Irreducible flavour & CP violation in SUGRA flavour models
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1 UK BSM 07 Liverpool, March Irreducible flavour & CP violation in SUGRA flavour models Southampton
2 Outline Flavour models, SUSY FV and CPV & SUGRA Flavon F-terms F X contra F φ Irreducible SUGRA flavour & CP violation in flavour models 2/8
3 Models of flavour Flavour symmetries provide a handle to the generic Yukawa sector of the Standard Model. If matter is charged with respect to F some or even all of the couplings arrise at the effective level only after the proper breakdown of F by means of gauge-singlet F-nonsinglet Higgs fiedls. flavons, φ 3/8
4 Exampe: U1 flavour symmetry Q F [Q 3 ] = Q F [q c 3] = 0 Q F [Q 2 ] = Q F [q c 2] = 1 Models of flavour Flavour symmetries provide a handle to the generic Yukawa sector of the Standard Model. If matter is charged with respect to F some or even all of the couplings arrise at the effective level only after the proper breakdown of F by means of gauge-singlet F-nonsinglet Higgs fiedls. flavons, φ Q F [Q 1 ] = Q F [q c 1] = 2 Q F [H] = 0 Q F [φ] = 1 Q i... H... φ q c j ε φ M m Y ε 4 ε 3 ε 2 ε 3 ε 2 ε ε 2 ε 1 3/8
5 Exampe: U1 flavour symmetry Q F [Q 3 ] = Q F [q c 3] = 0 Q F [Q 2 ] = Q F [q c 2] = 1 Q F [Q 1 ] = Q F [q c 1] = 2 Q F [H] = 0 Q F [φ] = 1 Models of flavour Flavour symmetries provide a handle to the generic Yukawa sector of the Standard Model. If matter is charged with respect to F some or even all of the couplings arrise at the effective level only after the proper breakdown of F by means of gauge-singlet F-nonsinglet Higgs fiedls. flavons, φ Q i... H... φ q c j ε φ M m Y ε 4 ε 3 ε 2 ε 3 ε 2 ε ε 2 ε 1 In practice, the neutrinos tend to call for non-abelian symmetries like for example SU3 F or their discrete subgroups. In such a case matter fields and flavons enter higher dimensional irreps of the flavour symmetry group and the Yukawa patterns arise as a consequence of flavour-nontrivial vacuum alignment of φ s. L Y 1 Mm 2 Q. φ q c. φh /8
6 Exampe: U1 flavour symmetry Q F [Q 3 ] = Q F [q c 3] = 0 Q F [Q 2 ] = Q F [q c 2] = 1 Q F [Q 1 ] = Q F [q c 1] = 2 Q F [H] = 0 Q F [φ] = 1 Models of flavour Flavour symmetries provide a handle to the generic Yukawa sector of the Standard Model. If matter is charged with respect to F some or even all of the couplings arrise at the effective level only after the proper breakdown of F by means of gauge-singlet F-nonsinglet Higgs fiedls. flavons, φ Q i... H... φ q c j ε φ M m Y ε 4 ε 3 ε 2 ε 3 ε 2 ε ε 2 ε 1 In practice, the neutrinos tend to call for non-abelian symmetries like for example SU3 F or their discrete subgroups. In such a case matter fields and flavons enter higher dimensional irreps of the flavour symmetry group and the Yukawa patterns arise as a consequence of flavour-nontrivial vacuum alignment of φ s. L Y 1 Mm 2 Q. φ q c. φh +... Currently, there is a plenty of models like this... Extra input is badly needed to constrain them. One such option is SUSY with the constraints coming from SUSY flavour and CP puzzles... 3/8
7 SUSY flavour and CP puzzle MSSM: W Y ε αβ [Ĥα ˆQβi u Yij u û cj + Ĥα ˆQ d βi Yij d + Ĥα ˆL u βi Yij ν + Ĥα ˆL d βi Yijê e + ˆN ci cj M R ij ˆN L soft [ ε αβ Hu α Q βi A u ijũ cj + Hd α Q βi A d d ij cj + Hu α L βi A ν ijñ cj + Hd α L βi A e ijẽ cj] + Ñ c m 2 N i jñ cj c + Q iαm 2 Q i Q j αj + ũ c i m 2 u i jũ cj + c d c i m 2 d i d c j cj + L iαm 2 L i L j αj + ẽ c i m 2 e i jẽ cj c i 4/8
