T_RENTo 3D 1.0

Three-dimensional Extended Reduced Thickness Event-by-event Nuclear Topology

This is the first attempt at an extension of T_RENTo to three dimensions. This repo is listed for historical purposes and this version of T_RENTo 3D was used for the below publications. For the current 3D extension of T_RENTo please use the T_RENTo 3D 2.0 repo.

A three-dimensional initial condition model for high-energy nuclear collisions. For a documentation of the original boost-invariant T_RENTo model, please read the docs at qcd.phy.duke.edu/trento. For model details please refer to PRC 92 011901, PRC 96 044912.

Figure 1: An event from T_RENTo 3D. Left: the event projected on to x-y plane at midrapidty; right: same event projected on to y-η plane.

Installation

First, install the dependencies: a C++11 compiler, Boost, GSL and HDF5. Then download the source code and compile with CMake:

mkdir build && cd build
cmake ..
make install

Usage:

T_RENTo 3D keeps all the options in the original boost-invariant model with additional options listed in Table 1. Note that to work in three-dimensional mode, --eta-max must be set to a positive value.

Examples:

• Genereate 10 Pb Pb events at s^1/2 = 5020 GeV in boost-invariant mode and output to a .hdf5 file

trento3d Pb Pb 10 -e 5020 -o PbPb.hdf5

• Same as above but generate three-dimensional initial condition with -10<η<10, dη=0.2.

trento3d Pb Pb 10 -e 5020 --eta-max=10.0 --eta-step=0.2 -o PbPb.hdf5

• Use the absolute-skewness parametrization (see Table 2) instead of the relative-skewness parametrization, with skew coefficient γ₀= 1.0.

trento3d Pb Pb 10 -e 5020 -r 2 -t 1.0 --eta-max=10.0 --eta-step=0.2 -o PbPb.hdf5

Table 1: Additional program options

Options	Default	Description
-m, --mean-coeff	1.0 (float>0)	rapidity mean coefficient μ0
-s, --std-coeff	3.0 (float>0)	rapidity std coefficient σ0
-t, --skew-coeff	0.0 (float>0)	rapidity skew coefficient γ0
-r, --skew-type	1 (int)	1 = relative skewness 2 = absolute skewness else = no skewness
-j, --jacobian	0.8 (float>0)	<pt/mt> used in Jacobian dy/dη
-e, --beam-energy	2760 (float>0)	collision beam energy s1/2 [GeV], initializes cross section
--xy-max	10.0 (float)	transverse x [fm] and y [fm] maximum (x,y grid from -max to +max)
--xy-step	0.2 (float)	transverse x [fm] and y [fm] step size
--eta-max	0.0 (float)	space-time rapidity maximum (η grid from -max to +max)
--eta-step	0.5 (float)	space-time rapidity step size

Longitudinal extension:

T_RENTo 3D reproduces T_RENTo at midrapidity (η=0) exactly. At finite space-time rapidity, the entropy production is the product of its midrapidity value and a longitudinal profile function that varies at each transvese location. The profile is characterized by its first η-cumulants: mean, stadard deviationa and skewness. They are parametrized in terms of nuclear thickness function:

Table 2: cumulant parametrization

Cumulants	Parametrization
mean	μ0/2 log [(TA eY+ TB e-Y ) / (TA e-Y+ TB eY)], Y is the beam rapidity
standard deviation	σ0
skewness	Relative skewness, γ0 (TA- TB )/(TA+ TB) Absolute skewness, γ0 (TA- TB )