Lepton Flavor Violation I. The (Extended) Standard Model Flavor Puzzle SSI 2010 : Neutrinos Nature s mysterious messengers SLAC, 9 August 2010 Yossi Nir (Weizmann Institute of Science) LFV 1/39
Lepton Flavor Violation Plan of Lectures 1. The (extended) Standard Model flavor puzzle Introduction The Standard Model The extended Standard Model 2. The New Physics flavor puzzle 3. Leptogenesis LFV 2/39
LFV Introduction LFV 3/39
Introduction What are flavors? Copies of the same gauge representation: SU(3) C U(1) EM Up-type quarks (3) +2/3 u, c, t Down-type quarks (3) 1/3 d, s, b Charged leptons (1) 1 e, µ, τ Neutrinos (1) 0 ν 1, ν 2, ν 3 LFV 4/39
Introduction What are flavors? In the interaction basis: SU(3) C SU(2) L U(1) Y Quark doublets (3, 2) +1/6 Q Li Up-type quark singlets (3, 1) +2/3 U Ri Down-type quark singlets (3, 1) 1/3 D Ri Lepton doublets (1, 2) 1/2 L Li Charged lepton singlets (1, 1) 1 E Ri In QCD: SU(3) C Quarks (3) u, d, s, c, b, t LFV 5/39
Introduction What is flavor physics? Interactions that distinguish among the generations: Neither strong nor electromagnetic interactions Within the SM: Only weak and Yukawa interactions In the interaction basis: The weak interactions are also flavor-universal The source of all SM flavor physics: Yukawa interactions among the gauge interaction eigenstates Flavor parameters: Parameters with flavor index (m i, V ij ) LFV 6/39
Introduction More flavor dictionary Flavor universal: Coupling/paremeters 1 ij in flavor space Example: strong interactions U R G µa λ a γ µ 1U R Flavor diagonal: Coupling/paremeters that are diagonal in flavor space Example: SM Yukawa interactions in mass basis U L λ u U R H, λ u = diag(y u, y c, y t ) LFV 7/39
Introduction And more flavor dictionary Flavor changing: Initial flavor number final flavor number Flavor number = # particles # antiparticles B ψk ( b cc s); K µ ν 2 (sū µ ν 2 ) Flavor changing neutral current processes: Flavor changing processes that involve either U or D but not both and/or either l or ν but not both µ eγ; K πν ν (s dν ν); D 0 D 0 mixing (cū u c)... FCNC are highly suppressed in the SM LFV 8/39
Introduction Why is flavor physics interesting? Flavor physics is sensitive to new physics at Λ NP E experiment The Standard Model flavor puzzle: Why are the flavor parameters small and hierarchical? (Why) are the neutrino flavor parameters different? The New Physics flavor puzzle: If there is NP at the TeV scale, why are FCNC so small? LFV provides theoretically clean null tests of the SM LFV could be present even in MFV models δ KM cannot explain the baryon asymmetry a puzzle: There must exist new sources of CPV Electroweak baryogenesis? (Testable at the LHC) Leptogenesis? (Window to Λ seesaw ) LFV 9/39
Introduction A brief history of FV Γ(K µµ) Γ(K µν) = Charm [GIM, 1970] m K = m c 1.5 GeV [Gaillard-Lee, 1974] ε K 0 = Third generation [KM, 1973] m B = m t m W [Various, 1986] LFV 10/39
Introduction A brief history of FV Γ(K µµ) Γ(K µν) = Charm [GIM, 1970] m K = m c 1.5 GeV [Gaillard-Lee, 1974] ε K 0 = Third generation [KM, 1973] m B = m t m W [Various, 1986]...and hopes for the future history: Γ(µ eγ) 0 =??? d e 0 =??? m2 µẽ 0 =??? LFV 10/39
Lepton Flavor Violation The Standard Model LFV 11/39
