What can a heavy $U(1{)}_{\mathrm{B}-\mathrm{L}}$ $Z^{\prime }$ boson do to the muon $(g-2{)}_{\mu }$ anomaly and to a new Higgs boson mass?

Abstract

The minimal $U(1{)}_{\mathrm{B}-\mathrm{L}}$ extension of the Standard Model (B-L-SM) offers an explanation for neutrino mass generation via a seesaw mechanism as well as contains two new physics states such as an extra Higgs boson and a new $Z^{\prime }$ gauge boson. The emergence of a second Higgs particle as well as a new $Z^{\prime }$ gauge boson, both linked to the breaking of a local $U(1{)}_{\mathrm{B}-\mathrm{L}}$ symmetry, makes the B-L-SM rather constrained by direct searches at the Large Hadron Collider (LHC) experiments. We investigate the phenomenological status of the B-L-SM by confronting the new physics predictions with the LHC and electroweak precision data. Taking into account the current bounds from direct LHC searches, we demonstrate that the prediction for the muon $(g-2{)}_{\mu }$ anomaly in the B-L-SM yields at most a contribution of approximately $8.9\times 10^{-12}$ which represents a tension of $3.28$ standard deviations, with the current $1\sigma$ uncertainty, by means of a $Z^{\prime }$ boson if its mass lies in a range of $6.3$ to $6.5$ TeV, within the reach of future LHC runs. This means that the B-L-SM, with heavy yet allowed $Z^{\prime }$ boson mass range, in practice does not resolve the tension between the observed anomaly in the muon $(g-2{)}_{\mu }$ and the theoretical prediction in the Standard Model. Such a heavy $Z^{\prime }$ boson also implies that the minimal value for a new Higgs mass is of the order of 400 GeV.

Comments: 20 pages, 9 figures; discussion extended, an extra figure and references added, conclusions unchanged; final version