Lepton Universality Tests with Kaons

Transcription

1 Lepton Universality Tests with Kaons Rainer Wanke Institut für Physik, Universität Mainz for the Flavianet Working Group on Kaon Decays KAON 2007 Frascati, May 24, 2007 Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.1/32

2 Flavianet Kaon Working Group Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.2/32

3 Introduction & Outline Violation of Lepton Universality: Predicted by practically every New Physics model. Kaon physics: Two main possibilites to test Lepton Universality: K l3 decays K l2 decays K e3 /K µ3, form factors K e2 /K µ2 So far precisions poor (compared to e.g. pion decay), tests on levels of 1-2% (K l3 ) or even 4% (K e2 /K µ2 ). Since 2005: Many new data available (blue: first reported at KAON07) K l3 : KLOE (K ± e3, K± µ3, K L,l3 form factors), ISTRA+ (K e3 ), NA48 (K ± e3, K± µ3, K L,µ3 form factors). K e2 /K µ2 : 2 NA48/2, KLOE. Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.3/32

4 K l3 Decays Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.4/32

5 K l3 Introduction Expectations in for LFV in K l3 : Test for LFV in the vector current (different from K l2, π l2 decays!). = To be compared with searches for LFV in τ decays: τ eν ν/τ µν ν = g 2 µ/g 2 e = ± SM transitions proceed via tree-level diagrams: Possible violations of Lepton Universality from New Physics will always be small. = Precision measurements necessary! Two possibilities to search for violation of Lepton Universality: Deviation of Γ(K µ3 )/Γ(K e3 ) from SM prediction. Possible differences in form factors between K µ3 and K e3. Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.5/32

6 K l3 Widths and Lepton Universality K l3 master formula: Γ(K l3(γ) ) = G2 Fm 5 K 192π 3 C2 K S EW V us 2 f + (0) 2 I l K (1 + δl K )2 with: C 2 K = 1 for K0, = 1 2 for K±. S EW = : short-distance EW correction. f + (0): hadronic matrix element at q 2 = 0 (different for K ±, K 0 ). I l K = Il K (λ +, λ 0 ): integral of form factors over phase space. (1 + δk l ) δSU(2) l + 2δl EM : form factor corrections for SU(2) breaking and long-distance EM interactions. Lepton flavour independent: Lepton flavour dependent: C K, S EW, δ l SU(2) I l K, δl EM In case of Lepton Non-Universality: G µ F Ge F Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.6/32

7 K l3 Widths and Lepton Universality EM corrections are small (Cirigliano et al. (2002), updated by Cirigliano, Neufeld; errors are taken as uncorrelated [has to be improved].) δ e EM [%] δµ EM [%] (1 + δµ K )2 /(1 + δ e K )2 K 0 l (10) +0.80(15) 1.006(4) K ± l (10) 0.12(15) 0.997(4) Phase space corrections are large and depend on form factor slopes λ +, λ +, λ 0. Use form factor values from global Flavianet fit (assuming lepton universality in the slopes and taking correlations into account). I e K I µ K I µ K /Ie K K L,l (29) (31) (16) K ± l (30) (32) (16) Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.7/32

8 K l3 Widths and Lepton Universality = Standard Model expectation: R Kµ3/Ke3 Γ(K µ3) Γ(K e3 ) = ( G µ F G e F ) 2 I µ K I e K (1 + δ µ K )2 (1 + δ e K )2 = { (31) KL (31) K ± (Comparable uncertainties from I K estimation and EM corrections.) Parameter for Lepton Universality violation: r µe = (R Kµ3/Ke3) obs = Γ(K µ3) IK e (1 + δ (R Kµ3/Ke3 ) SM Γ(K e3 ) I µ K e )2 K (1 + δ µ = Gµ F K )2 G e F Situation with 2004 data (using current form factor slopes and EM corrections): K ± modes: r ± µe = 1.019(13) K L modes: r L µe = 1.054(15) = Intriguing deviation from Unity?! (Compare with τ lν ν: g 2 µ/g 2 e = (40)) Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.8/32

9 Direct Measurements on Γ(K µ3 )/Γ(K e3 ) Channel Γ(K µ3 )/Γ(K e3 ) KTeV K L ± (PRL 93, 2004) KEK-E246 K ± Using stopped kaons. (PLB 513, 2001) NA48/2 K ± ± EPJ value corrected (EPJC 50, 2007) at KAON07. KLOE K ± ± (prelim. 2007) 4.5 KEK-E246 (2001) NA48/2 (2007), corr KLOE (2007), prel KTeV (2004), K L 1 (corrected for K+) SM expectation ± Γ (K ) / Γ (K µ3 ± ) e3 Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.9/32

