Finding the vertex position using the SPD in stand alone mode and the effects of the off-axis vertexm

The Inner T rac king System (ITS) detector of the Al- ice apparatus giv es a go o d opp ortunit y to determine the v ertex p osition, along the b eam axis (z co ordinate), ev en in the absence of trac king and, therefore, without ev en t reconstruction. This can b e obtained b y using only the information of the t w o Silicon Pixel Detector (SPD) la y ers. In principle it is suÆcien t to lo ok at the correlation b et w een the z- co ordinate of the t w o hits generated, b y the same trac k, in these t w ola y ers. In fact in the plane r-z, where r the distance of the hit from z axis (r= p x 2 + y 2 ), the pro jec- tion of a trac k app ears as a straigh tline. Consequen tly the z-p osition of the v ertex corresp onds to the crossing bet w een this line and the b eam axis if the trac kis due to a primary particle. Ob viously it is not p ossible to distinguish the primary particles from the pro ducts of the secondary deca y with- out ev en t reconstruction. Ho w ev er, the con tribution of the secondary trac ks, to the total distribution is statisti- cally negligible. This can b e seen in Fig. 1 whic hsho ws the densit y of the c harged particle in the t w oSPD la y ers for an ev en t generated with v ertex in (0,0,0). In partic- ular the distributions of the secondary particles (the one with lo w er statistics) is an order of magnitude smaller than the inclusiv e distribution. T o optimize the v ertex determination w etookin to ac- coun tsev eral sources of uncertain t yand w e reduced their e ects as far as p ossible. Moreo v er, t w o di eren t algo- rithms for the v ertex determination w ere dev elop ed and their p erformances w ere studied and compared