Directly global transverse thrust

Definition of the observable

One minus the directly global transverse thrust is defined as

$$1 - T_{\perp,g} \equiv 1 - \max_{\vec n_T} \frac{\sum_i \vert{\vec p}_{\perp i}\cdot {\vec n_T}\vert}{\sum_i p_{\perp i}}\,,$$ (1)

where the sum runs over all particles in the final state, $p_\perp$ is the momentum transverse to the beam direction, and $\vec n_T$ is the transverse vector that maximises the projection.

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	$1.000$	$0.000$	tabulated	$1.021$	$-1.859$
2	$1.000$	$0.000$	tabulated	$1.021$	$-1.859$
3	$1.000$	$1.000$	$\Vert sin^2\phi\vert$	$1.042$	$-2\ln(2)$
4	$1.000$	$1.000$	$\Vert sin^2\phi\vert$	$1.042$	$-2\ln(2)$

Azimuthal dependence

Multiple emission tests

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

Information regarding the presence of possible zeros

No zeroes or small values found. Since this observable does not exponentiate, multiple emission effects have not been computed.

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