Dispersive determination of fourth generation quark masses

We determine the masses of the sequential fourth generation quarks $b'$ and $t'$ in the extension of the Standard Model by solving the dispersion relations associated with the mixing between the neutral states $Q\bar q$ and $\bar Qq$, $Q$ ($q$) being a heavy (light) quark. The box diagrams responsible for the mixing, which provide the perturbative inputs to the dispersion relations, involve multiple intermediate channels, i.e., the $ut$ and $ct$ channels, $u$ ($c$, $t$) being an up (charm, top) quark, in the $b'$ case, and the $db'$, $sb'$ and $bb'$ ones, $d$ ($s$, $b$) being a down (strange, bottom) quark, in the $t'$ case. The common solutions for the above channels lead to the masses $m_{b'}=(2.7\pm 0.1)$ TeV and $m_{t'}\approx 200$ TeV unambiguously. We show that these superheavy quarks, forming bound states in a Yukawa potential, barely contribute to Higgs boson production via gluon fusion and decay to photon pairs, and bypass current experimental constraints. The mass of the $\bar b'b'$ ground state is estimated to be about 3.2 TeV. It is thus worthwhile to continue the search for $b'$ quarks or $\bar b'b'$ resonances at the (high-luminosity) large hadron collider.