings to gluons with momentum compontents equal to $\pi$ in any direction, with tadpole factors included
Asqtad: All tree level order a2 errors corrected - paths up to seven links, plus the Naik term, plus Lepage's term correcting a2 p2errors, again with tadpole improvement.


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The second graph shows the same thing on a slightly finer lattice, with 10/g2=7.5. As expected, the finer lattice has better flavor symmetry properties for all of the actions tested.


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Finally, we show the results on a very fine lattice. These masses were calculated on quenched lattices generated with the conventional one-plaquette gauge action, at 6/g2=6.15.


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Most of the computations were done on the T3E at NERSC and on the Paragon at ORNL. This work was supported by DOE grant DE-FG03-95ER-40906.


 
Doug Toussaint
1999-07-29