Central y3 (kt algorithm, DeltaR, E-scheme) with exponentially suppressed forward term

Definition of the observable

We make the central three-jet resolution parameter in eq. (34) global via the addition of the exponentially suppressed term ${\cal E}_{{\cal{\bar C}}}$ of eq. (5) as follows:

$$y_{23,{\cal E}} \equiv y_{23,{\cal C}} + {\cal E}_{{\cal{\bar C}}}^2\,.$$ (35)

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	$2.000$	$2.000$	1	$1.042$	0
2	$2.000$	$2.000$	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

No zeroes or small values found.

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	${\cal F}_2 =-0.78861\pm 0.13029$
qg -> qg	${\cal F}_2 =-0.99363\pm 0.18980$
qg -> gq	${\cal F}_2 =-0.88016\pm 0.15447$
gq -> gq	${\cal F}_2 =-1.43008\pm 0.29454$
gq -> qg	${\cal F}_2 =-1.11024\pm 0.17882$
qq -> gg	${\cal F}_2 =-0.86258\pm 0.25231$
gg -> qq	${\cal F}_2 =-0.97255\pm 0.14896$
gg -> gg	${\cal F}_2 =-0.51058\pm 0.07859$

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

The multiple emission function ${\cal F}$

Number of events used: 1436050

Collection of automatically generated results

y3_DeltaRE_HH_exp.tar.gz collects all files produced automatically by Caesar.