Fundamental Symmetries - 2
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1 HUGS 2018 Jefferson Lab, Newport News, VA May 29- June Fundamental Symmetries - 2 Vincenzo Cirigliano Los Alamos National Laboratory
2 Plan of the lectures Review symmetry and symmetry breaking Introduce the Standard Model and its symmetries Beyond the SM: hints from current discrepancies? effective theory perspective Discuss a number of worked examples Precision measurements: charged current (beta decays); neutral current (Parity Violating Electron Scattering). Symmetry tests: CP (T) violation and EDMs; Lepton Number violation and neutrino-less double beta decay.
3 The making of the Standard Model (theory-centric, simplified perspective) Fermi, 1934 p ν Fermi s theory of beta decays (n p e νe): Postulate local interaction in terms of light degrees of freedom (n,p,e,ν) _ n GF e Current-current, parity conserving Fermi scale: Λ = GF -1/2 ~ 250 GeV Coupling constant GF 1/Λ 2 determined by fitting the slow beta decay rates point to mass scale Λ >> mn~ GeV (Note: this is an effective theory ante litteram )
4 The making of the Standard Model (theory-centric, simplified perspective) Fermi, 1934 Lee and Yang, 1956 Lee and Yang: use most general Lorentzinvariant interaction p ν n GF e p? ν Current-current, parity conserving Fermi scale: Λ = GF -1/2 ~ 250 GeV n e Parity conserving: VV, AA, SS, TT... Parity violating: VA, SP,...
5 The making of the Standard Model (theory-centric, simplified perspective) Fermi, 1934 Lee and Yang, 1956 Lee and Yang: use most general Lorentzinvariant interaction p ν n GF e Current-current, parity conserving Fermi scale: Λ = GF -1/2 ~ 250 GeV p n? ν e Parity conserving: VV, AA, SS, TT... Parity violating: VA, SP,... Experiment: dγ ~ A J p e C-S Wu parity is violated! (but could be VA, SP, )
6 The making of the Standard Model (theory-centric, simplified perspective) Fermi, 1934 Lee and Yang, 1956 Differential decay distributions depend on operator structure p ν n GF e p? ν Current-current, parity conserving Fermi scale: Λ = GF -1/2 ~ 250 GeV n e Parity conserving: VV, AA, SS, TT... Parity violating: VA, SP,... Model diagnosing!
7 The making of the Standard Model (theory-centric, simplified perspective) Fermi, 1934 Lee and Yang, 1956 Marshak & Sudarshan, Feynman & Gell-Mann 1958 p ν n GF e p? ν Current-current, parity conserving Fermi scale: Λ = GF -1/2 ~ 250 GeV n e Parity conserving: VV, AA, SS, TT... Parity violating: VA, SP,... It s (V-A)*(V-A)!! V-A was the key S. Weinberg
8 The making of the Standard Model (theory-centric, simplified perspective) Fermi, 1934 Lee and Yang, 1956 Marshak & Sudarshan, Feynman & Gell-Mann 1958 p ν Glashow, Salam, Weinberg n GF e p? ν Current-current, parity conserving Fermi scale: Λ = GF -1/2 ~ 250 GeV n e Parity conserving: VV, AA, SS, TT... Parity violating: VA, SP,... It s (V-A)*(V-A)!! V-A was the key S. Weinberg ul W νl dl el Embed in non-abelian chiral gauge theory, predict neutral currents
9 The making of the Standard Model Features of underlying (gauge) theory emerging from phenomenology 1. It involves non-abelian gauge group under which (n,p) [or (u,d)] and (e,ν) transform in same representation ν e
10 The making of the Standard Model Features of underlying (gauge) theory emerging from phenomenology 1. It involves non-abelian gauge group under which (n,p) [or (u,d)] and (e,ν) transform in same representation ν e 2. It involves chiral fermions (V-A structure) ΨL,R : chiral fields. For m=0, ΨL : L-handed (h=-1) particles, R-handed anti-particles (h=+1) ΨR : R-handed (h=+1) particles, L-handed anti-particles (h=-1)
11 The Standard Model in pictures
12 The Standard Model in pictures Spin 1/2: ordinary matter + 2 heavier generations
13 The Standard Model in pictures Spin 1: force carriers Spin 1/2: ordinary matter + 2 heavier generations Interactions governed by gauge symmetry principle SU(3)c x SU(2)W x U(1)Y
14 The Standard Model in pictures Spin 0: Higgs boson Spin 1: force carriers Spin 1/2: ordinary matter + 2 heavier generations Interactions governed by gauge symmetry principle SU(3)c x SU(2)W x U(1)Y V(H)
15 The Standard Model in pictures Spin 0: Higgs boson Spin 1: force carriers Spin 1/2: ordinary matter + 2 heavier generations Interactions governed by gauge symmetry principle SU(3)c x SU(2)W x U(1)Y x Higgs mechanism V(H) x x Massive quarks and leptons H=v Massive EW gauge bosons (short range weak force)
16 The Standard Model Gauge group: SU(3)c x SU(2)W x U(1)Y Fundamental representation (color triplets and weak doublets)
17 Q = T3 + Y The Standard Model
18 Q = T3 + Y The Standard Model
19 The Standard Model U(3) 5 symmetry: no notion of flavor (three identical copies)
20 The Standard Model EWSB
21 The Standard Model EWSB Higgs h couples to W ± Z proportionally to their mass squared
22 The Standard Model EWSB Ye,u,d are the only couplings that distinguish the three families! 14
23 Fermion-Higgs couplings Fermion mass matrices diagonalized by bi-unitary transformation Higgs coupling to fermions is flavor-diagonal and proportional to mass
