Fractal dimension of pi+/e+ clusters

Shpak Kostiantyn, LLR

Cuts

• In beem: Number of used SCA (all chips) per spill >200 (max 240)

• Correctly operational central chips 3,5,10,12: number of SCA>0 and <16 for each chip

• bx.cor correction, because bx.cor is not correlated between chips

Fractal dimension of pi+/e+ clustersHistory and theory:#lines with GB coastline #cells with GB coastline:

Possible to apply for cluster dimension calculation

Difficult to apply for cluster dimension calculation, typical cluster has main core and some separated regions

Fractal dimension of pi+/e+ clusters

Box size rangeThe default range of box sizes is usually optimal but not always so. They should only be changed when you have some experience and understanding of the processes involved. The following graph is the result of performing the box counting where the box size ranged from being 5 times the width (or height) of the image to 1 pixel. For successful choice of the box size range it is important to understand the regions of the graph illustrated here.

History and theory:

Fractal dimension of pi+/e+ clusters

• For tests 8.4 X0W detector configuration was chosen

• Trigger threshold 230 ADC

Fractal dimension of pi+/e+ clusters

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233070489

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Procedure: 1) no intersensor gap 2) covering of event with few size grids: grid_cell=m*prototype_pixel m - integer 1,2,4,8,163) counting of #boxes with part of event (not only perimeter) 4) prototype_pixel=5.5mm 5) minimal grid_cell=5.5mm 6) maximal grid_cell=88mm entire sensor

method

Fractal dimension of pi+/e+ clusters3rd method

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log(count)

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slopes (FD) and shifts for 150GeV e+/pi+

log(1/zoom)> -2.5 log(1/zoom)< -0.5

used grids: 1x pixel 2x pixel 4x pixel

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100GeV e+/pi+ run211, DIF1(same statistics for all thr)

100GeV pi+ run280, full statistics in DIFs

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