Status of
Compton
Analysis
Yelena Prok
PrimEx Collaboration meeting
December 17, 2006
Outline
• Changes in basic analysis
• Absolute Cross Section Results
• Yield Stability in time
• Differential Cross Section Results
• Radiative Corrections
• Summary / What remains to be done
Basic Analysis
• Starting with raw (not skim) files
• Applying cuts used to create skim files
– (e1+e2)>3.5 GeV (for 4.9<e0<5.5 GeV)
– |px1+px2|<0.025 GeV
– |py1+py2|<0.025 GeV
• Choose first recorded bit 2 per event to give
HyCal time
• Look for photons within 10 ns window of HyCal
• Choose the one “closest” in time to Hycal
• Form all possible combinations of clusters in
events with at least 2 clusters, with emin=0.5 GeV
Some Basic Distributions
Multiplicity of bit 2
Multiplicity of clusters
Multiplicity of TAGM photons
Cluster energies, no cuts
Cut on 0.5 GeV
Geometric Cuts
• Central opening of
Hycal and the
adjacent layer of
modules are cut out
by eliminating events
with their coordinates
within the square of
|x0|<2*2.077 cm and
|y0|<2*2.075 cm
• Optional cut on the
vertical strip
(|x0|<2*2.077 cm)
Pair Contamination
VETO Cut
Pairs of e+e- are difficult to distinguish kinematically from e pairs
Eliminating cluster pairs where both clusters are charged cleans up
distributions but efficiency of this cut is unknown.
Solution in the present analysis is to cut out contaminated region
Event Selection (Be)
Reconstruct the vertex of Compton reaction
Z=(x2+y2)0.5[/(E/e-1)]0.5
Apply kinematic constraints:
energy and momentum conservation
Reconstruct Z again
Z (cm)
2<100
removes most
of the background
PS exit window
Z (cm)
Z (cm)
Calculation of Efficiency
• Efficiency () is defined as the
fraction of Compton events
generated over 4
reconstructed by HyCal using
standard PrimEx software
• To obtain , use gkprim
package and ‘prim_ana’-type
reconstruction code
• This efficiency includes
geometric acceptance,
radiative losses in the target,
as well as the detection and
reconstruction inefficiency.
(please see the note for more
details)
Total Efficiency
Beryllium target
Carbon target,
7 groups of runs
Efficiency (by tcounter) is evaluated separately for every group
of runs with similar conditions as the HyCal gains, beam alignment
parameters and target material affect the result.
Counting Events
9Be,
MC
9Be,
data
12C,
MC
12C,
data
Reconstructed vertex z is fitted with a double gaussian (target signal),
single gaussian (He bag window signal) + second order polynomial (
combinatorial background)
Absolute Cross Section,1
Total Cross Section (per electron)
•
•
•
•
•
•
•
•
•
•
T=N/(L*F*A*)
N=nevents
L=luminosity=*t*NA/
t=target thickness
=target density
NA=Avogadro’s Number
=atomic mass
=efficiency (from MC)
A=atomic number
F=photon flux
•
•
Error bars are statistical only
Radiative corrections are not
applied
Klein-Nishina (4)
NIST (KN+radiative corr.+double Compton)
9Be
12C
Absolute Cross Section,2
Normalized Yield
• For every run of sufficient
statistics we calculate the
normalized yield defined as :
9Be
All TC
R=N/F/L/tc=1tc=11[tckn*tc*ftc]
ftc=Ftotal/Ftc
tc – eff. by tc
F – total flux
Ftc – flux per TC
L – luminosity
N – experimental yield
tckn – KN for tc
12C
All TC
Normalized Yield vs Run #
Differential Cross Section,1
• d/d or d/de
• Can sum over the two distributions ! don’t need to
distinguish between electrons and photons
• Total cross section in a bin of  , i ,is
(i)=sminmax[[d/d]2 sind+[d/de]2 sin ede]
Angular Efficiency
Angular efficiency , tc()
is calculated by finding the ratio of
generated events in a given
angular bin after cuts
and the initially generated ones
Differential Cross Section,2
• Compare theory with experiment
• Theory: kn()=tc[ftc*tckn()]
• Experiment:exp()=N()/L/F/A £ tc[ftc/tc]
<>=0.7±
12C
<>=0.7
±
9Be
Differential Cross Section,3
Radiative Corrections
• Virtual: possibility of
emission and re-absorption
of virtual photon by an
electron during the
scattering process
• Double Compton scattering
– Soft: secondary photon of
energy k<<kmax, not
accessible to the
experiment
– Hard: secondary photon of
energy k>kmax, accessible
to the experiment
‘Virtual and Soft’ Correction, SV
• Virtual corrections alone do not have a physical meaning
because they contain an infrared divergence, which is a
consequence of the fact that it is impossible to distinguish
experimentally between virtual and real photons of very low
energy. For this reason virtual corrections are considered
simultaneously with the soft double compton process,
which contains an infrared divergence as well. The
divergencies cancel out in every order in , giving a
physically meaningful cross section that corresponds to the
probability for the Compton process to occur and no other
free photons emitted.
• Cross section reduces to the Born term times a factor:
d = d0[1+SV]
• SV – function of one variable (energy or angle of the
scattered photon), makes a negative contribution
‘Double Hard’ Correction, dh
• Another class of corrections to consider is the double
Compton scattering where both final photons are accessible
to the experiment
• Differential cross section for an incident photon of energy k
striking an electron at rest to produce one photon with
energy k1 emitted into an element of solid angle d1 in the
direction 1, and a second photon with energy k2 to be
emitted into an element of solid angle d2 in the direction
2,  , is a function of 4 independent variables (besides the
initial beam energy):
d(k; k1,1,2,)=f(k1,1,2,)
Possible to integrate over d2 to obtain the total correction
d = d0[1+SV+dh]
Radiative Corrections, cont
• Numeric integrations carried out using code from M. Konchatnyi
(see more details in the note)
• To make the result relevant to a particular experiment need to
consider:
– Detector resolution,  E or/and 
– Minimum detected energy,  E
– How many particles are detected
• Some reasonable values (approximation only)
 E=50 MeV,   = 0.002 rad,  E = 500 MeV, lower limit of
integration determined by the minimum registered angle (set
=0.00476 rad (3.5 cm on HyCal), and maximum determined by
the minimum registered energy on the calorimeter.
This method also assumes that we can distinguish within our
defined resolution between events with 2 particles in the final
state from events with 3 particles in the final state
RC to diff. xs,  E
RC to diff. xs. , 
RC to diff. xs.,  E + 
RC to integrated xs, 1 part.
RC to integrated xs., 2 part.
Summary
 Analyzed » 90 % of carbon and all of beryllium data with
the initial beam energy of 4.9-5.5 GeV
 We observe agreement with KN prediction in both total and
differential cross sections at the level of » 2 %. Systematic
error in the present result is estimated to be about 3 %.
 We do not observe any systematic shifts over the entire run
period: no major changes in the tagging ratios?
 Work in progress
 RC generator (hope to complete by next month)
 Analysis of tcounters 30-42: would be good to have more
accurate tagging ratios, currently they are all 0.95
 Systematic error evaluation