LEPTONS
General
Leptons are elementary particles and a fundamental building block of matter in the Standard Model of particle physics. They are part of a broader category of particles known as fermions, which include quarks as well. Leptons are considered "elementary" because, as far as current experimental evidence and theoretical understanding go, they are not composed of smaller sub-particles.
There are six types, or flavors, of leptons in the Standard Model, organized into three generations:
First Generation:
Electron (e): This is the most familiar lepton and is commonly found in atoms, orbiting the nucleus. It carries a negative electric charge.
Electron Neutrino (νe): Neutrinos are neutral and extremely difficult to detect because they interact very weakly with matter. There are three types of neutrinos, and the electron neutrino is associated with the electron.
Second Generation:
Muon (μ): The muon is similar to the electron but is about 200 times more massive. It also carries a negative electric charge.
Muon Neutrino (νμ): Similar to the electron neutrino, but associated with the muon.
Third Generation:
Tau (τ): The tau is even more massive than the muon and electron, making it the heaviest of the charged leptons. It carries a negative electric charge.
Tau Neutrino (ντ): Associated with the tau, similar to the electron and muon neutrinos.
Leptons interact with other particles through the electromagnetic and weak nuclear forces. The weak force is responsible for processes such as beta decay, where a neutron can transform into a proton by emitting a W- boson and converting into a proton along with an electron and an electron antineutrino.
Leptons, along with quarks, make up all the known matter in the universe. However, they differ from quarks in that they do not experience the strong nuclear force directly, which binds quarks together to form protons, neutrons, and other strongly interacting particles.
Leptons are crucial to our understanding of particle physics, and their behavior is extensively studied in high-energy physics experiments, such as those conducted at particle accelerators like the Large Hadron Collider (LHC). These experiments help scientists probe the fundamental forces and particles that make up the fabric of the universe
Spin and chirality
Leptons exhibit a spin of 1/2, classifying them as fermions according to the spin-statistics theorem. Consequently, they adhere to the Pauli exclusion principle, preventing the coexistence of two leptons of the same type in the same state simultaneously. This restriction results in only two possible spin states for a lepton: up or down.
Chirality, closely linked to the more intuitively understandable property called helicity, is another pertinent characteristic. Helicity denotes the direction of a particle's spin in relation to its momentum, categorizing particles with spin aligned with their momentum as right-handed and those with opposing alignment as left-handed. When dealing with massless particles, the momentum-to-spin direction remains consistent across all reference frames. For massive particles, choosing a faster-moving reference frame can alter the helicity, demonstrating that it is frame-dependent. Chirality, a technical property defined by its transformation behavior under the Poincaré group, retains its definition across various reference frames and is designed to align with helicity for massless particles.
While many quantum field theories, including quantum electrodynamics and quantum chromodynamics, treat left- and right-handed fermions as identical, the Standard Model's Weak interaction distinguishes between them. Only left-handed fermions (and right-handed anti-fermions) participate in the weak interaction, a notable instance of parity violation explicitly embedded in the model. In the literature, left-handed fields are often represented by a capital L subscript (e.g., the standard electron: eL−), while right-handed fields carry a capital R subscript (e.g., a positron eR+).
Notably, right-handed neutrinos and left-handed anti-neutrinos lack interactions with other particles (referred to as sterile neutrinos), rendering them non-functional within the Standard Model. Although their exclusion is not obligatory, they are occasionally included in particle tables to underscore their inactive role in the model. Despite the lack of specific engagement in the weak interaction, electrically charged right-handed particles (such as electrons, muons, or taus) can still interact electromagnetically and contribute to the combined electro-weak force, albeit with varying strengths (YW).
Electromagnetic Interaction
One of the key characteristics defining leptons is their electric charge, denoted as Q, which plays a crucial role in determining the intensity of their electromagnetic interactions. This charge dictates the magnitude of the electric field produced by the lepton, as described by Coulomb's law, and influences how the particle responds to external electric or magnetic fields, as elucidated by the Lorentz force. Within each generation of leptons, one member carries a charge of Q = -1e, while another possesses a neutral electric charge. The charged lepton is commonly known simply as a "charged lepton," while its electrically neutral counterpart is referred to as a "neutrino." For instance, in the first generation, the electron (e⁻) bears a negative electric charge, while the electrically neutral electron neutrino (νₑ) complements it.
