T violation search in K decays using stopped K+

J. ImazatoIPNS, KEK

Workshop on Physics at an Upgraded FermilabProton Driver Workshop

October 8, 2004

1. Transverse muon polarization in K+

2. KEK E246 experiment3. Future experiments4. J-PARC experiment

Transverse muon polarization in K+→0+

K3 decay form factors and T violation

History of K3 transverse polarization experiments

• KL→−+ Bevatron 1967 Im = -0.02 ±0.08• KL→−+ Argonne 1973 Im = -0.085 ±0.064• KL→−+ 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

PTspurious(Final State Interaction)= very small

T-odd correlation

Features of K+ PT

■ Small standard model contribution

– Bigi and Sanda “CP violation” (2000)– PT ~ 10-7

■ Small FSI spurious effects– Single photon contribution Zhitnitskii (1980) PT < ~ 10-6

– Two photon contribution Efrosinin et al. PL B493 (2000) 293 PT ~ 4 x 10-6

■ High sensitivity to CP violation beyond the SM

– Mult- Higgs doublet model– Leptoquark model– Some Supersymmetric models PT ~ 10- 4-10- 3

Three Higgs doublet model

SM

FSI (example)

Higgs doublet model

L = (2√(2)GF)1/2 [iULKMDDR + iURMUKDL + iNLMEER] Hi+ + h.c.

flavor conservation

Im = Im(11*) × (mK / mH+)2

= Im(11*) × (v2 /v3)2 × (mK / mH+)2

vi : vacuum expectation valuesi, i, i : mixing matrix elements

Only schematic

K PT

v2 /v3

Im(

11* )

Im(*) (v2 /v3 )2 / MH2 = 4.1×ImGeV-2

3HDM : constraints from other experiments

Neutron EDM (charged Higgs exchange)dn=Cn Im(11*) < 0.63 x 10-25 e cm ⇨ Im(11*) < ~10

b→sA = ASM + A3HDM(*) ⇨ Im(*) ≦ 3.2 (for mH ~2mZ)

[Grossman and Nir (1993), Kiers et al.(2000)]

but stringent constraint b→X

A = ASM + A3HDM(*)Im(ii*)=Im(*) (v2 /v3 )2 < 7400 (for mH ~2mZ)

[Grossman, Haber and Nir (1995)]

c.f. PT : Im(*) (v2 /v3 )2 = 1.36 ×105 Im(for mH ~2mZ) For v2 /v3 > ~ 10, PT is the most stringent constraint on 3HDM [Garisto and kane (1991)]

Other models

Charged Higgs exchangeConstraints onMH+

=tan(+Atcot)/mg~

× Im[V33H+* V32

DL * V31UR]

slepton exchange +down-type squark exchangeConstraints onMIm[2i2(’i12)*] and Im[’21k(’22k)*]

scalar leptoquark exchangeConstraints on k

2/Mk2

R- parity violating SUSY

W = WMSSM + WRPV __ __ __ __ __

WRPV =ijkLiLjEk + ’ijkLiQjDk + ”IjkUiDjDk

Li, Qi : lepton and quark doublet superfield

Ei, Di , Ui : electron, down- and up-quark singlet superfield

Constraint from Im on Im[2i2(’i12)*]/M2 and Im[’21k(’22k)*]/M2

Constraint on from ImE246) Im[2i2(’i12)*] and Im[’21k(’22k)*] ×@ M=100 GeVwhile constraint from other experiments : ≤ 4 × 10-2 @ M=100 GeV

PT (K+→no SM contribution, but induced by pseudoscalar interactionscomplementary to PT (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

PT(K+ 0+) 2 PT(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 : PT = -0.0064 ± 0.0185 (stat) ± 0.0010 (syst) Phys. Letters B561, 166 (2003)

PT = -0.0067 ± 0.0143 (stat) ± 0.0014 (syst)

KEK E246 experiment

Japan ● KEK ● Univ. of Tsukuba, ● Tokyo Institute of Technology

● Univ. of Tokyo ● Osaka Univ.Russia ● Institute for Nuclear ResearchCanada ● TRIUMF ● Univ. of British Columbia

● Univ. of Saskatchewan ● Univ. of MontrealKorea ● Yonsei Univ. ● Korea Univ.U.S.A. ● Virginia Polytech Institute ● Princeton Univ.Taiwan ● National Taiwan Univ.

E246 experimental setup using stopped K+

End view Side view

[J.Macdonald et al.; NIM A506 (2003) 60]

K+→0+

E246 muon polarimeter

Cross section One-sector view

y(cm)

B

Double ratio measurement

CsI barrel fwd and bwd 0 /

PT directions

fwd -bwd -

Double ratio measurement

768

Afwd - AbwdAT = 2

E246 result and model implication

PT = - 0.0017 ± 0.0023(stat) ± 0.0011(syst) ( |PT | < 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(11*) < 2176 (at mH=

2mZ) cf. BR (B→X) ⇒ Im(11

*) < 7400 (at mH=2mZ)

