Two models with extra Higgs doublets and Axions

Transcription

1 Two models with extra Higgs doublets and Axions H Serôdio (KAIST) 4 th KIAS Workshop Particle Physics and Cosmology, 30 October 2014 In collaboration with: Alejandro Celis, Javier Fuentes-Martin Works: PLB700(2011); PLB737(2014); arxiv: and arxiv: Hugo Serôdio (KAIST) October 30, / 24

2 Hugo Serôdio (KAIST) October 30, / 24

3 Outline 1 Introduction 2 Effective A2HDM with an Axion 3 3 Higgs Flavored PQ Model 4 Conclusion Hugo Serôdio (KAIST) October 30, / 24

4 Introduction: The Strong CP Problem in a nutshell U(1) A is anomalous (Good η is massive) A new term is introduce due to this anomaly θ g s 2 32π 2 G µν a,µν G a θ violates T and P, and therefore also CP From the neutron electric dipole moment θ With just QCD θ = 0 as initial condition would be stable under radiative corrections No longer true in the SM θ = θ QCD + Arg(Det(M q )) Hugo Serôdio (KAIST) October 30, / 24

5 Introduction: The Strong CP Problem in a nutshell U(1) A is anomalous (Good η is massive) A new term is introduce due to this anomaly θ g s 2 32π 2 G µν a,µν G a θ violates T and P, and therefore also CP From the neutron electric dipole moment θ With just QCD θ = 0 as initial condition would be stable under radiative corrections No longer true in the SM Problem: Why is θ so small? θ = θ QCD + Arg(Det(M q )) Hugo Serôdio (KAIST) October 30, / 24

6 Introduction: The Strong CP Problem in a nutshell U(1) A is anomalous (Good η is massive) A new term is introduce due to this anomaly θ g s 2 32π 2 G µν a,µν G a θ violates T and P, and therefore also CP From the neutron electric dipole moment θ With just QCD θ = 0 as initial condition would be stable under radiative corrections No longer true in the SM θ = θ QCD + Arg(Det(M q )) Problem: Why is θ so small? One interesting solution: promote this phase to a dynamical field, the Axion Hugo Serôdio (KAIST) October 30, / 24

7 Introduction: Standard Axion Models The original axion model: PQ: SM + Φ 2 = 2HDM (axion scale = electroweak scale, ruled out) [Peccei, Quinn (1977)] One way out: split both scales ( S ϕ i ) KSVZ: SM (blind) + Q L,R + S [Kim (1979); Shifman, Vainshtein, Zakharov (1980)] DFSZ: SM + Φ 2 + S = 2HDM + S [Zhitnitskii (1980); Dine, Fischler, Srednicki (1981)] Hugo Serôdio (KAIST) October 30, / 24

8 Introduction: Standard Axion Models The original axion model: PQ: SM + Φ 2 = 2HDM (axion scale = electroweak scale, ruled out) [Peccei, Quinn (1977)] One way out: split both scales ( S ϕ i ) KSVZ: SM (blind) + Q L,R + S [Kim (1979); Shifman, Vainshtein, Zakharov (1980)] DFSZ: SM + Φ 2 + S = 2HDM + S [Zhitnitskii (1980); Dine, Fischler, Srednicki (1981)] I will work on DFSZ-like extensions, ie NHDM + S Hugo Serôdio (KAIST) October 30, / 24

9 Introduction: Adding scalar doublets New sources of CPV CP can be spontaneously generated Dark matter candidates New mechanisms for neutrino mass Hugo Serôdio (KAIST) October 30, / 24

10 Introduction: Adding scalar doublets New sources of CPV CP can be spontaneously generated Dark matter candidates New mechanisms for neutrino mass Drawback: FCNCs are no longer strongly suppressed Hugo Serôdio (KAIST) October 30, / 24

11 Introduction: Adding scalar doublets New sources of CPV CP can be spontaneously generated Dark matter candidates New mechanisms for neutrino mass Drawback: FCNCs are no longer strongly suppressed Natural Flavour Conservation [Weinberg, Glashow (1977); Pachos (1997)] Idea: Allow just one Yukawa coupling in each sector Model up down lepton Type-I Φ 2 Φ 2 Φ 2 Type-II Φ 2 Φ 1 Φ 1 Lepton-specific Φ 2 Φ 2 Φ 1 Flipped Φ 2 Φ 1 Φ 2 Pros: No FCNCs at tree level; Easy to implement with a symmetry Cons: No spontaneous CPV PQ symmetry: invisible DFSZ axion model Hugo Serôdio (KAIST) October 30, / 24