8 SUSY flavour and CP puzzle MSSM: W Y ε αβ [Ĥα ˆQβi u Yij u û cj + Ĥα ˆQ d βi Yij d + Ĥα ˆL u βi Yij ν + Ĥα ˆL d βi Yijê e + ˆN ci cj M R ij ˆN L soft [ ε αβ Hu α Q βi A u ijũ cj + Hd α Q βi A d d ij cj + Hu α L βi A ν ijñ cj + Hd α L βi A e ijẽ cj] + Ñ c m 2 N i jñ cj c + Q iαm 2 Q i Q j αj + ũ c i m 2 u i jũ cj + c d c i m 2 d i d c j cj + L iαm 2 L i L j αj + ẽ c i m 2 e i jẽ cj c i Convenience - the super CKM basis: Dugan, Grinstein, Hall, Nucl.Phys.B basis in which the neutralino couplings to matter are flavour diagonal l - obtained by rotating the soft masses and trilinears by the matter sector rotations l χ 0 4/8
9 SUSY flavour and CP puzzle MSSM: W Y ε αβ [Ĥα ˆQβi u Yij u û cj + Ĥα ˆQ d βi Yij d + Ĥα ˆL u βi Yij ν + Ĥα ˆL d βi Yijê e + ˆN ci cj M R ij ˆN L soft [ ε αβ Hu α Q βi A u ijũ cj + Hd α Q βi A d d ij cj + Hu α L βi A ν ijñ cj + Hd α L βi A e ijẽ cj] + Ñ c m 2 N i jñ cj c + Q iαm 2 Q i Q j αj + ũ c i m 2 u i jũ cj + c d c i m 2 d i d c j cj + L iαm 2 L i L j αj + ẽ c i m 2 e i jẽ cj c i Convenience - the super CKM basis: Dugan, Grinstein, Hall, Nucl.Phys.B basis in which the neutralino couplings to matter are flavour diagonal l - obtained by rotating the soft masses and trilinears by the matter sector rotations l χ 0 SUSY flavour and CP problem: - no reason for the soft terms to be flavour diagonal and real in the superckm basis! - mixing and extra phases lead to dramatic enhancement of the FCNC and CPV 4/8
10 SUSY flavour and CP puzzle MSSM: W Y ε αβ [Ĥα ˆQβi u Yij u û cj + Ĥα ˆQ d βi Yij d + Ĥα ˆL u βi Yij ν + Ĥα ˆL d βi Yijê e + ˆN ci cj M R ij ˆN L soft [ ε αβ Hu α Q βi A u ijũ cj + Hd α Q βi A d d ij cj + Hu α L βi A ν ijñ cj + Hd α L βi A e ijẽ cj] + Ñ c m 2 N i jñ cj c + Q iαm 2 Q i Q j αj + ũ c i m 2 u i jũ cj + c d c i m 2 d i d c j cj + L iαm 2 L i L j αj + ẽ c i m 2 e i jẽ cj c i Convenience - the super CKM basis: Dugan, Grinstein, Hall, Nucl.Phys.B basis in which the neutralino couplings to matter are flavour diagonal l - obtained by rotating the soft masses and trilinears by the matter sector rotations l χ 0 SUSY flavour and CP problem: - no reason for the soft terms to be flavour diagonal and real in the superckm basis! - mixing and extra phases lead to dramatic enhancement of the FCNC and CPV strong constraints on off-diagonalities & phases of soft terms 4/8
11 SUSY flavour and CP puzzle MSSM: W Y ε αβ [Ĥα ˆQβi u Yij u û cj + Ĥα ˆQ d βi Yij d + Ĥα ˆL u βi Yij ν + Ĥα ˆL d βi Yijê e + ˆN ci cj M R ij ˆN L soft [ ε αβ Hu α Q βi A u ijũ cj + Hd α Q βi A d d ij cj + Hu α L βi A ν ijñ cj + Hd α L βi A e ijẽ cj] + Ñ c m 2 N i jñ cj c + Q iαm 2 Q i Q j αj + ũ c i m 2 u i jũ cj + c d c i m 2 d i d c j cj + L iαm 2 L i L j αj + ẽ c i m 2 e i jẽ cj c i Convenience - the super CKM basis: Dugan, Grinstein, Hall, Nucl.Phys.B basis in which the neutralino couplings to matter are flavour diagonal l - obtained by rotating the soft masses and trilinears by the matter sector rotations l χ 0 SUSY flavour and CP problem: - no reason for the soft terms to be flavour diagonal and real in the superckm basis! - mixing and extra phases lead to dramatic enhancement of the FCNC and CPV strong constraints on off-diagonalities & phases of soft terms Minimal flavour violation: m 2 soft m 2 0, A f A 0 Y f 4/8
12 SUGRA solution to SUSY flavour and CP puzzles m 2 soft = m 2 3/2 K ab S,S F S A abc Y abc S [ S S Kab S Kac K 1 cd S Kdb ] { 1 F S MP 2 S K hid. Y abc + S Y abc l F S [ K ] } 1 de S Kea Y dbc + cycl. where Kψ, X,... = K ab X,...ψ aψ b K hid. X,... F X 0 5/8