In the realm of quantum field theory, the electromagnetic interaction of charged leptons manifests in their interaction with the quantum of the electromagnetic field—the photon. The electron-photon interaction is visually represented by the Feynman diagram depicted on the right.
Due to the inherent rotation carried by their spin, charged leptons generate a magnetic field. The magnitude of their magnetic dipole moment (μ) is determined by the formula
where m is the mass of the lepton and g is the so-called "g factor" for the lepton.
In the realm of first-order quantum mechanics, the predicted g factor for all leptons is 2. However, more intricate quantum effects arising from loops in Feynman diagrams introduce corrections to this value. These corrections, known as the anomalous magnetic dipole moment, are highly sensitive to the specifics of a quantum field theory model. Consequently, they offer a valuable avenue for precise examinations of the standard model. Notably, the agreement between theoretical and measured values for the electron's anomalous magnetic dipole moment spans eight significant figures. On the other hand, the results for the muon present a challenge, suggesting a subtle yet persistent deviation between the Standard Model and experimental observations.
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Figure 199 - Electromagnetic Interaction
Weak Interaction
Within the Standard Model, the left-handed charged lepton and left-handed neutrino are organized into a doublet (νₑL, e⁻L), constituting a spinor representation (T = 1⁄2) of the weak isospin SU(2) gauge symmetry. This arrangement implies that these particles are eigenstates of the isospin projection T3, possessing eigenvalues of +1⁄2 and −1⁄2, respectively. In contrast, the right-handed charged lepton transforms as a weak isospin scalar (T = 0) and thus remains uninvolved in the weak interaction. Notably, there is currently no evidence supporting the existence of a right-handed neutrino.
The Higgs mechanism plays a pivotal role in unifying the gauge fields of the weak isospin SU(2) and the weak hypercharge U(1) symmetries. This amalgamation gives rise to three massive vector bosons (W⁺, W⁻, Z⁰) that mediate the weak interaction, alongside a massless vector boson, the photon, responsible for the electromagnetic interaction. The electric charge Q can be derived using the Gell-Mann–Nishijima formula, which relates it to the isospin projection T3 and weak hypercharge YW :
To recover the observed electric charges for all particles, the left-handed weak isospin doublet (νₑL, e⁻L) must thus have YW = −1, while the right-handed isospin scalar e⁻R must have YW = −2. The interaction of the leptons with the massive weak interaction vector bosons is shown in figure 200.
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Figure 199 - Electromagnetic Interaction
Mass
In the Standard Model, initial leptons lack intrinsic mass. Charged leptons (such as the electron, muon, and tau) acquire effective mass through interaction with the Higgs field, while neutrinos remain massless. The absence of neutrino mass leads to the absence of mixing among different generations of charged leptons, unlike quarks. Experimental observations align with the neutrinos having zero mass.
However, indirect experiments, particularly neutrino oscillations, suggest a nonzero mass for neutrinos, likely below 2 eV/c². This discovery implies the presence of physics beyond the Standard Model. The currently favored extension is the "seesaw mechanism," which offers an explanation for the lightness of left-handed neutrinos compared to corresponding charged leptons and the absence of observed right-handed neutrinos.
Lepton Number and flavor conservation [1]
Lepton numbers are quantum numbers associated with leptons, which are a type of elementary particle. Leptons are fundamental particles that do not experience the strong nuclear force and include three charged particles: the electron (e⁻), the muon (μ⁻), the tau (τ⁻), and their corresponding neutrinos (νe, νμ, ντ). Lepton numbers are conserved in particle interactions, and they help in understanding and predicting the outcome of particle processes.
There are two types of lepton numbers: the lepton number (L) and the individual lepton flavor numbers (Lₑ, Lₘ, Lₜ) associated with electrons, muons, and taus, respectively.
Lepton Number (L): The total lepton number is the sum of the lepton flavor numbers. It is conserved in all known particle interactions. For leptons, the lepton number is assigned +1 for particles and -1 for antiparticles, while for non-leptonic particles, the lepton number is zero.
