A systematic approach to neutrino masses and their phenomenology - PowerPoint PPT Presentation

A systematic approach to neutrino masses and their phenomenology Michael A. Schmidt TeV Particle Astrophysics 2019 5 December 2019 based on work in collaboration with Juan Herrero-Garcia 1903.10552 [Eur.Phys.J. C79 (2019) no.11, 938]

Neutrino masses The Standard Model is very successful... ...but incomplete In particular neutrinos are massive Hint: lowest dimensional effective operator O 1 = LLHH ( d = 5, Weinberg) violates lepton number by 2 units After EWSB, naturally light Majorana neutrino masses What is the underlying theory of neutrino masses? 1 22

Overview Mechanisms for neutrino masses 1 Upper limits 2 Lower limits 3 Summary and conclusions 4 2 22

Mechanisms for neutrino masses

Majorana neutrino masses T ree-level. Only a few: seesaws I/II/III simple, GUT connection, leptogenesis, but huge scales → very hard to test and hierarchy problem Radiative. In principle more testable, but hundreds of them. Classified by 1. Topologies at a given loop order (up to 3 loops) 2. ∆ L = 2 EFT operators beyond Weinberg operator 3 22

Tree level: seesaws SS II: ∆ ∼ ( 1 , 2 , 1 ) yL ∆ L + µ H ∆ † H SS I: ¯ N ∼ ( 1 , 1 , 0 ) SS III: ¯ Σ ∼ ( 1 , 3 , 0 ) yLH ¯ N + m ¯ N ¯ N yLH ¯ Σ + m ¯ Σ¯ Σ H H H H H H L L L L L L Foot, Lew, He, Joshi. Minkowski; Yanagida; Glashow; Gell-Mann, Ramond, Slansky; Mohapatra, Senjanovic; Mohapatra, Senjanovic. Magg, Wetterich; Lazarides, Shafi, Wetterich; Schechter, Valle. 4 22

Loop level models 1 loop 2 loop Review: "From the Trees to the Forest" Cai, Herrero-Garcia, MS, Vicente, Volkas 1706.08524 3 loop 5 22

Examples of loop models [Zee, Cheng, Li, Babu] Singly-charged scalar: fLLh + Zee model Zee-Babu model y ¯ e φ † L + µ h − H φ ek −− + µ h + h + k −− g ¯ e ¯ H / Φ h + h + Φ / H h + k ++ L L L L L e e L ¯ ¯ L e ¯ H H H / Φ 6 22

∆ L = 2 EFT operators [Babu, Leung, De Gouvea, Jenkins] Z ee model Zee-Babu model O 2 = L i L j L k ¯ eH l ǫ ij ǫ kl O 3 a = L i L j Q k ¯ dH l ǫ ij ǫ kl O 3 a = L i L j Q k ¯ dH l ǫ ik ǫ jl O 4 a = L i L j Q † u † H k ǫ jk O 4 b = L i L j Q † u † H k ǫ ij O 8 = L i ¯ u † H j ǫ ij d ¯ e † ¯ i ¯ k ¯ O 9 = L i L j L k ¯ eL l ¯ O 10 = L i L j L k ¯ eQ l ¯ e ǫ ij ǫ kl d ǫ ij ǫ kl O 11 a = L i L j Q k ¯ dQ l ¯ O 11 b = L i L j Q k ¯ dQ l ¯ d ǫ ij ǫ kl d ǫ ik ǫ jl O 12 a = L i L j Q † O 12 b = L i L j Q † u † ǫ ij ǫ kl u † Q † u † u † Q † i ¯ j ¯ k ¯ l ¯ . . . O 59 = L i Q j ¯ u † H k H † O 60 = L i ¯ u † H j H † d ¯ d ¯ e † ¯ dQ † u † ¯ e † ¯ j ¯ i ǫ jk i operators up to dimension 11 classified 7 22

EFT estimate H / Φ H / Φ H / Φ L L L L Φ / H h + e L ¯ e L L L ¯ L e ¯ H / Φ H / Φ Operator UV model: Zee Estimate fm 2 O 2 = LLL ¯ eH chirality flip y τ τ µ m ν ≃ 16 π 2 m 2 1 c 2 v 2 h + m ν ≃ 16 π 2 y τ Λ 1 loop factor 16 π 2 8 22

