Machine learning the trilinear and light-quark Yukawa couplings from Higgs pair kinematic shapes

Revealing the Higgs pair production process is the next big challenge in high energy physics. In this work, we explore the use of interpretable machine learning and cooperative game theory for extraction of the trilinear Higgs self-coupling in Higgs pair production. In particular, we show how a topological decomposition of the gluon-gluon fusion Higgs pair production process can be used to simplify the machine learning analysis flow. Furthermore, we extend the analysis to include $q\bar{q}\to hh$ production, which is strongly suppressed in the Standard Model, to extract the trilinear Higgs coupling and to bound large deviations of the light-quark Yukawa couplings from the Standard Model values. The constraints on the rescaling of the trilinear Higgs self-coupling, $κ_λ$, and the rescaling of light-quark Yukawa couplings, $κ_u$ and $κ_d$, at HL-LHC (FCC-hh) from single parameter fits are: \begin{eqnarray} κ_λ&=&[0.53,1.7] \;\;([0.97, 1.03])\nonumber \newline κ_u&=&[-470,430] \;\;([-58,55])\nonumber \newline κ_d&=&[-360,360] \;\;([-26,28])\nonumber \end{eqnarray} We show that the simultaneous modification of the Yukawa couplings can dilute the constraints on the trilinear coupling significantly. We perform similar analyses for FCC-hh. We discuss some motivated flavourful new physics scenarios where such an analysis prevails.