Rare allowed pion and muon decays

Rare allowed pion and muon decays Dinko Počanić Institute of Nuclear and Particle Physics, University of Virginia 11 August 2014 Gordon Research Conference Photonuclear reactions: From quarks to nuclei Holderness School, NH, 10 15 Aug 2014

D. Počanić (UVa) Rare pi & mu decays: Outline 11 Aug 14 2/ 29 Outline Introduction and overview of π, µ decays The π + e + ν e (π e2 ), electronic decay The π + e + ν e γ (π e2γ ), radiative decay The π + π 0 e + ν (π e3 ), pion beta decay Radiative muon decay Summary

D. Počanić (UVa) Rare pi & mu decays: Outline 11 Aug 14 2/ 29 Outline Introduction and overview of π, µ decays The π + e + ν e (π e2 ), electronic decay The π + e + ν e γ (π e2γ ), radiative decay The π + π 0 e + ν (π e3 ), pion beta decay (not enough time) Radiative muon decay Summary

Discovery of the pion: Cecil Powell s emulsion tracks 1947 D. Počanić (UVa) Rare pi & mu decays: Introduction and overview 11 Aug 14 3/ 29

Discovery of the pion: Cecil Powell s emulsion tracks 1947 1 mm D. Počanić (UVa) Rare pi & mu decays: Introduction and overview 11 Aug 14 3/ 29 µ e π

D. Počanić (UVa) Rare pi & mu decays: Introduction and overview 11 Aug 14 4/ 29 Pions, muons, symmetries and conservation laws Why isn t π e the dominant decay mode? Deep link to V A nature of the weak interaction PV; Pion triplet (π +, π 0, π ), are the Goldstone bosons in the spontaneous breaking of Chiral Symmetry; Explicit breaking of χs: m 2 π m q (Gell-Mann Oakes Renner rel.); Conserved Vector Current: SU(2) V ; Why is the beta energy spectrum in µ e decay continuous? and many other questions... Lepton Flavor Conservation,...

D. Počanić (UVa) Rare pi & mu decays: Introduction and overview 11 Aug 14 5/ 29 Known and measured pion and muon decays Decay BR π + µ + ν 0.9998770 (4) (π µ2 ) µ + νγ 2.00 (25) 10 4 (π µ2γ ) e + ν 1.230 (4) 10 4 (π e2 ) e + νγ 7.39(5) 10 7 (π e2γ ) π 0 e + ν 1.036 (6) 10 8 (π e3, π β ) e + νe + e 3.2 (5) 10 9 (π e2ee ) π 0 γγ 0.98798 (32) e + e γ 1.198 (32) 10 2 (Dalitz) e + e e + e 3.14 (30) 10 5 e + e 6.2 (5) 10 8 µ + e + ν ν 1.0 (Michel) e + ν νγ 0.014 (4) (RMD) e + ν νe + e 3.4 (4) 10 5

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 6/ 29 The electronic (π e2 ) decay: π + e + ν BR 10 4

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 7/ 29 π e2 decay: SM calculations, lepton universality Early evidence for V A nature of weak interaction. R π e/µ Γ(π e ν(γ)) = Γ(π µ ν(γ)) = g e 2 me 2 (1 me/m 2 µ) 2 2 ( ) 1 + δre/µ gµ 2 mµ 2 (1 mµ/m 2 π) 2 2 Modern SM calculations: Re/µ π Γ(π e ν(γ)) = = Γ(π µ ν(γ)) CALC 1.2352 (5) 10 4 Marciano and Sirlin, [PRL 71 (1993) 3629] 1.2354 (2) 10 4 Finkemeier, [PL B 387 (1996) 391] 1.2352 (1) 10 4 Cirigliano and Rosell, [PRL 99 (2007) 231801]

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 7/ 29 π e2 decay: SM calculations, lepton universality Early evidence for V A nature of weak interaction. 2.5 10 5 R π e/µ = Γ(π e ν(γ)) Γ(π µ ν(γ)) = g 2 e g 2 µ me 2 mµ 2 (1 me/m 2 µ) 2 2 ( ) 1 + δre/µ (1 mµ/m 2 π) 2 2 Modern SM calculations: Re/µ π Γ(π e ν(γ)) = = Γ(π µ ν(γ)) CALC 1.2352 (5) 10 4 Marciano and Sirlin, [PRL 71 (1993) 3629] 1.2354 (2) 10 4 Finkemeier, [PL B 387 (1996) 391] 1.2352 (1) 10 4 Cirigliano and Rosell, [PRL 99 (2007) 231801] Strong SM helicity suppression amplifies sensitivity to PS terms ( door for New Physics) by factor 2m π /m e (m u + m d ) 8000.

