Dark photon kinetic mixing effects for the CDF <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>-mass measurement
Yu Cheng, Xiao-Gang He, Fei Huang, J. F. Sun, Zhi-Peng Xing
Abstract
A new $U(1{)}_{X}$ gauge boson $X$ primarily interacting with a dark sector can have renormalizable kinetic mixing with the standard model (SM) $U(1{)}_{Y}$ gauge boson $Y$. This mixing besides introduces interactions of dark photon and dark sector with SM particles, it also modifies interactions among SM particles. The modified interactions can be casted into the oblique $S$, $T$, and $U$ parameters. We find that with the dark photon mass larger than the $Z$ boson mass, the kinetic mixing effects can reduce the tension of the $W$-mass excess problem reported recently by CDF from $7\ensuremath{\sigma}$ deviation to within $3\ensuremath{\sigma}$ compared with theory prediction. If there is non-Abelian kinetic mixing between $U(1{)}_{X}$ and $SU(2{)}_{L}$ gauge bosons, in simple renormalizable models of this type a triplet Higgs is required to generate the mixing. We find that this triplet with a vacuum expectation value of order 5 GeV can naturally explain the $W$-mass excess.