Elementarteilchenphysik. Weak interaction

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1 Elementarteilchenphysik Antonio Ereditato LHEP University of Bern Weak interaction 1

2 Weak Interaction Weak interaction is the only interaction that does not produce fermion bound states: weakness and short range Link with lepton flavor conservation Characteristic feature: neutrinos quasi point-like interaction mediated by three massive bosons: W + W - Z 0 Charged Current (CC) reactions: mediated by a W; Neutral Currents (NC) mediated by Z Three types of weak reactions: leptonic, semileptonic, non leptonic First theory of weak interaction: Fermi (circa 1930, after the hypothesis of the neutrino by Pauli) (Address NC reactions later, in the context of the electroweak unification theory) 2

3 Lepton number conservation 3

4 Examples of charged current weak interaction processes Leptonic neutral current Semleptonic Non leptonic 4

5 More charged current weak interactions Electron capture Inverse beta decay 5

6 4-fermion interaction (Fermi) d ν e g g 1 q 2 + M W 2 u e - n ν e p G =10 5 GeV 2 e - f (q 2 ) = g 2 q M (W,Z ) G = g GeV 2 2 M (W,Z ) 6

7 Lepton universality The weak coupling is the same for all leptons (e, µ, τ) but not for different quarks. Take the example of a leptonic weak process, such as muon decay: G = g2 2 M (W ) Dimensionally: G [GeV -2 ], decay amplitude G, rate G 2 Γ(µ e + ν e + ν µ) G 2 m 5 µ = g 4 µ m 5 4 µ = 1 M (W ) τ µ Remember: t[gev -1 ] # % $ g τ g µ & ( ' 4 In a similar way, the weak decay of the τ, with a branching ratio of 17.8%, gives # = m & µ % ( $ ' m τ 5 Γ(τ e + ν e + ν τ ) G 2 m τ 5 = # % $ τ µ τ τ & ' g 4 τ m 5 4 τ = 1 M (W ) τ τ ( (inserting the experimental values) g τ g µ = ± Similarly, universality holds for neutral currents (Z 0 ) 7

8 Historical link between the understanding of the β-decay and the hypothesis of the neutrino events ν Before 1930: N N + e - After 1930: N N + e - + ν m ν > 0? The β-decay problem e - energy Available energy = Δm nuclei c 2 Pauli's letter of December 4 th, 1930 Dear Radioactive Ladies and Gentlemen, As the bearer of these lines, to whom I graciously ask you to listen, will explain to you in more detail, how because of the "wrong" statistics of the N and Li6 nuclei and the continuous beta spectrum, I have hit upon a desperate remedy to save the "exchange theorem" of statistics and the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin 1/2 and obey the exclusion principle and which further differ from light quanta in that they do not travel with the velocity of light. The mass of the neutrons should be of the same order of magnitude as the electron mass and in any event not larger than 0.01 proton masses. The continuous beta spectrum would then become understandable by the assumption that in beta decay a neutron is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant. I agree that my remedy could seem incredible because one should have seen those neutrons very earlier if they really exist. But only the one who dare can win. Your humble servant W. Pauli 8

9 ! Solvay congress in Brussels (1933, after the discovery of the neutron): Fermi invented the name of neutrino! Soon after, in 1934, Fermi developed a theory of beta decay to include the neutrino, presumed to be massless as well as chargeless! The paper was published in Zeitschrift für Physik, Vol. 88, (1934) 161: Versuch einer Theorie der beta-strahlen. It had been originally rejected by Nature because: it contains speculations too remote from reality to be of interest to the reader! Treating the beta decay as a transition that depended on the strength of coupling between the initial and final states, Fermi developed a relationship which is now referred to as Fermi's Golden Rule λ if = M if 2 ρ f! However, the nature of the interaction which led to beta decay was unknown in Fermi's time (the weak interaction) 9

10 β-decay Negative beta-decay (e.g. neutron decay) Inside a nucleus (need to supply ΔE) we could have a positive beta-decay: and an electron capture The results is a different nucleus (same A, different Z): β - β + e-capture The beta-decay rate can be calculated according to the Fermi theory by means of Fermi s Golden rule. This brings to the Kurie plot, usually exploited to determine the electron-neutrino mass. 10

