Editing R-parity (section)

==Possible origins of R-parity==
A very attractive way to motivate R-parity is with a {{nowrap|{{mvar|B − L}}}} continuous gauge symmetry which is spontaneously broken at a scale inaccessible to current experiments. A continuous <math>U(1)_{B-L}</math> forbids renormalizable terms which violate {{mvar|B}} and {{mvar|L}}.<ref>
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}}</ref> If <math>U(1)_{B-L}</math> is only broken by scalar vacuum expectation values (or other order parameters) that carry even integer values of {{nowrap|3({{mvar|B − L}})}}, then there exist an exactly conserved discrete remnant subgroup which has the desired properties.<ref>
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}}</ref> The crucial issue is to determine whether the [[sneutrino]] (the supersymmetric partner of neutrino), which is odd under R-parity, develops a vacuum expectation value. It can be shown, on phenomenological grounds, that this cannot happen in any theory where <math>U(1)_{B-L}</math> is broken at a scale much above the [[electroweak]] one. This is true in any theory based on a large-scale [[seesaw mechanism]].<ref>
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}}</ref> As a consequence, in such theories R-parity remains exact at all energies.

This phenomenon can arise as an automatic symmetry in [[SO(10)]] [[grand unified theory|grand unified theories]]. This natural occurrence of R-parity is possible because in SO(10) the Standard Model fermions arise from the 16&nbsp;dimensional [[spinor representation]], while the Higgs arises from a 10&nbsp;dimensional vector representation. In order to make an SO(10) invariant coupling, one must have an even number of spinor fields (i.e. there is a spinor parity). After GUT symmetry breaking, this spinor parity descends into R-parity so long as no spinor fields were used to break the GUT symmetry. Explicit examples of such SO(10) theories have been constructed.<ref>
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