Andr´ e de Gouvˆ ea Northwestern Phenomenological Perspective on (Charged-)LFV Processes Andr´ e de Gouvˆ ea Northwestern University NuFlavor 2009 June 8–10, 2009, Cosener’s House, UK [session: interplay between neutrino masses and other phenomenological signatures] June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Outline 1. Brief Introduction; 2. Old and ν Standard Model Expectations; 3. A Model Independent Approach; 4. Interplay with ν Masses, Leptogenesis and the LHC via Examples; 5. Conclusions. June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Ever since it was established that µ → eν ¯ ν , people have searched for µ → eγ , which naively could arise at one-loop: ν e µ γ The fact that µ → eγ did not happen, led one to postulate that the two neutrino states produced in muon decay were distinct, and that µ → eγ , and other similar processes, were forbidden due to symmetries. To this date, these so-called individual lepton-flavor numbers seem to be conserved in the case of charged lepton processes, in spite of many decades of (so far) fruitless searching. . . June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Searches for Lepton Number Violation ( µ and e ) UL Branching Ratio (Conversion Probability) -1 10 -3 10 -5 10 -7 10 -9 10 µ → e γ -11 µ - N → e - N 10 µ + e - → µ - e + -13 10 µ → e e e K L → π + µ e -15 10 K L → µ e K L → π 0 µ e -17 10 -19 10 1950 1960 1970 1980 1990 2000 2010 Year [hep-ph/0109217] June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern SM Expectations In the old SM, the rate for charged lepton flavor violating processes is trivial to predict. It vanishes because individual lepton flavor number is conserved: • N α (in) = N α (out), for α = e, µ, τ . ———————— However, the old SM is wrong: NEUTRINOS change flavor after propagating a finite distance. • ν µ → ν τ and ¯ ν µ → ¯ ν τ — atmospheric experiments [“indisputable”]; • ν e → ν µ,τ — solar experiments [“indisputable”]; • ¯ ν e → ¯ ν other — reactor neutrinos [“indisputable”]; • ν µ → ν other from accelerator experiments [“indisputable”]. Lepton Flavor Number NOT a good quantum number. June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Hence, in the “New Standard Model” ( ν SM, equal to the old Standard Model plus operators that lead to neutrino masses) µ → eγ is allowed (along with all other charged lepton flavor violating processes). These are Flavor Changing Neutral Current processes, observed in the quark sector ( b → sγ , K 0 ↔ ¯ K 0 , etc). Unfortunately, we do not know the ν SM expectation for charged lepton flavor violating processes → we don’t know the ν SM Lagrangian ! June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern One contribution known to be there: active neutrino loops (same as quark sector). In the case of charged leptons, the GIM suppression is very efficient . . . 2 � ∆ m 2 � 3 α < 10 − 54 � e.g.: Br ( µ → eγ ) = i =2 , 3 U ∗ µi U ei 1 i � � M 2 32 π � � W [ U αi are the elements of the leptonic mixing matrix, ∆ m 2 1 i ≡ m 2 i − m 2 1 , i = 2 , 3 are the neutrino mass-squared differences] June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern e.g.: SeeSaw Mechanism [minus “Theoretical Prejudice”] MAX B(CLFV) -9 τ → µγ 10 -10 10 τ → µµµ -11 10 µ → e conv in 48 Ti -12 10 µ → e γ -13 10 -14 10 µ → eee -15 10 -16 10 20 40 60 80 100 120 140 160 180 200 arXiv:0706.1732 [hep-ph] m 4 (GeV) June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Independent from neutrino masses, there are strong theoretical reasons to believe that the expected rate for flavor changing violating processes is much, much larger than naive ν SM predictions and that discovery is just around the corner. Due to the lack of SM “backgrounds,” searches for rare muon processes, including µ → eγ , µ → e + e − e and µ + N → e + N ( µ - e –conversion in nuclei) are considered ideal laboratories to probe effects of new physics at or even above the electroweak scale. Indeed, if there is new physics at the electroweak scale (as many theorists will have you believe) and if mixing in the lepton sector is large “everywhere” the