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Weak Interactions – I Weak Interactions – I Susan Gardner Department of Physics and Astronomy University of Kentucky Lexington, KY 40506 USA [email protected] Lecture 1: A survey of basic principles and features with an emphasis on low-energy probes Lecture 2: The electroweak Standard Model — and interpreting it as an effective field theory How “Weak” is the Weak Interaction? We know of four fundamental interactions: electromagnetic, strong, weak, and gravitational. Let’s set gravity aside and focus on the others. Particles of comparable mass can have very different lifetimes. + + + −8 π ! µ νµ [99.98% of all π decays] ; τπ+ ∼ 2:6 · 10 s 0 0 −17 π ! 2γ [98.8% of all π decays] ; τπ0 ∼ 8:4 · 10 s: jgemj2 Γ / τ −1 =) eff ∼ 108 =) jgemj ∼ 104jgweak j weak 2 eff eff jgeff j whereas ρ0 ! π+π− [∼ 100% of all ρ0 decays] ρ0 ! µ+µ− [∼ 4:6 · 10−5 of all ρ0 decays] jgemj2 =) eff ∼ 4 · 10−5 =) jgstr j ∼ 102jgemj str 2 eff eff jgeff j Conclude weak interaction is ∼ 106 times weaker than the strong interaction! S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 2 Building a “Standard Model” A first thought: perhaps we can describe all 3 interactions independently? What precepts should we impose? A list circa 1980: Particle Content (i.e., 3 generations of quarks and leptons) Symmetries CPT (and Lorentz) Symmetry Gauge Symmetry (SU(3)×...×...) Unitarity Renormalizability This makes our theory predictive even as E ! 1! It is “UV complete”! This line of thinking ultimately yields a SU(3)c × SU(2)L × U(1)Y gauge theory we call the Standard Model (SM). It is predictive — and successful — once all its parameters are fixed. In 2015 the existence of known unknowns (e.g., dark matter) is now definite. Perhaps we can describe these new features within the context of a theory with a SM-like gauge symmetry? Let’s take just “baby steps” beyond the SM! S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 3 on Effective Field Theory To explain phenomena at some fixed energy scale, we need only include the degrees of freedom operative at that energy scale. E.g., we can predict the outcome of chemical reactions without understanding how the electron gets it mass! A simple application of effective field theory: “Why is the sky blue?” Here we consider low-energy scattering of photons from neutral atoms 2 −1 Eγ ∆E ∼ α me a0 ∼ meα Matom The low-energy interactions of the atom ( ) are fixed by symmetry: gauge and P and C invariance.... 3 y µν Lint = c1a0 Fµν F + ::: 3 with the a0 factor fixed by common sense and “power counting” so that µν c1 ∼ O(1).(dim[ ] = 3=2 and dim[F ] = 2) 3 2 6 4 Thus A ∼ c1a0Eγ =) σ ∼ a0Eγ [~ = c = 1] and we conclude that blue light is scattered more strongly than red light! Thus a theory need not be “UV complete” to be predictive. Through identifying traces of new physics at low energy we hope to identify the nature of E ! 1 physics! We return now to the path that led to the rise of the SM.... S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 4 The Discrete Symmetries – C, P, and T In particle interactions, can we tell... Left from Right? (P) Positive Charge from Negative Charge? (C) Forward in Time from Backward in Time? (T) Matter from Antimatter? (CP) If we “observed” a box of photons at constant temperature T ∼ me, interacting via electromagnetic forces, the answer would be No. − e e− However, ... e+ e+ S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 5 On the Possibility of Parity Violation Context: Dirac – the existence of a magnetic monopole can explain the quantization of electric charge! [Dirac, Proc. Roy. Soc. London A 133, 60 (1931)] r · E = 4πρ ; r · B = 0 =) 4πρM Dirac also showed that the circulation of opposite magnetic monopoles in the nucleon could give rise to a nonzero electric dipole moment. [Dirac, Phys. Rev. 74, 817 (1948).] The electric dipole moment d of a nonrelativistic particle with spin S is S defined via H = −d S · E But both quantities violate P and T ! E. M. Purcell and N. F. Ramsey, “On the Possibility of Electric Dipole Moments for Elementary Particles and Nuclei,” Phys. Rev. 78, 807 (1950): The argument against electric dipoles, in another form, raises the question of parity.... But there is no compelling