Flavor without symmetries Alex Pomarol, UAB (Barcelona)
Flavor without symmetries Alex Pomarol, UAB (Barcelona) Apologizes: I am not going to talk on glances at the energy frontier
Flavor without symmetries Alex Pomarol, UAB (Barcelona) Apologizes: I am not going to talk on glances at the energy frontier Interpreting other “null results”: the absence of new flavor sources beyond the SM
After many years, no clear progress on the origin of flavor in the SM: Many ideas, but without sharp predictions s n o M i s n e m i a d a r s t x e n s i n e o i t a z s i l a gauge flavor symmetries c o L f r o m Froggatt-Nielsen l o o p s … contrary to gauge couplings → predictions from GUTs Higgs quartic → predictions from SUSY or Composite Higgs
After many years, no clear progress on the origin of flavor in the SM: Many ideas, but without sharp predictions s n o M i s n e m i a d a r s t x e n s i n e o i t a z s i l a gauge flavor symmetries c o L f r o m Froggatt-Nielsen l o o p s … contrary to gauge couplings → predictions from GUTs Higgs quartic → predictions from SUSY or Composite Higgs In BSMs for the hierarchy problem things are even worse (or more interesting) , as generically predict new sources of flavor… ( ¯ f i γ µ f j )( ¯ ϵ K , ϵ ’/ ϵ , Δ M B , B → Xll, … f l γ µ f k ) not serious deviation seen!
“Cheap” way to avoid them: ☛ Demand similar BSM flavor-structure as in the SM: Minimal Flavor Violation (MFV) Flavor under control for new physics scale at ~TeV but global symmetries are accidental So, why/how they arise?
Symmetries from dynamics!
Symmetries from dynamics! But only few examples known: SUSY: Gauge Mediated Susy Breaking (GMSB) soft-masses through gauge interactions (flavor blind) x ~ ~ Q Q but today minimal GMSB highly tuned to reproduce m h ~125 GeV Beyond minimal models… EDMs are sizable! ◆ 2 ✓ M S d e ∼ 10 − 28 cm e tan β 10 TeV
Symmetries from dynamics! But only few examples known: Composite Higgs: More difficult, as we must address the origin of Yukawas: Higgs associated to a composite operator: O H ∼ ¯ ψψ As dimension of O H is larger than 1 ( d H >1 ) Yukawas, ff O H , are irrelevant couplings! We cannot push their origin to Planck-physics!
Symmetries from dynamics! But only few examples known: Composite Higgs: Most interesting possibility: Yukawas from linear mixing to operators of the strong sector: L lin = ✏ f i ¯ f i O f i (portal of f i to the strong sector) ⤷ depending on the dimension of O f , we can have relevant or irrelevant couplings ☛ large or small mixings ϵ f
O(1) numbers (anomalous dimensions γ i of O f i ) can lead to large hierarchies: From the RGE: ◆ γ i ✓ Λ IR ✏ f i ( Λ IR ) ∼ γ i = Dim[ O f i ] − 5 / 2 > 1 M P ☛ small mixings at Λ IR The smaller mixing, the smaller the mass: ☛ Y f ⇠ g ∗ ✏ f i ✏ f j , f j f i ⤷ coupling of the strong sector
Explicit example (for the top): arXiv:1502.00390 SU(4) strong sector a) three ∈ 4 (fundamental) Ψ L,R } Fermions: ΨΥΨ = O top n Υ b) five ∈ 6 (antisym. matrix) Operator that can be coupled to the top Global sym. G = SU (5) × SU (3) × SU (3) ′ × U (1) X × U (1) ′ H = SO (5) × SU (3) color × U (1) X dimension at weak coupling: 9/2 dimension needed at strong coupling: 5/2 ( γ = 2) Possible? lattice could tell us!
AdS/CFT perspective x b L , b R s L , s R x d L , d R x x Higgs Λ IR ☛ easier from string theory?
Flavor & CP-violation constraints g 2 ✏ f i ✏ f j ✏ f k ✏ f l ¯ f i � µ f j ¯ ∗ f k � µ f l , Λ 2 IR ⤷ scale of the strong sector: expected ~TeV ϵ K bound: Λ IR > 10 TeV g 2 g ∗ v ✏ f i ✏ f j ¯ f i � µ ν f j gF µ ν ∗ Λ 2 16 ⇡ 2 IR ⇣ g ∗ ⌘ EDM bound: Λ IR > 100 TeV 3 ⇣ g ∗ ⌘ μ→ e γ bound: Λ IR > 60 TeV 3
arXiv:1106.6357 Other alternatives: arXiv:1203.4220 Consider some SM fermion fully composite: For example: Q R u R , d R If arise from a strong sector with elementary fermions, it is not unconceivable to be flavor symmetric All flavor mixings from left-handed: ☛ MFV Q R u R ∝ Y u g 2 But also generated: u R � µ u R ) 2 ⇤ (¯ Λ 2 IR ⇣ g ∗ ⌘ give deviation in dijets distributions, pp → jj : Λ IR & 20 TeV 3
Towards suppressing EDMs: Avoid linear mixing of light fermions to BSM: L lin = ✏ f i ¯ f i O f i BSM BSM L bil ⇠ ¯ Bilinear mixing: f i O H f j EDM at most at Not possible in the MSSM, two-loop! but possible in composite Higgs models
Possibility considered here: G.Panico, AP 1603.06609 (also related work by Matsedonskyi 15, Cacciapaglia etal 15) L lin = ✏ f i ¯ f i O f i ⤷ portal decouples at higher energies: E.g. if a constituent get a mass ~ Λ f L bil ⇠ ¯ f i O H f j bilinear mixing generated at Λ f ⤷ Operator of the strong sector that at Λ IR projects into the Higgs: O H h 0 |O H | H i 6 = 0, e.g. O H ∼ ¯ ψψ The larger the scale of decoupling, the smaller the fermion mass!