13 SUGRA solution to SUSY flavour and CP puzzles m 2 soft = m 2 3/2 K ab S,S F S A abc Y abc S [ S S Kab S Kac K 1 cd S Kdb ] { 1 F S MP 2 S K hid. Y abc + S Y abc l F S [ K ] } 1 de S Kea Y dbc + cycl. where Kψ, X,... = K ab X,...ψ aψ b K hid. X,... F X 0 Example: Sequestered shape of a Kähler potential makes the soft masses universal! after canonical normalization of ψ a Kab D µ γ µ ψ b If, moreover, the Yukawas do not feel X or do in a flavour-blind way, the A-terms are aligned to Y s and CP and FV is essentially O.K. 5/8
14 SUGRA solution to SUSY flavour and CP puzzles m 2 soft = m 2 3/2 K ab S,S F S A abc Y abc S [ S S Kab S Kac K 1 cd S Kdb ] { 1 F S MP 2 S K hid. Y abc + S Y abc l F S [ K ] } 1 de S Kea Y dbc + cycl. where Kψ, X,... = K ab X,...ψ aψ b K hid. X,... F X 0 Example: Sequestered shape of a Kähler potential makes the soft masses universal! after canonical normalization of ψ a Kab D µ γ µ ψ b If, moreover, the Yukawas do not feel X or do in a flavour-blind way, the A-terms are aligned to Y s and CP and FV is essentially O.K. If not happy about sequestered or factorized Kähler potentials... Flavour symmetries can still control the Kähler so that one does not get far from universality. However, in flavour models, there are always fields with nonzero F-terms felt by the Yukawas! 5/8
15 SUGRA solution to SUSY flavour and CP puzzles m 2 soft = m 2 3/2 K ab S,S F S A abc Y abc S [ S S Kab S Kac K 1 cd S Kdb ] { 1 F S MP 2 S K hid. Y abc + S Y abc l F S [ K ] } 1 de S Kea Y dbc + cycl. where Kψ, X,... = K ab X,...ψ aψ b K hid. X,... F X 0 Example: Sequestered shape of a Kähler potential makes the soft masses universal! after canonical normalization of ψ a Kab D µ γ µ ψ b If, moreover, the Yukawas do not feel X or do in a flavour-blind way, the A-terms are aligned to Y s and CP and FV is essentially O.K. If not happy about sequestered or factorized Kähler potentials... Flavour symmetries can still control the Kähler so that one does not get far from universality. However, in flavour models, there are always fields with nonzero F-terms felt by the Yukawas! THE FLAVONS... 5/8
16 Induced flavon F-terms & irreducible flavour The generic SUGRA F-term: violation in SUGRA flavour models F I = e K/2M 2 P l K 1 IJ 1 M 2 P l W K J + W J = K 1 IJ m 3/2 K J e K/2M 2 P l W J 6/8
17 Induced flavon F-terms & irreducible flavour The generic SUGRA F-term: violation in SUGRA flavour models F I = e K/2M 2 P l K 1 IJ 1 M 2 P l W K J + W J = K 1 IJ m 3/2 K J e K/2M 2 P l W J and thus F φ = φ K f 1 m φφ 3/2 K f φ e K/2M 2 P l W φ m 3/2 φ +... Ross, Vives, Phys.Rev.D /8
18 Induced flavon F-terms & irreducible flavour The generic SUGRA F-term: violation in SUGRA flavour models F I = e K/2M 2 P l K 1 IJ 1 M 2 P l W K J + W J = K 1 IJ m 3/2 K J e K/2M 2 P l W J and thus F φ = φ K f 1 m φφ 3/2 K f φ e K/2M 2 P l W φ m 3/2 φ +... Ross, Vives, Phys.Rev.D This means that the following pieces are always present in the soft masses and trilinears: m 2 soft = m 2 K 3/2 ab F φ [ φ φ Kab φ Kac K ] 1 cd φ Kdb φ,φ F φ A abc Y abc = k F X M 2 P l X K hid. Y abc + φ F φ φ Y abc φ F φ [ K ] 1 de φ Kea Y dbc + cycl. and give an irreducible contribution to flavour violation... 6/8
19 Induced flavon F-terms & irreducible flavour The generic SUGRA F-term: violation in SUGRA flavour models F I = e K/2M 2 P l K 1 IJ 1 M 2 P l W K J + W J = K 1 IJ m 3/2 K J e K/2M 2 P l W J and thus F φ = φ K f 1 m φφ 3/2 K f φ e K/2M 2 P l W φ m 3/2 φ +... Ross, Vives, Phys.Rev.D This means that the following pieces are always present in the soft masses and trilinears: m 2 soft = m 2 K 3/2 ab F φ [ φ φ Kab φ Kac K ] 1 cd φ Kdb φ,φ F φ A abc Y abc = k F X M 2 P l X K hid. Y abc + φ F φ φ Y abc φ F φ [ K ] 1 de φ Kea Y dbc + cycl. and give an irreducible contribution to flavour violation... How about the magnitude? 6/8