11 Inverse beta decay ν e + p n + e + This reaction has a kinematical threshold of 1.80 MeV, required to produce the positron at rest in the laboratory The cross section of the process is calculated from: One obtains: σ(ν e + p n + e + ) = G2 π M if 2 p 2 v i v f dσ dω (a + b c + d) = 1 4π 2 h M 4 if 2 This gives an incredibly small value: 2 ρ f v i v f σ(ν e + p n + e + ) =10 38 cm 2 E ν (GeV ) Mean free path for a 1 MeV neutrino: 50 light years of water!!! This explains why it took ~25 years from the neutrino hypothesis to the first detection of a neutrino This is balanced by the huge number of neutrinos around us: 330 neutrinos/cm 3 of Universe from the Big Bang (very low energy: 10-4 ev) Solar neutrino flux on Earth: 60 billion neutrinos/cm 2 x s Neutrinos from Supernova explosion, from cosmic-rays, from all the stars Neutrinos from Earth radioactivity and geo-neutrinos from the Earth core (30 TW power, equivalent to nuclear plants) Neutrinos from mankind (nuclear plants, accelerators) 11

12 Neutrinos and the human body Electromagnetic radiation interacts with our body depositing its energy. Due to their extremely low cross section neutrinos go through our body without interacting and releasing their energy. Thanks to this life is possible on Earth! γ ν Every second a human being is crossed by: 4 x neutrinos from the Sun 5 x neutrinos from Earth rock radioactivity x 10 9 neutrinos from all nuclear plants in the world NOTICE: the human body contains about 20 mg of Potassium 40, which is a β-emitter. Therefore, we produce 340 million neutrinos per day, that leave us at the speed of light, transmitting a signal of our presence down to the far corners of the Universe 12

13 Neutrino discovery Reines and Cowan (1956) Experiment at the Savannah River nuclear reactor (~10 20 neutrinos/s) : Pontecorvo s idea: ν e + p -> e + + n Cadmium Chloride 13

14 Inverse muon decay: i.e. how to build an accelerator neutrino beam Conceptual layout of an accelerator neutrino beam far detector near detectors absorber decay tunnel focusing magnets target 14

15 Questions (apparently not related to experimental particle physics.) 1) Suppose to communicate with an intelligent alien-being in a distant planet e.g. via radio. You can explain to him (her?) many things about our world asking him to perform experiments and to make observations and in the same way you can understand about him and his world. A problem arise when you want to explain him what is left and what is right.really?? 2) Is the world in the mirror identical to our world? 15

16 The establishment of parity violation in weak interactions In 1848 Pasteur discovered the property of optical isomerism. Two forms of the same chemical compound, isomers, were found to rotate polarized light in two different directions. Living organisms synthesize and use only one isomer and never the other. But nature itself appeared to have no preference over which form it produced. The concept of parity originated with the development of quantum mechanics. In 1924 Laporte classified the wave functions of an atom as either even or odd, depending upon the symmetry of the wave function. Laporte discovered that when in atomic transitions a photon is emitted, the wave function changes from even to odd or vice-versa. Parity is conserved in atomic transitions. If the initial wave function was odd (-1 parity), Laporte's rule asserts the final wave function must be even (+1 parity). Since the initial system has -1 parity and the final system has as its parity the product of parities of the final wave function and the parity of the emitted photon, (+1)(-1) = -1, parity is conserved in the transition. In 1927 Wigner proved that Laporte's rule was a consequence of right-left symmetry (or mirror image symmetry) of the electromagnetic force. In 1949 Powell identified a cosmic-ray particle which disintegrated into three pions. He named it taumeson. Another particle called the theta-meson was also discovered, disintegrating into two pions. Both particles decayed via weak interaction. However, the two particles turned out to be indistinguishable other than their mode of decay. Their masses and lifetimes were identical within the experimental uncertainties. The problem itself was not that the tau and theta, if they were the same particle, decayed in two different modes, one by two pions, the other by three pions. The problem dealt with the conservation of parity in weak interactions. Dalitz argued that since the pion has parity of -1, if the conservation of parity holds, they could not be the same particle. (Today we know that the tau and the theta are the same particle, the kaon, which can decay by weak interaction in two or three charged pions) 16

17 Lee Yang Wu Lee and Yang proposed in April 1956 an idea for ending the theta-tau puzzle. Their idea was that certain kinds of elementary particles occur in two forms with different parities, parity doubling. Feynman brought up the question of non-conservation of parity. Wigner also suggested that perhaps parity conservation was violated in weak interactions. Lee and Yang pursued a careful study of all known experiments involving weak interactions. After several weeks of reviewing they had come to the conclusion that past experiments on weak interactions had actually no bearing on the question of parity conservation, while there were solid proofs that parity was conserved in EM and strong interactions. On October 1st, 1956 Lee and Yang's published a paper stating: "To decide unequivocally whether parity is conserved in weak interactions, one must perform an experiment to determine whether weak interactions differentiate right from left." They proposed several experiments. One of the (conceptually) simplest involved measurements of Cobalt-60 beta-decay. Wu was the first to act on the proposed experiment involving beta decay in Cobalt 60. The experiment was very difficult: temperatures as low as one hundredth of a Kelvin were necessary to attain a high degree of spin orientations for the Cobalt nuclei. After several trials the experiment was successful on December 27th, Lederman realized that he could perform an independent test with the cyclotron in Columbia, by studying the decay of pions and muons, as also been proposed by Lee and Yang. Also this experiment showed parity violation in weak interactions. The two groups published together on on January 15th, 1957, with a press release at Columbia University. 17

