F-parameter

Definition of the observable

Given the 2-dimensional momentum tensor in (10), the F parameter is a new observable defined as

$$F \equiv (\Lambda )\>.$$ (12)

For planar 3-jet events the F-parameter trivially vanishes. Accordingly we resum this observable in the 3-jet limit.

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	$0.000$	$\sin^2\phi$	0.866	$-2\ln(2)$
2	1.000	$1.000$	$\sin^2\phi$	1.400	$-2\ln(2)$
3	1.000	$1.000$	$\sin^2\phi$	1.000	$-2\ln(2)$

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	F

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	${\cal F}_2 =-0.54279\pm 0.00986$
gmed	${\cal F}_2 =-0.73403\pm 0.01013$
gsoft	${\cal F}_2 =-0.74815\pm 0.01024$

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

The multiple emission function ${\cal F}$

Number of events used: 1800

Collection of automatically generated results

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