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Subsections

D-parameter


Definition of the observable

The D parameter is defined as [6,8]

$\displaystyle D \equiv \lambda_1 \lambda_2\lambda_3\>,$ (8)

where $ \lambda_\alpha$ $ ( 0 \leq \lambda_\alpha \leq 1 , \, \sum_\alpha
\lambda_\alpha = 1)$ are the eigenvalues of the linearized momentum tensor defined in eq. (5).

The D parameter has been resummed in the 3-jet limit in [9].

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 $ $ 1.000 $ $ \sin^2\phi$ $ 11.571 $ $ -2\ln(2)$
2 $ 1.000 $ $ 1.000 $ $ \sin^2\phi$ $ 11.571 $ $ -2\ln(2)$
3 $ 1.000 $ $ 1.000 $ $ \sin^2\phi$ $ 11.571 $ $ -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 T
eliminate subleading effects T
opt. probe region exists T

Information regarding the presence of possible zeros

No zeroes or small values found.

Multiple emission effects

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

The observable is additive, therefore $ {\cal F}_2 =-\frac{\pi^2}{12}$.

The multiple emission function $ {\cal F}$

The observable is additive, therefore $ {\cal F}(R')=e{^{-\gamma_E R'}}/\Gamma(1+R')$.

Collection of automatically generated results

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