Thermal String Fragmentation
The thermal model [Fis16] is an attempt to combine global
flavour and pT concepts familiar from the heavy-ion
community with the local conservation rules obtained in a string
framework. To replace the standard Lund fragmentation model with
the thermal one you need to set Fragmentation:model = 1
in your main program.
One can give at least three arguments why it is not a
completely crazy variation of the standard Lund fragmentation
setup. Firstly, low-energy low-pT data for many
hadron species are empirically well described by pT
spectra of the shape exp(-6 mT), where mT
is the hadron transverse mass. Secondly, Hagedorn's
thermodynamical arguments suggest that indeed hadron pT
spectra should be of the shape exp(-mT / T),
where T is the temperature of the particle-producing
source. Thirdly, one could imagine that a string is fluctuating
along its length, where a contraction leads to an increased string
tension, and vice versa. Bialas showed that a reasonable ansatz
for such fluctuations can turn a Gaussian pT distribution
into an exponential one.
The current framework keeps most of the string fragmentation code
unchanged. The big differences are that the new derived classes
ThermalStringFlav and ThermalStringpT
take care of flavour and pT selection, with free parameters as
described below. The longitudinal selection in StringZ
remains unchanged, so the settings on the
z Selection page can be used also
here.
In the thermal fragmentation, as implemented here, the pT
selection has to be done before the flavour one, which is opposite
to the order in normal string fragmentation. (Although of less
relevance there.) To cover both possibilities, the
StringFragmentation class has a method
setFlavBeforePT to fix the order. In either option the
z selection occurs last.
Transverse momentum selection
The quark pT is generated according to a complicated
expression (involving the Bessel K_{1/4} function),
such that the resulting hadron pT follows a thermal
distribution
d(Prob) = exp( -pT_had/T) d^2pT_had
with temperature T, whose value is given by
parm StringPT:temperature
(default = 0.21; minimum = 0.1; maximum = 0.5)
the temperature T in the fragmentation process, in units of GeV.
parm StringPT:tempPreFactor
(default = 1.21; minimum = 1.0; maximum = 1.5)
Temperature prefactor for strange quarks and diquarks. Default is
determined so as to give the same average pT in
u/d → s and s → u/d transitions, which
also is the reason this parameter has been introduced.
Flavour selection
With the hadronic pT generated according to the thermal
distribution, 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,
ClosePacking:doClosePacking = 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. The octet-singlet mixing angles in the
light-quark meson nonets are taken the same as for Lund strings.
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).