ELEMENTARY PARTICLE PHYSICS

Transverse momentum dependent parton distribution functions

Principal Investigator:
Dr. Fernanda Steffens

Affiliation:
HISKP – University of Bonn, Germany

Local Project ID:
TMDPDF1

HPC Platform used:
JUWELS BOOSTER of JSC

Date published:

We are all made of atoms, different types of atoms, and different combinations of them, which, by their turn, are composed of a cloud of electrons and a nucleus. A nucleus contains at least one proton in its simplest form, the hydrogen atom.  Comprehending the proton, the origin of its measured properties, like its mass and electric charge, and its structure is, thus, one of the most important endeavors of the physical sciences. How can we probe/see the proton and its structure?

The act of seeing is basically a result of scattering: light is scattered from a given object and absorbed by our eyes, with the information encoded by this light being, eventually, processed in our brains, resulting in the images we have of the macroscopic world around us. For the case of the proton, the chain of events is similar, only now we are dealing with objects that are incredibly small, around one hundred thousand times smaller than the atoms themselves. To see these objects, we need light with a wavelength of the same order of magnitude of the proton size. As our eyes are not built to be sensitive to this kind of wavelength, we build detectors that do a job like the job done by our eyes. In its simplest form, the whole process goes as follows: we accelerate electrons and then smash these electrons into targets containing the proton. The electrons interact with the proton exchanging quanta of light, the photons. That is so because in this kind of scattering, at such high energies and very short distances, light is quantized in packets of energy, or particles, called photons. Our detectors can then absorb the remains of the scattering, measure the angle and the energy of the electron after the scattering, and with this information we can rebuild the form of the object. In this sense, the scattering process as described here is like a huge microscope.

And what we “see” is astonishing: the proton has a rich and complex structure made of interacting quarks and gluons, collective called “partons”. A quark is like an electron, the main difference being that they have not only an electric charge, but also what we call a color charge. Color here does not refer to color as used in our everyday life but refers to the fact that quarks with a color charge can interact with other particles that also have a color charge, independent from the electric charge they carry. Thus, a quark can interact with particles with no electric charge, like the gluons.  The gluons are the carriers of this interaction in analogy to the photons, who are the carriers of the electromagnetic interaction, with a big difference: unlike photons, which do not have an electric charge, the gluons have themselves color and, thus, can interact with themselves. This aspect makes the underlying theory describing the interaction of quarks and gluons terribly difficult to use. The theory describing the dynamics of quarks and gluons is called Quantum Chromodynamics (QCD), as opposed to the theory describing the dynamics of electrons and photons, Quantum Electrodynamics (QED). For the case of short distances, distances smaller than the proton itself, the coupling between quarks and gluons is not so strong, and usual analytical techniques can be used within QCD. But when we try to pull out one of the quarks from the proton, the coupling becomes so large that all those analytical tools fail. We can, however, simulate the theory in a computer.

That is done by discretizing the space-time, and reformulating QCD in a discretized version, called Lattice QCD. Because the space-time has 4 dimensions, the number of mathematical operations to be done to simulate this self-interacting system is beyond grasp, and that is way we need supercomputers like the Juwels Booster, which allows us to do more than 1015 mathematical operations per second.  

But what can/want we compute? As mentioned, the scattering process tells us that the proton is made of partons. Thus, we can study how these partons are distributed inside the proton, and the functions that describe them are called Parton Distribution Functions (PDFs). Now, there are different kind of distributions we may want to study, as the electric charge density or how the proton momentum is distributed among the partons, among other properties. In the case of the momentum, it has three spatial dimensions: one longitudinal and two transverse components. If we want a full internal image of the proton, we need to access all components. Unlike the case of the longitudinal momentum-dependent PDFs, which can be determined by measuring the energy and angle of the scattered electron, the transverse components require more information, meaning the detectors must also measure the energy of other particles produced in the scattering, which make the experiments much more complex and difficult. As a result, the extracted transverse momentum-dependent PDFs (TMDPDFs) are not well determined experimentally. Theoretically, also the expressions to be used in the computer simulation are difficult to formulate, and only recently we have been able to build such formulation and, consequently, to start computing them using Lattice QCD. The present project is among the first in the world attempting to compute TMDPDFs in its simplest form, that is, we are away from what we call the physical point, which means a computation with physical quark masses with an extrapolation of the results to the continuum space-time. However, our results are the first necessary steps that, eventually, will allow us to have a full 3-dimentional picture of this fundamental object, the proton.