Flavor Physics Part 2
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1 Flavor Physics Part 2 Wolfgang Altmannshofer altmanwg@ucmail.uc.edu Summer School on Symmetries, Fundamental Interactions and Cosmology 2016, Abtei Frauenwörth, September 20, 2016 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
2 Summary of the First Lecture In the SM, all flavor violation is due to the Higgs At tree level there are no FCNCs; flavor violation occurs only in charged currents, parametrized by the CKM matrix FCNCs arise at the 1-loop level. Example: meson mixing; gives access to CKM elements V td and V ts and their phases Where do the hierarchies in the CKM elements and the fermion masses come from? Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
3 Outline of the Lectures 1 Flavor Physics in the Standard Model Flavor Symmetry and Flavor Symmetry Breaking The CKM Matrix Meson Mixing and CP Asymmetries The Standard Model Flavor Puzzle 2 Flavor Physics Beyond the Standard Model The New Physics Flavor Puzzle Flavor in BSM Models Flavor Anomalies Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
4 Part 2 Flavor Physics Beyond the Standard Model Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
5 The Standard Model as Effective Theory Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
6 The Standard Model as Effective Theory Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
7 The Hierarchy Problem What gives mass to the Higgs itself? The Higgs mass parameter is not forbidden by any symmetry of the Standard Model m 2 = m 2 (0) + m2 (125GeV) 2 1) can be added by hand 2) not protected from 2) quantum corrections Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
8 The Hierarchy Problem What gives mass to the Higgs itself? The Higgs mass parameter is not forbidden by any symmetry of the Standard Model 1) can be added by hand 2) not protected from 2) quantum corrections m 2 = m 2 (0) + m2 (125GeV) 2 quantum corrections to the Higgs mass are sensitive to the largest scales m π 2 M2 Planck 1036 GeV 2 fine tuned cancellation between the quantum corrections and the bare mass is required Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
9 The Hierarchy Problem Canada United States 9,984,670 km 2 9,826,675 km 2 = 157,995 km 2 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
10 The Hierarchy Problem = 1 Å 2 Canada United States 9,984,670 km 2 9,826,675 km 2 = 157,995 km 2 tuning of the Higgs mass would correspond to the surface area of Canada and the United States differing by approximately the size of an atom! In order to protect the Higgs mass from huge quantum corrections and to avoid finetuning, we expect New Physics at the TeV scale Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
11 How can we get information on New Physics at high scales from low energy experiments?
12 Beta Decay Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
13 Beta Decay n p G F e ν e effective low energy description of nuclear beta decay by a 4 fermion contact interaction the interaction strength is given by the Fermi constant G F GeV 2 this defines an energy scale Λ = (G F 2) 1/2 246 GeV Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
14 Beta Decay n G F p e ν e d W u e ν e effective low energy description of nuclear beta decay by a 4 fermion contact interaction the interaction strength is given by the Fermi constant G F GeV 2 this defines an energy scale Λ = (G F 2) 1/2 246 GeV bla in the Standard Model we understand beta decay as consequence of the exchange of virtual weak gauge bosons G F 2 = g2 2 8m 2 W m W 80 GeV Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
15 New Physics in Flavor Changing Neutral Currents b G s µ + = µ b W t γ s µ + µ + b NP s µ + µ Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
16 Example: CP Violation in Kaon mixing Standard Model amplitude is loop suppressed and CKM suppressed d t s K s W t W d K g4 mt 2 (V 16π 2 MW 4 td Vts) 2 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
17 Example: CP Violation in Kaon mixing Standard Model amplitude is loop suppressed and CKM suppressed d t s K s W t W d K g4 mt 2 (V 16π 2 MW 4 td Vts) 2 Generic New Physics amplitude only suppressed by New Physics scale d s K K 1 Λ 2 NP s d Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