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 7/ 29 π e2 decay: SM calculations, lepton universality Early evidence for V A nature of weak interaction. 2.5 10 5 R π e/µ = Γ(π e ν(γ)) Γ(π µ ν(γ)) = g 2 e g 2 µ me 2 mµ 2 (1 me/m 2 µ) 2 2 ( ) 1 + δre/µ (1 mµ/m 2 π) 2 2 Modern SM calculations: Re/µ π Γ(π e ν(γ)) = = Γ(π µ ν(γ)) CALC 1.2352 (5) 10 4 Marciano and Sirlin, [PRL 71 (1993) 3629] 1.2354 (2) 10 4 Finkemeier, [PL B 387 (1996) 391] 1.2352 (1) 10 4 Cirigliano and Rosell, [PRL 99 (2007) 231801] Strong SM helicity suppression amplifies sensitivity to PS terms ( door for New Physics) by factor 2m π /m e (m u + m d ) 8000. tests lepton universality: in SM e, µ, τ differ by Higgs couplings only; there could also be new S or PS bosons with non-universal couplings (New Physics). R π e/µ

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 8/ 29 π e2 decay: experiments Experimental world average is 40 less accurate than SM calculations: Γ(π e ν(γ)) = 1.230(4) 10 4 [ ; 1.2352(1) 10 4 ] Γ(π µ ν(γ)) SM calc EXP

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 8/ 29 π e2 decay: experiments Experimental world average is 40 less accurate than SM calculations: Γ(π e ν(γ)) = 1.230(4) 10 4 [ ; 1.2352(1) 10 4 ] Γ(π µ ν(γ)) SM calc EXP Most recent and relevant experiments for world average: TRIUMF TINA (NaI det) Bern PSI (BGO array) Britton et al, PRL 68 (1992) 3000 Czapek et al, 1993 PRL 70 (1993) 17

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 8/ 29 π e2 decay: experiments Experimental world average is 40 less accurate than SM calculations: Γ(π e ν(γ)) = 1.230(4) 10 4 [ ; 1.2352(1) 10 4 ] Γ(π µ ν(γ)) SM calc EXP Most recent and relevant experiments for world average: TRIUMF TINA (NaI det) Bern PSI (BGO array) Britton et al, PRL 68 (1992) 3000 Czapek et al, 1993 PRL 70 (1993) 17 Why should we improve the current 0.4% result?

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 9/ 29 Reach of π e2 decay beyond the SM (New Physics) L NP = [ ± π + 2Λ 2 V ūγ α d ± [ ± π 2Λ 2 ūd ± S π 2Λ 2 A π 2Λ 2 P ] ūγ α γ 5 d ēγ α (1 γ 5 )ν ] ūγ 5 d ē(1 γ 5 )ν, (Λ i... scale of NP)

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 9/ 29 Reach of π e2 decay beyond the SM (New Physics) L NP = [ ± π + 2Λ 2 V ūγ α d ± [ ± π 2Λ 2 ūd ± S π 2Λ 2 A π 2Λ 2 P ] ūγ α γ 5 d ēγ α (1 γ 5 )ν ] ūγ 5 d ē(1 γ 5 )ν, (Λ i... scale of NP) CKM unitarity and superallowed Fermi nuclear decays currently limit: Λ V 20 TeV, and Λ S 10 TeV.

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 9/ 29 Reach of π e2 decay beyond the SM (New Physics) L NP = [ ± π + 2Λ 2 V ūγ α d ± [ ± π 2Λ 2 ūd ± S π 2Λ 2 A π 2Λ 2 P ] ūγ α γ 5 d ēγ α (1 γ 5 )ν ] ūγ 5 d ē(1 γ 5 )ν, (Λ i... scale of NP) CKM unitarity and superallowed Fermi nuclear decays currently limit: Λ V 20 TeV, and Λ S 10 TeV. At R π e/µ /Rπ e/µ = 10 3, π e2 decay is directly sensitive to: Λ P 1000 TeV and Λ A 20 TeV, and indirectly, through loop effects to Λ S 60 TeV.

