New Results in Rare Pion and Muon Decays

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1 New Results in Rare Pion and Muon Decays Dinko Počanić, University of Virginia Motivation for new measurements: the PIBETA experiment Recent results: pion beta decay: π + π 0 e + ν (π β ) radiative pion decay: π + e + νγ (π e2γ ) radiative muon decay: µ + e + ν νγ Opportunities Conclusions DNP 2006, Nashville, Tenn. 27 October 2006

2 2 Known and Measured Pion and Muon Decays (PDG 2004) Decay BR π + µ + ν (4) (π µ2 ) µ + νγ 2.00 (25) 10 4 (π µ2γ ) e + ν (4) 10 4 (π e2 ) e + νγ 1.61 (23) 10 7 (π e2γ ) π 0 e + ν (34) 10 8 (π e3, π β ) e + νe + e 3.2 (5) 10 9 (π e2ee ) π 0 γγ (32) µ + e + ν ν 1.0 e + e γ (32) 10 2 e + ν νγ (4) e + e e + e 3.14 (30) 10 5 e + ν νe + e 3.4 (4) 10 5 e + e 6.2 (5) 10 8

3 3 The PIBETA program of measurements Perform precision checks of Standard Model and QCD predictions: - π + π 0 e + ν e main goal SM checks related to CKM unitarity - π + e + ν e γ(or e + e ) pion F A /F V, π polarizability (χpt prediction) tensor coupling besides V A (?) - µ + e + ν e ν µ γ(or e + e ) departures from V A in L weak 2nd phase: - π + e + ν e The PEN experiment e-µ universality pseudoscalar coupling besides V A neutrino sector anomalies, Majoron,...

4 4 Experiment R (PIBETA) collaboration members: V. A. Baranov, c W. Bertl, b M. Bychkov, a Yu.M. Bystritsky, c E. Frlež, a N.V. Khomutov, c A.S. Korenchenko, c S.M. Korenchenko, c M. Korolija, f T. Kozlowski, d N.P. Kravchuk, c N.A. Kuchinsky, c D. Mzhavia, c,e D. Počanić, a P. Robmann, g O.A. Rondon-Aramayo, a A.M. Rozhdestvensky, c T. Sakhelashvili, b S. Scheu, g V.V. Sidorkin, c U. Straumann, g I. Supek, f Z. Tsamalaidze, e A. van der Schaaf, g B. A. VanDevender, a E.P. Velicheva, c V.V. Volnykh, c and Y. Wang a a Dept of Physics, Univ of Virginia, Charlottesville, VA , USA b Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland c Joint Institute for Nuclear Research, RU Dubna, Russia d Institute for Nuclear Studies, PL Swierk, Poland e IHEP, Tbilisi, State University, GUS Tbilisi, Georgia f Rudjer Bošković Institute, HR Zagreb, Croatia g Physik Institut der Universität Zürich, CH-8057 Zürich, Switzerland

5 5 The PIBETA Experiment: stopped π + beam segmented active tgt. 240-det. CsI(p) calo. central tracking digitized PMT signals stable temp./humidity cosmic µ antihouse pure CsI PV BC π + beam AC1 AC2 AD AT MWPC1 MWPC2 10 cm

6 PIBETA Detector Assembly (1998) 6

7 7 Pion beta decay: π + π 0 e + ν Results, runs

8 The π + π 0 e + ν decay 8

9 Normalizing decay: π + e + ν 9

10 Extracting the π eν Signal 10

11 11 π eν decay: SM predictions and measurements Marciano and Sirlin, [PRL 71 (1993) 3629]: Γ(π e ν(γ)) Γ(π µ ν(γ)) calc = ( ± ) 10 4 Decker and Finkemeier, [NP B 438 (1995) 17]: Γ(π e ν(γ)) Γ(π µ ν(γ)) calc = ( ± ) 10 4 Experiment, world average (PDG 2004): Γ(π e ν(γ)) Γ(π µ ν(γ)) exp = (1.230 ± 0.004) 10 4