18 Example: CP Violation in Kaon mixing Standard Model amplitude is loop suppressed and CKM suppressed d t s K s W t W d K g4 mt 2 (V 16π 2 MW 4 td Vts) 2 Generic New Physics amplitude only suppressed by New Physics scale d s K K 1 Λ 2 NP s d CP Violation in Kaon Mixing can probe extremely high scales Λ NP M2 W m t 4π 1 g 2 V td Vts 104 TeV Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
19 Example: CP Violation in Kaon mixing Standard Model amplitude is loop suppressed and CKM suppressed d t s K s W t W d K g4 mt 2 (V 16π 2 MW 4 td Vts) 2 Generic New Physics amplitude only suppressed by New Physics scale d s K K 1 Λ 2 NP s d CP Violation in Kaon Mixing can probe extremely high scales Λ NP M2 W m t 4π 1 g 2 V td Vts 104 TeV [Exercise: estimate the scale that can be probed with rare B decays] Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
20 Many Flavor Violating Dimension Six Operators 2499 baryon number conserving dim. 6 operators in total Grzadkowski et al , Alonso et al Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
21 Many Flavor Violating Dimension Six Operators 2499 baryon number conserving dim. 6 operators in total Grzadkowski et al , Alonso et al fermion interactions Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
22 Many Flavor Violating Dimension Six Operators 2499 baryon number conserving dim. 6 operators in total Grzadkowski et al , Alonso et al fermion interactions dipole transitions Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
23 Many Flavor Violating Dimension Six Operators 2499 baryon number conserving dim. 6 operators in total Grzadkowski et al , Alonso et al fermion interactions dipole transitions Z-penguins Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
24 Many Flavor Violating Dimension Six Operators 2499 baryon number conserving dim. 6 operators in total Grzadkowski et al , Alonso et al fermion interactions dipole transitions Z-penguins Higgs penguins Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
25 Higgs Penguin Operators Higgs penguin operators O eh = (H H)( l 1 P R e 2 )H O uh = (H H)( q 1 P R u 2 )H c O dh = (H H)( q 1 P R d 2 )H Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
26 Higgs Penguin Operators Higgs penguin operators O eh = (H H)( l 1 P R e 2 )H O uh = (H H)( q 1 P R u 2 )H c O dh = (H H)( q 1 P R d 2 )H [Exercise: show that these interactions lead indeed to flavor violating Higgs couplings] Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
27 Higgs Penguin Operators Higgs penguin operators O eh = (H H)( l 1 P R e 2 )H O uh = (H H)( q 1 P R u 2 )H c O dh = (H H)( q 1 P R d 2 )H [Exercise: show that these interactions lead indeed to flavor violating Higgs couplings] e 2 h h e 1 h induced processes: h τµ, τ µγ, τ 3µ,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
28 Higgs Penguin Operators Higgs penguin operators O eh = (H H)( l 1 P R e 2 )H O uh = (H H)( q 1 P R u 2 )H c O dh = (H H)( q 1 P R d 2 )H [Exercise: show that these interactions lead indeed to flavor violating Higgs couplings] u 2 h h u 1 h induced processes: h τµ, τ µγ, τ 3µ,... t hu, D 0 D 0 mixing, D 0 µ + µ,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
29 Higgs Penguin Operators Higgs penguin operators O eh = (H H)( l 1 P R e 2 )H O uh = (H H)( q 1 P R u 2 )H c O dh = (H H)( q 1 P R d 2 )H [Exercise: show that these interactions lead indeed to flavor violating Higgs couplings] d 2 h h d 1 h induced processes: h τµ, τ µγ, τ 3µ,... t hu, D 0 D 0 mixing, D 0 µ + µ,... h bs, B meson mixing, Kaon mixing, B s µ + µ,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
30 Z Penguin Operators Z-penguin operators O (3) hl = (H i D a µh)( l 1 γ µ σ a P L l 2 ) Õ (1) hl = (H i D µ H)( l 1 γ µ P L l 2 ) O he = (H i D µ H)(ē 1 γ µ P R e 2 )... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
31 Z Penguin Operators Z-penguin operators O (3) hl = (H i D a µh)( l 1 γ µ σ a P L l 2 ) Õ (1) hl = (H i D µ H)( l 1 γ µ P L l 2 ) O he = (H i D µ H)(ē 1 γ µ P R e 2 )... e 2 h h e 1 Z induced processes: Z τµ, τ 3µ, µ e conversion,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
