Code Examples (in progress)

Diffpack

This repository is the basis of many of my projects. It is used to extract functions that describe the internal structure of protons and neutrons. We model this internal structure, calculate its relation to experimental measurements, and perform a $\chi^2$ minimization to match our model to the experimental data.

It consists of the following modules:

• database: Experimental data is stored here
• fitlib: This module contains the central code that performs the $\chi^2$ minimization
• qcdlib: This module is where the functions are modeled
• obslib: This module calculates the complex relations between the functions and the experimental measurements
• tools: This module contains functions used elsewhere, including parallelization and reading Excel files

Analysis

This repository contains the code used to submit the $\chi^2$ minimizations and analyze them afterwards. It contains the following folders:

• inputs: Contains input files that specify the theory, model, experimental, and parameterization inputs for each $\chi^2$ minimization
• results: Where the results are stored after the $\chi^2$ minimization
• analysis: Contains code that allows one to analyze the resulting fit to experimental data as well as the extracted functions
• plots: Contains code used to visualize data and create figures ready for publication

Here are some example plots made in this directory:

Caption: This plot shows the comparison between my theoretical model with fitted parameters and experimental data for the experimental process known as Deep Inelastic Scattering (DIS), where a high energy electron scatters off (in this case) a proton target. The theory result was derived in collaboration with the Jefferson Lab Angular Momentum Collaboration (JAM) and is labeled as JAM. The experimental data come from the Bologna-CERN-Dubna-Munich-Saclay (BCDMS) collaboration [1], Stanford Linear Accelerator Center (SLAC) [2], New Muon Collaboration (NMC) [3], and Hadron-Electron Ring Accelerator [4].

Caption: This plot shows the parameterized functions after they have been fit to the experimental data. The functions shown here are known as unpolarized Parton Distribution Functions (PDFs), which describe the 1-dimensional momentum distribution of partons (quarks and gluons) within an unpolarized proton. The top left plot shows the up $u_v$ and down $d_v$ quarks, the top right plot the gluon $g$, the bottom left plot the anti-up $\bar{u}$ and anti-down $\bar{d}$ quarks, and the bottom right plot the strange $s$ and anti-strange $\bar{s}$ quarks. They are a function of $x$, the parton's momentum relative to the proton's momentum. The result is compared to the NNPDF3.1 [1], ABMP16 [2], CJ15 [3], and CT18 [4] analyses.

Caption: This plot shows the (truncated) contribution to the proton's overall spin from the up $\Delta u^+$ and down $\Delta d^+$ quarks on the left panel, and the anti-up $\Delta \bar{u}$ and anti-down $\Delta \bar{d}$ quarks on the right panel. Integrating over the momentum fraction $x$ gives the contribution to the proton's spin. The primary result is shown in red and is compared to results from the NNPDFpol1.1 [1] and DSSV08 [2] analyses.

TensorFlow

This repository...

Caption: This plot shows a comparison between three methods of calculating an experimental observable as a function of three variables: $M_h$, $P_{hT}$, and $\eta$. The bottom row shows the "unpolarized cross section," the middle row shows the "polarized cross section," while the top row shows the "asymmetry," which is simply the ratio of the polarized and unpolarized cross sections. The exact result is shown as red points. The result after performing a Mellin transform and then an inverse Mellin transform, as well as a 3D interpolation, are shown in blue. The result after approximating the inverse Mellin transform using a neural network, performing the inverse Mellin transform, and interpolating are shown in green. Great agreement is seen between the three results.