Kinematics RelatedSystematic Uncertainties

via MCEEP

P.E. Ulmer

Old Dominion University

12/11/02

Hall A Analysis Workshop

Breaking News:Cross sections depend on

kinematics! Uncertainties run wild!

• Coincidence cross section can vary strongly with kinematics.

• Results in systematic uncertainties:– need to evaluate changes in cross section for

variations of kinematical quantities.

• Account for kinematical constraints:– For example, fixed missing mass.

– May include constraints from various calibration measurements, such as H(e,e’p)

• Must acceptance average derivatives.

• It’s a snap with new MCEEP tools:– Cross sections handled at present.

– Other observables could be added easily.

– Satisfaction guaranteed or your money back.

Procedure

MCEEP Hbook file

Process MCEEP Ntuple:

Get cross sections for variations of kinematical quantities

Determine cross section derivatives and total

uncertainty, including any kinematical correlations

Process NtupleFortran Program: systerr

• Start with MCEEP Ntuple, containing Transport coordinates at target

• Vary nine quantities, in turn:

(beam, scatt. electron, ejectile)

x

(delta, phi, theta)

• Produce new Ntuple, consisting of original variables plus 10 cross sections (nominal and nine “shifted”).

• Program links to MCEEP subroutines and has access to its physics models.

Acceptance AveragePAW: systerr.kumac

• Error sum: positive definite quantity– Must first acceptance average.

• Sum the “weights”:– Produce vectors of summed cross

sections (10 in total).

– Bin vectors in terms of any kinematical quantity within Ntuple.

• Diagnostic histograms:– Fractional derivatives of cross section

with respect to each of the nine varied kinematical quantities.

Combine Errors Fortran Program: toterr

• Produce cross section uncertainty, given kinematical uncertainties and correlations. For each bin, form:

1,0

where

2

)(

;,

29

1

2

ij

jijiji

jiij

ii

i

c

xxxx

c

xx

• www.physics.odu.edu/~ulmer/mceep/mceep.html– Includes:

• Sources• Installation Instructions• User manual

– In particular, see: ~/mceep/systerr/README

• JLAB-TN-02-015Systematic Uncertainties in E89-003(K. Fissum & P.E. Ulmer)See:

http://hallaweb.jlab.org/publications/Technotes/files/2002/02-015.ps

More Information

Figures

Both figures are based on Experiment E94-004 D(e,e’p)n

cross section vs. Pm– Cross section derivatives for each of the

nine quantities:• Kinematics centered on Pm=100 MeV/c

• Units: fractional derivatives per 1 mr or per 10^-3 in momentum.

– Total error vs. Pm• All kinematics for E94-004 included, from

Pm=0 to Pm=500 MeV/c (central values)

• Uncorrelated analysis

• Correlated analysis: assumes constraints from 1H(e,e’p)