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

Definition of the observable

The central three-jet resolution parameter with recoil term can be obtained from the central three-jet resolution parameter via the addition of the recoil term ${\cal R}_{\perp,{\cal C}}$ defined in eq. (8) as follows:

$$y_{23,{\cal R}} \equiv y_{23,{\cal C}} + {\cal R}_{\perp,{\cal C}}^2\,.$$ (36)

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: 1000

Result for each colour configuration

qq -> qq	${\cal F}_2 =-0.41162\pm 0.19817$
qg -> qg	${\cal F}_2 =-0.83533\pm 0.19610$
qg -> gq	${\cal F}_2 =-0.88267\pm 0.21309$
gq -> gq	${\cal F}_2 =-0.83058\pm 0.25240$
gq -> qg	${\cal F}_2 =-0.65468\pm 0.28205$
qq -> gg	${\cal F}_2 =-0.61367\pm 0.14371$
gg -> qq	${\cal F}_2 =-0.58429\pm 0.28259$
gg -> gg	${\cal F}_2 =-0.39698\pm 0.18679$

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

The multiple emission function ${\cal F}$

Number of events used: 183850

Collection of automatically generated results

y3_DeltaRE_HH_rec.tar.gz collects all files produced automatically by Caesar.