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bunchin
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There are 7 letters in BUNCHIN ( B3C3H4I1N1U1 )
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BUNCHIN - In statistics as applied in particular in particle physics, when fluctuations of some observables are measured, it is convenient to transform the mul...
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In statistics as applied in particular in particle physics, when fluctuations of some observables are measured, * it is convenient to transform the multiplicity distribution to the bunching parameters:* * * * * η * * q * * * = * * * q * * q * − * 1 * * * * * * * * P * * q * * * * P * * q * − * 2 * * * * * P * * q * − * 1 * * * 2 * * * * * , * * * {\displaystyle \eta _{q}={\frac {q}{q-1}}{\frac {P_{q}P_{q-2}}{P_{q-1}^{2}}},} * where * * * * * P * * n * * * * * {\displaystyle P_{n}} * is probability of observing * * * * * n * * * {\displaystyle n} * objects inside of some phase space regions. * The bunching parameters measure deviations of * the multiplicity distribution * * * * * P * * n * * * * * {\displaystyle P_{n}} * * from a Poisson distribution, since * for this distribution * * * * * * η * * q * * * = * 1 * * * {\displaystyle \eta _{q}=1} * .Uncorrelated particle production leads * to the Poisson statistics, thus * deviations of the bunching parameters from the Poisson values * mean correlations between particles and dynamical fluctuations. * Normalised factorial moments * have also similar properties. * They are defined as * * * * * * F * * q * * * = * ⟨ * n * * ⟩ * * − * q * * * * ∑ * * n * = * q * * * ∞ * * * * * * n * ! * * * ( * n * − * q * ) * ! * * * * * P * * n * * * . * * * {\displaystyle F_{q}=\langle n\rangle ^{-q}\sum _{n=q}^{\infty }{\frac {n!}{(n-q)!}}P_{n}.} |