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Combinatorial Background

Combinatorial Background. PHENIX EWG Electron Working Group (A.Toia). Data Selection. ZVertex ± 30 cm p T cuts 150 MeV/c – 20 GeV/c Matching D ch quality RICH ring quality. “systematics are of much bigger concern than statistics“.

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Combinatorial Background

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  1. Combinatorial Background • PHENIX • EWG Electron Working Group (A.Toia)

  2. Data Selection • ZVertex ±30 cm • pT cuts 150 MeV/c – 20 GeV/c • Matching • Dch quality • RICH ring quality

  3. “systematics are of much bigger concern than statistics“ • Out of ~ 9000 files 3000 files have been cut away, due to • Wrong field • Bad quality from certain detectors • Momentum average • Readout trouble • Event selection: • Minimum bias as only criterion

  4. Cuts • Single Cuts • RICH ring properties • EMC matching • Energy-Momentum matching • pT cuts • Pair Cuts, battling • “geometrical ghosts“ (no sharing of detector hits) • “optical ghosts“ (e.g. RICH ring sharing)

  5. Background Calculation • A priori assumption: • Positive and negative particles have unequal acceptances • To be proved (cornerstone): • “despite initial thoughts to the contrary, we shall prove, even in the presence of wildly differing acceptances, that the integral number of like-sign measured pairs can be directly related to the integral of the combinatorial background“

  6. Like Sign Method (I) • Starting from a single event generated into 4p: • Np positrons, Ne electrons, Possibility to be measured: ep/e • Probability to measure np/e out of Np/e (Binomial distribution)

  7. Like Sign Method (II) • Having np positrongs and ne electrons in the acceptance can be built. • For a single event under consideration (Np,Ne)

  8. Like Sign Method (III) • equivalent: • Pair survival probability: • where “ep is the probability that a single positron survives everything in the event that was present to itself …“ • “kpp is the probability that once each of the two positrons survived the environment of the rest of surrounding event, that they additionally survive each other!“ • PHENIX: large acceptance and segmentation, granularity kpp is nearly identical to 1.0.

  9. Like Sign Method (VI) • To get the mean npp averaged over all events <npp>, properly weighted sum over all possible intitial events, (Np, Ne), weighted by the probability of each of the two primary multiplicities, (P(Np), P(Ne)): • Assumption: P(Np) follows Poisson statistics:

  10. Like Sign Method (V) • Unlike sign combinatorial background : • (w/o any assumption about underlying statistics) • Assuming and by inspection:

  11. “We make no assumptions about the apertures or efficiences of the spectrometer. Despite this generality we have a result that states that the mean number of combinatorial ep per event is identically related to the mean number of measured like-sign pairs per event“ • Having measured Nevt events „we can find that the total integral of combinatorial pairs is fixed by the integrals of the measured like-sign pairs“ • To summarize: “The like-sign method instructs the experimentalist to measure the shape of the combinatorial background using the event mixing technique. The normalization of the resulting shape is then defined by the measured like-sign yield“

  12. Poisson statistics ?

  13. Nevt Nevt-1 Npool size buffered events Nevt-Npool size Event Mixing - Event Buffering • Mixing the present event with all buffered events • Npool size are generated by the positrons and • Npool size are generated by mixing the electrons from the present event with the Npool size sets of positrons/electrons • 2 x Npool size mixed events • Also possible for like-sign pairs

  14. Comparison of Like-Sign (same event) and Event mixing Buffering • For like-sign pairs: • The buffering techique has the advantage that it is sensitive to a signal in the like sign pairs either physical or detector response generated. • Tool to ensure that detector effects are properly removed • The buffering technique does suffer one drawback: • Relies upon a mixed events internal Poisson statistic. • Not true for a real event, but sub samples in centrality may be Poisson

  15. Nevt Nevt-1 Npool size buffered events Nevt-Npool size Event characterization (centrality, vertex, (event plane))

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