Connection between g − 2, EDMs, CLFV and LHC Paride Paradisi University of Padua EPS 2015 10-15 August 2015 Rio de Janeiro, Brazil Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 1 / 21
Open questions • The origin of flavour is still, to a large extent, a mystery. The most important open questions can be summarized as follow: ◮ Which is the organizing principle behind the observed pattern of fermion masses and mixing angles? ◮ Are there extra sources of flavour symmetry breaking beside the SM Yukawa couplings which are relevant at the TeV scale? • Related important questions are: ◮ Which is the role of flavor physics in the LHC era? ◮ Do we expect to understand the (SM and NP) flavor puzzles through the synergy and interplay of flavor physics and the LHC? Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 2 / 21
NP search strategies • High-energy frontier: A unique effort to determine the NP scale • High-intensity frontier (flavor physics): A collective effort to determine the flavor structure of NP Where to look for New Physics at the low energy? • Processes very suppressed or even forbidden in the SM ◮ FCNC processes ( µ → e γ , µ → eee , µ → e in N, τ → µγ , B 0 s , d → µ + µ − ...) ◮ CPV effects in the electron/neutron EDMs, d e , n ... ◮ FCNC & CPV in B s , d & D decay/mixing amplitudes • Processes predicted with high precision in the SM a exp ◮ EWPO as ( g − 2 ) µ, e : − a SM ≈ ( 3 ± 1 ) × 10 − 9 , a discrepancy at 3 σ ! µ µ ◮ LU in R e /µ = Γ( M → e ν ) / Γ( M → µν ) with M = π, K M Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 3 / 21
Experimental status LFV process Experiment Future limits Year (expected) O ( 10 − 14 ) BR( µ → e γ ) MEG ∼ 2017 O ( 10 − 15 ) Project X > 2021 O ( 10 − 15 ) BR( µ → eee ) Mu3e ∼ 2017 O ( 10 − 16 ) Mu3e > 2017 O ( 10 − 16 ) MUSIC ∼ 2017 O ( 10 − 17 ) Project X > 2021 O ( 10 − 17 ) CR( µ → e ) COMET ∼ 2017 O ( 10 − 17 ) Mu2e ∼ 2020 O ( 10 − 18 ) PRISM/PRIME ∼ 2020 O ( 10 − 19 ) Project X > 2021 O ( 10 − 8 ) BR( τ → µγ ) Belle II > 2020 O ( 10 − 10 ) BR( τ → µµµ ) Belle II > 2020 O ( 10 − 9 ) BR( τ → e γ ) Belle II > 2020 O ( 10 − 10 ) BR( τ → µµµ ) Belle II > 2020 Table: Future sensitivities of next-generation experiments. Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 4 / 21
The NP “scale” ⇒ Λ Planck ∼ 10 18 − 19 ●❡❱ • Gravity = ⇒ Λ see − saw � 10 15 ●❡❱ • Neutrino masses = • BAU : evidence of CPV beyond SM ◮ Electroweak Baryogenesis = ⇒ Λ NP � ❚❡❱ ⇒ Λ see − saw � 10 15 ●❡❱ ◮ Leptogenesis = • Hierarchy problem : = ⇒ Λ NP � ❚❡❱ • Dark Matter = ⇒ Λ NP � ❚❡❱ SM = effective theory at the EW scale c ( d ) X ij O ( d ) L ❡✛ = L ❙▼ + ij Λ d − 4 NP d ≥ 5 y ij • L d = 5 = Λ s❡❡ − s❛✇ L i L j φφ , ν ❡✛ BR ( ℓ i → ℓ j γ ) ∼ v 4 • L d = 6 generates FCNC operators Λ 4 ❡✛ NP Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 5 / 21
Hierarchy see-saw Hierarchy see-saw • Hierarchy problem : Λ NP � ❚❡❱ • SM Yukawas : M W � Λ NP � M P • Flavor problem : Λ NP ≫ ❚❡❱ Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 6 / 21
Why LFV is interesting? • Neutrino Oscillation ⇒ m ν i � = m ν j ⇒ LFV v 2 M R ∼ eV ⇒ M R ∼ 10 14 − 16 • see-saw : m ν ∼ • LFV transitions like µ → e γ @ 1 loop with exchange of ◮ W and ν in the SM with Λ NP ≡ M R ≡ Λ see − saw Br ( µ → e γ ) ∼ v 4 ≤ 10 − 50 GIM M 4 R ◮ If Λ NP ≪ Λ see − saw ( Λ NP ≡ m susy in the MSSM) v 4 Br ( µ → e γ ) ∼ Λ 4 NP ⇓ • LFV generally detectable in (multi) TeV scale NP scenarios like the MSSM, .... Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 7 / 21
The NP “scale” vs. LFV Calibbi @ IFAE2014 Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 8 / 21
