Cone y3 (kt algorithm, DeltaR, E-scheme) with recoil term

Definition of the observable

The cone central recoil enhanced three-jet resolution parameter is defined as eq. (36), however the region ${\cal C}$ is defined as in eq. (9).

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	$2.000$	$0.000$	1	$1.042$	0
2	$2.000$	$0.000$	1	$1.042$	0
3	$2.000$	$0.000$	1	$1.042$	0
4	$2.000$	$0.000$	1	$1.042$	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

leg	1	2	3	4
1	good zero	good zero	no zero	no zero
2	good zero	good zero	no zero	no zero
3	no zero	no zero	no zero	no zero
4	no zero	no zero	no zero	no zero

Classification of legs into divergent sequences with shared properties

Sequence number 1 has 2 legs
Legs in the sequence: 1 2
Orientation of the legs: 1 -1
Type of zero: zt_sumvecVf
Position of the divergence: $\sum_{i \in seq.} R_i = 1.000$

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	${\cal F}_2 = 8.85259\pm 8.62740$
qg -> qg	${\cal F}_2 =-0.40990\pm 0.29857$
qg -> gq	${\cal F}_2 =-3.55752\pm 3.37508$
gq -> gq	${\cal F}_2 =-0.33673\pm 0.31433$
gq -> qg	${\cal F}_2 =-0.05824\pm 0.06838$
qq -> gg	${\cal F}_2 =-0.01879\pm 0.01783$
gg -> qq	${\cal F}_2 =-0.61169\pm 1.13483$
gg -> gg	${\cal F}_2 =-0.45478\pm 0.37308$

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

The multiple emission function ${\cal F}$

Number of events used: 1083150

Collection of automatically generated results

y3_DeltaRE_HH_Cone_rec.tar.gz collects all files produced automatically by Caesar.