A Domino Theory of Flavor

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1 A Domino Theory of Flavor Peter Graham Stanford with Surjeet Rajendran arxiv:

2 Outline 1. General Domino Framework 2. Yukawa Predictions 3. Experimental Signatures

3 General Domino Framework

4 Inspiration Radiative fermion mass generation models have a long history 1. Georgi & Glashow (1973) - e from µ 2. Babu, Balakrishna, & Mohapatra (1990) - in Pati-Salam 3. Arkani-Hamed, Cheng, & Hall (1996) - 1st generation masses & some CKM 4. Fox & Dobrescu (2008) - up and lepton masses 5. and many more...

5 mass (GeV) t Flavor Philosophy Xing, Zhang & Zhou (2008) Not randomly distributed, even on log scale All Yukawas b τ c µ s u d e ups downs leptons Equal hierarchy between successive generations Pattern may be suggestive of a framework beyond just generating small numbers

6 Domino Mechanism work in SU(5) GUT: W H u λ ij φ 10 i 5 j all allowed coefficients (e.g. ) are λ ij O(1) φ can be H d so add no new fields to MSSM

7 Domino Mechanism work in SU(5) GUT: W H u λ ij φ 10 i 5 j all allowed coefficients (e.g. ) are λ ij O(1) φ can be H d so add no new fields to MSSM tree-level top mass may appear to violate our flavor philosophy but can be written: W H u (c i 10 i )(c j 10 j )+λ ij φ 10 i 5 j

8 Domino Mechanism work in SU(5) GUT: W H u λ ij φ 10 i 5 j all allowed coefficients (e.g. ) are λ ij O(1) φ can be H d so add no new fields to MSSM tree-level top mass may appear to violate our flavor philosophy but can be written: W H u (c i 10 i )(c j 10 j )+λ ij φ 10 i 5 j two arbitrary flavor directions: c i and λ ij these spurions break all flavor symmetries: U(3)10 U(3)5 These will generate all fermion masses (and mixings) in a hierarchical pattern

9 Top Yukawa - UV Completion forbid all Yukawas and introduce two new fields: σ and a (vector-like) 10N W = c i σ 10 i 10 N + H u 10 N 10 N + M N 10 N 10 N U(1) PQ σ i 1 H u 0 H d 0 5 i N 0

10 Top Yukawa - UV Completion forbid all Yukawas and introduce two new fields: σ and a (vector-like) 10N W = c i σ 10 i 10 N + H u 10 N 10 N + M N 10 N 10 N N 10 N σ H u σ U(1) PQ σ i 1 H u 0 H d 0 5 i N 0 generates top yukawa W = σ 2 M 2 N H u

11 Up Yukawas W H u (c i 10 i )(c j 10 j )+φ 10 i λ ij 5 j c c = top mass 1 H 10 y u 10 ( ) y u 1

12 Up Yukawas W H u (c i 10 i )(c j 10 j )+φ 10 i λ ij 5 j c c = top mass 1 ( λλ ) c ( λλ ) c = charm mass ɛ 2 H 10 y u 10 ( ) y u ɛ 2 1

13 Up Yukawas W H u (c i 10 i )(c j 10 j )+φ 10 i λ ij 5 j c c = top mass 1 ( λλ ) c ( λλ ) c = charm mass ɛ 2 ( λλ ) 2 ( c λλ ) 2 c = up mass ɛ 4 H 10 y u 10 ( ) y u ɛ 4 ɛ 2 1

14 Up Yukawas W H u (c i 10 i )(c j 10 j )+φ 10 i λ ij 5 j c c = top mass 1 ( λλ ) c ( λλ ) c = charm mass ɛ 2 ( λλ ) 2 ( c λλ ) 2 c = up mass ɛ 4 H 10 y u 10 ( ɛ 3 ɛ 2 ) y u ɛ ɛ 4 ɛ 3 ɛ 2 ɛ 2 ɛ 1 c ( λλ ) c = top-charm mixing ɛ CKM mixing angles can arise at intermediate order between masses

15 Up Yukawa Diagrams W H u (c i 10 i )(c j 10 j )+φ 10 i λ ij 5 j φ φ H u

16 Up Yukawa Diagrams W H u (c i 10 i )(c j 10 j )+φ 10 i λ ij 5 j λ φ φ 5 λ c c 5 λ λ ( λλ ) c ( λλ ) c = charm mass ɛ 2 H u

