Low Energy Precision Measurements

Transcription

1 Low Energy Precision Measurements Shufang Su U. of Arizona For details, see review paper M. RamseyMusolf, S. Su, hepph/ S. Su

2 Precision measurements vs. direct detection (indirect) (direct) Direct vs. indirect detection provide complementary m t =178.0 ± 4.3 GeV information success of SM consistency check of any LEP EWWG new physics scenario LEP EWWG 2004 winter S. Su 2

3 Low energy precision measurements address questions difficult to study at high energy weak interactions (parity violation) high precision low energy experiment available size of loop effects from new physics: (α/π)(m/m new ) 2 muon g2: M=m µ, δ new 2x10 9, δ exp < 10 9 βdecay, πdecay: M=m W, δ new 10 3, δ exp 10 3 parityviolating electron scattering: M=m W, δ new /Q W e,p 10 more sensitive to new physics need δ exp 10 2 Q W e,p 14 sin 2 θ W 0.1 easier experiment probe new physics off the resonance sensitive to new physics not mix with S. Su 3

4 Outline Neutral current experiments Determination of sin2 θ eff Neutral current measurements PVES DISparity APV NuTeV Charge current processes Pure leptonic CC interactions: muon decay semileptonic CC processes pion leptonic decays neutron and nuclear β decay pion β decay kaon β decay Flavor, CP and Neutrinos µ eγ, µ e conversion EDM S. Su 4

5 Outline Neutral current experiments Determination of sin2 θ eff Neutral current measurements PVES DISparity APV NuTeV Charge current processes Pure leptonic CC interactions: muon decay semileptonic CC processes pion leptonic decays neutron and nuclear β decay pion β decay Flavor, CP and Neutrinos µ eγ, µ e conversion kaon β decay John Hardy, Superallowed nuclear beta decay: test of CVC and CKM unitarity Bertram Blank, New experimental studies of superallowed 0+ to 0+ decays EDM Nathal S. Su Severjins, Searches for physics beyond the standard electroweak model 4 in beta decay

6 Outline Neutral current experiments Determination of sin2 θ eff Neutral current measurements PVES DISparity APV NuTeV Charge current processes Pure leptonic CC interactions: muon decay semileptonic CC processes pion leptonic decays neutron and nuclear β decay pion β decay kaon β decay Flavor, CP and Neutrinos µ eγ, µ e conversion EDM S. Su 4

7 Outline Neutral current experiments Determination of sin2 θ eff Neutral current measurements PVES DISparity Oscar NaviliatCuncic, The neutron electric dipole moment Jon Engel, Schiff moments and atomic EDMs Eli Ben Haim, Overview of CP violation in the quark sector Mauro Mezzetto, Future CP violation searches in the lepton sector Annelise Malkus, Physics beyond the Standard Models of particle and solar physics with solar neutrinos APV S. Su 4 NuTeV Hiro Ejiri, Present and future of double beta decay searches Charge current processes Pure leptonic CC interactions: muon decay semileptonic CC processes pion leptonic decays neutron and nuclear β decay Fedor Simkovic, Double beta decay: a problem of particles, nuclear and atomic physics Serguey Petcov, Neutrino mixing, dirac and majorana leptonic CPviolation and the baryon asymmetry of the Universe Rimantas Lazauskas, Aspect of neutrino interaction studies using beta beams Julien Welzel, The neutrino magnetic moment and nucleosysthesis George Fuller, Surprising new results on neutrino flavor transformation in supernovae... pion β decay Flavor, CP and Neutrinos µ eγ, µ e conversion kaon β decay EDM

8 Outline Neutral current experiments Determination of sin2 θ eff Neutral current measurements PVES DISparity APV NuTeV Charge current processes Pure leptonic CC interactions: muon decay semileptonic CC processes pion leptonic decays neutron and nuclear β decay pion β decay kaon β decay Flavor, CP and Neutrinos µ eγ, µ e conversion EDM S. Su 4

