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 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 , where 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) The new popcorn
parameters and
.
Used to suppress popcorn mesons of total invariant mass by
. Larger
`PARJ(9)`leads to a stronger suppression of popcorn systems surrounded by an pair, and also a little stronger suppression of strangeness in diquarks. `PARJ(10) :`- (D = 0.6 GeV) Corresponding parameter for
suppression of leading rank mesons of transverse mass 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 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 in the old model.
`PARF(132-134) :`- Leading rank meson ratio in the old model, for original diquark with 0, 1 and 2 -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 , original and original 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 popcorn mesons is started with weight proportional
to
`PARF(139)`. 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) :`-
suppression if
`MSTJ(12) = 5`, derived from`PARJ(18)`. `PARF(151-190) :`- Production ratios for different diquarks. Stored
in four groups, handling
,
,
and finally
in the case of original diquarks. In each group
is stored:
- 1 : colour fluctuation ratio.
- 2,3 : ratio for the vertex quark if the colour fluctuation quark is light or strange, respectively.
- 4 : vertex quark ratio if the colour fluctuation quark is light and .
- 5-7 : (spin 1)/(spin 0) ratio for , and , where the first flavour is the colour fluctuation quark.
- 8-10 : Unused.

`PARF(191) :`- (D = 0.2) Non-constituent mass in GeV of a
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- suppression
of diquark vertices in the
`MSTJ(12)`options.`PARF(192)`represents , i.e. the suppression is of the form`1. - PARF(192)`, in GeV. `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 , the weights for M and the new diquark depends not only on and : 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 diquark will go into a baryon or not. With five possible flavours for and this gives 80 different situations when selecting and . However, quarks heavier than only exist in the string endpoints, and if more popcorn mesons are to be produced, the diquark does not influence the weights and the dependence reduces to what factor (`PARJ(8 - 10)`) that is used. Then 40 distinct situations remains, i.e.:``true popcorn' final meson`

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,,u'.

In every situation can be , or . if 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 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 mesons, with in increasing order. If , this occupies three spots, and the final two are unused. If , the final three spots are used for the diagonal states when .

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)`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
, where .
Diquarks created in the fragmentation process now have the longer code
, i.e. one further digit is set.
Here is the curtain quark, i.e. the flavour of the quark-antiquark
pair that is shared between the baryon and the antibaryon, either
or . The non-curtain quark, the other of and , 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 and . 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.