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Unravelling the proton and beyond

By Dr Neelakshi NK Borah

The most fasciting test for modern physics has been to understand the basic constituents of matter. In this direction, the early decades of 20th century had been one of the best times for physics as many important theories had come out from many eminent scientists. The electron had already been discovered by Thomson in 1897 and in 1900 Planck’s quantum hypothesis had captivated the world. Development of quantum mechanics as well as theory of relativity had challenged the validity of classical mechanics at subatomic level. Further, Rutherford had put forward a new concept of the nucleus, which successfully established that it consisted of nucleons (proton and neutron), leading us to a new era in nuclear physics.

Even after a century of its discovery, the composition of the proton is still not completely understood, rather it has proven to be an extremely complex entity. Gradually, both theoretically and experimentally, the studies have been unravelling the rich structure of this fundamental component of ordiry matter. The composition of the proton is now described by partons, which is consisted of quarks and the particles carrying the force that binds them, gluons. After the development of accelerators, in the 1960s, high energy electron beams were used to probe the hadronic structure of proton. Such experiments confirmed that the nucleons (proton or neutron) are not elementary particles but made of so called partons.

After theoretical hypothesis by Gell-Mann and Zweig in 1964, it took some time to identify the experimentally observed partons inside the proton as the “quarks”. As per the quark-parton model, the proton is a much more intricate structure than that of the three “valence” quarks and these sub-components are known to be sea quarks and gluons. However, in reality, the measurements have also demonstrated the presence of a multitude of gluons and sea quark-antiquark pairs, which generally carry a small fraction of the proton’s momentum with a large summed momentum contribution overall. The success of simple quark counting in explaining the gross features of the proton needs further investigations as certain puzzles still persists.

Likewise, the subject of nucleon structure has been investigated extensively for last several decades. Customarily, the constituents of a system have been investigated either by the study of static properties such as mass, magnetic moments, spin, parity, etc. or by scattering experiments i.e. the scattering of charged particles. In understanding the microscopic structure of matter, we have so far relied mainly on two types of physical quantities. The first is the spatial distribution of matter (charge or current) in a system, which can be probed through elastic scattering of electrons, photons, neutrons, etc. The observables in these experiments are elastic form (structure) factors that are dependent on the momentum transferred to the system. The second type of quantity is the distribution of constituents in momentum space, or simply the momentum distributions, which can be measured through deep inelastic scattering (DIS). The well known examples of such processes are of measuring the proton distribution in nuclei through quasi-elastic electron scattering. With some modifications to accommodate the relativistic ture of the system, both elastic and inelastic scattering approaches have been used to explore the inside of the nucleons.

The form factors can interpret the spatial charge or current distributions of quarks within a proton. On the other hand, Feynman parton distributions measured in high-energy hard scattering (DIS) processes are the longitudil-momentum distributions of the quarks and gluons in the so called infinite momentum frame. Both observables have taught us a great deal about the nucleon, but they are not free from deficiencies. The form factors contain no dymical information on the constituents, such as their velocity and angular momentum, and the momentum distributions provide no knowledge of their spatial locations. Thus, the complete understanding of proton structure function rests in establishing a co-relation between momentums and spatial coordites, which is nothing but the simultaneous knowledge of a constituent’s location and velocity. In case of a classical system one can define and study the phase-space distribution. However, in case of a quantum mechanical system, the phase-space distribution seems less useful because of the uncertainty principle i.e. one cannot determine the position and conjugate momentum of a particle simultaneously.

So is it possible to generalize the concept of phase-space transition to the relativistic quarks and gluons in a hadron? Answer to this question is the new physical observable med “Generalized Parton Distributions”. Generalized Parton Distributions (GPD) give us more detailed information about the longitudil as well as transverse momentum distributions of quarks and gluons, their orbital angular momentum etc., and give an opportunity to reveal the contributions to the nucleon’s spin by mapping down the three-dimensiol picture of the proton in terms of quark and gluon distributions. Unifying the concept of parton distributions and of hadronic form factors, GPDs have been recognized as a tool to study hadron structure in new ways. Or we can say that GPD is a one body matrix element that combines the kinematics of both elastic form factors and Feynman parton distributions, and is measurable in hard exclusive processes.

The two most important hard exclusive processes are Deeply Virtual Compton Scattering (DVCS) and exclusive meson production. In DVCS, an incoming virtual photon scatters on the nucleon and the fil states are the nucleon and a (real or virtual) photon which are both detected in the experiment. In the exclusive meson production, the fil states are also a nucleon with a meson instead of a photon. They provide information about the structure of the proton which cannot be accessed by inclusive measurements. Initially these functions were known as non-forward or off-forward parton distribution, off-diagol parton distributions or skewed parton distributions.

Nowadays, these Generalized Parton Distributions (GPDs), as first proposed by two eminent theoretical physicists Xiangdong Ji and Atoly Radyushkin way back in 1996-97, are the recent challenges in theoretical and experimental physics. Experimental studies for the GPDs have been pioneered at particle detectors HERMES and JLab (Jefferson Lab). Despite many challenges and complications, interesting alysis has come out and many breakthroughs have been made so far. Still, the search for a conclusive understanding of the secrets of ture inside the proton is on.

(The writer is a research scholar at the Department of Physics, Gauhati University )

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Ankur Kalita