9 Neutral Current experiments S. Su 5

10 Møller Scattering e e γ e e Purely Leptonic QWeak (JLab) e γ Coherent quarks in p Results in ~2009 2(2C 1u +C 1d ) e DISParity p n e γ Isoscaler quark scattering (2C 1u C 1d )+Y(2C 2u C 2d ) e Atomic Parity Violation e γ Cs 133 Coherent quarks in entire nucleus Nuclear structure uncertainties 376 C 1u 422 C 1d Neutrino Scattering ν µ ν S. Su 6 Courtesy of P. Reimer and R. Arnold W + Quark scattering (from nucleus) Weak charged and neutral current difference ν

11 Test of sin 2 θ W running Weak mixing angle sinθ W g sinθ W = g cosθ W = e Q W e Jlab Moller Qweak SLAC E158 NuTeV Cs APV Standard Model Prediction Erler, Kurylov & RamseyMusolf, Phys. Rev. D 72, (2005) DISparity S. Su 7

12 Precision of sin 2 θ W determination Measurement Δsin 2 θ W /sin 2 θ W Δsin 2 θ W pole 0.07% % Q w (Cs) 0.7% NuTeV 0.7% % Q w (e) SLAC 0.5% % Q w (e) Jlab 0.1% (on par with pole) 4% Q W (p) 0.3% % DISparity 0.45% reactor based νee scattering 1% Joao S. Su H. De Jesus, Measurement of the Weinberg angle with betabeams 8

13 Sensitivity to new physics scale RamseyMusolf(1999) Λ: new physics scale O(1) Take δq Wp =4% courtesy of Carlini probe new physics scale comparable to LHC confirmation of LHC discovery (couplings, charges) S. Su 9

14 Misc. model sensitivities (nonsusy) Experiment M( Χ ) M( LR ) (TeV) (TeV) Leptoquarks M LQ (up) M LQ (down) (TeV) (TeV) Courtesy of D. Mack Compositeness (LL) eq (TeV) direct limits ee (TeV) EW fit % Q w (Cs) % Q w (e) % Q w (e) % Q w (p) under construction scaled from RMusolf, PRC 60 (1999), Collider limits from Erler and Langacker, hepph/ S. Su 10

15 Moller and Qweak A V weak charge Q W f = 2g f V = 2 If 3 4Q f s2 S. Su 11

16 Moller and Qweak Q W p (Qweak) Q W e (SLAC) Q W e (Jlab) Q e,p W tree 14s 2 (14s 2 ) Q e,p W loop q GeV GeV GeV 2 A LR 0.29 ppm ppm 0.04 ppm exp precision 4% 13% 2.5% δ sin 2 θ W clean environment: Hydrogen target theoretically clean: small hadronic uncertainties tree level 0.1 sensitive to new physics S. Su 12

17 SUSY contributions Kurylov, RamseyMusolf, Su (2003) RPV 95% CL No SUSY DM MSSM loop S. Su 13

18 SUSY contributions Kurylov, RamseyMusolf, Su (2003) RPV 95% CL No SUSY DM MSSM loop 4% Qweak S. Su 13

19 SUSY contributions Kurylov, RamseyMusolf, Su (2003) RPV 95% CL No SUSY DM MSSM loop 4% Qweak Future 2.5% Moller S. Su 13

20 Correlation between Q Wp, QW e Distinguish new physics Δ Q W p Erler, Kurylov and RamseyMusolf (2003) Δ Q W e exp MSSM extra RPV SUSY leptonquark ± SM ± SM Distinguish via APV Q W Cs S. Su 14

21 Correlation between Q Wp, QW e Distinguish new physics Δ Q W p Erler, Kurylov and RamseyMusolf (2003) Δ Q W e exp MSSM extra RPV SUSY leptonquark ± SM ± SM Distinguish via APV Q W Cs Combinations of NC exps could be used to distinguish various new physics S. Su 14

22 Extract Q W p use kinematics to simplify: at forward angle θ Musolf et. al., (1994) measure F(θ,q 2 ) over finite range in q 2, extrapolate F to small q 2 existing PVES: SAMPLE, HAPPEX, G0, A4 minimize effect of F by making q 2 small q GeV 2, still enough statistics δ Q p W / Qp W hadronic effects 2 % S. Su 15

