Developing an Effective Field Theory for Rotations in Odd-odd Nuclei

We develop an effective field theory to understand rotational bands in deformed odd-odd nuclei. Effective theories are bottom-up approaches where operators are expanded order-by-order in a power counting with adjustable low-energy constants denoting their strength. This enables uncertainty estimation. We employ an axially symmetric rotor for the even-even core and couple the unpaired proton and neutron to it via gauge potentials. The separation of scales between the low-energy collective rotation and higher-energy excitations of the core allows us to introduce an expansion in powers of the rotational energy over the lowest intrinsic excitation energy, i.e., to order operators in the Hamiltonian by their relevance. At leading order, the effective theory is similar to that for deformed odd mass nuclei. At next-to-leading order, couplings are predicted in band heads differing by two units of angular momentum. This yields a self-coupling in $K=1$ states, for example in ${}^{180}$Ta, and manifests itself as a staggering in the moment of inertia. The theory also allows couplings between different bands though these cases are more rare. We discuss successes and limits of the effective theory.