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The future Compact Linear Collider (CLIC) offers a possibility for a richprecision physics programme, in particular in the Higgs sector through theenergy staging. This is the first paper addressing the measurement of theStandard Model Higgs boson decay into two muons at 1.4 TeV CLIC. With respectto similar studies at future linear colliders, this paper includes severalnovel contributions to the statistical uncertainty of the measurement. Thelater includes the Equivalent Photon Approximation and realistic forwardelectron tagging based on energy deposition maps in the forward calorimeters,as well as several processes with the Beamstrahlung photons that results inirreducible contribution to the signal. In addition, coincidence of the Bhabhascattering with the signal and background processes is considered, altering thesignal selection efficiency. The study is performed using a fully simulatedCLIC_ILD detector model. It is shown that the branching ratio for the Higgsdecay into a pair of muons BR(${H\rightarrow\mu^+\mu^-}$) times the Higgsproduction cross-section in $WW$-fusion $\sigma(H\nu\bar{\nu})$ can be measuredwith 38% statistical accuracy at ${\sqrt{s} =\text{1.4 TeV}}$, assuming anintegrated luminosity of 1.5 ab$^{-1}$ with unpolarised beams. If 80% electronbeam polarisation is considered, the statistical uncertainty of the measurementis reduced to 25%. Systematic uncertainties are negligible in comparison to thestatistical uncertainty.

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