12 12 PIBETA Current Result for π β Decay [PRL 93, (2004)] B exp πβ = [1.040 ± (stat) ± (syst)] 10 8, B exp πβ = [1.036 ± (stat) ± (syst) ± (π e2)] 10 8, McFarlane et al. [PRD 1985]: B = (1.026 ± 0.039) 10 8 SM Prediction (PDG, 2004): B = (90% C.L.) ( excl. rad. corr.) PDG 2004: V ud = (5) PIBETA current: V ud = (25) or V ud = (30).

13 Radiative pion decay: π eνγ 13

14 14 π + e + νγ: Standard IB and V A terms SM A tensor interaction, too? Exchange of S=0 leptoquarks P Herczeg, PRD 49 (1994) 247

15 15 AVAILABLE DATA on Pion Form Factors F V cvc = 1 α 2 πτ π 0m π = (5). F A 10 4 reference note 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)

16 15-a AVAILABLE DATA on Pion Form Factors F V cvc = 1 α 2 πτ π 0m π = (5). 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)

17 16 π + e + νγ (S/B) data set Region A: E γ, E e + > 51.7 MeV Region B: E γ > 55.6 MeV E e + > 20 MeV θ eγ > 40 Region C: E γ > 20 MeV E e + > 55.6 MeV θ eγ > 40

18 17 π + e + νγ data set (timing)

19 18 Results of the SM fit [Phys. Rev. Lett. 93, (2004)] Best-fit π eνγ branching ratios obtained with: F V = (fixed) and F A = (4) (fit) χ 2 /d.o.f. = Radiative corrections are included in the calculations. E min e + E min γ θ min eγ B exp B the no. of (MeV) (MeV) ( 10 8 ) ( 10 8 ) events (5) 2.583(1) 30.6 k (3) 14.34(1) 5.2 k (13) 37.83(1) 5.7 k

20 19 Region B: global fits [F T = ( 16 ± 2) 10 4 ] projected uncertainties in 2004 run

21 20 π + e + νγ (S/B) 2004 Region A: E γ, E e + > 51.7 MeV Region B: E γ > 55.6 MeV E e + > 20 MeV θ eγ > 40 Region C: E γ > 20 MeV E e + > 55.6 MeV θ eγ > 40

22 21 Analysis of 2004 data [M. Bychkov, PhD thesis, Aug 2005] Number of events Simulation Data λ=(2e e /m π )sin 2 (Θ eγ /2) Standard Model fit (V A) only.

23 Analysis of 2004 data, 8 regions [M. Bychkov, PhD thesis, Aug 05] Number of events y=2(e e )/m π λ=(2e e /m π )sin 2 (Θ eγ /2) x=2(e γ /m π )

24 23 Preliminary results of 2004 analysis [M. Bychkov] E min e + E min γ θ min eγ B exp B the no. of (MeV) (MeV) ( 10 8 ) ( 10 8 ) events (58) (5) 4.4 k (26) (5) 10.3 k (60) 37.90(3) 13.4 k!! PRELIMINARY!! COMBO (99-01)+04: a new exp. value of F V = ± (9 ) improved value of F A = ± (8 ) first meas t of q 2 dep.: a = ± ( )

25 24 Experimental History of Pion F A and F V THIS WORK (2005) POCANIC (2004) BOLOTOV (1990) F V = F V = F V = CVC PREDICTION (2005) DOMINGUEZ 2 (1988) EGLI 1 (1986) THIS WORK (2005) PIILONEN (1986) BOLOTOV (1990) BAY (1986) STETZ (1978) EGLI (1986) DEPOMMIER (1963) γ=f A /F V F V

26 25 π eνγ: Pion form factors and polarizability in χpt To first order in χpt the pion weak form form factors fix: F A F V = 32π 2 (l r 9 + l r 10), while the pion polarizability is given by α E = 4α m π F 2 π (l r 9 + l r 10), so that α α E = 8π 2 m π Fπ 2 FA F V fm 3 FA F V [= 2.71(5) 10 4 fm 3 ].