The Standard Model The Standard Model G SM = SU(3) C SU(2) L U(1) Y φ(1, 2) +1/2 0 breaks G SM SU(3) C U(1) EM Quarks: 3 { Q L (3, 2) +1/6 + U R (3, 1) +2/3 + D R (3, 1) 1/3 } Leptons: 3 { L L (1, 2) 1/2 + E R (1, 1) 1 } L SM = L kinetic+gauge + L Higgs + L Yukawa L SM depends on 18 parameters All but one (m H ) have been measured LFV 12/39
The Standard Model Flavor Symmetry L kinetic+gauge + L Higgs has a large global symmetry: G global = U(3) Q U(3) U U(3) D U(3) L U(3) E Q L V Q Q L, U R V U U R, D R V D D R, L L V L L L, E R V E E R Take, for example L kinetic+gauge for Q L (3, 2) +1/6 : iq L i( µ + i 2 g sg a µλ a + i 2 g sw b µτ b + i 6 g B µ )γ µ δ ij Q Lj Q L 1Q L Q L V Q 1V QQ L = Q L 1Q L Another example: L kinetic+gauge for L L (1, 2) 1/2 : il L i( µ + i 2 g sw b µτ b i 2 g B µ )γ µ δ ij L Lj L L 1L L L L V L 1V LL L = L L 1L L LFV 13/39
The Standard Model Flavor Violation L Yukawa = Q L iy u ij φu Rj + Q L iy d ij φd Rj + L L iy e ij φe Rj breaks G global U(1) B U(1) e U(1) µ U(1) τ Flavor physics: interactions that break the [SU(3)] 5 symmetry Q L V Q Q L, U R V U U R, D R V D D R L L V L L L, E R V E E R = Change of interaction basis Y d V Q Y d V D, Y u V Q Y u V U, Y e V L Y e V E Can be used to reduce the number of parameters in Y u, Y d, Y e LFV 14/39
The Standard Model The quark flavor parameters Convenient (but not unique) interaction basis: Y d V Q Y d V D = λd, Y u V Q Y u V U = V λ u λ d, λ u diagonal and real: λ d = y d y s y b ; λu = y u y c y t V unitary with 3 real (λ, A, ρ) and 1 imaginary (η) parameters: 1 λ Aλ 3 (ρ + iη) V λ 1 Aλ 2 Aλ 3 (1 ρ + iη) Aλ 2 1 Another convenient basis: Y d V λ d, Y u λ u LFV 15/39
The Standard Model Kobayashi and Maskawa CP violation Complex couplings: Hermiticity: L g ijk φ i φ j φ k + g ijk φ i φ j φ k CP transformation: φ i φ j φ k φ i φ j φ k CP is a good symmetry if g ijk = g ijk The number of real and imaginary quark flavor parameters: With two generations: 2 (4 R + 4 I ) 3 (1 R + 3 I ) + 1 I = 5 R + 0 I With three generations: 2 (9 R + 9 I ) 3 (3 R + 6 I ) + 1 I = 9 R + 1 I The two generation SM is CP conserving The three generation SM is CP violating LFV 16/39
The Standard Model The mass basis To transform to the mass basis: D L D L, U L V U L m q = y q φ V = The CKM matrix L W = g 2 U L V γ µ D L W + µ + h.c. V = V ud V us V ub V cd V cs V cb V td V ts V tb η - the only source of CP violation LFV 17/39
The Standard Model The lepton flavor parameters Convenient interaction basis: Y e V L Y e V E = λe λ e diagonal and real [SU(3) L SU(3) E U(1) e U(1) µ U(1) τ ]: λ e = y e y µ y τ The number of real and imaginary lepton flavor parameters: With three generations: 1 (9 R + 9 I ) 2 (3 R + 6 I ) + 3 I = 3 R + 0 I The mass basis: m l = y l φ The lepton sector of the SM: neither mixing nor CP violation LFV 18/39
Lepton Flavor Violation The SM Flavor Puzzle LFV 19/39
The SM flavor puzzle Smallness and Hierarchy y t 1, y c 10 2, y u 10 5 y b 10 2, y s 10 3, y d 10 4 y τ 10 2, y µ 10 3, y e 10 6 V us 0.2, V cb 0.04, V ub 0.004, δ KM 1 For comparison: g s 1, g 0.6, g 0.3, λ 1 The SM flavor parameters have structure: smallness and hierarchy Why? = The SM flavor puzzle LFV 20/39
