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Subsections

F-parameter


Definition of the observable

Given the 2-dimensional momentum tensor in (10), the F parameter is a new observable defined as

$\displaystyle F \equiv$   det$\displaystyle (\Lambda )\>.$ (12)

For planar 3-jet events the F-parameter trivially vanishes. Accordingly we resum this observable in the 3-jet limit.

Born event used for the analysis

The hard scale (Q) is taken to be the center-of-mass energy.
Born parton energy fractions (2E/Q) are 0.800, 0.700 and 0.500.

Elementary tests on the observable

Test result
check number of jets T
all legs positive T
globalness T

Single emission properties

leg $ \ell$ $ a_{\ell}$ $ b_{\ell}$ $ g_{\ell}(\phi)$ $ d_{\ell}$ $ \langle \ln g_{\ell}(\phi) \rangle$
1 1.000 $ 0.000$ $ \sin^2\phi$ 0.866 $ -2\ln(2)$
2 1.000 $ 1.000 $ $ \sin^2\phi$ 1.400 $ -2\ln(2)$
3 1.000 $ 1.000 $ $ \sin^2\phi$ 1.000 $ -2\ln(2)$

Multiple emission tests

Test result
continuously global T
exponentiation (condition 1) T
exponentiation (condition 2a) T
exponentiation (condition 2b) T
exponentiation T
additivity F
eliminate subleading effects T
opt. probe region exists F

Information regarding the presence of possible zeros

leg 1 2 3
1 small value no zero no zero
2 no zero no zero no zero
3 no zero no zero no zero

Classification of legs into divergent sequences with shared properties

Multiple emission effects

Second order coefficient $ {\cal F}_2$ of the function $ {\cal F}$

Number of events used: 100000

Result for each colour configuration
ghard $ {\cal F}_2 =-0.54279\pm 0.00986$
gmed $ {\cal F}_2 =-0.73403\pm 0.01013$
gsoft $ {\cal F}_2 =-0.74815\pm 0.01024$

For a precise definition of the configurations see [5].

The multiple emission function $ {\cal F}$

Number of events used: 1800
\begin{figure}\centering \epsfig{file=../OutputAnalysis/fpar_ee.ff.eps, width=.7\textwidth, angle=0} \end{figure}

Collection of automatically generated results

fpar_ee.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: Total broadening Up: Observables in e+e- Previous: E-parameter
Giulia Zanderighi 2004-11-19