Flavour Selection

The StringFlav class handles the choice of a new flavour in the fragmentation process, and the production of a new hadron from a set of input flavours. It is mainly used by the string fragmentation machinery (including ministrings), but also e.g. in some particle decays and for some beam-remnant cases. The basic concepts are in agreement with [And83]. The baryon-sector implementation is based on the MSTJ(12)=3 option of PYTHIA 6, i.e. new SU(6) weights scheme with at most one popcorn meson.

The relative production rates of different particle species is influenced by the parameters below. Some have only an impact on one specific quantity, but most directly or indirectly have consequences for many observables. Therefore the values to use have to be viewed in the context of a complete tune.

New flavours

The main parameters of the selection of a new flavour are

parm  StringFlav:probStoUD   (default = 0.19; minimum = 0.0; maximum = 1.0)
the suppression of s quark production relative to ordinary u or d one.

parm  StringFlav:probQQtoQ   (default = 0.09; minimum = 0.0; maximum = 1.0)
the suppression of diquark production relative to quark production, i.e. of baryon relative to meson production.

parm  StringFlav:probSQtoQQ   (default = 1.00; minimum = 0.0; maximum = 1.0)
the suppression of strange diquark production relative to light diquark production, over and above the one already given by probStoU.

parm  StringFlav:probQQ1toQQ0   (default = 0.027; minimum = 0.0; maximum = 1.0)
the suppression of spin 1 diquark production relative to spin 0 one, apart from the factor of 3 enhancement of spin 1 from counting the number of states.

pvec  StringFlav:probQQ1toQQ0join   (default = 0.5,0.7,0.9,1.0; minimum = 0.0; maximum = 1.0)
when two already produced quarks are to be combined to a diquark, e.g. in the junction framework, these numbers give the suppression of spin 1 diquark production relative to spin 0 one, apart from the factor of 3 enhancement of spin 1 from counting the number of states. The four components give the suppression when the heaviest quark is u/d, s, c or b, respectively. These parameters are seldom used and currently not constrained by any data, so very much a guesswork.

Standard-meson production

The bulk of the particle production corresponds to the lowest-lying pseudoscalar and vector multiplets. Their production rates are determined by the parameters in this section.

For a given set of flavours, produced according to the probabilities outlined above, the ratio of vector-to-pseudocalar meson production is described by the parameters below. The maximum allowed rate for each case has been set according to spin-counting rules, but we expect the real rates to be lower, especially for lighter mesons, owing to the vector-pseudoscalar mass splitting.

parm  StringFlav:mesonUDvector   (default = 0.62; minimum = 0.; maximum = 3.)
the relative production ratio vector/pseudoscalar for light (u, d) mesons.

parm  StringFlav:mesonSvector   (default = 0.725; minimum = 0.; maximum = 3.)
the relative production ratio vector/pseudoscalar for strange mesons.

parm  StringFlav:mesonCvector   (default = 1.06; minimum = 0.; maximum = 3.)
the relative production ratio vector/pseudoscalar for charm mesons.

parm  StringFlav:mesonBvector   (default = 3.0; minimum = 0.; maximum = 3.)
the relative production ratio vector/pseudoscalar for bottom mesons.

Inside each light-quark meson nonet, an octet-singlet mixing angle describes the mixing of the two flavour-diagonal isoscalar = 0 states. (For terminology and details see [Yao06], chapter 14 on the quark model.) This angle is needed to specify the probability for such a q qbar state to project onto a specific meson. More transparent formulae are obtained by introducing the angle alpha = theta + 54.7 degrees:
f = (uubar + ddbar)/sqrt(2) * sin(alpha) + ssbar * cos(alpha)
f' = (uubar + ddbar)/sqrt(2) * cos(alpha) - ssbar * sin(alpha)

parm  StringFlav:thetaPS   (default = -15.; minimum = -90.; maximum = 90.)
gives the mixing angle theta_PS in the pseudoscalar meson sector (which is rather poorly determined), expressed in degrees. Here f is associated with eta' and f' with eta. (This standard but counterintuitive choice is fixed up in the code by replacing alpha → 90^0 - alpha so that eta ↔ eta'; relative signs do not matter since we are interested in probabilities only.)

parm  StringFlav:thetaV   (default = 36.; minimum = -90.; maximum = 90.)
gives the mixing angle theta_V in the vector meson sector (which is somewhat better determined), expressed in degrees. Here f is associated with omega and f' with phi.

