Out-of-plane momentum

Definition of the observable

We measure the radiation out of the plane (yz) containing the photon axis and the thrust-major axis normalised to the photon virtuality $Q$

$$\frac{K_{out}}{Q} \equiv \frac{\sum_{i} \vert p_{xi}\vert}{Q} \>.$$ (12)

This observable has been resummed in the 3-jet limit in [5].

Born event used for the analysis

The hard scale (Q) is taken to be photon virtuality.
$x= Q^2/(2p_1 q)=$ 0.800
$z= (p_1.p_2)/(p_1.q) =$ 0.700

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

No zeroes or small values found.

Multiple emission effects

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

Number of events used: 1000000

Result for each colour configuration

q -> qg	${\cal F}_2 =-0.59564\pm 0.00176$
q -> gq	${\cal F}_2 =-0.59628\pm 0.00177$
g -> qq	${\cal F}_2 =-0.61479\pm 0.00179$

For a precise definition of the configurations see [6].

The multiple emission function ${\cal F}$

Number of events used: 1000000

Collection of automatically generated results

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