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Subsections

Cone transverse thrust with exponentially suppressed forward term


Definition of the observable

One minus the cone central transverse thrust with exponentially suppressed term is defined as (4), however the region $ {\cal C}$ is defined as the union of two cones of radius $ R$, one around each of the two hardest outgoing jets (after clustering the final state into jets with an inclusive kt-algorithm, see for instance [5])

$\displaystyle p_i \in {\cal C}\quad \Leftrightarrow\quad \sqrt{(\eta_i - \eta_{J, j})^2+(\phi_i - \phi_{J, j})^2} <= R$ (9)

Here $ \eta_i$ and $ phi_i$ denote the rapidity and azimuthal angle of particle $ i$, similarly $ \eta_{J, j}$ and $ \phi_{J, j}$ ($ j=1,2$) denote the rapidity and azimuth of the 2 jets. As before $ \bar {\cal C}$ denotes the region complementary to $ {\cal C}$.

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 $ $ \Vert sin^2\phi\vert$ $ 1.042 $ $ -2\ln(2)$
4 $ 1.000 $ $ 1.000 $ $ \Vert sin^2\phi\vert$ $ 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_Cone_exp.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: Cone transverse thrust with Up: Observables in hadronic dijet Previous: Central transverse thrust with
Giulia Zanderighi 2005-05-27