Three- and four-jet production is measured in deep-inelastic $ep$ scattering at low $x$ and $Q^2$ with the H1 detector using an integrated luminosity of $44{.}2 {\rm pb}^{-1}$. Several phase space regions are selected for the three-jet analysis in order to study the underlying parton dynamics from global topologies to the more restrictive regions of forward jets close to the proton direction. The measurements of cross sections for events with at least three jets are compared to fixed order QCD predictions of ${\mathcal{O}}(\alpha_{\rm s}^2)$ and ${\mathcal{O}}(\alpha_{\rm s}^3) $ and with Monte Carlo simulation programs where higher order effects are approximated by parton showers. A good overall description is provided by the ${\mathcal{O}}(\alpha_{\rm s}^3) $ calculation. Too few events are predicted at the lowest $x \sim 10^{-4}$, especially for topologies with two forward jets. This hints to large contributions at low $x$ from initial state radiation of gluons close to the proton direction and unordered in transverse momentum. The Monte Carlo program in which gluon radiation is generated by the colour dipole model gives a good description of both the three- and the four-jet data in absolute normalisation and shape.
A precision measurement of jet cross sections in neutral current deep-inelastic scattering for photon virtualities $5.5<Q^2<80\,{\rm GeV}^2$ and inelasticities $0.2<y<0.6$ is presented, using data taken with the H1 detector at HERA, corresponding to an integrated luminosity of $290\,{\rm pb}^{-1}$. Double-differential inclusive jet, dijet and trijet cross sections are measured simultaneously and are 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 respective $Q^2$-interval are also determined. Previous results of inclusive jet cross sections in the range $150<Q^2<15\,000\,{\rm GeV}^2$ are extended to low transverse jet momenta $5<P_{T}^{\rm jet}<7\,{\rm GeV}$. The data are compared to predictions from perturbative QCD in next-to-leading order in the strong coupling, 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.
Inclusive jet cross sections for $P_T^{\rm jet}$ = 5-7 GeV$^2$ measured as a function of $Q^2$ in the range 150-15000 GeV$^2$. The cross section values and uncertainties have been determined in the scope of the analysis of an earlier H1 publication (<a href="https://inspirehep.net/record/1301218">INSPIRE</a>, <a href="https://www.hepdata.net/record/ins1301218">HEPData</a>). See Table 5 of arXiv:1406.4709v2 for details of the correlation model.
Normalised inclusive jet cross sections for $P_T^{\rm jet}$ = 5-7 GeV$^2$ measured as a function of $Q^2$ in the range 150-15000 GeV$^2$. The cross section values and uncertainties have been determined in the scope of the analysis of an earlier H1 publication (<a href="https://inspirehep.net/record/1301218">INSPIRE</a>, <a href="https://www.hepdata.net/record/ins1301218">HEPData</a>). See Table 5 of arXiv:1406.4709v2 for details of the correlation model.
Matrix of statistical correlation coefficients of the unfolded jet cross sections at high $Q^2$. The statistical correlations have been determined in the scope of the analysis of an earlier H1 publication (<a href="https://inspirehep.net/record/1301218">INSPIRE</a>, <a href="https://www.hepdata.net/record/ins1301218">HEPData</a>).
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