10 Determination of Γ(K µ3 )/Γ(K e3 ) Global Flavianet fit to all Kaon data Includes: All K ±, K L, K S BR s, form factor slopes, lifetimes. = M. Palutan, KAON07 K L,S K + + form factor slopes Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.10/32

11 Determination of Γ(K µ3 )/Γ(K e3 ) K ± modes: r ± µe = (87) (was 1.019(13) before) Error dominated by experiments (incl. scale factors). K L,S modes: r L,S µe = (56) (was 1.054(15) before) Similar errors from experiments and knowledge on δ EM. Combination of both modes: r µe = (50) (taking into account ρ = 0.12) = No indication of Lepton universality violation. Conclusions on Γ(K µ3 )/Γ(K e3 ): Kaon sensitivity coming closer to τ decays! ((g 2 µ/g 2 e) τ lν ν = (40)) Experimental (BR, ff s) and theoretical errors (δ EM ) comparable. Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.11/32

12 K l3 Form Factors K l3 form factors: K l3 matrix element: M f + (q 2 )(p K + p π ) µ ū l γ µ (1 + γ 5 )u v + f (q 2 )m l ū l γ µ (1 + γ 5 )u v Scalar form factor: f 0 (q 2 ) = f + (q 2 ) + q 2 m 2 K m 2 f (q 2 ) π Linear/quadratic expansion: f + (q 2 ) = f + (0) f 0 (q 2 ) = f + (0) ( 1 + λ q 2 + m π 2 λ + + q (1 2 ) + λ 0 m 2 π + q 4 m 4 π + ) (Not necessarily the best but used by all experiments.) Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.12/32

13 K l3 Form Factor Data Current Data on K l3 form factor slopes: Channel λ λ λ KTeV 2004 K L e ± ± 0.8 K L µ ± ± ± 1.8 KLOE 2006 K L e ± ± 0.8 KLOE prel. K L µ3 with K L e3 with K L e ± 2.6 NA K L e ± ± 0.9 NA K L µ ± ± ± 1.4 ISTRA 2004 K e ± ± 0.9 ISTRA 2004 K µ ± ± ± 2.2 (KLOE K µ3 data not used due to combined fit with K e3.) Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.13/32

14 K l3 Form Factor Slopes K e3 slopes only: Combined fit: λ + = (25.1 ± 0.9) 10 3 λ + " ISTRA+ λ + = (1.6 ± 0.4) 10 3 Correlation ρ = 94.1% 2 KTeV Ke3 fit KLOE (Ellipses = 1 σ contours) 0 NA λ + ' 10 3 Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.14/32

15 K l3 Form Factor Slopes K µ3 slopes only: λ + = (22.0 ± 2.2) 10 3 λ + = (2.3 ± 0.9) 10 3 λ 0 = (13.5 ± 2.1) 10 3 Correlations: λ + λ + λ λ λ + " KTeV ISTRA+ λ + ' Ke3 fit NA48 Kµ3 fit KTeV ISTRA+ 0 NA48 Kµ3 fit Ke3 fit λ + " NA48 Ke3 fit KTeV Kµ3 fit ISTRA λ + ' 10 3 λ Agreement with K e3 poor, mostly driven by NA48/2 value on λ 0. Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.15/32

16 K l3 Form Factor Slopes Excluding NA48 K L,µ3 from the fit: λ + " 10 3 KTeV λ + ' Ke3 fit No NA48 5 ISTRA+ 20 KTeV ISTRA+ No NA48 Ke3 fit λ + " KTeV ISTRA+ 0 0 Ke3 fit No NA λ + ' λ Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.16/32

17 Non-SM Interactions in K l3 Right-handed currents in the quark sector: Charged current interaction: [ ( ) L CC = g l µ u c t (Bernard, Oertel, Passemar, Stern, PLB 638 (2006). = Talks Passemar, Stern, KAON07) (V eff γ µ + A eff γ µ γ 5 ) ( d s b )] W µ + h.c. Standard Model: V eff = A eff = V CKM Absence of right-handed CC well-tested in the lepton sector. However: Need not to be the same in the quark sector. No stringent tests of right-handed quark couplings so far! Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.17/32

