Directly global thrust minor

Definition of the observable

The directly global thrust minor is defined as

$$T_{m,g} \equiv \frac{\sum_i \vert p_{xi}\vert}{\sum_i \vert\vec{p}_{\perp i}\vert}\,,$$ (10)

where the sum extends to all outgoing particles in the event, $x$ is direction perpendicular to the beam and to the global transverse thrust axis defined in (1) and $\vec{p}_{\perp i}$ denote the momenta transverse to the beam axis.

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	$1.000$	$0.000$	$\vert sin(\phi)\vert$	$2.041$	$-\ln(2)$
2	$1.000$	$0.000$	$\vert sin(\phi)\vert$	$2.041$	$-\ln(2)$
3	$1.000$	$0.000$	$\vert sin(\phi)\vert$	$2.041$	$-\ln(2)$
4	$1.000$	$0.000$	$\vert sin(\phi)\vert$	$2.041$	$-\ln(2)$

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

No zeroes or small values found.

Multiple emission effects

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

Number of events used: 10

Result for each colour configuration

qq -> qq	${\cal F}_2 =-0.93537\pm 0.84263$
qg -> qg	${\cal F}_2 =-0.96262\pm 0.59850$
qg -> gq	${\cal F}_2 =-0.39913\pm 0.22024$
gq -> gq	${\cal F}_2 =-0.01073\pm 0.00783$
gq -> qg	${\cal F}_2 =-1.73337\pm 1.25527$
qq -> gg	${\cal F}_2 =-2.52002\pm 1.55523$
gg -> qq	${\cal F}_2 =-1.24599\pm 0.77187$
gg -> gg	${\cal F}_2 =-0.30327\pm 0.18513$

For a precise definition of the configurations see [3].

The multiple emission function ${\cal F}$

Number of events used: 5575500

Collection of automatically generated results

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