1. Lepton flavour and neutrino mass aspects of the Ma-model Alexander Merle Max-Planck-Institute for Nuclear Physics Heidelberg, Germany Based on: Adulpravitchai, Lindner, AM: Confronting Flavour Symmetries and extended Scalar Sectors with Lepton Flavour Violation Bounds, Phys. Rev. D80 (2009) 055031 Adulpravitchai, Lindner, AM, Mohapatra: Radiative Trans- mission of Lepton Flavor Hierarchies, Phys. Lett. B680 (2009) 476 - 479 Southampton, Friday Seminar, October 30, 2009

2. Contents: 1.Introduction 2.The Ma-model 3.Flavour and the Ma-model 4.The LR-extension of the Ma-model 5.Conclusions

3. 1. Introduction: Particle masses

4. the masses of the Standard Model particles seem to increase with the generation number HOWEVER: neutrinos have masses that are (at least) a factor of 10 6 smaller than the one of the electron → neutrino masses do not seem to have the same origin as the other masses there are different possibilities to generate small neutrino masses

5. the masses of the Standard Model particles seem to increase with the generation number HOWEVER: neutrinos have masses that are (at least) a factor of 10 6 smaller than the one of the electron → neutrino masses do not seem to have the same origin as the other masses there are different possibilities to generate small neutrino masses

6. the masses of the Standard Model particles seem to increase with the generation number HOWEVER: neutrinos have masses that are (at least) a factor of 10 6 smaller than the one of the electron → neutrino masses do not seem to have the same origin as the other masses there are different possibilities to generate small neutrino masses

7. Tree-level diagrams: e.g. seesaw type I

9. good: “natural” value for the Yukawa coupling “natural” explanation for large M R bad: scale for M R is arbitrary

10. Radiative masses: e.g. Zee/Wolfenstein model

12. good: neutrino mass loop suppressed bad: this model is ruled out…

13. 2. Ma’s scotogenic model (Ma-model)

14. Ingredients apart from the SM: 3 heavy right-handed Majorana neutrinos N k (SM singlets) second Higgs doublet η without VEV (with SM-like quantum numbers) additional Z 2 -parity, under which all particles are even except for N k and η

15. 2. Ma’s scotogenic model (Ma-model) Ingredients apart from the SM: 3 heavy right-handed Majorana neutrinos N k (SM singlets) second Higgs doublet η without VEV (with SM-like quantum numbers) additional Z 2 -parity, under which all particles are even except for N k and η

16. 2. Ma’s scotogenic model (Ma-model) Ingredients apart from the SM: 3 heavy right-handed Majorana neutrinos N k (SM singlets) second Higgs doublet η without VEV (with SM-like quantum numbers) additional Z 2 -parity, under which all particles are even except for N k and η

17. 2. Ma’s scotogenic model (Ma-model) Ingredients apart from the SM: 3 heavy right-handed Majorana neutrinos N k (SM singlets) second Higgs doublet η without VEV (with SM-like quantum numbers) additional Z 2 -parity, under which all particles are even except for N k and η

18. Features of the Ma-model: relatively minimal extension of the SM (essentially a 2HDM) Z 2 -parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η 0 or lightest heavy Neutrino N 1 tree-level neutrino mass vanishes → generated at 1 loop

19. Features of the Ma-model: relatively minimal extension of the SM (essentially a 2HDM) Z 2 -parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η 0 or lightest heavy Neutrino N 1 tree-level neutrino mass vanishes → generated at 1 loop

20. Features of the Ma-model: relatively minimal extension of the SM (essentially a 2HDM) Z 2 -parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η 0 or lightest heavy Neutrino N 1 tree-level neutrino mass vanishes → generated at 1 loop

21. Features of the Ma-model: relatively minimal extension of the SM (essentially a 2HDM) Z 2 -parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η 0 or lightest heavy Neutrino N 1 tree-level neutrino mass vanishes → generated at 1 loop

22. The Ma-model neutrino mass:

23. Yukawa coupling:

24. The Ma-model neutrino mass: Yukawa coupling: This part would lead to a neutrino mass. BUT: ‹η 0 ›=0 → tree-level contribution vanishes

25. The Ma-model neutrino mass: Yukawa coupling: This part would lead to a neutrino mass. BUT: ‹η 0 ›=0 → tree-level contribution vanishes