For a lepton: L = +1
For an antilepton: L = -1
For non-leptonic particles: L = 0
The conservation of lepton number ensures that processes like electron-positron annihilation or neutrino interactions preserve the overall lepton content of the system.
Lepton Flavor Numbers (Lₑ, Lₘ, Lₜ): These represent the individual conservation of electron, muon, and tau flavors. Each flavor has its own lepton number, and in a reaction, the total lepton flavor number must be conserved.
For electron flavor (Lₑ): +1 for electrons, -1 for electron antineutrinos, and 0 for other particles.
For muon flavor (Lₘ): +1 for muons, -1 for muon antineutrinos, and 0 for other particles.
For tau flavor (Lₜ): +1 for taus, -1 for tau antineutrinos, and 0 for other particles.
Lepton flavor number conservation ensures that processes like muon decay or tau interactions do not violate the distinct flavors of leptons.
It's important to note that while lepton numbers are conserved individually, they are not conserved universally. The phenomenon of neutrino oscillation, for example, implies a mixing of lepton flavors, where a neutrino produced as one flavor may later be detected as a different flavor. However, the total lepton number is still conserved.
In summary, lepton numbers play a crucial role in understanding and describing the conservation laws governing interactions involving leptons. The conservation of lepton numbers provides valuable insights into the underlying symmetries and fundamental principles of particle physics.
Properties of leptons - overview
Figure 201 - Properties of leptons – overview
Neutrinos
Neutrinos are elementary particles that belong to the lepton family, which also includes electrons, muons, and tau particles. They are incredibly tiny, electrically neutral, and have very little mass, making them challenging to detect. Neutrinos are one of the fundamental particles in the Standard Model of particle physics, which describes the basic building blocks of matter and their interactions.
Roughly 100 trillion neutrinos pass through our body every second of every day, most of which were produced in the Sun as a by-product of nuclear fusion. [6]
[i] Dan Hooper. At the Edge of Time, Exploring the mysteries of our universe’s first seconds. Princeton University Press (2019)
Here are some key characteristics of neutrinos:
Elementary Particle: Neutrinos are elementary particles, meaning they are not composed of smaller constituents. In the Standard Model, there are three types, or "flavors," of neutrinos: electron neutrinos (νe), muon neutrinos (νμ), and tau neutrinos (ντ).
Electrically Neutral: Neutrinos have no electric charge, which means they do not interact with electromagnetic forces. This property makes them challenging to detect because they do not experience the electromagnetic forces that other charged particles do.
Tiny Mass: Neutrinos have masses, but these masses are extremely small compared to other elementary particles. The exact values of neutrino masses are still not precisely known, and scientists are actively conducting experiments to measure them more accurately.
Weak Interactions: Neutrinos primarily interact via the weak force, one of the four fundamental forces of nature. Weak interactions are responsible for processes such as beta decay in radioactive substances. Neutrinos also interact gravitationally, but the gravitational force is extremely weak compared to the other fundamental forces.
High Penetrating Power: Because they interact weakly, neutrinos can travel long distances through matter without being significantly scattered or absorbed. This property makes them unique tools for studying astrophysical phenomena and for probing the properties of matter.
Helicity and Spin: Neutrinos have spin-1/2, and they exhibit a property called helicity, which is the projection of their spin onto their direction of motion. Neutrinos are left-handed, meaning their helicity is aligned with their direction of motion, while their antiparticles, antineutrinos, are right-handed.
Production: Neutrinos are produced in various processes, including nuclear reactions in the sun, nuclear reactors, cosmic-ray interactions in the Earth's atmosphere, and high-energy particle collisions in accelerators.
As well as specific sources, a general background level of neutrinos is expected to pervade the universe, theorized to occur due to two main sources.
Cosmic neutrino background (Big Bang originated)
Around 1 second after the Big Bang, neutrinos decoupled, giving rise to a background level of neutrinos known as the cosmic neutrino background (CNB).
