1. T violation search in K decays using stopped K + J. Imazato IPNS, KEK Workshop on Physics at an Upgraded Fermilab Proton Driver Workshop October 8, 2004 1. Transverse muon polarization in K +  2. KEK E246 experiment 3. Future experiments 4. J-PARC experiment

2. Transverse muon polarization in K + →  0  + K  3 decay form factors and T violation History of K  3 transverse polarization experiments K L →  −  + Bevatron 1967 Im  = -0.02 ±0.08 K L →  −  + Argonne 1973 Im  = -0.085 ±0.064 K L →  −  + BNL-AGS 1980 Im  = 0.009 ±0.030 K + →  0  + BNL-AGS 1983 Im  = -0.016 ±0.025 K + →  0  +  KEK-E246 2004 Im  = -0.0053 ±0.0071 ±0.0036 P T spurious ( Final State Interaction )= very small T-odd correlation

3. Features of K +  P T ■ Small standard model contribution – Bigi and Sanda “CP violation” (2000) – P T ~ 10 -7 ■ Small FSI spurious effects –Single photon contribution Zhitnitskii (1980) P T < ~ 10 -6 –Two photon contribution Efrosinin et al. PL B493 (2000) 293 P T ~ 4 x 10 -6 ■ High sensitivity to CP violation beyond the SM – Mult- Higgs doublet model – Leptoquark model – Some Supersymmetric models P T ~ 10 - 4 -10 - 3 Three Higgs doublet model SM FSI (example)

4.  Higgs doublet model L = (2√(2)G F ) 1/2  [  i U L KM D D R +  i U R M U KD L +  i N L M E E R ] H i + + h.c.    flavor conservation Im  = Im(  1  1 * ) × (m K / m H + ) 2 = Im(  1  1 * ) × ( v 2 /v 3 ) 2 × (m K / m H + ) 2 v i : vacuum expectation values  i,  i,  i : mixing matrix elements Only schematic K  P T v 2 /v 3 Im(  1  1 * ) Im(     *) (v 2 /v 3 ) 2 / M H 2 = 4.1×Im  GeV -2 

5. 3HDM : constraints from other experiments Neutron EDM (charged Higgs exchange) d n =C n Im(  1  1 *) < 0.63 x 10 -25 e cm ⇨ Im(  1  1 *) < ~10 b→s  A = A SM + A 3HDM (     *) ⇨ Im(     *) ≦ 3.2 (for m H ~2m Z ) [Grossman and Nir (1993), Kiers et al.(2000)]             but  stringent constraint b→X  A = A SM + A 3HDM (     *) Im(  i  i *)=Im(     *) (v 2 /v 3 ) 2 < 7400 (for m H ~2m Z ) [Grossman, Haber and Nir (1995)] c.f. P T : Im(     *) (v 2 /v 3 ) 2 = 1.36 ×10 5 Im  (for m H ~2m Z ) For v 2 /v 3 > ~ 10, P T is the most stringent constraint on 3HDM [Garisto and kane (1991)]

6. Other models Charged Higgs exchange Constraints on M H +  =tan  (  +A t cot  )/m g~ × Im[V 33 H+* V 32 D L * V 31 U R ] slepton exchange + down-type squark exchange Constraints on M Im[ 2i2 ( ’ i12 ) * ] and Im[ ’ 21k ( ’ 22k ) * ] scalar leptoquark exchange Constraints on k 2 /M  k 2

7. R- parity violating SUSY W = W MSSM + W RPV __ __ __ __ __ W RPV = ijk L i L j E k + ’ ijk L i Q j D k + ” Ijk U i D j D k L i, Q i : lepton and quark doublet superfield E i, D i, U i : electron, down- and up-quark singlet superfield Constraint from Im  on Im[ 2i2 ( ’ i12 ) * ]/M 2 and Im[ ’ 21k ( ’ 22k ) * ]/M 2 Constraint on from Im  E246) Im[ 2i2 ( ’ i12 ) * ] and Im[ ’ 21k ( ’ 22k ) * ]  ×   @ M=100 GeV  while constraint from other experiments : ≤ 4 × 10 -2 @ M=100 GeV

8. P T (K + →    no SM contribution, but induced by pseudoscalar interactions complementary to P T (K→  [Kobayashi et al. (1996)] FSI is not large : O(10 -4 ) [Efrosinin and Kudenko (1999), Hiller and Isidori (1999)] Model K +   0  + K +   +  ■ Standard Model <10 -7 <10 -7 ■ Final State Interactions <10 -5 <10 -3 ■ Multi-Higgs  10 -2  10 -2 P T (K +   0  + )  2 P T (K +   0  +  ) ■ SUSY with sqarks mixing  10 -3  3x10 -3 ■ SUSY with R-parity breaking  4x10 -4  3x10 -4 ■ Leptoquarks  10 -2  5x10 -3 E246 : P T = -0.0064 ± 0.0185 (stat) ± 0.0010 (syst) Phys. Letters B561, 166 (2003) P T = -0.0067 ± 0.0143 (stat) ± 0.0014 (syst)

