Cabibbo s dream. Belén Gavela. (Alonso, Gavela, D.Hernandez, Merlo, Rigolin) (Alonso, Gavela, Isidori, Maiani)

Transcription

1 Cabibbo s dream Belén Gavela (Alonso, Gavela, D.Hernandez, Merlo, Rigolin) (Alonso, Gavela, Isidori, Maiani)

2 Cabibbo s dream: dynamical origin of mass Belén Gavela (Alonso, Gavela, D.Hernandez, Merlo, Rigolin) (Alonso, Gavela, Isidori, Maiani)

3 BSM because 1) Experimental evidence for new particle physics: *** Neutrino masses *** Dark matter *** CMB polarization?

4 BSM because 1) Experimental evidence for new particle physics: *** Neutrino masses *** Dark matter *** CMB polarization? Bicep2!

5 BSM because 1) Experimental evidence for new particle physics: *** Neutrino masses *** Dark matter *** CMB polarization? Bicep2! New energy-density scale? V~ GeV ~ m φ 2 φ 2 à m φ ~ GeV or higher mass scale"

6 BSM because 1) Experimental evidence for new particle physics: *** Neutrino masses *** Dark matter *** CMB polarization? 2) SM fine-tunings/uneasiness

7 SU(3) x SU(2) x U(1) x classical gravity We ~understand ordinary particles= excitations over the vacuum We DO NOT understand the vacuum = state of lowest energy:

8 SU(3) x SU(2) x U(1) x classical gravity We ~understand ordinary particles= excitations over the vacuum We DO NOT understand the vacuum = state of lowest energy: The gravity vaccuum: cosmological cte. Λ, Λ Μ Planck 4

9 SU(3) x SU(2) x U(1) x classical gravity We ~understand ordinary particles= excitations over the vacuum We DO NOT understand the vacuum = state of lowest energy: The gravity vaccuum: cosmological cte. Λ, Λ Μ Planck 4 * The QCD vaccuum : Strong CP problem, θ QCD <10 _ -10

10 SU(3) x SU(2) x U(1) x classical gravity We ~understand ordinary particles= excitations over the vacuum We DO NOT understand the vacuum = state of lowest energy: The gravity vaccuum: cosmological cte. Λ, Λ Μ Planck 4 * The QCD vaccuum : Strong CP problem, θ QCD _ <10-10 * The electroweak vaccuum: Higgs-mass, v.e.v.~o (100) GeV

11 SU(3) x SU(2) x U(1) x classical gravity We ~understand ordinary particles= excitations over the vacuum We DO NOT understand the vacuum = state of lowest energy: The gravity vaccuum: cosmological cte. Λ, Λ Μ Planck 4 * The QCD vaccuum : Strong CP problem, θ QCD _ <10-10 * The electroweak vaccuum: Higgs-mass, v.e.v.~o (100) GeV The Higgs excitation has the quantum numbers of the EW vacuum

12 BSM because 1) Experimental evidence for new particle physics: *** Neutrino masses *** Dark matter *** CMB polarization? 2) SM fine-tunings/uneasiness, i.e. in electroweak: *** Hierarchy problem *** Flavour puzzle

13 BSM electroweak * HIERARCHY PROBLEM fine-tuning issue: if there is BSM physics, why is the Higgs so light? à SUSY?, strong-int. Higgs?, extra-dim?. In practice, none without further fine-tunings FLAVOUR PUZZLE

14 No se puede mostrar la imagen. Puede que su equipo no tenga suficiente memoria para abrir la imagen o que ésta esté dañada. Reinicie el equipo y, a continuación, abra el archivo de nuevo. Si sigue apareciendo la x roja, puede que tenga que borrar la imagen e insertarla de nuevo.

15 The Flavour Puzzle u ν e c ν µ t ν τ d e s µ b τ Why so diferent masses and mixing angles?

16 The Flavour Puzzle u ν e c ν µ t ν τ d e s µ b τ Why has nature chosen the number and properties of families so as to allow for CP violation... and explain nothing? (i.e. not enough for matter-antimatter asymmetry) (quark)!

17 BSM electroweak * HIERARCHY PROBLEM fine-tuning issue: if there is BSM physics, why is the Higgs so light? à SUSY?, strong-int. Higgs?, extra-dim?. In practice, none without further fine-tunings FLAVOUR PUZZLE: no progress Understanding stalled since 30 years. Only new B physics data AND neutrino masses and mixings BSMs tend to make it worse

18 BSM electroweak * HIERARCHY PROBLEM fine-tuning issue: if there is BSM physics, why is the Higgs so light? à SUSY?, strong-int. Higgs?, extra-dim?. In practice, none without further fine-tunings FLAVOUR PUZZLE: no progress Understanding stalled since 30 years. Only new B physics data AND neutrino masses and mixings BSMs tend to make it worse Λ electroweak ~ 1 TeV? Λ flavour ~ 100 TeVs???

