Editing Proton decay (section)

== Decay operators ==

=== Dimension-6 proton decay operators ===
The [[classical scaling dimension|dimension]]-6 proton decay operators are <math display="inline"> qqq\ell/\Lambda^2, </math> <math display="inline"> d^c u^c u^c e^c/\Lambda^2, </math> <math display="inline"> \overline{e^c}\overline{u^c}qq/\Lambda^2, </math> and <math display="inline"> \overline{d^c}\overline{u^c}q\ell/\Lambda^2, </math> where <math>\Lambda</math> is the [[Cutoff (physics)|cutoff scale]] for the [[Standard Model]]. All of these operators violate both baryon number ({{mvar|B}}) and [[lepton number]] ({{mvar|L}}) conservation but not the combination [[B - L|{{mvar|B}}&nbsp;&minus;&nbsp;{{mvar|L}}]].

In <abbr title="Grand Unified Theory">GUT</abbr> models, the exchange of an [[X and Y bosons|X or Y&nbsp;boson]] with the mass {{math|Λ}}{{sub|GUT}} can lead to the last two operators suppressed by <math display="inline"> 1/\Lambda_\text{GUT}^2 </math>. The exchange of a triplet Higgs with mass {{mvar|M}} can lead to all of the operators suppressed by <math display="inline"> 1/M^2 </math>. See ''[[Doublet–triplet splitting problem]]''.

<gallery caption="Proton decay. These graphics refer to the [[X and Y bosons|X bosons]] and [[Higgs boson]]s." widths="250px" heights="300px" perrow="3">
Image:Proton decay2.svg|Dimension-6 proton decay mediated by the '''X boson (3,2){{su|b=−{{frac|5|6}}}}''' in SU(5) GUT
Image:proton decay3.svg|Dimension-6 proton decay mediated by the<br>'''X boson (3,2){{su|b={{frac|1|6}}}}''' in flipped SU(5) GUT
Image:proton decay4.svg|Dimension-6 proton decay mediated by the<br>'''triplet Higgs T (3,1){{su|b=−{{frac|1|3}}}}''' and the<br>'''anti-triplet Higgs {{overline|T}} ({{overline|3}},1){{su|b={{frac|1|3}}}}''' in SU(5) GUT
</gallery>

=== Dimension-5 proton decay operators ===
In supersymmetric extensions (such as the [[Minimal Supersymmetric Standard Model|MSSM]]), we can also have dimension-5 operators involving two fermions and two [[sfermion]]s caused by the exchange of a tripletino of mass {{mvar|M}}. The sfermions will then exchange a [[gaugino]] or [[Higgsino]] or [[gravitino]] leaving two fermions. The overall [[Feynman diagram]] has a loop (and other complications due to strong interaction physics). This decay rate is suppressed by <math display="inline"> 1/ M M_\text{SUSY} </math> where {{math|''M''{{sub|SUSY}}}} is the mass scale of the [[superpartner]]s.

=== Dimension-4 proton decay operators ===

[[Image:R-parity violating decay.svg|frame|right]]

In the absence of [[matter parity]], supersymmetric extensions of the Standard Model can give rise to the last operator suppressed by the inverse square of [[sdown]] quark mass. This is due to the dimension-4 operators {{math|{{SubatomicParticle|Quark}}{{SubatomicParticle|Lepton}}{{SubatomicParticle|Down squark}}{{sup|c}}}} and {{math|{{SubatomicParticle|Up quark}}{{sup|c}}{{SubatomicParticle|Down quark}}{{sup|c}}{{SubatomicParticle|Down squark}}{{sup|c}}}}.

The proton decay rate is only suppressed by <math display="inline"> 1/M_\text{SUSY}^2 </math> which is far too fast unless the couplings are very small.