32 Z Penguin Operators Z-penguin operators O (3) hl = (H i D a µh)( l 1 γ µ σ a P L l 2 ) Õ (1) hl = (H i D µ H)( l 1 γ µ P L l 2 ) O he = (H i D µ H)(ē 1 γ µ P R e 2 )... u 2 h h u 1 Z induced processes: Z τµ, τ 3µ, µ e conversion,... t Zu, D 0 D 0 mixing, D 0 µ + µ,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
33 Z Penguin Operators Z-penguin operators O (3) hl = (H i D a µh)( l 1 γ µ σ a P L l 2 ) Õ (1) hl = (H i D µ H)( l 1 γ µ P L l 2 ) O he = (H i D µ H)(ē 1 γ µ P R e 2 )... d 2 h h d 1 Z induced processes: Z τµ, τ 3µ, µ e conversion,... t Zu, D 0 D 0 mixing, D 0 µ + µ,... Z bs, B meson mixing, Kaon mixing, B K l + l,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
34 Dipole Operators dipole operators O dg = ( q 1 σ µν T A P R d 2 )H G A µν O dw = ( q 1 σ µν P R d 2 )σ a H W a µν O db = ( q 1 σ µν P R d 2 )H B µν... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
35 Dipole Operators dipole operators h e 1 O dg = ( q 1 σ µν T A P R d 2 )H G A µν e 2 O dw = ( q 1 σ µν P R d 2 )σ a H W a µν O db = ( q 1 σ µν P R d 2 )H B µν... γ/z/g induced processes: µ eγ, τ 3µ, µ e conversion,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
36 Dipole Operators dipole operators h u 1 O dg = ( q 1 σ µν T A P R d 2 )H G A µν u 2 O dw = ( q 1 σ µν P R d 2 )σ a H W a µν O db = ( q 1 σ µν P R d 2 )H B µν... γ/z/g induced processes: µ eγ, τ 3µ, µ e conversion,... t uγ, t cz, D 0 ρµ + µ,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
37 Dipole Operators dipole operators h d 1 O dg = ( q 1 σ µν T A P R d 2 )H G A µν d 2 O dw = ( q 1 σ µν P R d 2 )σ a H W a µν O db = ( q 1 σ µν P R d 2 )H B µν... γ/z/g induced processes: µ eγ, τ 3µ, µ e conversion,... t uγ, t cz, D 0 ρµ + µ,... b sγ, B K ( ) l + l,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
38 Four Fermion Contact Interactions 4 fermion interactions O dd = ( d 1 γ µ P R d 2 )( d 3 γ µ P R d 4 ) O lu = ( l 1 γ µ P L l 2 )(ū 1 γ µ P R u 2 ) + many other Dirac and flavor structures Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
39 Four Fermion Contact Interactions 4 fermion interactions f 1 f 2 O dd = ( d 1 γ µ P R d 2 )( d 3 γ µ P R d 4 ) O lu = ( l 1 γ µ P L l 2 )(ū 1 γ µ P R u 2 ) + many other Dirac and flavor structures f 3 f 4 induced processes: Kaon mixing, D 0 mixing, B d mixing, B s mixing,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
40 Four Fermion Contact Interactions 4 fermion interactions f 1 f 2 O dd = ( d 1 γ µ P R d 2 )( d 3 γ µ P R d 4 ) O lu = ( l 1 γ µ P L l 2 )(ū 1 γ µ P R u 2 ) + many other Dirac and flavor structures f 3 f 4 induced processes: Kaon mixing, D 0 mixing, B d mixing, B s mixing,... t uµµ, D 0 ρµ + µ, B d µ + µ, B K ( ) l + l,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
41 Four Fermion Contact Interactions 4 fermion interactions f 1 f 2 O dd = ( d 1 γ µ P R d 2 )( d 3 γ µ P R d 4 ) O lu = ( l 1 γ µ P L l 2 )(ū 1 γ µ P R u 2 ) + many other Dirac and flavor structures f 3 f 4 induced processes: Kaon mixing, D 0 mixing, B d mixing, B s mixing,... t uµµ, D 0 ρµ + µ, B d µ + µ, B K ( ) l + l,... τ eµµ, µ 3e, µ e conversion,... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
42 Bounds From Meson Mixing 4 fermion contact interactions leading to Kaon mixing C 1 Λ 2 ( dγ µ P L s)( dγ µ P L s) C 2 Λ 2 ( dp L s)( dp L s) C 3 Λ 2 ( d α P L s β )( d β P L s α ) C 4 Λ 2 ( dp L s)( dp R s) C 5 Λ 2 ( d α P L s β )( d β P R s α ) (analogous for other meson systems) need hadronic matrix elements from lattice to translate measurements into NP bounds Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
43 Bounds From Meson Mixing 4 fermion contact interactions leading to Kaon mixing C 1 Λ 2 ( dγ µ P L s)( dγ µ P L s) C 2 Λ 2 ( dp L s)( dp L s) C 3 Λ 2 ( d α P L s β )( d β P L s α ) C 4 Λ 2 ( dp L s)( dp R s) C 5 Λ 2 ( d α P L s β )( d β P R s α ) (analogous for other meson systems) need hadronic matrix elements from lattice to translate measurements into NP bounds (bounds on Λ assuming C i = 1) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
44 The New Physics Flavor Puzzle Low energy flavor observables are sensitive to New Physics far beyond the TeV scale Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
45 The New Physics Flavor Puzzle Low energy flavor observables are sensitive to New Physics far beyond the TeV scale solutions of the hierarchy problem require New Physics at or below the TeV scale Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