19 The FLAVOUR WALL for BSM BSM theories usually die or are very unsatisfactory when confronted with: i) Electric dipole moments (quarks and leptons) ii) FCNC processes (quarks and leptons) iii) Strong CP problem iii) Matter-antimatter asymmetry competing with SM at one-loop

20 BSM because 1) Experimental evidence for new particle physics: *** Neutrino masses *** Dark matter *** CMB polarization? 2) SM fine-tunings/uneasiness, i.e. in electroweak: *** Hierarchy problem *** Flavour puzzle Pattern of masses and mixings in visible universe "

21 Masses of the matter particles of the visible universe

22

23 Masses of the matter particles of the visible universe

24 Masses in SM In SM, mass is a sort of friction with a field that permeates vaccuum: the Higgs field t m t Higgs

25 Masses in SM In SM, mass is a sort of friction with a field that permeates vaccuum: the Higgs field H m H Higgs

26 The Higgs field is the source of masses in the SM ~" δl m = Q Y d H d + Q Y u H u + h.c." Η Yd m d ~ Y d v" d d Η u Yu u m u ~ Y u v"

27 The Higgs field is the source of masses in the SM ~" δl m = Q Y d H d + Q Y u H u + h.c." <Η>=v= 250 GeV Yd m d ~ Y d v" d d <Η>=v u Yu u m u ~ Y u v"

28 The Higgs field is the source of masses in the SM ~" δl m = Q Y d H d + Q Y u H u + h.c." YUKAWAs" are numbers" <Η>=v= 250 GeV Yd m d ~ Y d v" d d <Η>=v u Yu u m u ~ Y u v"

29 The mass spectrum in terms of YUKAWA couplings Y! ~10-12 ~10-6 ~1

30 Neutrino light on flavour? 30!3

31 Neutrinos lighter because Majorana?

32 Neutrinos lighter because Majorana? - ν = ν

33 * To have a Majorana mass - ν= ν * (that is, Majorana neutrino) * L non conserved are all equivalent concepts Any of them implies the other two Kayser

34 Simple case: add right-handed neutrino to SM

35 S E E S A W Simple case: add right-handed neutrino to SM allowed by SM gauge invariance "

36 S E E S A W Simple case: add right-handed neutrino to SM allowed by SM gauge invariance " M" * For M > v :" " m 1 ~ M" m 2 ~ Y 2 v 2 /M"

37 S E E S A W Simple case: add right-handed neutrino to SM

38 S E E S A W Simple case: add right-handed neutrino to SM At energies E<M: "

39 In pure SM, the mass spectrum in terms of YUKAWA couplings: Y! ~10-12 ~10-6 ~1

40 Within seesaw, the size of neutrino Yukawa couplings is similar to that for other fermions: M" Y! M" Y! Pilar Hernandez drawings

41 Neutrino oscillations demonstrated leptonic flavour violation in nature

42 VCKM u d VPMNS l + ν

43 DIRAC O MAJORANA" IF MAJORANA"

44 Leptons V PMNS = ~ 9º Quarks V CKM = ~1 λ λ 3 λ ~1 λ 2 λ 3 λ 2 ~1 Why so different? λ~0.2

45 Leptons V PMNS = ~ 9º Quarks V CKM = ~1 λ λ 3 λ ~1 λ 2 λ 3 λ 2 ~1 λ~0.2 Perhaps also because νs may be Majorana?

46 Neutrino are optimal windows into the exotic -dark- sectors * Can mix with new neutral fermions, heavy or light * Interactions not obscured by strong and e.m. ones

47 Dark portals Only three singlet combinations in SM with d < 4: H + H Scalar Bµν Vector L H Fermionic Any hidden sector, singlet under SM, can couple to the dark portals 47

48 Dark portals H + H S Scalar Bµν Vμν Vector L H Ψ Fermionic Any hidden sector, singlet under SM, can couple to the dark portals 48

49 Dark portals H + H S 2 Scalar Bµν Vμν Vector L H Ψ Fermionic Any hidden sector, singlet under SM, can couple to the dark portals 49

50 Dark portals H + H S 2 Scalar Bµν Vμν Vector L H Ψ Fermionic Yukawa coupling fermion singlets Ψ = right-handed neutrino 50