Down-quark sector Decoupling Operator energy scale Λ d O d R , O Q L 1 Λ s O s R R , O Q L 2 Λ b O b R R , O Q L 3 Λ IR
Envisaging from explicit examples: SU(4) strong sector a) three ∈ 4 (fundamental) Ψ L,R } Fermions: ΨΥΨ = O top n Υ b) five ∈ 6 (antisym. matrix) add more elementary fermions Ψ with explicit masses M Ψ d ΨΥΨ d d ΨΥΨ M Ψ s s s ΨΥΨ M Ψ b b b
AdS/CFT perspective x b L , b R s L , s R x d L , d R x x Higgs Λ IR x I b L , b R I s L , s R x I I x d L , d R x I I Higgs Λ d Λ s Λ b Λ IR
AdS/CFT perspective x b L , b R s L , s R x d L , d R x x Higgs Λ IR x I b L , b R I s L , s R x I I x d L , d R x I I Higgs Λ d Λ s Λ b Λ IR CFT 3 → CFT 2 → CFT 1 → CFT 0
Arising flavor structure Down-quark sector Decoupling Operator energy scale Λ d O d R , O Q L 1 Λ s O s R R , O Q L 2 Λ b O b R R , O Q L 3 Λ IR
Arising flavor structure Down-quark sector d bottom, b R : Decoupling L (3) lin = ✏ (3) Q L 3 O Q L 3 + ✏ (3) b L ¯ b R ¯ Operator b R O b R . energy scale below Λ b : O Λ d O d R , O Q L 1 1 L (3) ( ✏ (3) Q L 3 ) O H ( ✏ (3) b L ¯ bil = b R b R ) Λ d H − 1 b Λ s O s R R , O Q L 2 C below Λ IR : A 0 0 0 0 1 ◆ d H − 1 ✓ Λ IR 0 0 0 + g ∗ Y down = B C Λ b @ A Λ b 0 0 ✏ (3) b L ✏ (3) O b R R , O Q L 3 b R Λ IR
Arising flavor structure Down-quark sector L (2) lin = ( ✏ (2) b L ¯ s L ¯ Q L 3 + ✏ (2) Q L 2 ) O Q L 2 Decoupling Operator energy scale 2 + ( ✏ (2) b R b R + ✏ (2) s R s R ) O s R Λ d O d R , O Q L 1 below Λ s : O O 1 L (1) ( ✏ (1) Q L 2 + ✏ (1) Q L 1 ) O H ( ✏ (1) s R s R + ✏ (1) b L ¯ s L ¯ d L ¯ Q L 3 + ✏ (1) b R b R + ✏ (1) bil = d R d R ) Λ d H − 1 Λ s d O s R R , O Q L 2 below Λ IR : 0 0 0 0 1 Λ b ◆ d H − 1 O b R R , O Q L 3 ✓ Λ IR 0 ✏ (2) s L ✏ (2) ✏ (2) s L ✏ (2) + g ∗ Y down = B C s R b R Λ s @ A 0 ✏ (2) b L ✏ (2) s R Λ IR
Arising flavor structure Down-quark sector Decoupling Operator energy scale Λ d O d R , O Q L 1 Λ s O s R R , O Q L 2 below Λ IR : ✏ (1) d L ✏ (1) ✏ (1) d L ✏ (1) ✏ (1) d L ✏ (1) 0 1 s R d R b R ◆ d H − 1 ✓ Λ IR ✏ (1) s L ✏ (1) B C = g ∗ Y down = B C d R Λ d @ A Λ b ✏ (1) b L ✏ (1) O b R R , O Q L 3 d R 0 1 Λ IR
Arising flavor structure “onion” structure: ↵ ds R Y d ↵ db 0 Y d R Y d 1 ↵ ds ↵ sb L Y d Y s R Y s Y down ' B C @ A ↵ db ↵ sb L Y d L Y s Y b @ ◆ d H − 1 ✓ Λ IR Y f ⌘ g ∗ ✏ ( i ) f Li ✏ ( i ) f ' m f /v . T f Ri Λ f ● S maller Yukawas for large decoupling scale! ● M ixing angles suppressed by Yukawas: 𝛊 ij ~ Y i / Y j CKM mostly the rotation in the down-quark sector!
Similarly for the up-quark sector (and lepton sector) Operator Decoupling scale O u R Λ u Λ d O d R , O Q L 1 Λ s O s R Λ c O c R , O Q L 2 Λ b O b R O t R , O Q L 3 Λ t ∼ Λ IR
Scales of decoupling: �� � �� - ���� ���� - ���� ������� �� � [ ��� ] � �� ���� �� � � �� ���� Λ � ��� � �� ���� ��� ��� ��� ��� ��� ��� � � dimension of the Higgs operator ( ) O H ∼ ¯ ΥΥ
Scales of decoupling: �� � �� - ���� ���� - ���� ������� �� � [ ��� ] � �� ���� �� � � �� ���� Λ � ��� � �� ���� ��� ��� ��� ��� ��� ��� � � dimension of the Higgs operator ( ) d H ~2 needed to pass FCNC O H ∼ ¯ ΥΥ (“walking TC”: d H ~2 instead of ~3)
Flavor and CP-violating effects
Different effects at different scales: Effects from the top Λ u ∆ F = 2 transitions Λ d ∼ Y 2 2 t ( Q L 3 � µ Q L 3 ) 2 t Λ s Λ 2 IR physical basis Λ c rotation ~ V CKM Λ b ϵ K , Δ M B d , Δ M Bs correlated and all close Λ t ∼ Λ IR to the experimental value for Λ IR ~2-3 TeV
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