Flavour Selection for Gaussian pT Distribution
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]. An alternative
"thermal model" is described further below.
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 = 0.217; minimum = 0.0; maximum = 1.0)
the suppression of s quark production relative to ordinary
u or d one.
parm StringFlav:probQQtoQ
(default = 0.081; 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 = 0.915; 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 = 0.0275; 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. Character-string input of this vector
should be as a comma-separated list, without any blanks.
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 = 0.50; minimum = 0.; maximum = 3.)
the relative production ratio vector/pseudoscalar for light
(u, d) mesons.
parm StringFlav:mesonSvector
(default = 0.55; minimum = 0.; maximum = 3.)
the relative production ratio vector/pseudoscalar for strange mesons.
parm StringFlav:mesonCvector
(default = 0.88; minimum = 0.; maximum = 3.)
the relative production ratio vector/pseudoscalar for charm mesons.
parm StringFlav:mesonBvector
(default = 2.20; 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 = 0.60; 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:
- a pseudovector multiplet with L=1, S=0, J=1;
- a scalar multiplet with L=1, S=1, J=0;
- a pseudovector multiplet with L=1, S=1, J=1;
- a tensor multiplet with L=1, S=1, J=2.
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 = 0.9; 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.
Flavour Selection for Thermal pT Distribution
If the hadronic pT is generated according to the non-default
thermal distribution, i.e. if StringPT:thermalModel = on,
the choice of a new flavour in the fragmentation process, and the
production of a new hadron from a set of input flavours, depends mainly on
the hadron mass [Fis16]. For a given pT value the new
flavour is chosen according to
exp( -mT_had/T) = exp( - sqrt( pT_had^2 + mT_had^2 )/T).
Here T is primarily given by StringPT:temperature,
but can be further modified in the context of closely packed strings,
StringPT:closePacking = on.
Additional factors are included from theory arguments, for instance
the ratio of vector-to-pseudocalar meson production is set according
to spin-counting rules.
Note that the octet-singlet mixing angles in the light-quark meson
nonets are taken from the parameters above.
Currently popcorn production has not been implemented, i.e. a baryon
and an antibaryon are nearest neighbours in the flavour fragmentation
chain, and share the flavours of one diquark.
In addition the following two factors are introduced to provide an
improved description of the flavour composition, although not as good
as obtained in the default Gaussian scenario, with its bigger selection
of free parameters.
parm StringFlav:BtoMratio
(default = 0.357; minimum = 0.1; maximum = 10.0)
Ratio of the relative rate of baryon to meson production, i.e. every
baryon Clebsch-Gordan coefficient gets multiplied by this factor.
parm StringFlav:StrangeSuppression
(default = 0.5; minimum = 0.01; maximum = 1.0)
Extra suppression factor for strange quarks. Note that in case of more
than one strange quark in the hadron the factor gets squared or tripled
respectively.
The following parameters are used to determine which hadrons to choose
from. By default only the pseudoscalar and vector meson nonet (L=0)
and baryons with u/d/s quarks are included. For an already-existing
heavier flavour, say c or b, this corresponds to picking only u/d/s
for the new quark(s).
Note: The computer time for selecting the flavour of new
hadrons goes linearly with the number of hadrons included. Therefore
we recommend sticking to the default options as heavier hadrons are
produced less likely anyway.
mode StringFlav:nQuark
(default = 3; minimum = 3; maximum = 5)
Selects the newly produced quark flavours that may be included in hadrons.
The default corresponds to only include u/d/s quarks.
flag StringFlav:mesonNonetL1
(default = off)
Switch on to include the pseudovector, scalar, pseudovector, and tensor
nonet (L=1).