51 DARK FLAVOURS?... they can be fermions

52 DARK FLAVOURS?

53 DARK FLAVOURS?

54 DARK FLAVOURS?

55 DARK FLAVOURS?

56 For the rest of the talk: 3 light families of quarks and leptons

57 Dynamical Yukawas

58 Yukawa couplings are the source of flavour in the SM ~" δl m = Q Y d H d + Q Y u H u + h.c." H YD QL DR H YU QL UR

59 Yukawa couplings are the source of flavour in the νsm H (i.e. Seesaw type-i) YE L ER H Yν L νr

60 May they correspond to dynamical fields (e.g. vev of fields that carry flavor)? Many attempts: discrete symmetries, continuous symmetries

61 Instead of inventing an ad-hoc symmetry group, why not use the continuous flavour group suggested by the SM itself?

62 We have realized that the different pattern for quarks versus leptons may be a simple consequence of the continuous flavour group of the SM (+ seesaw) (Alonso, Gavela, D.Hernandez, Merlo, Rigolin) 2013 (Alonso, Gavela, Isidori, Maiani)

63 We have realized that the different pattern for quarks versus leptons may be a simple consequence of the continuous flavour group of the SM (+ seesaw) Our guideline is to use: - maximal symmetry - minimal field content 2013 (Alonso, Gavela, D.Hernandez, Merlo, Rigolin) (Alonso, Gavela, Isidori, Maiani)

64 Global flavour symmetry of the SM * QCD has a global -chiral- symmetry in the limit of massless quarks. For n generations: fermions * In the SM, fermion masses and mixings result from Yukawa couplings. For massless quarks, the SM has a global flavour symmetry: Quarks fermions SM Gflavour [Georgi, Chivukula, 1987]

65 Global flavour symmetry of the SM * QCD has a global -chiral- symmetry in the limit of massless quarks. For n generations: fermions * In e.g., the for SM, n=3 fermion : u, d, s masses. The massless and mixings QCD result Lag. is from invariant Yukawa " couplings. interchanging:" For massless quarks, the SM has a global flavour symmetry: u L " u R " Quarks fermions SM s L " Gflavour d L " or" SU(3) L! SU(3) R! s R " d R " [Georgi, Chivukula, 1987]

66 Global flavour symmetry of the SM * QCD has a global -chiral- symmetry in the limit of massless quarks. For n generations: fermions * In the SM, fermion masses and mixings result from Yukawa couplings. For massless quarks, the SM has a global flavour symmetry: Quarks fermions SM Gflavour [Georgi, Chivukula, 1987]

67 There are n=3 quark families. With null Yukawa couplings,! the SM Lag. is invariant under SU(3) QL x SU(3) UR x SU(3) DR " Q L = " u L " d L " c L " s L " t L " b L " Q L 1 " Q 3 u R " L " SU(3) QL! Q L 2 " d R " t R " SU(3) UR! Gflavour c R " or" b R " SU(3) DR! s R "

68 This continuous global symmetry of the SM Gflavour is phenomenologically very successful and at the basis of Minimal Flavour Violation in which the Yukawa couplings are only spurions! H QL Y αβ DR D Ambrosio+Giudice+Isidori+Strumia; Cirigliano+Isidori+Grinstein+Wise

69 This continuous global symmetry of the SM Gflavour is phenomenologically very successful and at the basis of Minimal Flavour Violation in which the Yukawa couplings are only spurions! _" _" Υαβ + Υδγ Qα γµqβ Qγ γ µ Qδ Λf 2 H QL Y αβ DR D Ambrosio+Giudice+Isidori+Strumia; Cirigliano+Isidori+Grinstein+Wise

70 Straub Moriond 2012 AFTER LHCb 2012

71 One step further : dynamical Ys (Alonso, Gavela, D.Hernandez, Merlo, Rigolin, ) (Alonso, Gavela, Isidori, Maiani, 2013)

72 Quarks"

73 For this talk: each YSM -- >one single field Y quarks: YSM ~ < Y > Λf H <Yd > H <Yu > QL DR QL UR Anselm+Berezhiani 96; Berezhiani+Rossi Alonso+Gavela+Merlo+Rigolin Gflavour= SU(3)QL x SU(3)UR x SU(3)DR...

74 For this talk: each YSM -- >one single field Y quarks: H <Yd > YSM ~ < Y > Λ Λf H <Yu > QL _" Yd ~ (3,1,3) DR bifundamentals " QL _" Yu ~ (3,3,1) UR Gflavour= SU(3)QL x SU(3)UR x SU(3)DR...

75 Gflavour= SU(3)QL x SU(3)UR x SU(3)DR... - Yd ~ (3,1,3) - Yu ~ (3,3,1) That is, two dynamical scalars H <Yd > H <Yu > QL DR QL UR

76 Gflavour= SU(3)QL x SU(3)UR x SU(3)DR... - Yd ~ (3,1,3) - Yu ~ (3,3,1) That is, two dynamical scalars H <Yd > H <Yu > QL DR QL UR V(Yd, Yu)?

