Atmospheric Neutrinos Can Make Beauty Strange

The large observed mixing angle in atmospheric neutrinos, coupled with Grand Unification, motivates the search for a large mixing between right-handed strange and bottom squarks. Such mixing does not appear in the standard CKM phenomenology, but may induce significant b {yields} s transitions through gluino diagrams. Working in the mass eigenbasis, we show quantitatively that an order one effect on CP violation in B{sub d}{sup 0} {yields} {pi}K{sub S} is possible due to a large mixing between right-handed b and s squarks, while still satisfying constraints from b {yields} s {gamma}. We also include the effect of right- and left-handed bottom squark mixing proportional to m{sub b}{mu} tan{beta}. For small {mu}tan{beta} there may also be a large effect in B{sub s} mixing correlated with a large effect in B{sub d}{sup 0} {yields} {phi}K{sub S}, typically yielding an unambiguous signal of new physics at Tevatron Run II.