Heavy Ion Collisions

To allow for the generation of collisions with heavy ions, PYTHIA includes a handful of nuclei with PDG numbers on the form 100ZZZAAAI: ⁴He (1000020040), ⁶Li (1000030060), ¹²C (1000060120), ¹⁶O (1000080160), ⁶³Cu (1000290630), ¹²⁹Xe (1000541290), ¹⁹⁷Au (1000791970), and ²⁰⁸Pb (1000822080), but more can be added using the function ParticleData::addParticle.

mode  HeavyIon:mode   (default = 1; minimum = 1; maximum = 2)
This is the master switch for heavy ions, and determines the mode of operation of the HeavyIon model.
option 1 : The heavy ion machinery will be used in case of ion beams.
option 2 : Even collisions without ions are treated using the heavy ion machinery. (Typically only used for debugging purposes.)

If HeavyIon:mode is on, the normal initialization in Pythia::init() is early on diverted to an object with the base class HeavyIons which may instantiate secondary Pythia objects needed to generate different types of nucleon-nucleon collisions that can be merged together into a full heavy ion event. This is all done in the virtual HeavyIons::init() function. Subsequent calls to Pythia::next() will then also be diverted to the virtual function HeavyIons::next() which will be responsible for building up the heavy ion collision. The final event will be available in the primary Pythia object.

flag  HeavyIon:showInit   (default = on)
Output detailed initialization information from the heavy ion model. Typically there will be several Pythia object initialised in a heavy ion run, this flag can be used to reduce the amount of output. If off, only the output from initialisation of the primary Pythia object will be shown

The HeavyIon class is very simple and flexible and basically only specifies that the HeavyIons::init() and HeavyIons::next() functions are overridden in a subclass. But there are a few additional helper classes that should be generic enough to be used by any model implemented.

• The Nucleon class represents a single nucleon in a nuclei. It can be a proton or a neutron (id()), it has a position in impact parameter space (Vec2), both absolute (bPos()) and relative to the nuclei (nPos()), and optionally it can be in a particular state represented by a vector of real numbers which are completely model dependent.
• The SubCollision class represents a potential nucleon-nucleon collision between a projectile and a target Nucleon.
• The NucleusModel class is a base class for implementing a model for the distribution in impact parameter space of nucleons in a nucleus. There are two ready-made subclasses called WoodsSaxonModel, implementing a standard Woods-Saxon distribution, and GLISSANDOModel, implementing the more advanced model in [Bro09,Ryb14].

  flag  HeavyIon:WSHardCore   (default = on)
  In the default Woods-Saxon model for nucleon distributions, assume that there is a minimum distance between nucleons defined by a hard core radius in HeavyIon:WSRh.

  parm  HeavyIon:WSRh   (default = 0.9; minimum = 0.0)
  The hard core radius in units of fermi, defining the minimum distance between nucleons in a nucleus in the default Woods-Saxon model for nucleon distributions.

  flag  HeavyIon:gaussHardCore   (default = off)
  Option to use a Gaussian profile of the hard core instead of a sharp cut-off, inspired by [Bay95].

  parm  HeavyIon:WSR   (default = 0.0; minimum = 0.0)
  The radius of a nucleon in units of fermi in the default Woods-Saxon model for nucleon distributions. If zero, the size is given by the formulae [Ryb14], based on the number of nucleons in the nuclei and whether a hard core is used or not.

  parm  HeavyIon:WSa   (default = 0.0; minimum = 0.0)
  The skin width of a nucleus in units of fermi in the default Woods-Saxon model for nucleon distributions. If zero, the size is given by the numbers in [Ryb14], based on the number of nucleons in the nuclus and whether a hard core is used or not.

• The ImpactParameterGenerator is used to sample the impact parameter space for the colliding nuclei. The base class implements a Gaussian sampling, which means that the events produced will always be weighted. Other distributions can be implemented in subclasses.

  parm  HeavyIon:bWidth   (default = 0.0; minimum = 0.0)
  The width in fermi of the distribution by which the impact parameter is sampled. If zero, a suitable width must be guessed by the ImpactParamerGenerator itself.

• The SubCollisionModel is used to generate individual, potential nucleon-nucleon SubCollisions. Two subclasses are available, one called NaiveSubCollisionModel which treats nucleons as simple black disks, and one implementing a more advanced model called DoubleStrikman described below.
• The HIInfo class contains information related to the generated heavy ion events.
• The HIUserHooks class is provided to simplify the customization of a model implemented as a HeavyIons subclass. It can be used to eg. change the ImpactParamerGenerator used, in a way similar to how the UserHooks and MergingHooks classes are used.