77 Gflavour= SU(3)QL x SU(3)UR x SU(3)DR... - Yd ~ (3,1,3) - Yu ~ (3,3,1) That is, two dynamical scalars H <Yd > H <Yu > QL DR QL UR * Does the minimum of the scalar potential justify the observed masses and mixings?

78 Yd Yu <Yd> <Yu> =" ="

79 V(Yd, Yu) * Invariant under the SM gauge symmetry * Invariant under its global flavour symmetry Gflavour Gflavour= U(3)QL x U(3)UR x U(3)DR

80 L. Michel+Radicati 70, Cabibbo+Maiani71 for the spectrum of masses List of possible invariants for quarks: Hanani, Jenkins, Manohar 2010

81 L. Michel+Radicati 70, Cabibbo+Maiani71 for the spectrum of masses List of possible invariants: Hanani, Jenkins, Manohar 2010 Cabibbo s dream

82 Flavour Symmetry Breaking Spontaneous breaking of flavour symmetry dangerous To prevent Goldstone Bosons the symmetry can be Gauged [Grinstein, Redi, Villadoro Guadagnoli, Mohapatra, Sung Feldman]

83 V(Yd, Yu) * Invariant under the SM gauge symmetry * Invariant under its global flavour symmetry Gflavour Gflavour= U(3)QL x U(3)UR x U(3)DR There are as many independent invariants I as physical variables V(Yd, Yu) = V( I(Yd, Yu))

84 Minimization a variational principle fixes the vevs of Fields" masses, mixing angles etc. This is an homogenous linear equation; if the rank of the Jacobian, Maximum: then the only solution is: is: Less than Maximum: then the number of equations reduces to a number equal to the rank

85 Boundaries for a reduced rank of the Jacobian, there exists (at least) a direction for which a variation of the field variables does not vary the invariants that is a Boundary of the I-manifold [Cabibbo, Maiani,1969] Boundaries Exhibit Unbroken Symmetry [Michel, Radicati, 1969] (maximal subgroups)

86 Boundaries Exhibit Unbroken Symmetry" Extra-dimensions Example" The smallest boundaries are extremal points of any function [Michel, Radicati, 1969]

87 ancestors of dynamical Yukawas decades ago (only to explain the mass spectrum) in Cabibbo Michel,+Radicati, Cabibbo+Maiani... C. D. Froggat, H. B. Nielsen

88 Well before the electroweak SM: masses Jacobian Analysis: [40 years ago ]" Breaking of" [Cabibbo, Maiani] -

89 quark case Bi-fundamental Flavour Fields For quarks: 10 independent invariants (because 6 masses+ 3 angles + 1 phase) that we may choose as [Feldmann, Jung, Mannel; Jenkins, Manohar]

90 Jacobian Analysis: Masses" [U(3)xU(3) broken to] (Alonso, Gavela, Isidori, Maiani 2013)

91 quark case Bi-fundamental Flavour Fields only masses masses and mixings" [Feldmann, Jung, Mannel; Jenkins, Manohar Alonso, Gavela, Isidori, Maiani 2013]

92 Jacobian Analysis: Mixing the rank is reduced the most for: VCKM= PERMUTATION no mixing: reordering of states (Alonso, Gavela, Isidori, Maiani 2013)

93 Quark Natural Flavour Pattern Summarizing, a possible and natural breaking pattern arises: Gflavour (quarks) giving a hierarchical mass spectrum without mixing < YD > < YU > a good approximation to the observed Yukawas to order (λc) 2

94 And what happens for leptons? Any difference with Majorana neutrinos?

95 Leptons

96 Global flavour symmetry of the SM + seesaw * In the SM, for quarks the maximal global symmetry in the limit of massless quarks was: quarks SM Gflavour = * In SM +type I seesaw, for leptons: the maximal leptonic global symmetry in the limit of massless light leptons is -> degenerate heavy neutrinos

97 There are n=3 lepton families. With null Yukawa couplings,! the maximal symmetry of the Lag. is SU(3) L x SU(3) ER x O(3) NR " L = " ν el " e L " ν μl " μ L " ν τl " τ L " L 1 " e R " L 3 " SU(3) L! L 2 " Ν R1 " τ R " SU(3) ΕR! Gflavour μ R " or" Ν R3 " Ο(3) NR! Ν R2 "

98 Ilustration: 2 families (Casas-Ibarra parametrization) for 2 generations, the mixing terms in V(YE, Yν) is : Leptons" Tr(YE YE + Yν Yν + ) Casas-Ibarra variable in R where UPMNS= cosθ sinθ -sinθ cosθ e -iα 0 0 e iα Quarks" Tr(Yu Yu + Yd Yd + )

