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Subsections

BKS observable with x=0.5


Definition of the observable

Following [14] we define

$\displaystyle \tau_x \equiv \frac{\sum_i E_i \vert\sin \theta_i\vert^x \left( 1-\vert\cos\theta_i\vert\right)^{1-x}} {\sum_i \vert\vec{p}_i\vert }\>,$ (30)

where the $ \theta_i$ are the angles with respect to the thrust axis (see eq. (1)). We study here $ \tau_{1/2}$.

Born event used for the analysis

The hard scale (Q) is taken to be the center-of-mass energy.

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 $ $ 0.500$ 1 $ 1.000 $ 0
2 $ 1.000 $ $ 0.500$ 1 $ 1.000 $ 0

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

bks_x05_ee.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: BKS observable with x=1.5 Up: Observables in e+e- Previous: Oblateness
Giulia Zanderighi 2004-11-19