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Subsections

E-parameter


Definition of the observable

Given the thrust axis of an event $ \vec{n}_T$, see (1), all particle momenta are first projected in the plane orthogonal to the thrust axis

$\displaystyle \vec{q}_i = \vec{p}_i -(\vec{q}_i\cdot \vec{n}_T)\, \vec{n}_T\qquad q_{i,4}= \vert\vec{q}_i\vert\>.$ (9)

We then define $ \vec{n}_\alpha$ as the unit vector along the most energetic momentum $ \vec{q}_i$ and $ \vec{n}_\beta$ as a unit vector ortoghonal to $ \vec{n}_\alpha$ and $ \vec{n}_T$.

In analogy to (5) we define a 2-dimentional momentum tensor

$\displaystyle \Lambda^{\alpha \beta} = \frac{\sum_i (\vec{q}_i\cdot \vec{n}_\al...
.../\vert\vec{q}_i\vert}{\sum_j \vert\vec{p}_j\vert}\qquad (\alpha, \beta =1,2)\>,$ (10)

with eigenvalues $ \lambda_1, \lambda_2$.

The E parameter is then a new observable defined as

$\displaystyle E \equiv \max\{\lambda_1, \lambda_2\}\>.$ (11)

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 2.000 0
2 1.000 $ 0.000$ 1 2.000 0

Multiple emission tests

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

Information regarding the presence of possible zeros

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

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: 1000000

Result for each colour configuration
  $ {\cal F}_2 =-0.35060\pm 0.00141$

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

The multiple emission function $ {\cal F}$

Number of events used: 1000000
\begin{figure}\centering \epsfig{file=../OutputAnalysis/epar_ee.ff.eps, width=.7\textwidth, angle=0} \end{figure}

Collection of automatically generated results

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