Physics potential for the measurement of ${\sigma(H\nu\bar{\nu})\times \text{BR}(H\rightarrow\mu^+\mu^-)}$ at the 1.4 TeV CLIC collider

The future Compact Linear Collider (CLIC) offers a possibility for a rich precision physics programme, in particular in the Higgs sector through the energy staging. This is the first paper addressing the measurement of the Standard Model Higgs boson decay into two muons at 1.4 TeV CLIC. With respect to similar studies at future linear colliders, this paper includes several novel contributions to the statistical uncertainty of the measurement. The later includes the Equivalent Photon Approximation and realistic forward electron tagging based on energy deposition maps in the forward calorimeters, as well as several processes with the Beamstrahlung photons that results in irreducible contribution to the signal. In addition, coincidence of the Bhabha scattering with the signal and background processes is considered, altering the signal selection efficiency. The study is performed using a fully simulated CLIC_ILD detector model. It is shown that the branching ratio for the Higgs decay into a pair of muons BR(${H\rightarrow\mu^+\mu^-}$) times the Higgs production cross-section in $WW$-fusion $\sigma(H\nu\bar{\nu})$ can be measured with 38% statistical accuracy at ${\sqrt{s} =\text{1.4 TeV}}$, assuming an integrated luminosity of 1.5 ab$^{-1}$ with unpolarised beams. If 80% electron beam polarisation is considered, the statistical uncertainty of the measurement is reduced to 25%. Systematic uncertainties are negligible in comparison to the statistical uncertainty.