46 The New Physics Flavor Puzzle Low energy flavor observables are sensitive to New Physics far beyond the TeV scale currently no convincing evidence for deviations from Standard Model predictions in flavor experiments solutions of the hierarchy problem require New Physics at or below the TeV scale Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
47 The New Physics Flavor Puzzle Low energy flavor observables are sensitive to New Physics far beyond the TeV scale currently no convincing evidence for deviations from Standard Model predictions in flavor experiments If there is New Physics at or below the TeV scale, why have we not seen it yet in flavor observables? solutions of the hierarchy problem require New Physics at or below the TeV scale Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
48 Reactions to the New Physics Flavor Puzzle Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
49 Reactions to the New Physics Flavor Puzzle Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
50 Reactions to the New Physics Flavor Puzzle Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
51 Minimal Flavor Violation recall from the first lecture that without the Yukawa couplings, the SM has a large global flavor symmetry SU(3) Q SU(3) U SU(3) D SU(3) L SU(3) E U(1) 5 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
52 Minimal Flavor Violation recall from the first lecture that without the Yukawa couplings, the SM has a large global flavor symmetry SU(3) Q SU(3) U SU(3) D SU(3) L SU(3) E U(1) 5 The SU(3) 5 symmetry can be formally restored if one promotes the Yukawa couplings to spurions that transform in the following way Y u = 3 Q 3 U, Y d = 3 Q 3 D, Y l = 3 L 3 E Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
53 Minimal Flavor Violation recall from the first lecture that without the Yukawa couplings, the SM has a large global flavor symmetry SU(3) Q SU(3) U SU(3) D SU(3) L SU(3) E U(1) 5 The SU(3) 5 symmetry can be formally restored if one promotes the Yukawa couplings to spurions that transform in the following way Y u = 3 Q 3 U, Y d = 3 Q 3 D, Y l = 3 L 3 E the Yukawa interactions are now formally flavor invariant L H c ( QY u U) + H c ( QY d D) + H( LY l E) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
54 Minimal Flavor Violation Minimal Flavor Violation the SM Yukawas remain the only sources of flavor breaking also in theories beyond the SM Chivukula, Georgi 87; D Ambrosio et al. 02 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
55 Minimal Flavor Violation and FCNCs What happens to flavor changing interactions among down quarks? d L = 3 Q, d R = 3 D, Y u = 3 Q 3 U, Y d = 3 Q 3 D Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
56 Minimal Flavor Violation and FCNCs What happens to flavor changing interactions among down quarks? d L = 3 Q, d R = 3 D, Y u = 3 Q 3 U, Y d = 3 Q 3 D lets write down flavor invariant terms and then rotate to mass eigenstates Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
57 Minimal Flavor Violation and FCNCs What happens to flavor changing interactions among down quarks? d L = 3 Q, d R = 3 D, Y u = 3 Q 3 U, Y d = 3 Q 3 D lets write down flavor invariant terms and then rotate to mass eigenstates ( d L γ µ d L ) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
58 Minimal Flavor Violation and FCNCs What happens to flavor changing interactions among down quarks? d L = 3 Q, d R = 3 D, Y u = 3 Q 3 U, Y d = 3 Q 3 D lets write down flavor invariant terms and then rotate to mass eigenstates ( d L γ µ d L ) ( d L γ µ d L ) no flavor change Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
59 Minimal Flavor Violation and FCNCs What happens to flavor changing interactions among down quarks? d L = 3 Q, d R = 3 D, Y u = 3 Q 3 U, Y d = 3 Q 3 D lets write down flavor invariant terms and then rotate to mass eigenstates ( d L γ µ d L ) ( d L γ µ d L ) no flavor change ( d L Y d Y d γµ d L ) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
60 Minimal Flavor Violation and FCNCs What happens to flavor changing interactions among down quarks? d L = 3 Q, d R = 3 D, Y u = 3 Q 3 U, Y d = 3 Q 3 D lets write down flavor invariant terms and then rotate to mass eigenstates ( d L γ µ d L ) ( d L γ µ d L ) no flavor change ( d L Y d Y d γµ d L ) ( d L (Y diag d ) 2 γ µ d L ) no flavor change Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
