Restrictions on the mass of the KK excitation W ′ from the Higgs boson diphoton decay and the single top production

In the framework of stabilized brane-world models we consider the contribution of the W ′ boson and the rest of the W boson KK tower to the Higgs boson decay to two photons and to the single top production process. Comparing the signal strengths calculated in this approach with the experimental ones obtained at the LHC and taking into account the expected improvements at future high luminosity HL-LHC, high energy HE-LHC, and FCC-hh projects, we get predictions for the limits on the W’ boson mass depending on its coupling to SM fermions.


Introduction
We consider a stabilized Randall-Sundrum brane-world model.
The lowest KK excitation of the W is called W'.
The distance between the branes is stabilized by a bulk scalar field.
If only SM gauge fields propagate in the RS bulk, the masses of the KK excitations of the SM gauge bosons have to be larger than 20 TeV in order not to contradict the EW precision data.
In the stabilized brane-world models, where the warp factor is different from the exponential of a linear function, lighter KK excitations of the SM fields may be allowed.

Motivation
The excitations of the W boson (W boson KK tower) contribute to the single top quark production, as well as to the diphoton decay of the Higgs boson via the triangle diagrams.
The correlation between these contributions and the growing precision of experimental measurements may allow one to use these processes for analyzing finer deviations from the SM predictions and gives new stronger bounds on the W′ boson mass.

Diphoton decay of the Higgs boson
The amplitude of the Higgs boson decay to two photons The decay width in terms of the dimensionless amplitude A The dominant contributions of the t-quark and W boson are taken into account The contribution of the W boson KK tower to the Higgs decay to two photons the first excitation should be identified with the W′ The parameterization for the rest KK tower is chosen as in Theor. Math. Phys.170 (2012) 90 Finally, we present the Higgs decay width to two gamma as a function of the W' coupling and W' mass Single top quark s-channel production The effective interaction Lagrangian of the W boson KK tower in the energy range close to the mass of the W′ boson The SM part of Lagrangian Using the same parameterization: Then the process amplitude is This assumption allows one to present the single top quark production cross section as a function of the W' coupling and W' mass as well.
Numerical calculations have been done in a special version of the CompHEP package which includes functions for table calculations and also a routine for chi2-analysis of the signal strength.

Single top quark s-channel production modelling
We provide scan over W' mass and coupling and look for deviations in the region of W' mass 6 SM W' W' width changes with its mass and coupling dynamically Cross section with W' and KK tower impact is calculated with similar cut on the invariant tB mass.
With W' mass growth it width comes more then 600GeV and its resonant impact becomes negligible. The available experimental data on signal strength do not allow one to obtain restrictions on the W' mass.
The high luminosity programme is scheduled to start in 2024 Combination with provides additional restrictions on model parameters

Conclusions
• Simultaneous calculations of the signal strengths of the single top quark production and Higgs boson decay to two photons processes for the W′ boson masses in the range from 2 TeV to 20 TeV and the coupling from 0 to 1 have been done.
• It is shown that the available experimental data do not allow one to obtain restrictions on the W' mass from the diphoton Higgs decay channel or the single top quark production.
• The restrictions on the W′ boson mass have been estimated for future colliders.