Massless Fermions: Physics & Existence

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Does modern physics allow for the existence of massless fermions?
 
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Sure. In the Standard Model, all the fundamental fermions are massless; they only acquire mass through their interaction with the Higgs boson.
 
In graphene, there are emergent particles at low energies whose behaviour is well described by a theory of massless fermions. http://arxiv.org/abs/cond-mat/0509330
 

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