Francis Halzen is the principal investigator of the IceCube project, and Hilldale and Gregory Breit Professor in the Department of Physics at the University of Wisconsin–Madison. DNA Deoxyribonucleic acid (the genetic basis of life) DONUT Direct observation of the”¿ (experiment at Fermilab) DSA Diffusive shock acceleration (of cosmic rays).
Understanding the Universe: Cosmology, Astrophysics, Particles, and Their
Interactions
Particle and Astroparticle Physics
This model was clearly rejected by Rutherford, who showed in the early twentieth century that the positive charges should be concentrated in a very small nucleus. That is the domain and ambition of the new field of fundamental physics, astroparticle physics.
Particles and Fields
The antineutronn¯ is the antiparticle of the neutron (note the different quark composition of the two). In the quantum mechanical view of interactions, the interaction itself is mediated by quanta of the force field.
The Particles of Everyday Life
Particles in current theory are intrinsically massless, and it is their interaction with the Higgs field that causes their mass: the physical properties of particles are related to the properties of the quantum vacuum. Last but not least, a "field particle" is fundamental to our daily lives: the quantum of electromagnetic radiation, the photon (γ).
The Modern View of Interactions: Quantum Fields and Feynman Diagramsand Feynman Diagrams
Associated with Feynman's diagrams are mathematical rules (called "Feynman's rules") that enable the calculation of the probability (quantum mechanically, the square of the absolute value of the amplitude) that a given reaction occurs; we will describe the quantitative aspects in detail in Chapters 6 and 7. Feynman's rules allow the association at each vertex of a multiplication factor that contributes to the total "amplitude"; the probability of a process is proportional to the square of the amplitude.
A Quick Look at the Universe
Dark energy contributes to the total energy budget of the Universe three times more than dark matter. The evolution of the Universe and our daily lives depend on this unknown external world.
Cosmic Rays
The ultimate driver of cosmic ray acceleration is thought to be gravity. We define as galactic longitude (lorλ) the angle between the projection of the object in the galactic plane and the primary direction.
Multimessenger Astrophysics
The sources are marked as circles - the colors represent the different types of emitters, which will be explained in Chapter 10. In the last decade, astrophysical neutrino detection, especially gravitational wave detection, has allowed us to learn about objects that were invisible to other astronomical methods, such as systems with merging black holes.
Further Reading
The new observations opened the way for a new field of research called multimessenger astrophysics: the combination of information obtained from the detection of photons, neutrinos, charged particles and gravitational waves can shed light on completely new phenomena and objects.
Exercises
The universe. Find a dark place near where you live and go there at night. Galactic and extragalactic emitters of gamma rays. In fig. 1.12 more than half of the emitters of high-energy photons lie in the galactic plane (the equatorial line).
Basics of Particle Physics
The Atom
Mendeleev's periodic table has been expanded and refined with the discovery of new elements and a better theoretical understanding of chemistry. Thanks to Mendeleev's table, a solid conjecture was formulated that atoms are compound states, including protons and loosely bound electrons.
The Rutherford Experiment
But how to experimentally understand the internal structure of the atom; i.e. how were protons and electrons arranged inside the atom. The result of the observation was that about 1 in 8000α particles were deflected at very large angles (greater than 90◦).
Inside the Nuclei: β Decay and the Neutrino
It was not until 1956 that Reines and Cowan proved the existence of neutrinos and placed a water tank near a nuclear reactor. The mass of the neutrino is indeed very small (but not equal to zero, as was found at the end of the twentieth century by observing fluctuations between neutrinos of different families, a phenomenon that is only possible if the neutrinos have a mass different from zero) and is determined by the maximum energy that it may have an electron in beta decay (the end point of the energy spectrum).
A Look into the Quantum World: Schrödinger’s EquationEquation
- Properties of Schrödinger’s Equation and of its SolutionsSolutions
- The Meaning of Wavefunctions
- Measurement and Operators
- Dirac Notation
- Good Operators Must be Hermitian
- Time-Independent Schrödinger’s Equation
- Time Evolution of Expectation Values
- Probability Density and Probability Current; Continuity Equation
- Uncertainty Relations
- Uncertainty and the Scale of Measurements
The solutions of the equation are generally complex wave functions, which can be seen as probability density amplitudes (probability is the square of the modulus of the amplitude). The time evolution of the expectation value of a measurement described by a Hermitian operator Aˆ is given by the equation.
