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Subsections

Directly global y3 (kt algorithm, DeltaR, E-scheme)


Definition of the observable

We recall the $ k_t$-invariant jet algorithm of ref. [2].
  1. One defines, for all $ n$ final-state (pseudo)particles still in the event,

    $\displaystyle d_{kB} = p_{\perp k}^2\,,$ (29)

    and for each pair of final state particles

    $\displaystyle d_{kl} = \min\{{p_{\perp k}^2,p_{\perp l}^2}\} \left((\eta_k-\eta_l)^2+(\phi_k-\phi_l)^2\right)\,.$ (30)

  2. One determines the minimum over $ k$ and $ l$ of the $ d_{kl}$ and the $ d_{kB}$ and calls it $ d^{(n)}$. If $ d^{(n)}=d_{iB}$ then particle $ q_{i}$ is included in the beam and eliminated from the final state particles. If $ d^{(n)}=d_{ij}$ then particles $ p_{i}$ and $ p_{j}$ are recombined into a pseudoparticle (jet) in the E-scheme:

    $\displaystyle p_{i j} = p_{i}+p_{j}\,.$ (31)

  3. The procedure is repeated until only 3 pseudoparticles are left in the final state.

We apply the algorithm to all particles in the event and consider

$\displaystyle y_{23} = \frac{1}{E_{\perp}^2} \max_{n \ge 3}\{d^{(n)}\}\>,$ (32)

where $ E_{\perp}$ is defined by further clustering the event until only two jets remain and taking $ E_{\perp}$ as the sum of the two jet transverse energies,

$\displaystyle E_{\perp} = E_{\perp,1} + E_{\perp,2}\,.$ (33)

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

No zeroes or small values found.

Multiple emission effects

Second order coefficient $ {\cal F}_2$ of the function $ {\cal F}$

Number of events used: 10000

Result for each colour configuration
qq -> qq $ {\cal F}_2 =-0.07456\pm 0.01270$
qg -> qg $ {\cal F}_2 =-0.15933\pm 0.02429$
qg -> gq $ {\cal F}_2 =-0.16162\pm 0.02271$
gq -> gq $ {\cal F}_2 =-0.16244\pm 0.02366$
gq -> qg $ {\cal F}_2 =-0.14758\pm 0.02179$
qq -> gg $ {\cal F}_2 =-0.24593\pm 0.02975$
gg -> qq $ {\cal F}_2 =-0.01242\pm 0.00328$
gg -> gg $ {\cal F}_2 =-0.09860\pm 0.01456$

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

The multiple emission function $ {\cal F}$

Number of events used: 256550
\begin{figure}\centering \epsfig{file=../OutputAnalysis/y3_DeltaRE_HH_dir.ff.eps, width=.7\textwidth, angle=0} \end{figure}

Collection of automatically generated results

y3_DeltaRE_HH_dir.tar.gz collects all files produced automatically by Caesar.
next up previous
Next: Central y3 (kt algorithm, Up: Observables in hadronic dijet Previous: Cone wide broadening with
Giulia Zanderighi 2005-05-27