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 9/ 29 Reach of π e2 decay beyond the SM (New Physics) L NP = [ ± π + 2Λ 2 V ūγ α d ± [ ± π 2Λ 2 ūd ± S π 2Λ 2 A π 2Λ 2 P ] ūγ α γ 5 d ēγ α (1 γ 5 )ν ] ūγ 5 d ē(1 γ 5 )ν, (Λ i... scale of NP) CKM unitarity and superallowed Fermi nuclear decays currently limit: Λ V 20 TeV, and Λ S 10 TeV. At R π e/µ /Rπ e/µ = 10 3, π e2 decay is directly sensitive to: Λ P 1000 TeV and Λ A 20 TeV, and indirectly, through loop effects to Λ S 60 TeV. In general multi-higgs models with charged-higgs couplings λ eν λ µν λ τν, at 0.1 % precision, R π eµ probes m H ± 400 GeV.

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 10/ 29 MSSM calculations (R parity cons.) [Ramsey-Musolf et al., PR D76 (2007) 095017] 0.005 0.005 CURRENT UL (90% c.l.) CURRENT UL (90% c.l.) minimal selectron, smuon masses: Re Μ SUSY R e Μ 0.002 0.001 0.0005 0.0002 PEN GOAL lowest mass chargino: Re µ SUSY R e µ 0.002 0.001 0.0005 0.0002 PEN GOAL 0.005 100 150 200 300 500 700 1000 Min mel,mµ L GeV CURRENT UL (90% c.l.) 100 150 200 300 500 700 1000 m GeV mχ1 slepton mass degeneracy: Re µ SUSY R e µ 0.002 0.001 0.0005 0.0002 PEN GOAL Higgsino mass param s. µ, mũl : PEN GOAL 0.1 1 10 mel mµ L (R parity violating scenario constraints also discussed.)

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 11/ 29 Lepton universality (and neutrinos) R e/µ = R τ/π = Γ(π e ν(γ)) Γ(π µ ν(γ)) = g e 2 me 2 (1 me/m 2 µ) 2 2 ( ) 1 + δre/µ gµ 2 mµ 2 (1 mµ/m 2 π) 2 2 Γ(τ e ν(γ)) Γ(π µ ν(γ)) = g τ 2 mτ 3 (1 mπ/m 2 τ 2 ) 2 ( ) 1 + δrτ/π gµ 2 2mµm 2 π (1 mµ/m 2 π) 2 2 lead to these limits: ( ) ge = 1.0021 ± 0.0016 and g µ π For comparison ( ) ge = 0.999 ± 0.011 and g µ W ( gτ g µ ( gτ g e ) πτ ) W = 1.0030 ± 0.0034. = 1.029 ± 0.014. [Presently allowed level of LUV could account for NuTeV anomaly. ]

The PEN/PIBETA apparatus stopped π + beam active target counter 240-detector, spherical pure CsI calorimeter central tracking beam tracking digitized waveforms stable temp./humidity BC π + beam VACUUM pure CsI mtpc AD AT PMT PEN detector 2009-10 PH MWPC1 MWPC2 ~3 m flightpath 10 cm D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 12/ 29

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 12/ 29 The PEN/PIBETA apparatus stopped π + beam active target counter 240-detector, spherical pure CsI calorimeter central tracking beam tracking digitized waveforms stable temp./humidity PEN Goal: R π pure CsI e/µ /Rπ e/µ 0.05% mtpc VACUUM AD AT BC PEN runs: 2008 2010 ~3 m flightpath π + beam > 22M π e, and > 200M π µ e recorded. PMT PEN detector 2009-10 PH MWPC1 MWPC2 10 cm

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 13/ 29 Highlights and challenges of PEN analysis (under way) Active target waveforms: separating the decay particle pulses! Early pion decay (extremely common) Early muon decay (still annoying) 30000 25000 20000 TGT waveform TGT waveform h_tgtwave1 filtered Entries 18791 TGT waveform, Mean pion 588.7 and e+ prediction RMS 28.1 TGT waveform, found muon 25000 20000 TGT waveform TGT waveform filtered h_tgtwave1 Entries 5934 TGT waveform, pion and e+ prediction Mean 604.5 TGT RMS waveform, found 26.58 muon 15000 15000 10000 10000 5000 5000 0 0 550 600 650 700 target waveform bin 550 600 650 700 target waveform bin π and e + pulse time and amplitude predicted from other detector systems (mtpc, MWPCs, PH)! Waveform system functions evaluated based on prompt hadronic events. Hypotheses with/without a µ pulse evaluated.

