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Subsections

Heavy-jet squared mass


Definition of the observable

Given a set of $ n$ momenta $ p_i$, the thrust axis $ \vec{n}_T$ in (1) naturally divides particles in any event in two hemispheres, the right $ R$ and the left one $ L$. The squared heavy jet mass is defined as

$\displaystyle M_h^2 \equiv \max \left\{M_R^2, M_L^2\right\}\>,$ (17)

where $ M_R^2$, $ M_L^2$ are the single hemisphere squared masses

$\displaystyle M_R^2 \equiv \sum_{i \in R} \left(\frac{p_i}{\sum_i \vert\vec{p}_...
...\equiv \sum_{i \in L} \left(\frac{p_i}{\sum_i \vert\vec{p}_i \vert}\right)^2\>.$ (18)

The heavy jet mass was resummed in [10].

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 $ 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 F
eliminate subleading effects T
opt. probe region exists T

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 =-0.41150\pm 0.00159$

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/mh_ee.ff.eps, width=.7\textwidth, angle=0} \end{figure}

Collection of automatically generated results

mh_ee.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: Light-jet squared mass Up: Observables in e+e- Previous: Single-jet broadening
Giulia Zanderighi 2004-11-19