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Subsections

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


Definition of the observable

The thrust $ T_Q$ is defined by the sum of the longitudinal momenta in the current hemisphere normalized to $ Q/2$, with $ Q$ the virtuality of the photon

$\displaystyle T_Q = \frac{2}{Q} \sum_{a \in {\cal H_C}} p_{z a}\>.$ (1)

We then consider the resummation for

$\displaystyle \tau_{zQ} =1 - T_Q\>.$ (2)

This observable has been resummed in [1].

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 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_zQ.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: Thrust with respect to Up: Observables in DIS Previous: Observables in DIS
Giulia Zanderighi 2004-11-19