Measurement of non-statistical fluctuations

D. Kresan

GSI, Darmstadt

Three contributions to data

• due to the finite number of particles produced and observed per event, the ratio of particle multiplicities measured event-by-event will exhibit statistical fluctuations with a width dictated by the individual particle multiplicities within the acceptance

• due to non-ideal particle identification, these statistical fluctuations will be smeared by the experimental dE/dx resolution and the event-by-event fitting procedure

• due to genuine non-statistical fluctuations, which if they exist are superimposed on the background of statistical and experimental fluctuations

Event mixingThe combined contributions of finite number fluctuationsin the particle multiplicities and effects of detector resolutionare estimated using a mixed event technique.

The contributions from the statistical and experimental fluctuationsdominate the event-by-event particle ratio distributions, and haveto be subtracted carefully

2222mixdatamixdatadyn sign

MEAN

RMSdata

NN

NNCov

N

NVar

N

NVar

K

K

K

Kdata

,222

2

NNK

mix

112

NN

NNCov

N

NNVar

N

NNVar

K

K

K

KKdyn

,222

2

Systematic studies

The measurement relies on the absence of additional detector-related fluctuations not accounted for by the mixed event technique and on the reliability of the event-by-event fitting procedure

Several tests on input from transport model calculations were performed to verify this requirements

Sensitivity of fluctuation measurement (by C.Roland)

Non-statistical Gaussian variations of magnitude dyn

inp in the K/ ratio were introduced as a “signal”

The extracted magnitude of fluctuations is found to be equal to the input amplitude within statistical errors

Simulations with UrQMD (by C.Roland)

A dE/dx value was assigned to each particle from the generated by UrQMD events.

Event by event fit to extract the particle ratios.

Two methods (MC PID and e-b-e fit) yield the same magnitude of non-statistical fluctuations at each collision energy, within statistical errors

Simulations with UrQMD (by D.K.)

Simulations with UrQMD (by D.K.)

Conclusion

• The “spike” at zero is the artifact of the event-by-event fit

• As was proved by the UrQMD simulations detector-related effects are taken into account in the mixed events distribution for all collision energies

• The method is sensitive to the fluctuations in the range from 1% to 20%

UrQMD

NA49 data

UrQMD

NA49 data

UrQMD

NA49 data

Open symbols – UrQMDFull symbols – NA49 data

Same ordinate for UrQMD