Thrust with respect to the photon axis (normalized to E)

Definition of the observable

We consider here the current jet thrust normalised to the total energy in the current hemisphere

$$T_E = T_Q/(1-\varepsilon)\,,$$ (3)

where $T_Q$ is defined in (1) and the quantity $\varepsilon$, called the energy deficit in the current hemisphere, is [3]

$$\varepsilon \equiv 1-\frac 2 Q \sum_{a\in {\cal H}_{\mathrm{C}}}E_a\;.$$ (4)

We consider here the resummation for

$$\tau_{zE} =1 - T_E\>.$$ (5)

This observable has been resummed in [1].

Born event used for the analysis

The hard scale (Q) is taken to be photon virtuality.

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

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
1	good zero	no zero
2	no zero	no zero

Classification of legs into divergent sequences with shared properties

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

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

Collection of automatically generated results

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