Neutrino masses C lassification in terms of effective ∆ L = 2 operators Babu, Leung hep-ph/0106054; deGouvea, Jenkins 0708.1344 Bonnet, Hernandez, Ota, Winter 0907.3143 � v 2 � n c R v 2 m ν ≃ c R ≃ g i × ǫ × � ( 16 π 2 ) l Λ , with Λ 2 i Loop factor LLHH ( H † H ) n µ/ Λ l = 1 → Λ < 10 12 GeV    m ν � 0 . 05 eV ⇒ l = 2 → Λ < 10 10 GeV l = 3 → Λ < 10 8 GeV   → no information on ∆ L = 0 processes Systematic construction of models Angel, Rodd, Volkas 1212.5862; Cai, Clarke, MS, Volkas 1308.0463; Gargalionis, Volkas (in prep) Bonnet, Hirsch, Ota, Winter 1204.5862; Aristizabal Sierra, Degee, Dorame, Hirsch 1411.7038; Cepedello, Fonseca, Hirsch 1807.00629 Volkas (NuFact 2019): "exploding! ∆ L = 2 operators" ..."1000s of models" → too many models! 9 22

Neutrino masses C lassification in terms of effective ∆ L = 2 operators Babu, Leung hep-ph/0106054; deGouvea, Jenkins 0708.1344 Bonnet, Hernandez, Ota, Winter 0907.3143 � v 2 � n c R v 2 m ν ≃ c R ≃ g i × ǫ × � ( 16 π 2 ) l Λ , with Λ 2 i Loop factor LLHH ( H † H ) n µ/ Λ l = 1 → Λ < 10 12 GeV    m ν � 0 . 05 eV ⇒ l = 2 → Λ < 10 10 GeV l = 3 → Λ < 10 8 GeV   → no information on ∆ L = 0 processes Systematic construction of models Angel, Rodd, Volkas 1212.5862; Cai, Clarke, MS, Volkas 1308.0463; Gargalionis, Volkas (in prep) Bonnet, Hirsch, Ota, Winter 1204.5862; Aristizabal Sierra, Degee, Dorame, Hirsch 1411.7038; Cepedello, Fonseca, Hirsch 1807.00629 Volkas (NuFact 2019): "exploding! ∆ L = 2 operators" ..."1000s of models" → too many models! 9 22

Neutrino masses C lassification in terms of effective ∆ L = 2 operators Babu, Leung hep-ph/0106054; deGouvea, Jenkins 0708.1344 Bonnet, Hernandez, Ota, Winter 0907.3143 � v 2 � n c R v 2 m ν ≃ c R ≃ g i × ǫ × � ( 16 π 2 ) l Λ , with Λ 2 i Loop factor LLHH ( H † H ) n µ/ Λ l = 1 → Λ < 10 12 GeV    m ν � 0 . 05 eV ⇒ l = 2 → Λ < 10 10 GeV l = 3 → Λ < 10 8 GeV   → no information on ∆ L = 0 processes Systematic construction of models Angel, Rodd, Volkas 1212.5862; Cai, Clarke, MS, Volkas 1308.0463; Gargalionis, Volkas (in prep) Bonnet, Hirsch, Ota, Winter 1204.5862; Aristizabal Sierra, Degee, Dorame, Hirsch 1411.7038; Cepedello, Fonseca, Hirsch 1807.00629 Volkas (NuFact 2019): "exploding! ∆ L = 2 operators" ..."1000s of models" → too many models! 9 22

Can we do better? → Hybrid approach

Can we do better? → Hybrid approach

Questions 1. How can we classify the plethora of models? 2. What are the most testable ones, with the lightest particles? 3. Is any class of models already ruled-out? 4. Can we study the phenomenology without going to a particular model? 10 22

Upper limits

Main idea 1. m ν requires at least one new particle X (mass M) coupled to SM lepton(s), carrying L (and maybe B ). 2. QFT: L is violated (by two units) via new operators at scale Λ which encode the (model-dependent) UV physics. 3. Majorana neutrino masses, m ν ∝ 1 / Λ , are generated. 4. m ν > 0 . 05 eV & M ≤ Λ ⇒ conservative upper bound on M . 5. L -conserving pheno mostly determined by renormalizable ∆ L = 0 operator Bounds apply to all models where X is the lightest particle. 11 22

Example at tree level SM bilinear LH (seesaw type I): 1. New particle: fermion singlet N with Y = 0 and L = − 1. 2. L is violated (by two units) via MNN ( + yLHN ) 3. Neutrino masses, m ν = y 2 v 2 / M , are generated. 4. m ν > 0 . 05 eV & y ≤ 1 ⇒ conservative upper bound M ≤ 10 15 GeV 12 22

