Intro SMEFT From EW to EM Conclusion SMEFT and charged lepton flavour violation Giovanni Marco Pruna Paul Scherrer Institut Villigen, CH NUFACT2017, Uppsala, 29 September 2017
Intro SMEFT From EW to EM Conclusion Standard Model and open issues The SM does not take into account the following observations: • neutrino oscillations; • dark matter observation; • baryogenesis; • gravity. It does not provide a convincing explanation for: • hierarchy problem; • flavour puzzle; • QCD theta term; • gauge couplings unification.
Intro SMEFT From EW to EM Conclusion Lepton Flavour Violation: a conceptual challenge The Dim-4 SM provides an accidental flavour symmetry: • it holds in QCD and EM interactions; • in the quark sector, it’s broken by EW interactions. The lepton sector strictly conserves flavour and CP . At the same time, we have remarkable phenomenological evidences of FV in the neutrino sector, but. . . . . . No evidence of the following phenomenological realisations: • l ± h → γ + l ± where h, i = e, µ, τ , i • l ± h → l ± i l ± j l ∓ h, i, j, k = e, µ, τ , where k • Z → l ± h l ∓ where h, i = e, µ, τ , i • H → l ± h l ∓ where h, i = e, µ, τ . i
Intro SMEFT From EW to EM Conclusion Lepton flavour and CP violation are new physics Leptons come in three generations and mix: CPV is expected. Neutral sector: neutrino mass generation mechanism ν oscillation is a BSM signal, but what is the underlying picture? Charged sector: lepton flavour and CP puzzle cLFV & CPV are severely constrained, why BSM is so elusive? The handhold: leptonic electric dipole moment “The KM phase in the quark sector can induce a lepton EDM via a diagram with a closed quark loop, but a non-vanishing result appears first at the four-loop level and therefore is even more suppressed, below the level of d CKM ≤ 10 − 38 e cm , e and so small that the EDMs of paramagnetic atoms and molecules would be induced more efficiently by e.g. Schiff moments and other CP-odd nuclear momenta. [. . . ] The electron EDM is not the best way to probe CP violation in the lepton sector. M. Pospelov and A. Ritz, Annals Phys. 318 (2005) 119
Intro SMEFT From EW to EM Conclusion A selection of limits on leptonic observables Lepton EDMs: • d e < 0 . 87 × 10 − 28 e cm at the 90% C.L. ACME Collaboration, Science 343 (2014) 269; • d µ < ( − 0 . 1 ± 0 . 9) × 10 − 19 e cm at the 90% C.L. Muon ( g − 2) Collaboration, Phys. Rev. D 80 (2009) 052008; • − 0 . 22 × 10 − 16 e cm < d τ < 0 . 45 × 10 − 16 e cm at the 95% C.L. Belle Collaboration, Phys. Lett. B 551 (2003) 16. cLFV in the muon sector: • BR( µ → 3 e ) < 1 . 0 × 10 − 12 at the 90% C.L. SINDRUM collaboration, Nucl. Phys. B 299 (1988) 1; � Au < 7 . 0 × 10 − 13 at the 90% C.L. • σ ( µ − → e − ) /σ ( capt. ) � SINDRUM II collaboration, Eur. Phys. J. C 47 (2006) 337; • BR( µ → γ + e ) < 4 . 2 × 10 − 13 at the 90% C.L. MEG collaboration, Eur. Phys. J. C 76 (2016) 434;
Intro SMEFT From EW to EM Conclusion Recent developments One can contribute in two ways: 1 performing precise calculations for backgrounds; 2 interpreting properly the current absence of signals. 1) Typical low-energy cLFV background computations: • radiative decays, l 1 → l 2 + γ + 2 ν ; • rare decays, l 1 → 3 l 2 + 2 ν , l 1 → 2 l 2 + l 3 + 2 ν . Previous talk from Yannick Ulrich 2) Typical interpretive approaches: • bottom-up, effective field theoretical formulations; • top-down, UV-complete extensions of the SM.
