Status of Status of Compton Compton AnalysisAnalysis

Yelena ProkYelena ProkPrimEx Collaboration meetingPrimEx Collaboration meeting

December 17, 2006December 17, 2006

OutlineOutline• 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 AnalysisBasic 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 DistributionsSome Basic DistributionsMultiplicity of bit 2 Multiplicity of TAGM photons

Multiplicity of clusters Cluster energies, no cuts

Cut on 0.5 GeV

Geometric CutsGeometric 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 ContaminationPair Contamination

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

VETO Cut

Event Selection (Be)Event Selection (Be)Reconstruct the vertex of Compton reactionZ=(x2+y2)0.5[/(E/e-1)]0.5

Z (cm)

Apply kinematic constraints:energy and momentum conservationReconstruct Z again

2<100 removes mostof the background

PS exit window

Z (cm) Z (cm)

Calculation of EfficiencyCalculation 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 Total Efficiency

Efficiency (by tcounter) is evaluated separately for every group of runs with similar conditions as the HyCal gains, beam alignmentparameters and target material affect the result.

Beryllium targetCarbon target,7 groups of runs

Counting EventsCounting Events

9Be, MC 12C, MC

9Be,data

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,1Absolute Cross Section,1Total 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

9Be

12CKlein-Nishina (4)NIST (KN+radiative corr.+double Compton)

Absolute Cross Section,2Absolute Cross Section,2

Normalized YieldNormalized Yield• For every run of sufficient

statistics we calculate the normalized yield defined as :

R=N/F/L/tc=1tc=11[tc

kn*tc*ftc]

ftc=Ftotal/Ftc

tc – eff. by tc F – total flux Ftc – flux per TC L – luminosity N – experimental yield tc

kn – KN for tc

9Be

All TC

12C

All TC

Normalized Yield vs Run #Normalized Yield vs Run #

Differential Cross Section,1Differential Cross Section,1• d/d or d/de

• 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)=smin

max[[d/d]2 sind+[d/de]2 sin ede]

Angular EfficiencyAngular Efficiency

Angular efficiency , tc() is calculated by finding the ratio of generated events in a given angular bin after cutsand the initially generated ones

Differential Cross Section,2Differential Cross Section,2• Compare theory with experiment

• Theory: kn()=tc[ftc*tckn()]

• Experiment:exp()=N()/L/F/A £ tc[ftc/tc]

9Be

<>=0.7±

<>=0.7±

12C

Differential Cross Section,3Differential Cross Section,3

Radiative CorrectionsRadiative 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, Virtual and Soft’ Correction, SVSV

• 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 = d0[1+SV]• SV – function of one variable (energy or angle of the

scattered photon), makes a negative contribution

‘‘Double Hard’ Correction, Double Hard’ Correction, dhdh

• 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 d1 in the direction 1, and a second photon with energy k2 to be emitted into an element of solid angle d2 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 d2 to obtain the total correction d = d0[1+SV+dh]

Radiative Corrections, contRadiative 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, RC to diff. xs, E E

RC to diff. xs. ,RC to diff. xs. ,

RC to diff. xs., RC to diff. xs., E + E +

RC to integrated xs, 1 part.RC to integrated xs, 1 part.

RC to integrated xs., 2 part.RC to integrated xs., 2 part.

Summary 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