Further, the simple model overestimates the production of eta and, in particular, eta' mesons, which can be rectified by

parm  StringFlav:etaSup   (default = 0.63; minimum = 0.; maximum = 1.)
the additional suppression of eta production, multiplying the normal production probability. Thus 0 means no eta at all are produced, while 1 means full rate.

parm  StringFlav:etaPrimeSup   (default = 0.12; minimum = 0.; maximum = 1.)
the additional suppression of eta' production, multiplying the normal production probability. Thus 0 means no eta' at all are produced, while 1 means full rate.

Excited-meson production

Several excited mesons, ie. with radial or orbital excitations, have been observed at non-negligible production rates. Extrapolated to all states a fair fraction of all particle production might proceed through such states. There are big uncertainties, however, since these excited mesons in many cases are extremely poorly known. This also means that the modeling of their production and decay is very primitive, and even that the inclusion of the production of such states may lead to a degraded agreement with data. Currently the default is that all such production is switched off.

Parameters are provided to switch them on. By demand, this machinery has been made more flexible than in the past. Therefore one parameter is provided for each combination of heaviest flavour (u/d, s, c or b) and multiplet produced. In each case the production rate is normalized to that of the lowest-lying pseudoscalar of the same flavour content, as for the vector-meson rates introduced above. The multiplets available are the four obtained for one unit of orbital angular momentum, in the nonrelativistic classification. Using J to denote the sum of quark spin S and orbital angular momentum L, i.e. what would normally be called the spin of the meson, one has:

The maximum allowed rate for each case has been set according to spin-counting rules, but we expect the real rates to be significantly lower, owing to mass suppression.

parm  StringFlav:mesonUDL1S0J1   (default = 0.0; minimum = 0.; maximum = 3.)
the relative pseudovector production ratio (L=1,S=0,J=1)/pseudoscalar for light (u, d) mesons.

parm  StringFlav:mesonUDL1S1J0   (default = 0.0; minimum = 0.; maximum = 1.)
the relative scalar production ratio (L=1,S=1,J=0)/pseudoscalar for light (u, d) mesons.

parm  StringFlav:mesonUDL1S1J1   (default = 0.0; minimum = 0.; maximum = 3.)
the relative pseudovector production ratio (L=1,S=1,J=1)/pseudoscalar for light (u, d) mesons.

parm  StringFlav:mesonUDL1S1J2   (default = 0.0; minimum = 0.; maximum = 5.)
the relative tensor production ratio (L=1,S=1,J=2)/pseudoscalar for light (u, d) mesons.

parm  StringFlav:mesonSL1S0J1   (default = 0.0; minimum = 0.; maximum = 3.)
the relative pseudovector production ratio (L=1,S=0,J=1)/pseudoscalar for strange mesons.

parm  StringFlav:mesonSL1S1J0   (default = 0.0; minimum = 0.; maximum = 1.)
the relative scalar production ratio (L=1,S=1,J=0)/pseudoscalar for strange mesons.

parm  StringFlav:mesonSL1S1J1   (default = 0.0; minimum = 0.; maximum = 3.)
the relative pseudovector production ratio (L=1,S=1,J=1)/pseudoscalar for strange mesons.

parm  StringFlav:mesonSL1S1J2   (default = 0.0; minimum = 0.; maximum = 5.)
the relative tensor production ratio (L=1,S=1,J=2)/pseudoscalar for strange mesons.

parm  StringFlav:mesonCL1S0J1   (default = 0.0; minimum = 0.; maximum = 3.)
the relative pseudovector production ratio (L=1,S=0,J=1)/pseudoscalar for charm mesons.

parm  StringFlav:mesonCL1S1J0   (default = 0.0; minimum = 0.; maximum = 1.)
the relative scalar production ratio (L=1,S=1,J=0)/pseudoscalar for charm mesons.

parm  StringFlav:mesonCL1S1J1   (default = 0.0; minimum = 0.; maximum = 3.)
the relative pseudovector production ratio (L=1,S=1,J=1)/pseudoscalar for charm mesons.

parm  StringFlav:mesonCL1S1J2   (default = 0.0; minimum = 0.; maximum = 5.)
the relative tensor production ratio (L=1,S=1,J=2)/pseudoscalar for charm mesons.

parm  StringFlav:mesonBL1S0J1   (default = 0.0; minimum = 0.; maximum = 3.)
the relative pseudovector production ratio (L=1,S=0,J=1)/pseudoscalar for bottom mesons.

parm  StringFlav:mesonBL1S1J0   (default = 0.0; minimum = 0.; maximum = 1.)
the relative scalar production ratio (L=1,S=1,J=0)/pseudoscalar for bottom mesons.

parm  StringFlav:mesonBL1S1J1   (default = 0.0; minimum = 0.; maximum = 3.)
the relative pseudovector production ratio (L=1,S=1,J=1)/pseudoscalar for bottom mesons.

parm  StringFlav:mesonBL1S1J2   (default = 0.0; minimum = 0.; maximum = 5.)
the relative tensor production ratio (L=1,S=1,J=2)/pseudoscalar for bottom mesons.