27 26 Is there a Tensor Term, after all? Based on either 3-region or 8-region analysis (M. Bychkov), keeping F V, F A and a fixed, we get: F T = (+0.08 ± 3.95) 10 4, or F T < F T < at 68 % C.L. at 90 % C.L. Simultaneous variation of F A and F T gives essentially the same result.

28 27 Summary of Pion Rare Decay Results We ve improved the π β branching ratio precision sevenfold. We are on track to improve the precision of pion form factors F A and F V, eightfold and ninefold, respectively. We have determined for the first time the momentum dependence of the pion FF s. Will soon complete unified analysis of 99/ π e2γ data sets and finalize above results. Our radiative π, µ results provide critical input in controlling the systematics of the approved π eν (PEN) experiment, R The PEN experiment will double the R data set on radiative π, µ decays, with yet lower backgrounds. A final analysis will also reduce both systematic and statistical uncertainties of the π β BR.

29 Radiative muon decay: µ eν νγ 28

30 29 Michel Parameters of Muon Decay: µ eν ν d 2 Γ dx d(cos θ) = m µ 4π W eµg F x 2 x 2 0 [ F IS (x) + P µ + cos θf AS (x) ] [ 1 + P e +(x, θ) ˆζ ] F IS (x) = x(1 x) ρ(4x2 3x x 2 0) + η x 0 (1 x) F AS (x) = 1 3 ξ x 2 x 2 0 (1 x + 23 δ [ 4x 3 + ( 1 x 20 1 )])

31 Michel Parameters of Radiative Muon Decay: µ eν νγ 30 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 = [ g V LR 2 + g V RL g T LR g T RL 2 ] + R(gRLg S RL T + glrg S LR) T SM 3 4, η = ( g V RL 2 + g V LR 2) ( g S LR + 2g T LR 2 + g S RL + 2g T RL 2) + 2 ( g T LR 2 + g T RL 2) SM 0.

32 31 Experimental Limits (90 % C.L.) on g γ αβ g γ αβ S V T LL > LR RL RR max. values: g γ αβ gγ αβ g γ max 1 [For more details cf. reviews and publications by W. Fetscher et al.]

33 32 RMD analysis (2004 data) [B. VanDevender s thesis]

34 µ eν νγ Differential Branching Ratio [B. VanDevender] 33 B exp = [4.40 ± 0.02 (stat.) ± 0.09 (syst.)] ! B theo = (E γ > 10 MeV, θ > 30 )

35 34 RMD analysis: η and ρ [B. VanDevender s thesis] χ 2 contours for fits of Michel parameters η and ρ for relevant RMD kinematics.

36 35 RMD analysis: Final η and ρ [B. VanDevender s thesis] data set η ρ nine-piece target ± ± one-piece target ± ± 0.011

37 35-a RMD analysis: Final η and ρ [B. VanDevender s thesis] data set η ρ nine-piece target ± ± ± (fixed) one-piece target ± ± ± (fixed)

38 35-b RMD analysis: Final η and ρ [B. VanDevender s thesis] data set η ρ nine-piece target ± ± ± (fixed) one-piece target ± ± ± (fixed) Combined: η = ± 0.050(stat.) ± 0.034(syst.)

39 35-c RMD analysis: Final η and ρ [B. VanDevender s thesis] data set η ρ nine-piece target ± ± ± (fixed) one-piece target ± ± ± (fixed) Combined: η = ± 0.050(stat.) ± 0.034(syst.) η (68 % c.l.) or η (90 % c.l.)