The SM flavor puzzle The Froggatt-Nielsen (FN) mechanism Approximate horizontal symmetry (e.g. U(1) H ) Small breaking parameter ɛ = S 1 /Λ 1 Each quark or lepton field carries an FN charge H(ψ) Selection rules: Y d ij ɛh(q i)+h( d j )+H(φ d ) Y u ij ɛh(q i)+h(ū j )+H(φ u ) Y e ij ɛh(l i)+h( l j )+H(φ d ) LFV 21/39
The SM flavor puzzle The FN mechanism: An example H(Q i ) = 2, 1, 0, H(ū j ) = 2, 1, 0, H(φ u ) = 0 y t : y c : y u 1 : ɛ 2 : ɛ 4 Y u ɛ 4 ɛ 3 ɛ 2 ɛ 3 ɛ 2 ɛ ɛ 2 ɛ 1 (V u L ) 12 ɛ, (V u L ) 23 ɛ, (V u L ) 13 ɛ 2 LFV 22/39
The SM flavor puzzle The FN mechanism: a viable model Approximate horizontal symmetry (e.g. U(1) H ) Small breaking parameter ɛ = S 1 /Λ 1 10(2, 1, 0), 5(0, 0, 0) y t : y c : y u 1 : ɛ 2 : ɛ 4 y b : y s : y d 1 : ɛ : ɛ 2 y τ : y µ : y e 1 : ɛ : ɛ 2 V us V cb ɛ, V ub ɛ 2, δ KM 1 LFV 23/39
The SM flavor puzzle The FN mechanism: Predictions (quarks) In the quark sector: 8 FN charges, 9 observables One prediction that is independent of charge assignments: V ub V us V cb Experimentally correct to within a factor of 2 In addition, six inequalities: V us > m d m s, m u m c ; V ub > m d m b, m u Experimentally fulfilled m t ; V cb > m s m b, m c m t When ordering the quarks by mass: V CKM 1 (diagonal terms not suppressed parameterically) Experimentally fulfilled LFV 24/39
Lepton Flavor Violation The Extended Standard Model LFV 25/39
The Extended Standard Model Neutrino Masses experimentally m 2 21 = (7.6 ± 0.2) 10 5 ev 2 m 2 32 = (2.4 ± 0.1) 10 3 ev 2 sin 2 2θ 12 = 0.87 ± 0.03 sin 2 2θ 23 > 0.92 LFV 26/39
The Extended Standard Model Neutrino Masses theoretically The only neutrino mass terms that can be written with the SM particle content: L Mν = 1 2 3 k=1 m k(ν c k ν k + h.c.) L Mν violates B L = Forbidden Within the SM, neutrino masses vanish to all orders in perturbation theory and even non-perturbatively The SM must be extended LFV 27/39
The Extended Standard Model The Extended Standard Model The SM: G SM = SU(3) C SU(2) L U(1) Y φ(1, 2) +1/2 0 breaks G SM SU(3) C U(1) EM Quarks: 3 { Q L (3, 2) +1/6 + U R (3, 1) +2/3 + D R (3, 1) 1/3 } Leptons: 3 { L L (1, 2) 1/2 + E R (1, 1) 1 } The ESM: It is possible to extend the SM while maintaining the symmetry, the pattern of SSB, and the particle content, by giving up on renormalizability The SM = Low energy effective theory Not valid above a certain mass scale LFV 28/39
The Extended Standard Model The ESM Lagrangian L ESM = L SM + L d=5 L d=5 = Zν ij Λ L il j φφ + h.c. L Mν = Zν ij 2 (M ν ) ij = Z ν ij v 2 Λ ν iν c j + h.c. v 2 Λ LFV 29/39
The Extended Standard Model Flavor Violation L kinetic+gauge + L Higgs has a large global symmetry: G global = [U(3)] 5 L Yukawa + L d=5 break G global U(1) B Q L V Q Q L, U R V U U R, D R V D D R L L V L L L, E R V E E R = Change of interaction basis Y d V Q Y d V D, Y u V Q Y u V U, Y e V L Y e V E, Zν V L Z ν V T L Can be used to reduce the number of parameters in Y u, Y d, Y e, Z ν LFV 30/39
The Standard Model The lepton flavor parameters (9 R + 9 I ) + (6 R + 6 I ) 2 (3 R + 6 I ) = 9 R + 3 I Convenient (but not unique) interaction basis: Y e λ e, Z ν U λ ν U vλ e = diag(m e, m µ, m τ ) (v 2 /Λ)λ ν = diag(m 1, m 2, m 3 ) U = the leptonic mixing matrix: L l W ± = g 2 E Li γ µ U ij ν Lj W µ + h.c. with 3 real and 3 imaginary parameters The lepton sector of the ESM: mixing and CP violation LFV 31/39
