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The advanced popcorn code for baryon production

In section [*] a new advanced popcorn code for baryon production model was presented, based on [Edé97]. It partly overwrites and redefines the meaning of some of the parameters above. Therefore the full description of these new options are given separately in this section, together with a listing of the new routines involved.

In order to use the new options, a few possibilities are open.

Use of the old diquark and popcorn models, MSTJ(12) = 1 and = 2, is essentially unchanged. Note, however, that PARJ(19) is available for an ad-hoc suppression of first-rank baryon production.
Use of the old popcorn model with new SU(6) weighting:
Set MSTJ(12) = 3.
Increase PARJ(1) by approximately a factor 1.2 to retain about the same effective baryon production rate as in MSTJ(12) = 2.
Note: the new SU(6) weighting e.g. implies that the total production rate of charm and bottom baryons is reduced.
Use of the old flavour model with new SU(6) treatment and modified fragmentation function for diquark vertices (which softens baryon spectra):
Set MSTJ(12) = 4.
Increase PARJ(1) by about a factor 1.7 and PARJ(5) by about a factor 1.2 to restore the baryon and popcorn rates of the MSTJ(12) = 2 default.
Use of the new flavour model (automatically with modified diquark fragmentation function.)
Set MSTJ(12) = 5.
Increase PARJ(1) by approximately a factor 2.
Change PARJ(18) from 1 to approx. 0.19.
Instead of PARJ(3) - PARJ(7), tune PARJ(8), PARJ(9), PARJ(10) and PARJ(18). (Here PARJ(10) is used only in collisions having remnants of baryon beam particles.)
Note: the proposed parameter values are based on a global fit to all baryon production rates. This e.g. means that the proton rate is lower than in the MSTJ(12) = 2 option, with current data somewhere in between. The PARJ(1) value would have to be about 3 times higher in MSTJ(12) = 5 than in = 2 to have the same total baryon production rate (=proton+neutron), but then other baryon rates would not match at all.
The new options MSTJ(12) = 4 and = 5 (and, to some extent, = 3) soften baryon spectra in such a way that PARJ(45) (the change of $a$ for diquarks in the Lund symmetric fragmentation function) is available for a retune. It affects i.e. baryon-antibaryon rapidity correlations and the baryon excess over antibaryons in quark jets.

The changes in and additions to the common blocks are as follows.

MSTU(121) - MSTU(125) :
Internal flags and counters; only MSTU(123) may be touched by you.
MSTU(121) :
Popcorn meson counter.
MSTU(122) :
Points at the proper diquark production weights, to distinguish between ordinary popcorn and rank 0 diquark systems. Only needed if MSTJ(12) = 5.
MSTU(123) :
Initialization flag. If MSTU(123) is 0 in a PYKFDI call, PYKFIN is called and MSTU(123) set to 1. Would need to be reset by you if flavour parameters are changed in the middle of a run.
MSTU(124) :
First parton flavour in decay call, stored to easily find random flavour partner in a popcorn system.
MSTU(125) :
Maximum number of popcorn mesons allowed in decay flavour generation. If a larger popcorn system passes the fake string suppressions, the error KF = 0 is returned and the flavour generation for the decay is restarted.
MSTU(131) - MSTU(140) :
Store of popcorn meson flavour codes in decay algorithm. Purely internal.

MSTJ(12) :
(D = 2) Main switch for choice of baryon production model. Suppression of rank 1 baryons by a parameter PARJ(19) is no longer governed by the MSTJ(12) switch, but instead turned on by setting PARJ(19) < 1. Three new options are available:
= 3 :
as = 2, but additionally the production of first rank baryons may be suppressed by a factor PARJ(19).
= 4 :
as = 2, but diquark vertices suffers an extra suppression of the form $1-\exp(\rho\Gamma)$, where $\rho\approx 0.7~\mathrm{GeV}^{-2}$ is stored in PARF(192).
= 5 :
Advanced version of the popcorn model. Independent of PARJ(3 - 7). Instead depending on PARJ(8 - 10). When using this option PARJ(1) needs to enhanced by approx. a factor 2 (i.e. it losses a bit of its normal meaning), and PARJ(18) is suggested to be set to 0.19.