Angantyr - the default heavy ion model

To determine which projectile nucleon interacts with which target nucleon, special care is taken to determine in which way the nucleons interact. In a standard Glauber calculations one typicaly only cares about if a sub-collision is inelastic or not, but in Angantyr this is divided up, so that each inelastic sub-collision can either be single-diffractive, double-diffractive or absorptive (ie. non-diffractive). To achieve this, Angantyr uses a model with fluctuating radii of the nucleons resulting in a fluctuating nucleon-nucleon cross section inspired by the model by Strikman et al. [Alv13]. The model for this includes a number of parameters which should be fitted to reproduce inclusive nucleon-nucleon cross sections. To be consistent, the values used comes from PYTHIA's internal model of total cross sections.

The default model for nucleon fluctuations has three parameters, the general fitting machinery in SubCollisionModel allows for up to eight parameters.

pvec  HeavyIon:SigFitDefPar   (default = {17.24,2.15,0.33,0.0,0.0,0.0,0.0,0.0})
These are the default values of the parameters of the SubCollisionModel in Angantyr. They will be used as starting point when fitting to the inclusive nucleon cross sections.

The fitting procedure in SubCollisionModel is a kind of genetic algorith where a population of parameter values are allowed to evolve for a number of generations. In the end the the parameter set in the final population which gives the best inclusive cross sections is picked. Eight different cross sections may be fitted to but it is possible to select only some of them:

pvec  HeavyIon:SigFitErr   (default = {0.02,0.02,0.1,0.05,0.05,0.0,0.1,0.0}; minimum = 0.0; maximum = 1.0)
The relative error assumed in the calculation of goodness of fit corresponding to the different cross sections fitted to. The cross sections are obtained from the SigmaTotal and are given as (in order) total, non-diffractive, double diffractive, wounded target, wounded projectile, central diffractive, and elastic cross sections, and in addition the elastic slope parameter. A relative error of zero for one of these cross sections means the corresponding cross section not be used in the fit.

mode  HeavyIon:SigFitNInt   (default = 100000; minimum = 0)
The number of integration points used for each parameter setting to calculate the cross sections.

mode  HeavyIon:SigFitNPop   (default = 20; minimum = 1)
The number individuals (parameter settings) in a population in each generation.

mode  HeavyIon:SigFitNGen   (default = 20; minimum = 0)
The number of generation used in the genetic algorithm. If set to zero, no fitting will be performed and the values in HeavyIon:SigFitDefPar will be used.

parm  HeavyIon:SigFitFuzz   (default = 0.2; minimum = 0.0; maximum = 0.5)
A parameter determining the probability that an individual parameter setting will evolves further away from the best parameter set in each generation.

flag  HeavyIon:SigFitPrint   (default = on)
fitting procedure. If on, extensive information about the fitting will be printed.

mode  Angantyr:CollisionModel   (default = 1; minimum = 0; maximum = 3)
The Angantyr model has a couple of option for the SubCollisionModel
option 0 : A simplified model with fixed nucleon radii.
option 1 : The default model with fluctuating radii and cross sections.
option 2 : Fluctuating radii and cross sections but different treatment of opacity.
option 3 : Black disks with no fluctuations, ie. no diffraction.

flag  Angantyr:GlauberOnly   (default = off)
event generation will stop after SubCollisions has been determined, allowing the user to read out the nucleon configuration only.

After all possible nucleon-nucleon sub-collisions has been determined, they are ordered in increasing nucleon-nucleon impact parameter. This list is then gone through in order several time. First all absorptive sub-collisions are treated. One full nucleon-nucleon non-diffractive minimum bias event is generated for each possible absorptive sub-colision. These are also ordered in impact parameter. Note that one target nucleon can interact absorptively with several target nucleons, in a first round only those absorptive sub-collisions involving nucleons that have not already interacted absorptively are are assigned a non-diffractive event.

If PYTHIA is not set up to generate minimum bias events, one or more of the generated non-diffractive events will be replaced by events generated with the selected signal process, and the cross section reported will be modified accordingly.