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 14/ 29 PEN separating π e and π µ e events Entries 2.188072e+07 positron target energy [MeV] 4 3 2 1 10 4 3 10 10 2 10 5 10 4 10 3 10 2 10 E e + Entries 50 MeV, τ: 0 50-200 ns 0 1 10 E e + 60 MeV, τ 20 ns 5 10 15 20 25 positron target pathlength [mm] (MeV) E e + 80 70-3 -2.5-2 -1.5-1 -0.5 0 0.5 1 2 0.3 (χ ) 60 50 0.2 40 30 20 0.1 10 0 0 50 100 150 200 Time between pion and positron (ns) 0.0

Entries 776 0 Entries 600 D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 15/ 29 PEN: agreement with predictions (2010 data analysis) 5 10 4 10 events per 0.5 ns 3 10 2 10 10 τ = 26.03 ns, 0.5 ns smeared Entries Entries 0 0 0 π eν π eν distribution folded with µ decaytime π µ e, probability of extra µ below 2.5% 0 50 100 150 200 1.1 1.05 1 0.95 observed/predicted π eν events 1.04 1.02 1 0.98 observed/predicted π µ e events 50 100 150 200 decay time [ns]

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 16/ 29 Key PEN systematic: low E tail response 3 10 background background subtracted Entries subtracted 0 error 2.2-5.0 error 0.0-0.9 pie simulation 2008 π µ e (DIF bgd) π e 400 350 300 background subtracted background Entries 0subtracted error 2.2-5.0 error 0.0-0.9 pie simulation 2008 250 2 10 200 150 10 100 50 1 0 10 20 30 40 50 60 70 80 90 total energy [MeV] 10 20 30 40 50 60 70 80 90 total energy [MeV]

D. Počanić (UVa) Rare pi & mu decays: The π e2 decay 11 Aug 14 17/ 29 PiENu experiment at TRIUMF Csl ring x Goal: B/B 0.001 y π + B1 S1 S1 S3 WC3 WC1 V1 V1 WC2 V3 V2 T2 V2 V3 Csl ring Nal (TI) Excellent E resolution Very precise tracking with Si-strip detectors and MWPCs Data taking completed in 2012 O(10 7 ) π e2 events collected analysis under way B2 Tg T1

D. Počanić (UVa) Rare pi & mu decays: The π e2γ decay 11 Aug 14 18/ 29 Radiative electronic (π e2γ ) decay: π + e + ν e γ BR non-ib 10 7

D. Počanić (UVa) Rare pi & mu decays: The π e2γ decay 11 Aug 14 19/ 29 Physics of π + e + νγ (RPD): QED IB terms: SM and SD V, A terms: A tensor interaction, too? Exchange of S=0 leptoquarks P Herczeg, PRD 49 (1994) 247

D. Počanić (UVa) Rare pi & mu decays: The π e2γ decay 11 Aug 14 20/ 29 The π eνγ amplitude and FF s The IB amplitude (QED uninteresting!): M IB = i eg F V ud f π m e ɛ µ ē 2 ( kµ kq p µ pq + σ µνq ν 2kq The structure-dependent amplitude (interesting!): ) (1 γ 5 ) ν. M SD = eg F V ud m π 2 ɛ ν ēγ µ (1 γ 5 )ν [F V ɛ µνστ p σ q τ + if A (g µν pq p ν q µ )]. The SM branching ratio (x = 2E γ /m π ; y = 2E e /m π ), dγ πe2γ dx dy = α { ( ) m 2 2 2π Γ πe2 IB (x, y) + π 2f π m e [ (F V + F A ) 2 SD + (x, y) + (F V F A ) 2 SD (x, y) ] + m π f π [ (FV + F A ) S + int (x, y) + (F V F A ) S int (x, y)] }.