40 Experimental History of η 36

41 37 Radiative Muon Decay Summary First precise measurement of B(µ eν νγ) over a large phase space 313 events (bubble chamber) events 30 % uncertainty 2 % uncertainty B exp = (4.40 ± 0.09) 10 3, (B theo = )

42 37-a Radiative Muon Decay Summary First precise measurement of B(µ eν νγ) over a large phase space 313 events (bubble chamber) events 30 % uncertainty 2 % uncertainty B exp = (4.40 ± 0.09) 10 3, (B theo = ) New measurement of Michel parameter η η η (68 % c.l.) new world average: η (68 % c.l.) reduced by a factor of 2.5.

43 37-b Radiative Muon Decay Summary First precise measurement of B(µ eν νγ) over a large phase space 313 events (bubble chamber) events 30 % uncertainty 2 % uncertainty B exp = (4.40 ± 0.09) 10 3, (B theo = ) New measurement of Michel parameter η η η (68 % c.l.) new world average: η (68 % c.l.) reduced by a factor of 2.5. Above results based on our 2004 run data set; the PEN experiment will double this data set with lower backgrounds.

44 OPPORTUNITIES 38

45 39 Remaining opportunities in pion decay 1. Improve the π eν decay precision highly motivated! 2. Improve the π β decay precision not as urgent (+ very hard). 3. A new search for the π 0 γγγ decay? sets the best limit on C-violation 4. Search for the allowed π 0 4γ decay? qed γ splitting B (2.6 ± 0.1) Bratkovskaya et al, PL B359 (95) 217

46 40 Final Comments This line of experiments provides useful crosschecks of the SM in a small corner of the total available physics space. Theoretical precision is unparalleled; experiments are catching up. Excellent training ground for graduate students and postdocs. Cost of experiments is moderate; measurements are great fun.

47 BACKUP TRANSPARENCIES 41

48 42 Quark-Lepton (Cabibbo) Universality The basic weak-interaction V -A form (e.g., µ decay): persists 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 (plain CVC) comes from weak quark mixing (Cabibbo 1963): G V = G µ cos θ C (= G µ V ud ) cos θ C q generations lead to the Cabibbo-Kobayashi-Maskawa matrix (1973): V ud V us V ub V cd V cs V cb V td V ts V tb CKM unitarity cond.: V ud 2 + V us 2 + V ub 2? = 1, can test the SM.

49 43 STATUS OF CKM UNITARITY (PDG before) V us = (26) from K e3 decays. V ub = (7) from B decays. V ud from superallowed Fermi nuclear β decays 1990 Hardy reconciled Ormand & Brown s and Towner s f t values: V ud 2 + V us 2 + V ub 2 = (16), or 1 2.4σ. V ud from neutron β decay (many results; currently incompatible) Vui 2 = (28), or 1 3.0σ. [perkeo ii (2002)] V ud from pion β decay pibeta expt discussed below. 2004: V us revised upward; CKM unitarity discrepancy removed!

50 44 The Pion Beta Decay: π ± π 0 e ± ν: B , pure vector trans.: 0 0. Theoretical decay rate at tree level: 1 = G2 F V ud 2 τ 0 30π 3 ( 1 2M + = (22) V ud 2 (s 1 ). ) 3 5 f(ɛ, ) With radiative and loop corrections: branching ratio becomes: 1 τ = 1 τ 0 (1 + δ), so that the B(πβ) = τ + τ 0 (1 + δ) = (6) 10 8 (1 + δ) V ud 2.

51 45 Recent calculations of pion beta decay radiative corrections (1) In the light-front quark model W. Jaus, Phys. Rev. D 63 (2001) total RC for pion beta decay: δ = (3.230 ± 0.002) (2) In chiral perturbation theory Cirigliano, Knecht, Neufeld and Pichl, Eur. Phys. J. C 27 (2003) 255. χpt with e-m terms up to O(e 2 p 2 ) theoretical uncertainty of in extracting V ud from π e3. (3) Marciano and Sirlin recently further reduced theoretical uncert s in all beta decays [hep-ph/ , PRL 96, (2006)].

