Oblateness

Definition of the observable

Given the thrust major defined in (2) and the thrust minor defined in (3), the oblateness is given by

$$O \equiv T_M - T_{min}\>.$$ (29)

This observable was resummed semi-numerically 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	1.000	$0.000$	1	2.000	0
2	1.000	$0.000$	1	2.000	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

leg	1	2
1	small value	good zero
2	good zero	small value

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: 0 0
Type of zero: zt_unrecognised
Position of the divergence could not be determined

Multiple emission effects

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

Number of events used: 1000000

Result for each colour configuration

${\cal F}_2 = 0.38035\pm 0.00361$

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

The multiple emission function ${\cal F}$

Number of events used: 1000000

Collection of automatically generated results

obl_ee.tar.gz collects all files produced automatically by Caesar.