23 Extract Q W p use kinematics to simplify: at forward angle θ Musolf et. al., (1994)? measure F(θ,q 2 ) over finite range in q 2, extrapolate F to small q 2 existing PVES: SAMPLE, HAPPEX, G0, A4 minimize effect of F by making q 2 small q GeV 2, still enough statistics δ Q p W / Qp W hadronic effects 2 % S. Su 15

24 Extract Q W p use kinematics to simplify: at forward angle θ Musolf et. al., (1994)? measure F(θ,q 2 ) over finite range in q 2, extrapolate F to small q 2 existing PVES: SAMPLE, HAPPEX, G0, A4 minimize effect of F by making q 2 small q GeV 2, still enough statistics δ Q p W / Qp W hadronic effects 2 % S. Su 15

25 QCD correction to ep scattering P Box diagram contribution to Q W e p e p Erler, Kurylov and RamseyMusolf (2003) e p W δ Q W P W γ e p e p e p 26% 3% 6% k loop O(m W ) k loop O(m ) Λ QCD < k loop < O(m ) using OPE (pqcd) δ Q P W (QCD) 0.7% 0.08% nonperturbative S. Su 16

26 QCD correction to ep scattering P Box diagram contribution to Q W e p e p Erler, Kurylov and RamseyMusolf (2003) e p e p W δ Q W P W γ γ e p e p e p e p 26% 3% 6% k loop O(m W ) k loop O(m ) Λ QCD < k loop < O(m ) using OPE (pqcd) δ Q P W (QCD) 0.7% 0.08% nonperturbative S. Su 16

27 QCD correction to ep scattering P Box diagram contribution to Q W e p e p Erler, Kurylov and RamseyMusolf (2003) e p e p W δ Q W P W γ γ e p e p e p e p 26% 3% 6% k loop O(m W ) k loop O(m ) Λ QCD < k loop < O(m ) using OPE (pqcd) δ Q P W (QCD) 0.7% 0.08% nonperturbative S. Su 16

28 QCD correction to ep scattering P Box diagram contribution to Q W e p e p Erler, Kurylov and RamseyMusolf (2003) e p e p δ Q W P W noncalculable W γ γ e p e p e p e p 26% 3% 6% k loop O(m W ) k loop O(m ) Λ QCD < k loop < O(m ) using OPE (pqcd) δ Q P W (QCD) 0.7% 0.08% nonperturbative S. Su 16

29 QCD correction to ep scattering P Box diagram contribution to Q W e p e p Erler, Kurylov and RamseyMusolf (2003) e p e p δ Q W P W suppression noncalculable W γ γ e p e p e p e p 26% 3% 6% k loop O(m W ) k loop O(m ) Λ QCD < k loop < O(m ) using OPE (pqcd) δ Q P W (QCD) 0.7% 0.08% nonperturbative S. Su 16

30 QCD correction to ep scattering P Box diagram contribution to Q W e p e p Erler, Kurylov and RamseyMusolf (2003) e p e p Similar to nuclear βdecay W δ Q W P e ν e γ W suppression noncalculable p γ γ e p e p e p e p 26% 3% 6% kw loop O(m W ) k loop O(m ) Λ QCD < k loop < O(m ) n using OPE (pqcd) δ Q P W (QCD) 0.7% 0.08% nonperturbative S. Su 16

31 QCD correction to ep scattering P Box diagram contribution to Q W e p e p Erler, Kurylov and RamseyMusolf (2003) e p e p Similar to nuclear βdecay W δ Q W P e ν e γ W suppression noncalculable p γ γ e p e p e p e p 26% 3% 6% kw loop O(m W ) k loop O(m ) Λ QCD < k loop < O(m ) n C using OPE (pqcd) nonperturbative γw < 2 (CKM unitarity) δ Q P W (QCD) C 0.7% γ < % 0.65% S. Su 16

