Exploring Proton Collisions at the Large Hadron Collider: Insights into Quantum Billiards

by Santiago Fernandez
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quantum interactions

A recent study conducted by the ATLAS experiment at the Large Hadron Collider (LHC) has provided valuable insights into the properties of strong interactions between protons at ultra-high energies. By investigating elastic scattering in proton-proton collisions, the research team discovered disparities with existing theoretical models, prompting a reevaluation of our current understanding of these interactions.

In the quantum realm, even simple processes like elastic scattering can yield profound conclusions about the interactions between elementary particles. The ATLAS experiment at the LHC has reported measurements of fundamental properties of strong interactions between protons at ultra-high energies.

In classical physics, the concept of billiard ball collisions is familiar, where collisions are predominantly elastic, conserving both momentum and energy. The scattering angle in these collisions depends on the centrality of the collision, often quantified by the impact parameter—the distance between the centers of the balls in a plane perpendicular to their motion. In highly central collisions with a small impact parameter, the scattering angles are large. As the impact parameter increases, the scattering angle decreases.

Similarly, in particle physics, elastic collisions occur when two particles maintain their identities and scatter at a specific angle relative to their original motion. The scattering angle also correlates with the collision parameter. By measuring these scattering angles, valuable information about the spatial structure of colliding particles and their interactions can be obtained.

Physicists from the Institute of Nuclear Physics Polish Academy of Sciences, as part of the ATLAS Collaboration, conducted a measurement of elastic scattering in proton-proton collisions at the LHC with a center-of-mass energy of 13 TeV. Due to the extremely small scattering angles in these interactions (less than a thousandth of a degree), a dedicated measurement system was required. This system involved placing detectors over 200 meters from the collision point, capable of measuring scattered protons at distances as close as a few millimeters from the accelerator beam. The technique utilized “Roman pots,” which allowed detectors to be placed inside the accelerator beam pipe, ensuring close proximity to the beam during data collection. The Krakow group made significant contributions to the development of the trigger and data acquisition system, which enabled data recording.

The experimental setup also incorporated a unique configuration of magnetic fields that shaped the LHC accelerator beam. Typically, beam focusing is maximized in measurements to increase the frequency of interesting interactions. However, tightly focused beams exhibit a large angular divergence, making the measurement of elastic scattering practically impossible. To address this, the special magnet configuration minimized the beam’s angular divergence, enabling precise measurements.

The main result of the measurement, published in the European Physical Journal C, is the distribution of the scattering angle or, more precisely, the distribution of the variable “t,” which is proportional to the square of the angle. The shape of this distribution allowed researchers to draw conclusions about the fundamental properties of nuclear strong interactions between protons at very high energies—insights that cannot be observed in the game of billiards.

One crucial property in this quantum scattering analysis is the “optical theorem,” which arises from probability conservation in quantum processes. It connects elastic interactions to inelastic ones, where additional particles are produced. Since the studied collisions involved protons with very high energy, inelastic processes occurred frequently. The optical theorem enabled the determination of a parameter called the total cross-section solely from measurements of elastic interactions.

The total cross-section is a quantity used in particle physics to describe the likelihood of a specific reaction. It characterizes the probability of any type of proton-proton collision and is related to the size of the proton. The result published by the ATLAS Collaboration represents the most precise measurement of this parameter at 13 TeV energy. The high precision was achieved, in part, through the accurate determination of detector position, for which the IFJ PAN group was responsible. The obtained result confirms an essential property of strong interactions—the increase of the total cross-section as collision energy rises. This increase can be interpreted as the size of the proton growing with energy.

Precise knowledge of the total cross-section is not only crucial for studying strong interactions but also relevant in other areas of particle physics. In experiments at the LHC, strong interactions act as background noise in the search for new physics. They also play a significant role in cosmic ray research, particularly in the development of cosmic air showers. Precise measurements of quantities like the total cross-section contribute to accurate modeling of these processes.

