Rope Hadronization
- Main settings
- String shoving
- Flavour Ropes
In collisions of protons, there are often tens of multiparton interactions,
all producing Lund strings occupying the same area in transverse space of
~1 fm^2. The Rope Hadronization framework describes the
interactions between such overlapping strings, by (a) allowing nearby strings
to shove each other with an interaction potential derived from the colour
superconductor analogy [Bie16b], [Bie17] and (b) at
hadronization time, colour charges at string endpoints and in gluon "kinks"
can act together coherently to form a "rope", which is hadronized with a
larger, effective string tension [Bie14].
The latter has noticeable effects on the flavour composition of the hadronic
final state [Bie15], and this effect is denoted "flavour ropes"
below.
Since both models deal with string overlaps in transverse space, it is
necessary to provide such information, as it is not present in the
Pythia MPI model. The information is provided through the
Parton Vertex methods. The string
shoving mechanism is exemplified in the main441.cc example,
and the flavour ropes in main442.cc.
A simpler version of flavour composition ropes exist [Bie16c],
which do not require vertex information. This can be enabled by a switch.
Main settings
The main settings are common for both the string shoving and the flavour rope
models.
flag Ropewalk:RopeHadronization
(default = off)
Master switch for all aspects of rope hadronization.
The Rope Hadronization framework is intended to work seamlessly with the rest
of Pythia 8. It is, however, still a new model, and no Pythia tunes with ropes
enabled exists yet. Therefore Rope Hadronization must be explicitly switched
on, and it is up to the user to provide a sensible tune.
flag Ropewalk:doShoving
(default = off)
Enable the string shoving mechanism. In addition to this, the above
Ropewalk:RopeHadronization flag must also be switched on.
flag Ropewalk:doFlavour
(default = off)
Enable the flavour ropes mechanism. In addition to this, the above
Ropewalk:RopeHadronization flag must also be switched on.
parm Ropewalk:r0
(default = 0.5; minimum = 0.; maximum = 10.)
The transverse radius of a string, in units of fm. This can be viewed as an
overall strength parameter of the Rope Hadronization framework, as all effects
scale with increasing string overlap. Notice that the value for the string
radius must be seen compared to the parameters which determines string
placement in the transverse plane, as described in
Parton Vertex Information.
parm Ropewalk:m0
(default = 0.2; minimum = 0.01; maximum = 5.0)
Imposed lower mass cutoff to allow for calculation of rapidities of dipoles
composed of massless gluons.
String shoving
The string shoving mechanism allows strings to push each other, before
hadronization, as described in [Bie16b].
String shoving divides the event up in many small rapidity slices (in
the lab frame), and all string pieces in all slices are allowed to push
each other with a force:
f(d_\perp) = \frac{g_A \kappa d_\perp}{R^2}
\exp\left(-\frac{d^2_\perp }{4R^2}\right),
where d_\perp is the distance in transverse space between two string
pieces, calculated dynamically using
Vertex Information. Model
parameters are g_A, the amplitude of the shoving force,
R, the string radius, and g_E, a parameter dividing
the equilibrium string radius to account for the effect of strings
starting out with a vanishing string radius.
The model should be used with some caution. Simply switching it on, one will
not retain full description of single particle observables in minimum bias pp
collisions, as the excitation gluons will increase multiplicity. Besides
normal tuning, one can use the parameter
FragmentationSystems:mJoin to join the excitation gluons
together, in order to recover single particle observables.
parm Ropewalk:rCutOff
(default = 6.0; minimum = 0.; maximum = 100.)
This parameter gives the maximum cut-off radius, at which strings stops
interacting. The purpose of the parameter is to decrease computation time by
not calculating arbitrarily small pushes. In pp collisions at LHC energies,
no significant variation in the results is observed by increasing this value
above the default.
parm Ropewalk:gAmplitude
(default = 5.0; minimum = 0.; maximum = 100.)
The amplitude of the shoving force. Note that many traditional
Min Bias/UE observables, such as multiplicity and p_\perp, as
well as transverse quantities, are sensitive to this parameter. As
such, a change of this, in principle warrants a full retuning of the
MPI framework.
parm Ropewalk:gExponent
(default = 1.0; minimum = 0.; maximum = 100.)
This value multiplies the string radius in the shoving
force, allowing for a variation between string radius in the flavour rope
treatment and the shoving treatment, if one wishes to run both simultaneously.
parm Ropewalk:deltay
(default = 0.2; minimum = 0.01; maximum = 10.)
This value gives the width of the rapidity slices in which the event is
split before shoving.
parm Ropewalk:tShove
(default = 1.0; minimum = 0.; maximum = 100.)
The total shoving time in units of fm/c.
parm Ropewalk:deltat
(default = 0.1; minimum = 0.01; maximum = 100.0)
The size of the steps taken in time during shoving. Since the whole
event needs to be retraced after every time step, this should not be
too small.
parm Ropewalk:tInit
(default = 1.5; minimum = 0.; maximum = 100.)