18 The Wu experiment 18

19 Helicity: λ = s p / p = ± 1/2 s is a axial-vector: does not change for spatial inversion The mirror changes (e.g.) a left handed neutrino (existing in nature) into a right handed neutrino, that does not exist in nature. One is then able to distinguish our world from its mirror image: parity is not conserved in weak interactions. However, if we also apply C operation, we get a right handed antineutrino (that exists!). This implies that CP is conserved in weak interactions 19

20 Pion decay Why the pion decays into a muon and not into an electron? The fraction of left-helicity in the RH antilepton (proportional to m/e) is larger for the muon than for the electron 20

21 W and Z bosons Indirect evidence for Z (neutral currents) from the CERN Gargamelle experiment (1973) The W and Z bosons were directly observed for the first time at CERN (UA1 and UA2 experiments) in 1983 They were found thanks to the the SPS proton collider (270 GeV protons 270 GeV antiprotons) Nobel Prize to Rubbia and Van der Meer: UA1 and antiproton cooling p (uud) p (uud) u d g W - g e - ν e d (u) d (u) g Z 0 g e + (µ + ) e - (µ - ) V-A theory: only LH fermions and RH anti-fermions involved Color factor 1/3 to match quark-antiquark of color-anticolor Quark density functions to be taken into account 21

22 Mass- and weak- quark eigenstates Experimental indication of a difference in the weak coupling strength between muon and neutron decay (by 4% lower in the case of neutron decay), and in the decay rate of ΔS=1 and ΔS=0 weak reactions (factor ~20!), such as neutron decay vs Λ decay. This is in apparent contrast with the principle of universality of the weak interaction. The problem was solved by Cabibbo assuming that the states actually involved in the weak interaction processes are a linear combination (mixing) of the quark mass-eigenstates u, d, s with a mixing angle θ c (experimentally ~12.9 0, sinθ c = 0.221, cosθ c =0.974 ) Mass- and weak-eigenstates do not coincide for quarks ( u ) d cosθ c +s sinθ c 22

23 Comparison of n and Λ weak decay Proportional to cos 2 θ c = Proportional to sin 2 θ c = Good agreement with the experiments, but another problem arises 23

24 GIM mechanism and CKM matrix Experimentally, weak neutral currents follow the selection rule ΔS=0 (no flavor changing neutral currents ΔS=1): NC/CC: K + π + + ν + ν K + π 0 + µ + + ν µ <10 8 However, the Cabibbo theory, although successful, allows for ΔS=1 transitions: K + u s Z 0 u d ν ν π + u Z 0 + d cosθ c + s sinθ c Z 0 K + u s W + u u µ + π 0 u d cosθ c + s sinθ c ν µ ΔS=1 neutral current! uu + (dd cos 2 θ c + ss sin 2 θ c ) + (sd + ds)sinθ c cosθ c How to cancel the unwanted flavor changing neutral currents?? GIM mechanism, i.e. introducing a new up-like quark, the charm 24

25 1970: Glashow, Iliopoulos and Maiani (GIM) postulated the charm quark (discovered in1974) arranged with the strange quark in a second doublet, in addition to the up and down doublet ( u ) d cosθ c +s sinθ c ( c ) s cosθ c - d sinθ c ( ) " d' % " $ ' = cosθ c sinθ c % $ # s' & # sinθ c cosθ c & ' " $ d% # s ' & 25

26 u Z 0 + d cosθ c + s sinθ c Z 0 + c Z 0 + s cosθ c - d sinθ c Z 0 u d cosθ c + s sinθ c c s cosθ c - d sinθ c uu + cc + (dd + ss )cos 2 θ c + (ss + dd)sin 2 θ c ΔS = 0 + (sd + sd sd sd) sinθ c cosθ c ΔS = 1 The discovery of the other quark bottom led to a natural extension of the 2x2 matrix and to the prediction of the 6 th up-like quark (top). Cabibbo-Kobayashi-Maskawa 3x3 unitary matrix Rotation matrix in 3D space " d' % " V ud V us V ub %" d% $ ' s' $ ' = $ ' $ ' V cd V cs V cb s $ ' $ ' # b' & # V td V ts V tb &# b& 3 angles and one phase The phase can introduce CP violation Elements determined by experiments, e.g. studying the decay of heavy quarks (V ub from b u decays, etc.) Exploit unitarity condition: Σ j V ij 2 =1 Diagonal terms close to 1: t b, c s and u d 26