Elastic scattering in proton-proton collisions can occur through two mechanisms: the strong nuclear interaction and the Coulomb interaction resulting from the repulsion between electric charges. The quantum nature of the studied process introduces another aspect—the interference between these mechanisms, which depends on their scattering amplitudes. Scattering amplitude, a measure of probability in quantum physics, is described by complex numbers rather than real numbers, requiring the consideration of magnitude, phase, or real and imaginary parts. Since Coulomb interactions can be well understood and their scattering amplitude can be calculated, measuring the interference provides insights into both the real and imaginary parts of the nuclear amplitude.

The measured ratio of the real to the imaginary parts of the nuclear amplitude is significantly lower than predicted by pre-LHC theoretical models. These models are based on assumptions about the properties of strong interactions. The observed discrepancy challenges these assumptions.

One assumption is that the properties of proton-antiproton collisions at very high energies are the same as those of proton-proton and antiproton-antiproton collisions. This assumption arises because, despite protons being composed of quarks and gluons, high-energy collisions predominantly occur between gluons. Since the gluon structure of protons and antiprotons is identical, it is natural to assume identical interactions in different systems. However, allowing for differences, made possible by the quantum nature of interactions, helps theoretical models describe the experimental data.

The second assumption concerns the growth of the total cross-section with energy. It was previously assumed that the character of this growth for energies beyond those currently measured at the LHC would be the same as observed thus far. The observed discrepancy may be explained by a slowing down of this growth at energies above those achievable at the LHC.

Both hypotheses address fundamental properties of strong interactions at high energies. Regardless of which hypothesis proves correct, the reported measurements provide valuable insights into our understanding of the fundamental interactions of particles.

Currently, the detectors used in these studies are being prepared for further measurements of elastic scattering at even higher energies. The Institute of Nuclear Physics Polish Academy of Sciences is also conducting research on other processes where strong and electromagnetic interactions are significant factors. The technique of Roman pots plays a crucial role in these studies, facilitated by the support of an NCN grant (SONATA BIS 2021/42/E/ST2/00350).

Frequently Asked Questions (FAQs) about quantum interactions

What is the focus of the study conducted at the Large Hadron Collider?

The study conducted at the Large Hadron Collider focuses on exploring the properties of strong interactions between protons at ultra-high energies through elastic scattering in proton-proton collisions.

What were the findings of the research?

The research found discrepancies with pre-existing theoretical models, challenging the current understanding of strong interactions. The measurements of elastic scattering provided insights into the spatial structure of colliding particles and their interaction properties.

How were the measurements of elastic scattering performed?

The measurements required the use of a dedicated measurement system, including detectors placed over 200 meters from the collision point. Roman pots, a technique allowing detectors to be placed inside the accelerator beam pipe, were used to measure scattered protons at distances of just a few millimeters from the accelerator beam.

Why is the measurement of the total cross-section important?

The measurement of the total cross-section, which describes the likelihood of a proton-proton collision, is crucial for studying strong interactions and has implications in various areas of particle physics. It provides information about the proton size and helps in the accurate modeling of processes involving strong interactions.

What did the observed discrepancy in the scattering amplitudes indicate?

The observed discrepancy in the interference between the strong nuclear interaction and Coulomb interaction, as revealed by the scattering amplitudes, challenged the assumptions made by pre-LHC theoretical models. It suggested a difference in the properties of proton-proton and proton-antiproton collisions at high energies.

What are the implications of the research findings?

The research findings shed light on our understanding of fundamental particle interactions, particularly strong interactions. They prompt a reconsideration of current theoretical models and provide insights for further studies in particle physics, including the search for new physics and cosmic ray research.

More about quantum interactions

  • “ATLAS experiment at the Large Hadron Collider”
  • “European Physical Journal C”
  • “Measurement of the total cross section and ρ-parameter from elastic scattering in pp collisions at s√=13TeV with the ATLAS detector”

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