reason for exclud- ing this possibility.... S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 6 Discrete Symmetries — P, T, and C Parity P: Parity reverses the momentum of a particle without flipping its spin. s y s s y s y 0 PapP = a−p ; PbpP = −b−p =) P (t; x)P = γ (t; −x) Time-Reversal T : Time-reversal reverses the momentum of a particle and flips its spin. It is also antiunitary; note [x; p] = i~. s y −s s y −s y 1 3 TapT = a−p TbpT = b−p =) T (t; x)T = −γ γ (−t; x) Charge-Conjugation C: Charge conjugation converts a fermion with a given spin into an antifermion with the same spin. s y s s y s y 2 ∗ CapC = bp ; CbpC = ap =) C (t; x)C = −iγ (t; x) S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 7 The Weak Interactions Violate Parity There is a “fore-aft” asymmetry in the e− intensity in 60Co~ β-decay.... [Wu, Ambler, Hayward, Hoppes, and Hudson, Phys. Rev. 105, 1413 (1957); note also Garwin, Lederman, and Weinrich, Phys. Rev. 105, 1415 (1957); http://focus.aps.org/story/v22/st19 .] Schematically ν e e + + 60 60 * ν Co Ni e e (J=5) (J=4) ~ J·~pe Ie(θ) = 1 − Ee P is violated in the weak interactions! BothP andC are violated “maximally” + + + + Γ(π ! µ νL) 6= Γ(π ! µ νR) = 0 ; P violation + + − − Γ(π ! µ νL) 6= Γ(π ! µ νL) = 0 ; C violation S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 8 The “Two-Component” Neutrino A Dirac spinor can be formed from two 2-dimensional representations: L = R In the Weyl representation for γµ, µ −m i(@0 + σ · r) L (iγ @µ − m) = = 0 i(@0 − σ · r) −m R If m=0, L and R decouple and are of definite helicity for all p. Thus, e.g., i(@0 − σ · r) L(x) =) E L = −σ · p L σ · p^ L = − L ¯ y 0 Note L ≡ Lγ transforms as a right-handed field. Experiments =) No “mirror image states”: neither νL nor νR exist. Possible only if the neutrino is of zero mass. S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 9 The Weak Interactions Can Also Violate CP CP could be a good symmetry even ifP andC were violated. Schematically ν + e CP e ν e e + + − − Γ(π ! µ νL) = Γ(π ! µ νR); CP invariance! Weak decays into hadrons, though, can violate CP. There are “short-lived” and “long-lived” K states: 1 0 0 + − KS ∼ p (K − K ) ! π π (CP even) 2 1 0 0 + − 0 KL ∼ p (K + K ) ! π π π (CP odd) 2 However, KL ! 2π as well! KS and KL do not have definite CP! [Christenson, Cronin, Fitch, Turlay, PRL 13, 138 (1964).] S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 10 Matter and Antimatter are Distinguishable 0 ¯ 0 + − 0 ¯ 0 The decay rates for K ; K ! π π and B ; B ! J= KS are appreciably different. [I.I. Bigi, arXiv:0703132v2 and references therein.] S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 11 All Observed Interactions Conserve CPT The CPT Theorem Any Lorentz-invariant, local quantum field theory in which the observables are represented by Hermitian operators must respect CPT. [Pauli, 1955; Lüders, 1954] Coda: CPT violation implies Lorentz violation. [Greenberg, PRL 89, 231602 (2002)] CPT =) the lifetimes, masses, and the absolute values of the magnetic moments of particles and anti-particles are the same! Note, e.g., jM 0 − M ¯ j K K0 < 6 × 10−19 @90% CL Mavg jM − M¯j p p < 7 × 10−10 @90% CL Mp Thus CP $ T violation. Tests of CPT and Lorentz invariance are ongoing. e.g., ATRAP Collaboration, arXiv:1301.6310, “... For the first time a single trapped p¯ is used to measure the p¯ magnetic moment µp¯. ... The 4.4 parts per million (ppm) uncertainty is 680 times smaller than previously realized. Comparing to the proton moment measured using the same method and trap electrodes gives µp¯/µp = −1:000 000 ± 0:000 005 to 5 ppm, for a proton moment µp = µpS=(~=2), consistent with the prediction of the CPT theorem.” S. Gardner (Univ. of Kentucky) Weak Interactions – I FNP Summer School, UTK, 6/15 12 Transformations of Lorentz Bilinears under P, T, and C Notation: ξµ = 1 for µ = 0 and ξµ = −1 for µ 6= 0. 5 0 1 2 3 µν i µ ν γ ≡ iγ γ γ γ ; σ ≡ 2 [γ ; γ ] µ µ µν ¯ i ¯γ5 ¯γ ¯γ γ5 ¯σ @µ SPVAT P +1 −1 ξµ −ξµ ξµξν ξµ T +1 −1 ξµ ξµ −ξµξν −ξµ C +1 +1 −1 +1 −1 +1 CPT +1 +1 −1 −1 +1 −1 S is for Scalar P is for Pseudoscalar V is for Vector A is for Axial-Vector T is for Tensor All scalar fermion bilinears are invariant under CPT.
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