61 Minimal Flavor Violation and FCNCs What happens to flavor changing interactions among down quarks? d L = 3 Q, d R = 3 D, Y u = 3 Q 3 U, Y d = 3 Q 3 D lets write down flavor invariant terms and then rotate to mass eigenstates ( d L γ µ d L ) ( d L γ µ d L ) no flavor change ( d L Y d Y d γµ d L ) ( d L (Y diag d ) 2 γ µ d L ) no flavor change ( d L Y u Y u γ µ d L ) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
62 Minimal Flavor Violation and FCNCs What happens to flavor changing interactions among down quarks? d L = 3 Q, d R = 3 D, Y u = 3 Q 3 U, Y d = 3 Q 3 D lets write down flavor invariant terms and then rotate to mass eigenstates ( d L γ µ d L ) ( d L γ µ d L ) no flavor change ( d L Y d Y d γµ d L ) ( d L (Y diag d ) 2 γ µ d L ) no flavor change ( d L Y u Y u γ µ d L ) ( d i L Vti V tkyt 2 γ µ dk L ) flavor change! Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
63 Minimal Flavor Violation and FCNCs What happens to flavor changing interactions among down quarks? d L = 3 Q, d R = 3 D, Y u = 3 Q 3 U, Y d = 3 Q 3 D lets write down flavor invariant terms and then rotate to mass eigenstates ( d L γ µ d L ) ( d L γ µ d L ) no flavor change ( d L Y d Y d γµ d L ) ( d L (Y diag d ) 2 γ µ d L ) no flavor change ( d L Y u Y u γ µ d L ) ( d i L Vti V tkyt 2 γ µ dk L ) flavor change! flavor changing transitions are proportional to small CKM elements (same as in the SM) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
64 Minimal Flavor Violation and FCNCs What happens to flavor changing interactions among down quarks? d L = 3 Q, d R = 3 D, Y u = 3 Q 3 U, Y d = 3 Q 3 D lets write down flavor invariant terms and then rotate to mass eigenstates ( d L γ µ d L ) ( d L γ µ d L ) no flavor change ( d L Y d Y d γµ d L ) ( d L (Y diag d ) 2 γ µ d L ) no flavor change ( d L Y u Y u γ µ d L ) ( d i L Vti V tkyt 2 γ µ dk L ) flavor change! flavor changing transitions are proportional to small CKM elements (same as in the SM) transitions involving right handed quarks are further suppressed by small Yukawa couplings Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
65 Bounds From Meson Mixing with MFV Meson mixing constraints are strongly relaxed in the MFV framework The couplings C i are now suppressed Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
66 Bounds From Meson Mixing with MFV Meson mixing constraints are strongly relaxed in the MFV framework The couplings C i are now suppressed C 1 Λ 2 ( dγ µ P L s)( dγ µ P L s), C 1 (y 2 t V td V ts) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
67 Bounds From Meson Mixing with MFV Meson mixing constraints are strongly relaxed in the MFV framework The couplings C i are now suppressed C 1 Λ 2 ( dγ µ P L s)( dγ µ P L s), C 1 (y 2 t V td V ts) C 4 Λ 2 ( dp L s)( dp R s), C 4 y d y s (y 2 t V td V ts) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
68 Bounds From Meson Mixing with MFV Meson mixing constraints are strongly relaxed in the MFV framework The couplings C i are now suppressed C 1 Λ 2 ( dγ µ P L s)( dγ µ P L s), C 1 (y 2 t V td V ts) C 4 Λ 2 ( dp L s)( dp R s), C 4 y d y s (y 2 t V td V ts) new physics can be at the TeV scale without violating the bounds Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
69 Flavor Violation in Models of New Physics
70 Two Higgs Doublet Models one of the simplest extensions of the SM Higgs sector two Higgs doublets H 1 and H 2 with hypercharges -1/2 and +1/2 ( H 2 = H + ) (vs β + h 2 + ia 2 ) ( 1 2 ) (vc β + h 1 + ia 1 ), H 1 = H 1 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
71 Two Higgs Doublet Models one of the simplest extensions of the SM Higgs sector two Higgs doublets H 1 and H 2 with hypercharges -1/2 and +1/2 ( H 2 = H + ) (vs β + h 2 + ia 2 ) ( 1 2 ) (vc β + h 1 + ia 1 ), H 1 = H 1 5 physical degrees of freedom: h and H, A, and H ± assuming CP conservation: ( ) ( ) ( ) G ± sβ c H ± = β H ± 2 c β s β H ± 1 ( ( ) ( ) ( ( ) ( ) h cα s = α h2 G sβ c, = β a2 H) c α h 1 A) s β a 1 s α c β Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