12 Introduction: Two additional solutions to FCNCs in 2HDM Hugo Serôdio (KAIST) October 30, / 24

13 Introduction: Two additional solutions to FCNCs in 2HDM Yukawa alignment [Pich, Tuzon (2009)] Idea: Request that in each sector all Yukawas are proportional Pros: No FCNCs at tree level; General scalar sector; Contains the NFC cases as particular limits; Allows spontaneous CPV Cons: Not implemented by symmetry [Ferreira, Lavoura, Silva (2010)] See it as a low energy effective aligned 2HDM [Bae (2012); HS (2011)] Hugo Serôdio (KAIST) October 30, / 24

14 Introduction: Two additional solutions to FCNCs in 2HDM Yukawa alignment [Pich, Tuzon (2009)] Idea: Request that in each sector all Yukawas are proportional Pros: No FCNCs at tree level; General scalar sector; Contains the NFC cases as particular limits; Allows spontaneous CPV Cons: Not implemented by symmetry [Ferreira, Lavoura, Silva (2010)] See it as a low energy effective aligned 2HDM [Bae (2012); HS (2011)] The BGL model [Branco, Grimus, Lavoura (1996)] Idea: Allow FCNCs in just one sector Up Yukawas: 1 = 0, 2 = Down Yukawas: Γ 1 =, Γ 2 = No FCNCs in the up sector, FCNCs in the down sector small Unique implementation in 2HDM [Ferreira, Silva (2011); HS (2013)] Hugo Serôdio (KAIST) October 30, / 24

15 Effective A2HDM with an Hugo Serôdio (KAIST) October 30, / 24

16 Matter content and Lagrangian Under the U(1) PQ symmetry Fermions: Scalars: Q Lα Q Lα, l Lα e ix l θ l Lα, u Rα e ixu θ u Rα, e Rα e ixe θ e Rα, d Rα e ix d θ d Rα, [ S e ix S θ S, Φ j e ix j θ Φ j, ϕ j ϕ j Φ j are active fields, ie they interact with fermions (a la NFC) L Y = Q L Γ Φ 1 d R + Q L Φ 2 u R + l L Π Φ k e R + hc ϕ j are passive fields, ie they don t interact directly with fermions but they mix with the actives V µ 1,j Φ 1 ϕ js + µ 2,j Φ 2 ϕ js + hc Hugo Serôdio (KAIST) October 30, / 24

17 Matter content and Lagrangian Under the U(1) PQ symmetry Fermions: Scalars: Q Lα Q Lα, l Lα e ix l θ l Lα, u Rα e ixu θ u Rα, e Rα e ixe θ e Rα, d Rα e ix d θ d Rα, [ S e ix S θ S, Φ j e ix j θ Φ j, ϕ j ϕ j Φ j are active fields, ie they interact with fermions (a la NFC) L Y = Q L Γ Φ 1 d R + Q L Φ 2 u R + l L Π Φ k e R + hc ϕ j are passive fields, ie they don t interact directly with fermions but they mix with the actives V µ 1,j Φ 1 ϕ js + µ 2,j Φ 2 ϕ js + hc The scalar singlet vev: v 2 PQ 2µ2 S /λ S v 2 Hugo Serôdio (KAIST) October 30, / 24

18 Matter content and Lagrangian Under the U(1) PQ symmetry Fermions: Scalars: Q Lα Q Lα, l Lα e ix l θ l Lα, u Rα e ixu θ u Rα, e Rα e ixe θ e Rα, d Rα e ix d θ d Rα, [ S e ix S θ S, Φ j e ix j θ Φ j, ϕ j ϕ j Φ j are active fields, ie they interact with fermions (a la NFC) L Y = Q L Γ Φ 1 d R + Q L Φ 2 u R + l L Π Φ k e R + hc ϕ j are passive fields, ie they don t interact directly with fermions but they mix with the actives V µ 1,j Φ 1 ϕ js + µ 2,j Φ 2 ϕ js + hc The scalar singlet vev: v 2 PQ 2µ2 S /λ S v 2 active-passive mixing Hugo Serôdio (KAIST) October 30, / 24

19 A decoupling limit We have in leading order a SU(2) L conserving mixing between doublets Defining φ = (Φ 1, Φ 2, ϕ 1, ϕ 2 ) T, we want to diagonalize the mass terms for the doublets ( ) φ i M MA M ij φ j with M = B M B M C The mass eigenstates are H i, with M H1 M H2 M H3 M H4 Hugo Serôdio (KAIST) October 30, / 24