Figure 266 - Cosmic Neutrino Background (CNB) [2]
Diffuse supernova neutrino background (Supernova originated)
R. Davis and M. Koshiba were jointly awarded the 2002 Nobel Prize in Physics. Both conducted pioneering work on solar neutrino detection, and Koshiba's work also resulted in the first real-time observation of neutrinos from the SN 1987A supernova in the nearby Large Magellanic Cloud. These efforts marked the beginning of neutrino astronomy. [3]
SN 1987A represents the only verified detection of neutrinos from a supernova. However, many stars have gone supernova in the universe, leaving a theorized diffuse supernova neutrino background.
Neutrinos are notoriously difficult to detect because of their weak interactions, but scientists have developed sophisticated experiments to observe them indirectly. These experiments often involve large detectors located deep underground to shield against cosmic rays and other background radiation.
Where does the mass of neutrinos comes from ?
Neutrinos, produced in celestial events like solar fusion and supernovas, remain enigmatic despite being the universe's second most abundant particle. The Standard Model fails to explain their small, non-zero mass, prompting various theories. One challenge is the left-handedness of measured neutrinos, hinting at possible undiscovered right-handed neutrinos. The seesaw mechanism proposes heavy right-handed neutrinos balancing light left-handed ones, with models predicting additional particles and even a new Higgs boson.
Critics cite challenges in testing these theories due to predicted particle masses and the yet-unseen self-interaction of neutrinos. Radiative mass generation is another theory requiring new particles. Lacking direct experimental support, physicists eagerly await precise neutrino measurements to explore new physics and potentially challenge current understanding. Ongoing experiments worldwide aim to unravel the mysteries surrounding neutrinos and their masses, offering a wide-ranging approach to understand these elusive particles.
Neutrino Oscilation
Neutrino oscillation, also known as neutrino flavor oscillation, is a phenomenon in which a neutrino created as a specific flavor (electron, muon, or tau) can be detected as a different flavor after it has traveled a certain distance. This effect is due to the fact that the three flavor states of neutrinos are not the same as the three mass states, and the neutrino wave function evolves over time as it propagates.
The theory of neutrino oscillation is based on the fact that neutrinos have mass, which was first discovered through the observation of the deficit of electron neutrinos produced by the Sun in experiments on Earth. This deficit could not be explained by any known physics and led to the realization that neutrinos could oscillate between flavors as they travel through space.
The phenomenon of neutrino oscillation can be described mathematically by the PMNS matrix, which relates the flavor eigenstates of the neutrinos to the mass eigenstates. The PMNS matrix is a unitary matrix that depends on three mixing angles and a complex phase. The mixing angles describe the degree to which the three mass states contribute to each of the three flavor states.
As a neutrino travels through space, the wave function of the particle changes due to its interaction with the surrounding medium. This interaction causes the neutrino to evolve from its initial flavor state to a superposition of all three flavor states, with the relative amplitudes of the different flavors changing as the neutrino propagates. The probability of detecting a neutrino in a specific flavor state at a particular distance from its source is determined by the PMNS matrix and the distance traveled.
Deep Underground Neutrino Experiment (DUNE) [4]
The Deep Underground Neutrino Experiment (DUNE) is a cutting-edge scientific project designed to study neutrinos, their properties, and their role in the universe. It is a large-scale international collaboration involving scientists and researchers from around the world. The experiment aims to address several key questions in the field of neutrino physics, astrophysics, and cosmology.
Objective and Goals: DUNE's primary goals include investigating the fundamental properties of neutrinos, such as their masses and mixing parameters, as well as exploring the phenomenon of neutrino oscillations. Additionally, the experiment aims to study the differences in behavior between neutrinos and antineutrinos, examine potential violations of fundamental symmetries in the neutrino sector, and contribute to our understanding of astrophysical processes involving neutrinos.
Experimental Setup: DUNE comprises a state-of-the-art neutrino detector located deep underground to minimize interference from cosmic rays and other background radiation. The experiment uses a powerful particle accelerator to generate intense beams of neutrinos and antineutrinos. The accelerator, known as the Long-Baseline Neutrino Facility (LBNF), is positioned at Fermilab in the United States.
