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Unveiling the Mystery: New Insights into Mass Distribution in Hadrons

Introduction to Mass in Subatomic Particles

Examining the Energy and Momentum of Quarks

Scientists determine the mass of subatomic particles made of quarks by examining their energy and momentum in four-dimensional spacetime.

The Trace Anomaly and Its Role

The trace anomaly, an essential metric, ties to the energy/momentum scale dependence observed in high-energy physics.

The Importance of the Trace Anomaly in Quark Binding

How the Trace Anomaly Affects Quark Binding

Scientists posit that the trace anomaly plays an essential role in maintaining the binding of quarks within subatomic particles.

Study Insights: Calculating the Trace Anomaly

A study published in Physical Review D presented calculations of the trace anomaly for nucleons, including protons and neutrons, as well as for pions, composed of one quark and one antiquark.

The result indicate that in pions, the mass distribution closely resembles the charge distribution observed in neutrons, whereas in nucleons, it parallels the charge distribution of protons.

Scientific Goals of the Electron-ion Collider (EIC)

Uncovering the Origin of Nucleon Mass

One of the primary scientific objectives of the Electron-ion Collider (EIC) is to uncover the origin of nucleon mass.

Mapping the Mass Distribution of Quarks and Gluons

Researchers also aim to map the mass distribution of quarks and gluons within hadrons, subatomic particles like protons and neutrons, bound by the strong nuclear force.

New Methods for Calculating Mass Distribution

First-Principle Methods for Mass Distribution

The new calculations show that mass distribution can be derived numerically using first-principle methods based on fundamental physical principles.

Supporting Nuclear Physics Data Interpretation

This technique will also support scientists in interpreting nuclear physics experimental data.

Future Experiments at the Electron-Ion Collider

Investigating Nucleon Mass with Electron-Proton Scattering

Future experiments at the Electron-Ion Collider (EIC) at Brookhaven National Laboratory aim to investigate the origins of nucleon mass. These experiments will utilize electron-proton scattering to generate heavy states that probe the proton's internal structure, focusing on gluon distributions.

Analyzing Scattering Data to Understand Mass Distribution

Scientists analyze scattering data to determine how quarks and gluons contribute to the proton's mass distribution, a method comparable to using X-ray diffraction to uncover DNA's double-helix structure.

Insights and Future Directions

Aligning with the Standard Model

These calculations align with the Standard Model and shape the design of upcoming experiments.

The Significance of the Pion's Structure

The results provide valuable insights into the mass distribution within particles such as nucleons and pions. They emphasize the pion's significance in connecting two Standard Model characteristics: the presence of an absolute scale and the asymmetry between left- and right- handed elements.

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First Coherent Representation of Atomic Nucleus: Uniting Quarks and Gluons in Nuclear Physics

Introduction to the Atomic Nucleus

The atomic nucleus consists of protons and neutrons, whose existence arises from the interaction of quarks bound together by gluons. One might assume, then, that recreating all the properties of atomic nuclei observed in nuclear experiments using only quarks and gluons would be straightforward. Yet, it is only recently that physicists, including those at the Institute of Nuclear Physics of the Polish Academy of Sciences in Krakow, have achieved this.

Historical Context

Discovery of Protons and Neutrons

Nearly a century has passed since the discovery of the key components of atomic nuclei: Protons and Neutrons. At first, these particles were believed to be indivisible. However, in the 1960s, it was proposed that at sufficiently high energies, protons and neutrons would expose their internal structure--quarks bound together by gluons.

Confirmation of Quarks

Shortly thereafter, the existence of quarks was experimentally confirmed. It is therefore surprising that, despite the many decades that have passed, quark-gluon models have been unable to replicate the results of nuclear experiments at low energies, where only protons and neutrons are visible in atomic nuclei.

Recent Breakthrough

Overcoming the Impasse

This enduring impasse has only recently been overcome, as detailed in a paper published in Physical Review Letters. The principal authors are researchers from the international nCTEQ collaboration on quark-gluon distributions, including members from the Institute of Nuclear Physics of the Polish Academy of Sciences (IFJ PAN) in Krakow.

Unifying Distinct Frameworks

Up to now, atomic nuclei have been described in two separate frameworks:

• One involving protons and neutrons observable to low energies.
• Another at high energies, focusing on quarks and gluons.

In our study, we succeeded in unifying these previously distinct realms, explains Dr. Aleksander Kusina, one of the three IFJ PAN theorists involved in the research.

Methodology

Observing Atomic Nuclei

Humans observe their surroundings through their eyes, which serve as innate detectors, capturing photons scattered from the atoms and molecules in the objects around them. In much the same way, physicists gain insights into atomic nuclei by colliding them with smaller particles and carefully examining the collision results.

The Role of Charged Elementary Particles

For practical purposes, physicists do not use electrically neutral photons but rather charged elementary particles, typically electrons. Experimental results demonstrate that, at low energies, atomic nuclei behave as though they consist of nucleons (protons and neutrons), while at high energies, partons (quarks and gluons) within the nuclei become "visible."

The outcomes of colliding atomic nuclei with electrons have been reasonably well modeled by assuming nucleons alone for low-energy collisions and partons for high-energy ones. However, a unified description combining these two models has yet to be achieved.

Research Findings

High-Energy Collision Data Analyzing

In their research, physicists from IFJ PAN analyzed high-energy collision data, including that obtained from the LHC accelerator at CERN in Geneva. Their primary aim was to explore the partonic structure of atomic nuclei at high energies, described by parton distribution functions (PDFs).

Understanding Parton Distribution Functions (PDFs)

Parton distribution functions (PDFs) are employed to illustrate the distribution of quarks and gluons within partons, neutrons, and the atomic nucleus as a whole. Utilizing these PDF functions, researchers can experimentally ascertain measurable parameters, such as the likelihood of a particular particle being produced during collisions between electrons or protons and the nucleus.

Theoretical Innovations

Extension of Parton Distribution Functions

The theoretical innovation presented in this paper lies in the adept extension of parton distribution functions, drawing inspiration from nuclear models that describe low-energy collisions. In these models, partons and neutrons are treated as forming strongly interacting pairs of nucleons, such as proton-neutron, proton-proton, and neutron-neutron combinations.

Results of the Study

This innovative approach enabled the researchers to ascertain parton distribution functions for the 18 atomic nuclei examined, as well as the distributions of partons in correlated nucleon pairs and the quantities of these correlated pairs.

The results validated the well-established observation from low-energy experiments that proton-neutron pairs constitute the majority of correlated pairs, especially notable in heavy nuclei like gold and lead.

Conclusion

Advancements in Theoretical Modeling

The method proposed in this paper enhances the description of experimental data, outperforming conventional techniques for assessing parton distributions in atomic nuclei.

"We improved our model to better simulate the pairing of certain nucleons, as we identified this effect's relevance at the parton level. This advancement resulted in a conceptual simplification of the theoretical description, allowing for more precise future studies of parton distributions in individual atomic nuclei," explains Dr. Kusina.

Bridging High and Low-Energy Characteristics

The alignment between theoretical predictions and experimental data indicates that, for the first time, the parton model, alongside high-energy data, has successfully replicated the behavior of atomic nuclei, previously understood only through nucleonic descriptions and low-energy collision data. The outcomes of this research provide fresh insights into the atomic nucleus's structure, bridging its high- and low-energy characteristics.

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