26. Leading order: 1-loop diagram

31. Light neutrino mass matrix:

34. Higgs masses:

35. Light neutrino mass matrix: Features: “natural” Yukawa couplings loop suppression 1/(16π 2 ) radiative seesaw → TeV-scale heavy neutrinos

36. Light neutrino mass matrix: Features: “natural” Yukawa couplings loop suppression 1/(16π 2 ) radiative seesaw → TeV-scale heavy neutrinos

37. Light neutrino mass matrix: Features: “natural” Yukawa couplings loop suppression 1/(16π 2 ) radiative seesaw → TeV-scale heavy neutrinos

38. Light neutrino mass matrix: Features: “natural” Yukawa couplings loop suppression 1/(16π 2 ) radiative seesaw → TeV-scale heavy neutrinos

39. 3. Flavour and the Ma-model:

40. The Yukawa coupling that enters into the neutrino mass also generates LFV processes:

41. 3. Flavour and the Ma-model: The Yukawa coupling that enters into the neutrino mass also generates LFV processes:

42. 3. Flavour and the Ma-model: The Yukawa coupling that enters into the neutrino mass also generates LFV processes:

43. LFV-processes are strongly constrained (MEGA experiment):

44. BUT: these bounds only constrain combinations of Yukawa coupling elements → cancellations possible → no problem for the Ma-model

45. LFV-processes are strongly constrained (MEGA experiment): BUT: these bounds only constrain combinations of Yukawa coupling elements → cancellations possible → no problem for the Ma-model

46. What will happen if a (discrete) flavour symmetry is imposed?

47. without symmetry, the combination of Yukawa coupling matrix elements can be zero a flavour symmetry imposes structure on the Yukawa matrix → easy example: h 11 =h 12 =h 13 =h 21 =h 22 =h 23 =a, h 31 =h 32 =h 33 =0 → then, the above amounts to: 3|a| 2 → trivial or non-zero → may get in conflict with the constraints

48. What will happen if a (discrete) flavour symmetry is imposed? without symmetry, the combination of Yukawa coupling matrix elements can be zero a flavour symmetry imposes structure on the Yukawa matrix → easy example: h 11 =h 12 =h 13 =h 21 =h 22 =h 23 =a, h 31 =h 32 =h 33 =0 → then, the above amounts to: 3|a| 2 → trivial or non-zero → may get in conflict with the constraints

49. What will happen if a (discrete) flavour symmetry is imposed? without symmetry, the combination of Yukawa coupling matrix elements can be zero a flavour symmetry imposes structure on the Yukawa matrix → easy example: h 11 =h 12 =h 13 =h 21 =h 22 =h 23 =a, h 31 =h 32 =h 33 =0 → then, the above amounts to: 3|a| 2 → trivial or non-zero → may get in conflict with the constraints

50. What will happen if a (discrete) flavour symmetry is imposed? without symmetry, the combination of Yukawa coupling matrix elements can be zero a flavour symmetry imposes structure on the Yukawa matrix → easy example: h 11 =h 12 =h 13 =h 21 =h 22 =h 23 =a, h 31 =h 32 =h 33 =0 → then, the above amounts to: 3|a| 2 → trivial or non-zero → may get in conflict with the constraints

51. What will happen if a (discrete) flavour symmetry is imposed? without symmetry, the combination of Yukawa coupling matrix elements can be zero a flavour symmetry imposes structure on the Yukawa matrix → easy example: h 11 =h 12 =h 13 =h 21 =h 22 =h 23 =a, h 31 =h 32 =h 33 =0 → then, the above amounts to: 3|a| 2 → trivial or non-zero → may get in conflict with the constraints

52. What will happen if a (discrete) flavour symmetry is imposed? without symmetry, the combination of Yukawa coupling matrix elements can be zero a flavour symmetry imposes structure on the Yukawa matrix → easy example: h 11 =h 12 =h 13 =h 21 =h 22 =h 23 =a, h 31 =h 32 =h 33 =0 → then, the above amounts to: 3|a| 2 → trivial or non-zero → may get in conflict with the constraints

53. What will happen if a (discrete) flavour symmetry is imposed? without symmetry, the combination of Yukawa coupling matrix elements can be zero a flavour symmetry imposes structure on the Yukawa matrix → easy example: h 11 =h 12 =h 13 =h 21 =h 22 =h 23 =a, h 31 =h 32 =h 33 =0 → then, the above amounts to: 3|a| 2 → trivial or non-zero → may get in conflict with the constraints

54. Key points (for multi-scalar models): the Yukawa coupling elements are not arbitrary: - flavour symmetry imposes structure - correct neutrino masses required - Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate) these ingredients are easily sufficient to destroy the models consistency with LFV- constraints!