20 A decoupling limit We have in leading order a SU(2) L conserving mixing between doublets Defining φ = (Φ 1, Φ 2, ϕ 1, ϕ 2 ) T, we want to diagonalize the mass terms for the doublets ( ) φ i M MA M ij φ j with M = B M B M C The mass eigenstates are H i, with M H1 M H2 M H3 M H4 Φ 1 Φ 2 ϕ 1 = ϕ 2 since after the H 1 and H 2 decoupling L eff Y R 13 R 14 R 23 R 24 Hugo Serôdio (KAIST) October 30, / 24 H 1 H 2 H 3 H 4 = Q L Γ (R 13 H 3 + R 14 H 4 )d R + Q L (R 23 H 3 + R 24 H 4 )u R + l L Π (R k3 H 3 + R k4 H 4 )e R + hc

21 A decoupling limit We have in leading order a SU(2) L conserving mixing between doublets Defining φ = (Φ 1, Φ 2, ϕ 1, ϕ 2 ) T, we want to diagonalize the mass terms for the doublets ( ) φ i M MA M ij φ j with M = B M B M C The mass eigenstates are H i, with M H1 M H2 M H3 M H4 Φ 1 Φ 2 ϕ 1 = ϕ 2 since after the H 1 and H 2 decoupling L eff Y R 13 R 14 R 23 R 24 Hugo Serôdio (KAIST) October 30, / 24 H 1 H 2 H 3 H 4 = Q L Γ (R 13 H 3 + R 14 H 4 )d R + Q L (R 23 H 3 + R 24 H 4 )u R + l L Π (R k3 H 3 + R k4 H 4 )e R + hcthis is alignment

22 Axion properties Axion-gluon coupling a g 2 s C ag 32π 2 v PQ G a,µν G µν a, with C ag = 6 N DW 1 Hugo Serôdio (KAIST) October 30, / 24

23 Axion properties Axion-gluon coupling a g 2 s C ag 32π 2 v PQ G a,µν G µν a, with C ag = 6 N DW 1 just as DFSZ Hugo Serôdio (KAIST) October 30, / 24

24 Axion properties Axion-gluon coupling a g 2 s C ag 32π 2 v PQ G a,µν G µν a, with C ag = 6 N DW 1 Axion-photon coupling α a C ag C eff µν aγ F µν F with 8πv PQ { 8/3, Φd C aγ /C ag = 2/3, Φ u C eff aγ C aγ 2 C ag 3 just as DFSZ 4 + z 1 + z, Hugo Serôdio (KAIST) October 30, / 24

25 Axion properties Axion-gluon coupling a g 2 s C ag 32π 2 v PQ G a,µν G µν a, with C ag = 6 N DW 1 just as DFSZ Axion-photon coupling α a C ag C eff µν aγ F µν F with C eff aγ C aγ z 8πv PQ C ag z, { 8/3, Φd C aγ /C ag = 2/3, Φ u just as DFSZ Hugo Serôdio (KAIST) October 30, / 24

26 Axion properties Axion-gluon coupling a g 2 s C ag 32π 2 v PQ G a,µν G µν a, with C ag = 6 N DW 1 just as DFSZ Axion-photon coupling α a C ag C eff µν aγ F µν F with C eff aγ C aγ z 8πv PQ C ag z, { 8/3, Φd C aγ /C ag = 2/3, Φ u just as DFSZ Axion-electron axial coupling g A ee µ a 2v PQ e γ µ γ 5 e, g A ee = 2 u2 2 v 2 + v v 2 2 v 2 2 u2 1 v 2 v v 2 2 v 2 for Φ d for Φ u Hugo Serôdio (KAIST) October 30, / 24

27 Conclusions I Hugo Serôdio (KAIST) October 30, / 24

28 3 Higgs Flavored PQ Model (3HFPQ) Hugo Serôdio (KAIST) October 30, / 24

29 Why is BGL safe from large FCNCs? Up Yukawas: 1 = 0, 2 = Down Yukawas: Γ 1 =, Γ 2 = In the mass basis N d = v 2 D d v ( 2 v1 + v ) 2 U v 1 2 v 2 v dl eiθ Γ 2 U dr 1 Hugo Serôdio (KAIST) October 30, / 24

