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.

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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.

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Use of the old popcorn model with new SU(6) weighting:

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Set MSTJ(12) = 3.

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Increase PARJ(1) by approximately a factor 1.2 to retain about the same effective baryon production rate as in MSTJ(12) = 2.

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Note: the new SU(6) weighting e.g. implies that the total production rate of charm and bottom baryons is reduced.

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Use of the old flavour model with new SU(6) treatment and modified fragmentation function for diquark vertices (which softens baryon spectra):

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Set MSTJ(12) = 4.

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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.

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Use of the new flavour model (automatically with modified diquark fragmentation function.)

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Set MSTJ(12) = 5.

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Increase PARJ(1) by approximately a factor 2.

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Change PARJ(18) from 1 to approx. 0.19.

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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.)

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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.

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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.

SUBROUTINE PYKFIN :

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.

SUBROUTINE PYNMES(KFDIQ) :

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.

KFDIQ :

Flavour of the diquark in a diquark string. If starting a popcorn system inside a string, KFDIQ is 0.

SUBROUTINE PYDCYK(KFL1,KFL2,KFL3,KF) :

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.

KFL1,KFL2,KFL3,KF :

See SUBROUTINE PYKFDI.

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.