9. KEK E246 experiment Japan ● KEK ● Univ. of Tsukuba, ● Tokyo Institute of Technology ● Univ. of Tokyo ● Osaka Univ. Russia ● Institute for Nuclear Research Canada ● TRIUMF ● Univ. of British Columbia ● Univ. of Saskatchewan ● Univ. of Montreal Korea ● Yonsei Univ. ● Korea Univ. U.S.A. ● Virginia Polytech Institute ● Princeton Univ. Taiwan ● National Taiwan Univ.

10. E246 experimental setup using stopped K + End viewSide view [J.Macdonald et al.; NIM A506 (2003) 60] K + →  0  +

11. E246 muon polarimeter Cross section One-sector view y(cm) B

12. Double ratio measurement CsI barrel fwd and bwd  0 /  P T directions fwd -    bwd -    Double ratio measurement 768 A fwd - A bwd A T = 2

13. E246 result and model implication P T = - 0.0017 ± 0.0023(stat) ± 0.0011(syst) ( |P T | < 0.0050 : 90% C.L. ) Im  = - 0.0053 ± 0.0071(stat) ± 0.0036(syst) ( |Im  | <0.016 : 90% C.L. ) [M.Abe et al., Phys. Rev. Letters 93 (2004) 131601] Three Higgs doublet model |Im  | < 0.016 (90% C.L.) ⇒ Im(  1  1 * ) < 2176 (at m H =2m Z ) cf. BR (B→X   ) ⇒ Im(  1  1 * ) < 7400 (at m H =2m Z ) [R.Garisto and G.Kane, Phys. Rev. D44 (1991)2789] v 2 / v 3 = m t /m  d n ~ 4/3 d d ∝ Im(  1  1 * ) × m d / m H 2 |Im  | < 0.016 (90% C.L.) ⇒ d n < 5 ×10 -27 e cm cf. d n exp < 6.3×10 -26 e cm KLKL K+K+

14. Systematic errors Source of Error  12fwd/bwd  P T x 10 4 e + counter r-rotationxo0.5 e + counter z-rotationxo0.2 e + counter f-offsetxo2.8 e + counter r-offsetoo<0.1 e + counter z-offsetoo<0.1  + counter f-offsetxo<0.1 MWPC  -offset (C4)xo2.0 CsI misalignmentoo1.6 B offset (  )xo3.0 B rotation (  x )xo0.4 B rotation (  z )xx5.3 K + stopping distributionoo<3.0  + multiple scatteringxx 7.1 Decay plane rotation (  r )xo1.2 Decay plane rotation (  z )xx0.7 K  2 DIF backgroundxo0.6 K + DIF backgroundox< 1.9 Analysis--3.8 Total11.4  12 : 12-fold rotational cancellation fwd/bwd :  0 forward/backward cancellation

15. Stopped K + vs. in-flight decay method stopped K + method in-flight-decay method Example E246 old BNL experiment K + beam momentum low p for stopping high p K + beam intensity low high Decay kinematics isotropic boosted forward  0 detection all directions only forward decay? Sensitive region to P T possible not always Kinematic resolution good poor Double ratio exp. possible difficult

16.  + polarization measurement for K  3 P T Method longitudinal field transverse field Configuration Observable Experiment E246 old BNL experiment Relative sensitivity 1 1/√2 Systematic error double ratio B field reverse reduction A T, -A T  t+  T, -  t+  T Matching with stopped K + good good Systematic error small ● error due to B reverse ● t 0 calibration necessary

17. Future T violation experiment and sensitivity limitations ■ Methodology : Stopped K + method rather than an in-flight decay experiment Double ratio measurement in the decay kinematic space Longitudinal field on the P T component ■ Desirable detector : Large K  3 acceptance Simultaneous K  P T measurement Small instrumental systematic errors ■ Sensitivity goal : E246 :  P T stat (E246) >  P T syst (E246) Future experiment (FE) :  P T syst (FE) ~ 1/10  P T syst (E246) ~ 10 -4  P T stat (FE) ~  P T syst (FE) ~ 10 -4  P T syst (FE) ~ 10 -4 might be feasible, but  P T syst (FE) ~ 10 -5 will be vey difficult.