30 Why is BGL safe from large FCNCs? Up Yukawas: 1 = 0, 2 = Down Yukawas: Γ 1 =, Γ 2 = In the mass basis N d = v 2 D d v ( 2 v1 + v ) 2 U v 1 2 v dl eiθ Γ 2 U dr 2 [N d ] ij = v ( 2 v2 [D d ] ij + v ) 1 V v 1 v 1 v 3iV 3j [D d ] jj 2 [Botella, Branco, Carmona, Nebot, Pedro, Rebelo (2014)] [Bhattacharyya, Das, Kundu (2014)] Hugo Serôdio (KAIST) October 30, / 24 v 1 [ S = 2 transitions Vtd V ts 2 λ 10

31 Why is BGL safe from large FCNCs? Up Yukawas: 1 = 0, 2 = Down Yukawas: Γ 1 =, Γ 2 = In the mass basis N d = v 2 D d v ( 2 v1 + v ) 2 U v 1 2 v dl eiθ Γ 2 U dr 2 [N d ] ij = v ( 2 v2 [D d ] ij + v ) 1 V v 1 v 1 v 3iV 3j [D d ] jj 2 [Botella, Branco, Carmona, Nebot, Pedro, Rebelo (2014)] [Bhattacharyya, Das, Kundu (2014)] Can we add an axion to this setup? Hugo Serôdio (KAIST) October 30, / 24 v 1 [ S = 2 transitions Vtd V ts 2 λ 10

32 Finding the anomalous implementation Up sector block diagonal S L = diag (1, ) 1, e ix tl θ, SR (e ) u = diag ix ur θ, e ix ur θ, e ix tr θ Down sector unconstrained SR d = eixdrθ I Yukawa phase transformation matrix X ur X ur X tr Θ u =θ X ur X ur X tr X ur X tl X ur X tl X tr X tl X dr X dr X dr Θ d =θ X dr X dr X dr X dr X tl X dr X tl X dr X tl Hugo Serôdio (KAIST) October 30, / 24

33 Finding the anomalous implementation Up sector block diagonal S L = diag (1, ) 1, e ix tl θ, SR (e ) u = diag ix ur θ, e ix ur θ, e ix tr θ Down sector unconstrained SR d = eixdrθ I Yukawa phase transformation matrix X ur X ur X tr Θ u =θ X ur X ur X tr X ur X tl X ur X tl X tr X tl X dr X dr X dr Θ d =θ X dr X dr X dr X dr X tl X dr X tl X dr X tl Anomaly free condition: 2X tl (2X ur + X tr 3X dr ) = 0 Hugo Serôdio (KAIST) October 30, / 24

34 Finding the anomalous implementation Up sector block diagonal S L = diag (1, ) 1, e ix tl θ, SR (e ) u = diag ix ur θ, e ix ur θ, e ix tr θ Down sector unconstrained SR d = eixdrθ I Yukawa phase transformation matrix X ur X ur X tr Θ u =θ X ur X ur X tr X ur X tl X ur X tl X tr X tl X dr X dr X dr Θ d =θ X dr X dr X dr X dr X tl X dr X tl X dr X tl Anomaly free condition: 2X tl (2X ur + X tr 3X dr ) = 0 BGL 2HDM is anomaly free We need at least 3 Higgs Hugo Serôdio (KAIST) October 30, / 24

35 3HFPQ model Γ 1 =, Γ 2 = 0, Γ 3 = 0 0 0, = 0, 2 = 0 0 0, 3 = 0, Field transformations Lagrangian X Q αl = (0, 0, 2), X u αr = (5/2, 5/2, 1/2), X d R = 5/2 X l αl = (0, 0, 1), X l αr = 1/2, X N R = 1/2, X S = 1 L Y =Q 0 L [Γ 1 Φ 1 + Γ 3 Φ 3 ] d 0 R + Q0 L [ 1 Φ Φ2 ]u 0 R + L 0 L [Π 2 Φ 2 + Π 3 Φ 3 ] l 0 R + L0 L Σ 3 Φ 3 N 0 R + (N0 R )c AN 0 R S + hc, Hugo Serôdio (KAIST) October 30, / 24

36 The leptonic sector Π 1 = 0, Π 2 = 0 0 0, Π 3 =, Two right-handed neutrinos Σ 3 = 0 0 m ν v 2 3 ei(α PQ 2α 3 ) 2 2v PQ Σ 3 A 1 Σ 3 T = One massless light neutrino Leptonic sector with a BGL suppression, but with CKM replaced by PMNS ( N e )ij = (v v 2 2 ) v 2 3 (D e ) ij + v 2 (U ) i3 (U) 3j (D e ) jj Hugo Serôdio (KAIST) October 30, / 24 v 2 3

