Testing Symmetries in Lepton Decays

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1 Testing Symmetries in Lepton Decays Simon Eidelman Budker Institute of Nuclear Physics, Novosibirsk, Russia 1. Lepton universality Outline 2. Lepton Flavor Violation (LFV) 3. Conclusions p.1/34

2 General I Some milestones of the Standard Model: There are three generations (families) of quarks and leptons, each has a charged lepton (e, µ, τ ) and its neutrino (ν e, ν µ, ν τ ) Each generation has its unique conserved flavor (family number), i.e., µ e ν µ ν e and there are no neutrinoless decays Coupling of W with leptons is family-independent: G e = G µ = G τ = G F (lepton universality) Discovery of neutrino oscillations reconsideraton of these concepts p.2/34

3 General II BaBar ( 520 fb 1 ) and Belle ( 1000 fb 1 ) collected together about τ + τ Two SuperB factories will bring a factor of 100 more, i.e. about τ decays will be available Super-τ-charm factory (10 35 cm 2 s 1 ) with Ldt = 10 ab 1 will yield τ + τ pairs!! The number of muons used in the muon decay experiments exceeds and will be increased in close future p.3/34

4 Lepton universality and M τ r = ( G τ eντ νe G µ eν µ νe ) 2 = ( M µ M τ ) 5 ( t µ t τ )B(τ eν τ ν e ) F cor(m µ,m e ) F cor (M τ,m e ) r t τ, fs B(τ eν τ ν e ), % M τ, MeV Comments ± ± PDG, 1992 ± ± ± σ ± ± PDG, 1996 ± ± ± ± σ ± ± PDG, 2004 ± ± ± ± σ p.4/34

5 Group Progress of m τ m τ, MeV BES, PDG, KEDR, ± 0.15 Belle, ± 0.13 ± 0.35 PDG, ± 0.17 BaBar, ± 0.12 ± 0.41 PDG, ± 0.16 KEDR, ± 0.15 r = ± (0.99σ) Leptonic universality is OK! p.5/34

6 Summary of M τ Measurements m τ , MeV KEDR BABAR 2008 BELLE 2007 KEDR 2007 OPAL 2000 CLEO 1997 BES 1996 ARGUS Red error bars - systematics, blue - total error p.6/34

7 Summary of τ τ Measurements ± 2.8 ± 4.0 CLEO ± 1.7 ± 1.2 OPAL ± 1.5 ± 1.1 ALEPH ± 2.0 ± 1.5 L ± 1.4 ± 1.0 DELPHI ± 1.0 PDG mean xxx.x ± 0.37 ± 0.33? Belle τ τ (fs) With τ τ syst τ τ stat the final result of Belle will be twice more precise than the current PDG mean. p.7/34

8 Lifetime Difference for τ + and τ D(cτ) = cτ + cτ = 0.16 ± 0.22µm D syst < D stat τ + τ /τ av < p.8/34

9 CPT Tests Quantity e µ τ m + m /m av < < τ + τ /τ av < < What can theory say about CPT tests? p.9/34

10 Charged Current Universality I G µ /G e B(τ µ)/b(τ e) ± B(π µ)/b(π e) ± B(K µ)/b(k e) ± B(K πµ)/b(k πe) ± B(W µ)/b(w e) ± A. Pich: NPB (Proc. Suppl.) , 300 (2008) p.10/34

11 Charged Current Universality II G τ /G e B(τ µ)τ µ /τ τ ± B(W τ)/b(w e) ± G τ /G µ B(τ e)τ µ /τ τ ± Γ(τ π)/γ(π µ) ± Γ(τ K)/Γ(K µ) ± B(W τ)/b(w µ) ± p.11/34

