Measurement of multi-jet final states in photoproduction with ZEUS at HERA
 
Three- and four-jet final states were measured in photoproduction 
at HERA using the ZEUS detector using an integrated luminosity of 121 pb-1. 
The three-jet results are presented in a wider phase-space and are based 
on over seven times the luminosity of the previous HERA publication. 
The four-jet photoproduction cross section was measured for the 
first time and represents the highest order process studied at HERA. 
The events were studied in  a low-, 25 < Mnj < 50 GeV, and a 
high-mass region, Mnj > 50 GeV, where Mnj is the invariant mass of 
the n-jet system.  The three-jet cross sections are compared 
to an order alpha_s squared perturbative QCD calculation. 
In addition, both the three- and four-jet cross sections are 
compared with leading-logarithmic parton-shower Monte Carlo 
models, with and without multi-parton interactions.