pdfxtmd 1.0.0

PDFxTMD is a library for parton distribution functions (PDFs) that integrates both collinear PDFs (cPDFs) and transverse momentum-dependent PDFs (TMDs).

PDFxTMDLib Python API

PDFxTMDLib provides a powerful and easy-to-use Python interface for high-performance Parton Distribution Function (PDF) calculations. It offers unified access to collinear PDFs (cPDFs), Transverse Momentum-Dependent PDFs (TMDs), uncertainty analysis, and QCD coupling calculations.

This guide covers the installation and usage of the Python bindings.

---

Installation

You can install the package directly from PyPI:

pip install pdfxtmd

---

High-Level API: PDFSet

The PDFSet interface is the recommended way to work with PDF sets. It handles the entire collection of PDF members (central value and error sets) and provides a simple API for calculating uncertainties and correlations.

1. Collinear PDF (cPDF) Uncertainty

import pdfxtmd

# 1. Initialize a CPDFSet for a given PDF set name
cpdf_set = pdfxtmd.CPDFSet("CT18NLO")
print(f"Loaded CPDF Set: CT18NLO with {len(cpdf_set)} members.")

# 2. Define kinematics
x = 0.01
mu2 = 100

# 3. Get the central value PDF from member 0
central_cpdf = cpdf_set[0]
up_pdf_central = central_cpdf.pdf(pdfxtmd.PartonFlavor.u, x, mu2)
print(f"Central Up Quark PDF: {up_pdf_central:.6f}")

# 4. Calculate the PDF uncertainty (the result is a PDFUncertainty object)
uncertainty = cpdf_set.Uncertainty(pdfxtmd.PartonFlavor.u, x, mu2)
print(f"Uncertainty: central={uncertainty.central:.6f}, +{uncertainty.errplus:.6f}, -{uncertainty.errminus:.6f}")

# 5. Calculate the correlation between two different partons
correlation = cpdf_set.Correlation(
    pdfxtmd.PartonFlavor.u, x, mu2,  # PDF A
    pdfxtmd.PartonFlavor.d, x, mu2   # PDF B
)
print(f"Correlation between u and d quarks: {correlation:.4f}")

2. TMD Uncertainty

The interface for TMDs is analogous. Just use TMDSet and include the transverse momentum kt2.

import pdfxtmd

# 1. Initialize a TMDSet
tmd_set = pdfxtmd.TMDSet("PB-NLO-HERAI+II-2018-set2")
print(f"\nLoaded TMD Set: {tmd_set.info().get_string('SetDesc')} with {len(tmd_set)} members.")

# 2. Define kinematics
x = 0.01
mu2 = 100
kt2 = 10

# 3. Calculate the TMD uncertainty
uncertainty_tmd = tmd_set.Uncertainty(pdfxtmd.PartonFlavor.g, x, kt2, mu2)
print(f"Gluon TMD Uncertainty: central={uncertainty_tmd.central:.6f}, +{uncertainty_tmd.errplus:.6f}, -{uncertainty_tmd.errminus:.6f}")

---

Low-Level API: Factories

For applications where you only need to evaluate a single PDF member and do not require uncertainty analysis, the factory interface offers a more direct approach.

import pdfxtmd

x = 0.01
mu2 = 100
kt2 = 10

# --- Collinear PDFs (cPDF) using Factory ---
cpdf_factory = pdfxtmd.GenericCPDFFactory()
cpdf = cpdf_factory.mkCPDF("CT18NLO", 0) # Get member 0

# Evaluate a single flavor
up_pdf = cpdf.pdf(pdfxtmd.PartonFlavor.u, x, mu2)
print(f"CPDF (Up Quark) from Factory: {up_pdf:.6f}")

# Evaluate all flavors at once (returns a numpy array)
all_flavors_cpdf = cpdf.pdf(x, mu2)
print(f"All CPDF Flavors from Factory: {all_flavors_cpdf}")


# --- TMDs using Factory ---
tmd_factory = pdfxtmd.GenericTMDFactory()
tmd = tmd_factory.mkTMD("PB-NLO-HERAI+II-2018-set2", 0) # Get member 0

# Evaluate a single flavor
gluon_tmd = tmd.tmd(pdfxtmd.PartonFlavor.g, x, kt2, mu2)
print(f"\nTMD (Gluon) from Factory: {gluon_tmd:.6f}")

# Evaluate all TMD flavors at once (returns a numpy array)
all_flavors_tmd = tmd.tmd(x, kt2, mu2)
print(f"All TMD Flavors from Factory: {all_flavors_tmd}")

---

QCD Coupling ($\alpha_s$) Calculations

You can calculate the strong coupling constant $\alpha_s$ in two ways.