32 QCD correction to ep scattering P Box diagram contribution to Q W e p e p Erler, Kurylov and RamseyMusolf (2003) e p e p W δ Q W P W γ γ e p e p e p e p 26% 3% 6% k loop O(m W ) k loop O(m ) Λ QCD < k loop < O(m ) using OPE (pqcd) nonperturbative δ Q P W (QCD) 0.7% 0.08% 0.65% S. Su 16

33 QCD correction to ep scattering P Box diagram contribution to Q W e p e p Erler, Kurylov and RamseyMusolf (2003) e p e p W δ Q W P W γ γ e p e p e p e p 26% 3% 6% k loop O(m W ) k loop O(m ) Λ QCD < k loop < O(m ) using OPE (pqcd) nonperturbative δ Q P W (QCD) 0.7% 0.08% 0.65% Total theoretical uncertainty 0.8% S. Su 16

34 DISparity: ed scattering Longitudinally polarized electrons on unpolarized deuterium target Cahn and Gilman (1978) e e δ A d /A d = 0.8% δ sin 2 θ W /sin 2 θ W = 0.45% S. Su 17

35 Ranges of C 1u, C 1d, C 2u, C 2d Courtesy of P. Reimer S. Su 18

36 Ranges of C 1u, C 1d, C 2u, C 2d Courtesy of P. Reimer S. Su 18

37 Atomic parity violation Two approaches rotation of polarization plane of linearly polarized light apply external E field parity forbidden atomic transition Boulder group: cesium APV 0.35% exp uncertainty wood et. Al. (1997) S. Su 19

38 Atomic parity violation Two approaches rotation of polarization plane of linearly polarized light apply external E field parity forbidden atomic transition Boulder group: cesium APV 0.35% exp uncertainty wood et. Al. (1997) Q W Cs (exp) = ± 0.48 Q W Cs (SM)=72.09 (3) agree S. Su 19

39 Sensitivity to new physics Distinguish new physics MSSM δ Q W (,N)=(2+N) δ Q W u +(2N+) δ QW d δ Q W u >0 δ Q W d <0 δ Q W (,N) / Q W (,N) < 0.2 % for Cs δ Q W p δ Q W e δ Q W Cs exp MSSM extra ± ± small SM SM sizable Erler, Kurylov and RamseyMusolf (2003) S. Su 20

40 NuTeV experiment NC CC g L,R2 =(ε u L,R )2 +(ε d L,R )2 δr ν = ± δr ν = ± exp fit (ρ=1): sin2 θ W onshell = ± SM fit to pole: sin2 θ W onshell = ± (3 σ away) S. Su 21

41 NuTeV anomaly SM QCD effects: nuclear shadowing Miller and Thomas (2002), eller et. Al. (2002), Kovalenkov, schmidt and Yang (2002) asymmetry in strange sea distribution Davidson, Forte, Gambino, Rius and Strumia (2002), Goncharov et. al. (2001) isospin symmetry breaking Bodek et. al. (1999), eller et. Al. (2002) QCD corrections Dobrescu and Ellis (2003), Kretzer et. al. (2003), Davidson et. al. (2002) S. Su 22

42 New physics explanation Difficult! Supersymmetry: δ R ν, ν > 0 Kurylov, RamseyMusolf, Su (2003), Davidson, Forte, Gambino, Rius and Strumia (2002) Extra : family nonuniversal, finetuning Langacker and Plumacher (2000) Leptoquark: tune mass splitting Davidson, Forte, Gambino, Rius and Strumia (2002) ν µ mixing with extra heavy neutrino: constraints from other observables Babu and Pati (2002), Loinaz et. al. (2003) S. Su 23

43 New physics explanation Difficult! Supersymmetry: δ R ν, ν > 0 Kurylov, RamseyMusolf, SS (2002) Kurylov, RamseyMusolf, Su (2003), Davidson, Forte, Gambino, Rius and Strumia (2002) Extra : family nonuniversal, finetuning Langacker and Plumacher (2000) Leptoquark: tune mass splitting Davidson, Forte, Gambino, Rius and Strumia (2002) ν µ mixing with extra heavy neutrino: MSSM constraints from other observables Babu and Pati (2002), Loinaz et. al. (2003) RPV S. Su 23

