Status of Compton Analysis

Status of Status of Compton AnalysisCompton Analysis

Yelena ProkYelena ProkPrimEx Collaboration meetingPrimEx Collaboration meeting

February 25, 2007February 25, 2007

Outline• Analysis Note posted before the last

meeting; no comments received ->it must be perfect• Since the last meeting:

– Study of integrated vs total cross section– Implementation of radiative corrections,

Primex Note

Integrated (Partial) XS• Data with the beam energy in the

range of 4.9<E<5.5 GeV covers the angular range of ~ 0.2-3.0 degrees (due to our geometry).

• When evaluating the total cross section, a large fraction of the final result comes from the extrapolation in the rest of the region

• Is there any systematic uncertainty introduced by this extrapolation?

• To answer this question we evaluate cross section, integrated over four regions of the photons’ scattering angle:

– 0.1 < < 90– 0.1 < < 10– 0.1 < < 5– 0.1 < < 3

Generated kinematics

Scattering angle (deg)

photon electron

Scattering angle (deg)

photon electron

0.1 < < 5.00.0 < < 180

Efficiency

Integrated Cross Section, (Be target)

Experimental result relative to theory is independent of which region is chosen

BornBorn+RC• Cross section

evaluation– Yield, N– Efficiency, – Theory, theory

expt =N/ theory,bornexpt

In order to evaluate radiative corrections, need: 1. ’Radiated’ theory: theory,BORN theory, BORN+RC

2. ’Radiated’ efficiency: 0 RC

• 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

Radiative Corrections

Total (RC) Cross Section (1)• Integrate differential cross sections for 2 processes, ‘soft-

virtual’ and ‘hard double’ scattering. • Corrections separated into 2 based on whether the energy of

secondary emitted photon is greater or smaller than some parameter 2max << me

• ‘Soft-Virtual’ term, based on ref. [4] of PN 42, contains a term ‘ln(2max/me); integrated over the scattered photon’s polar angle

• ‘Double-hard’ term, according to ref. [5] of PN 42, 2max is a lower limit of integration over the energy of one of the scattered photons; integration is carried also over the 2 polar angles of the scattered photons, and azimuthal angle between their planes.

• Result must be independent of the choice of 2max

Total correction wrt Born term(independent of the choice of

2max )

Total (RC) Cross Section

Uncertainties:NIST (5+ %)Integration ( » 1 %)

Used 2 independent methods of numeric integration to check the values of total cross section and compare with NIST

• Utilizing BASES/SPRING package created event generators for 2-particle and 3-particle processes• Generated 2-particle and 3-particle events

according to their total cross section ratio• Propagated events through the setup using GEANT-3• Calculated ‘radiated’ efficiency

Event Generators

Generated Kinematics

Scattered energy (GeV) Scattering angle (deg)

electron

photon

electron

photon

Born vs Born+SV vs Double Compton Scattering

Generated Occupancy on HyCal

X (cm)

Y(cm)

Born Born+SV Double Compton

Cut: 2 particles outside of the central hole

Y(cm)

Y(cm)

Born Born+SV Double Compton

Cut: 2 particles outside of the central hole

Generated Occupancy on Hycal

Clusters on CalorimeterBorn +SV event Double Compton event

‘Radiated’ Efficiency

Born

Born+SV+DC

‘Radiated’ efficiency is ~ 5% smaller (needs more checks)

Carbon Target

Radiatively Corrected Cross Section

~ 1 % agreement between the data and theory (more checks are needed)

Total, integrated, and differential cross sections are evaluated at the Born level for all carbon and beryllium data for 4.9<E<5.5 GeV beam

Mechanism for implementation of radiative corrections has been developed and is documented in Primex Note 42

Initial evaluation of radiatively corrected cross section with the carbon target shows very good agreement with theory (~1 %)

• New flux/binning scheme

• More work on RC (also for the Be target)

• Systematic Errors• Low energy data set

Done To Do