Experimental constraints and a possible quantum Hall state at $\nu$=5/2*

Several topological orders have been proposed to explain the quantum Hall plateau at $\nu$=5/2. The observation of an upstream neutral mode on the sample edge [Bid {\it et al.}, Nature (London) {\bf 466}, 585 (2010)] supports the non-Abelian anti-Pfaffian state. On the other hand, the tunneling experiments [Radu {\it et al.}, Science {\bf 320}, 899 (2008); Lin {\it et al.}, Phys. Rev. B {\bf 85}, 165321 (2012); Baer {\it et al.}, Phys. Rev. B {\bf 90}, 075403 (2014)] favor the 331 state which exhibits no upstream modes. We find a topological order, compatible with the results of both types of experiments. That order allows both finite and zero spin polarizations. It is Abelian but its signatures in Aharonov-Bohm interferometry can be similar to those of the Pfaffian and anti-Pfaffian states.