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Introduction à la Physique des Particules
Eric Kajfasz (CPPM - 308)
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Qu’est-ce que la p.d.p.? ESSAYER de decouvrir les constituents fondamentaux de ce qui compose notre Univers ESSAYER d’apprehender et de formaliser les lois qui regissent les interactions de ces constituents deux approches complementaires: Theorique qui fournit des modeles expliquant les donnees connues des generalisations pour tenter d’unifier des phenomenes apparemment sans rapport (e.g. E et B) Experimentale: verifie les predictions des modeles theoriques fournit de nouvelles donnees pour affiner les modeles ou en elaborer de nouveaux tente de mettre en defaut les modeles disponibles deux terrains d’etude: etudier les particules qui nous entourent: rayons cosmiques, neutrinos solaires ou de supernovae, ... => experiences hors accelerateurs produire des particules et les etudier en laboratoire: => experiences aupres d’accelerateurs
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Review of Special Relativity and Relativistic Kinematics
Space and time form a Lorentz four-vector The spacetime point which describes an event in one inertial reference frame and the spacetime point which describes the same event in another inertial reference frame are related by a Lorentz transformation. Energy and momentum form a Lorentz four-vector we call the four-momentum. The four-momentum of an object in one inertial frame is related to the four-momentum in another inertial frame by a Lorentz transformation. Energy and momentum are conserved in all inertial frames.
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Some Notations The components of a four vector will be denoted by
Lorentz Transformation
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Lorentz Invariants We define the covariant vector in terms of the components of its cousin, the contravariant vector The dot product of two four vectors a and b is defined to be: By explicit calculation, we can find that a·b is Lorentz invariant, i.e., a'·b'=a·b
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An Example, Muon Decay We are going to watch a muon () decay. In its own rest frame, this will take 10-6 seconds. In the laboratory, let the muon move with which gives In the rest frame of the muon, the laboratory is moving with In its own rest frame,it is born at and it dies at with seconds. In the laboratory we calculate its birth and death times From which we calculate the lifetime in the laboratory seconds
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Four-momentum We denote the four-vector corresponding to energy and momentum Because we expect this to be a Lorentz four-vector, should be Lorentz invariant. We do the calculation for the general case, and then specialize to the center-of-momentum frame (where the object is at rest, so has momentum zero). If we do not set
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Four-momentum, continued
The equation was “derived” assuming that a particle at rest has zero momentum. But what about a particle with no mass? Classically, the less mass a particle has, the lower its momentum: , so a massless particle would have zero momentum. Relativistically, this is no longer true. A massless particle can have any energy as long a , in which case we can satisfy for any value of For a particle at rest with mass m we can find the energy and momentum in any other inertial frame using a Lorentz transformation (note: if the particle is moving with velocity in the direction, the laboratory is moving in the direction according to the particle): E
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“Classical” Limits
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What we can measure in the Laboratory
We measure momenta of charged tracks from their radii of curvature in a magnetic field: Cerenkov light and specific ionization depend directly on the speed of a particle, .
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Conservation of Energy and Momentum
The Lorentz transformation is a linear transformation. It can be written generally as: If conservation of energy and momentum is true if one inertial reference frame: then Conservation of momentum and energy is not required by special relativity, but it is consistent with special relativity. with ( ) L n m p 1 + 2 = 3 4
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Measuring Invariant Mass
We can measure the invariant mass of a pair (collection) of particles by measuring the energy and momentum of each, and then summing to get the four-momentum of the ensemble: from which we can calculate the mass of the ensemble
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Invariant Mass Distributions
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E = h n
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Diffusion: Principe cible diffuse cible ponctuelle
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structure du proton e- p années 50-60:
Le proton a une certaine étendue dans l’espace en 1970, à plus haute énergie (20 Gev): Dans le proton, il y a des grains durs! p e-
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spin 1 + un boson de Higgs de spin 0 spin 1/2
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Le champs de Higgs Ou le mystère de la masse:
Dans le modèle standard, un mécanisme est introduit, appelé mécanisme de Higgs (Higgs, Brout et Englert), pour rendre compte des masses des particules. Ce mécanisme implique l’existence d’une particule supplémentaire: le boson de Higgs, à laquelle est associée un champ, le champ de Higgs. le champ de Higgs une particule le traverse:
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Le champs de Higgs Ou le mystère de la masse: la particule acquiert
sa masse rumeur: boson de Higgs: encore à découvrir!
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d u s
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Mecanisme d’echange Les particules de matière interagissent à distance en échangeant une particule de rayonnement. La portée de l’interaction diminue lorsque la masse de la particule échangée augmente.
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(h: constante de Planck)
Particules vituelles Le principe d’incertitude d’Heisenberg: x: position p: quantité de mouvement (h: constante de Planck) E: énergie t: temps Donc, pendant un temps très court, l’incertitude sur l’énergie peut être très grande! h Δx Δp ΔE Δt
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exprimee en barns, 1b = 10-24 cm2
Typiquement 3 types de mesures effectuees proprietes des particles (masse, charge, etc.) taux de desintegration (duree de vie, branching ratios) sections efficaces
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Corrections d’ordres superieurs
M = + + + + + + ...
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Le SM n’est pas la théorie ultime:
n’englobe pas la gravitation pourquoi 3 familles de fermions? ne prédit pas leur masse n’unifie pas toutes les forces Les théories de grande unification (GUT):
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