55. Key points (for multi-scalar models): the Yukawa coupling elements are not arbitrary: - flavour symmetry imposes structure - correct neutrino masses required - Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate) these ingredients are easily sufficient to destroy the models consistency with LFV- constraints!

56. Key points (for multi-scalar models): the Yukawa coupling elements are not arbitrary: - flavour symmetry imposes structure - correct neutrino masses required - Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate) these ingredients are easily sufficient to destroy the models consistency with LFV- constraints!

57. Key points (for multi-scalar models): the Yukawa coupling elements are not arbitrary: - flavour symmetry imposes structure - correct neutrino masses required - Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate) these ingredients are easily sufficient to destroy the models consistency with LFV- constraints!

58. Key points (for multi-scalar models): the Yukawa coupling elements are not arbitrary: - flavour symmetry imposes structure - correct neutrino masses required - Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate) these ingredients are easily sufficient to destroy the models consistency with LFV- constraints!

59. Key points (for multi-scalar models): the Yukawa coupling elements are not arbitrary: - flavour symmetry imposes structure - correct neutrino masses required - Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate) these ingredients are easily sufficient to destroy the models consistency with LFV- constraints!

60. Two explicit examples:

61. Model 1: A 4 x Z 4,aux → very predictive

62. Two explicit examples: Model 1: A 4 x Z 4,aux → very predictive

63. Two explicit examples: Model 1: A 4 x Z 4,aux → very predictive

64. Two explicit examples: Model 1: A 4 x Z 4,aux → very predictive

65. Two explicit examples: Model 1: A 4 x Z 4,aux → very predictive 3 free parameters: a, b, M

66. Two explicit examples: Model 2: D 4 x Z 2,aux → less predictive

67. Two explicit examples: Model 2: D 4 x Z 2,aux → less predictive

68. Two explicit examples: Model 2: D 4 x Z 2,aux → less predictive

69. Two explicit examples: Model 2: D 4 x Z 2,aux → less predictive M R diagonal

70. Two explicit examples: Model 2: D 4 x Z 2,aux → less predictive 7 free parameters: a, b, c, d, M 1, M 2, M 3 M R diagonal

71. Constraints on the Higgs sector with η 0 as DM:

72. DM: only a few parameter ranges lead to the correct abundance ρ-parameter decay widths of W ± and Z 0 & collider limits stability & consistency

73. Constraints on the Higgs sector with η 0 as DM: DM: only a few parameter ranges lead to the correct abundance ρ-parameter decay widths of W ± and Z 0 & collider limits stability & consistency

74. Constraints on the Higgs sector with η 0 as DM: DM: only a few parameter ranges lead to the correct abundance ρ-parameter decay widths of W ± and Z 0 & collider limits stability & consistency

75. Constraints on the Higgs sector with η 0 as DM: DM: only a few parameter ranges lead to the correct abundance ρ-parameter decay widths of W ± and Z 0 & collider limits stability & consistency

76. Constraints on the Higgs sector with η 0 as DM: DM: only a few parameter ranges lead to the correct abundance ρ-parameter decay widths of W ± and Z 0 & collider limits stability & consistency → 4 scenarios:

77. Then, one can fit the neutrino data:

78. Model 1:

79. Then, one can fit the neutrino data: Model 2:Model 1:

80. Then, one can fit the neutrino data: Model 2:Model 1:

81. Example: Model 1 & Scenario α

82. Method: χ 2 -fit

83. Example: Model 1 & Scenario α Method: χ 2 -fit Best-fit parameters: model fits neutrino data

84. Example: Model 1 & Scenario α Method: χ 2 -fit Best-fit parameters: model fits neutrino data 1σ- and 3σ-ranges: quite narrow

85. LFV: e i →e j γ and μ-e conversion

89. Results for Model 1 (A 4 -model, 3 D.O.F.):

91. the model is very predictive (3 params) when fitted to neutrino data, this model is already ruled out by μ→eγ

92. Results for Model 2 (D 4 -model, 7 D.O.F.):

94. the model is less predictive (7 params) BUT: even this model is (can be) excluded by current (future) data for 2 scenarios