The Description of Scattering: Cross Section and Interaction Lengthand Interaction Length
- Total Cross Section
- Differential Cross Sections
- Cross Sections at Colliders
- Partial Cross Sections
- Interaction Length
Since one can only extract a finite energy from finite regions of the Universe (and perhaps the Universe itself has a finite energy), there is an intrinsic limit to the investigation of the structure of matter, below which the quest no longer doesn't make sense. The maximum energy achievable by man-made accelerators is believed to be of the order of the PeV. In this simplified model, we neglect the interactions between the scattered particles, the interactions between beam particles, the binding energies of the target particles, the absorption and the multiscattering of the beam within the target.
Description of Decay: Width and Lifetime
For this reason, to study the interaction between cosmic particles on their path in the atmosphere, the relevant quantity is not the path length, but rather the amount of matter that has been traversed. In a rough approximation, the atmosphere is isothermal; under this hypothesis, its depthxin g cm−2 varies exponentially with height(km), according to the formula. Therefore, all the Breit-Wigner functions related to the decays of the same particle have the same widthΓt, but different normalization factors, which are proportional to the proportion of the decays in each specific channel, also called the branching ratio.
Fermi Golden Rule and Rutherford Scattering
- Transition Amplitude
- Flux
- Density of States
- Rutherford Cross Section
The density of final states ρ(Ei) is determined by the dimension of the normalization field. At the boundaries of the box, the wave function should be zero, so in the case of free particles only harmonic waves are possible. In the special case of Rutherford's experiment (α particles with a kinetic energy of 7.7 MeV against gold foil), λdminand happens to be a valid classical approximation.
Particle Scattering in Static Fields
- Extended Charge Distributions (Nonrelativistic)
- Finite Range Interactions
- Electron Scattering
In the case of the proton, the differential cross section at low transverse momentum is described by such a formula, and the shape factor is given by the dipole formula. The size of the proton is then determined on the scale of 1 fm. The scalea =1 fm corresponds to the size of nucleons, and the mass of the exchanged particle comes to M 200 MeV/c2 (see Section 2.10 for the conversion).
Special Relativity
- Lorentz Transformations
- Tensors
- An Example: The Metric Tensor
- Covariant Derivatives
- Space–Time Interval
- Velocity Four-Vector
- Energy and Momentum
- Examples of Relativistic Dynamics
- Decay
- Elastic Scattering
- Mandelstam Variables
- Lorentz Invariant Fermi Rule
- The Electromagnetic Tensor and the Covariant Formulation of ElectromagnetismFormulation of Electromagnetism
They are closely related to the invariance of physical laws regarding temporal and spatial translations. In the same way, the kinetic energy Kof a body is still the result of the work W done on that body. The laws of conservation of momentum and energy in a collision can be written together as an equation for the conservation of four momentums:.
Natural Units
LHC collisions.√ The LHC run parameters in 2012 were, for a c.m. energy s 8 TeV: number of bundles=1400; time interval between bursts50 ns;. number of protons per bundle1.1×1011; beam width at the crossing point 16µm. a) Determine the maximum instantaneous luminosity of the LHC in 2012. Classical momentum is not conserved in special relativity. Consider the completely inelastic collision of two particles, each of mass m, in their c.m. the two particles become one particle at rest after the collision). Three-body decay. Consider the decay K+→π+π+π−. a) the minimum and maximum values for π−energy and momentum in the K+ rest system;.
Cosmic Rays and the Development of Particle Physics
The Puzzle of Atmospheric Ionization and the Discovery of Cosmic RaysDiscovery of Cosmic Rays
- Underwater Experiments and Experiments Carried Out at Altitudeat Altitude
- The Nature of Cosmic Rays
During the first decade of the twentieth century, several researchers in Europe and in the New World presented progress in the study of ionization phenomena. Under the hypothesis that most of the radiation was of terrestrial origin, he expected the ionization rate to be significantly smaller than the value on the ground. A key experiment on the nature of cosmic rays was the measurement of the intensity variation with geomagnetic latitude.
Cosmic Rays and the Beginning of Particle Physics
- Relativistic Quantum Mechanics and Antimatter: From the Schrödinger Equation to the Klein–Gordon andthe Schrödinger Equation to the Klein–Gordon and
- The Klein–Gordon Equation
- Hole Theory and the Positron
- The Discovery of Antimatter
- Cosmic Rays and the Progress of Particle Physics
- The μ Lepton and the π Mesons
- The Neutral Pion
- Strange Particles
- The τ - θ Puzzle
- Mountain-Top Laboratories
In addition, solutions to the Klein–Gordon equation do not allow for statistical interpretation. In the late 1920s, Bothe and Kolhörster introduced the coincidence technique for studying cosmic rays with a Geiger counter. It became clear that it would be appropriate to equip mountaintop laboratories for the study of cosmic rays.
