From femtoscale boxes to exotic hadrons: a frontier in lattice QCD calculations

One of the major aims of lattice QCD (LQCD) is to understand, from the known underlying theory, QCD, the spectrum and properties of hadrons—strongly interacting particles composed of quarks and gluons. Historically, a semi-quantitative understanding of the lightest hadrons was obtained using the quark model, in which the complicated dynamics of the many-body system were approximately described by the interactions of “constituent” quarks—composite objects with the quantum numbers of the underlying quarks. Experimental results over the last two decades have shown that there are many hadrons that do not fit the quark-model paradigm: these are the so-called exotic mesons. A striking example is the doubly-charmed $T_{cc}^+$, decaying to DDpi, discovered by LHCb in 2022. This has the flavor content $cc \bar u \bar d$, and cannot be understood as a $q \bar q$ meson in the quark model. It is dubbed a “tetraquark”. In this talk, I describe how theoretical and computational developments with LQCD over the last decade have provided the tools to study such states from first principles, and present the status of the implementation of these tools.