99 e.g., for 2 generations, the mixing terms in V(YE, Yν) is : Leptons Tr(YE YE + Yν Yν + ) This mixing term unphysical if either up or down fermions degenerate Quarks Tr(Yu Yu + Yd Yd + ) Mixing physical even with degenerate neutrino masses, if Majorana phase non-trivial

100 e.g. for the case of two families: Tr(Yu Yu + Yd Yd + ) at the minimum: V -> NO MIXING mq θ same conclusion for 3 families Berezhiani-Rossi; Anselm, Berezhiani; Alonso, Gavela, Merlo, Rigolin!

101 e.g., for 2 generations, the mixing terms in V(YE, Yν) is : Minimisation (for non trivial sin2ω) Tr(YE YE + Yν Yν + ) * sin2ω α= π/4 or 3π/4 * tgh 2ω Maximal Majorana phase Large angles correlated with degenerate masses

102 * For instance for two generations: O(2)NR e.g. two families mν ~Yν v 2 Yν Τ = y1 y2 v 2 M M UPMNS = e iπ/4 0 0 e -iπ/4 " " " " Degenerate neutrino masses" Generically, O(2) allows : - one mixing angle maximal - one relative Majorana phase of π/2 - two degenerate light neutrinos

103 Now for three generations and considering all possible independent invariants

104 Bi-fundamental Flavour Fields Physical parameters =Independent Invariants Very direct results using the bi-unitary parametrization: Yν= < Yν > = Λf YΕ= < YΕ > = ye Λf * m e, μ, τ= v ye *But the relation of Y with light neutrino masses is through: mν =Y v 2 Y Τ M

105 Bi-fundamental Flavour Fields Physical parameters =Independent Invariants Very direct results using the bi-unitary parametrization: Yν= < Yν > = Λf YΕ= < YΕ > = ye Λf * m e, μ, τ= v ye *But the relation of Y with light neutrino masses is through:

106 Bi-fundamental Flavour Fields Physical parameters =Independent Invariants Very direct results using the bi-unitary parametrization: Yν= < Yν > = Λf YΕ= < YΕ > = ye Λf * m e, μ, τ= v ye *But the relation of Y with light neutrino masses is through: UR is relevant for leptons

107 Number of Physical parameters = number of Independent Invariants 15 invariants for Gflavour (leptons) = Leptons UL and eigenvalues UR and eigenvalues (Alonso, Gavela, Isidori, Maiani 2013) New Invariants wrt Quarks

108 Number of Physical parameters = number of Independent Invariants 15 invariants for Gflavour (leptons) = Leptons UL and eigenvalues UR and eigenvalues (Alonso, Gavela, Isidori, Maiani 2013) New Invariants wrt Quarks

109 Number of Physical parameters = number of Independent Invariants 15 invariants for Gflavour (leptons) = Leptons UL and eigenvalues UR and eigenvalues (Alonso, Gavela, Isidori, Maiani 2013) New Invariants wrt Quarks

110 Jacobian

111 Jacobian Analysis: Mixing same as for VCKM O(3) vs U(3)

112 Jacobian Analysis: Mixing...which is now not trivial mixing......in fact it allows maximal mixing:

113 Jacobian Analysis: Mixing...which is now not trivial mixing... -"...in fact it allows maximal mixing: mν2=mν3 and maximal Majorana phase

114 Jacobian Analysis: Mixing...which is now not trivial mixing... -"...in fact it leads to one maximal mixing angle: θ23 =45 o ; Majorana Phase Pattern (-i,-i,1) & at this level mass degeneracy: mν2 = mν3 related to the O(2) substructure [Alonso, Gavela, D. Hernández, L. Merlo; [Alonso, Gavela, D. Hernández, L. Merlo, S. Rigolin]

115 If the three neutrinos are quasidegenerate, perturbations: -" This very simple structure is signaled by the extrema of the potential and has eigenvalues (1,1,-1) 3 degenerate light neutrinos + a maximal Majorana phase and is diagonalized by a maximal θ = 45º

116 With hierarchical charged leptons, always (either two or three" neutrinos degenerate), the symmetry pattern at this stage is" SU(3) L x SU(3) E x O(3) N! SU(2) E x U(1) diag "

117 Generalization to any seesaw model the effective Weinberg Operator C d=5 shall have a flavour structure that breaks U(3)L to O(3) v 2 C d=5 = -" mν then the results apply to any seesaw model

118 First conclusion: * at the same order in which the minimum of the potential does NOT allow quark mixing, it allows: - hierarchical charged leptons - quasi-degenerate neutrino masses - one angle of ~45 degrees - one maximal Majorana phase

119 The conclusions hold irrespective of the!! renormalizability of the potential,!! and are thus stable under radiative corrections!!

