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Subsections

Durham-P 3-jet resolution y3


Definition of the observable

It is useful to start by recalling the definition of the Durham jet finding algorithm [13], given in terms of a resolution parameter $ y_\mathrm{cut}$ as follows:
  1. For all pairs of (pseudo-)particles $ i,j$ calculate

    $\displaystyle y_{ij} = \frac{2\mathrm{min} (E^2_i, E_j^2) (1 - \cos \theta_{ij})}{E_{vis}^2}\,,$ (22)

    with $ E_{vis}$ is the visible energy defined as $ E_{vis} = \sum_i
E_i$, here $ E_i$ are the energies before any recombination.
  2. Go back to step 1.
  3. If all $ y_{ij} > y_\mathrm{cut}$ stop. The number of jets is then defined to be equal to the number of (pseudo-)particles left.
  4. Otherwise recombine the pair with the smallest $ y_{ij}$ into a single pseudoparticle of momentum $ p$ according to the P-recombination scheme:

    $\displaystyle \vec{p} = \vec{p}_i + \vec{p}_j \qquad \qquad E_p = \vert\vec{p}\vert\>;$ (23)

  5. Go back to step 1.
The three-jet resolution parameter $ y_3$ is defined as the maximum value of $ y_\mathrm{cut}$ that leads to a $ 3$-jet event.

This observable was fully resummed at NLL accuracy for the first time in [3].

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 2.000 $ 0.000$ 1 1.000 0
2 2.000 $ 0.000$ 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 F
eliminate subleading effects F
opt. probe region exists F

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}$

Number of events used: 1000000

Result for each colour configuration
  $ {\cal F}_2 =-0.31120\pm 0.00273$

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

The multiple emission function $ {\cal F}$

Number of events used: 4050
\begin{figure}\centering \epsfig{file=../OutputAnalysis/y3_DurP_ee.ff.eps, width=.7\textwidth, angle=0} \end{figure}

Collection of automatically generated results

y3_DurP_ee.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: Durham-P0 3-jet resolution y3 Up: Observables in e+e- Previous: Single-jet squared mass
Giulia Zanderighi 2004-11-19