52 46 Experimental accuracy of the pion beta decay rate Best result until recently: [McFarlane et al., PRD 32 (1985) 547.] B(π + π 0 e + ν) = (1.026 ± 0.039) 10 8, (i.e., 4 %) Accuracy: 1 % check CVC and rad. corrections 0.5 % add to SAF & n β input to V ud < 0.3 % check for failure of CKM unitarity: 4 th generation coupling m Z Λ of compositeness SUSY viol. of q-l universality signal of a smaller G F (ν osc.)

53 47 CENTRAL DETECTOR REGION Active TGT MWPC-1 MWPC-2 PV array (beam is perpendicular at center)

54 48 Experimental Method: Summary Detect π + decays at rest (during a delayed 180 ns gate) ns Use π + e + ν prescaled for normalization. π stop π gate beam veto Accept every πβ trigger unbiased (γγ coincidences above Michel endpoint) 1 = 1 τ πβ τ π + Beνf presc B π0 γγ Aeν A πβ Nπβ N eν A πβ, A eν are acceptances for the decay modes, respectively.

55 Key acceptances compared 49 GEANT calculated acceptances for the π β and π e2 decays as a function of cos θ.

56 50 Online πβ Energy Spectrum: True πβ events buried deep under overwhelming background!

57 The π + π 0 e + ν decay 51

58 52 Summary of the main πβ uncertainties Type Quantity Value Uncertainty (%) external: π + lifetime ns 0.02 R exp π 0 γγ R exp πe internal: N tot πe2 (syst.) A HT πβ /AHT πe r πg = f πβ πe2 πg /fπg π β accid. bgd < 0.1 f CPP correction f ph correction statistical: N πβ

59 53 Experimental Limits (90 % C.L.) on g γ αβ g γ αβ S V T LL LR RL RR max. values: g S αβ 2, gv αβ 1, gt αβ

60 53-a Experimental Limits (90 % C.L.) on g γ αβ g γ αβ S V T LL > LR RL RR 0 max. values: g S αβ 2, gv αβ 1, gt αβ

61 53-b Experimental Limits (90 % C.L.) on g γ αβ g γ αβ S V T LL > LR RL RR max. values: g S αβ 2, gv αβ 1, gt αβ

62 54 Lepton universality From R e/µ = Γ(π e ν(γ)) Γ(π µ ν(γ)) = g2 e g 2 µ m 2 e m 2 µ (1 m 2 e/m 2 µ) 2 ( ) 1 + δre/µ (1 m 2 µ/m 2 π) 2 R τ/π = Γ(τ e ν(γ)) Γ(π µ ν(γ)) = g2 τ g 2 µ one can evaluate ( ) ge = ± and g µ π For comparison ( ) ge = ± and g µ W m 3 τ (1 m 2 π/m 2 τ ) 2 ( ) 1 + δrτ/π 2m 2 µm π (1 m 2 µ/m 2 π) 2 ( gτ g µ ( gτ g e ) πτ ) W = ± = ±

63 55 Departures from lepton universality Various models beyond the SM predict flavor non-universal suppressions of the lepton coupling constants in W lν: g l g l = g l (1 ɛ l 2 ) where l = e, µ, τ Linear combinations constrained by W, τ, π, K decays are: g µ = 1 + ɛ e ɛ µ, g e 2 g τ = 1 + ɛ µ ɛ τ g µ 2, g τ = 1 + ɛ e ɛ τ g e 2, Two of the three are independent; experimental constraints are on: eµ ɛ e ɛ µ, µτ ɛ µ ɛ τ, eτ ɛ e ɛ τ. Recent comprehensive reviews: A. Pich, Nucl. Phys. Proc. Suppl. 123 (2003) 1; (hep-ph/ ) W. Loinaz et al., PRD 70 (2004) ; (hep-ph/ ).

64 From Loinaz et al., PRD 70 (2004)

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