95. The general principle behind:

96. any model with an extended scalar sector will lead to flavour changing neutral currents (under “normal” circumstances) as LFV only constrains combinations of Yukawa matrix elements, cancellations can always rescue the model flavour symmetries impose more structure and can destroy the possibility of cancellations → will be true in a much more general context

97. The general principle behind: any model with an extended scalar sector will lead to flavour changing neutral currents (under “normal” circumstances) as LFV only constrains combinations of Yukawa matrix elements, cancellations can always rescue the model flavour symmetries impose more structure and can destroy the possibility of cancellations → will be true in a much more general context

98. The general principle behind: any model with an extended scalar sector will lead to flavour changing neutral currents (under “normal” circumstances) as LFV only constrains combinations of Yukawa matrix elements, cancellations can always rescue the model flavour symmetries impose more structure and can destroy the possibility of cancellations → will be true in a much more general context

99. The general principle behind: any model with an extended scalar sector will lead to flavour changing neutral currents (under “normal” circumstances) as LFV only constrains combinations of Yukawa matrix elements, cancellations can always rescue the model flavour symmetries impose more structure and can destroy the possibility of cancellations → will be true in a much more general context

100. 4. The LR-version of the Ma-model:

101. There are still questions left:

102. 4. The LR-version of the Ma-model: There are still questions left: Can the Ma-model be extended to the quark sector? Is there an “origin” of the Ma-model structure? Can the model be embedded into a GUT?

103. 4. The LR-version of the Ma-model: There are still questions left: Can the Ma-model be extended to the quark sector? Is there an “origin” of the Ma-model structure? Can the model be embedded into a GUT?

104. 4. The LR-version of the Ma-model: There are still questions left: Can the Ma-model be extended to the quark sector? Is there an “origin” of the Ma-model structure? Can the model be embedded into a GUT?

105. 4. The LR-version of the Ma-model: There are still questions left: Can the Ma-model be extended to the quark sector? Is there an “origin” of the Ma-model structure? Can the model be embedded into a GUT? → consider a left-right symmetric extension

106. Particle content:

108. scalar bi-doublet: contains the SM-Higgs as well as the inert Higgs η Higgs triplets: allow for a symmetry breaking pattern that leads to an effective Ma-model in the lepton sector (LR → Ma → effective SM) additional Z 4 -symmetry → will play the role of an effective Z 2 -parity in the lepton sector

109. Particle content: scalar bi-doublet: contains the SM-Higgs as well as the inert Higgs η Higgs triplets: allow for a symmetry breaking pattern that leads to an effective Ma-model in the lepton sector (LR → Ma → effective SM) additional Z 4 -symmetry → will play the role of an effective Z 2 -parity in the lepton sector

110. Particle content: scalar bi-doublet: contains the SM-Higgs as well as the inert Higgs η Higgs triplets: allow for a symmetry breaking pattern that leads to an effective Ma-model in the lepton sector (LR → Ma → effective SM) additional Z 4 -symmetry → will play the role of an effective Z 2 -parity in the lepton sector

111. VEV structure:

112. → like in the Ma-model

113. VEV structure: → like in the Ma-model → LR-breaking

114. VEV structure: → like in the Ma-model → LR-breaking → no tree-level light neutrino mass

115. VEV structure: → like in the Ma-model → LR-breaking → below SU(2) R x U(1) B-L breaking scale, the model is an effective Ma-like model → no tree-level light neutrino mass

116. The neutrino mass formula:

117. most general Yukawa coupling:

118. The neutrino mass formula: most general Yukawa coupling: key point: the neutrino Yukawa couplings are the same as the ones of the charged leptons

119. The neutrino mass formula: most general Yukawa coupling: key point: the neutrino Yukawa couplings are the same as the ones of the charged leptons → then, the neutrino mass formula looks like:

120. The neutrino mass formula: most general Yukawa coupling: key point: the neutrino Yukawa couplings are the same as the ones of the charged leptons → then, the neutrino mass formula looks like: IMPORTANT: charged lepton masses involved

122. Plausible assumption for scalar Dark Matter:

123. → this leads to:

124. Plausible assumption for scalar Dark Matter: → this leads to: The log-term can be absorbed into M N …

125. Then, the light neutrino mass matrix is given by:

126. m l =diag(m e,m μ,m τ )

127. Then, the light neutrino mass matrix is given by: m l =diag(m e,m μ,m τ ) → everything known except for λ 5 and M N

128. Then, the light neutrino mass matrix is given by: m l =diag(m e,m μ,m τ ) → everything known except for λ 5 and M N → with a certain form for the light neutrino mass matrix, it is possible to reconstruct M N !