72 FCNCs at Tree Level both Higgs doublets can couple to the SM fermions L (y u ) ik H 2 Qi U k + (ỹ u ) ik H Q 1 i U k +(y d ) ik H 1 Qi D k + (ỹ d ) ik H Q 2 i D k +(y l ) ik H 1 Li E k + (ỹ l ) ik H L 2 i E k + h.c. Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
73 FCNCs at Tree Level both Higgs doublets can couple to the SM fermions L (y u ) ik H 2 Qi U k + (ỹ u ) ik H Q 1 i U k +(y d ) ik H 1 Qi D k + (ỹ d ) ik H Q 2 i D k +(y l ) ik H 1 Li E k + (ỹ l ) ik H L 2 i E k + h.c. for generic couplings y and ỹ, quark masses and Higgs couplings are not aligned, e.g. (m d ) ik = v 2 ( c β (y d ) ik +s β (ỹ d ) ik ), (g A d ) ik = 1 2 ( s β (y d ) ik c β (ỹ d ) ik ) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
74 FCNCs at Tree Level both Higgs doublets can couple to the SM fermions L (y u ) ik H 2 Qi U k + (ỹ u ) ik H Q 1 i U k +(y d ) ik H 1 Qi D k + (ỹ d ) ik H Q 2 i D k +(y l ) ik H 1 Li E k + (ỹ l ) ik H L 2 i E k + h.c. for generic couplings y and ỹ, quark masses and Higgs couplings are not aligned, e.g. (m d ) ik = v 2 ( c β (y d ) ik +s β (ỹ d ) ik ), (g A d ) ik = 1 2 ( s β (y d ) ik c β (ỹ d ) ik ) tree level FCNCs incredible strong constraints from meson mixing K d s A, H s d K Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
75 2HDMs with Natural Flavor Conservation Natural Flavor Conservation: no tree level FCNCs if all types of fermions couple only to one Higgs doublet (Glashow, Weinberg 77) Can be enforced by: (softly broken) continuous symmetries (Peccei-Quinn) or discrete symmetries (Z 2 ) 4 possibilities: (y u ) ik H 2 Qi U k + (ỹ d ) ik H 2 Q i D k + (ỹ l ) ik H 2 L i E k type I type II type III type IV up quarks H 2 H 2 H 2 H 2 down quarks H 2 H 1 H 2 H 1 leptons H 2 H 1 H 1 H 2 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
76 2HDMs with Natural Flavor Conservation Natural Flavor Conservation: no tree level FCNCs if all types of fermions couple only to one Higgs doublet (Glashow, Weinberg 77) Can be enforced by: (softly broken) continuous symmetries (Peccei-Quinn) or discrete symmetries (Z 2 ) 4 possibilities: (y u ) ik H 2 Qi U k + (y d ) ik H 1 Qi D k + (y l ) ik H 1 Li E k type I type II type III type IV up quarks H 2 H 2 H 2 H 2 down quarks H 2 H 1 H 2 H 1 leptons H 2 H 1 H 1 H 2 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
77 2HDMs with Natural Flavor Conservation Natural Flavor Conservation: no tree level FCNCs if all types of fermions couple only to one Higgs doublet (Glashow, Weinberg 77) Can be enforced by: (softly broken) continuous symmetries (Peccei-Quinn) or discrete symmetries (Z 2 ) 4 possibilities: (y u ) ik H 2 Qi U k + (ỹ d ) ik H 2 Q i D k + (y l ) ik H 1 Li E k type I type II type III type IV up quarks H 2 H 2 H 2 H 2 down quarks H 2 H 1 H 2 H 1 leptons H 2 H 1 H 1 H 2 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
78 2HDMs with Natural Flavor Conservation Natural Flavor Conservation: no tree level FCNCs if all types of fermions couple only to one Higgs doublet (Glashow, Weinberg 77) Can be enforced by: (softly broken) continuous symmetries (Peccei-Quinn) or discrete symmetries (Z 2 ) 4 possibilities: (y u ) ik H 2 Qi U k + (y d ) ik H 1 Qi D k + (ỹ l ) ik H 2 L i E k type I type II type III type IV up quarks H 2 H 2 H 2 H 2 down quarks H 2 H 1 H 2 H 1 leptons H 2 H 1 H 1 H 2 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
79 2HDMs with Minimal Flavor Violation expansion of the wrong Higgs couplings ỹ u = ɛ u y u + ɛ uy u y u y u + ɛ uy d y d y u +... ỹ d = ɛ d y d + ɛ d y dy d y d + ɛ d y uy u y d +... ỹ l = ɛ l y l + ɛ ly l y l y l +... still Flavor Changing Neutral Currents at tree level, but controlled by small Yukawas and CKM elements Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
80 2HDMs with Minimal Flavor Violation expansion of the wrong Higgs couplings ỹ u = ɛ u y u + ɛ uy u y u y u + ɛ uy d y d y u +... ỹ d = ɛ d y d + ɛ d y dy d y d + ɛ d y uy u y d +... ỹ l = ɛ l y l + ɛ ly l y l y l +... Exercise part 1: demonstrate that these terms are formally invariant under the flavor group still Flavor Changing Neutral Currents at tree level, but controlled by small Yukawas and CKM elements Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
