T violation in K decays using stopped K+

J. ImazatoIPNS, KEK

NP04 workshopAugust 3, 2004 Tokai

Transverse muon polarizationKEK E246 experimentJ-PARC experiment

E246 upgrade?LOI-19

Transverse muon polarization in K+→π0µ+ν

= very small

Kµ3 decay form factors and

T violation

History of Kµ3 transverse polarization experiments

• KL→π－µ+ν Bevatron 1967 Imξ = -0.02 ±0.08• KL→π－µ+ν Argonne 1973 Imξ = -0.085 ±0.064• KL→π－µ+ν BNL-AGS 1980 Imξ = 0.009 ±0.030• K+→π0µ+ν BNL-AGS 1983 Imξ = -0.016 ±0.025

Feature of K+µ3 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 contributionEfrosinin et al. PL B493 (2000) 293PT ~ 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

s i j u

W

K µ

π

ν

γ++

0

ππ K µ

π

ν

γ++

0

γ

SM

FSI (example)

Three Higgs doublet model

s µ s µ

u ν u ν

W H+ α γ

Higgs doublet model

L = (2√(2)GF)1/2 Σ[αiULKMDDR + βiURMUKDL + γiNLMEER] Hi+ + h.c.

flavor conservation

Imξ = Im(α1γ1*) x (mK / mH+)2

= Im(α1β1*) x (v2 /v3)2 x (mK / mH+)2

vi : vacuum expectation valuesαi, βi, γi : mixing matrix elements

s µ s µ

u ν u ν

W H+ α γ

0 2 0 4

0 6

0 8

0 1

0

0

1 0-

2

1 0-

1

1

1 0

1 02

Im(α

1β1* )

v2 / v3

mH = mZ × 2

KEK-E246 Imξ < 7 × 10−3

n-EDM

b → sγ

b → τνX

Kµ3 previous

Only schematic

Kµ3 PT

3HDM : constraints from other experiments

Neutron EDM (charged Higgs exchange)dn=Cn Im(α1β1*) < 0.63 x 10-25 e cm Im(α1β1*) < ~10

b→sγA = ASM + A3HDM(α1β1*) Im(α1β1*) ≦ 3.2 (for mH~2mZ)

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

ε /ε = (α1β1∗)) : but stringent constraintb→XτνA = ASM + A3HDM(α1γ1*)Im(αiγi*)=Im(α1β1*) (v2 /v3 )2 < 0.48 (for mH~2mZ)

[Grossman, Haber and Nir (1995)]

c.f. PT : Im(α1β1*) (v2 /v3 )2 < Imξ / 0.10

For v2 /v3 > ~ 10, PT is the most stringent constraint on 3HDM[Garisto and kane (1991)]

Other modelsSUSY + squark mixing

Su

µ ν

H+

bL~

g~tR~ PT

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M. Fabbrichesi and F. Vissani, Phys. Rev. D55 (1997) 5334

Guo-Hon Wu and John N. Ng, Phys. Rev. D56 (1997) 93 Charged Higgs exchangeConstraints onMH+

Λ=tanβ (µ+Atcotβ)/mg~x Im[V33

H+* V32DL * V31

UR]

slepton exchange +down-type squark exchangeConstraints onMH+

Im[λ2i2(λ’i12)*] and Im[λ’21k(λ’22k)*]

scalar leptoquark exchangeConstraints onλk

2/Mφk2

PT (K+→µ+νγ )no SM contribution, but induced by pseudoscalarcomplementary to PT (K→ πµν ) [Kobayashi et al. (1996)]FSI is not large : O(10-4 ) [Efrosinin and Kudenko (1999), Hiller and Isidori (1999)]

Model K+ → π0µ+ν K+ → µ+νγ

Standard Model <10-7 <10-7

Final State Interactions <10-5 <10-3

Multi-Higgs 　 ≤ 10-2 ≤ 10-2

PT(K+ → π0µ+ν) ≈ 2 PT(K+ → π0µ+γ)

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)

E246 experimental setup[J.Macdonald et al.; NIM A506 (2003) 60]

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PT

µ+

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0 0.5 1.0 m

π0

f

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w

a

r

d

π0

b

a

c

k

w

a

r

d

A = NCW - NCCW

NCW + NCCW COILGAP

IRON POLE

µ+ STOPPER

e+ COUNTER

TARGET

CsI(Tl)

