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Subsections

Thrust


Definition of the observable

Given a set of $ n$ final state momenta $ p_i$, the thrust is defined as

$\displaystyle 1-T \equiv 1 - \max_{\vec n} \frac{\sum_i \vert\vec p_i .\vec n\vert}{ \sum_i \vert\vec p_i\vert}\>.$ (1)

This observable was first defined in [1], its NLL resummed distribution was computed in [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 $ $ 1.000 $ 1 $ 1.000 $ 0
2 $ 1.000 $ $ 1.000 $ 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

thr_ee.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: Thrust-major Up: Observables in e+e- Previous: Observables in e+e-
Giulia Zanderighi 2004-11-19