D. Počanić (UVa) Rare pi & mu decays: The π e2γ decay 11 Aug 14 21/ 29 PIBETA results for π eνγ Best values of pion Form Factor Parameters: 150 140 χ 2 Contours Combined analysis of 1999-01 and 2004 data sets [Bychkov et al., PRL 103, 051802 (2009)] F A Form Factor x 10 4 130 120 110 100 90 4σ 2σ 1σ F V CVC = 255(3) x 10-4 F V Vector Form Factor 0.028 0.027 0.026 0.025 slope = 0.10 ± 0.06 [PIBETA, 2009] Res-χPT calculation [Mateu & Portoles, 2007] 80 220 230 240 250 260 270 F V Form Factor x 10 4 280 290 0.024 0 0.1 0.2 q 2 0.3 0.4 0.5 = 1-2E γ /m π

D. Počanić (UVa) Rare pi & mu decays: The π e2γ decay 11 Aug 14 22/ 29 Summary of PIBETA results on π eνγ [PRL 103, 051802 (2009)] F V = 0.0258 ± 0.0017 (8 ) F A = 0.0119 ± 0.0001 exp (F CVC V ) (16 ) a = 0.10 ± 0.06 (q 2 dep of F V ) ( ) 5.2 10 4 < F T < 4.0 10 4 90 % C.L. B πe2γ (E γ > 10 MeV, θ eγ > 40 ) = 73.86(54) 10 8 (17 )

D. Počanić (UVa) Rare pi & mu decays: The π e2γ decay 11 Aug 14 22/ 29 Summary of PIBETA results on π eνγ [PRL 103, 051802 (2009)] F V = 0.0258 ± 0.0017 (8 ) F A = 0.0119 ± 0.0001 exp (F CVC V ) (16 ) a = 0.10 ± 0.06 (q 2 dep of F V ) ( ) 5.2 10 4 < F T < 4.0 10 4 90 % C.L. B πe2γ (E γ > 10 MeV, θ eγ > 40 ) = 73.86(54) 10 8 (17 ) Above results will be improved with the new PEN data analysis.

D. Počanić (UVa) Rare pi & mu decays: The π e2γ decay 11 Aug 14 22/ 29 Summary of PIBETA results on π eνγ [PRL 103, 051802 (2009)] F V = 0.0258 ± 0.0017 (8 ) F A = 0.0119 ± 0.0001 exp (F CVC V ) (16 ) a = 0.10 ± 0.06 (q 2 dep of F V ) ( ) 5.2 10 4 < F T < 4.0 10 4 90 % C.L. B πe2γ (E γ > 10 MeV, θ eγ > 40 ) = 73.86(54) 10 8 (17 ) Above results will be improved with the new PEN data analysis. At L.O. (l 9 + l 10 ), F A, F V are related to pion polarizability and π 0 lifetime αe LO = βlo M = (2.783 ± 0.023 exp) 10 4 fm 3 { τ π 0 = (8.5 ± 1.1) 10 17 current PDG avg: 8.52 (12) s PrimEx PRL 10: 8.32 (23)

D. Počanić (UVa) Rare pi & mu decays: The π beta decay 11 Aug 14 23/ 29 Pion beta (π e3 ) decay: π + π 0 e + ν e BR 10 8 Theoretically the cleanest path to access CKM V ud

D. Počanić (UVa) Rare pi & mu decays: The π beta decay 11 Aug 14 24/ 29 Current status of V ud : 0.98 ft(0 + 0 + ) [Hardy09] PIBETA [Pocanic04] 0.975 Neutron β decay results need to be sorted out before returning to π e3. V ud 0.97 0.965 0.96 PKO1 DD-ME2 ft(0 + 0 + ) [Liang09] τ n [PDG 2012] λ [UCNA 2013] λ [PERKEO II 2013] CKM unitarity [PDG 2012] λ [PDG 2012] -1.29-1.28-1.27-1.26 λ = g A /g V τ 1 n V ud 2 g V 2 (1 + 3 λ 2 )

D. Počanić (UVa) Rare pi & mu decays: Radiative muon decay 11 Aug 14 25/ 29 Radiative muon decay: µ + e + ν e ν µ γ BR 10 3 for energetic γ s Sensitive to admixtures beyond V A Limiting factor in µ eγ LFV searches