[R.Garisto and G.Kane, Phys. Rev. D44 (1991)2789] v2/v3 = mt /m

dn ~ 4/3 dd ∝ Im(11*) × md / mH

2

|Im| < 0.016 (90% C.L.) ⇒ dn < 5 ×10-27 e cm cf. dn

exp < 6.3×10-26 e cm

KL

K+

Systematic errors

Source of Error 12 fwd/bwd PT x 104

e+ counter r-rotation x o 0.5e+ counter z-rotation x o 0.2e+ counter f-offset x o 2.8e+ counter r-offset o o <0.1e+ counter z-offset o o <0.1+ counter f-offset x o <0.1MWPC-offset (C4) x o 2.0CsI misalignment o o 1.6B offset () x o 3.0B rotation (x) x o 0.4B rotation (z) x x 5.3K+ stopping distribution o o <3.0+ multiple scattering x x 7.1Decay plane rotation (r) x o 1.2Decay plane rotation (z) x x 0.7K2 DIF background x o 0.6K+ DIF background o x < 1.9Analysis - - 3.8

Total 11.4

12 : 12-fold rotational cancellation fwd/bwd : 0 forward/backward cancellation

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 regionto PT possible not always

Kinematic resolution good poor

Double ratio exp. possible difficult

+ polarization measurement for K3 PT 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 AT, -AT t+T, -t+T

• Matching with stopped K+ good good

• Systematic error small ● error due to B reverse ● t0 calibration necessary

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 PT component

■ Desirable detector : Large K3 acceptance Simultaneous K PT measurement Small instrumental systematic errors

■ Sensitivity goal : E246 : PT

stat(E246) > PTsyst(E246)

Future experiment (FE) : PT

syst(FE) ~ 1/10 PTsyst(E246) ~ 10-4

PT

stat(FE) ~ PTsyst(FE) ~ 10-4

PTsyst(FE) ~ 10-4 might be feasible, but PT

syst(FE) ~ 10-5 will be vey difficult.

E246 upgrade at J-PARC ?

E246 was statistically limited.■ Polarimeter field by a new magnet Parallel holding field of PT 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

Expectation for E246-upgrade

Gain from E246 Polarimeter : 3.8 Beam intensity : √10 Run time : √0.66 Total = 9.8 Statistical error : PT = 3.0 x 10-4

Systematic errors

Total errorPT syst ~ 10-4

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

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+ --> : PT <10-4 K+--> : PT ~10-4

■ Detector components Target calorimeter Pre-shower counter + tracker Polarimeter veto counters Large solenoid

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

Symmetrization of K+ stopping distribution

z

■ Adjustment of null asymmetry

A0= ( Aleft + Aright)/2

N(zK)=symmetric => A0= 0 N(zK)=asymmetric=> A0≠0

■ AT= ( Aleft - Aright)/2No effect in AT from asymmetric z-distribution due to left-right cancellation but unknown higher order systematics

Artificial z- symmetrization by using tracker ===> A0 = 0

0- L/R scheme ==> e+- F/B asymmetry measurement

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

Active polarimeter

■ Measurement of Muon stopping position Positron emission direction Positron energy Electromagnetic shower

■ location■ energy deposit

■ AnalysisMichel spectrum

■ Problem of use of plastics• formation of muonium• muon spin depolarization

B=3kG enough for decoupling?

Better choice will bemuon tubes made of Al

k k

a system with the highest sensitivity to polarization

Rejection of K2 background

+

< 79o < 39o

Optimization of K2 background rejection by Opening angle cuts, and X-parameter cut on photon spectrum X= (E1-E2)/ (E1+E2)

K2 was a significant background in E246..

Instrumental systematics Most dangerous systematics will be instrumental misalignments

magnet calorimeter

Cancellation by azimuthal integration

spurious PT decay plane rotation

Sensitivity forKPT

•FoM = √•Run time 1 = 107 s•Loi-19 estimate based on fwd/bwd scheme

_

10-5 10-5

Estimate of K PT sensitivity

1. Photon energy 20 – 200 MeV2. Muon energy 200 MeV3. 120O

Acceptance per K+ 0.7 x 10-4 N(K+ +) 0.7 x 1010

Statistical sensitivity : PT(1) 0.7 x 10-4

(estimate based on F/B scheme)

Kaon beam

K0.8 at T1 targetIn Phase 1 for stopped K+/- beam

T2 target in Phase2

p= 650~800 MeV/c K/ > 1 with two DCS’sp/p < 3% K+ intensity =106 ~ 107 /s low p kaon line

K+ beam for stopped K+ experiments

K+stop = Ip K+(Ep) C T(pK) stop(pK)

Ip : proton beam intensity K+(Ep) : K+ production rate at Ep ↑with Ep

C : channel acceptance T(pK) : channel transmission ↑with pK

stop(pK): stopping efficiency ↓with pK

K+/+ ratio ↓with pK

Optimum pK @ Ep=12 GeV (E246) : 650 MeV/c with one DCS @ Ep= 30-50 GeV (J-PARC) : 650~800 MeV/c longer channel with two DCS’s

K+(Ep) : nearly constant with Ep in the relevant Ep region for pK= 650~800 MeV/c

consideration on optimum beam momentum

Summary

■ Transverse muon polarization PT is a clean and very sensitive probe of new physics.

■ KEK-E246 has recently improved the limit of PT and Im.

■ Future experiments aiming for PT ~10-4 will be important and desired.

■ The experiment at J-PARC using a stopped beam will be very promising:

K+ 0+ PT <10-4 K+ + PT ~ 10-4