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Subsections

Thrust with respect to the thrust axis (normalized to Q)


Definition of the observable

We consider one minus the thrust with respect to the thrust axis normalised to $ Q/2$

$\displaystyle \tau_{tQ} \equiv 1- T_{tQ} = 1- \frac{2}{Q} \max_{\vec{n}} \sum_{i \in {\cal H}_{\mathrm{C}}} \vert\vec{p_i} \cdot \vec{n}\vert\,.$ (9)

Born event used for the analysis

The hard scale (Q) is taken to be photon virtuality.

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

tau_tQ.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: Thrust with respect to Up: Observables in DIS Previous: C-parameter (normalized to E)
Giulia Zanderighi 2004-11-19