Long-range interactions in double heavy tetraquarks $\bar{Q}\bar{Q}qq$

At the large distances compared to the chiral symmetry breaking scale, a four-quark system $\bar{Q}\bar{Q}qq$ (with $Q$ as heavy and $q$ as light quarks) can be treated as two asymptotic mesons interacting via strong residual forces. The static heavy quark assumption enables using the Born-Oppenheimer approximation, where one can compute the potential between two heavy antiquarks in the presence of two light quarks of finite mass – a prescription utilized in several lattice QCD studies. To analyse the long-range strong force in a $\bar{Q}\bar{Q}qq$ system, we study the interaction between two bottom mesons in the heavy quark limit using chiral effective field theory and dispersion theory with unphysical pion mass. We present methods to obtain two-pion-exchange potential between two static heavy mesons at non-physical pion mass and compare our preliminary results with the corresponding lattice QCD potentials.