beta decay operator**]{}

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[**Florian Bonnet$^{a,}$[^1], Martin Hirsch$^{b,}$[^2], Toshihiko Ota$^{c,d,}$[^3], and Walter Winter$^{a,}$[^4]**]{}

[*$^{a}$ Institut für Theoretische Physik und Astrophysik, Universität Würzburg,\
97074 Würzburg, Germany* ]{}\
[*$^{b}$ AHEP Group, Instituto de Física Corpuscular – C.S.I.C./Universitat de Val[è]{}ncia\
Edificio de Institutos de Paterna, Apartado 22085, 46071 Val[è]{}ncia, Spain* ]{}\
[*$^{c}$ Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),\
Föhringer Ring 6, 80805 München, Germany* ]{}\
[*$^{d}$ Department of Physics, Saitama University,\
Shimo-Okubo 255, 338-8570 Saitama-Sakura, Japan* ]{}

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Introduction {#sect:Intro}
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Neutrinoless double beta ([$0\nu\beta\beta$ ]{}) decay is mostly known as a sensitive probe for Majorana neutrino masses [@Avignone:2007fu; @GomezCadenas:2011it; @Rodejohann:2012xd; @Barabash:1209.4241]. However, the mass mechanism is only one out of many possible contributions to the [$0\nu\beta\beta$ ]{}decay amplitude [@Rodejohann:2011mu; @Deppisch:2012nb]. The aim of the current paper is to provide a (tree-level) complete list of all possible contributions to the neutrinoless double beta decay dimension nine ($d=9$) operator: $$\mathcal{O} \propto \bar u \bar u  \, d d \, \bar e \bar e \, 
\label{equ:effop}$$ From this list one can easily recover all known contributions to [$0\nu\beta\beta$ ]{}decay. More interestingly, however, we will identify a number of new possibilities to generate [$0\nu\beta\beta$ ]{}decay not discussed in the literature previously.

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