Symmetries/Asymmetries in Particle Physics

Dear Colleagues,

Symmetry is one of the most powerful tools in particle physics, because it has become evident that it represents the origin of practically all laws of nature. Violations of symmetry therefore present theoretical and experimental puzzles that, when solved, lead to a deeper understanding of nature. Asymmetries in experimental measurements also provide powerful data that are often relatively free from background or systematic uncertainties.

The Standard Model (SM) of particle physics provides the most precise description to date of elementary particles and their interactions. In particle physics, many cases of symmetries and asymmetries have been found, providing a solid foundation for the SM and beyond.

Precise measurements of the SM parameters, combined with precise theoretical calculations, yield remarkable predictive power that allows phenomena to be determined even before they are directly observed. In this way, the SM successfully constrained the masses of the W and Z bosons, discovered at CERN in 1983; the top quark, discovered at Fermilab in 1995; and, most recently, the Higgs boson, discovered at CERN in 2012. Once these particles were discovered, these predictions became consistency markers for the SM, allowing for exploration of the limits of the theory’s validity. In parallel with this, precision measurements of the properties of these particles are a powerful tool for searching for new phenomena beyond the SM, called “new physics”, as new phenomena manifest as discrepancies between various measured and calculated quantities.

A principal effect of asymmetry in the universe was the absence of anti-matter, just few small time steps after the Big Bang (BB) and the creation of the elementary particles. On the other hand, a small imbalance, or asymmetry, in the amount of matter and antimatter created led to a slight excess of matter, from which the universe eventually formed. This ‘broken symmetry’ is one of the keys to our existence.

On the other hand, the three-family model of double quarks and leptons creates holy symmetry in the SM, which, internally, has shown asymmetrical properties among quarks, i.e., their charge (+2/3e (up, charm, top) vs. −1/3e (down, strange, bottom)) and the evolution of their mass from up–down to top–bottom quarks. The existence of experimental charge asymmetry in the pair production of a fermion and its antiparticle has been recognized for many decades. The discovery of experimental charge asymmetry in top-quark pair production reveals possible new physics beyond the current theory of elementary particles.

The additional asymmetry effects in the electron–positron annihilation process, the neutrinos’ oscillations and their properties, and the effective leptonic electroweak mixing angle allow us to better understand the laws of the fundamental building blocks of matter.

The electroweak mixing angle is a key element of these consistency checks. It is a fundamental parameter of the SM, determining how the unified electroweak interaction gives rise to electromagnetic and weak interactions through a process known as electroweak symmetry breaking. At the same time, it mathematically ties together the masses of the W and Z bosons, which are the carriers of the weak interaction. So, measurements of the W and Z bosons or the mixing angle enable effective experimental cross-checking of the SM.

The two most precise measurements of the weak mixing angle were performed in experiments at the CERN LEP collider and in the SLD experiment at the Stanford Linear Accelerator Center (SLAC). The values of these experiments disagree with each other, which has puzzled physicists for over a decade. The most recent result is in good agreement with the SM prediction and represents a step towards resolving the discrepancy between the latter and the LEP and SLD measurements.

The Standard Model also incorporates parity violation by expressing the weak interaction as a chiral gauge interaction. Only the left-handed components of particles and right-handed components of antiparticles participate in weak interactions in the SM. A consequence of parity violation in particle physics is that neutrinos have only been observed as left-handed particles and antineutrinos as right-handed particles.

In 1956–1957 Chien-Shiung Wu and her team found a clear violation of parity conservation in the beta decay of Cobalt-60. Simultaneously, Leon Lederman and his colleagues modified an existing cyclotron experiment and immediately verified parity violation.

It was believed that the combined symmetry of parity (P) and simultaneous charge conjugation (C), called CP, was preserved. For example, CP transforms a left-handed neutrino into a right-handed antineutrino. In 1964, however, James Cronin and Val Fitch provided clear evidence that CP symmetry was also violated in an experiment with neutral kaons (K⁰).

In collider experiments, because the weak interactions violate parity, collider processes that involve weak interactions typically exhibit asymmetries in the distribution of the final-state particles. These asymmetries are typically sensitive to differences in the interaction between particles and antiparticles or between left-handed and right-handed particles. They can thus be used as a sensitive measurement of differences in interaction strength and/or to distinguish a small asymmetric signal from a large but symmetric background.

Forward–backward asymmetry is defined as A_FB=(N_F − N_B)/(N_F + N_B), where N_F is the number of events in which a particular final-state particle is moving "forward" in a chosen direction (e.g., a final-state electron moving in the same direction as the initial-state electron beam in electron–positron collisions), while N_B is the number of events with the final-state particle moving "backward". Forward–backward asymmetries were used in the LEP experiments to measure the difference in the interaction strength of the Z boson between left-handed and right-handed fermions, which enabled precision measurement of the weak mixing angle.

Left-right asymmetry is defined as A_LR=(N_L − N_R)/(N_L + N_R), where N_L is the number of events in which an initial- or final-state particle is left-polarized, while N_R is the corresponding number of right-polarized events. Left–right asymmetries in Z boson production and decay were measured at the Stanford Linear Collider using the event rates obtained with left-polarized versus right-polarized initial electron beams. Left–right asymmetries can also be defined as asymmetries in the polarization of final-state particles whose polarizations can be measured, e.g., tau leptons.

Charge asymmetry, or particle–antiparticle asymmetry, is defined in a similar way. This type of asymmetry has been used to constrain the parton distribution functions of protons at the Tevatron from events in which a produced W boson decays to a charged lepton. The asymmetry between positively and negatively charged leptons as a function of the direction of the W boson relative to the proton beam provides information on the relative distributions of up and down quarks in the proton. Particle–antiparticle asymmetries are also used to extract measurements of CP violation from B meson and anti-B meson production in the BaBar and Belle experiments.

The LHCb/LHC-CERN experiment specializes in the study of B hadrons, particles that contain a bottom quark or its antiparticle, and the researchers have developed expertise in measuring parameters that can be used to determine the probability that a quark will transform into another via a weak interaction. These transformation processes were first described by Nicola Cabibbo, Makoto Kobayashi and Toshihide Maskawa-CKM, and can be calculated using the well-known CKM matrix. The CKM matrix is made up of four free parameters—like the masses of particles—that are measured in experiments. Measurements can be carried out via different processes to test the robustness of the Standard Model. The structure of the CKM matrix can be represented graphically by triangles, with the parameters represented by the lengths of the sides and the angles. This work is linked to work on the phenomenon of charge-parity (CP) violation, which is at the origin of differences in behaviour between matter and antimatter.

It is well understood that many of experimental and theoretical data pertaining to  symmetries and asymmetries in particle physics have been obtained in the last 50 years . Individual authors and research groups are therefore invited to contribute current research to this special issue.

Prof. Dr. Evangelos Gazis
Guest Editor

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• particles
• standard model
• big bang
• quark
• symmetry