In addition, an octet-singlet mixing angle is needed for each multiplet, as for the pseudoscalar and vector multiplets above. Only for the tensor multiplet does any determination exist; for the other multiplets default has been chose so that ssbar does not mix with the light quarks, and so that the ssbar state is the heavier of the two.

parm  StringFlav:thetaL1S0J1   (default = 35.3; minimum = -90.; maximum = 90.)
gives the mixing angle theta in the (L=1,S=0,J=1) pseudovector meson sector, expressed in degrees.

parm  StringFlav:thetaL1S1J0   (default = 35.3; minimum = -90.; maximum = 90.)
gives the mixing angle theta in the (L=1,S=1,J=0) scalar meson sector, expressed in degrees.

parm  StringFlav:thetaL1S1J1   (default = 35.3; minimum = -90.; maximum = 90.)
gives the mixing angle theta in the (L=1,S=1,J=1) pseudovector meson sector, expressed in degrees.

parm  StringFlav:thetaL1S1J2   (default = 28.0; minimum = -90.; maximum = 90.)
gives the mixing angle theta in the (L=1,S=1,J=2) tensor meson sector, expressed in degrees.

Baryon production

The relative rate of baryon production is mainly given by the quark and diquark production parameters above, plus SU(6) Clebsch-Gordans. The one modifiable parameter related to these coefficients is

parm  StringFlav:decupletSup   (default = 1.0; minimum = 0.0; maximum = 1.0)
the suppression, relative to default SU(6) factors, of decuplet baryon production. Default corresponds to no suppression, while 0 corresponds to no decuplet production at all.

In addition, if popcorn production is allowed, wherein a set of mesons (M) may be produced in between the baryon (B) and the antibaryon (Bbar), a set of further parameters is introduced. Currently only the simplest scenario is implemented, wherein at most one intermediate meson may be produced.

parm  StringFlav:popcornRate   (default = 0.5; minimum = 0.; maximum = 2.0)
gives the relative rates of B Bbar and B M Bbar production, roughly as
Prob(B M Bbar) / (Prob(B Bbar) + Prob(B M Bbar)) = popcornRate / (0.5 + popcornRate)
(the complete expression depends on all the quark and diquark production parameters and is therefore not so useful).

parm  StringFlav:popcornSpair   (default = 0.5; minimum = 0.; maximum = 1.0)
extra suppression for having an s sbar pair shared between the B and Bbar in a B M Bbar configuration.

parm  StringFlav:popcornSmeson   (default = 0.5; minimum = 0.; maximum = 1.0)
extra suppression for having a strange meson M in a B M Bbar configuration.

Finally, there are some indications that leading-baryon production may be further suppressed. A proper description should probably be based on a suppression of early production times [Ede97], but we here only implement a simpler version where production near the end of a string, as defined by rank, is suppressed. The more detailed studies suggest that leading c and b baryon production will be less suppressed, so we leave it open to set light- and heavy-baryon suppression separately.

flag  StringFlav:suppressLeadingB   (default = off)
Suppress leading-baryon production.
option off : No suppression.
option on : Suppress the production of a diquark in the string breaking closest to a quark end of a string, by either of the factors below. This suppresses the production of first-rank baryons by the same amount. Indirectly also the second-rank and, if popcorn production is switched on, third-rank (anti)baryon production is affected.

parm  StringFlav:lightLeadingBSup   (default = 0.5; minimum = 0.; maximum = 1.0)
extra suppression of leading-baryon production for a light-quark jet, i.e. d, u or s, when suppressLeadingB = on. Thus 0 means no leading-baryon production at all, while 1 means full rate.

parm  StringFlav:heavyLeadingBSup   (default = 0.9; minimum = 0.; maximum = 1.0)
extra suppression of leading-baryon production for a heavy-quark jet, i.e. c or b, when suppressLeadingB = on. Thus 0 means no leading-baryon production at all, while 1 means full rate.