Intro SMEFT From EW to EM Conclusion Extending the interactions of the SM Assumptions: SM is merely an effective theory, valid up to some scale Λ . It can be extended to a field theory that satisfies the following requirements: • its gauge group should contain SU (3) C × SU (2) L × U (1) Y ; • all the SM degrees of freedom must be incorporated; • at low energies (i.e. when Λ → ∞ ), it should reduce to SM. Assuming that such reduction proceeds via decoupling of New Physics (NP), the Appelquist-Carazzone theorem allows us to write such theory in the form: � 1 � � � L = L SM + 1 + 1 C (5) k Q (5) C (6) k Q (6) + O . k k Λ 2 Λ 3 Λ k k
Intro SMEFT From EW to EM Conclusion Dimension-five operator Only one dimension 5 operator is allowed by gauge symmetry: p ) T Cl n ϕ † l p ) T C ( � Q νν = ε jk ε mn ϕ j ϕ m ( l k ϕ † l r ) . r ≡ ( � After the EW symmetry breaking, it can generate neutrino masses and mixing (no other operator can do the job). Its contribution to LFV has been studied since the late 70s: • in the context of higher dimensional effective realisations; S. T. Petcov, Sov. J. Nucl. Phys. 25 (1977) 340 [Yad. Fiz. 25 (1977) 641] • in connection with the “see-saw” mechanism. P . Minkowski, Phys. Lett. B 67 , 421 (1977) “[. . . ] This effect is beyond the reach of presently planned experiments.” J. P . Archambault, A. Czarnecki and M. Pospelov, Phys. Rev. D 70 (2004) 073006
Intro SMEFT From EW to EM Conclusion Dimension-six operators 2-leptons 4-fermions (¯ l p σ µν e r ) τ I ϕW I Q (1) (¯ Q eW = µν ; q s γ µ q t ) = l p γ µ l r )(¯ lq (¯ l p σ µν e r ) ϕB µν . Q (3) (¯ l p γ µ τ I l r )(¯ q s γ µ τ I q t ) Q eB = = lq u s γ µ u t ) Q eu = (¯ e p γ µ e r )(¯ ↔ Q (1) D µ ϕ )(¯ ( ϕ † i l p γ µ l r ) = ϕl e p γ µ e r )( ¯ d s γ µ d t ) Q ed = (¯ ↔ Q (3) µ ϕ )(¯ l p τ I γ µ l r ) ( ϕ † i D I (¯ u s γ µ u t ) = Q lu = l p γ µ l r )(¯ ϕl (¯ l p γ µ l r )( ¯ d s γ µ d t ) ↔ Q ld = ( ϕ † i e p γ µ e r ) Q ϕe = D µ ϕ )(¯ e s γ µ e t ) Q qe = (¯ q p γ µ q r )(¯ ( ϕ † ϕ )(¯ Q eϕ = l p e r ϕ ) (¯ l j p e r )( ¯ d s q j Q ledq = t ) 4-leptons Q (1) (¯ l j q k = p e r ) ε jk (¯ s u t ) lequ (¯ l p γ µ l r )(¯ l s γ µ l t ) Q ll = e s γ µ e t ) Q (3) (¯ l j q k s σ µν u t ) Q ee = (¯ e p γ µ e r )(¯ = p σ µν e r ) ε jk (¯ lequ (¯ e s γ µ e t ) Q le = l p γ µ l r )(¯
Intro SMEFT From EW to EM Conclusion Leptonic tensorial current at the tree level One dimension-six operator can produce tensorial current: B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, JHEP 1010 (2010) 085 Working in the physical basis, we consider: C eB → C eγ c W − C eZ s W , C eW → − C eγ s W − C eZ c W , where s W = sin( θ W ) and c W = cos( θ W ) are the sine and cosine of the weak mixing angle. Λ 2 Q eγ + h.c. = C pr L eγ ≡ C eγ eγ Λ 2 (¯ l p σ µν e r ) ϕF µν + h.c.
Intro SMEFT From EW to EM Conclusion Lepton dipole moments Dimension-six operators contribute to the Wilson coefficients C TL and C TR of the dipole interaction: Λ 2 iσ µν � � V µ = 1 C TL ( p 2 γ ) ω L + C TR ( p 2 γ ) ω R ( p γ ) ν . Anomalous magnetic and electric-dipole moments: a l ∝ ℜ ( C TR + C TL ) | p 2 CPC γ → 0 ∝ ℑ ( C TR − C TL ) | p 2 CPV d l γ → 0 If flavour is not diagonal, then the momenta are “transitional”. In all generalities, UV-complete theories produce both CPV and FV effective dipole contributions.
Intro SMEFT From EW to EM Conclusion Low-energy LFV observables Neutrinoless radiative decay �� 2 � � � � Br ( µ → eγ ) = α e m 5 2 � � � � µ � C D � C D � + � . L R Λ 4 Γ µ Neutrinoless three-body decay �� 2 � � � m µ � � � � � α 2 e m 5 2 � � � � µ � C D � C D Br( µ → 3 e ) = + 8 log − 11 � � L R 12 π Λ 4 Γ µ m e � � � � � � � m 5 2 2 2 � � � � � � µ � C S LL � C V LL � C V LR + + 16 + 8 � � � ee ee ee 3(16 π ) 3 Λ 4 Γ µ 2 � � � � � � � 2 2 � � � � � � � C S RR � C V RR � C V RL + + 16 + 8 . � � � ee ee ee Coherent conversion in nuclei � � �� µ → e = m 5 2 � � µ ( p ) S ( p ) ( p ) V ( p ) Γ N � e C D G F m µ m p ˜ C SL + ˜ C V R L D N + 4 + p → n + L ↔ R. � N N 4Λ 4
Intro SMEFT From EW to EM Conclusion High-energy LFV observables Flavour-violating Z decays can be parametrised at the tree level by means of the following four operators: �� 2 ) = m 3 Z v 2 � � � � 2 + � 2 Γ( Z → l ± 1 l ∓ � C 12 � C 21 eZ eZ 12 π Λ 4 2 � � � � � � � � 2 + 2 � � � � � C 12 � C 12 � C 12 + + � � , ϕe ϕl (1) ϕl (3) and all of their contributions occur at the same order. We have summed over the two possible final states, l + 1 l − 2 and l − 1 l + 2 . For the Higgs boson decay H → l ± 1 l ∓ 2 , one has �� � 2 � 2 ) = m H v 4 � � � � 2 + � C 12 � C 21 Γ( H → l ± 1 l ∓ , eϕ eϕ 16 π Λ 4 where only one operator contributes at tree level. Again, we have summed over the two possible decays l + 1 l − 2 and l − 1 l + 2 .
Intro SMEFT From EW to EM Conclusion Dimension-six operators: lepton current at one loop From a point-like interaction. . . . . . to quantum fluctuations!
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