Thrust

Definition of the observable

Given a set of $n$ final state momenta $p_i$, the thrust is defined as

$$1-T \equiv 1 - \max_{\vec n} \frac{\sum_i \vert\vec p_i .\vec n\vert}{ \sum_i \vert\vec p_i\vert}\>.$$ (1)

This observable was first defined in [1], its NLL resummed distribution was computed in [2].

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	T
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 ${\cal F}$

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

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