120 Perturbations can produce a second large angle if the three neutrinos are quasidegenerate, perturbations: -" produce a second large angle and a perturbative one together with mass splittings"

121 Perturbations can produce a second large angle if the three neutrinos are quasidegenerate, perturbations: -" produce a second large angle and a perturbative one together with mass splittings" Majorana phases: 1 maximal, 1 large" " Dirac-like CP phase generically large" ~ degenerate spectrum"

122 Perturbations can produce a second large angle if the three neutrinos are quasidegenerate, perturbations: -" produce a second large angle and a perturbative one together with mass splittings" Majorana phases: 1 maximal, 1 large" " Dirac-like CP phase generically large" ~ degenerate spectrum" only this vanishes with the perturbations this angle does not vanish with vanishing perturbations

123 Perturbations can produce a second large angle if the three neutrinos are quasidegenerate, perturbations: -" produce a second large angle and a perturbative one together with mass splittings" Majorana phases: 1 maximal, 1 large" " Dirac-like CP phase generically large" ~ degenerate spectrum"

124 courtesy S. Pascoli"

125 accommodation of angles requires degenerate spectrum at reach in future neutrinoless double β exps.! courtesy S. Pascoli"

126 Cosmology " Battye and Moss"

127 Where do the differences in Mixing originated? in the symmetries of the Quark and Lepton sectors for the type I seesaw employed here;

128 Where do the differences in Mixing originated? in the symmetries of the Quark and Lepton sectors for the type I seesaw employed here; in general

129 Where do the differences in Mixing originated? From the MAJORANA vs DIRAC nature of fermions

130 Conclusions Spontaneous Flavour Symmetry Breaking is a predictive dynamical scenario Simple solutions arise that resemble nature in first approximation The differences in the mixing pattern of Quarks and Leptons arise from their Dirac vs Majorana nature (U vs. O symmetries). O(2) singled out -> O(3). A correlation between large angles and degenerate spectrum emerges. Explicitly, for neutrinos we find: one maximal Majorana phases (α,1,i), θ23 =45 o, θ12 large, θ13 small and deg. ν s This scenario will be tested in the near future by 0ν2β experiments (~.1eV)... or cosmology!!!

131

132 We set the perturbations by hand. Can we predict them also dynamically? Fundamental Fields May provide dynamically the perturbations In the case of quarks they can give the right corrections: [Alonso, Gavela, Merlo, Rigolin] under study in the lepton sector

133 Jacobian Analysis: Eigenvalues [U(3)LxU(3)ER broken to]

134 Renormalizable Potential

135 Invariants at the Renormalizable Level

136 Renormalizable Potential with the definition the potential which contains 8 parameters mass spectrum

137 Renormalizable Potential with the definition the potential mixing which contains 8 parameters

138 Renormalizable Potential, mixing three families Von Neumann Trace Inequality coefficient in the potential normal Hierarchy So the Potential selects: inverted Hierarchy No mixing, independently of the mass spectrum

139 Some good ideas: Minimal Flavour Violation: H QL Ψ σπυριον DR - Use the flavour symmetry of the SM in the limit of massless (Chivukula+ Georgi) fermions quarks: Gflavour= U(3)QL x U(3)UR x U(3)DR - Assume that Yukawas are the only source of flavour in the SM and beyond Υαβ + Υδγ Qα γµqβ Qγ γ µ Qδ Λflavour 2... agrees with flavour data being aligned with SM... allows to bring down Λflavour --> TeV D Ambrosio+Giudice+Isidori+Strumia; Cirigliano+Isidori+Grinstein+Wise

140 Some good ideas: Minimal Flavour Violation: H QL Ψ σπυριον DR - Use the flavour symmetry of the SM in the limit of massless (Chivukula+ Georgi) fermions quarks: Gflavour= U(3)QL x U(3)UR x U(3)DR - Assume that Yukawas are the only source of flavour in the SM and beyond Υαβ + Υδγ Qα γµqβ Qγ γ µ Qδ Λflavour 2... agrees with flavour data being aligned with SM... allows to bring down Λflavour --> TeV (Chivukula+Georgi 87; Hall+Randall; D Ambrosio+Giudice+Isidori+Strumia; Cirigliano+Isidori+Grisntein+Wise; Davidson+Pallorini; Kagan+G. Perez + Volanski+Zupan,... ) Lalak, Pokorski, Ross; Fitzpatrick, Perez, Randall; Grinstein, Redi, Villadoro

