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Subsections

Thrust-minor


Definition of the observable

Given a set of $ n$ momenta $ p_i$, define the event plane, spanned by the thrust axis (1) and the thrust major axis (2) as the $ yz$-plane. The thrust minor measures the radiation out of this plane

$\displaystyle T_{min} \equiv \frac{\sum_i \vert p_{ix}\vert}{\sum_i \vert\vec{p}_i\vert}\>,$ (3)

The thrust minor has been resummed at NLL accuracy in the 3-jet limit in [4].

Born event used for the analysis

The hard scale (Q) is taken to be the center-of-mass energy.
Born parton energy fractions (2E/Q) are 0.800, 0.700 and 0.500.

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$ $ \vert\sin(\phi)\vert$ 4.000 $ -\ln(2)$
2 1.000 $ 0.000$ $ \vert\sin(\phi)\vert$ 2.000 $ -\ln(2)$
3 1.000 $ 0.000$ $ \vert\sin(\phi)\vert$ 2.000 $ -\ln(2)$

Multiple emission tests

Test result
continuously global T
exponentiation (condition 1) T
exponentiation (condition 2a) T
exponentiation (condition 2b) T
exponentiation T
additivity F
eliminate subleading effects T
opt. probe region exists T

Information regarding the presence of possible zeros

leg 1 2 3
1 small value no zero no zero
2 no zero no zero no zero
3 no zero no zero no zero

Classification of legs into divergent sequences with shared properties

Multiple emission effects

Second order coefficient $ {\cal F}_2$ of the function $ {\cal F}$

Number of events used: 100000

Result for each colour configuration
ghard $ {\cal F}_2 =-0.42324\pm 0.00593$
gmed $ {\cal F}_2 =-0.53969\pm 0.00583$
gsoft $ {\cal F}_2 =-0.54937\pm 0.00587$

For a precise definition of the configurations see [5].

The multiple emission function $ {\cal F}$

Number of events used: 10800
\begin{figure}\centering \epsfig{file=../OutputAnalysis/tmin_ee.ff.eps, width=.7\textwidth, angle=0} \end{figure}

Collection of automatically generated results

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