HF Misalignment

Generator Level Study

HF is shifted maximum 10 mm in transverse plane. Eta values of the rings and Delta phi size for the readouts are changed. In the ideal case, center of the HF detector is on the beam axis and readouts on the rings are on the same eta interval. Because energy flow is phi symmetric on the same eta values, total energy flow on the readouts needed to be same. Because of the shift readouts are not on the same eta interval and their eta values are not same anymore. So that, uniformity of Energy flow with respect to phi is affected. In this study we investigate how shift affect readouts’ energy flow on the same ring, delta phi sizes, eta values of the readouts, change of solid angle and effect of solid angle change on the energy flow. An analytical function depends on shift value and explains the total energy flow is also found.

Eta and Delta Phi

Figure 1: a) edges of the ring 12 before vertex shift,b) edges of the ring 12 after vertex shift

Figure 2:a)edges of the ring 1 before vertex shift, b)edges of the ring 1 after vertex shift

Because Ring 12(ieta 41) is the closest ring to beam axis, homogeneity of the eta is much affected under transverse shift.

  Figure 3:delta phi vs phi graphs for ring 12 and ring 1  

Delta Phi is the difference between edge of the readout’s phi values in ideal case and in shifted case. As mentioned above phi values of readout change and delta phis reach peak values at 90 and 270. Moreover Phi intervals of the readouts are not constant. (in genlevel study we assume that ieta 40 and 41 rings have 36 parts)

Energy Flow vs Phi

       figure 4: energy flow for 10 mm shifted HF and not shifted hf for Ring 1 and Ring 12   

Red dots represent energy flow in ideal case and Blue dots represent energy flow in 10 mm shift case. As it can be seen Energy flows of readouts are almost same in ideal case. However, in 10 mm shifted case, energy flows are minimal at side farthest from the beam line(0°) and maximal otherwise (180°). Because radius of ring 12 is between 125mm and 169mm, 10 mm shift causes big effect on energy flow. However change of energy flow on ring 1 can be negligible.