12 Lepton Universality and Branching Fractions I Three recent measurements at BaBar (467 fb 1 ): Ratio BaBar PDG-08 B(τ µ ν µ ν τ )/B(τ e ν e ν τ ) ± ± ± B(τ π ν τ )/B(τ e ν e ν τ ) ± ± ± B(τ K ν τ )/B(τ e ν e ν τ ) ± ± ± Mode e ν e ν τ µ ν µ ν τ π ν τ K ν τ N ev, Gµ G e «2 = B(τ µ ν µ ν τ ) B(τ e ν e ν τ ) f(m 2 e/m 2 τ) f(m 2 µ/m 2 τ), where f(x) = 1 8x + 8x 3 x 4 12x 2 log x, m ν = 0. G µ /G e = ± , consistent with ± (A. Pich, 2008). B. Aubert et al., Phys. Rev. Lett. 105, (2010) p.12/34

13 Lepton Universality and Branching Fractions II ( Gτ G µ ) 2 = B(τ π ν τ ) B(π µ ν µ ) 2m π m 2 µτ π δ τ π ν/π µ νm 3 ττ τ ( 1 m 2 µ /m 2 π 1 m 2 π/m 2 τ ) 2, ( Gτ G µ ) 2 = B(τ K ν τ ) B(K µ ν µ ) 2m k m 2 µτ K δ τ K ν/k µ νm 3 ττ τ ( 1 m 2 µ /m 2 K 1 m 2 K /m2 τ ) 2, where the radiative corrections are δ τ π ν/π µ ν = ± and δ τ K ν/k µ ν = ± G τ /G µ = ± ( ± ) with pions (kaons) compared to ± 0.005(0.979 ± 0.017). p.13/34

14 Measurement of R K at NA62 I R SM K = ( Me M µ ) 2 ( M 2 K M 2 e M 2 K M2 µ where δr QED = ( 3.79 ± 0.04)% is an e/m correction for IB and structure-dependent terms. ) 2 (1 + δr QED) = (2.477 ± 0.001) 10 5, NA62 has 4 times more K e2 decays: N Ke2 = 59813, N Kµ2 = R K = (2.487 ± ± 0.007) 10 5 The previous best result from KLOE dominates the world average: R K = (2.493 ± ± 0.019) 10 5 Still one order of magnitude less precise than the SM prediction C. Lazzeroni et al., Phys. Lett. B698, 105 (2011) p.14/34

15 Measurement of R K at NA62 II High-precision measurements of R K probe new physics: In two-higgs doublet models R K is sensitive to LFV effects appearing at the one-loop level via the H ± exchange: R LFV K R SM K [1 + MK M H «4 Mτ M e «2 31 R 2 tan 6 β], where 31 R is the mixing parameter between the superpartners of the right-handed leptons, can reach These effects can enhance R K by O(1%) not affecting other constraints, e.g., various LFV τ ex decays. A. Masiero, P. Paradisi, R. Petronzio, Phys. Rev. D74, (2008), JHEP 0811:042 (2008) R K is sensitive to the neutrino mixing parameters within the SM extension involving a fourth generation, CKM fitter, H. Lacker and A. Menzel, JHEP 1007:006 (2010) p.15/34

16 Measurement of τ µ + and G F Determination at MuLan I 1 = G2 F m5 µ (1 + q), τ µ 192π3 where q phase space, QED and hadronic corrections, q to finite m e : A. Pak and A. Czarnecki, Phys. Rev. Lett. 100, (2008) More than muon decays τ µ = ( ± 2.2) s ( 10 6 ) Precision is 15 times higher than in any previous experiment G F = ( ± 7) 10 5 GeV 2 ( ) D.M. Webber et al., Phys. Rev. Lett. 106, (2011) p.16/34

17 Measurement of τ µ + and G F Determination at MuLan II Balandin Giovanetti Bardin Chitwood Barczyk MuLan - R Lifetime (µs) MuLan - R07 Dominates the new world average and is 2.5σ below the current one p.17/34