141 Bi-fundamental Flavour Fields Physical parameters =Independent Invariants These are (proportional to): 3 masses in de up sector, 3 masses in de down sector, 4 mixing parameters in VCKM

142 Renormalizable Potential, masses

143 This region s size nonetheless depends on the rest of paramters (λ,g) Renormalizable Potential, Stability

144 Renormalizable Potential: Masses

145 * What is the role of the neutrino flavour group? To analyze this in general, use common parametrization for quarks and leptons: Y = UL y diag. UR * Quarks, for instance: UR unphysical, UL --> UCKM YD = UCKM diag(yd, ys, yb) ; YU = diag(yu, yc, yt) * Leptons: YE = diag(ye, yµ, yτ) ; Yν = UL y diag. UR UPMNS diagonalize mν ~Yν v 2 Yν Τ = M UL yν diag. UR v 2 UR T yν diag. UL T M

146 * What is the role of the neutrino flavour group? U(n)

147 * What is the role of the neutrino flavour group? U(n) i.e.: U(3)L x U(3)ER x U(2)NR or: U(3)L x U(3)ER x U(3)NR

148 * What is the role of the neutrino flavour group? e.g. generic seesaw e.g. U(n)NR... leptons M with M carrying flavour M spurion More invariants in this case: Tr ( YE YE + ) Tr ( YE YE + ) 2 Tr ( YE YE + Yν Yν + ) Tr ( Yν Yν + ) Tr ( Yν Yν + ) 2 Tr ( MN MN + ) Tr ( MN MN + ) 2 Tr ( MN MN + Yν + Yν ) Result: no mixing for flavour groups U(n)

149 SU(n)

150 * What is the role of the neutrino flavour group? e.g. generic seesaw e.g. SU(n)NR... leptons M with M carrying flavour M spurion More invariants in this case: Tr ( YE YE + ) Tr ( YE YE + ) 2 Tr ( YE YE + Yν Yν + ) Tr ( Yν Yν + ) Tr ( Yν Yν + ) 2 Tr ( MN MN + ) Tr ( MN MN + ) 2 Tr ( MN MN + Yν + Yν) At the minimum: * Tr ( Yν Yν + YΕ YΕ + ) = Tr ( UL yν diag. 2 UL + yl diag. 2 ) UL=1 * Tr ( MN MN + Yν Yν + ) = Tr ( UR yν diag. 2 UR + Mi diag. 2 ) UR=1

151 same conclusion for 3 families of quarks: Y = UL y diag. UR * Quarks, for instance: UR unphysical, UL --> UCKM YD = UCKM diag(yd, ys, yb) ; YU = diag(yu, yc, yt) Tr ( Yu Yu + Yd Yd + ) = Tr ( UL yu diag. 2 UL + yd diag. 2 ) UL=U CKM ~1 at the minimum NO MIXING

152 In many BSM the Yukawas do not come from dynamical fields:

153 Some good ideas: D.B. Kaplan-Georgi in the 80 s proposed a light SM scalar because being a (quasi) goldstone boson: composite Higgs (D.B. Kaplan, Georgi, Dimopoulos, Banks, Dugan, Galison...Contino, Nomura, Pomarol; Agashe, Contino, Pomarol; Giudice, Pomarol, Ratazzi, Grojean; Contino, Grojean, Moretti; Azatov, Galloway, Contino... Frigerio, Pomarol, Riva, Urbano...)

154 Some good ideas: D.B. Kaplan-Georgi in the 80 s proposed a light SM scalar because being a (quasi) goldstone boson: composite Higgs Flavour Partial compositeness D.B Kaplan 91: A sort of seesaw for quarks (nowadays sometimes justified from extra-dim physics ) H ΨΣΜ QL UR mq= v YSM (D.B Kaplan 91; Redi, Weiler; Contino, Kramer, Son, Sundrum; da Rold, Delauney, Grojean, G. Perez; Contino, Nomura, Pomarol, Agashe, Giudice, Perez, Panico, Redi, Wulzer...)

155 Some good ideas: D.B. Kaplan-Georgi in the 80 s proposed a Higgs light because being a (quasi) goldstone boson: composite Higgs Partial compositeness : A sort of seesaw for quarks (nowadays sometimes justified from extra-dim physics ) H QL ΔL Ψ M ΔR UR ΨΣΜ = ΨΔL ΔR/M 2 mq= v YSM (D.B Kaplan 91; Redi, Weiler; Contino, Kramer, Son, Sundrum; da Rold, Delauney, Grojean, G. Perez; Contino, Nomura, Pomarol, Agashe, Giudice, Perez, Panico, Redi, Wulzer...)