44 Charged Current Processes S. Su 24

45 Charged current processes PV asymmetry in the beta decay of polarized 60 Co and µ + decay confirmation of PV weak interaction and VA structure muon life time Gµ (9x10 6 ), one of the three exp input nuclear β decay Vud (most precisely known CKM element) branching ratio of kaon leptonic decay Vus, test of CKM unitarity comparison of Γ(π µνµ(γ)) and Γ(π eνe(γ)) test of universality in CC leptonic interaction at few parts per thousand level S. Su 25

46 Recent developments Recent experimental developments New measurements of Michel parameters that characterize the µ decay New effort to measure τ μ with an order of magnitude improvement in precision Recent penning trap measurement of superallowed nuclear βdecay Q values test of CKM unitarity New measurement of τ n and decay correlation coefficients determine Vud free from possible nuclear structure ambiguities New measurements of Kaon leptonic decay branching ratios Vus Improved precision in pion βdecay branching ratios New effort to measure Ratio Re/µ = Γ(π eνe(γ))/γ(π µνµ(γ)) S. Su 26

47 Recent developments Recent theoretical developments New analysis in strong interaction uncertainties in Δrβ V that associated with Wγ box graphs reduced theoretical uncertainties in Vud from β decay rate by a factor of two Computations of O(p 6 ) loop correction to kaon decay form factor f+ K (t) Vus from kaon decay branching ratio New analysis of O(p 6 ) counterterm contributions to f+ K (0) using large Nc QCD and lattice QCD computations S. Su 27

48 Charged current processes Pure leptonic CC interactions: muon decay semileptonic CC processes pion leptonic decays neutron and nuclear β decay pion β decay kaon β decay S. Su 28

49 Charged current processes Pure leptonic CC interactions: muon decay semileptonic CC processes pion leptonic decays neutron and nuclear β decay pion β decay kaon β decay S. Su 28

50 Muon decay muon decay spectrum, angular distribution and electron polarization are described by 11 Michel parameters { dγ = G2 µm 5 µ dω 1 + h(x) 192π 3 4π x2 dx 1 + 4η(m e /m µ ) ±P µ ξ cos θ [ 4(1 x) δ(8x 6) + α 2π in SM, ρ = δ = 3/4, P µ ξ = 1, and η = 0, [ 12(1 x) + 4 [ 3 ρ(8x 6) + 24 m e { (1 x) m µ x ] η ] } g(x), (91) x 2 x = p e / p e max, θ = cos 1 (ˆp e ŝ µ ), entum dependent radiative correcti η affect τ µ in pure (VA) theory 1 τ µ = m5 µ 192π 3 G2 µ [1 + δ QED ] [ 1 + 4η m e m µ 8 Danneberg et. al. (2005) ( me m µ ) 2 ] [ ( mµ M W ) 2 ] S. Su 29

51 Muon decay muon decay spectrum, angular distribution and electron polarization are described by 11 Michel parameters { dγ = G2 µm 5 µ dω 1 + h(x) 192π 3 4π x2 dx 1 + 4η(m e /m µ ) ±P µ ξ cos θ [ 4(1 x) δ(8x 6) + α 2π in SM, ρ = δ = 3/4, P µ ξ = 1, and η = 0, [ 12(1 x) + 4 [ 3 ρ(8x 6) + 24 m e { (1 x) m µ x ] η ] } g(x), (91) x 2 x = p e / p e max, θ = cos 1 (ˆp e ŝ µ ), entum dependent radiative correcti η affect τ µ in pure (VA) theory Danneberg et. al. (2005) η = (71±37±5) 10 3 (transverse positron polarization from µ + decay) increase in the δgµ by a factor of 40 S. Su 29

52 Muon decay effective, four fermion lagrangians (SM, g LL V =1) µ ν ν µ L µ decay = 4G µ 2 γ g γ ɛµ ēɛγ γ ν e ν µ Γ γ µ µ ν e χ + χ gll V and grr S (few X10 4 ) l e 1 ξ δ ρ = 2 gv RR gs RR gs LR 2gT LR 2 ξ =... Exp result: Stoker et. al. (1985); Jodidio et. al. (1986) P µ ξ δ = ± ρ ξ = 1.00 ± 0.04 grr S < 90% C.L. Gagliardi, Tribble and Williams (2005) S. Su 30

