Three- and four-jet final states have been measured in photoproduction at HERA using the ZEUS detector with an integrated luminosity of 121 pb^-1. The results are presented for jets with transverse energy E_T^jet>6 GeV and pseudorapidity |eta^jet|<2.4, in the kinematic region given by the virtuality of the photon Q^2<1 GeV^2 and the inelasticity 0.2<y<0.85 and in two mass regions defined as 25<M_nj<50 GeV and M_nj>50 GeV, where M_nj is the invariant mass of the n-jet system. The four-jet photoproduction cross section has been measured for the first time and represents the highest-order process studied at HERA. Both the three- and four-jet cross sections have been compared with leading-logarithmic parton-shower Monte Carlo models, with and without multi-parton interactions. The three-jet cross sections have been compared to an order(alpha alpha_s^2) perturbative QCD calculation.
Cross section D(SIG)/COS(PSI(3)) as a function of COS(PSI(3)) in two jet invariant mass regions, 25 to 50 and > 50 GeV . PSI(3) is the angle in the 3-jet CM frame between the plane containing the highest energy jet (P=4) and the beam, and the plane containing the three jets .
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