Parton Vertex Information
 
  - Hadronization Parameters
- External models
While the setting of secondary production vertices of unstable 
hadrons and leptons is a standard part of the particle decay 
routines, no corresponding standardized handling is in place for 
the evolution in the partonic or hadronization phases 
of the event generation. The intention is to provide such methods 
in due course. 
 
 
There are some cases where such information is needed already now, 
specifically for the 
Rope Hadronization and the 
Hadronic Rescattering 
frameworks. Therefore the beginning of a framework is available, 
that can be used to set impact-parameter-plane vertices for 
partonic production by MPI, FSR, ISR and beam remnants. This is 
done in thePartonVertex class. 
 
 
This is a base class, with a default implementation, but the user 
can replace it with a derived class that does a more sophisticated 
handling. Improvements and extensions are likely to come to the 
base class. So, while people are welcome to write their own derived 
classes, it is likely that these may need to be modified in later 
PYTHIA versions. 
 
 
Hadronization Parameters
 
 
Currently the base class implements a few alternative approaches to 
picking a partonic vertex, for use inside the rope hadronization and 
hadronic rescattering frameworks. There are also some free parameters 
in the models. 
 
flag   PartonVertex:setVertex   
 (default = off)
Master switch to allow the setting of partonic vertices. 
   
 
mode   PartonVertex:modeVertex   
 (default = 2; minimum = 1; maximum = 4)
Choice between alternative procedures to select vertex. 
option  1 : Proton profile is a (Lorentz-contracted) 
uniform-parton-density ball. This gives an almond-shaped 
overlap region between two colliding hadrons, favouring MPI being 
displaced perpendicularly to the collision plane. 
   
option  2 : Proton profile is a (Lorentz-contracted) 
three-dimensional Gaussian, or equivalently a two-dimensional one, 
since a Gaussian easily factorizes so that the z can be 
integrated out. This gives a Gaussian overlap region between the 
two colliding hadrons, since the product of two displaced Gaussians 
is another Gaussian. 
   
option  3 : Proton profile is a Gaussian, as above, but 
elongated by a scale factor rEps in the x direction 
and compressed by the same factor in the y direction. 
Here rEps = sqrt( (1 + epsilon) / (1 - epsilon) ), where 
epsilon is described further below. If epsilon < 0 
then the role of elongation and compression is exchanged. 
   
option  4 : Proton profile is Gaussian, as above, but with a 
further modulation factor 1 + epsilon * cos(2 * phi), where 
the asymmetry parameter epsilon is described further below. 
The azimuthal angle phi is defined with respect the the 
hadron-hadron collision plane. Among rotationally symmetric parton 
distributions only the Gaussian one (or a sum of Gaussians) do not 
give rise to azimuthal asymmetries, so this option offers some 
further flexibility. 
   
Warning: In the first option collisions cannot happen 
if the impact parameter is larger than twice the proton/hadron radius. 
The MPI machinery has a separate framework for selecting impact 
parameters, however, by default closer to option 2, and thus able 
to produce larger separations. To this end, the impact parameter 
is limited to be at most 0.95 of the maximal in option 1, 
and a warning is issued for values initially above that. 
   
 
parm   PartonVertex:phiAsym   
 (default = 0.; minimum = -0.9; maximum = 0.9)
The azimuthal asymmetry parameter epsilon defined above for 
PartonVertex:modeVertex = 3 and 4. A positive (negative) value 
favours MPI production in (out of) the collision frame, as could be 
expected for a matter distribution with a flatter-(sharper-)than-Gaussian 
edge. 
   
 
parm   PartonVertex:ProtonRadius   
 (default = 0.85; minimum = 0.; maximum = 10.)
The proton radius and shape depends on the collision energy and on the 
context in which it is used. The default value is based on the static 
charge-radius definition. If the DIPSY model [Fle11] is used, 
then for a description at LHC collision energies, say 14 TeV, the required 
profile corresponds roughly to a Gaussian with a width of around 0.7 fm. 
   
 
parm   PartonVertex:EmissionWidth   
 (default = 0.1; minimum = 0.; maximum = 10.)
Vertices of ISR+FSR partons are smeared relative to their mother by a 
Gaussian distribution with a width of EmissionWidth/pT, 
where pT is the transverse momentum of the produced parton (in GeV). 
This parameter thus determined the overall strength of the transverse space 
smearing. 
   
 
parm   PartonVertex:pTmin   
 (default = 0.2; minimum = 0.05; maximum = 1.)
The parton transverse smearing is assumed proportional to 1 / pT, 
but pT is limited to be above this parameter so as to avoid 
unreasonable values. 
   
 
flag   PartonVertex:randomPlane   
 (default = on)
If off then the impact parameter vector lies in the xz plane, 
which is convenient for theoretical studies of azimuthal distributions. 
If on then the event will be rotated a random angle around the z axis 
so as to be more realistic. The angle can still be reconstructed from 
the vertices of the two incoming hadrons. 
   
