0-Lifetime Physics Function

Last Update: 08-Dec-05

Implementation in Code

The 0-lifetime physics function is approximately a delta-function in Lxy(true) or VPDL(true). This is implemented in code as:

n_cc(x^tr,tag;δ) = P_tag / δ	for 0 < x^tr < δ
n_cc(x^tr,tag;δ) = 0	for x^tr >= δ

This is correctly normalized to P_tag if:

_i=bins

n_cc

x_i,tag

x_bin

with

x_bin

When looping over x^tr (to fill histo's or calculate pdf normalizations, for example) have to be sure that x < δ is a point in the loop.
Normalization integrals have to use Δx_bin = δ which generally means a lot of steps since δ should be small to avoid the problem below.
δ needs to be small or the 0-lifetime PDF will get too much weight (will be non-zero for too many events).

The issue is evaluating the sum giving the Phys-Func * Eff normalization:

n_cc

x_i

This can simply be set to

P_tag

Then, as long as histo's are filled with an x-loop using Δx = δ, the full PDF will be correctly normalized:

PDF_cc

H(y)

K H(K)

n_cc

x^tr

where y = P_t^m for Lxy fits or σ(vpdl) for VPDL fits.