question we need to address is quite different: Why haven’t we seen charged lepton flavor violation yet? June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Model Independent Approach As far as charged lepton flavor violating processes are concern, new physics effects can be parameterized via a handful of higher dimensional operators. For example, say that the following effective Lagrangian dominates CLFV phenomena: m µ κ µ R σ µν e L F µν + u L γ µ u L + ¯ d L γ µ d L � � L CLFV = ( κ + 1)Λ 2 ¯ (1 + κ )Λ 2 ¯ ¯ µ L γ µ e L First term: mediates µ → eγ and, at order α , µ → eee and µ + Z → e + Z Second term: mediates µ + Z → e + Z and, at one-loop, µ → eγ and µ → eee Λ is the “scale of new physics”. κ interpolates between transition dipole moment and four-fermion operators. Which term wins? → Model Dependent June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Λ (TeV) • µ → e -conv at 10 − 17 “guaranteed” deeper probe than µ → eγ at 10 − 14 . B( µ→ e conv in 48 Ti) > 10 -18 • We don’t think we can do µ → eγ better than 10 − 14 . µ → e –conv “only” way forward after MEG. 10 4 B( µ→ e conv in 48 Ti) > 10 -16 • If the LHC does not discover new states µ → e -conv among very few process that can B( µ→ e γ ) > 10 -14 access 10,000+ TeV new physics scale: Λ 2 ∼ g 2 θ eµ 1 tree-level new physics: κ ≫ 1, new . M 2 B( µ→ e γ ) > 10 -13 10 3 EXCLUDED -2 -1 2 10 10 1 10 10 κ June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Other Example: µ → ee + e − Λ (TeV) 4000 B( µ→ eee) > 10 -16 m µ µ R σ µν e L F µν + L CLFV = ( κ +1)Λ 2 ¯ 3000 κ B( µ→ e γ ) > 10 -13 eγ µ e + (1+ κ )Λ 2 ¯ µ L γ µ e L ¯ B( µ→ eee) > 10 -15 2000 • µ → eee -conv at 10 − 16 “guaranteed” deeper B( µ→ eee) > 10 -14 probe than µ → eγ at 10 − 14 . 1000 • µ → eee another way forward after MEG? 900 800 700 600 • If the LHC does not discover new states 500 µ → eee among very few process that can 400 access 1,000+ TeV new physics scale: EXCLUDED 300 Λ 2 ∼ g 2 θ eµ 1 tree-level new physics: κ ≫ 1, new . M 2 -2 -1 2 10 10 1 10 10 κ June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern What is This Good For? While specific models (discussed in several earlier talks) provide estimates for the rates for CLFV processes, the observation of one specific CLFV process cannot determine the underlying physics mechanism (this is always true when all you measure is the coefficient of an effective operator). Real strength lies in combinations of different measurements, including: • kinematical observables (e.g. angular distributions in µ → eee ); • other CLFV channels; • neutrino oscillations; • measurements of g − 2 and EDMs; • collider searches for new, heavy states; • etc. June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Vector 4-Fermion Interaction ( Z ) qγ α q ) ∝ (¯ µγ α e )(¯ Vector 4-Fermion Interaction ( γ ) µσ αβ eF αβ ) Dipole ( ∝ ¯ Scalar 4-Fermion Interaction ∝ (¯ µe )(¯ qq ) [Cirigliano, Kitano, Okada, Tuzon, 0904.0957] June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Example: Anomalous Magnetic Moment of the Muon, ( g − 2) / 2 ≡ a µ June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern Model Independent Comparison Between g − 2 and CLFV : The dipole effective operators that mediate µ → eγ and contribute to a µ are virtually the same: m µ m µ µσ µν µF µν µσ µν eF µν Λ 2 ¯ θ eµ Λ 2 ¯ × θ eµ measures how much flavor is violated. θ eµ = 1 in a flavor indifferent theory, θ eµ = 0 in a theory where individual lepton flavor number is exactly conserved. If θ eµ ∼ 1, µ → eγ is a much more stringent probe of Λ. On the other hand, if the current discrepancy in a µ is due to new physics, θ eµ ≪ 1 ( θ eµ < 10 − 4 ). This is hard to satisfy in, say, high energy SUSY breaking models. . . [Hisano, Tobe, hep-ph/0102315] Comparison restricted to dipole operator. If four-fermion operators are relevant, they will “only” enhance rate for CLFV with respect to expectations from g − 2. June 9, 2009 NuFlavor
Andr´ e de Gouvˆ ea Northwestern [Hisano, Tobe, hep-ph/0102315] June 9, 2009 NuFlavor
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