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Subsections

Central transverse thrust with exponentially suppressed forward term


Definition of the observable

One minus the central transverse thrust with exponentially suppressed term is defined as

$\displaystyle \tau_{\perp,{\cal E}} \equiv 1 - T_{\perp,{\cal C}} + {\cal E}_{\bar {\cal C}}\,,$ (4)

where the central transverse thrust $ T_{\perp,{\cal C}}$ is defined in (3), and $ {\cal E}_{\cal{\bar C}}$ denotes the exponentially suppressed term

$\displaystyle {\cal E}_{\cal{\bar C}}\equiv \frac{1}{Q_{\perp,{\cal C}}} \sum_{i \notin {\cal C}} p_{\perp i} \,e^{-\vert\eta_i - \eta_{\cal C}\vert}\,,$ (5)

with

$\displaystyle \eta_{\cal C}\equiv \frac{1}{ Q_{\perp,{\cal C}}} \sum_{i\in{\cal...
... i}\,,\qquad\quad Q_{\perp,{\cal C}} \equiv \sum_{i\in {\cal C}} p_{\perp i}\,.$ (6)

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 $ $ 1.000 $ 1 $ 1.021 $ 0
2 $ 1.000 $ $ 1.000 $ 1 $ 1.021 $ 0
3 $ 1.000 $ $ 1.000 $ $ \sin^2\phi$ $ 1.042 $ $ -2\ln(2)$
4 $ 1.000 $ $ 1.000 $ $ \sin^2\phi$ $ 1.042 $ $ -2\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 T
eliminate subleading effects T
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}$

The observable is additive, therefore $ {\cal F}_2 =-\frac{\pi^2}{12}$.

The multiple emission function $ {\cal F}$

The observable is additive, therefore $ {\cal F}(R')=e{^{-\gamma_E R'}}/\Gamma(1+R')$.

Collection of automatically generated results

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