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Elementarteilchenphysik

Elementarteilchenphysik. Antonio Ereditato LHEP University of Bern. Lesson on: Invariance principles (3) Exercises: spin and parity of pions. Invariance, conservation, parity. Invariance of states under operations (operators) implies conservation laws

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Elementarteilchenphysik

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  1. Elementarteilchenphysik Antonio Ereditato LHEP University of Bern Lesson on: Invariance principles (3) Exercises: spin and parity of pions A.Ereditato SS 2008

  2. Invariance, conservation, parity • Invariance of states under operations (operators) implies conservation laws • Example: invariance of energy under space translation  momentum conservation (dp/dt=0) • invariance of energy under space rotation  angular momentum conservation (dJ/dt=0) • Global and discrete operations: e.g. translation r  r+r is global, reflection through the origin of coordinates: x, y, z  -x, -y, -z is discrete. This is the parity operation: • P2 = 1 (P is unitary operator) and its eigenvalues (if any) are ±1 (the parity of the system) • Parity is a multiplicative quantum number: if  =  +  then P = P x P A.Ereditato SS 2008

  3. The hydrogen atom with a potential V(r) = V(-r) must have a well defined parity Its wave-functions are the product of radial and angular functions (spherical harmonics): Electric dipole transitions with photon emission have l= ± 1. In order to conserve the parity of the global system (atom + photon) the latter must have NEGATIVE PARITY. Parity IS FOUND to be conserved in EM and strong interactions, but not in weak interactions (see later) • The “intrinsic” parity of the proton and of the neutron are assumed by convention +1 (baryons are conserved) • The “intrinsic” parity of the charged pion is -1: from an experiment on - + d  n + n • While pions can be created singly, particles carrying “strange quarks” are created in pairs, whose parity is -1 Link between the total angular momentum of a particle: J = L + Sand the parity: J P =0+ scalar particle J P =0- pseudoscalar particle J P =1- vector particle J P =1+ axial-vector particle A.Ereditato SS 2008

  4. Examples: scalar pseudoscalar vector axial-vector Parity of a meson with no angular momentum Meson with angular momentum Baryon with angular momentum Anti-baryon with angular momentum A.Ereditato SS 2008

  5. Charge conjugation (C): discrete transformation that reverses sign of electric charge and magnetic moment: Maxwell equations are invariant for C. C implies change from particle to anti-particle. Strong and EM interactions are C-invariant C-parity eigenvalues are ± 1 i.e. charged pions are not C eigenstates, while The photon has C-parity -1 Therefore: The 0 decay in 3 photons occurs at the level of 10-8 w.r.t. the decay in 2 photons, because EM interactions are C-invariant Charge conjugation A.Ereditato SS 2008

  6. Weak interactions are not C-invariant: (RH neutrinos do not exist) But, if we apply both P and C operations (CP transformation): Existing LH neutrino However, as we will see later on, CP is violated at the level of 10-4 If we also apply the time reversal transformation (T), the CPT theorem tells us that all interactions are invariant under CPT transformation. The theorem is based on very general assumptions. It can be verified by comparing the properties of particles and antiparticles, e.g.: A.Ereditato SS 2008

  7. Isospin symmetry Proton and neutron are different states of the nucleon, with the quantum number of ISOSPIN (I = 1/2) Heisenberg Complete analogy with the quantum number of spin. Strong interactions conserve isospin (I) and do not depend on I3: do not distinguish p from n • Observed equivalence of n-p, n-n, p-p forces once EM effects are subtracted (the proton is heavier than the neutron thanks to the energy needed to “bring” electric charge on the proton) • The isospin symmetry is transferred from the p-n equality to the quark level u-d their nearly mass equality is the source of the isospin symmetry • Therefore, the symmetry extend to all baryons and mesons that are associated by u-d quark exchange Mass of + and - (equal for C-symmetry): 140 MeV Mass of 0: 135 MeV A.Ereditato SS 2008

  8. EM and weak interactions do not conserve I A.Ereditato SS 2008

  9. (its conservation implies the stability of matter: no proton decay) We remind that baryon number is With Y = B + S defined as hypercharge Isospin, strangeness and hypercharge There is a compact way to express the relation between electric charge, third component of the isospin and baryon number: If we also include the other quantum number associated to the s quark (strangeness S): Where does S come from ?? A.Ereditato SS 2008

  10. ‘Stange” particles are produced in pair (S = 0) via strong interaction (Pais, associated production, 1952) but they decay weakly (S = ±1) A.Ereditato SS 2008

  11. A.Ereditato SS 2008

  12. Associated production of a ss quark pair, weak decay of the s (s) quark Strangeness is conserved in strong and EM interactions, not in weak processes strong EM weak weak A.Ereditato SS 2008

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