Heavy-Quark Production in the Target Fragmentation Region

Abstract

Fixed-target experiments permit the study of hadron production in the target fragmentation region. It is expected that the tagging of specific particles in the target fragments can be employed to introduce a bias in the hard scattering process towards a specific flavour content. The case of hadrons containing a heavy quark is particularly attractive because of the clear experimental signatures and the applicability of perturbative QCD. The standard approach to one-particle inclusive processes based on fragmentation functions is valid in the current fragmentation region and for large transverse momenta $p_T$ in the target fragmentation region, but it fails for particle production at small $p_T$ in the target fragmentation region. A collinear singularity, which cannot be absorbed in the standard way into the phenomenological distribution functions, prohibits the application of this procedure. This situation is remedied by the introduction of a new set of distribution functions, the target fragmentation functions. They describe particle production in the target fragmentation region, and can be viewed as correlated distribution functions in the momentum fractions of the observed particle and of the parton initiating the hard scattering process. It is shown in a next-to-leading-order calculation for the case of deeply inelastic lepton-nucleon scattering that the additional singularity can be consistently absorbed into the renormalized target fragmentation functions on the one-loop level. The formalism is derived in detail and is applied to the production of heavy quarks. The renormalization group equation of the target fragmentation functions for the perturbative contribution is solved numerically, and the results of a case study for deeply inelastic lepton-nucleon scattering at DESY (H1 and ZEUS at HERA), at CERN (NA47) and at Fermilab (E665) are discussed. We also comment briefly on the case of an intrinsic heavy-quark content of the proton.Comment: Habilitationsschrift, Universitaet Hamburg, submitted in April 1996. 118 pages (LATEX); figures are included via epsfig; The AMSTEX fonts are required. See also http://wwwcn.cern.ch/~graudenz/publications.html for a complete (compressed) postscript fil

Phenomenology of multiple parton radiation in semi-inclusive deep-inelastic scattering

“…5 shows the x F -distribution for the charged particle multiplicity (1/σ tot )dσ/dx F . We see that both the resummed and fixed-order distributions are in reasonable agreement with the data and with earlier published theoretical results for the O(α s ) x F -distributions [15]. For the fixed-order multiplicity, we present two additional curves corresponding to different choices of the factorization scale µ F in (5); the lower and upper dotted curves correspond to µ F = 0.5Q and 2Q, respectively.…”

Measurement of semi-inclusiveπ+electroproduction off the proton

“…The fracture function M h i ðx; zÞ gives the combined probability of striking a parton of flavor i at x and producing a hadron h at z from the proton remnant. This function obeys the pQCD evolution equations [1,66] similar to those for f i ðxÞ and D h i ðzÞ. The factorization of the hard photon-parton scattering and a soft part described by M h i ðx; zÞ has been proved in Refs.…”

“…where D h i ðzÞ is the fragmentation function, M h i ðx; zÞ is the fracture function [1] and Að h Þ is the angular distribution of the observed hadron [66]. The fracture function M h i ðx; zÞ gives the combined probability of striking a parton of flavor i at x and producing a hadron h at z from the proton remnant.…”

Confronting fragmentation function universality with single hadron inclusive production at HERA ande+e−colliders

“…Because of the resulting uncertainties in the FFs at small x p , and because ep reaction data suffer from similar uncertainties at small x p , we only study ep reaction data for which x p > 0.1. Cross sections are calculated to NLO in the MS scheme using the CYCLOPS software [25]. We set the number of active quark flavours n f = 5.…”