81 2HDMs with Minimal Flavor Violation expansion of the wrong Higgs couplings ỹ u = ɛ u y u + ɛ uy u y u y u + ɛ uy d y d y u +... ỹ d = ɛ d y d + ɛ d y dy d y d + ɛ d y uy u y d +... ỹ l = ɛ l y l + ɛ ly l y l y l +... Exercise part 1: demonstrate that these terms are formally invariant under the flavor group Exercise part 2: rotate into the quark mass eigenstate basis and show that off-diagonal entries in ỹ u and ỹ d are suppressed by small CKM elements still Flavor Changing Neutral Currents at tree level, but controlled by small Yukawas and CKM elements Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
82 The Minimal Supersymmetric Standard Model Supersymmetry (SUSY) implies: every fermion has a bosonic partner and vice versa requires 2 Higgs doublets to give mass to up-type and down-type fermions (2HDM type II) tan β = H u / H d expect at least some SUSY particles (Higgsinos, stops, gluinos) at or below O(TeV) for a natural electro-weak scale Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
83 Flavor and CP Violation in the MSSM bla The MSSM can contain many new sources of flavor and CP violation Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
84 Flavor and CP Violation in the MSSM The MSSM can contain many new sources of flavor and CP violation bla Higgsino and Higgs masses 2 phases µ H u Hd +BµH u H d +m 2 H u H u 2 +m 2 H d H d 2 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
85 Flavor and CP Violation in the MSSM The MSSM can contain many new sources of flavor and CP violation bla Higgsino and Higgs masses 2 phases squark and slepton masses 15 angles + 15 phases µ H u Hd +BµH u H d +m 2 H u H u 2 +m 2 H d H d 2 m 2 Q Q L Q L +m 2 UŨ RŨR +m 2 D D R D R +m 2 L L L L L + m 2 EẼ RẼR Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
86 Flavor and CP Violation in the MSSM The MSSM can contain many new sources of flavor and CP violation bla Higgsino and Higgs masses 2 phases squark and slepton masses 15 angles + 15 phases gaugino masses 3 phases µ H u Hd +BµH u H d +mh 2 u H u 2 +mh 2 d H d 2 mq 2 Q Q L L +m UŨ 2 RŨR +md 2 D D R R +ml L 2 L L L + meẽ 2 RẼR m 1 B B +m2 W W +m3 g g Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
87 Flavor and CP Violation in the MSSM The MSSM can contain many new sources of flavor and CP violation bla Higgsino and Higgs masses 2 phases squark and slepton masses 15 angles + 15 phases gaugino masses 3 phases trilinear couplings 18 angles + 27 phases µ H u Hd +BµH u H d +m 2 H u H u 2 +m 2 H d H d 2 m 2 Q Q L Q L +m 2 UŨ RŨR +m 2 D D R D R +m 2 L L L L L + m 2 EẼ RẼR m 1 B B +m2 W W +m3 g g A u H u Q LŨR+A d H d Q L D R +A l H d L LẼR Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
88 Flavor and CP Violation in the MSSM The MSSM can contain many new sources of flavor and CP violation bla Higgsino and Higgs masses 2 phases squark and slepton masses 15 angles + 15 phases gaugino masses 3 phases trilinear couplings 18 angles + 27 phases µ H u Hd +BµH u H d +m 2 H u H u 2 +m 2 H d H d 2 m 2 Q Q L Q L +m 2 UŨ RŨR +m 2 D D R D R +m 2 L L L L L + m 2 EẼ RẼR m 1 B B +m2 W W +m3 g g A u H u Q LŨR+A d H d Q L D R +A l H d L LẼR not all phases are physical! (like in the case of the CKM matrix) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
89 Flavor and CP Violation in the MSSM The MSSM can contain many new sources of flavor and CP violation bla Higgsino and Higgs masses 2 phases squark and slepton masses 15 angles + 15 phases gaugino masses 3 phases trilinear couplings 18 angles + 27 phases µ H u Hd +BµH u H d +m 2 H u H u 2 +m 2 H d H d 2 m 2 Q Q L Q L +m 2 UŨ RŨR +m 2 D D R D R +m 2 L L L L L + m 2 EẼ RẼR m 1 B B +m2 W W +m3 g g A u H u Q LŨR+A d H d Q L D R +A l H d L LẼR not all phases are physical! (like in the case of the CKM matrix) 2 phases can be rotated away... Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
90 The SUSY Flavor Problem squark flavor mixing can lead to large FCNCs at the 1-loop level most transparent parametrization in terms of mass insertions b L δ L bs s L mq 2 = ( ) m2 Q 11 + δq δ R sd mu 2 = ( ) m2 U 11 + δu md 2 = ( ) m2 D 11 + δd s R dr Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
91 Probing PeV Scale Squarks K Mixing s R g s L 6 s R s L ΦK R sd 0.3 e Φ K 2 sd L d R d R M K 12 α2 s m 2 q g d L (δ L sd δr sd ) d L m q TeV squarks of several TeV can be probed if relevant phases are not suppressed Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