The strings are allowed to propagate for some time, given in fm/c
by this parameter, before shoving takes place. This accounts for the
fact that the strings are created with a vanishing transverse size,
and only shove each other when their transverse size is large enough
for interaction. Furthermore, the physical value of this parameter is
largely connected to the values set for
Parton Vertex Information.
flag Ropewalk:shoveGluonLoops
(default = on)
Allow for shoving of strings which form a gluon loop.
This is mainly a technical setting, and should be kept switched on,
unless the user has a specific intention of switching it off.
flag Ropewalk:shoveJunctionStrings
(default = on)
Allow for shoving of strings that includes a junction topology from
eg. beam remnants. This is mainly a technical setting, and should be
kept switched on, unless the user has a specific intention of
switching it off.
flag Ropewalk:shoveMiniStrings
(default = on)
Allow for shoving of ministrings. This is mainly a technical setting, and
should be kept switched on, unless the user has a specific intention of
switching it off.
flag Ropewalk:limitMom
(default = on)
It is possible to switch off shoving for dipoles with a p_\perp
above a given value. This is intended as a cut-off to disallow string segments
moving so fast that they would anyway escape shoving from soft strings to
have gluonic excitations added to them.
parm Ropewalk:pTcut
(default = 2.0; minimum = 0.; maximum = 1000.)
The value of p_\perp at which shoving is turned off, if the flag
Ropewalk:limitMom is on.
Flavour Ropes
The Flavour Ropes mechanism allows strings situated close in impact parameter
space to interact coherently, forming a rope, which hadronizes with a larger,
effective string tension. The model is described in ref. [Bie14],
building on an older idea by Biro et al. [Bir84].
In the flavour rope formalism, a rope is described as an SU(3) multiplet,
characterized uniquely by two quantum numbers p and q.
The quantum numbers are calculated, following ref. [Bir84], by
a random walk procedure in colour space, taking m, n steps,
where m and n signify the number of overlapping
strings which are respectively parallel or anti-parallel to the
hadronizing string.
When the rope quantum numbers have been determined, the effective string
tension is calculated per individual breaking, using a lattice QCD
determination of the string tension [Bal00]. The effective
string tension is then used to rescale the hadronization parameters
described in the section on String
Fragmentation. One point to note regarding the rescaling is the
fragmentation parameter StringFlav:probQQtoQ, describing
baryon relative to meson production. Baryon production is, as suggested
by eg. the popcorn hadronization model [Ede97], more complicated
than meson production. The current modelling of this in the flavour ropes
framework is limited, but intended to be extended in the future.
parm Ropewalk:beta
(default = 0.2; minimum = 0.; maximum = 1.0)
In the current implementation of the rope model, the theoretical ignorance
about baryon production has been parameterized, assuming that the parameter
StringFlav:probQQtoQ will factorize into two parts,
one which will scale with effective string tension, one which will not.
This parameter controls how large a fraction of the parameter will scale
with string tension.
flag Ropewalk:alwaysHighest
(default = off)
Setting this flag on will skip the random walk procedure for flavour ropes,
and assume that one always ends up in the highest possible SU(3) multiplet.
This would be adequate for situations where all lower multiplets are assumed
handled by colour reconnection and junction formation.
flag Ropewalk:doBuffon
(default = off)
Setting this flag on, enables a simpler treatment of flavour ropes. This is
not reliant on vertex information, but string-string overlaps are decided
randomly á la Buffon's needle [Bie16c]: All strings are
thrown randomly into a circular area in transverse space to estimate overlaps.
parm Ropewalk:stringProtonRatio
(default = 0.2; minimum = 0.; maximum = 10.0)
Only used if Ropewalk:buffonRope is enabled. The ratio of the
string transverse area to a proton transverse area. Determines the amount of
overlap in collisions.
parm Ropewalk:rapiditySpan
(default = 0.5; minimum = 0.; maximum = 10.0)
Only used if Ropewalk:buffonRope is enabled. Determines how far
in rapidity from a string break overlaps are counted.
flag Ropewalk:setFixedKappa
(default = off)
Setting this flag gives the user the possibility to ignore the generator
space-time information altogether, using only a provided string tension.
This could be useful for (toy) studies of hadronization in very dense
environments, such as central heavy ion collisions.
parm Ropewalk:presetKappa
(default = 0.; minimum = 0.; maximum = 100.0)
The effective string tension is normally calculated dynamically using overlaps
of strings, based on Parton Vertex
information. By setting Ropewalk:setFixedKappa, this information
is ignored, and a preset value provided in the presetKappa
variable is used.
parm StringFlav:kappa
(default = 0.2; minimum = 0.0; maximum = 10.)
A base value of the string tension can be added, and modified along with other
parameters, to allow for studies of exotic quark production in the Rope model.