Possible new particles LH → N (SSI) , Σ (SSIII) LL → ∆ (SSII) , h (Z ee) e ¯ e → k (Zee-Babu) ¯ LH † → . . . eH † → . . . ¯ e σ µ L † → . . . ¯ . . . 13 22

Particles generating tree level neutrino masses X ∼ ( SU ( 3 ) c , SU ( 2 ) L , U ( 1 ) Y ) L , 3 B ∆ L = 2 operators S / F / V Seesaw type Particle ∆ L = 0 | ∆ L| = 2 BL m ν Upper bound ℓ y 2 v 2 M � 10 15 GeV N ∼ ( 1 , 1 , 0 ) − 1 , 0 y ¯ NHL M ¯ N ¯ N I 0 Seesaws ¯ O 1 F M y µ v 2 M � 10 15 GeV ∆ ∼ ( 1 , 3 , 1 ) − 2 , 0 y L ∆ L µ H ∆ † H II 0 O 1 M 2 S y 2 v 2 M � 10 15 GeV Σ 0 ∼ ( 1 , 3 , 0 ) − 1 , 0 ¯ y ¯ Σ 0 LH M ¯ Σ 0 ¯ III 0 Σ 0 O 1 F M v 2 M � 10 15 GeV L 1 ∼ ( 1 , 2 , − 1 / 2 ) 1 , 0 c c m m ¯ L 1 L Λ L 1 HLH 0 Λ c O 1 F M 14 22

Particles generating loop level neutrino masses Zee-Babu X ∼ ( SU ( 3 ) c , SU ( 2 ) L , U ( 1 ) Y ) L , 3 B S / F / V Z ee Loop order Particle ∆ L = 0 | ∆ L| = 2 BL m ν Upper bound ℓ y 2 v 2 M � 10 15 GeV N ∼ ( 1 , 1 , 0 ) − 1 , 0 Seesaws ¯ y ¯ NHL M ¯ N ¯ N 0 O 1 F M y µ v 2 M � 10 15 GeV ∆ ∼ ( 1 , 3 , 1 ) − 2 , 0 y L ∆ L µ H ∆ † H 0 O 1 M 2 S y 2 v 2 M � 10 15 GeV Σ 0 ∼ ( 1 , 3 , 0 ) − 1 , 0 ¯ y ¯ Σ 0 LH M ¯ Σ 0 ¯ 0 Σ 0 O 1 F M v 2 M � 10 15 GeV c c m m ¯ L 1 L Λ L 1 HLH 0 Λ c O 1 L 1 ∼ ( 1 , 2 , − 1 / 2 ) 1 , 0 M c yyu yd yl v 2 M � 10 7 GeV F c y H † eL 1 Λ 2 ¯ L 1 ¯ u ¯ d † L † O † 2 ( 4 π ) 4 8 Λ v 2 M � 10 10 GeV c y yl h ∼ ( 1 , 1 , 1 ) − 2 , 0 y LLh Λ h † eLH c 1 O 2 ( 4 π ) 2 S Λ c y y 2 v 2 M � 10 6 GeV k ∼ ( 1 , 1 , 2 ) − 2 , 0 c y ¯ e † ¯ e † k Λ 3 k † L † L † L † L † O † 2 l Radiative ( 4 π ) 4 S 9 Λ v 2 M � 10 10 GeV c c y yu y ¯ ELH † Λ 4 LEHQ † ¯ u † H 2 O 6 E ∼ ( 1 , 1 , 1 ) − 1 , 0 ( 4 π ) 4 ¯ Λ F v 2 M � 10 10 GeV yl c c m m ¯ eE Λ 3 ¯ ELLLH 1 O 2 M ( 4 π ) 2 Λ v 2 M � 10 12 GeV Σ 1 ∼ ( 1 , 3 , 1 ) − 1 , 0 y H † ¯ c O ′ 1 c y ¯ Σ 1 L Λ 2 LHH Σ 1 H 1 F 1 ( 4 π ) 2 Λ c y yl v 2 M � 10 11 GeV L 2 ∼ ( 1 , 2 , − 3 / 2 ) 1 , 0 c y HeL 2 Λ 2 ¯ L 2 LLL 1 O 2 ( 4 π ) 2 F Λ M � 10 7 GeV cy yuydye v 2 X 2 ∼ ( 1 , 2 , 3 / 2 ) − 2 , 0 e † ¯ u † ¯ y ¯ σ µ LX 2 µ c σ µ ¯ dX † 2 µ H 2 Λ ¯ O 8 ( 4 π ) 4 V Λ 15 22