gww sid july27

Using p0 mass constraint to improve particle flow ?: 

Using p0 mass constraint to improve particle flow ? Graham W. Wilson, Univ. of Kansas, July 27th 2005 Study prompted by looking at event displays like this one of a 5 GeV p0 in sidmay05 detector. Here photon energies are (3.1, 1.9 GeV), and clearly the photons are very well resolved. Prompt p0’s make up most of the EM component of the jet energy.

Investigating p0 Kinematic Fits: 

Investigating p0 Kinematic Fits Standard technique for p0’s is to apply the mass constraint to the measured gg system. Setting aside for now the combinatoric assignment problem in jets, I decided to look into the potential improvement in p0 energy measurement. In contrast to 'normal ECALs', the Si-W approach promises much better measurement of the gg opening distance, and hence the opening angle at fixed R. This precise qgg measurement therefore potentially can be used to improve the p0 energy resolution. How much ? ( My educated? guess was a factor of 2), and how does this affect the detector concepts ?

Slide3: 

c1 Motivation for good ECAL stochastic resolution

Methodology: 

Methodology Wrote toy MC to generate 5 GeV p0 with usual isotropic CM decay angle (dN/dcosq* = 1). Assumed photon energy resolution (sE/E) of 16%/E. Assumed g-g opening angle resolution of 2 mrad. Solved analytically from first principles, the constrained fit problem under the assumption of a diagonal error matrix in terms of (E1, E2, 2(1-cosq12)), and with a first order expansion. was hoping to get some insight into the analytic dependence on photon resolution assumptions, but problem was somewhat harder than I expected (had to solve a cubic) Note. m2 = 2 E1 E2 (1 - cosq12) p0 kinematics depends a lot on cosq*. Useful to define the energy asymmetry, a ≡ (E1-E2)/(E1+E2) = cosq*.

p0 mass resolution: 

p0 mass resolution Can show that for sE/E = c1/E that Dm/m = c1 / [(1-a2) Ep0]  3.70 Dq12Ep0  (1-a2) So the mass resolution has 2 terms i) depending on the EM energy resolution ii) depending on the opening angle resolution The relative importance of each depends on (Ep0, a)

Angular Resolution Studies: 

Angular Resolution Studies 5 GeV photon at 90°, sidmay05 detector. Phi resolution of 0.9 mrad just using cluster CoG. =andgt; q12 resolution of 2 mrad is reasonable for spatially resolved photons. NB Previous study (see backup slide, shows that a factor of 5 improvement in resolution is possible, (using 1mm pixels !) at fixed R)

p0 mass resolution: 

p0 mass resolution 5 GeV p0 E term q12 term Plots assume: c1 = 0.16 (SiD) Dq12 = 2 mrad For these detector resolutions, 5 GeV p0 mass resolution dominated by the E term

p0 mass resolution: 

p0 mass resolution 20 GeV p0 Asymmetry Contribution to dm/m E term q12 term Plots assume: c1 = 0.16 (SiD) Dq12 = 2 mrad For these detector resolutions, 20 GeV p0 mass resolution dominated by the q12 term (=andgt; KF less helpful)

p0 mass: 

p0 mass 5 GeV p0

Fit quality: 

Fit quality Probability distribution flat (as expected). Spike at low probability corresponds to asymmetric decays (|a|≈1). I think I need to iterate using the fitted values for the error estimation …. a = (E1-E2)/(E1+E2)

p0 energy: 

p0 energy Measured Fitted (improves from 0.36 GeV to 0.23 GeV) (factor of 0.64 !!)

p0 energy for |a| < 0.2: 

p0 energy for |a| andlt; 0.2 Improvement most dramatic : 0.35 -andgt; 0.17

p0 energy for 0.4<|a| < 0.6: 

p0 energy for 0.4andlt;|a| andlt; 0.6 Improvement from 0.36 to 0.21

p0 energy for |a| > 0.8: 

p0 energy for |a| andgt; 0.8 Improvement not so great. (as expected) 0.37 -andgt; 0.33

20 GeV p0, same resolution assumptions: 

20 GeV p0, same resolution assumptions Mass resolution degrades as expected. Constrained fit still works OK.

Slide16: 

20 GeV p0, same resolution assumptions Constrained fit No significant improvement. (as expected)

5 GeV p0, 4 times better q12 resolution: 

5 GeV p0, 4 times better q12 resolution Not much change in mass resolution (dominated by E-term) Fit still works.

p0 energy resolution improvement: 

p0 energy resolution improvement Dramatic ! Factor of 2 for ALL asymmetries.

p0 energy resolution improvement: 

p0 energy resolution improvement |a| andlt; 0.2 Improves by a factor of 0.35/0.065. i.e. a factor of 5 !

Conclusions: 

Conclusions p0 constrained fit has a lot of potential to improve the p0 energy resolution. Will investigate in more detail actual g-g separation capabilities. Puts a high premium on angular resolution if this is as useful as it looks. Looks worthwhile to also look into the assignment problem. May have some mileage for reconstructing the p0’s in hadronic interactions.

Backups: 

Backups

Position resolution from simple fit: 

Position resolution from simple fit C of G all layers Weighted fit of the C of G found in the first 12 layers with hits s = 1.5 mm s = 0.30 mm Using the first 12 layers with hits with Eandgt;180 keV, combine the measured C of G from each layer using a least-squares fit (errors varying from 0.32mm to 4.4mm). Iteratively drop up to 5 layers in the 'track fit'. Position resolution does indeed improve by a factor of 5 in a realistic 100% efficient algorithm! Neglect layer 0 (albedo) Still just d/12 !

Slide23: