Nucleon remnant and hadronization

The remnant system is the target nucleon `minus' the parton entering the hard scattering system (initial parton showers and matrix elements). This interacting parton can be either a valence quark, a sea-quark or a gluon.

When the interacting parton is a valence quark the nucleon remnant is simply a diquark composed of the two left-over valence quarks as spectators. In the Lund model [5] a colour triplet string is stretched between the colour triplet charged struck quark and the diquark which is a colour antitriplet. This system is then hadronized in the usual way [5, 26] by the production of quark-antiquark and diquark-antidiquark pairs from the energy in the field, leading to hadron production. The proton remnant diquark is not a single entity; its two quarks may go into a leading baryon but they can also be separated to produce a leading meson followed by a baryon.

In case the interacting parton is a sea quark ( ) or antiquark the nucleon remnant contains the corresponding antiquark or quark in addition to the three valence quarks ( ). This more complicated four-quark system or must be taken into account to conserve the flavour quantum numbers.

In the conventional way (default in LEPTO version 6.2 and earlier) the following treatment has been used. If or it is cancelled against a corresponding valence quark leaving a simple diquark system to be treated as above. For other flavours of it is joined with a valence quark of arbitrary flavour into a meson ( ). The is assumed to have no specific dynamic properties such that this splitting process into a meson and a diquark should be similar to normal hadronization. The meson is then given a fraction z of the remnants energy-momentum ( ) along the beam direction from a probability distribution P(z) (cf. LST(14)) and only a small Gaussian (cf.\ PARL(14)). The left-over diquark, with longitudinal momentum given by 1-z and equal but opposite , forms a string system with the scattered quark and hadronization proceeds as usual. If an antiquark ( ) was scattered the remnant is a four-quark system which is treated similarly to the previous case. Here, the corresponding quark ( ) is combined with a random diquark giving a baryon ( ) leaving the remaining valence quark to form a string system with the scattered antiquark. The split of the remnant is as before, taking account of the masses in the distribution for z (cf. LST(14)).

In LEPTO 6.3 a modified treatment of sea quarks in the remnant was introduced which is now default (cf. LST(35)). The essential difference is that the sea quark partners ( ) are treated dynamically and also u and d quarks can be considered as sea quarks. The interacting quark is assigned to be a valence or sea quark from the relative size of the corresponding parton distributions and , where is the momentum fraction of the quark `leaving' the proton and is the relevant scale (typically the cutoff of the initial state parton shower). In case of a valence quark the previous treatment is used, but in case of a sea quark a new treatment is used. The left-over partner is given a longitudinal momentum fraction from the Altarelli-Parisi splitting function and the transverse momentum follows from the masses of the partons in the splitting. Essentially the same results are obtained if the longitudinal momentum fraction is chosen from the corresponding sea quark momentum distribution. The former approach is presently used since this allows the mechanism to be simply implemented in the initial state parton shower routine as an additional, but non-perturbative, process. This partner sea quark will then be at the end-point of a string and not, as previously, go directly into a hadron together with another spectator parton. Depending on the momentum of the partner sea quark, this new string may extend more or less into the central region and through hadronization contribute to the particle and energy flow in the forward region. In particular, the transverse forward energy flow will be enhanced [44, 39] and improve the agreement with HERA data.

In boson-gluon fusion the removed gluon leaves the three valence quarks in a colour octet state. This remnant is split into a quark and a diquark, chosen with random flavours, which form two separate strings with the antiquark and quark, respectively, produced in the fusion process. Again the split of the remnant involves the same longitudinal momentum sharing and a Gaussian transverse momentum. For the order gluon radiation process (qg-event) the string is stretched from the scattered quark via the gluon to the target remnant.

In the parton shower case, the backwards evolution always results in one parton being removed from the nucleon as in the above cases such that the same procedures can be applied. The additional partons emitted in the PS case will, however, lead to a more complicated string configuration. The string follows the colour flow of the parton shower such that it starts from a colour triplet quark and goes via a number of colour octet gluons, which are kinks on the string, before ending up on a colour antitriplet antiquark or diquark. Where quark-antiquark pairs have been produced in the shower, the colour flow will be broken resulting in a termination of the first string piece and the start of a new one. The string system may thus be divided into subunits which then hadronize separately.

The ME and PS emissions may give a varying number of soft or collinear partons, depending on the details of the cut-offs. Although such partons cannot be observed as separate jets, they may give a `softening' and `fattening' of jets. The Lund string model is particularly suitable in this context, since it provides a stability in the sense that the hadron level result will not depend strongly on the presence of extra soft partons. Rather, one obtains a smooth transition to a configuration without them [45, 46]. The independent hadronization model, available as an option in [26] does not have the same property and is therefore not recommendable.

In this context one should also note that the two-string configuration for sea-quark initiated processes provides a desirable continuity between the two-string gluon-initiated -events and the one-string quark-initiated q-events. Depending on the partner sea-quark momentum, the corresponding string will extend more or less into the central region in rapidity. The hadronization of this extra string will contribute to the particle multiplicity and energy flow in this region [44, 39].

The parameters for the hadronization process in JETSET [26] are obtained from fits to data and are assumed to be the same in DIS based on jet universality. Nevertheless, they depend on which QCD effects are explicitly included in the Monte Carlo simulation. The default values are suitable when higher orders are taken into account via parton showers, whereas with first order ME alone the hadronization should be made slightly `softer' and `wider' to account for the additional parton emission not simulated explicitly.