Figure 267 - Long Baseline Neutrino Facility (LBNF) at Fermilab
The neutrino beam generated at Fermilab travels over a long distance (about 1,300 kilometers) through the Earth's crust to reach the far detector, which is situated at the Sanford Underground Research Facility (SURF) in Lead, South Dakota. The distance covered by the neutrinos allows scientists to observe oscillations in the neutrino beam, providing valuable information about neutrino properties.
Figure 268 - DUNE Far Detector and Near Detector
Far Detector: The far detector at SURF is a massive liquid argon time-projection chamber (LArTPC), a type of detector that records the interactions of neutrinos with argon atoms. Liquid argon is an excellent medium for detecting neutrinos because it allows for precise tracking of charged particles produced in neutrino interactions. The far detector is designed to capture and analyze the subtle signals generated by neutrino interactions, enabling researchers to reconstruct the properties of the incoming neutrinos.
Figure 269 - liquid argon time-projection chamber (LArTPC)
Neutrinos and dark matter
The role of neutrinos in dark matter remains a topic of speculation and active research in the scientific community. Neutrinos and dark matter are distinct entities, but certain theoretical frameworks propose potential connections between them. Here are some aspects of the ongoing discussions regarding the role of neutrinos in dark matter:
Neutrinos as Dark Matter Candidates:
While neutrinos themselves are unlikely to constitute all of dark matter due to their small mass and high abundance, they are considered one of the candidate particles for a fraction of the dark matter content.
The term "hot dark matter" refers to particles with masses like neutrinos, which are light compared to other dark matter candidates.
Common Origin in the Early Universe:
Some theoretical models suggest that neutrinos and dark matter particles may have shared a common origin during the early moments of the universe's evolution.
The extremely high temperatures and energies during this early period might have given rise to both neutrinos and specific types of dark matter particles.
Seesaw Mechanism:
The seesaw mechanism, originally proposed to explain the small mass of neutrinos, introduces the idea of right-handed neutrinos. If these right-handed neutrinos exist, they could play a role in mediating interactions between neutrinos and dark matter.
The seesaw mechanism suggests a hierarchical structure of masses, where the mass of one type of particle (e.g., neutrinos) is inversely proportional to another type (e.g., right-handed neutrinos or heavy dark matter particles).
Neutrino Oscillations and Dark Matter Interactions:
Neutrino oscillations, observed in experiments, indicate that neutrinos have mass. Some theories propose that interactions with dark matter could influence neutrino oscillation patterns.
The deviation from expected oscillation patterns could serve as indirect evidence of neutrino-dark matter interactions.
Experimental Challenges:
Experimentally verifying the role of neutrinos in dark matter poses significant challenges. The masses of neutrinos are extremely small, and the masses of potential dark matter candidates are uncertain and could span a wide range.
Detecting interactions between neutrinos and dark matter, especially if the dark matter particles are heavy, requires innovative experimental approaches.
Future Prospects:
Ongoing and upcoming experiments, such as upgrades to neutrino detectors and advancements in dark matter searches, may provide more insights into the connection between neutrinos and dark matter.
Precision measurements and improved theoretical models are essential for advancing our understanding of the possible interplay between these two fundamental components of the universe.
Near Detector: In addition to the far detector, DUNE includes a near detector located closer to the source of the neutrino beam at Fermilab. The near detector helps scientists characterize the initial properties of the neutrino beam before it undergoes oscillations. By comparing the data from the near and far detectors, researchers can enhance the precision of their measurements and reduce uncertainties related to the neutrino beam.
International Collaboration: DUNE is a global collaboration involving scientists from more than 30 countries. The international nature of the project allows researchers to pool their expertise, resources, and diverse perspectives to address complex scientific questions related to neutrinos.
Literature
Exploring the Quantum Universe. Pathways to innovation and discovery in Particle Physics (OLN B058)
Neutrino map of the Milky Way [5]
The IceCube Neutrino Observatory has unveiled the first map of the Milky Way in neutrinos, revealing a diffuse haze of cosmic neutrinos emanating from throughout the galaxy. The map, published in Science, surprisingly shows no individual sources standing out. Previous research connected cosmic neutrinos to an individual source in an active galaxy called NGC 1068.
