Muon anomalous magnetic moment from effective supersymmetry

We present a detailed analysis on the possible maximal value of the union (g - 2)(mu) equivalent to 2alpha(mu) within the context of effective SUSY models with R parity conservation. First of all, mixing among the second susy and the third family sleptons can contribute at one loop level to alpha(mu)(SUSY) and r --> mugamma simultaneously. One finds that alpha(mu)(SUSY) can be as large as (10-20) x 10(-10) for any tan beta, imposing an upper limit on the r --> mugamma susy branching ratio. Furthermore, the two loop Barr-Zee type contributions to alpha(mu)(SUSY) may be significant for large tan,3, if a stop is light and p and At are large enough (- 0 (1) TeV). In this case, it is possible to have alpha(mu)(SUSY) up to O(10) x 10(-10) without conflicting with r --> lgamma. We conclude that the possible maximal value for alpha(mu)(SUSY) is about similar to20 x 10(-10) for any tan beta. Therefore the BNL experiment on the muon alpha(mu) can exclude the effective SUSY models only if the measured deviation is larger than similar to 30 x 10(-10).