 
 
External models
 
 
A derived class for setting parton vertex information can be provided 
to PYTHIA with the 
 
bool Pythia::setPartonVertexPtr( PartonVertex* partonVertexPtrIn) 
 
method. The methods in the derived PartonVertex class 
can then be used to add vertex information to produced particles, 
at creation time, in MPI, FSR and ISR and beam remnants. The assigned 
vertex information will afterwards be accessible as properties of the 
individual particles. Particles produced in other types of processes 
than the ones mentioned above will not have vertex information 
assigned (e.g. hard process), neither will particles produced in the 
weak shower. 
 
 virtual void init()   
can be used to initialize various parameters of the model or precalculate 
common numbers. Note that a separate non-virtual method will already 
have provided pointers to the Info, Settings 
and Rndm classes, so that these are available in all derived 
classes. 
   
 
 virtual void vertexMPI( int iBeg, int nAdd, double bNow, Event& event)   
Method to assign a production vertex to a particle produced in the MPI 
framework. Should set the vertices vProd of the particles 
concerned. 
argument iBeg   :  is the index of the first parton of a MPI. 
   
argument nAdd   :  is the number of partons involved in the MPI, 
currently always four: two in and two out. 
   
argument bNow   :  is the impact parameter of the event. It is not 
expressed in physical units (like fm), but rescaled such that the average 
is unity for MPI events. See the section on 
Multiparton Interactions for 
a description of choices for the b dependence. 
   
argument event   :  reference to the whole event, to read information 
from and set the relevant vProd values into. 
   
   
 
 virtual Vec4 vertexFSR( int iNow, Event& event)   
Method to assign production vertex to a particle produced in the FSR 
(TimeShower). Should set the vertex vProd 
of the particle concerned. 
argument iNow   :  is the index of the parton concerned. In a 
branching the daughters automatically inherit the vertex of the mother, 
if it has one, and similarly for the recoiler. This method is called 
specifically for what is considered the emitted parton of the process, 
i.e. the gluon in a q → q g branching, and allows the 
vertex of this parton to be modified. 
   
argument event   :  reference to the whole event, to read information 
from and set the relevant vProd values into. 
   
   
 
 virtual Vec4 vertexISR( int iNow, Event& event)   
Method to assign production vertex to a particle produced in the ISR 
(SpaceShower). Should set the vertices vProd 
of the particle concerned. 
argument iNow   :  is the index of the parton concerned. This method 
is called three times for each ISR branching, for the daughter, the 
new recoiler and the sister. 
   
argument event   :  reference to the whole event, to read information 
from and set the relevant vProd values into. 
   
   
 
 virtual void vertexBeam( int iBeam, vector<int>& iRemn, vector<int>& iInit, Event& event)   
Method to assign production vertices for the beam itself and the beam 
remnants. 
argument iBeam   :  is 0 and 1, respectively, for the two beams. 
The two beam particles are then located in event record positions 1 
and 2, and normally you would set them to be displaced +-bNow 
along the x axis. 
   
argument vector<int>& iRemn   :  are the indices of the beam 
remnants that could be displaced by you. 
   
argument vector<int>& iInit   :  are the indices of the initiator 
partons for all the MPIs of the event. They already had their vertices 
assigned and should not be changed. But that information could be used 
e.g. to ensure that the energy-weighted average of all initiators and all 
remnants together give the proper beam impact parameter. 
   
argument event   :  reference to the whole event, to read information 
from and set the relevant vProd values into. 
   
   
 
 virtual void vertexHadrons( int nBefFrag, Event& event)   
Method to shift hadron production vertices by an amount related to 
that of the partons they come from. This may be the most complicated 
step of them all, since there is not a unique one-to-one association 
between a hadron and a parton. 
argument nBefFrag   :  is the size of the event record before the 
latest fragmentation step, and event.size() the one 
after. All the hadrons in that range come from the fragmentation of 
the partons given by their common mother indices, and are open to 
receive modified production vertices. 
   
argument event   :  reference to the whole event, to read information 
from and set the relevant vProd values into.