The findings open up possibilities for using neutrinos as a probe of fundamental physics, testing the Standard Model of particle physics and quantum descriptions of gravity. While identifying some cosmic neutrino sources is a significant step, the processes generating these particles around supermassive black holes remain unclear.
The IceCube observatory, with its kilometer-long strings of detectors in Antarctic ice, has been crucial in detecting and analyzing cosmic neutrinos. The study resolves a longstanding dispute between gamma-ray bursts and active galaxies as potential sources of cosmic neutrinos, favoring the latter.
Figure 270 - Neutrino map of the Milky Way
How it works :
The IceCube Neutrino Observatory has identified two active galactic nuclei (AGNs), TXS and NGC 1068, as the brightest sources of cosmic neutrinos in the sky. However, these AGNs exhibit differences, with TXS being a blazar that shoots high-energy radiation directly toward Earth, while NGC 1068 lacks a visible jet. This disparity suggests diverse mechanisms within active galaxies may produce cosmic neutrinos. The exact process in NGC 1068 remains unknown, with speculation about surrounding material obstructing gamma ray emissions during neutrino production. The origin of cosmic neutrinos within the Milky Way adds complexity, as there are no clear sources of high-energy particles, prompting speculation about cosmic rays from a previous active phase of the galaxy. The new neutrino-based sky image highlights the intense brightness of sources like NGC 1068 and TXS, overshadowing the Milky Way, and astrophysicists aim to use these distant sources to investigate dark matter, quantum gravity, and new neutrino behavior theories.
Impact to Fundamental Physics :
Neutrinos, elusive particles that deviate from the predictions of the Standard Model, provide unique insights into particle physics. While the Standard Model accurately describes most particles, it fails in predicting that neutrinos are massless. Neutrinos, discovered in 1998 to undergo shape-shifting between three types, offer a distinct perspective on oscillatory behavior when originating from active galactic nuclei (AGNs). These distant sources allow physicists to examine neutrino oscillations across vast distances, providing a sensitive probe beyond the Standard Model.
Cosmic neutrino studies may reveal deviations in oscillation patterns, challenging existing models. Additionally, interactions with dark matter or the quantum structure of space-time could impact neutrinos during their long intergalactic journeys. Physicists are exploring these possibilities, with some suggesting hints of space-time effects in IceCube data. Improved particle identification is crucial for more accurate observations.
Researchers aim to enhance neutrino detection capabilities by upgrading the IceCube observatory, expanding it to 10 cubic kilometers. Another detector in Siberia has observed cosmic neutrinos, and KM3NeT, a network of neutrino detectors in the Mediterranean, is being deployed for a complementary view of cosmic neutrinos. The collective effort seeks to unravel the mysteries of cosmic neutrinos, offering potential clues to dark matter, quantum gravity, and new physics beyond the established models.
Online Library
References
[1] Wikipedia
[2] Ripples In Cosmic Neutrino Background Measured For The First Time. Royal Astronomical Society (RAS). Phys.org June 2005
[3] Pagliaroli, Giulia; Vissani, Francesco; Costantini, Maria Laura; Ianni, Aldo (2009). "Improved analysis of SN1987A antineutrino events". Astroparticle Physics. 31 (3): 163–176. arXiv:0810.0466. Bibcode:2009APh....31..163P. doi:10.1016/j.astropartphys.2008.12.010. S2CID 119089069
[4] Source : Fermilab. LBNF/DUNE gears up for next stage of construction in South Dakota. Diana Kwon. July 2023
[5] Sources :
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IceCube Collaboration,Science380, 1338–1343 (2023)30 June 2023
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A New Map of the Universe, Painted With Cosmic Neutrinos. Quanta Magazine. Thomas Lewton. June 2023
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Evidence for neutrino emission from the nearby active galaxy NGC 1068. SCIENCE 3 Nov 2022. Vol 378, Issue 6619 pp. 538-543 DOI: 10.1126/science.abg3395
[6] Dan Hooper. At the Edge of Time, Exploring the mysteries of our universe’s first seconds. Princeton University Press (2019)