The Breit Frame

The intention of this analysis is to compare fragmentation functions measured in DIS at HERA with those measured by e⁺e^- experiments: in order to do so it is necessary to boost and rotate DIS events to the Breit frame. The Breit frame [4] is defined as the frame in which the exchanged boson is completely spacelike. Its velocity with respect to the laboratory frame is given by $\vec{\beta}\,$ = ($\vec{q}\,$ + 2x$\vec{P}\,$)/(q₀ + 2xP₀), where ( q₀,$\vec{q}\,$) and ( P₀,$\vec{P}\,$) are the 4-momenta of the exchanged boson and the incident proton beam respectively. DIS events are boosted and then rotated so that the virtual photon is along the negative z axis and the plane of the incoming and outgoing positron contains the $\phi$ = 0 direction - this maximises the separation of the outgoing parton from the incoming parton and the proton remnant. The region of z < 0 in this frame, containing the outgoing quark, is defined as the current region while the target region, defined as the region z > 0, contains the scattered positron and proton remnant. In the Quark Parton Model the outgoing struck quark carries momentum Q/2, compared with e⁺e^- annihilation where there are two outgoing quarks, each with momentum Q/2  $\equiv$  $\sqrt{s}$/2. Hence the current region of the Breit frame can be taken to be analogous to one hemisphere of an e⁺e^- annihilation event.