Measurement of Jet Production Cross Sections inDeep-inelastic ep Scattering at HERA

A precision measurement of jet cross sections in neutral current deep-inelastic scattering forphoton virtualities 5:5 < Q$^2$ < 80 Ge V$^2$and inelasticities 0:2 < y < 0:6 is presented, using datataken with the H1 detector at HERA, corresponding to an integrated luminosity of 290pb$^{-1}$. Double-differential inclusive jet, dijet and trijet cross sections are measured simultaneously andare presented as a function of jet transverse momentum observables and as a function of Q$^2$. Jet cross sections normalised to the inclusive neutral current DIS cross section in the respec-tive Q$^2$ interval are also determined. Previous results of inclusive jet cross sections in the range150 < Q$^2$ < 15000 GeV$^2$ are extended to low transverse jet jet momenta 5 < PT < 7 GeV. The data are compared to predictions from perturbative QCD in next-to-leading order in the strongcoupling, in approximate next-to-next-to-leading order and in full next-to-next-to-leading order. Using also the recently published H1 jet data at high values of Q$^2$, the strong coupling constant $\alpha_{s}(m_{Z})$ is determined in next-to-leading order to value of $\alpha_{s}(m_{Z})$ = 0.1172(4)$_{exp}(^{+53}_{-45})_{th}.