18 Tests of Standard Model in Muon Decay at TWIST I When only the e + energy and direction are measured, the muon decay spectrum has 4 parameters ρ, δ, P µ ξ, η In SM ρ = δ = 3/4, ξ = 1, η = 0 Previously Michel parameters were known to ( ) 10 3 Muon rate is (2 5) 10 3 /s, events recorded Precision improved by an order of magnitude R. Bayes et al., Phys. Rev. Lett. 106, (2011) p.18/34

19 Tests of Standard Model in Muon Decay at TWIST II Derenzo 69 TWIST 05 TWIST 08 This work Balke 88 TWIST 05 TWIST 08 This work Beltrami 87 TWIST 06 This work ρ δ π P µξ p.19/34

20 Tests of Standard Model in Muon Decay at TWIST III Constraints on the left-right symmetric models with a right-handed W P. Herczeg, Phys. Rev. D 34, 3449 )ζ L /g R Mixing angle (g Beltrami 87 Jodidio 88 This work (g /g )m (GeV/c ) L R 2 allowed The TWIST result for ρ provides the best limit on the mixing angle between the light and heavy mass eigenstates W 1 and W 2 : (g R /g L )ζ < at 90% CL (< 0.066) and on the mass of W 2 : (g L /g R )m 2 > 578 GeV/c 2 (> 400 GeV/c 2 ) p.20/34

21 Lepton Anomalous Magnetic Moments Lepton Experiment a l /a l e (28) µ (63) τ (0.017) 15 Theory expects a τ = (5) 10 8 SE, M. Passera, Mod. Phys. Lett. A 22, 159 (2007) p.21/34

22 New comparison of a exp µ and a th µ after BaBar HMNT 07 (e + e ) 276 ± 51 JN 09 (e + e ) 290 ± 65 Davier et al. 09 (τ) 148 ± 52 Davier et al. 09 (e + e ) 303 ± 51 This work (e + e w/ BABAR) 246 ± 49 BNL-E821 (WA) 0 ± 63 BNL-E a µ a µ exp Reestimation of a had µ after BaBar s ππ and increase of a exp µ by (CODATA changed µ µ /µ p ) 3.2σ, new I/B corrections make τ move to e + e M. Davier et al., EPJ C66, 127 (2010); EPJ C66, 1 (2010) p.22/34

23 CVC. e + e X 0 and τ ν τ X I 0.3 ( F π 2 [ee] F π 2 [τ]) / F π 2 [τ] Allowed I G J P = : X = π π 0, (4π), ωπ -0.2, ηπ π 0, K K 0, (6π), τ Average preliminary correcting for m(ρ +/0 ) and Γ(ρ +/0 ) KLOE CMD-2 CMD OLYA DM s (GeV 2 ) Large SU(2) breaking corrections from theory, V.Cirigliano et al., 2002 M(Γ) ρ 0 M(Γ) ρ ± helps, M.Davier, 2003; S.Ghozzi, F.Jegerlehner, 2004 Consistent ρ, ω, φ mixing, M. Benayoun et al., EPJ C 65, 211 (2010) p.23/34

24 CVC. e + e X 0 and τ ν τ X II F. Jegerlehner and R. Szafron, arxiv: p.24/34

25 CVC. e + e X 0 and τ ν τ X III FJ,RS claim that proper account for ρ γ mixing results in reconciliation of the e + e and τ spectra in the 2π mode After all IB corrections are considered: Quantity e + e τ B(τ π π 0 ν τ ), % ± 0.17 ± ± 0.06 ± 0.08 a had,lo µ, ± ± 4.65 p.25/34

26 The LBL Workshop in Seattle I Contribution a µ, Experiment ± 5.4 ± 3.3 (6.3) QED ± Electroweak 15.4 ± 0.1 had ± 0.2 Higgs Hadronic ± 4.9 Hadronic, LO ± 4.2 Hadronic, HO ± 0.09 Hadronic, LBL 10.5 ± 2.6 Theory ± 4.9 Exp. Theory 28.7 ± 8.0 (3.6σ) M. Davier et al., Eur. Phys. J. C71:1515 (2011) The precision of the LBL term will soon limit the test! p.26/34

