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Subsections

Central thrust minor


Definition of the observable

The central thrust minor is defined as

$\displaystyle T_{m,{\cal C}} \equiv \frac{ \sum_{i \in {\cal C}} \vert p_{xi}\vert}{\sum_{i \in {\cal C}} \vert\vec{p}_{\perp i}\vert}\,,$ (11)

where $ {\cal C}$ denotes a central rapidity region, $ x$ is direction perpendicular to the beam and to the central transverse thrust axis $ \vec n_{T,{\cal C}}$ defined in eq. (3) and $ \vec{p}_{\perp
i}$ denote the momenta transverse to the beam axis.

Born event used for the analysis

The hard scale (Q) is taken to be the Born partonic center-of-mass energy.
Rapidity of the center of mass of the outgoing pair: 0.000
Cosine of the angle between outgoing jet and beam (in the partonic CM frame): 0.200

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$ $ 1.021 $ $ -\ln(2)$
2 $ 1.000 $ $ 0.000$ $ \vert sin(\phi)\vert$ $ 1.021 $ $ -\ln(2)$
3 $ 1.000 $ $ 0.000$ $ \vert sin(\phi)\vert$ $ 2.041 $ $ -\ln(2)$
4 $ 1.000 $ $ 0.000$ $ \vert sin(\phi)\vert$ $ 2.041 $ $ -\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 4
1 good zero good zero no zero no zero
2 good zero good zero no zero no zero
3 no zero no zero no zero no zero
4 no zero no zero no zero no zero

Classification of legs into divergent sequences with shared properties

Sequence number 1 has 2 legs
Legs in the sequence: 1 2
Orientation of the legs: 1 1
Type of zero: zt_sumVsignkx
Position of the divergence: $ \sum_{i \in seq.} R_i = 1.000$

Multiple emission effects

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

Number of events used: 10000

Result for each colour configuration
qq -> qq $ {\cal F}_2 =-0.26641\pm 0.02438$
qg -> qg $ {\cal F}_2 =-0.29629\pm 0.03326$
qg -> gq $ {\cal F}_2 =-0.22687\pm 0.04079$
gq -> gq $ {\cal F}_2 =-0.24367\pm 0.03983$
gq -> qg $ {\cal F}_2 =-0.34707\pm 0.03439$
qq -> gg $ {\cal F}_2 =-0.65828\pm 0.02313$
gg -> qq $ {\cal F}_2 = 0.15011\pm 0.05586$
gg -> gg $ {\cal F}_2 =-0.27223\pm 0.02444$

For a precise definition of the configurations see [3].

The multiple emission function $ {\cal F}$

Number of events used: 109760
\begin{figure}\centering \epsfig{file=../OutputAnalysis/tmin_HH_cut.ff.eps, width=.7\textwidth, angle=0} \end{figure}

Collection of automatically generated results

tmin_HH_cut.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: Central thrust minor with Up: Observables in hadronic dijet Previous: Directly global thrust minor
Giulia Zanderighi 2005-05-27