1. Adam Para, November 29,2005 (Plan for/Thoughts on) Optimization the ILC detector for jet-jet mass resolution

2. Contributions to jet-jet mass resolution Physics: missing neutrinos, final state radiation Jet finding (particles level): ‘out of cone/jet’, ‘underlying event’, combinatorics Jet finding (detector level): from cells to particles, jet mass reconstruction Detector imperfections: cracks, dead areas, backscattering Calibration (measured signals to GeV): Detector linearity Difference in response to different species, detectable vs kinetic vs total energy EM/HAD calorimeters cross-calibration Detector resolution: sampling fluctuations, leakage, fluctuations of loss due to nuclear binding energy Reduced (not eliminated) by the PFA

3. Goals of the exercise Produce a curve/table of jet-jet mass resolution (s) as a function of the detector parameters: Overall thickness (containment) Absorber material (shower size) Active material (gas/silicon/scintillator) Sampling frequency (sampling fluctuations) Readout granularity Readout technology (digital/analog) In principle, the optimal performance of any particular detector may require ‘tuning’ of the underlying procedures, thus requiring an immense effort and/or creating excuses. It is very important, whenever possible, to express the critical parameters of the analysis algorithms in terms of physical parameters (like interaction/radiation length) rather than detector geometry specific terms, like layers, cells.

4. Particle Flow Algorithm What it is: a recipe to improve jet energy resolution by minimizing the contribution hadron energy resolution by reducing the function of a hadron calorimeter to the measurement of neutrons and K 0 ’s only What it is not: an universal and complete prescription for minimization of jet energy resolution. Examples: detector linearity, EM/HAD cross calibration are factors above and beyond the PFA. Why bother with academic distinctions: performance measures. Example: total event energy measurement at the Z0 pole. It ignores the issues of PFA performance as a function of jet environment, but includes various detector-induced effects.

5. PFA: functional description ‘Final’ list of hit cells has, in general, two problems: Missing hits, due to incorrect association with a charged track Spurious hit due to left-overs of charged particles showers. They can by isolated hits, or form clusters (a.k.a. ‘fragments’) List of reconstructed tracks and their momenta List of hits in EM and HAD calorimeters PFA List of hits which are NOT produced by charged particles

6. PFA and post-PFA decisions EM clusters (a.k.a.  ’s) identification: Inside or after the PFA algorithm? Does it matter? For jet energy measurement: does one need a positive identification of a cluster as  (a.k.a. H-matrix) ? (Why?) is it important to remove the MIP trace at the very beginning of the PFA? Classification of the resulting energy clusters as ‘primary neutral hadrons’ or ‘charged particles left-overs’: It is (should be) an integral part of the PFA Is it possible to differentiate n/ñ/K 0 showers (calibration!) Treatment of ‘single isolated hits’ (or very small clusters)?

7. PFA: performance measures Ideal PFA would produce the list of hit cells ‘hit’ by neutrals. Possible measures of the PFA algorithm performance, FOM: 1. |N hit (PFA) –N hit (true)| is minimal 2. |E hits (PFA) –E hits (true)| is minimal 3. |N hit clust (PFA) –N hit clust (true)| is minimal 4. Variance(N hit (PFA) –N hit (true)) is minimal 5. Variance(E hits (PFA) –E hits (true)) is minimal 6. Variance(N hit clust (PFA) –N hit clust (true)) is minimal Note: in cases 4-6 it is not necessary that the mean value is zero (effective calibration) These measures isolate the PFA performance from the detector-related contributions (non-linearities, calibrations)

8. Inside the PFA Step 1: Cluster hits Given two hits, X and Y, define a ‘distance’ between them (need not be symmetric!): Spatial separation Hit density weighted Gradient weighted Decide: X  cluster(Y) Y  cluster(X) Dist(X,Y) > ‘cut-off’, start a new cluster Step 2:Associate cluster(s) with charged track Distance of cluster from a track Closest point Centroid Goble up clusters until  E cluster ≈ p track