53 Michel parameters present limit is about two order of magnitude larger than SUSY expectations direct probe of g RR S loop via Michael parameters is challenging g RR S contribution to η could be large enough to affect the extraction of Gµ from τµ G µ G µ = m e Re gll V gs, RR, loop + ppm effect in m µ gll V 2 Gµ PSI experiment S. Su 31

54 [ ] Pion leptonic decay Γ(π+ µ + ν(γ)) pion decay constant Fπ [ 1 α π Γ[π + l + ν l (γ)] = G2 µ V ud 2 Fπ 2 m π m 2 l 4π { 3 2 ln µ + m C 1 (µ) + C 2 (µ) m2 l π Λ 2 χ ln µ2 m 2 l [ 1 m2 l m 2 π + C 3 (µ) m2 l Λ 2 χ ] 2 [ 1 + 2α π ln M µ ] }] [ α ] π F (x) Marciano and Sirline (1993) S. Su 32

55 [ ] Pion leptonic decay Γ(π+ µ + ν(γ)) pion decay constant Fπ [ 1 α π Γ[π + l + ν l (γ)] = G2 µ V ud 2 Fπ 2 m π m 2 l 4π { 3 2 ln µ + m C 1 (µ) + C 2 (µ) m2 l π Λ 2 χ ln µ2 m 2 l [ 1 m2 l m 2 π + C 3 (µ) m2 l Λ 2 χ ] 2 [ 1 + 2α π ln M µ ] }] [ α ] π F (x) Marciano and Sirline (1993) incalculable nonperturbative QCD effects ±0.56% uncertainty in Γ (dominating) S. Su 32

56 [ ] Pion leptonic decay Γ(π+ µ + ν(γ)) pion decay constant Fπ [ 1 α π Γ[π + l + ν l (γ)] = G2 µ V ud 2 Fπ 2 m π m 2 l 4π { 3 2 ln µ + m C 1 (µ) + C 2 (µ) m2 l π Λ 2 χ ln µ2 m 2 l [ 1 m2 l m 2 π + C 3 (µ) m2 l Λ 2 χ ] 2 [ 1 + 2α π ln M µ ] }] [ α ] π F (x) Marciano and Sirline (1993) S. Su 32

57 [ ] Pion leptonic decay Γ(π+ µ + ν(γ)) pion decay constant Fπ [ 1 α π Γ[π + l + ν l (γ)] = G2 µ V ud 2 Fπ 2 m π m 2 l 4π { 3 2 ln µ + m C 1 (µ) + C 2 (µ) m2 l π Λ 2 χ ln µ2 m 2 l [ 1 m2 l m 2 π + C 3 (µ) m2 l Λ 2 χ ] 2 [ 1 + 2α π ln M µ ] }] [ α ] π F (x) Marciano and Sirline (1993) pion lifetime (±0.02%), leptonic branching ratio (± %) F π = 92.4 ± ± 0.25 Vud Ci(mρ) MeV S. Su 32

58 [ ] Pion leptonic decay Γ(π+ µ + ν(γ)) pion decay constant Fπ [ 1 α π Γ[π + l + ν l (γ)] = G2 µ V ud 2 Fπ 2 m π m 2 l 4π { 3 2 ln µ + m C 1 (µ) + C 2 (µ) m2 l π Λ 2 χ ln µ2 m 2 l [ 1 m2 l m 2 π + C 3 (µ) m2 l Λ 2 χ ] 2 [ 1 + 2α π ln M µ ] }] [ α ] π F (x) Marciano and Sirline (1993) pion lifetime (±0.02%), leptonic branching ratio (± %) F π = 92.4 ± ± 0.25 Vud Ci(mρ) MeV measurement of Γ(π+ µ + ν(γ)) does not provide a probe of new physics effects; new physics alter the extracted value of Fπ. e.g., RPV SUSY, 0.25% in Fπ. S. Su 32

