Thrust-minor

Definition of the observable

Given a set of $n$ momenta $p_i$, define the event plane, spanned by the thrust axis (1) and the thrust major axis (2) as the $yz$-plane. The thrust minor measures the radiation out of this plane

$$T_{min} \equiv \frac{\sum_i \vert p_{ix}\vert}{\sum_i \vert\vec{p}_i\vert}\>,$$ (3)

The thrust minor has been resummed at NLL accuracy in the 3-jet limit in [4].

Born event used for the analysis

The hard scale (Q) is taken to be the center-of-mass energy.
Born parton energy fractions (2E/Q) are 0.800, 0.700 and 0.500.

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	$0.000$	$\vert\sin(\phi)\vert$	4.000	$-\ln(2)$
2	1.000	$0.000$	$\vert\sin(\phi)\vert$	2.000	$-\ln(2)$
3	1.000	$0.000$	$\vert\sin(\phi)\vert$	2.000	$-\ln(2)$

Multiple emission tests

Test	result
continuously global	T
exponentiation (condition 1)	T
exponentiation (condition 2a)	T
exponentiation (condition 2b)	T
exponentiation	T
additivity	F
eliminate subleading effects	T
opt. probe region exists	T

Information regarding the presence of possible zeros

leg	1	2	3
1	small value	no zero	no zero
2	no zero	no zero	no zero
3	no zero	no zero	no zero

Classification of legs into divergent sequences with shared properties

Multiple emission effects

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

Number of events used: 100000

Result for each colour configuration

ghard	${\cal F}_2 =-0.42324\pm 0.00593$
gmed	${\cal F}_2 =-0.53969\pm 0.00583$
gsoft	${\cal F}_2 =-0.54937\pm 0.00587$

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

The multiple emission function ${\cal F}$

Number of events used: 10800

Collection of automatically generated results

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