18. E246 upgrade at J-PARC ? E246 was statistically limited. ■ Polarimeter field by a new magnet Parallel holding field of P T Precise field distribution alignment reduction of the most serious systematic error ■ Active polarimeter 4  solid angle for decay positron Energy and angle of measurements of positrons FoM =  √  = 3.8 x E246 ■ Upgrade of readout electronics Rate performance = 10 x E246 under the condition of K/  >>1 Merit Lower cost than a completely new setup Well known detector performance and systematics

19. Expectation for E246-upgrade Gain from E246 Polarimeter : 3.8 Beam intensity : √10 Run time : √0.66 Total = 9.8 Statistical error :  P T = 3.0 x 10 -4 Systematic errors  Total error  P T syst ~ 10 -4

20. New detector proposal at J-PARC To go down below 10 -4, we need a new detector. ■ Experiment principle stopped kaons double ratio detector azimuthal symmetry complete reconstruction of kinematics ■ Detector concept larger  + acceptance high resolution  0 measurement active polarimeter photon veto to measure K  ■ Most important requirement suppression of systematic errors to the 10 -4 level

21. J-PARC proposal L-19 Large solenoid ■ Field parameters Strength : 1-3 kG Alignment+symmetry : 10 -4 100  over 1m Field measurement with a rotating coils Allowed stray field : 100 mG Use of the field for  + and e + tracking K + -->     :  P T    :  P T ~10 -4 ■ Detector components Target  calorimeter Pre-shower counter  + tracker Polarimeter  veto counters Large solenoid

22. Vector correlation At J-PARC Higher beam rate Different conditions for up- and down-stream side Double ratio between left -going  0 and right-going  0

23. Symmetrization of K + stopping distribution z ■ Adjustment of null asymmetry A 0 = ( A left + A right )/2 N(z K )=symmetric => A 0 = 0 N(z K )=asymmetric=> A 0 ≠0 ■ A T = ( A left - A right )/2 No effect in A T from asymmetric z- distribution due to left-right cancellation but unknown higher order systematics Artificial z- symmetrization by using tracker ===> A 0 = 0  0 - L/R scheme ==> e + - F/B asymmetry measurement

24. Effects of magnetic field on polarization Cancellation between +  and -  Null asymmetry check Cancellation between left and right Presence of B field has no influence on the validity of experiment Same situation as in the zero field case z=0

25. Active polarimeter ■ Measurement of Muon stopping position Positron emission direction Positron energy Electromagnetic shower ■ location ■ energy deposit ■ Analysis Michel spectrum ■ Problem of use of plastics formation of muonium muon spin depolarization B=3kG enough for decoupling? Better choice will be muon tubes made of Al k k a system with the highest sensitivity to polarization

26. Rejection of K  2 background  +   < 79 o   < 39 o Optimization of K  2 background rejection by Opening angle cuts, and X-parameter cut on photon spectrum X= (E  1 -E  2 )/ (E  1 +E  2 ) K  2 was a significant background in E246..

27. Instrumental systematics Most dangerous systematics will be instrumental misalignments magnet   calorimeter Cancellation by azimuthal integration spurious  P T decay plane rotation

28. Sensitivity for  K   P T FoM =  √  Run time 1 = 10 7 s Loi-19 estimate based on fwd/bwd scheme _ 10 -5

29. Estimate of K  P T sensitivity 1. Photon energy 20 – 200 MeV 2. Muon energy  200 MeV 3.    120 O Acceptance per K +  0.7 x 10 -4 N( K +   +  )  0.7 x 10 10 Statistical sensitivity :  P T (1  )  0.7 x 10 -4 (estimate based on F/B scheme)

30. Kaon beam K0.8 at T1 target In Phase 1 for stopped K +/- beam T2 target in Phase2 p= 650~800 MeV/c K/  > 1 with two DCS’s  p/p < 3% K + intensity =10 6 ~ 10 7 /s low p kaon line

31. K + beam for stopped K + experiments K + stop = I p  K + (E p )  C T(p K )  stop (p K ) I p : proton beam intensity  K +(E p ) : K + production rate at E p ↑with E p  C : channel acceptance T(p K ) : channel transmission↑with p K  stop (p K ): stopping efficiency↓with p K K + /  + ratio ↓with p K Optimum p K @ E p =12 GeV (E246) : 650 MeV/c with one DCS @ E p = 30-50 GeV (J-PARC) : 650~800 MeV/c longer channel with two DCS’s  K + (E p ) : nearly constant with E p in the relevant E p region for p K = 650~800 MeV/c consideration on optimum beam momentum

32. Summary ■ Transverse muon polarization P T is a clean and very sensitive probe of new physics. ■ KEK-E246 has recently improved the limit of P T and Im . ■ Future experiments aiming for  P T ~10 -4 will be important and desired. ■ The experiment at J-PARC using a stopped beam will be very promising: K +   0  +  P T <10 -4 K +   +   P T ~ 10 -4