Improved actions of the staggered fermion

To remove O(a) errors by using Symanzik’s program, we must find all possible dimension-6 terms which are scalars under the lattice symmetry transformations. Then, we add them to the original action and adjust their coefficients so that low-momentum physical quantities do not have O(a) errors. When he proposed this program, Symanzik applied it to scalar fields and proved the consistency of the improvement program to all orders of perturbation theory [1]. Lüscher and Weisz applied this program to pure gauge theory and developed the concept of on-shell improved action which demands only the improvement of all physical (on-shell) quantities [2]. Sheikholeslami and Wohlert applied this program to Wilson fermions and proposed a “Clover” term to remove all O(a) errors fromWilson fermions [3]. Naik applied this program to Dirac-Kähler fermions and proposed a three-link term [4]. Although the staggered fermion and the Dirac-Kähler fermion formalisms are the same in the free case, they are quite different when the gauge interaction is included. DiracKähler fermions have two drawbacks: First, the U(1)o ⊗ U(1)e symmetry does not prevent the gauge interaction from producing non-zero mass counterterms, therefore the bare mass parameters have to be tuned in the continuum limit, similar to Wilson fermions; Second, there is no massless Goldstone boson [5]. Therefore, in most applications, the standard staggered fermion formalism is used. Thus, it is important to investigate the improved action for the staggered fermion case. Sharpe’s pioneering work showed that there is no O(a) term for the staggered fermion [6]. Thus the leading order terms in the improved action for staggered fermions is O(a). In this talk, I will present all independent dimension-6 terms, and show which terms remain after a spectrumconserving transformation of the fields. A detailed discussion of these results can be found in ref. [7].