37 Axion properties Axion-gluon coupling: C ag = 1, N DW = 1 Hugo Serôdio (KAIST) October 30, / 24

38 Axion properties Axion-gluon coupling: C ag = 1, N DW = 1 Axion-photon coupling: C aγ /C ag = 26/3 Hugo Serôdio (KAIST) October 30, / 24

39 Axion properties Axion-gluon coupling: C ag = 1, N DW = 1 Axion-photon coupling: C aγ /C ag = 26/3 Axion flavor changing interaction µ a [ ( ) ( ) ] µγ µ gµe V + γ 5 gµe A e + sγ µ gsd V 2v + γ 5 gsd A d + PQ with g V,A sd = 2V tsv td, g V,A µe = U τ2u τ1 Hugo Serôdio (KAIST) October 30, / 24

40 Axion properties Axion-gluon coupling: C ag = 1, N DW = 1 Axion-photon coupling: C aγ /C ag = 26/3 Axion flavor changing interaction µ a [ ( ) ( ) ] µγ µ gµe V + γ 5 gµe A e + sγ µ gsd V 2v + γ 5 gsd A d + PQ with g V,A sd = 2V tsv td, g V,A µe = U τ2u τ1 K + π + a m a 18 mev µ + e + aγ m a 12 mev V CKM V PMNS V tsv td V τ2v τ Hugo Serôdio (KAIST) October 30, / 24

41 axion-electron axial coupling From stellar evolution and white-dwarf cooling considerations g A ee = 2 + U τ1 2 + v v 2 3 v 2, m a 15/ g A ee mev We can get g A ee [0, 18] In the top-vev dominance regime, ie when v 2 v, one obtains an upper bound on the axion mass m a 17 mev Hugo Serôdio (KAIST) October 30, / 24

42 axion-electron axial coupling From stellar evolution and white-dwarf cooling considerations g A ee = 2 + U τ1 2 + v v 2 3 v 2, m a 15/ g A ee mev We can get g A ee [0, 18] In the top-vev dominance regime, ie when v 2 v, one obtains an upper bound on the axion mass m a 17 mev Models KSVZ DFSZ 3HFPQ BSM fields Q+S Φ 2 +S Φ 2 +Φ 3 +S PQ fields Q, S q, l, Φ 1,2, S q, l, Φ 1,2,3, S (flavor blind) (flavor sensitive) C aγ /C ag 6(XQ em)2 2/3, 8/3 26/3 CtM No Yes Yes FCAI No No Yes N DW 1 3, 6 1 Hugo Serôdio (KAIST) October 30, / 24

43 Hugo Serôdio (KAIST) October 30, / 24

44 Model variations Hugo Serôdio (KAIST) October 30, / 24

45 Hugo Serôdio (KAIST) October 30, / 24

46 Permuting flavors Hugo Serôdio (KAIST) October 30, / 24

47 For: charm single out; up single out Hugo Serôdio (KAIST) October 30, / 24

48 Conclusions II Models with tree-level FCNCs in the down-quark or charged lepton sectors receive important constraints on the PQ scale from familon searches in kaon and muon decays Models with tree-level FCNCs in the down-quark sector for which the up (or charm) quark is singled out receive the strongest upper bound on the axion mass from K + π + a decays since in this case the flavor changing couplings are not as suppressed V usv ud V csv cd V tsv td A large variety of the models considered have N DW = 1 One interesting aspect is the fact that we are able to mimic the DFSZ axion coupling to photons and have at the same time N DW = 1 A zero C aγ can be achieved but only in models with N DW > 1 Hugo Serôdio (KAIST) October 30, / 24

49 Backup Hugo Serôdio (KAIST) October 30, / 24

50 The anomalous implementation Case I Restrictions: X dr = X ur, X tl (X ur X tr ) { XuR X Texture Matching: tr, X tl X tr X ur Anomaly: X tl 1 2 (X ur X tr ) Higgs charges: X Φ1 = X ur, X Φ2 = X tr X tl, X Φ3 = X tl + X ur Yukawa textures Γ 1 =, Γ 2 = 0, Γ 3 = 0 0 0, = 0, 2 = 0 0 0, 3 = 0, Hugo Serôdio (KAIST) October 30, / 24