129. Then, the light neutrino mass matrix is given by: m l =diag(m e,m μ,m τ ) → everything known except for λ 5 and M N → with a certain form for the light neutrino mass matrix, it is possible to reconstruct M N ! → radiative transmission of hierarchies!

130. Radiative transmission of hierarchies:

131. tri-bimaximal form for U PMNS (semi-realistic) → it is possible to reconstruct the heavy neutrino mass matrix:

132. Radiative transmission of hierarchies: a tri-bimaximal form for U PMNS (semi-realistic) → it is possible to reconstruct the heavy neutrino mass matrix:

133. Radiative transmission of hierarchies: tri-bimaximal form for U PMNS (semi-realistic) → it is possible to reconstruct the heavy neutrino mass matrix: → roughly:

134. Radiative transmission of hierarchies: tri-bimaximal form for U PMNS (semi-realistic) → it is possible to reconstruct the heavy neutrino mass matrix: → M N has a form that can easily be obtained by the Froggat-Nielsen mechanism! → roughly:

135. Key points:

136. the hierarchical structure of the charged lepton masses translates a (quasi) Froggat- Nielsen pattern of M N into an anarchical form of the light neutrino mass matrix this makes large mixing angles in the lepton sector perfectly possible! no flavour symmetry argument is required

137. Key points: the hierarchical structure of the charged lepton masses translates a (quasi) Froggat- Nielsen pattern of M N into an anarchical form of the light neutrino mass matrix this makes large mixing angles in the lepton sector perfectly possible! no flavour symmetry argument is required

138. Key points: the hierarchical structure of the charged lepton masses translates a (quasi) Froggat- Nielsen pattern of M N into an anarchical form of the light neutrino mass matrix this makes large mixing angles in the lepton sector perfectly possible! no flavour symmetry argument is required

139. Key points: the hierarchical structure of the charged lepton masses translates a (quasi) Froggat- Nielsen pattern of M N into an anarchical form of the light neutrino mass matrix this makes large mixing angles in the lepton sector perfectly possible! no flavour symmetry argument is required → the radiative transmission is a mechanism that can explain large mixings for leptons

140. Currently under investigation:

141. “problem”: ‹η 0 ›=0 → down quarks massless → two ways out: soft Z 2 -breaking with colour triplet scalars ω L,R (→ 1-loop d-mass) OR introduction of new vector-like down-quarks

142. Currently under investigation: FCNCs in the quark sector “problem”: ‹η 0 ›=0 → down quarks massless → two ways out: soft Z 2 -breaking with colour triplet scalars ω L,R (→ 1-loop d-mass) OR introduction of new vector-like down-quarks

143. Currently under investigation: FCNCs in the quark sector further investigations of radiative transmission “problem”: ‹η 0 ›=0 → down quarks massless → two ways out: soft Z 2 -breaking with colour triplet scalars ω L,R (→ 1-loop d-mass) OR introduction of new vector-like down-quarks

144. 5. Conclusions:

145. the Ma-model is an interesting toy with surprisingly many interesting features it is the prime example for the fact that extended scalar sectors in combination with flavour symmetries have trouble with LFV the LR-extension of the Ma-model even yields a new possibility to simultaneously generate small neutrino masses and large lepton mixings hopefully, the surprises will go on…

146. 5. Conclusions: the Ma-model is an interesting toy with surprisingly many interesting features it is the prime example for the fact that extended scalar sectors in combination with flavour symmetries have trouble with LFV the LR-extension of the Ma-model even yields a new possibility to simultaneously generate small neutrino masses and large lepton mixings hopefully, the surprises will go on…

147. 5. Conclusions: the Ma-model is an interesting toy with surprisingly many interesting features it is the prime example for the fact that extended scalar sectors in combination with flavour symmetries have trouble with LFV the LR-extension of the Ma-model even yields a new possibility to simultaneously generate small neutrino masses and large lepton mixings hopefully, the surprises will go on…

148. 5. Conclusions: the Ma-model is an interesting toy with surprisingly many interesting features it is the prime example for the fact that extended scalar sectors in combination with flavour symmetries have trouble with LFV the LR-extension of the Ma-model even yields a new possibility to simultaneously generate small neutrino masses and large lepton mixings hopefully, the surprises will go on…

149. THANK YOU!!!