17 Up Yukawa Diagrams W H u (c i 10 i )(c j 10 j )+φ 10 i λ ij 5 j λ φ φ 5 λ c c H u 5 λ λ ( λλ ) c ( λλ ) c = charm mass ɛ 2 m c m t f C (16π 2 ) 2 λ4 log ( Λ 2 m 2 φ ) 1 300

18 Up Yukawa Diagrams W H u (c i 10 i )(c j 10 j )+φ 10 i λ ij 5 j λ φ φ 5 λ c c H u 5 λ λ ( λλ ) c ( λλ ) c = charm mass ɛ 2 m c m t f C (16π 2 ) 2 λ4 log ( Λ 2 m 2 φ ) φ c ( λλ ) c = top-charm mixing ɛ λ λ

19 Mass Basis We have freedom to choose a basis in which: λ 11 λ 12 0 U(2) 10 U(3) 5 = λ = 0 λ 22 λ λ 33

20 Mass Basis We have freedom to choose a basis in which: λ 11 λ 12 0 U(2) 10 U(3) 5 = λ = 0 λ 22 λ λ ( λλ ) c ( λλ ) c = charm mass ɛ 2 c ( λλ ) c = top-charm mixing ɛ This basis is near mass basis for the Yukawa couplings

21 Downs & Leptons W H u (c i 10 i )(c j 10 j )+H d 10 i λ ij 5 j c λ c = b, τ mass δ y d δ( ) ɛ 4 ɛ 3 ɛ 3 ɛ 2 ɛ 2 ɛ ɛ 2 ɛ 1

22 Downs & Leptons W H u (c i 10 i )(c j 10 j )+H d 10 i λ ij 5 j c λ c ( λ λ ) c ( λ λ ) λ c = b, τ mass δ = s, µ mass δɛ 2 y d δ( ) ɛ 4 ɛ 3 ɛ 3 ɛ 2 ɛ 2 ɛ ɛ 2 ɛ 1

23 Downs & Leptons W H u (c i 10 i )(c j 10 j )+H d 10 i λ ij 5 j add SUSY breaking L Bµ H (3) u H (3) d c λ c ( λ λ ) c ( λ λ ) λ c = b, τ mass δ = s, µ mass δɛ 2 y d δ( ) ɛ 4 ɛ 3 ɛ 3 ɛ 2 ɛ 2 ɛ ɛ 2 ɛ 1 generates H u 10 y d 5 H u H d c c λ H u b, τ mass

24 Downs & Leptons W H u (c i 10 i )(c j 10 j )+H d 10 i λ ij 5 j add SUSY breaking L Bµ H (3) u H (3) d c λ c ( λ λ ) c ( λ λ ) λ c = b, τ mass δ = s, µ mass δɛ 2 y d δ( ) ɛ 4 ɛ 3 ɛ 3 ɛ 2 ɛ 2 ɛ ɛ 2 ɛ 1 generates H u 10 y d 5 H u H d c c λ H u b, τ mass s, µ mass

25 Downs & Leptons W H u (c i 10 i )(c j 10 j )+H d 10 i λ ij 5 j add SUSY breaking L Bµ H (3) u H (3) d c λ c ( λ λ ) c ( λ λ ) λ c = b, τ mass δ = s, µ mass δɛ 2 y d δ( ) ɛ 4 ɛ 3 ɛ 3 ɛ 2 ɛ 2 ɛ ɛ 2 ɛ 1 generates H u 10 y d 5 H u H d c c λ H u b, τ mass s, µ mass this simple structure works with only 2 spurions, so requires unification

26 Split SUSY Both 5 s and 45 s have proton decay causing components through φ 10 5 so must get mass at GUT scale (could project out components, spoils unification) SM flavor structure is generated near the GUT scale

27 Split SUSY Both 5 s and 45 s have proton decay causing components through φ 10 5 so must get mass at GUT scale (could project out components, spoils unification) SM flavor structure is generated near the GUT scale SUSY breaking in sector also at GUT scale so flavor diagrams unsuppressed Bµ σ M 2 N M 2 GUT SUSY breaking in sector feeds down to SM sector through loops so must work in Split SUSY with scalars at (or 1-loop below) GUT scale