PARJ(8), PARJ(9) :
(D = 0.6, 1.2 GeV$^{-1}$) The new popcorn parameters $\beta_{\u }$ and $\delta \beta = \beta_{\mathrm{s}} - \beta_{\u }$. Used to suppress popcorn mesons of total invariant mass $M_{\perp}$ by $\exp(-\beta_q*M_{\perp})$. Larger PARJ(9) leads to a stronger suppression of popcorn systems surrounded by an $\mathrm{s}\overline{\mathrm{s}}$ pair, and also a little stronger suppression of strangeness in diquarks.
PARJ(10) :
(D = 0.6 GeV$^{-1}$) Corresponding parameter for suppression of leading rank mesons of transverse mass $M_{\perp}$ in the fragmentation of diquark jets, used if MSTJ(12) = 5. The treatment of original diquarks is flavour independent, i.e. PARJ(10) is used even if the diquark contains $\mathrm{s}$ or heavier quarks.

PARF(131) - PARF(190) :
Different diquark and popcorn weights, calculated in PYKFIN, which is automatically called from PYKFDI.
PARF(131) :
Popcorn ratio $BM\overline{B}/B\overline{B}$ in the old model.
PARF(132-134) :
Leading rank meson ratio $MB/B$ in the old model, for original diquark with 0, 1 and 2 $\mathrm{s}$-quarks, respectively.
PARF(135-137) :
Colour fluctuation quark ratio, i.e. the relative probability that the heavier quark in a diquark fits into the baryon at the opposite side of the popcorn meson. For $\mathrm{s}\mathrm{q}$, original $\mathrm{s}\mathrm{q}$ and original $\c\mathrm{q}$ diquarks, respectively.
PARF(138) :
The extra suppression of strange colour fluctuation quarks, due to the requirement of surrounding a popcorn meson. (In the old model, it is simply PARJ(6).)
PARF(139) :
Preliminary suppression of a popcorn meson in the new model. A system of $N$ popcorn mesons is started with weight proportional to PARF(139)$^N$. It is then tested against the correct weight, derived from the mass of the system. For strange colour fluctuation quarks, the weight is PARF(138)*PARF(139).
PARF(140) :
Preliminary suppression of leading rank mesons in diquark strings, irrespective of flavour. Corresponds to PARF(139).
PARF(141-145) :
Maximal SU(6) factors for different types of diquarks.
PARF(146) :
$\Sigma/\Lambda$ suppression if MSTJ(12) = 5, derived from PARJ(18).
PARF(151-190) :
Production ratios for different diquarks. Stored in four groups, handling $\mathrm{q}\rightarrow B\overline{B}$, $\mathrm{q}\rightarrow BM...\overline{B}$, $\mathrm{q}\mathrm{q}\rightarrow MB$ and finally $\mathrm{q}\mathrm{q}\rightarrow MB$ in the case of original diquarks. In each group is stored:
  • 1 : $\mathrm{s}/ \u $ colour fluctuation ratio.
  • 2,3 : $\mathrm{s}/ \u $ ratio for the vertex quark if the colour fluctuation quark is light or strange, respectively.
  • 4 : $\mathrm{q}/\mathrm{q}'$ vertex quark ratio if the colour fluctuation quark is light and $=\mathrm{q}$.
  • 5-7 : (spin 1)/(spin 0) ratio for $\mathrm{s}\u $, $\u\mathrm{s}$ and $\u\d $, where the first flavour is the colour fluctuation quark.
  • 8-10 : Unused.
PARF(191) :
(D = 0.2) Non-constituent mass in GeV of a $\u\d _0$ diquark. Used in combination with diquark constituent mass differences to derive relative production rates for different diquark flavours in the MSTJ(12) = 5 option.
PARF(192) :
(D = 0.5) Parameter for the low-$\Gamma$ suppression of diquark vertices in the MSTJ(12)$\ge 4$ options. PARF(192) represents $e^{-\rho}$, i.e. the suppression is of the form 1. - PARF(192)$^\Gamma$, $\Gamma$ in GeV$^2$.
PARF(193,194) :
(I) Store of some popcorn weights used by the present popcorn system.
PARF(201-1400) :
(I) Weights for every possible popcorn meson construction in the MSTJ(12) = 5 option. Calculated from input parameters and meson masses in PYKFIN. When $\mathrm{q}_1\mathrm{q}_2 \rightarrow M+\mathrm{q}_1\mathrm{q}_3$, the weights for M and the new diquark depends not only on $\mathrm{q}_1$ and $\mathrm{q}_2$: it is also important if this is a `true' popcorn system, or a system which started with a diquark at the string end, and if M is the final meson of the popcorn system, i.e. if the $\mathrm{q}_1\mathrm{q}_3$ diquark will go into a baryon or not. With five possible flavours for $\mathrm{q}_1$ and $\mathrm{q}_2$ this gives 80 different situations when selecting $M$ and $\mathrm{q}_3$. However, quarks heavier than $\mathrm{s}$ only exist in the string endpoints, and if more popcorn mesons are to be produced, the $\mathrm{q}_1\mathrm{q}_3$ diquark does not influence the weights and the $\mathrm{q}_1$ dependence reduces to what $\beta$ factor (PARJ(8 - 10)) that is used. Then 40 distinct situations remains, i.e.:

