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Subsections

Fractional energy correlation with x = 1


Definition of the observable

The fractional moments of energy correlations are defined as

$\displaystyle FC_x \equiv \sum_{i\ne j}\frac{E_i E_j \vert\sin \theta_{ij}\vert...
...}{(\sum_i E_i)^2} \Theta[(\vec p_i \cdot \vec n_T)(\vec p_j \cdot \vec n_T)]\,,$ (31)

where the sum runs over all particles in the event, $ \theta_{ij}$ denotes the angle between particle $ i$ and $ j$ and $ \vec n_T$ is the thrust axis (see eq. (1)). We study here $ FC_1$.

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 $ $ 0.000$ 1 $ 1.000 $ 0
2 $ 1.000 $ $ 0.000$ 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

FEC_1_ee.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: Fractional energy correlation with Up: Observables in e+e- Previous: BKS observable with x=1.5
Giulia Zanderighi 2004-11-19