18 Non-SM Interactions in K l3 K µ3 Decays: In the chiral limit: Normalized scalar form factor f 0 (q 2 )/f + (0) known at the Callan-Treiman point q 2 = Kπ = m 2 K m2 π from BR measurements. RH currents would cause a deviation. lnc = lnf( Kπ ) can be measured using dispersive approach for form factor parametrization. NA48 fit of K L µ3 data: lnc = (80) stat (112) syst 2(ǫ S ǫ NS ) + CT = ± ǫ S, ǫ NS : Parameters of RH currents. CT : χpt correction O(10 3 ) Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.18/32

19 Non-SM Interactions in K l3 Conclusions on Right-Handed Quark Currents: NA48 sees effect ( 5σ) in K µ3 at the Callan-Treiman point. No other experiment has (yet) performed a fit with dispersive parametrization. However: Other experiments disagree with NA48 in slope λ 0 of scalar form factor. Correlation between λ 0 and lnc unclear. Data of other experiments need to be investigated. 4.5 KTeV (2004) ISTRA+ (2004) NA48 (2007) KLOE (2007), prel λ 0 [ 10-3 ] Situation not yet clarified. E. Passemar, KAON07 Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.19/32

20 K e2 /K µ2 Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.20/32

21 K e2 /K µ2 Introduction Standard Model Prediction: R K = Γ(K e2 )/Γ(K µ2 ) text book exercise for helicity suppression, but must include radiative corrections: (M. Finkemeier, PLB 387 (1996)) R K = R (0) K (1 + δrrad.corr. K ) = ( ± ) = (2.472 ± 0.001) 10 5 = SM prediction has precision of 0.04%! Caveat: Radiative corrections model dependent (VMD). More thorough χpt study underway (Cirigliano). Possibilities for non-sm Physics in K e2 /K µ2 : K e2 is strongly suppressed and extremely well-known in the SM = Non-SM effects a priori are easier to detect than in e.g. K l3. SUSY: LFV H ± couplings may enhance/lower SM K e2 decay width by up to 2 3%. (Masiero, Paradisi, Petronzio (2006) = P.Paradisi, KAON07) Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.21/32

22 K e2 /K µ2 Measurements PDG 2006: Three measurements from the 1970 s Γ(K e2 )/Γ(K µ2 ) = (2.45 ± 0.11) 10 5 Three new preliminary measurements: NA48/2 (2003 data), presented in 2005: About 4000 signal events from normal running period. Systematics dominated by trigger efficiencies. Γ(K e2 )/Γ(K µ2 ) = (2.416 ± ± 0.024) 10 5 NA48/2 (2004 data), presented at KAON07: About 4000 signal events from special minimum bias trigger. Small systematics, except background. (measured from data large statistical uncertainty in syst. error.) Completely uncorrelated with 2003 measurement. Γ(K e2 )/Γ(K µ2 ) = (2.455 ± ± 0.041) 10 5 Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.22/32

23 K e2 /K µ2 Measurements KLOE, presented at KAON07: About 8000 signal events from 1.7 fb 1. Statistics dominated by MC, conservative systematics estimation. Γ(K e2 )/Γ(K µ2 ) = (2.55 ± 0.05 ± 0.05) 10 5 Treatment of radiative corrections: SM prediction includes IB, excludes DE. All experiments measure inclusive Γ(K e2(γ) )/Γ(K µ2(γ) ), but correct for DE contributions. Direct Emission Inner Bremsstrahlung = Can easily be combined and compared with SM expectation. * E [GeV] γ Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.23/32

24 K e2 /K µ2 Measurements Combine all preliminary results and PDG2006: Γ(K e2 )/Γ(K µ2 ) = (2.457 ± 0.032) 10 5 (χ 2 /n dof = 2.44/3) Huge improvement w.r.t PDG 2006, σ rel. = 1.3% now! Perfect agreement with SM expectation. Clark, 1972 Heard, 1975 Heintze, PDG 2006 NA48/2 (2003), prel. 3 SM NA48/2 (2004), prel. 2 KAON07 KLOE, prelim Γ(K e2 ) / Γ(K µ2 ) [10 ] Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.24/32

25 K e2 /K µ2 Restrictions on New Physics Limit on LFV in H ± coupling: (Masiero, Paradisi, Petronzio, PRD 74, 2006) LFV Yukawa coupling: lh ± ν τ g 2 2 m τ M W 13 tan 2 β Lepton-flavour violating term: 13 (should be 10 3 from EW theory, but 0) tanβ < < 5x10-3 Limit on LFV in K e2 converts to limit on 13 = 13 (M H ±, tanβ): [ ( m R LFV K R SM 4 K 1 + K M 4 H ± )( m 2 τ M 2 e ) ] 13 2 tan 6 β < % CL limits charged higgs mass (GeV/c 2 ) Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.25/32

