Central transverse thrust

Definition of the observable

One minus the central transverse thrust is defined as

$$\tau_{\perp,{\cal C}} \equiv 1-T_{\perp,{\cal C}}\,,$$ (2)

where the transverse thrust $T_{\perp,{\cal C}}$ is measured from the directly observed particles in a central rapidity region ${\cal C}$:

$$T_{\perp,{\cal C}} \equiv \max_{\vec n_{T,{\cal C}}} \frac{\sum_{... ..._{\perp i}\cdot {\vec n_{T,{\cal C}}}\vert}{\sum_{i\in{\cal C}} p_{\perp i}}\,.$$ (3)

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	$2.000$	$0.000$	$\sin^2\phi$	$0.521$	$-2\ln(2)$
2	$2.000$	$0.000$	$\sin^2\phi$	$0.521$	$-2\ln(2)$
3	$1.000$	$1.000$	$\sin^2\phi$	$1.042$	$-2\ln(2)$
4	$1.000$	$1.000$	$\sin^2\phi$	$1.042$	$-2\ln(2)$

Multiple emission tests

Test	result
continuously global	F
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	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_sumVsignkx
Position of the divergence: $\sum_{i \in seq.} R_i = 0.500$

Since this observable is discontinuosly global, multiple emission effects have not been computed.

Collection of automatically generated results

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