27 The LBL Workshop in Seattle II The Institute for Nuclear Theory at the UW, Seattle held a meeting on the LBL term (35 people present) from to 4.03: There are 5-6 different approaches (even more groups), hot disputes but very close numbers Obvious progress of lattice calculations There is real interest to all possible experiments: γ ( ) γ ( ) π 0, η, η, radiative and Dalitz decays of vector and pseudoscalar mesons, π 0 e + e and KLOE has very good opportunities everywhere! An arxiv preprint expected in April, a detailed summary paper to appear in 6 months p.27/34

28 Searches for New Physics in the Lepton Sector Searches for µ e LFV: µ e conversion, µ e γ (B < ), µ e e + e (B < ) MEG running, COMET and Mu2e prepared Neutrino oscillations, in particular ν µ ν τ oscillations with a big mixing angle (S/K) searches for large µ τ LFV, e.g., τ µ γ In schemes with inverted hierarchy τ e is also possible, e.g., τ e γ Many models consider extensions of the Standard Model with enhanced LFV. Particularly popular are SUSY models, e.g. MSSM extension of SM, also discussed SUGRA, GUT, Higgs, little Higgs Predicted B(τ µ γ) reach different modes studied. The most stringent limit is B(τ µ ρ 0 ) < The sensitivity is limited by background suppression/statistics. p.28/34

29 Search for µ e γ 90% CL upper limits on the branching fraction B Group Date B, N µ, SIN NaI (LAMPF) NaI (TRIUMF) Cr. Box (LAMPF) MEGA (LAMPF) p.29/34

30 Summary on LFV with Muons The first result of MEG is B(µ + e + γ) < at 90% CL, J. Adam et al., Nucl. Phys. B 834, 1 (2010) Mode B or R today B or R expected µ e γ (MEGA) (10 14 ) (MEG) µ e e + e (SINDRUM)? (MEG) µ e 2γ (Cr.BOX)? (MEG) µ N e N (SINDRUM II) (Mu2e, COMET; Al) (PRISM; Ti) p.30/34

31 LFV in τ decays (SM and SUSY) w τ µ ν τ 2 mν ν µ γ τ µ τ µ χ 0 2 m τ µ γ In SM LFV is suppressed by m 2 ij /m2 W The effective m 2 in SUSY loops can be quite large, there might also be enhancement due to large tan β E. Arganda, M. Herrero, J. Portoles, JHEP 0806:079 (2008) consider various LFV decays in constrained MSSM-seesaw scenarios: B(τ µ η) = δ 32 2 ( 100 m A 0(GeV ) )4 ( tanβ 60 )6 p.31/34

32 Progress of LFV Studies τ µ γ Group Date L, pb 1 N ττ, 10 6 B 90 UL MARK II ARGUS DELPHI CLEO Belle Belle BaBar BaBar & Belle p.32/34

33 Prospects for LFV Studies With τ + τ and ǫ 3%: B < for N ev = 0 Background suppression needed (PID, higher ǫ) τ lγ, µη(γγ), lρ : BG 0, B 1/ N Achievable BR τ lll, µη(π + π π 0 ), Λπ : BG = 0, B 1/N CLEO msugra+seesaw SUSY+SO(10) SUSY+Higgs SM+seesaw B factories (Belle, BaBar) 2006 τ µγ τ µη τ µµµ Super B factory Luminosity (ab -1 ) p.33/34

34 Conclusions Huge data samples of decaying µ (10 14 ) and τ (10 9 ) available, 2 orders of magnitude more expected Advantages in statistics and searches. Systematic effects? Lepton universality holds, more precise τ τ and B e needed Problems with CVC in the 2π decay fixed? a µ Sensitivity of 10 8 achieved in LFV τ decays New generation of the µ decay experiments coming B factories are also unique τ factories: high potential for New Physics and precision studies in SM, more expected from SuperB and Super-c τ p.34/34