26 K e2 /K µ2 Comparison with B τν τ B ± τ ± ν τ Decays: Also in B ± τ ± ν τ : Possible transition via H ±, sensitivity to M H ±, tanβ. No LFV required = No 13 term Dependency on M H ±, tanβ: (Isidori, Paradisi,PLB 639,2006) ( ] m 2 2 B Br SUSY Br SM = [ 1 For non-tiny 13 : M 2 H ± ) tan 2 β 1 + ǫ 0 tanβ (ǫ ) Sensitivity to H ± in K e2 /K µ2 better than in B τν τ! tanβ B + b u W + H + τ + Br(B τν) = (1.42 ± 0.44) 10 4 (current BaBar/Belle average) B τν excluded 13 < < 5x charged higgs mass (GeV/c 2 ) ν 13 < % CL limits Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.26/32

27 K e2 /K µ2 Near Future KLOE: Has 20% more data on tape. Another 3000 events with other reconstruction method. Improve MC statistics & systematics = Should arrive at σ rel (R K ) ±1%. P-326: (also known as NA48/3) Similar setup as for NA48/2 (2004) prel. measurement, use of most parts of existing NA48 apparatus. Plan: 4 months (June-October 2007) run period = Collect K e2 decays. = Goal to reach σ rel (R K ) ±0.3%. Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.27/32

28 K e2 /K µ2 P-326 run 2007 Beam parameters 2007 optimized for K e2 /K µ2 w.r.t. 2004: Kaon mean momentum p: 60 GeV/c 75 GeV/c Kaon momentum bite p/p: ±3 GeV/c ±2.5 GeV/c p T kick from spectrometer magnet: 120 MeV/c 263 MeV/c = Improved kinematic separation of K e2! Minimum bias trigger: for K e2 : Hodoscope hits + min. energy in the LKr for K µ2 (downscaled): Just hodoscope (ǫ > 99%) Experience from 2004 run: Systematics under control. Only systematic > 0.2%: Background to K e2, error is statistical. V. Kozhuharov, KAON07 Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.28/32

29 Ke2 /Kµ2 P-326 run 2007 Background to Ke2 : Mainly Kµ2 in Ke2 sample. ptrack < 35 GeV/c: ( 43%) Kinematic separation 2 under Build Mmiss e-assumption ptrack > 35 GeV/c: ( 57%) x10 Electron identification Require electron-id from ELkr /ptrack electrons 3000 pions E/p: energy deposited in Lkr / track momentum Rainer Wanke, Universita t Mainz, KAON 2007, Frascati, May 24, 2007 p.29/32

30 K e2 /K µ2 P-326 run 2007 Problem at high momenta: Catastrophic energy-loss of of muons in the LKr. = mis-identified as electrons. Solution: Lead bar between hodoscope planes in front of LKr, covering 18% of acceptance = Only µ pass, E/p measured in LKr Kinematically selected K µ E/p 500 K e K µ2 bkg p track [GeV/c] Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.30/32

31 K e2 /K µ2 Expectations Expected precision on K e2 /K µ2 : Statistical: ±0.28% Systematic: ±0.2% Overall expected reach: SM 4.5 P-326, 2008? NA48/2 (2003), prel NA48/2 (2004), prel KLOE, prelim σ(r K )/R K ±0.32% -5 Γ(K e2 ) / Γ(K µ2 ) [10 ] tanβ KAON07: KAON09?! same R K central value 13 < < 5x10-3 tanβ % CL limits < < % CL limits charged higgs mass (GeV/c 2 ) < 5x < charged higgs mass (GeV/c 2 ) Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.31/32

32 Conclusions K l3 Decays: New BR results agree with SM expectation on 0.5% level. Theoretical uncertainties start to be important. Indication for non-sm couplings from NA48 K L µ3 decays needs to be investigated with data of other experiments. Ratio Γ(K e2 )/Γ(K µ2 ): Two new preliminary results reported by KLOE and NA48/2. = Precision on Γ(K e2 )/Γ(K µ2 ) now 1.3%. P-326 will perform dedicated run this year to reach σ rel (Γ(K e2 )/Γ(K µ2 )) 0.3% = Sensitivity to LFV in SUSY! Rainer Wanke, Universität Mainz, KAON 2007, Frascati, May 24, 2007 p.32/32