Mandatory keys

Init_Multiplicities — map<int,int>, required

Initial multiplicities per particle species. The value of this key shall be a map of PDG number and amount corresponding to it. Use this key to specify how many particles of each species will be initialized. This key cannot be used if Use_Thermal_Multiplicities is true.

Radius — double, required

Radius of the sphere in fm.

Start_Time — double, required

Starting time of sphere calculation in fm.

Temperature — double, required

Temperature in GeV to sample momenta in the sphere.

Optional keys

Account_Resonance_Widths — bool, optional, default = true

This key is considered only in case of thermal initialization and the following two behaviors can be chosen:

true → Account for resonance spectral functions, while computing multiplicities and sampling masses.
false → Simply use pole masses.

Add_Radial_Velocity — double, optional, default = -1.0

This can be used in order to give each particle in the sphere an additional velocity in radial direction of the size \(u_r = u_0 \, \left(\frac{r}{R}\right)^n\) with \(u_0\) being the parameter of this feature, \(r\) the radial coordinate of the particle and \(R\) the total radius of the sphere. \(u_0\) can only take values in \([0, 1]\) and a negative value is equivalent to omitting this key (i.e. not attributing any additional radial velocity). The exponent \(n\) is set by Add_Radial_Velocity_Exponent.

Add_Radial_Velocity_Exponent — double, optional, default = 1.0

Exponent in the initial radial flow profile (see Add_Radial_Velocity). It cannot be negative.

Baryon_Chemical_Potential — double, optional, default = 0.0

Baryon chemical potential \(\mu_B\) in GeV. This key is used to compute thermal densities \(n_i\) only if Use_Thermal_Multiplicities is true.

Charge_Chemical_Potential — double, optional, default = 0.0

Charge chemical potential \(\mu_Q\) in GeV. This key is used to compute thermal densities \(n_i\) only if Use_Thermal_Multiplicities is true.

Initial_Condition — string, optional, default = "thermal momenta"

Initial distribution to use for momenta of particles. Mainly used in the expanding universe scenario, options are:

"thermal momenta" → equilibrium Boltzmann distribution
"thermal momenta quantum" → equilibrium Fermi-Dirac or Bose-Einstein distribution
"IC_ES" → off-equilibrium distribution
"IC_1M" → off-equilibrium distribution
"IC_2M" → off-equilibrium distribution
"IC_Massive" → off-equilibrium distribution

See Bazow:2016oky [8] and Tindall:2016try [63] for further explanations about the different distribution functions.

Strange_Chemical_Potential — double, optional, default = 0.0

Strangeness chemical potential \(\mu_S\) in GeV. This key is used to compute thermal densities \(n_i\) only if Use_Thermal_Multiplicities is true.

Heavy_Flavor_Multiplier — double, optional, default = 0.0

Multiply the thermal multiplicity of heavy flavor particles. This is a way to perturbatively obtain more statistics on heavy hadron observables with fewer events, under the assumption that these hadrons are sufficiently rare to not interact with each other. It is the user's responsibility to ensure that such assumption holds and that particle yields are properly normalized in the analysis.

By default, it is set to 0 so that no heavy flavor is initialized. For any positive value, a partial density is computed as described in Use_Thermal_Multiplicities and multiplied by it. Naturally, with a value of 1, each hadron corresponds to a real thermalized hadron.

Use_Thermal_Multiplicities — bool, optional, default = false

The system is initialized with all particle species of the particle table that belong to the hadron gas equation of state, see HadronGasEos::is_eos_particle(). The multiplicities are sampled from Poisson distributions \(\mathrm{Poi}(n_i V)\), where \(n_i\) are the grand-canonical thermal densities of the corresponding species and \(V\) is the system volume. This option simulates the grand-canonical ensemble, where the number of particles is not fixed from event to event.

If this option is set to true, Init_Multiplicities cannot be used.

Specifying jets

The Jet section within the Sphere one is used to put a single high energy particle (a "jet") in the center of the system, on an outbound trajectory along the x-axis. If no PDG code is specified, but the section is given, an error about the missing key is raised.

Jet_PDG — int, required

The type of particle to be used as a jet, as given by its PDG code.

Jet_Momentum — double, optional, default = 20.0

The initial momentum in GeV to give to the jet particle.

Jet_Position — list of 3 doubles, optional, default = [0.0, 0.0, 0.0]

Coordinates (x,y,z) in fm where the jet particle is initially positioned.

Back_To_Back — bool, optional, default = false

Whether to create a jet with the corresponding antiparticle in the opposite direction with the same momentum. If the particle is a singlet, such as the neutral pion, it is considered its own antiparticle.

Back_To_Back_Separation — double, optional, default = 0.01

Separation in fm between the back to back jets. Each jet particle is translated by half of this value in the direction of motion. Can only be used if Back_To_Back is true. A small value is used by default to prevent interactions between the jets.

Configuring a sphere simulation

The following example configures an expanding sphere with a radius of 5 fm at a temperature of 200 MeV. The particles are initialized with thermal momenta at a start time of 0 fm. The particle numbers at initialization are 100 \( \pi^+ \), 100 \( \pi^0 \), 100 \( \pi^- \), 50 protons and 50 neutrons.

 Modi:
     Sphere:
         Radius: 5.0
         Temperature: 0.2
         Initial_Condition: "thermal momenta"
         Start_Time: 0.0
         Init_Multiplicities:
             211: 100
             111: 100
             -211: 100
             2212: 50
             2112: 50

It is also possible to initialize a sphere based on thermal multiplicities. This is done via

 Modi:
     Sphere:
         Radius: 10.0
         Temperature: 0.2
         Use_Thermal_Multiplicities: True

If one wants to simulate a jet in the hadronic medium, this can be done by using the following configuration setup:

 Modi:
     Sphere:
         Radius: 10.0
         Temperature: 0.2
         Use_Thermal_Multiplicities: True
         Jet:
             Jet_PDG: 211
             Jet_Momentum: 100.0

Note

SMASH is shipped with an example configuration file to set up an expanding sphere simulation initialized with predefined initial particle multiplicities. This file is located in the input/sphere folder at the top-level of SMASH codebase. To run SMASH with the provided example configuration for the sphere system, execute

    ./smash -i INPUT_DIR/sphere/config.yaml

where INPUT_DIR needs to be replaced by the path to the input directory at the top-level of SMASH codebase.