59 ( ) { ( [ Re/µ [ To circumvent the hadronic matrix element uncertainties, consider R e/µ = Γ[π+ e + ν e (γ)] Γ[π + µ + ν µ (γ)] { [ Re/µ SM ˆr A π (e) ˆr π A (µ) ] } new test of lepton universality. SM prediction R SM e/µ = ( ± ) 10 4 Marciano and Sirline (1993) = ( ± ) 10 4 Decker and Finkemeier (1994) World average (TRIUMF and PSI) R EXP T e/µ = (1.230 ± 0.004) 10 4 Future improvement: TRIUMF: < 1X10 3 ; PSI: < 5X10 4 S. Su 33

60 Re/µ : SUSY contributions RamseyMusolf, SS, Tulin (2007) ing the future expected experimental precision [18], assu SUSY loop µ) = +. It is clear that R SUSY e/µ is largest in 10 x 10!3 ns where either (1) µ is small, m ul is large, and st contributions to Re/µ SUSY are from V + L, 8 with Qweak is large, m ul is small, and the largest contri 6 Re/µ SUSY is from B. If both µ and m ul are n R SUSY 4 future e/µ can still be very small due to can, even though both V + L and B contrire large individually. More precisely, to satisfy 2 0 need either µ 150 GeV and m ul 175 GeV, current 50 GeV and m ul 200 GeV (for our particue of fixed parameters, which have been chosen!2 SUSY RPV toward large Re/µ SUSY ).! ! " 11k x 10! m e m Μ CONTRIBUTIONS FROM RPARITY FIG. 11: Present 95% C.L. constraints on RPV param VIOLATING PROCESSES j1k, j = 1, 2 that enter R e/µ obtained from a fit to cision electroweak observables. Interior of the blue con S. Su corresponds to the fit using the current value of R 34 e/µ / [15, 16], while the red (light) contour corresponds to the fi SUSY R e Μ R e Μ e L, µ L! " 21k

61 Pion β decay rate for pion βdecay G V β Vud (theoretical error: ±0.0005) Γ(π β ) = (Gβ V )2 m 5 π f π +(0) 2 I(λ π +) 64π 3 PIBETA Pocanic B πβ(γ) = [ et. al. (2004) ± 0.004(stat) ± 0.004(sys) ± 0.003(π ] e2(γ)) 10 8 ten times larger than the theoretical error fifteen times larger than combined exp+theory uncertainty in superallowed β decay ft value S. Su 35

62 Pion β decay rate for pion βdecay G V β Vud (theoretical error: ±0.0005) Γ(π β ) = (Gβ V )2 m 5 π f π +(0) 2 I(λ π +) 64π 3 PIBETA Pocanic B πβ(γ) = [ et. al. (2004) ± 0.004(stat) ± 0.004(sys) ± 0.003(π ] e2(γ)) 10 8 ten times larger than the theoretical error fifteen times larger than combined exp+theory uncertainty in superallowed β decay ft value need considerable improvement in both the exp and theory side S. Su 35

63 Kaon decays and Vus CKM unitarity V ud 2 + V us 2 + V ub 2 = 1 SM V ud = (11)(15)(19) V ub = ± superallowed β decay too small to affect the unitarity test Vus: critically important (value and its uncertainty) determination of V us: branching ratio for Kl3 decays K πlν dγ(k + l3 ) = G2 µ m5 K 128π 3 S EWC(t) V us 2 f K + (0) 2 [ 1 + λk + t m 2 π ] 2 [ K SU(2) + 2 Kl EM ] S. Su 36

64 Kaon decays and Vus CKM unitarity V ud 2 + V us 2 + V ub 2 = 1 SM V ud = (11)(15)(19) V ub = ± superallowed β decay too small to affect the unitarity test Vus: critically important (value and its uncertainty) determination of V us: branching ratio for Kl3 decays K πlν dγ(k + l3 ) = G2 µ m5 K 128π 3 S EWC(t) V us 2 f K + (0) 2 [ 1 + λk + t m 2 π Ktoπ transition form factor ] 2 [ K SU(2) + 2 Kl EM ] S. Su 36