28 Domino Mechanism W = H u H d 10 i λ ij 5 j add SUSY breaking L Bµ H (3) u H (3) d t

29 Domino Mechanism W = H u H d 10 i λ ij 5 j add SUSY breaking L Bµ H (3) u H (3) d t b, τ

30 Domino Mechanism W = H u H d 10 i λ ij 5 j add SUSY breaking L Bµ H (3) u H (3) d t b, τ c s, µ

31 Domino Mechanism W = H u H d 10 i λ ij 5 j add SUSY breaking L Bµ H (3) u H (3) d t b, τ c s, µ u d, e

32 Predictions for Yukawa Couplings

33 Parameters and Planck Slop W = H u φ 10 λ 5 L Bµ φφ U(2) 10 U(3) 5 = λ = λ 11 λ λ 22 λ λ 33

34 Parameters and Planck Slop W = H u φ 10 λ 5 L Bµ φφ U(2) 10 U(3) 5 = λ = λ 11 λ λ 22 λ λ 33 7 parameters vs. 6 masses, 3 mixings, and 1 phase in quark sector

35 Parameters and Planck Slop W = H u φ 10 λ 5 L Bµ φφ U(2) 10 U(3) 5 = λ = λ 11 λ λ 22 λ λ 33 7 parameters vs. 6 masses, 3 mixings, and 1 phase in quark sector Higher dim Planck suppressed ops: σ 2 M 2 p H u σ 2 M 2 p H d 10 5 Σ Σ M 2 p ( H uφ MGUT... M p ) contributes to 1st generation masses and CP phase, gives J Only exact predictions are between downs and leptons, but all 13 Yukawas predicted at O(1)

36 Up Yukawas m t = σ M N 1 f C (16π 2 ) 2 λ4 log ( Λ 2 m 2 φ ) log ( Λ 2 m 2 φ ) 4 ( φ, φ ) = ( 5, 5 ) ( 45, 45 ) m c m t = λ 2 33λ m u m c = λ 2 22λ Up Yukawas good with O(1) numbers

37 Down Yukawas ( ) f C y t λ m 2 16π 2 2 log φ Bµ m 2 φ + Bµ f C 16π 2 y t λ Bµ m 2 φ

38 Down Yukawas ( ) f C y t λ m 2 16π 2 2 log φ Bµ m 2 φ + Bµ f C 16π 2 y t λ Bµ m 2 φ 10 2 t 10 naturally generates m b m t 10 2 even though m c m t at 1-loop at 2-loop 1 c b Τ 10 1 Μ 10 2 s 10 3 u d e 10 4

39 Down Yukawas ( ) f C y t λ m 2 16π 2 2 log φ Bµ m 2 φ + Bµ f C 16π 2 y t λ Bµ m 2 φ t c b s naturally generates m b m t 10 2 even though Τ Μ m c m t at 1-loop at 2-loop ( φ, φ ) = ( 5, 5 ) ( 45, 45 ) λ 33 λ 32 λ / / u d e 10 4

40 Down Yukawas ( ) f C y t λ m 2 16π 2 2 log φ Bµ m 2 φ + Bµ f C 16π 2 y t λ Bµ m 2 φ t c b s naturally generates m b m t 10 2 even though Τ Μ m c m t at 1-loop at 2-loop ( φ, φ ) = ( 5, 5 ) ( 45, 45 ) λ 33 λ 32 λ / / u d e Planck slop generates all 1st generation masses at the same level

41 in minimal model: SU(5) Breaking Effects Q H (3) u H (3) d D E H (3) u H (3) d L Q U U Q H u bottom mass H u tau mass

42 in minimal model: SU(5) Breaking Effects Q H (3) u H (3) d D E H (3) u H (3) d L = m τ m b = 3 2 Q U U Q from ratio of color factors H u bottom mass H u tau mass this is often preferred to 1 Antusch & Spinrath (2009), Raby et. al. (2008)

43 in minimal model: SU(5) Breaking Effects Q H (3) u H (3) d D E H (3) u H (3) d L = m τ m b = 3 2 Q U U Q from ratio of color factors H u bottom mass H u tau mass this is often preferred to 1 Antusch & Spinrath (2009), Raby et. al. (2008) and = m µ m s 3 2 O(1) mass splittings in components of then easily give m µ φ 3 m s

44 Experimental Signatures

45 Proton Decay W λ ij 10 i 5 j φ h (3) d QL+ h(3) d UD hd gives dim 6 proton decay easily the dominant decay mode since not Yukawa suppressed because λ is O(1) Γ 1 8π λ4 m5 p M 4 h yr λ4 ( GeV M h ) 4 potentially observable at next generation experiments (DUSEL, Hyper-K)