End view Side view

K+→π0µ+ν

r

Double ratio measurement

: analyzing power

π0

0-forward

PT

π0

0-backward

PT

PT directions

fwd -π0 (γ )bwd -π0 (γ )

Double ratio measurement

Afwd - AbwdAT =2

Muon holes

K+ CsI crystals

1010

556

67

7

8

44

32

1

2

9

1

3

8

9

4

CsI barrel

768 CsI barrel

K + Target

π (γ )π (γ )0

θπ (γ )π (γ )0

µ+

fwdfwdbwdbwdπ (γ )π (γ )0

fwd and bwd π0 /γ

E246 result and model implication

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

1960 1980 2000

Year

Im(ξ)

BevatronArgonne

BNL

BNL KEKKEK

PT = - 0.0017 ± 0.0023(stat) ± 0.0011(syst)( |PT | < 0.0050 : 90% C.L. )

Imξ = - 0.0053 ± 0.0071(stat) ± 0.0036(syst)( |Imξ | <0.016 : 90% C.L. )

Three Higgs doublet model

|Imξ | < 0.016 (90% C.L.) ⇒ Im(α1γ1*) < 544 (at mH=mZ)

cf. BR (B→Xτντ) ⇒ Im(α1γ1*) < 1900 (at mH=mZ)

[R.Garisto and G.Kane, Phys. Rev. D44 (1991)2789] v2/v3 = mt /mτdn ≈ 4/3 dd ∝ Im(α1β1

*) × md / mH2

|Imξ | < 0.016 (90% C.L.) ⇒ dn < 5 ×10-27 e cmcf. dn

exp < 6.3×10-26 e cm

Systematic errorsΣ12 : 12-fold rotational cancellationfwd/bwd : π0 forward/backward cancellation

Source of Error Σ12 fwd/bwd δPT 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 <0.1µ+ counter f-offset x o <0.1MWPC φ-offset (C4) x o 2.0CsI misalignment o o 1.6B offset (ε) x o 3.0B rotation (δx) x o 0.4B rotation (δz) x x 5.3K+ stopping distribution o o <3.0µ+ multiple scattering x x 7.1Decay plane rotation (θr) x o 1.2Decay plane rotation (θz) x x 0.7Kπ2 DIF background x o 0.6K+ DIF background o x < 1.9Analysis - - 3.8

Total 11.4

E246 upgrade at J-PARC?E246 was statistically limitted.

Polarimeter field by a new magnet Parallel holding field of PT Precise field distribution alignment

reduction of the most serious systematic errorActive polarimeter

4π solid angle for decay positron Energy and angle of positrons

FoM = α√Ω = 3.8 x E246Time digitizer readout of CsI(Tl)

Rate performance = 10 x E246under the condition of K/π >>1

MeritLower cost than a completely new setupWell known detector performance and systematicsMany possibilities for kaon decay spectroscopy

E246 muon polarimeter

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AT

=

αPT

-10 -5 0 5 10 y (cm)

µ stopper Trigger counter

Cu degrager

TOF counter

C4 chamber

Left e counters Right e counters+ +

Fe field trim

µ+

e++

B

One-sector viewCross section

y(cm)

New polarimeter system

-10 -5 0 5 10 y (cm)

activepolarimeter

C4 chamber

µ+

activepolarimeter

BMagnet Magnet

Coil

B~ 300 Gauss

Expectation for E246-upgrade

Gain from E246Polarimeter : 3.8Beam intensity : √10Run time : √0.66Total = 9.8

Statistical error : δPT = 3.0 x 10-4

Systematic errors

Total error : δPTsyst ~ 10-4

J-PARC proposal LoI-19

Experiment principle• stopped kaons• double ratio• detector azimuthal symmetry • complete reconstruction of kinematics Detector concept• larger µ+ acceptance• high resolution π0 measurement• active polarimeter• photon veto Most important requirement• suppression of systematic errors to the 10-4 level

Original design

“PT in K+→π0µ+ν and K+→µ+νγwith δPT <10-4 and δPT ~10-4 ”

A new detector with• improved charged particle acceptance• a high resolution photon detection

)1)(cos1(

222

20

0 X

mE

−−=

ηππ

21

21EEEEX +

−=

22 )()()( 000ηπ

γππ

EErmsE ∆+∆=∆

ηπηπ βσγ 25.0 mE =∆

angular contribution = small for X -> 0

Further optimization are necessary taking into acount ;

