tParton - Transversity PDF Evolution

🎯 Overview

tParton is a Python package for evolving transversity parton distribution functions (PDFs) using the DGLAP equations. It provides two complementary methods implemented in modern Python, making transversity evolution accessible and efficient.

Transversity PDFs encode information about the transverse spin structure of hadrons and are essential for understanding QCD and analyzing high-energy physics experiments.

✨ Key Features

🔄 Two Methods

Direct integration (Hirai) and Mellin moment (Vogelsang) methods for different use cases

🚀 Modern Python

Built on NumPy & SciPy, easy to install via pip and integrate into workflows

✅ Validated

Extensively validated against APFEL++ and Mathematica implementations

📊 Examples Included

Comprehensive Jupyter notebooks with validation and parameter studies

🎓 LO & NLO

Supports both leading order and next-to-leading order evolution

⚡ Dual Interface

Command-line tools and Python API for flexibility

📥 Installation

Install from PyPI using pip:

pip install tparton

Or install from source:

git clone https://github.com/mikesha2/tParton.git
cd tParton
pip install -e .

🚀 Quick Start

Command-Line Usage

# Using Mellin moment method (faster)
python -m tparton m input.dat 3.1 10.6 --morp plus -o output.dat

# Using direct integration method (more control)
python -m tparton t input.dat 3.1 10.6 --morp plus -o output.dat

# Get help
python -m tparton m -h

Python API

from tparton.m_evolution import evolve as m_evolve
from tparton.t_evolution import evolve as t_evolve

# Evolve using Mellin method
result = m_evolve(
    input_pdf, 
    Q0_squared=3.1,  # Initial scale (GeV²)
    Q_squared=10.6,   # Final scale (GeV²)
    morp='plus',      # Distribution type: 'plus' or 'minus'
    order='NLO'       # 'LO' or 'NLO'
)

# Evolve using direct integration
result = t_evolve(
    input_pdf,
    Q0_squared=3.1,
    Q_squared=10.6,
    morp='plus',
    order='NLO'
)

🔬 Methods

Method 1: Direct Integration (Hirai Method)

Discretizes both momentum fraction x and energy scale Q² into grids and solves the integro-differential equation using:

Euler method for Q² evolution
Simpson's rule for x integration

Best for: When precise control over discretization is needed

Method 2: Mellin Moment Method (Vogelsang Method)

Exploits the convolution theorem for Mellin transforms. The solution is expressed as:

M[Δ_Tq^±](Q²;s) = K(s,Q²,Q₀²) M[Δ_Tq^±](Q₀²;s)

The evolved PDF is reconstructed via inverse Mellin transform using Talbot contour integration.

Best for: Faster computation with smooth PDFs, less sensitive to discretization

📖 Documentation

Complete API documentation is available:

→ Browse API Documentation

Key Modules

tparton.m_evolution - Mellin moment method implementation
tparton.t_evolution - Direct integration method implementation
tparton.constants - Physical constants and parameters

📚 Examples

The repository includes extensive examples in the examples/ directory:

Jupyter notebooks comparing both methods
Validation against APFEL++
Parameter sensitivity studies
Figure reproduction from the paper
Mathematica validation notebooks

View Complete Examples and Tutorials →

📄 Citation

If you use tParton in your research, please cite:

@article{sha2025tparton,
    author = {Sha, Congzhou M and Ma, Bailing},
    title = {tParton: Implementation of next-to-leading order evolution 
                     of transversity parton distribution functions},
    year = {2025},
    eprint = {2409.00221},
    archivePrefix = {arXiv},
    primaryClass = {hep-ph}
}

👥 Authors

Congzhou M Sha - Penn State College of Medicine
Bailing Ma - Wake Forest University School of Medicine

📜 License

MIT License - see the LICENSE file for details.