24 Does nature agree? Higgs boson: discovered in H γγ mode h!
25 Does nature agree? Many decay modes accessible: can test Standard Model BR pattern gg γγ
26 Does nature agree? Many decay modes accessible: can test Standard Model BR pattern h! Access to Higgs couplings h! `+` `0+`0
27 Does nature agree? Many decay modes accessible: can test Standard Model BR pattern Higgs couplings to heavy particles consistent with SM prediction (~10-20% level) Room for surprises in: coupling to light particles SM forbidden decays: h τμ, Major area of activity for Run 2 and opportunity for Precision / Intensity frontier
28 Fermion-gauge boson couplings Neutral current fi Flavor diagonal Both V and A: expect P-violation! Z fi
29 Fermion-gauge boson couplings Charged current: leptons ν α=e,μ,τ W e α=e,μ,τ Unitary transformation of el needed to diagonalize charged lepton mass matrix can be reabsorbed by a redefinition of νl (this will change for massive neutrinos) Flavor diagonal: individual lepton family numbers Le,μτ conserved
30 Fermion-gauge boson couplings Charged current: quarks W ui Unitary matrix encoding the physically observable mismatch in the transformation of ul and dl needed to diagonalize quark masses dj Cabibbo-Kobayashi-Maksawa matrix
31 CKM matrix is unitary: 9 real parameters, but redefinition of quark phases reduces physical parameters to 4: 3 mixing angles and 1 phase Irreducible phase implies CP violation: 5 independent parameters (phase differences) CP transformation CKM matrix and mq govern the pattern of flavor and CPV in the SM
32 CKM matrix is unitary: 9 real parameters, but redefinition of quark phases reduces physical parameters to 4: 3 mixing angles and 1 phase Irreducible phase implies CP violation: 5 independent parameters (phase differences) CP transformation CKM matrix and mq govern the pattern of flavor and CPV in the SM
33 Flavor and CP violation: quarks Tree-level flavor changing charged-current processes (semi-leptonic decays can be studied to extract all Vij, except for Vtd and Vts) Does not depend on lepton flavor: Lepton universality ui l Vij W dj ν Data indicates hierarchical structure of mixing matrix VCKM = Make explicit the hierarchical structure revealed by experiment: expand in λ Vus 0.225, with ρ,η,α ~O(1) (Wolfenstein 1983)
34 By connecting flavor-changing charged-current vertices obtain flavorchanging neutral currents (FCNC) at loop level: penguins and boxes ΔF=1 ΔF=2 Sensitive to Vtd,ts and phases of Vij Rare K and B decays Neutral meson mixing (Δm, CPV in mixing) 25
35 Important Example: CP violation in neutral kaon mixing KL,S not eigenstates of CP: non-zero asymmetries = CP violation in B-meson decays fully consistent with CKM paradigm!
36 Status of the CKM matrix: quark flavor physics (including CPV) is well described by 3 mixing angles and a phase!
37 Symmetries of the Standard Model Gauge symmetry is hidden (Higgs mechanism) Flavor symmetry: U(3) 5 explicitly broken only by Yukawa couplings: specific pattern of FCNC falsifiable! U(1) associated with B, L, and Lα=e,μ,τ survive Anomaly: only B-L is conserved P, C maximally violated by weak interactions CP (and T) violated by CKM (and QCD theta term*): specific pattern of CPV in flavor transitions and EDMs *
38 Symmetries of the Standard Model Gauge symmetry is hidden (Higgs mechanism) Flavor symmetry: U(3) 5 explicitly broken only by Yukawa couplings: specific pattern of FCNC falsifiable! U(1) associated with B, L, and Lα=e,μ,τ survive Anomaly: only B-L is conserved P, C maximally violated by weak interactions CP (and T) violated by CKM (and QCD theta term*): specific pattern of CPV in flavor transitions and EDMs * (Approximate) symmetries and symmetries broken in a very specific way offer great opportunity to probe non-standard physics at the Intensity Frontier
39 Additional material
40 SU(2) W x U(1) Y U(1) EM Expand around the minimum of the potential Generalization of the abelian Higgs model discussed in detail earlier on Q = T3 + Y annihilates the vacuum unbroken U(1)EM. Photon remains massless, other gauge bosons (W ±, Z) acquire mass
41 SU(2) W x U(1) Y U(1) EM Expand around the minimum of the potential Neutral scalar h couples to W ± Z proportionally to their mass squared Weak mixing angle
42 SU(2) W x U(1) Y U(1) EM Expand around the minimum of the potential Higgs mass controlled by v and Higgs self-coupling
43 Status of the Standard Model Standard Model tested at the quantum (loop) level in both electroweak and flavor sector Precision EW tests are at the 0.1% level. Example: A few tensions and anomalies, such as muon g-2
44 Symmetry breaking in the νsm CC vertex & mass terms: individual flavors not conserved (ν osc.) Loop-level charged lepton FCNC: GIM at work tiny effects! νi Current limit on BR ~ γ Petcov 77, Marciano-Sanda Lα=e,μ,τ broken: but unobservable effects in charged lepton sector. Extremely clean probe of BνSM dynamics: no background! L broken by Majorana mass specific expectations in 0νββ 34
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