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), double parton distributions (DPDs), 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: <tt>PDFSet</tt>

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}")

Double Parton Distributions (DPDs)

DPDs are available when the package is built with DPD support. The same Python API handles dense PDFxTMD-DPDB1 and hybrid PDFxTMD-DPDH1 sets.

import numpy as np
import pdfxtmd
 
print("DPD support:", pdfxtmd.__has_dpd__)
 
dpd = pdfxtmd.GenericCDPDFactory().mkCDPD(
    "MSTW2008lo68cl_GSDPDF_PDFxTMD", 0
)
 
value = dpd.dpd(
    pdfxtmd.PartonFlavor.g,
    pdfxtmd.PartonFlavor.g,
    1e-2, 100.0,
    2e-2, 400.0,
)
print("g-g DPD:", value)
 
x1 = np.array([1e-3, 1e-2, 5e-2])
x2 = np.array([2e-3, 2e-2, 1e-1])
mu1_2 = np.full_like(x1, 100.0)
mu2_2 = np.full_like(x2, 400.0)
 
values = dpd.dpd_batch(
    pdfxtmd.PartonFlavor.g,
    pdfxtmd.PartonFlavor.g,
    x1, mu1_2, x2, mu2_2,
)
print(values)

The NumPy batch overload accepts arrays with matching shapes and releases the Python GIL during native evaluation.

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:

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 raminkord92@gmail.com.