Particle Hunters Become Farmers
Particle physicists used cosmic rays as the main tool for their research until the appearance of particle accelerators in the 1950s, so the pioneering results in this field are due to cosmic rays. It should be noted that despite the great advances in accelerator technology, higher energies will always be reached by cosmic rays. The founding fathers of CERN in their Constitution (Convention Establishing the European Organization for Nuclear Research, 1953) explicitly stated that cosmic rays are one of the Laboratory's research objects.
The Recent Years
Thus, cosmic rays and cosmological sources are again central to highly energetic particle and gravitational physics. This was the subject of Schrödinger's dissertation in Wien in the early twentieth century. Very high energy neutrinos. The IceCube experiment at the South Pole can detect neutrinos crossing Earth from the North Pole.
Particle Detection
Interaction of Particles with Matter .1 Charged Particle Interactions.1Charged Particle Interactions
- High-Energy Radiation Effects
- Cherenkov Radiation
- Transition Radiation
- Range
- Multiple Scattering
- Photon Interactions
- Photoelectric Effect
- Compton Scattering
- Pair Production
- Rayleigh Scattering and Photonuclear Interactions
- Comparison Between Different Processes for Photons
- Nuclear (Hadronic) Interactions
- Interaction of Neutrinos
- Electromagnetic Showers
- Hadronic Showers
The average fractional energy loss by radiation for an electron with high energy (Emec2) is approximately independent of the energy itself and can be described by Let Ebe be the energy of the primary photon (corresponding to a wavelength λ) and assume that the electron is initially free and at rest. As in the case of the photoelectric effect, the ejected electron can be detected (possibly after multiplication) by a suitable sensor.
Particle Detectors
- Track Detectors
- Cloud Chamber and Bubble Chamber
- Nuclear Emulsions
- Ionization Counter, Proportional Counter and Geiger–Müller Counter
- Wire Chamber
- Streamer Chamber and Spark Chamber
- Drift Chamber
- Semiconductor Detectors
- Scintillators
- Resistive Plate Chambers
- Comparison of the Performance of Tracking Detectors
- Photosensors
- Photomultiplier Tubes
- Solid-State Photon Detectors
- Cherenkov Detectors
- Transition Radiation Detectors
- Calorimeters
- Electromagnetic Calorimeters
- Hadronic Calorimeters
The electrical signal of the wire can be amplified and read using an ammeter. The strips of two layers should be placed in perpendicular directions (let's call them horizontal and vertical). It can be assumed that the energy of the incident particles is proportional to the number of charged particles.
High-Energy Particles
- Artificial Accelerators
- Acceleration Methods
- Parameters of an Accelerator
- Cosmic Rays as Very-High-Energy Beams
The center-of-mass energyECM sets the scale for the maximum mass of the particles we can produce (the actual value of the available energy is generally smaller due to limitations related to conservation laws). However, colliding two beams is not trivial: one has to control the fact that the beams tend to defocus due to mutual repulsion of the particles. In a collider, the brightness is proportional to the product of the number of particles,n1and2,in the two beams.
Detector Systems and Experiments at Accelerators
- Examples of Detectors for Fixed-Target Experiments
- The European Hybrid Spectrometer at the SPS
- LHCb at LHC
- Examples of Detectors for Colliders
- UA1 at the Sp pS ¯
The first detectors along the beamline should be non-destructive; at the end of the beamline one can have calorimeters. They are designed to cover most of the solid angle around the point of interaction (a limitation is given by the presence of the beam pipe). In the standard coordinate system, the z-axis is in the direction of the radius, the x-axis points to the center of the ring, and the axis points upwards.
DELPHI
- DELPHI at LEP
- CMS at LHC
- ATLAS at LHC
- Cosmic-Ray Detectors
- Interaction of Cosmic Rays with the Atmosphere
- Detectors of Charged Cosmic Rays
The hadronic interaction length in air is about 90 g/cm2 for protons (750 m for air at NTP), being shorter for heavier nuclei - the dependence of the cross section on mass number is approximately A2/3. 16 In the isothermal approximation, the depth of the atmosphere at a height (ie, the amount of atmosphere above) can be approximated as. Since the internal angular spread of charged particles in an electromagnetic shower is about 0.5◦ , the opening of the light cone is dominated by the Cherenkov angle.
