Jet production in ep neutral current deep inelastic scattering (DIS) provides a rich testing ground for QCD. Within a frame of quark parton model (QPM), one jet event can be explained as events where only struck quark get scattered and the rest of the proton remnants disappear in the original direction of the proton. Dijet events can be described at leading order (LO) by the O(a_s) processes: the boson-gluon fusion (BGF) and QCD Compton Scattering (QCDC), which give rise to two hard jets with opposite transverse momenta. Events with trijet can be seen as dijet processes with a gluon radiation by quarks added or splitting of a gluon in a quark-antiquark pair, which are directly sensitive to  O (a_s²) QCD effects. Due to the extensive previous results of dijets study at HERA, measurement of trijet production in DIS provides an ideal laboratory for testing QCD with higher sensitivity and in more details. For example, it can be used to explore the role of gluons in the DIS process and thus, proton structure. Also, by taking a ratio of trijet to dijet cross section which cancels both experimental and some theoretical uncertainties, it can be used to extract a_s value with very competitive errors.

Figure: On the top, the differential inclusive trijet over dijet cross section is shown as a function of Q². The data are corrected to hadron level to compare with the predictions of perturbative QCD in next-to-leading order.  The yellow band indicates the calorimeter energy scale uncertainty and the hatched band indicates theoretical uncertainties. At the bottom,a_s values extracted from the cross section ratios in each Q² bin are shown together with the world average value. Data and QCD calculations agree well over a wide kinematic range with substaintially decreased uncertanties. The extracted  a_s value is consistant with the world average.