Experiment Proposal - opera - Infn

known. Because of these uncertainties, we adopt an empirical parametrisation as a function of the
neutrino energy (Fig. 140) which reproduces the E531 data [80]. By convoluting this parametrisation
with the CNGS neutrino spectrum [58] one obtains
σ(ν µ N → µ − cX)
σ(ν µ N → µ − X) ≡
σ c
σ CC
=(3.3 ± 0.5)% (3)
Figure 140: Parametrisation of the relative charmed-particle production rate in ν µ CC interactions, as
a function of the neutrino energy reproducing the E531 data. The vertical scale is in %.
We then assume the factorisation theorem to obtain the charmed hadron (C) cross section, which
can be related to the charm quark (c) cross section through fragmentation functions
d 5 σ(ν µ N → µ − CX)
dxdydzdp 2 t
= d2 σ(ν µ N → µ − cX)
dxdy
× ∑ h
f h × D h c (z,p 2 t ) (4)
where D h c (z,p 2 t ) is the probability distribution for the charm quark fragmenting into a hadron h
carrying a fraction z of the longitudinal momentum of the quark and transverse momentum p t with
respect to the quark direction.
The quantity f h is the fraction of σ c in which a charmed hadron h is produced. We assume ∑ h f h =1
with the sum extended to the hadrons considered below. From equation (4) it follows that f h depends on
the chosen hadronisation scheme i.e. on the functions Dc h(z,p2 t ). Several sets of the Dh c (z,p2 t ) exist [79].
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