Telltale Traces of U(1) Fields in Noncommutative Standard Model Extensions

الأصل · EN

Restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet/infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the Standard Model. In this paper, we study a general class of 4-dimensional noncommutative models consistent with these restrictions. Specifically we consider models based upon a gauge theory with the gauge group U(N₁)× U(N₂) ×... × U(Nₘ) coupled to matter fields transforming in the (anti)-fundamental, bi-fundamental and adjoint representations. Noncommutativity is introduced using the Weyl-Moyal star-product approach on a continuous space-time. We pay particular attention to overall trace-U(1) factors of the gauge group which are affected by the ultraviolet/infrared mixing. We show that, in general, these trace-U(1) gauge fields do not decouple sufficiently fast in the infrared, and lead to sizable Lorentz symmetry violating effects in the low-energy effective theory. Making these effects unobservable in the class of models we consider would require pushing the constraint on the noncommutativity mass scale far beyond the Planck mass (MNC 10¹⁰⁰ Mₚ) and severely limits the phenomenological prospects of such models.