  The existence of a mass-metallicity (MZ) relation in star forming galaxies at
all redshift has been recently established. We aim at studying some possible
physical mechanisms contributing to the MZ relation by adopting analytical
solutions of chemical evolution models including infall and outflow. We explore
the hypotheses of a variable galactic wind rate, infall rate and yield per
stellar generation (i.e. a variation in the IMF), as possible causes for the MZ
relation. By means of analytical models we compute the expected O abundance for
galaxies of a given total baryonic mass and gas mass.The stellar mass is
derived observationally and the gas mass is derived by inverting the Kennicutt
law of star formation, once the star formation rate is known. Then we test how
the parameters describing the outflow, infall and IMF should vary to reproduce
the MZ relation, and we exclude the cases where such a variation leads to
unrealistic situations. We find that a galactic wind rate increasing with
decreasing galactic mass or a variable IMF are both viable solutions for the MZ
relation. A variable infall rate instead is not acceptable. It is difficult to
disentangle among the outflow and IMF solutions only by considering the MZ
relation, and other observational constraints should be taken into account to
select a specific solution. For example, a variable efficiency of star
formation increasing with galactic mass can also reproduce the MZ relation and
explain the downsizing in star formation suggested for ellipticals. The best
solution could be a variable efficiency of star formation coupled with galactic
winds, which are indeed observed in low mass galaxies.