51 The anomalous implementation Case II Restrictions: X tr = 2X tl X dr, X tl (X ur X tr ) { XtL X Texture Matching: ur + X dr, X tl 1 2 (X ur + X dr ) Anomaly: X ur X dr Higgs charges: X Φ1 = X ur, X Φ2 = X dr, X Φ3 = X tl X dr Yukawa textures Γ 1 = 0, Γ 2 =, Γ 3 = 0 0 0, = 0, 2 = 0, 3 = Hugo Serôdio (KAIST) October 30, / 24

52 The anomalous implementation Case III Restrictions: X tr = X ur + X tl { XuR X Texture Matching: dr, X tl X ur + X dr, X tl (X ur + X dr ), X tl 1 2 (X ur + X dr ) Anomaly: X tl 3 (X ur + X dr ) Higgs charges: same as in Case II Yukawa textures Γ 1 = 0, Γ 2 =, Γ 3 = 0 0 0, = 0, 2 = 0, 3 = Hugo Serôdio (KAIST) October 30, / 24

53 The scalar sector Add complex scalar singlet: S e ix S θ S, with 0 S 0 0 Φ i 0 The scalar potential: V (Φ, S) = [V (Φ, S)] blind + [V (Φ, S)] sen [V (Φ, S)] blind =m 2 i Φ i Φ i + λ ii,jj (Φ i Φ i + m 2 S S 2 + λ S S 4 + λ ΦS i (Φ i Φ i) S 2 ) ( ) ( ) ( ) Φ j Φ j + λ ij,ji Φ i Φ j Φ j Φ i Hugo Serôdio (KAIST) October 30, / 24

54 The scalar sector Add complex scalar singlet: S e ix S θ S, with 0 S 0 0 Φ i 0 The scalar potential: V (Φ, S) = [V (Φ, S)] blind + [V (Φ, S)] sen [V (Φ, S)] blind =m 2 i Φ i Φ i + λ ii,jj (Φ i Φ i + m 2 S S 2 + λ S S 4 + λ ΦS i (Φ i Φ i) S 2 ) ( ) ( ) ( ) Φ j Φ j + λ ij,ji Φ i Φ j Φ j Φ i [V (Φ, S)] blind is U(1) 4 invariant We need two phase sensitive terms U(1) 4 U(1) PQ U(1) Y Hugo Serôdio (KAIST) October 30, / 24

55 The anomalous implementation Case Phase sensitive ( ) ( ) Constraint (1) Φ 1 Φ 2 Φ 1 Φ 3 ( ) ( ) X Φ2 + X Φ3 2X Φ1 = 0 (2) Φ 2 Φ 1 Φ 2 Φ 3 ( ) ( ) X Φ3 + X Φ1 2X Φ2 = 0 (3) Φ 3 Φ 1 ( ) Φ 3 Φ 2 X Φ1 + X Φ2 2X Φ3 = 0 (4) Φ 1 Φ 2 {S, S } k 1 ( ) k 1 X S = (X Φ2 X Φ1 ) (5) Φ 1 Φ 3 {S, S } k 2 ( ) k 2 X S = (X Φ3 X Φ1 ) (6) Φ 2 Φ 3 {S, S } k 3 k 3 X S = (X Φ3 X Φ2 ) Combinations T 1,2 : (4) + (5), T 3,4 : (4) + (6), T 5,6 : (5) + (6), T 7 : (4) + (5) + (1), T 8 : (4) + (6) + (2), T 9 : (5) + (6) + (3) T 10 : (4) + (5) + (6) + (1), T 11 : (4) + (5) + (6) + (2), T 12 : (4) + (5) + (6) + (3) Hugo Serôdio (KAIST) October 30, / 24

56 Axion properties T 1 T 2 T 3 T 4 T 5 T 6 T 7 T 8 T 9 T 10 T 11 T 12 N I DW N II DW N III DW Hugo Serôdio (KAIST) October 30, / 24

57 Hugo Serôdio (KAIST) October 30, / 24

58 Hugo Serôdio (KAIST) October 30, / 24

59 Models KSVZ DFSZ 3HFPQ BSM fields Q+S Φ 2 +S Φ 2 +Φ 3 +S PQ fields Q, S q, l, Φ 1,2, S q, l, Φ 1,2,3, S (flavor blind) (flavor sensitive) C aγ /C ag 6(XQ em)2 2/3, 8/3 [ 34/3, 44/3] Tree-level CtM No Yes Yes Tree-level FCAI No No Yes N DW 1 3, 6 1, 2,, 8 Hugo Serôdio (KAIST) October 30, / 24