`true popcorn'		final meson		$\mathrm{q}_1$		$\mathrm{q}_2$ 

YES YES d,u,s d,u,s
NO $<$s,s d,u,s
NO YES d,u,s,$>$s d,u,s,c,b
NO 1 case d,u,s,c,b

This table also shows the order in which the situations are stored. E.g. situation no. 1 is `YES,YES,d,d', situation no.11 is `YES,NO,$<s$,u'.
In every situation $\mathrm{q}_3$ can be $\d $, $\u $ or $\mathrm{s}$. if $\mathrm{q}_3=\mathrm{q}_2$ there are in the program three possible flavour mixing states available for the meson. This gives five possible meson flavours, and for each one of them there are six possible $L,S$ spin states. Thus 30 PARF positions are reserved for each situation, and these are used as follows:
For each spin multiplet (in the same order as in PARF(1 - 60)) five positions are reserved. First are stored the weights for the the $\mathrm{q}_3\ne\mathrm{q}_2$ mesons, with $\mathrm{q}_3$ in increasing order. If $\mathrm{q}_2>\mathrm{s}$, this occupies three spots, and the final two are unused. If $\mathrm{q}_2\le\mathrm{s}$, the final three spots are used for the diagonal states when $\mathrm{q}_3=\mathrm{q}_2$.

In summary, all common-block variables are completely internal, except MSTU(123), MSTJ(12), PARJ(8) - PARJ(10) and PARF(191), PARF(192). Among these, PARF(191) and PARF(192) should not need to be changed. MSTU(123) should be 0 when starting, and reset to 0 whenever changing a switch or parameter which influences flavour weight With MSTJ(12) = 4, PARJ(5) may need to increase. With MSTJ(12) = 5, a preliminary tune suggests PARJ(8) = 0.6, PARJ(9) = 1.2, PARJ(10) = 0.6, PARJ(1) = 0.20 and PARJ(18) = 0.19.

Three new subroutines are added, but are only needed for internal use.

to calculate a large set of diquark and popcorn weights from input parameters. Is called from PYKFDI if MSTU(123) = 0. Sets MSTU(123) to 1.

to calculate number of popcorn mesons to be generated in a popcorn system, or the number of leading rank mesons when fragmenting a diquark string. Stores the number in MSTU(121). Always returns 0 if MSTJ(12) < 2. Returns 0 or 1 if MSTJ(12) < 5.
Flavour of the diquark in a diquark string. If starting a popcorn system inside a string, KFDIQ is 0.

to generate flavours in the phase space model of hadron decays, and in cluster decays. Is essentially the same as a PYKFDI call, but also takes into account the effects of string dynamics in flavour production in the MSTJ(12)$\ge 4$ options. This is done in order to get a reasonable interpretation of the input parameters also for hadron decays with these options.

Internally the diquark codes have been extended to store the necessary further popcorn information. As before, an initially existing diquark has a code of the type $1000 q_a + 100 q_b + 2s+1$, where $q_a > q_b$. Diquarks created in the fragmentation process now have the longer code $10000 q_c + 1000 q_a + 100 q_b + 2s+1$, i.e. one further digit is set. Here $q_c$ is the curtain quark, i.e. the flavour of the quark-antiquark pair that is shared between the baryon and the antibaryon, either $q_a$ or $q_b$. The non-curtain quark, the other of $q_a$ and $q_b$, may have its antiquark partner in a popcorn meson. In case there are no popcorn mesons this information is not needed, but is still set at random to be either of $q_a$ and $q_b$. The extended code is used internally in PYSTRF and PYDECY and in some routines called by them, but is not visible in any event listings.

next up previous contents
Next: Further Parameters and Particle Up: The General Switches and Previous: The General Switches and   Contents
Stephen Mrenna 2007-10-30