SUSY Flavour after the Higgs discovery � � � 3 TeV , � m g � m B � � � � m W � � � 10 TeV 30 neutron Kaon EDM mixing Μ� 3e 10 tan Β . v n o c e � Μ electron EDM 3 Γ e � M h � 125.5 � 1 GeV Μ charm mixing 1 30 Μ� e conv. neutron M D EDM E n o r t c e 10 l e Kaon tan Β mixing 3 Γ e M h � 125.5 � 1 GeV � Μ Μ� 3e charm mixing 1 10 2 10 3 10 4 10 5 10 � � m l � � � Μ � � TeV � m q Low energy constraints fixing ( δ A ) ij = 0 . 3. The upper (lower) plot gives the reach of current (projected future) experimental results [Altmannshofer, Harnik, & Zupan, ’13] Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 9 / 21
SM vs. NP flavor problems • Can the SM and NP flavour problems have a common explanation? 10 � 6 10 � 4 0.01 1 Y i Μ ,s e u d c b t Τ V CKM ∼ � � � � � � � � � GeV 10 � 4 0.01 1 100 • Froggat-Nielsen ’79: Hierarchies from SSB of a Flavour Symmetry ǫ = � φ � M ≪ 1 ⇒ Y ij ∝ ǫ ( a i + b j ) ... • Flavor protection from flavor models: [Lalak, Pokorski & Ross ’10] U ( 1 ) 2 Operator U ( 1 ) SU ( 3 ) ▼❋❱ ( Q L X Q λ 5 λ 3 λ 5 LL Q L ) 12 λ ( D R X D λ 11 λ 3 ( y d y s ) × λ 5 RR D R ) 12 λ ( Q L X D λ 4 λ 9 λ 3 y s × λ 5 LR D R ) 12 • Is this flavor protection enough? • Can we disentangle flavour models through flavour physics? Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 10 / 21
The New Physics CP problem • Why CP violation? Motivation: ◮ Baryogenesis requires extra sources of CPV ◮ The QCD θ -term L CP = θ α s 8 π G ˜ G is a CPV source beyond the CKM ◮ Most UV completion of the SM, e.g. the MSSM, have many CPV sources ◮ However, TeV scale NP with O ( 1 ) CPV phases generally leads to EDMs many orders of magnitude above the current limits ⇒ the New Physics CP problem. • How to solve the New Physics CP problem? ◮ Decoupling some NP particles in the loop generating the EDMs (e.g. hierarchical sfermions, split SUSY, 2HDM limit...) ◮ Generating CPV phases radiatively φ f CP ∼ α w / 4 π ∼ 10 − 3 ◮ Generating CPV phases via small flavour mixing angles φ f CP ∼ δ fj δ fj with f = e , u , d : maybe the suppression of FCNC processes and EDMs have a common origin? Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 11 / 21
Not only µ → e γ ... • LFV operators @ dim-6 1 O dim − 6 + . . . . L ❡✛ = L ❙▼ + Λ 2 LFV O ❞✐♠ − ✻ ∋ µ R σ µν H e L F µν , (¯ µ L γ µ e L ) ` ¯ f L γ µ f L ` ¯ ¯ ´ , (¯ µ R e L ) ´ , f = e , u , d f R f L • the dipole-operator leads to ℓ → ℓ ′ γ while 4-fermion operators generate processes like ℓ i → ℓ j ¯ ℓ k ℓ k and µ → e conversion in Nuclei. • When the dipole-operator is dominant: « ❇❘ ( ℓ i → ℓ j γ ) log m 2 ❇❘ ( ℓ i → ℓ j ℓ k ¯ ℓ k ) α el „ ℓ i ≃ − 3 ν j ν i ) , ❇❘ ( ℓ i → ℓ j ¯ ν j ν i ) 3 π m 2 ❇❘ ( ℓ i → ℓ j ¯ ℓ k ❈❘ ( µ → e in N ) ≃ α ❡♠ × ❇❘ ( µ → e γ ) . • ❇❘ ( µ → e γ ) ∼ 5 × 10 − 13 implies ❇❘ ( µ → 3e ) ❇❘ ( µ → e γ ) ≈ ❈❘ ( µ → e in N ) ≈ 3 × 10 − 15 5 × 10 − 13 3 × 10 − 15 • µ + N → e + N on different N discriminates the operator at work [Okada et al. 2004] . • An angular analysis for µ → eee can test operator which is at work. Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 12 / 21
Pattern of LFV in NP models • Ratios like Br ( µ → e γ ) / Br ( τ → µγ ) probe the NP flavor structure • Ratios like Br ( µ → e γ ) / Br ( µ → eee ) probe the NP operator at work ratio LHT MSSM SM4 Br ( µ → eee ) ∼ 2 · 10 − 3 0.02. . . 1 0 . 06 . . . 2 . 2 Br ( µ → e γ ) Br ( τ → eee ) ∼ 1 · 10 − 2 0.04. . . 0.4 0 . 07 . . . 2 . 2 Br ( τ → e γ ) Br ( τ → µµµ ) ∼ 2 · 10 − 3 0.04. . . 0.4 0 . 06 . . . 2 . 2 Br ( τ → µγ ) Br ( τ → e µµ ) ∼ 2 · 10 − 3 0.04. . . 0.3 0 . 03 . . . 1 . 3 Br ( τ → e γ ) Br ( τ → µ ee ) ∼ 1 · 10 − 2 0.04. . . 0.3 0 . 04 . . . 1 . 4 Br ( τ → µγ ) Br ( τ → eee ) ∼ 5 1 . 5 . . . 2 . 3 0.8. . . 2 Br ( τ → e µµ ) Br ( τ → µµµ ) 0.7. . . 1.6 ∼ 0 . 2 1 . 4 . . . 1 . 7 Br ( τ → µ ee ) 10 − 3 . . . 10 2 10 − 12 . . . 26 ❘ ( µ Ti → e Ti ) ∼ 5 · 10 − 3 Br ( µ → e γ ) [Buras et al., ’07, ’10] Paride Paradisi (University of Padua) Connection between g − 2, EDMs, CLFV and LHC EPS 2015 13 / 21
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