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This paper proposes new symmetries (the body-centred cubic periodicsymmetries) beyond the standard model. Using a free particle expandedSchrodinger equation with the body-centred cubic periodic symmetry condition,the paper deduces a full baryon spectrum (including mass M, I, S, C, B, Q, Jand P) of all 116 observed baryons. All quantum numbers of all deduced baryonsare completely consistent with the corresponding experimental results. Thededuced masses of all 116 baryons agree with (more than average 98 percent) theexperimental baryon masses using only four constant parameters. Thebody-centred cubic periodic symmetries with a periodic constant ``a'' about$10^{-23}$m play a crucial rule. The results strongly suggest that the newsymmetries really exist. This paper predicts some kind of ``Zeeman effect'' ofbaryons, for example: one experimental baryon N(1720)${3/2}^{+}$ with $ \Gamma$= 200 Mev is composed of two N baryons [(N(1659)${3/2}^{+}$ +N(1839)${3/2}^{+}$] = $\bar{N(1749)}$${3/2}^{+}$ with $\Gamma$ = 1839-1659 =180 Mev.

The New Symmetries Beyond the Standard Model (The Body-centred Cubic Periodic Symmetries in Particle Physics)