Lepton Flavor Violation The ESM Flavor Puzzle LFV 32/39
The ESM flavor puzzle The Froggatt-Nielsen (FN) mechanism Approximate horizontal symmetry (e.g. U(1) H ) Small breaking parameter ɛ = S 1 /Λ 1 Each quark and lepton field carries an FN charge H(φ) Selection rules: Y d ij ɛh(q i)+h( d j )+H(φ d ) Y u ij ɛh(q i)+h(ū j )+H(φ u ) Y e ij ɛh(l i)+h( l j )+H(φ d ) Z ν ij ɛh(l i)+h(l j )+2H(φ u ) LFV 33/39
The ESM flavor puzzle The FN mechanism: Predictions (leptons) In the lepton sector: 5 FN charges, 9 observables Four predictions that are independent of charge assignments: m νi /m νj U ij 2 U e3 U e2 U µ3 In addition, three inequalities: U e2 > m e m µ ; U e3 > m e m τ ; U µ3 > m µ m τ When ordering the leptons by mass: U 1 LFV 34/39
The ESM flavor puzzle Testing FN with Neutrinos The data: m 2 21/ m 2 32 = 0.030 ± 0.003 sin θ 12 = 0.57 ± 0.02, sin θ 23 = 0.67 0.04 +0.07, sin θ 13 = 0 +0.07 0.0 The tests: s 23 1, m 2 /m 3 ɛ x? Inconsistent with FN s 23 1, s 12 1, s 13 ɛ x? Inconsistent with FN sin 2 2θ 23 = 1 ɛ x? Inconsistent with FN LFV 35/39
The SM flavor puzzle Neutrino Mass Anarchy Facts: sin θ 23 0.7 > any V ij sin θ 12 0.6 > any V ij m 2 /m 3 > 1/6 > any m i /m j for charged fermions sin θ 13 0.1 is still possible Possible interpretation: Neutrino parameters are all of O(1) (no structure): Neutrino mass anarchy Consistent with FN Close to SU(5)-GUT+FN predictions: s 23 m s/m b V cb 1; s 12 m d/m s V us 0.2; s 13 m d/m b V ub 0.5 LFV 36/39
The ESM flavor puzzle The FN mechanism: a viable model Approximate horizontal symmetry (e.g. U(1) H ) Small breaking parameter ɛ = S 1 /Λ 1 10(2, 1, 0), 5(0, 0, 0) y t : y c : y u 1 : ɛ 2 : ɛ 4 y b : y s : y d 1 : ɛ : ɛ 2 y τ : y µ : y e 1 : ɛ : ɛ 2 V us V cb ɛ, V ub ɛ 2, δ KM 1 + m 3 : m 2 : m 1 1 : 1 : 1 U e2 1, U µ3 1, U e3 1 LFV 37/39
The ESM flavor puzzle Structure is in the eye of the beholder 0.79 0.86 0.50 0.61 0.0 0.2 U 3σ = 0.25 0.53 0.47 0.73 0.56 0.79 0.21 0.51 0.42 0.69 0.61 0.83 Tribimaximal-ists: 2/3 1/3 0 U T BM = 1/6 1/3 1/2 1/6 1/3 1/2 Anarch-ists: U anarchy = O(0.6) O(0.6) O(0.6) O(0.6) O(0.6) O(0.6) O(0.6) O(0.6) O(0.6) LFV 38/39
The ESM flavor puzzle The (E)SM flavor confusion The charged fermion flavor parameters: smallness and hierarchy Possibly a hint for NP: approximate symmetry, dynamics... Strong hierarchy, small mixing = Abelian symmetry? The three measured neutrino flavor parameters: neither small nor hierarchical Anarchy? Tribimaximal mixing? Neither? No symmetry? Non-Ablian symmetry? U e3 likely to provide further guidance The difference between neutrinos and charged fermions is probably a hint to something deep... LFV 39/39
Thanks to my low-energy-physics collaborators: Gudrun Hiller, YN JHEP 0803 (2008) 046 [arxiv:0802.0916] Gudrun Hiller, Yonit Hochberg, YN JHEP 0903 (2009) 115 [arxiv:0812.0511] JHEP 1003 (2010) 079 [arxiv:1001.1513] Kfir Blum, Yuval Grossman, YN, Gilad Perez Phys. Rev. Lett. 102 (2009) 211802 [arxiv:0903.2118] Yuval Grossman, YN, Gilad Perez Phys. Rev. Lett. 103 (2009) 071602 [arxiv:0904.0305] Oram Gedalia, Yuval Grossman, YN, Gilad Perez Phys. Rev. D80 (2009) 055024 [arxiv:0906.1879] Kfir Blum, Yonit Hochberg, YN arxiv:1007.1872 Helen Quinn + YN The Mystery of the Missing Antimatter (PUP) LFV 40/39