9. Tuning of the PFA, I How many clustering algorithms? EM and HAD the same, or dedicated EM-shower finder exploiting known shower characteristics Clustering cut-off parameter Too high: too large clusters, eat up energy from the neutrals Too low: fragment the hadronic shower into several clusters. They will usually be associated with the charged tracks, but small clusters displaced laterally may be left over Track-cluster(s) association Too restrictive – create fragments Too loose – eat up neutral energy

10. Tuning of the PFA, II PFA parameters need not to be fixed, they may depend on the charged track momentum (known at this point) PFA parameters may depend on the running conditions and/or physics analysis (ZH/tŦ/ZHH/other) hence Study FOM of PFA as a function of charged/neutral shower separation, charged shower energy Study the neutral/charged shower separation and their energy imbalance for different √s and physics processes to optimize the PFA parameters for the physics goal

11. PFA performance The dominant contribution to the energy resolution, so far, seems to be due to the fluctuations in the left-over ‘fragments’ of charged hadrons. It is a result of a tuning of the clustering/association parameters to balance the cluster growth of charged particles (hence loss of neutral energy) and the creation of spurious neutral clusters. These ‘fragments’ are presumably clusters of energy deposited by neutral particles (fast neutrons and/or K0’s) produced in the charged hadron shower Modeling of neutral component of hadronic shower is poorly constrained by the existing data, hence large variation between various simulation packages. It may lead to large error on the claimed PFA performance Perhaps… Fine grained MINOS Calibration detector was exposed to hadron test beam 1-10 GeV. Perhaps one can compare the frequency and energy distribution of detached energy clusters in the data and simulation. Hadron shower simulation technology is making significant progress, but substantial differences exist at this point in time. One should compare the PFA performance with different showering codes. Ideally, the PFA would be robust against simulation changes. If not – stand alone FLUKA is probably the best guess.

12. Possible(?) improvements of the current algorithms Or… what can be done differently.. The goal is to attach more hits to the charged clusters without loosing the neutral clusters. 1. Use track more information. At the moment the hit clustering is done without any guidance from the tracking. But we want to remove the shower ‘caused’ by known energy charged hadron. Add to the ‘distance’ used for clustering a term involving the distance of the cell from the extrapolated trajectory? It may permit to relax the clustering cut-off and accumulate more of the energy deposition along the track while preventing a runaway cluser. It may also prevent clusters from growing ‘sideways’ and gobbling up hits from neighboring showers 2. (in the scintillator case): make use of the analog information in the ‘distance’ definition ? 3. Determine the angular resolution for neutral clusters. Use it to associate the neutral cluster with the charged hadron shower.

13. Fundamentals of Clustering All of the algorithms used so far are of ‘agglomerative’ nature: clusters are grown by attaching cells up to a certain cut-off value of the distance between the cells. While it is the most popular class of algorithms, it has certain shortcomings: 1. It depends on the arbitrary choice of the starting seeds (this is probably of very little importance here) 2. The cluster assignment (cell to a cluster) decision is irreversible, even if taken at the very early stages of the algorithm. Clusters can be merged, though. 3. It makes no use of a global information (event topology) until the very late stages of association of found clusters with the charged particle trajectory. 4. At the scale of granularity of the putative calorimeters our sets of hit cells represent a web of interconnected segments rather than isolated groups of closely packed points in phase space.

14. Possible Alternative: A Divisive Clustering Algorithm General concept: Put all hits into one cluster. Examine local cluster properties (configuration of links, local gradients) to break some links and divide the overall set of hits into several clusters. Potential advantages: It allows to utilize the global event information: the set of initial positions/directions and momenta of the charged hadrons. Positions and directions provide a good initial guess for the cluster seeds, whereas the momentum may provide cluster-dependent set of parameters for the divisive algorithm