CONVERTING BETWEEN EMT AND EMC COORDINATES (Based on BaBar Note #519 sec. 4.1)


1.INTRODUCTION

It is important for the DQM to be aware of the correspondance between the EMC crystal hitmaps and the L1T EMT
occupancy plots in JAS.  This is because the L1T references are only updated to reflect changes in Level 1 itself, for 
example if an EMT tower is masked, however any changes in the EMC will also show up in the EMT plots and cause them to 
differ from the reference.  Dead or masked areas in the EMC will cause the corresponding area of the EMT plots to show a 
lower occupancy than the reference.  Conversely, noisy EMC crystals will cause a higher occupancy and may give the
false impression of an EMT hot tower.  This second case is particularly important as the DQM needs to be able to
distinguish between a genuine hot tower in the EMT and noisy crystals in the EMC.  Note that the latter of these is
far more frequent and if this is the case the EMC expert should be contacted.

Unfortunately the EMT and EMC define the phi and theta geometry of the calorimeter sightly differently.  This has previously
led to some confusion for DQMs when comparing the EMT and EMC plots.  This page is intended to be a reference to explain these 
differences and in particular give the conversion rules between the EMT and EMC coordinates.

2.GEOMETERY OF THE EMC

The EMC has 6580 crystals in total, arranged in 56 rings in theta with between 80 and 120 crystals in phi in each ring.
The endcap has 8 rings, numbered THETA(emc)=1..8.  Counting out from the inside these consist of 2 rings of 80
crystals in phi, 3 rings of 100 crystals and 3 rings of 120 crystals.  There is an additional innermost ring at 
THETA(emc)=0 in the support structure which has no crystals installed.  The remaining 48 rings, numbered 
THETA(emc)=9..56, make up the barrel and all contain 120 crystals in phi.

3.GEOMETERY OF THE EMT

For trigger purposes the crystals are divided into 280 towers forming the 7x40 array in theta and phi which can be seen in the 
EMT occupancy plots; THETA(emt)=1..7 and PHI(emt)=1..40. (We would usually define the EMT coordinates from 0 but I don't 
think that is particularly clear in the JAS plots so I have modified the definition here).

In the barrel each tower contains 24 crystals in an 8x3 array, this corresponds to THETA(emt)=2..7.  Hence to convert between 
the crystal and tower numbering in the barrel;

	THETA(emt)=mod{[THETA(emc)-1]/8} +1	THETA(emc)=9..56

	PHI(emt)=mod{[PHI(emc)-1]/3} +1		PHI(emc)=1..120

where mod{..} implies integer division (always round down when the division is not exact).

The endcap does not have an exact 40-fold symmetric in phi because of the THETA(emc)=3..5 rings with 100 crystals.  This means an 
EMT tower in the endcap will consist of either 20 or 21 crystals.  Note that in total there are 820 crystals in the endcap and this
does give a 20-fold symmetery in phi with each module having 41 crystals.  As all 20 modules are indentical with respect 
to the crystal arrangement into towers, the conversion in the endcap goes as;

        THETA(emt)=1

	PHI(emt)=mod{[PHI(emc)-1]/2} +1		   THETA(emc)=1,2    PHI(emc)=1..80
	PHI(emt)=mod{2*[PHI(emc)-1]/5} +1	   THETA(emc)=3,4    PHI(emc)=1..100
	PHI(emt)=mod{2*[PHI(emc)+2]/5}		   THETA(emc)=5      PHI(emc)=1..100
	PHI(emt)=mod{[PHI(emc)-1]/3} +1		   THETA(emc)=6..8   PHI(emc)=1..120

again integer division is implied.