65 Kaon decays and Vus CKM unitarity V ud 2 + V us 2 + V ub 2 = 1 SM V ud = (11)(15)(19) V ub = ± superallowed β decay too small to affect the unitarity test Vus: critically important (value and its uncertainty) determination of V us: branching ratio for Kl3 decays K πlν dγ(k + l3 ) = G2 µ m5 K 128π 3 S EWC(t) V us 2 f K + (0) 2 [ 1 + λk + t m 2 π ] 2 [ K SU(2) + 2 Kl EM corrections generated by the breaking of flavor SU(2) and long distance EM corrections ] S. Su 36

66 Kaon decays and Vus CKM unitarity V ud 2 + V us 2 + V ub 2 = 1 SM V ud = (11)(15)(19) V ub = ± superallowed β decay too small to affect the unitarity test Vus: critically important (value and its uncertainty) determination of V us: branching ratio for Kl3 decays K πlν dγ(k + l3 ) = G2 µ m5 K 128π 3 S EWC(t) V us 2 f K + (0) 2 [ 1 + λk + t m 2 π ] 2 [ K SU(2) + 2 Kl EM ] S. Su 36

67 Kaon decays and Vus CKM unitarity V ud 2 + V us 2 + V ub 2 = 1 SM V ud = (11)(15)(19) V ub = ± superallowed β decay too small to affect the unitarity test Vus: critically important (value and its uncertainty) determination of V us: branching ratio for Kl3 decays K πlν dγ(k + l3 ) = G2 µ m5 K 128π 3 S EWC(t) V us 2 f K + (0) 2 [ 1 + λk + t m 2 π ] 2 [ K SU(2) + 2 Kl EM to test CKM unitarity at 0.1% level, must include Δ SU(2) K and ΔEM K l determine f + K (0) with 1% uncertainty or better ] S. Su 36

68 Vus new determination of K l3 Br + exp values for λ+ K and C(t) KTeV, KLOE, NA48 V us [ f K + (0)/0.961 ] = (9) Leutwyler and Roos (1984) f K + (0) large NC = ± Cirigliano et. al. (2005) f+ K (0) lattice = first row CKM V ud 2 + V us 2 + V ub 2 = ± stat ± sys quenched, Wilson[119] 0.962(6)(9) unquenched, staggered[120] 0.952(6) unquenched, Wilson[121] 0.955(12) unquenched, doman wall[122] { ± , large N C [118] ± , unquenched lattice, domain wall[122] can be used to test new physics e.g. SUSY, see Kurylov and RamseyMusolf (2002) S. Su 37

69 Conclusion Precision measurements played an important role in developing and testing SM They will be a crucial tool in probing new physics beyond the SM Low energy precision measurement can probe new physics not mix with (comparing with pole precision observables) precision frontier Complementary to what we may learn from LHC Opportunities and challenges (0.1%) for both experimentalists and theorists S. Su 38

70 back up slides S. Su 39

71 Neutron and nuclear β decay superallowed β decay: state, transition matrix element independent of nuclear structure initial/final state with nonzero spin: depend strongly on the details of hadronic and nuclear structure need both decay rate and one or more decay correlation coefficients K ft = (G β V )2 MF 2 + (Gβ A )2 MGT 2 K = (2π 3 ln 2)( c) 6 /(m e c 2 ) 5 dγ N (E e ) + σ { 1 + a p e p ν E e E ν + b Γm [ e + J E A p e + B p ν + D p e p ν e E e E ν E e E ν ] } dω e dω ν de e, [ N J + G p e E e + Q ˆp eˆp e J + R J p e E e ] S. Su 40

72 Superallowed nuclear decays M GT=0, ft only depends on M F G V β V ud Determination of half lives requires total decay half time branching ratio of decay to the 0+ ground state of the daughter nucleus energy release in the decay, or the Qvalue S. Su 41

73 β decay correlations beta spectral shape, angular distribution, polarization non (VA) (VA) interactions, Vud S. Su 42