Three jet production in neutral current deep inelastic scattering with ZEUS at HERA

Trijet production rates in neutral current deep inelastic scattering have been measured in the range of exchanged boson virtualities between 10 and 5000 GeV2. The data were taken at the ep collider HERA with centre-of-mass energy equal to 318 GeV using the ZEUS detector and correspond to an integrated luminosity of 82.2 inverse picobarns. Jets were identified in the Breit frame using the kT-cluster algorithm in the longitudinally invariant inclusive mode. Measurements of differential dijet and trijet cross sections are presented as functions of jet transverse energy, pseudorapidity and Q2 with jet transverse energy larger than 5 GeV and jet pseudorapidity between -1 and 2.5. Next-to-leading-order QCD calculations describe the data well. The value of the strong coupling constant at the scale of the mass of Z, determined from the ratio of the trijet to dijet cross sections, is 0.1179 +/- 0.0013 stat.+0.0028 -0.0046 exp.+0.0064 -0.0046 (th.).