156 Some good ideas: D.B. Kaplan-Georgi in the 80 s proposed a Higgs light because being a (quasi) goldstone boson: composite Higgs Partial compositeness : A sort of seesaw for quarks (nowadays sometimes justified from extra-dim physics ) H Neutrino masses: QL ΔL Ψ M ΔR UR H H ΨΣΜ = ΨΔL ΔR/M 2 mq= v YSM L d=5 Weinberg operator L (D.B Kaplan 91; Redi, Weiler; Contino, Kramer, Son, Sundrum; da Rold, Delauney, Grojean, G. Perez; Contino, Nomura, Pomarol, Agashe, Giudice, Perez, Panico, Redi, Wulzer...)

157 Some good ideas: D.B. Kaplan-Georgi in the 80 s proposed a Higgs light because being a (quasi) goldstone boson: composite Higgs Partial compositeness : QL A sort of seesaw for quarks (nowadays sometimes justified from extra-dim physics ) ΔL H Ψ M ΔR ΨΣΜ = ΨΔL ΔR/M 2 mq= v YSM UR Neutrino masses: (D.B Kaplan 91; Redi, Weiler; Contino, Kramer, Son, Sundrum; da Rold, Delauney, Grojean, G. Perez; Contino, Nomura, Pomarol, Agashe, Giudice, Perez, Panico, Redi, Wulzer...) L H Ψ M x Ψ mν= Y v 2 /M Y T H type I L

158 Some good ideas: D.B. Kaplan-Georgi in the 80 s proposed a Higgs light because being a (quasi) goldstone boson: composite Higgs Partial compositeness : A sort of seesaw for quarks (nowadays sometimes justified from extra-dim physics ) H Neutrino masses: QL ΔL Ψ M ΔR UR L H µ Ψ M H type II L ΨΣΜ = ΨΔL ΔR/M 2 mν= Y µ v 2 /M 2 mq= v YSM (D.B Kaplan 91; Redi, Weiler; Contino, Kramer, Son, Sundrum; da Rold, Delauney, Grojean, G. Perez; Contino, Nomura, Pomarol, Agashe, Giudice, Perez, Panico, Redi, Wulzer...)

159 For instance, in discrete symmetry ideas: The Yukawas are indeed explained in terms of dynamical fields. And they do not need to worry about goldstone bosons. In spite of θ13 not very small, there is activity. For instance, combine generalized CP (Bernabeu, Branco, Gronau 80s) with discrete Z2 groups in the neutrino sector : maximal θ23, strong constraints on values of CP phases (Feruglio, Hagedorn and Ziegler 2013; Holthausen, Lindner and Schmidt 2013) They were popular mainly because they can lead easily to large mixings (tribimaximal, bimaximal...) But: - Discrete approaches do not relate mixing to spectrum - Difficulties to consider both quarks and leptons

160 Some good ideas: H Ψ σπυριον Minimal Flavour Violation: QL DR - Use the flavour symmetry of the SM in the limit of massless (Chivukula+ Georgi) fermions quarks: Gflavour= U(3)QL x U(3)UR x U(3)DR Hybrid dynamical-non-dynamical Yukawas: U(2) (Pomarol, Tomasini; Barbieri, Dvali, Hall, Romanino...)... U(2) 3 (Craig, Green, Katz; Barbieri, Isidori, Jones-Peres, Lodone, Straub....Sala) U(2) Sequential ideas (Feldman, Jung, Mannel; Berezhiani+Nesti; Ferretti et al., Calibbi et al....)

161 Some good ideas, based on continuous symmetries: H φ s Frogatt-Nielsen 79: U(1)flavour symmetry QL DR - Yukawa couplings are effective couplings, - Fermions have U(1)flavour charges < φ > n Q H qr, Y ~ < φ > n n Λ Λ e.g. n=0 for the top, n large for light quarks, etc. --> FCNC?

162 The FLAVOUR WALL for BSM i) Typically, BSMs have electric dipole moments at one loop i.e susy MSSM: < 1 loop in SM ---> Best (precision) window of new physics ii) FCNC i.e susy MSSM: competing with SM at one-loop

163 Minimal Flavour violation (MFV) Flavour data (i.e. B physics) consistent with all flavour physics coming from Yukawa in BSM It is very predictive for quarks: L= L SM + c d=6 O d=6 + known function of Yukawas 2 Λ flavour (D Ambrosio, Cirigliano, Isidori, Grinstein, Wise.Buras.) O d=6 ~ Qα Q β Q γ Q δ

164 Smith Smith MFV region SM

165 Gonzalez-Alonso Minimal Flavour violation (MFV) Unitarity of CKM first row: *Restrict to flavour blind ops.-> 4 operators Correction is only multiplicative to β and µ decay rate

166 Gonzalez-Garcia, Maltoni, Salvado, Schwetz, "