# Presentation: 947498

## 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*

- Transverse muon polarization in *K*+
- KEK E246 experiment
- Future experiments
- J-PARC experiment

## 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

## Features of K+  PT

- 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)

##  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
- vi  : 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*H2  = 4.1×Im**GeV-2**

## 3HDM : constraints from other experiments

- Neutron EDM *(charged Higgs exchange)*
*d**n*=Cn 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 *~2*m*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 *~2*m*Z)
- [Grossman, Haber and Nir (1995)]
*c.f.*   *P**T*  :  Im(*****) (*v*2*  **/v*3* *)2  = 1.36 ×105  Im**(for *m**H *~2*m*Z)

***For v*****2*****  ******/v*****3***** > ~ *****10*****, P******T ****** is the most stringent constraint on 3HDM******  ***
***   ***** **[Garisto and kane (1991)]

##  Other models

- Charged Higgs exchange
- Constraints on
*M*H+
**=tan**(**+*A*tcot**)/*m**g~*
-    × Im[*V*33*H*+* *V*32*D**L ***  **V*31*U**R*]
- slepton exchange +
- down-type squark exchange
- Constraints on
*M*
- Im[**2*i*2(**’*i*12)*] and Im[**’21*k*(**’22*k*)*]
- scalar leptoquark exchange
- Constraints on
***k*2/*M**k*2

## 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[**2*i*2(**’*i*12)*]/*M*2   and Im[**’21*k*(**’22*k*)*]/*M*2
-  Constraint on from ImE246)
-           Im[**2*i*2(**’*i*12)*] and Im[**’21*k*(**’22*k*)*]    ×@ *M*=100 GeV
- while constraint from other experiments : ≤ 4 × 10-2  @ *M*=100 GeV

## PT (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
-                                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 :  *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*)

## 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.

## 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 /

*P**T* directions

***fwd -***************

***bwd -***************

- 768

-            A*fwd* - A*bwd*
*A**T* =
-                   2

## 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

*K**L*

*K*+

## Systematic errors

- Source of Error	12	*fwd/bwd*	***P**T* x 104
*e*+ counter r-rotation	x	o	0.5
*e*+ counter z-rotation	x	o	0.2
*e*+ counter f-offset	x	o	2.8
*e*+ counter r-offset	o	o	<0.1
*e*+ counter z-offset	o	o	<0.1
**+ counter f-offset	x	o	<0.1
- MWPC**-offset (C4)	x	o	2.0
- CsI misalignment	o	o	1.6
***B*** offset (**)	x	o	3.0
***B*** rotation (***x*)	x	o	0.4
***B*** rotation (***z*)	x	x	5.3
*K*+ stopping distribution	o	o	<3.0
**+ multiple scattering	x	x 	7.1
- Decay plane rotation (***r*)	x	o	1.2
- Decay plane rotation (***z*)	x	x	0.7
*K*2 DIF background	x	o	0.6
*K*+ DIF background	o	x	< 1.9
- Analysis	-	-	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 region**
**to *****P******T***                                        possible                                   not always
**Kinematic resolution**                 good                                          poor
**Double ratio exp****.**                    possible                                     difficult

## + polarization measurement for K3 PT 

-       Method                         **longitudinal field                   transverse field**
** ****Configuration**
** ****Observable**
** ****Experimen**t                                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

## 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.

## 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

## 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

## 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*+ -->   : *P**T* <10-4        *K*+-->   : *P**T *~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
*     **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

## 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

-  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*

## Rejection of K2 background

- 

- +

**< 79o               ** < 39o

- 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.*.

## Instrumental systematics

-  *Most dangerous systematics will be instrumental misalignments*

-  magnet

-  calorimeter

*Cancellation by azimuthal integration *

- spurious ***P**T*

- decay plane rotation

## Sensitivity forKPT

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

- _

- 10-5

- 10-5

## Estimate of K PT  sensitivity

- Photon energy                   20 – 200 MeV
- Muon energy                    200 MeV
- 3.*  *****                                                      120O
-      Acceptance per *K*+                      0.7 x 10-4
-      N(*K***+**** ******** ********+********)                        **** **0.7 x 1010** **
-      Statistical sensitivity :        *P**T*(1)  0.7 x 10-4

- (estimate based on F/B scheme)

## 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 =106 ~ 107 /s

-  low *p* kaon line

## 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*

## 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