Transverse Momentum Resolution

The formulae used to estimate transverse are taken from the Particle Data Group's Review of Particle Physics[#Yao:2006px##1###]. Using (for the most part) their notation and descriptions, for a particle with charge #tex2html_wrap_inline417# of momentum #tex2html_wrap_inline419# in a uniform magnetic field #tex2html_wrap_inline421# with a pitch3 angle #tex2html_wrap_inline427#

#math14#
#displaymath65# (1)

where #tex2html_wrap_inline429# is the radius of curvature in the projection of the trajectory onto the bend plane, #tex2html_wrap_inline431# is in GeV/c, #tex2html_wrap_inline433# is in Tesla, and #tex2html_wrap_inline435# is in meters. In the remainder of this note it will be assumed that #tex2html_wrap_inline437#. Further, the magnetic field is assumed to be uniform everywhere and in the #tex2html_wrap_inline439#-direction. The curvature #math15##tex2html_wrap_inline441#. The variance of #tex2html_wrap_inline443# has two contributions,
#math16#
#displaymath69# (2)


#math17#
#displaymath73# (3)

where #tex2html_wrap_inline445# is the position resolution in meters, #tex2html_wrap_inline447# is the projected length of the track onto the bending plane in meters and #tex2html_wrap_inline449# is the number of measurements.
#math18#
#displaymath79# (4)

where #tex2html_wrap_inline451# is the number of radiation lengths in the detector and #tex2html_wrap_inline453# is the total track length in the detector. For the momentum estimate, the amount of material in front of the detector is ignored.