D. Počanić (UVa) Rare pi & mu decays: Radiative muon decay 11 Aug 14 26/ 29 Radiative muon decay, µ + e + ν νγ, (new analysis of 2004 data) CsI Time Coincidence 3 10 3 10 Entries/0.5 ns 1200 1000 800 σ = 0.71 ns N0. of Events = 518813 ± 946 100 80 Signal MC Misid Events Signal MC + Misid. events cut DATA(measured) 600 60 400 40 200 20 0-10 -8-6 -4-2 0 2 4 6 8 10 t = [t - (ns) + t γ ] e 0-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 Cos θ 60000 50000 40000 cut Signal MC Misid Events Signal MC + Misid. events DATA(measured) cut 40000 Signal MC Misid Events 35000 Signal MC + Misid. events DATA(measured) 30000 25000 30000 20000 20000 15000 10000 10000 5000 0 15 20 25 30 35 40 45 50 55 10 15 20 25 30 35 40 45 50 55 Photon Energy [MeV] Positron Energy [MeV] Split clumps very well accounted for!

D. Počanić (UVa) Rare pi & mu decays: Radiative muon decay 11 Aug 14 27/ 29 RMD preliminary results, cont d. Preliminary result for RMD branching ratio (thesis E. Munyangabe): B exp = 4.365 (9) stat. (42) syst. 10 3, 29 B SM = 4.342 (5) stat-mc 10 3 (for E γ > 10 MeV, θ eγ > 30 )

D. Počanić (UVa) Rare pi & mu decays: Radiative muon decay 11 Aug 14 27/ 29 RMD preliminary results, cont d. Preliminary result for RMD branching ratio (thesis E. Munyangabe): B exp = 4.365 (9) stat. (42) syst. 10 3, 29 B SM = 4.342 (5) stat-mc 10 3 (for E γ > 10 MeV, θ eγ > 30 ) χ 2 18 16 14 12 10 8 6 4 2 η = 0.006 ± 0.017 χ 2 /NDF = 0.8-0.08-0.06-0.04-0.02 0 0.02 0.04 0.06 0.08 η NB: preliminary results! Analysis of PS subset: 13 MeV < E γ < 45 MeV, and 10 MeV < E e + < 43 MeV, yields η= 0.006 (17) stat. (18) syst., or η< 0.028 (68%CL). 4 better than best previous experiment (Eichenberger et al, 84).

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 28/ 29 Study of allowed π and µ decays in PEN A significant experimental effort is under way (in PEN and in other experiments) to make use of the unparalleled theoretical precision in the weak interactions of the lightest particles. Information obtained is complementary to expected collider results, and valuable for their proper interpretation. Improvements in precision for π eν, π eνγ (F V, FT ul ), and µ eν νγ. to be achieved in the near future.

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 29/ 29 Current and former PIBETA and PEN collaborators L. P. Alonzi a, K. Assamagan a, V. A. Baranov b, W. Bertl c, C. Broennimann c, S. Bruch a, M. Bychkov a, Yu.M. Bystritsky b, M. Daum c, T. Flügel c, E. Frlež a, R. Frosch c, K. Keeter a, V.A. Kalinnikov b, N.V. Khomutov b, J. Koglin a, A.S. Korenchenko b, S.M. Korenchenko b, M. Korolija d, T. Kozlowski e, N.P. Kravchuk b, N.A. Kuchinsky b, E. Munyangabe a, D. Lawrence h, W. Li a, J. S. McCarthy a, R. C. Minehart a, D. Mzhavia b,f, E. Munyangabe a, A. Palladino a,c, D. Počanić a, B. Ritchie h, S. Ritt a,c, P. Robmann g, O.A. Rondon-Aramayo a, A.M. Rozhdestvensky b, T. Sakhelashvili f, P. L. Slocum a, L. C. Smith a, N. Soić d, U. Straumann g, I. Supek d, P. Truöl g, Z. Tsamalaidze f, A. van der Schaaf g, E.P. Velicheva b, V.P. Volnykh b, Y. Wang a, C. Wigger c, H.-P. Wirtz c, K. Ziock a. a Univ. of Virginia, USA c PSI, Switzerland e Swierk, Poland g Univ. Zürich, Switzerland b JINR, Dubna, Russia d IRB, Zagreb, Croatia f IHEP, Tbilisi, Georgia h Arizona State Univ., USA Home pages: http://pibeta.phys.virginia.edu http://pen.phys.virginia.edu

Backup slides D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 30/ 29

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 31/ 29 Available data on pion form factors F V cvc = 1 α 2 πτ π 0m π = 0.0255(3).

