Nonrelativistic effective field theories for bound states: muonic hydrogen and the \(B_c\)
Clara Peset (Barcelona, Autonoma U.)

Nonrelativistic effective field theories have proven to be an extremely powerful tool in the description of diverse scenarios in particle physics. They provide us with a wide range of theoretical predictions otherwise out of reach for us. We will introduce the theoretical motivation and set up of these type of theories and as an application we will study two relevant bound state systems described by them: the Lamb shift in muonic hydrogen, from which the proton radius and the hyperfine splitting can be obtained, and the \(B_c\) system, which is a useful place where to obtain a determination of the heavy quark masses and the \(V_{cb}\) CKM-matrix element. The relevant theories in the description of these systems are potential nonrelativistic QED (pNRQED) and potential nonrelativistic QCD (pNRQCD) respectively. Both theories provide us with a well defined power counting, that gives us control both on out computations and on the size of the uncomputed terms. In order to gain enough precision to competitively compare to current experiments, we perform our computations at next-to-next-to-next-to leading order. This means we obtain the spectrum up to terms of order m*alpha^5.