20 Irreducible flavour violation in SUSY flavour models If flavour symmetry is broken well below the Planck scale, we get F φ F X. Does this mean the corrections are always subleading? F φ 7/8
21 Irreducible flavour violation in SUSY flavour models If flavour symmetry is broken well below the Planck scale, we get F φ F X. Does this mean the F φ corrections are always subleading? NO! 7/8
22 Irreducible flavour violation in SUSY flavour models If flavour symmetry is broken well below the Planck scale, we get F φ F X. Does this mean the F φ corrections are always subleading? NO! A trivial example: the sequestered Kähler setting - no and FV and CPV driven entirely by. F X F φ sensitivity up to overall scale 7/8
23 Irreducible flavour violation in SUSY flavour models If flavour symmetry is broken well below the Planck scale, we get F φ F X. Does this mean the F φ corrections are always subleading? NO! A trivial example: the sequestered Kähler setting - no sensitivity up to overall scale and FV and CPV driven entirely by F φ. How about the magnitude? The scale of trilinear couplings F φ φ Y abc does not dependent on F φ! Ross, Vives, Phys.Rev.D F X 7/8
24 Irreducible flavour violation in SUSY flavour models If flavour symmetry is broken well below the Planck scale, we get F φ F X. Does this mean the F φ corrections are always subleading? NO! A trivial example: the sequestered Kähler setting - no sensitivity up to overall scale and FV and CPV driven entirely by F φ. How about the magnitude? The scale of trilinear couplings F φ φ Y abc does not dependent on F φ! Ross, Vives, Phys.Rev.D F X A nontrivial example: generic Kähler with both X and φ mixed together X K X ab δ ab c 0 + d 0 MP 2 l + X X 1 c 2 + d 2 MP 2 l M 2 φφ ab +... m 2 soft = F X X X Kab F X F φ φ φ Kab F φ /8
25 Irreducible flavour violation in SUSY flavour models If flavour symmetry is broken well below the Planck scale, we get F φ F X. Does this mean the F φ corrections are always subleading? NO! A trivial example: the sequestered Kähler setting - no sensitivity up to overall scale and FV and CPV driven entirely by F φ. How about the magnitude? The scale of trilinear couplings F φ φ Y abc does not dependent on F φ! Ross, Vives, Phys.Rev.D F X A nontrivial example: generic Kähler with both X and φ mixed together X K X ab δ ab c 0 + d 0 MP 2 l + X X 1 c 2 + d 2 MP 2 l M 2 φφ ab +... m 2 soft = F X X X Kab F X F φ φ φ Kab F φ +... F φ φ φ Kab F φ m 2 X X 3/2 φ c 2 + d 2 F X X X Kab F X m 2 d0 3/2 X MP 2 l M 2 P l + d 2 M 2 P l 1 φ 2 M 2 φ m2 3/2 O M 2 1 M 2 φφ X m 2 3/2 [ O1 + O ] φ 2 Once the catastrophic leading order terms are tamed the the irreducible part is competitive! M 2 7/8
26 Conclusions SUSY flavour and CP puzzles challenge the flavour models Irreducible SUGRA flavour violation due to flavon in minimal models F φ -terms present even Although F φ F X the F φ -effects are important even for the soft masses 8/8
27 Conclusions SUSY flavour and CP puzzles challenge the flavour models Irreducible SUGRA flavour violation due to flavon in minimal models F φ -terms present even Although F φ F X the F φ -effects are important even for the soft masses Thanks for your kind attention! 8/8
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