46 Proton Decay Predictions near mass basis: λ = λ 11 λ λ 22 λ λ 33 potentially many observable predictions: Γ ( p e + π 0) λ 4 11 Γ (p ν e π + ) λ 4 11 Γ ( p µ + π 0) λ 2 11 λ 2 12 Γ (p ν µ π + ) λ 2 11 λ 2 12 Γ ( p e + K 0) λ 2 11 λ 2 12 Γ (p ν e K + ) λ 2 11 λ 2 12 Γ ( p µ + K 0) λ 4 12 Γ (p ν µ K + ) ( λ λ 11 λ 22 ) 2 Γ (n e + π ) λ 4 11 Γ ( n ν e π 0) λ 4 11 Γ (n µ + π ) λ 2 11 λ 2 12 Γ ( n ν µ π 0) λ 2 11 λ 2 12 Γ (n e + K ) 0 Γ ( n ν e K 0) λ 2 11 λ 2 12 Γ (n µ + K ) 0 Γ ( n ν µ K 0) ( λ λ 11 λ 22 ) 2 observe flavor mechanism of SM in proton branching ratios

47 The QCD Axion + Strong CP U(1) PQ our Yukawas are forbidden by a U(1)PQ and generated when it is broken: σ i 1 H u 0 H d 0 5 i N 0 U(1)PQ has a mixed anomaly with SU(3)C and thus have a QCD axion (mix of KSVZ and DFSZ) with f M GUT this flavor mechanism thus necessarily solves the strong CP problem

48 Long-Lived Particles the axino is often the LSP, so all superpartners decay to it through dim 5, GUT-suppressed operators W α s 4π S f G αg α + α EM 4π S f F αf α in particular, the gluino: G G +ã with ( ) 3 ( TeV τ f s GeV m G ) 2

49 Long-Lived Particles the axino is often the LSP, so all superpartners decay to it through dim 5, GUT-suppressed operators W α s 4π S f G αg α + α EM 4π S f F αf α in particular, the gluino: G G +ã with ( ) 3 ( TeV τ f s GeV m G ) 2 solves the cosmological long-lived gluino problem of Split SUSY, can solve the primordial Lithium problems of BBN gluinos stop in LHC detectors, observable through out of time decays to monojets measurement of mass and lifetime points to the GUT scale

50 Higgs Mass Higgs quartic determined at GUT scale by SUSY relation, RG evolve to low scale Higgs mass is sharply predicted (insensitive to exact value of scalar soft masses), most uncertainty arises from top mass and αs

51 Higgs Mass Higgs quartic determined at GUT scale by SUSY relation, RG evolve to low scale Higgs mass is sharply predicted (insensitive to exact value of scalar soft masses), most uncertainty arises from top mass and αs

52 Higgs Mass Higgs quartic determined at GUT scale by SUSY relation, RG evolve to low scale Higgs mass is sharply predicted (insensitive to exact value of scalar soft masses), most uncertainty arises from top mass and αs minimal model

53 Higgs Mass Higgs quartic determined at GUT scale by SUSY relation, RG evolve to low scale Higgs mass is sharply predicted (insensitive to exact value of scalar soft masses), most uncertainty arises from top mass and αs minimal model 45 model

54 Summary All three generations treated identically by fundamental theory Arbitrary O(1) couplings naturally generate the hierarchical pattern (not just the small sizes) of masses for all quarks and leptons Though flavor is generated at GUT scale, many observable predictions: Novel source of SU(5) breaking effects can change b-τ unification Predicts QCD axion solves strong CP, novel proton decay, long-lived particles at BBN and LHC, Higgs mass

56 Predictions for Yukawa Couplings

57 Color Factors ( φ, φ ) = ( 5, 5 ) ( 45, 45 ) H u 1010 H u H u wavefunction renormalizations bigger than vertex, but cancel for masses (not for mixing angles)

58 Color Factors ( φ, φ ) = ( 5, 5 ) ( 45, 45 ) H u mixing (also mass) H u s, µ mass tend to give smaller hierarchies between downs/leptons than ups

59 Model with 45 s 10 5 = = φ 10 5 all radiative generation works except b, tau at one-loop from top = 5 s + 45 a + 50 s = φ = 0

60 Model with 45 s 10 5 = = φ 10 5 all radiative generation works except b, tau at one-loop from top = 5 s + 45 a + 50 s = φ = 0 add two vector-like multiplets (instead of one): 10 N1 10 N S 10 N1 10 N2 φ 10 3 φ φ 5 10 N H u

Lecture 18 - Beyond the Standard Model

Lecture 18 - Beyond the Standard Model Why is the Standard Model incomplete? Grand Unification Baryon and Lepton Number Violation More Higgs Bosons? Supersymmetry (SUSY) Experimental signatures for SUSY