import pdfxtmd

cpdf_set = pdfxtmd.CPDFSet("CT18NLO")

# Method A: Directly from the PDFSet object (Recommended)
print("--- Method A: From PDFSet ---")
alpha_s_from_set = cpdf_set.alphasQ2(10000)
print(f"Alpha_s at mu2=10000: {alpha_s_from_set:.5f}")


# Method B: Using the low-level CouplingFactory
print("\n--- Method B: From CouplingFactory ---")
coupling_factory = pdfxtmd.CouplingFactory()
coupling = coupling_factory.mkCoupling("CT18NLO")
alpha_s_from_factory = coupling.AlphaQCDMu2(10000)
print(f"Alpha_s at mu2=10000: {alpha_s_from_factory:.5f}")

---

Complete Example: Plotting PDFs with Uncertainties

This example demonstrates a complete workflow: loading PDF/TMD sets, calculating values and uncertainties over a range of x, and plotting the results using matplotlib.

import pdfxtmd
import numpy as np
import matplotlib.pyplot as plt

# --- Part 1: Collinear PDF (cPDF) ---
cpdf_set = pdfxtmd.CPDFSet("CT18NLO")
print(f"Loaded cPDF set: {cpdf_set.info().get_string('SetDesc')}")

x_values = np.logspace(-4, -1, 100)
mu2 = 1000

# Calculate central values and uncertainties
uncertainties = [cpdf_set.Uncertainty(pdfxtmd.PartonFlavor.g, x, mu2) for x in x_values]
central_pdfs = [u.central for u in uncertainties]
upper_band = [u.central + u.errplus for u in uncertainties]
lower_band = [u.central - u.errminus for u in uncertainties]

# Plot the cPDF
plt.figure(figsize=(10, 6))
plt.plot(x_values, central_pdfs, label='Gluon PDF (CT18NLO)', color='blue')
plt.fill_between(x_values, lower_band, upper_band, color='blue', alpha=0.2, label='68% CL Uncertainty')
plt.xscale('log')
plt.xlabel('$x$')
plt.ylabel('$xg(x, \mu^2)$')
plt.title(f'Gluon PDF with Uncertainty at $\mu^2 = {mu2} \ GeV^2$')
plt.legend()
plt.grid(True, which="both", ls="--")
plt.savefig('gluon_pdf_plot.png')
print("Saved plot to gluon_pdf_plot.png")
plt.close()


# --- Part 2: Transverse Momentum-Dependent PDF (TMD) ---
tmd_set = pdfxtmd.TMDSet("PB-LO-HERAI+II-2020-set2")
print(f"Loaded TMD set: {tmd_set.info().get_string('SetDesc')}")

kt2 = 1

# Calculate central values and uncertainties
tmd_uncertainties = [tmd_set.Uncertainty(pdfxtmd.PartonFlavor.g, x, kt2, mu2) for x in x_values]
central_tmds = [u.central for u in tmd_uncertainties]
tmd_upper_band = [u.central + u.errplus for u in tmd_uncertainties]
tmd_lower_band = [u.central - u.errminus for u in tmd_uncertainties]

# Plot the TMD
plt.figure(figsize=(10, 6))
plt.plot(x_values, central_tmds, label='Gluon TMD (PB-LO-2020)', color='green')
plt.fill_between(x_values, tmd_lower_band, tmd_upper_band, color='green', alpha=0.2, label='68% CL Uncertainty')
plt.xscale('log')
plt.xlabel('$x$')
plt.ylabel('$xg(x, k_t^2, \mu^2)$')
plt.title(f'Gluon TMD with Uncertainty at $k_t^2 = {kt2} \ GeV^2, \mu^2 = {mu2} \ GeV^2$')
plt.legend()
plt.grid(True, which="both", ls="--")
plt.savefig('gluon_tmd_plot.png')
print("Saved plot to gluon_tmd_plot.png")
plt.close()

---

Additional Information

Error Handling

The API raises a RuntimeError for invalid kinematic inputs.

try:
    cpdf.pdf(pdfxtmd.PartonFlavor.u, -0.1, mu2)  # Invalid x
except RuntimeError as e:
    print(f"Caught expected error for invalid x: {e}")

Enumerating Parton Flavors

You can inspect all available parton flavors and their integer codes.

print("\n--- All PartonFlavor enum values ---")
for name, flavor in pdfxtmd.PartonFlavor.__members__.items():
    print(f"  {name}: {flavor.value}")

Full Code Examples

For more detailed examples, see the full tutorials in the project repository:

• python_tutorial.py
• Jupyter Notebook Tutorial (run online)

---

License

This project is licensed under the GNU General Public License v3.0. See the LICENSE file for details.

Contact

For questions or contributions, please contact [e-mail].