Detector acceptanceSystematic errorsEvent selection performance

Vector correlation

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Cryostat

At J-PARCHigher beam rateDifferent conditions forup- and down-stream side

Double ratio betweenleft -going π0 andright-going π0

Beam

µ µ

π

π

PTPT

E246 experiment J-PARC experiment

Symmetrization of K+ stopping distribution

K

µ

polarimeter

target

tracker

+

+

z

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

butunknown higher order systematics

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

Adjustment of null asymmetry

A0= ( Aleft + Aright)/2

Necessity of magnetic field

P (fwd)

P (bwd) δP

δP

δBrθ

θ = δω x τδP = θ x P

T

TN

N

NT

Zero field experimentnecessary condition= δBr < 1 m Gauss very difficult to make

+∝

+

Calorimeter

Preshower detectors

Degrader

Active targetK

Central tracker

Veto counters

Trackers

γ

γ

γ

Polarimeter

-veto and calorimeter

solenoid coil

0 0.5 1.0 m

Large solenoid

Field paremetersStrength : 1-3 kGAlignment+symmetry : 10-4

100 µ over 1mField measurement with arotating coils

Allowed stray field : 100 mG

Use of the field for tracking

Effects of magnetic field on polarization

B

PP

P

Lleft

right

PLP

P

left

rightδ

δP = P x sin δLT

Cancellation between +δ and -δNull asymmetry checkCancellation between left and right

Same situation as in the zero field case

Rejection of Kπ2 background

µ+

π0 π0

π πµ µ

φ =11゜max φ =11゜max

ϕ = 40゜max

γ (Eγ > 100 MeV)

two γ one γ

++ + +

θµπ< 79o θµγ < 39o

Optimization of Kπ2 background rejection byOpening angle cuts, andX-parameter cut

Active polarimeter

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

AnalysisMichel spectrum

k k

Measurement ofMuon stopping positionPositron emission directionPositron energyElectromagnetic shower

location energy deposit

B=3kG enough for decoupling?

Better choice will bemuon tubes made of Al

Instrumental systematicsMisalignments

⦿ ⦿

×× ××

⦿⦿⦿⦿

B

B

P

P

left

left

δP

δP

T

T

n

n

CsI

CsI

p π

p π

µp

pµp x pπ

πp x p

µ

µ

TOPTOP

Bottom Bottom

(a) (b)

π0 calorimeter

spurious δPT decay plane rotation

Magnet

Cancellation by azimuthal integration

Photon veto and Kµνγ

Identification of one γ eventsRejection of π0 -> 2γ events

∝+

K+

Trackers

γ

γDegrader

γ veto and calorimeter

Polarimeter

×Ο

µ+

γ

PT = σµ · (pµ × pγ )

µ stopper &Active polarimeter+ γ veto function

γ veto

µpµ= 100~210 MeV/c

~10X0

50g/cm2

~2X0

γBoth µ and γ in the polarimeter

Sensitivity for Kµ3 PT

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

Rough estimate of Kµνγ PT

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

Acceptance per K+ ∼ 0.7 x 10-4

N(K+ → µ+νγ) ∼ 0.7 x 1010

Statistical sensitivity ∆PT(1σ) ∼ 0.7 x 10-4

(estimate based on fwd/bwd scheme)

High rate performancej

Detector elements are designed from now on.

R&D of pre-shower counter started at INR.

Each element will be highly segmented.

Target : fiber targetTracker: high rate chamber + Scifiγ−detector: pre-shower counter + fast crystal or

fiber sampling shower counterγ-veto : highly segmented

Polarimeter: highly segmented.

Kaon beam

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

T2 target in Phase2

p= 650~800 MeV/cK/π > 1 with two DCSs∆p/p < 3%K+ intensity =106 ~ 107 /s

Is it possible to use the K1.1 line?C-type branch of K1.1

•　how to optimize beam optics?• how to put two DCS? • how to coexist with the future High-p line?

Summary

Search for T-violation in K decays at J-PARC isvery promising:

K+ → π0µ+νK+ → µ+νγ

We seek for the possibility to run in Phase 1.

A stopped K+ beam in the K hall in very important.

Detector design will be done toward a full proposal.

δPT (stat) ≤ 10-4

δPT (syst) ∼ 10-4