Durham-E 3-jet resolution y3

Definition of the observable

$y_3$ in the E-scheme is obtained following the algorithm described in Sec. 15.1, but with the recombination procedure in (23) is replaced by the following recombination procedure

$$p=p_i+p_j\>.$$ (25)

This observable was fully resummed at NLL accuracy for the first time in [3].

Born event used for the analysis

The hard scale (Q) is taken to be the center-of-mass energy.

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	2.000	$0.000$	1	1.000	0
2	2.000	$0.000$	1	1.000	0

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	F
opt. probe region exists	F

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

${\cal F}_2 =-0.31120\pm 0.00273$

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

The multiple emission function ${\cal F}$

Number of events used: 4050

Collection of automatically generated results

y3_DurE_ee.tar.gz collects all files produced automatically by Caesar.