The subsection Hard_String_Transition of the Collision_Term section controls how the non-diffractive string excitation is split into soft and hard components.

The transition mode is selected via the Mode key:

Exponential: use the exponential splitting of the non-diffractive cross section. The probability for a purely soft non-diffractive interaction is given by
\[ P_{\mathrm{soft}} = \exp\!\left(-\frac{\sigma_{\mathrm{hard}}} {\sigma_{\mathrm{ND}}}\right), \]
where \(\sigma_{\mathrm{hard}}\) is the hard string cross section and \(\sigma_{\mathrm{ND}}\) the total non-diffractive cross section. The hard non-diffractive contribution follows from \(\sigma_{\mathrm{ND,hard}} = \sigma_{\mathrm{ND}} - \sigma_{\mathrm{ND,soft}}\).
Custom_Range: use a smooth, user-defined transition from soft to hard string excitation as a function of the collision energy.

For Custom_Range, the transition is controlled by Energy_Range (in \(\sqrt{s}\) measured in GeV). The first value specifies the lower bound and the second value the upper bound of the transition region. Below this range only soft string excitation is used, above it only hard string excitation is used, and inside the range the probability for hard string excitation increases smoothly with energy.

For example:

 Collision_Term:
     Hard_String_Transition:
         Mode: Custom_Range
         Energy_Range: [10.0, 20.0]

Enabling hard string interactions at lower collision energies changes baryon stopping. Therefore, some string-fragmentation and MPI parameters may need to be adjusted. The following setup can be used as a starting point for studies with an early hard-string transition:

Collision_Term:
  Hard_String_Transition:
    Mode: Custom_Range
    Energy_Range: [10.0, 11.0]
  String_Parameters:
    StringZ_A_Leading: 0.2
    StringZ_B_Leading: 5.0
    Damp_Popcorn: 0.0
    String_Sigma_T: 0.3
    Pythia_Settings:
      - "MultipartonInteractions:ecmPow = 0.152"

These parameters are intended as a phenomenological starting point for dedicated studies. They should not be interpreted as a tuned parameter set, and further tuning may be required for quantitative applications.

Mode — string, optional, default = Exponential — Conditions on key value: Only valid strings

Select the mode used for the transition from soft to hard string excitation.

Exponential: use exponential suppression based on the hard string cross section in the Pythia multiparton interaction (MPI) framework.
Custom_Range: use a smooth transition from soft to hard string excitation within a user-defined invariant energy range.

In this mode, the transition follows a sinusoidal function within the interval defined by Energy_Range, ensuring a smooth and continuous interpolation between the soft and hard regimes.

For Custom_Range, the transition is controlled by Energy_Range.

Energy_Range — list of two doubles, optional, default = [10.0,200.0] — Conditions on key value: \(E_1 \ge 10\) and \(E_1 < E_2\)

Invariant energy range ( \(\sqrt{s}\)) GeV used for the custom transition from soft to hard string excitation.

This key is only used when Mode is set to Custom_Range. For \(\sqrt{s}\) below the lower bound, only soft string excitation is used. For \(\sqrt{s}\) above the upper bound, only hard string excitation is used.

Within the specified range, the transition probability is interpolated smoothly from the soft to the hard regime.

The lower bound must be greater than or equal to 10 GeV and strictly smaller than the upper bound.