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 31/ 29 Available data on pion form factors F V cvc = 1 α 2 πτ π 0m π = 0.0255(3). F A 10 4 reference 106 ± 60 Bolotov et al. (1990) 135 ± 16 Bay et al. (1986) 60 ± 30 Piilonen et al. (1986) 110 ± 30 Stetz et al. (1979) 116 ± 16 world average (PDG 2004)

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 31/ 29 Available data on pion form factors F V cvc = 1 α 2 πτ π 0m π = 0.0255(3). F A 10 4 reference note 106 ± 60 Bolotov et al. (1990) (F T = 56 ± 17) 135 ± 16 Bay et al. (1986) 60 ± 30 Piilonen et al. (1986) 110 ± 30 Stetz et al. (1979) 116 ± 16 world average (PDG 2004)

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 32/ 29 Can PIBETA say anything on the π e2 BR? YES!

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 32/ 29 Can PIBETA say anything on the π e2 BR? YES! We fix V ud to the extraordinarily precise PDG 2013 recommended value and adjust R π e/µ V ud = 0.97425 ± 0.00022 until the extracted value of V πβ ud (R π e/µ )PIBETA = (1.2366 ± 0.0064) 10 4, agrees. This exercise yields [recall (R π e/µ )SM = 1.2352(1) 10 4 ]

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 32/ 29 Can PIBETA say anything on the π e2 BR? YES! We fix V ud to the extraordinarily precise PDG 2013 recommended value and adjust R π e/µ V ud = 0.97425 ± 0.00022 until the extracted value of V πβ ud (R π e/µ )PIBETA = (1.2366 ± 0.0064) 10 4, agrees. This exercise yields [recall (R π e/µ )SM = 1.2352(1) 10 4 ] Adding the new value to the world data set would move the average slightly to (R π e/µ )new avg = (1.2317 ± 0.0031) 10 4.

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 33/ 29 What to do with Michel parameters? For µ eν µ ν e γ: ( ) x = Ee and y = Eγ E max E max d 3 B(x, y, θ) dx dy 2π d(cos θ) = f 1(x, y, θ) + ηf 2 (x, y, θ) + (1 4 3 ρ)f 3(x, y, θ)

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 33/ 29 What to do with Michel parameters? For µ eν µ ν e γ: ( ) x = Ee and y = Eγ E max E max d 3 B(x, y, θ) dx dy 2π d(cos θ) = f 1(x, y, θ) + ηf 2 (x, y, θ) + (1 4 3 ρ)f 3(x, y, θ) ρ = 3 4 3 4 [ ] glr V 2 + grl V 2 + 2 glr T 2 + 2 grl T 2 + R(gRLg S RL T + glrg S LR T ) SM 3 4, η = ( grl V 2 + glr V 2) + 1 ( glr S + 2gLR T 2 + grl S + 2gRL T 2) + 2 ( g LR T 2 + grl T 2) 8 SM 0.

D. Počanić (UVa) Rare pi & mu decays: Summary 11 Aug 14 33/ 29 What to do with Michel parameters? For µ eν µ ν e γ: ( ) x = Ee and y = Eγ E max E max d 3 B(x, y, θ) dx dy 2π d(cos θ) = f 1(x, y, θ) + ηf 2 (x, y, θ) + (1 4 3 ρ)f 3(x, y, θ) ρ = 3 4 3 4 [ ] glr V 2 + grl V 2 + 2 glr T 2 + 2 grl T 2 + R(gRLg S RL T + glrg S LR T ) SM 3 4, η = ( grl V 2 + glr V 2) + 1 ( glr S + 2gLR T 2 + grl S + 2gRL T 2) + 2 ( g LR T 2 + grl T 2) 8 SM 0. Combined with η, δ, ρ, parameters of OMD (TWIST), a global fit will yield model-independent limits on non (V A) couplings.