92 Minimal Flavor Violation in the MSSM blawolfgang Altmannshofer Flavor Physics 2 September 20, / 44 bla soft masses of squarks and sleptons m 2 Q = m 2 Q ( 1 + b 1 Y uy u + b 2 Y d Y d + ) + b 3 Y d Y d YuY u + b3 Y uy u Y d Y d +... ( ) mu 2 = m U b 4 Y u Y u +... ( ) md 2 = m D b 5 Y d Y d +... m1, m2, m3, µ, Bµ
93 Minimal Flavor Violation in the MSSM blawolfgang Altmannshofer Flavor Physics 2 September 20, / 44 bla soft masses of squarks and sleptons m 2 Q = m 2 Q ( 1 + b 1 Y uy u + b 2 Y d Y d + ) + b 3 Y d Y d YuY u + b3 Y uy u Y d Y d +... ( ) mu 2 = m U b 4 Y u Y u +... ( ) md 2 = m D b 5 Y d Y d +... trilinear couplings ( ) A u = Ãu 1 + b 6 Y d Y d + b 7Y uy u +... Y u A d = Ãd ( 1 + b 8 Y uy u + b 9 Y d Y d +... ) Y d m1, m2, m3, µ, Bµ
94 Minimal Flavor Violation in the MSSM flavor violation controlled by small CKM elements sources of CP violation beyond the CKM are allowed in MFV blawolfgang Altmannshofer Flavor Physics 2 September 20, / 44 bla soft masses of squarks and sleptons m 2 Q = m 2 Q ( 1 + b 1 Y uy u + b 2 Y d Y d + ) + b 3 Y d Y d YuY u + b3 Y uy u Y d Y d +... ( ) mu 2 = m U b 4 Y u Y u +... ( ) md 2 = m D b 5 Y d Y d +... trilinear couplings gaugino/higgsino/higgs masses ( ) A u = Ãu 1 + b 6 Y d Y d + b 7Y uy u +... Y u A d = Ãd ( 1 + b 8 Y uy u + b 9 Y d Y d +... ) Y d m 1, m 2, m 3, µ, Bµ
95 Flavor Anomalies
96 Overview of Current Flavor Anomalies Z. Ligeti Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
97 The B D ( ) τν Decays Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
98 The R D and R D Anomalies R D = BR(B Dτν) BR(B Dlν) R(D*) BaBar, PRL109,101802(2012) Belle, PRD92,072014(2015) LHCb, PRL115,111803(2015) Belle, arxiv: HFAG Average, P(χ 2 ) = 67% SM prediction 2 χ = 1.0 R D = BR(B D τν) BR(B D lν) SM predictions very well under control Fajfer, Kamenik, Nisandzic 12 HPQCD collaboration R(D), PRD92,054510(2015) R(D*), PRD85,094025(2012) HFAG Prel. Winter R(D) Belle, BaBar and LHCb results are all high combined significance 4σ Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
99 The B s φµ + µ Decay Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
100 The B s φµ + µ Anomaly LHCb branching ratio is 3.5σ below SM prediction for 1 GeV 2 < q 2 < 6 GeV 2 Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
101 The B K µ + µ Decay Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
102 The R K Anomaly LHCb σ hint for violation of lepton flavor universality (LFU) R K = BR(B K µ+ µ ) [1,6] BR(B Ke + e ) [1,6] = ± Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
103 The B K ( K π)µ + µ Decay Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
104
105 The B K µ + µ Anomaly LHCb P 5 characterizes the angular distribution of the decay products WA, Ball, Bharucha, Buras, Straub, Wick Bobeth et al Descotes-Genon et al , σ deviation in [4,6] GeV 2 bin (+3.0σ in [6,8] GeV 2 bin) Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
106 What Could It Be? branching angular LFU ratios observables ratios Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
107 What Could It Be? branching angular LFU ratios observables ratios statistical fluctuations? Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
108 What Could It Be? branching angular LFU ratios observables ratios statistical fluctuations? parametric uncertainties? Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
109 What Could It Be? branching angular LFU ratios observables ratios statistical fluctuations? parametric uncertainties? underestimated hadronic effects? Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
110 What Could It Be? branching angular LFU ratios observables ratios statistical fluctuations? parametric uncertainties? underestimated hadronic effects? New Physics? Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
111 Summary of the Second Lecture Low energy flavor observables have indirect sensitivity to very high scales If there is new physics at the TeV scale, why have we not seen it yet in flavor observables? The idea of Minimal Flavor Violation can tame flavor violation in new physics models Few anomalies exist in flavor measurements. Are they first hints for new physics? Wolfgang Altmannshofer Flavor Physics 2 September 20, / 44
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