In a second round only those potential absorptive sub-collisions are considered where one nucleon has already been assinged a full non-diffractive event. In the Angantyr model it is then assumed that the other nuclean will contribute to the final state as if it had just been diffractively excited. Therefore a corresponding single-diffractive event is generated, the elastically scattered beam particle is discarded and the rest is added to the previous non-diffractive event, shuffling a bit with the kinematics so that the total emergy and momentum is conserved.

To generate these single-diffraction events to emulate multiple absorptive sub-collisions a special Pythia object is used. To allow flexibility this object need not have exactly the same settings as the the one generating events for normal single-diffraction sub-collisions. To manipulate this Pythia object a special form of settings can be used. All settings available for Diffraction, MultipartonInteractions, PDF, SigmaDiffractive and PDF can be set separately for this Pythia object by prefixing their names with HI. As an example, setting HISigmaDiffractive:PomFlux and HIPDF:PomSet will set the SigmaDiffractive:PomFlux and PDF:PomSet options for this Pythia object.

mode  Angantyr:SASDmode   (default = 4; minimum = 0; maximum = 4)
Determines how to generate single-diffraction events as secondary absorptive (SASD) sub-collisions.
option 0 : Standard singel-diffraction events as speicfied by HIDiffraction settings above.
option 1 : Always use HIPDF:PomSet = 11 and use the same initial HIMultipartonInteractions:pT0Ref as for non-diffractive events for the total nucleon-nucleon collision energy, independent of the mass of the diffractive system.
option 2 : (Experimental) As for option 1 but also rescale the pomeron proton non-diffractive cross section to match the pp non-diffractive one.
option 3 : (Experimental) As for option 1 but use the full nucleon-nucleon cross section for the non-diffractive nucleon-Pomeron in the multiple interaction machinery. Also rescale the Pomeron PDF with the log of the ratio of maximum and minimum Pomeron-nucleon collision energy.
option 4 : As for option 3 but no rescaling of the Pomeron PDF.

mode  Angantyr:impactMode   (default = 2; minimum = 0; maximum = 2)
Determines how to bias non-diffractive minimum-bias sub-collisions in PYTHIA to be appropriately central.
option 0 : If we have N pirmary sub-collisions and Na secondary sub-collisions, generate N+Na non-diffractive events and pick the N most central.
option 1 : Use UserHooks to force Pythia to produce events with a particular impact parameter for the N primary sub collisions according to the generated impact parameter in the SubCollisionModel.
option 2 : As for option 1 but also the secondary absorptive sub-collisions have their impact parameter set.

parm  Angantyr:impactFudge   (default = 0.85; minimum = 0.0; maximum = 4.0)
Multiplicative factor used to compensate for the fact that the SubColllisionModel in Angantyr may have a different impact parameter profile than what is assumed in the MPI overlap calculation in Pythia.

mode  Angantyr:SDTries   (default = 1; minimum = 1)
When adding single diffractive sub-collisions to other sub-collisions, there might not be enough energy for the diffractive mass. One option here is to say that the diffractive sub-event simply fails, but setting this larger than unity allows for regenerating the single diffractive sub-event a number of times to see if a small enough diffractive system is produced.

mode  Angantyr:SDRecoil   (default = 1; minimum = 1; maximum = 2)
Determines which particles in a primary sub-collision will take the recoil when adding single diffractive sub-collisions to other sub-collisions. The choice may be overridded by a user-defined HIUserHooks::findRecoilers function.
option 1 : Only elastically scattered nucleons and nucleon remnants will take recoil.
option 2 : All particles outside the added diffractive system's rapidity range are considered.

flag  Angantyr:SDTest   (default = off)
Used in conjunction with HeavyIon:mode = 2 and proton beams to generate single diffractive events that would be used as secondary non-diffractive scatterings in the Angantyr heavy ion model for the given nucleon energies. Used for tuning special HI-prefixed parameters of the secondary absorptive sub-collisions.

parm  Angantyr:SDTestB   (default = -1.0)
In conjunction with Angantyr:SDTest = on and Angantyr:impactMode = 2 only pick diffractive events with a particular impact parameter (as defined by the scaled value given in Info::bMPI()). If negative, the standard impact parameter distribution is used.

After all absorptive sub-collisions have been dealt with, the diffractive and elastic sub-collisions are dealt with in a similar way. In the end there will be a number of parton level events which are finally stacked together, and then hadronised. Finally nucleus remnants constructed from the non-interacting nucleans, are added to complete the full nucleaus-nucleus collision.