D. Počanić (UVa) Rare pi & mu decays: Pion beta decay 11 Aug 14 34/ 29 π e3 decay: quark-lepton (Cabibbo) universality The basic weak-interaction V-A form (e.g., µ decay): is replicated in hadronic weak decays M e l α ν e ū e γ α (1 γ 5 )u ν M p h α n ū p γ α (G V G A γ 5 )u n with G V,A 1. Departure from G V = 1 (CVC) comes from weak quark (Cabibbo) mixing: G V = G µ cos θ C (= G µ V ud ) cos θ C 0.97 3 q generations lead to the Cabibbo-Kobayashi-Maskawa (CKM) matrix (1973): V ud V us V ub V cd V cs V cb V td V ts V tb CKM unitarity cond.: V 2 = 1 ( V ud 2 + V us 2 + V ub 2 )? = 0, stringently tests the SM. Until 2004 appeared violated by 3σ!

D. Počanić (UVa) Rare pi & mu decays: Pion beta decay 11 Aug 14 35/ 29 π e3 decay rate in the SM where while Γ = Γ 0 (1 + δ π ) = G F 2 V ud 2 5 ( 30π 3 f (ɛ, ) 1 ) 3 (1 + δ π ), 2m + = m + m 0 = 4.5936(5) MeV and ɛ = ( me ) 2 1 81 f (ɛ, ) = 1 ɛ (1 92 ) ( ) ɛ 4ɛ2 + ɛ2 1 1 ɛ 4 ln ɛ 3 7 2 (m + + m 0 ) 2 0.941 and δ π 0.035 is the sum of radiative/loop corrections with 0.05% uncertainty.

D. Počanić (UVa) Rare pi & mu decays: Pion beta decay 11 Aug 14 35/ 29 π e3 decay rate in the SM where while Γ = Γ 0 (1 + δ π ) = G F 2 V ud 2 5 ( 30π 3 f (ɛ, ) 1 ) 3 (1 + δ π ), 2m + = m + m 0 = 4.5936(5) MeV and ɛ = ( me ) 2 1 81 f (ɛ, ) = 1 ɛ (1 92 ) ( ) ɛ 4ɛ2 + ɛ2 1 1 ɛ 4 ln ɛ 3 7 2 (m + + m 0 ) 2 0.941 and δ π 0.035 is the sum of radiative/loop corrections with 0.05% uncertainty. Pion beta decay provides the theoretically cleanest access to V ud.

π e3 decay: experimental studies 1967 CERN: B/B 10% [Depommier etal NP B4 (68) 189] 1984 LAMPF: B/B 4% [McFarlane etal PRD 32 (85) 547] 1999-2001 PIBETA at PSI (below) D. Počanić (UVa) Rare pi & mu decays: Pion beta decay 11 Aug 14 36/ 29

PIBETA results; 1999-2001 runs D. Počanić (UVa) Rare pi & mu decays: Pion beta decay 11 Aug 14 37/ 29 Number of events 7000 6000 5000 4000 3000 2000 π + π 0 e + ν γ1 γ2 Simulation Data Number of Events 40000 30000 20000 10000 Simulation Data π e ν 1000 0 160 165 170 175 180 Opening angle θ γ1γ2 (degr) 0 45 50 55 60 65 70 75 Positron Energy (MeV)

D. Počanić (UVa) Rare pi & mu decays: Pion beta decay 11 Aug 14 38/ 29 PIBETA result for π + π 0 e + ν (π β ) decay [PRL 93, 181803 (2004)] Pion beta decay yield normalized to measured π eν events: B exp-t πβ = [1.040 ± 0.004 (stat) ± 0.004 (syst)] 10 8, B exp-e πβ = [1.036 ± 0.004 (stat) ± 0.004 (syst) ± 0.003 (π e2 )] 10 8, McFarlane et al. [PRD 1985]: B = (1.026 ± 0.039) 10 8 SM Prediction (PDG): B = 1.038 1.041 10 8 (90% C.L.) (1.005 1.007 10 8 excl. rad. corr.) Most sensitive test of CVC/radiative corr. in a meson to date! PDG 2012: V ud = 0.97425(22) PIBETA: V ud = 0.9748(25) or V ud = 0.9728(30).