CP and CPT Studies with Kaons

a r X i v :h e p -e x /0209042v 1 18 S e p 2002

CP AND CPT STUDIES WITH KAONS

JULIET LEE-FRANZINI a

Laboratori Nazionali di Frascati,Via E.Fermi 40,Frascati,I-00044Italy

Three European experiments are engaged at present in the study of CP violation in the kaon system.In particular,NA48/1and KLOE are concerned with the K -short decaying into three pions,while NA48/2and KLOE study the charged kaon decaying into three pions’Dalitz plot asymmetries.I will discuss the physics involved as well as summarize the anticipated sensitivities which can be reached by the experiments.

1Introduction

I will precede my discussion of what is expected,from on-going and future experiments on CP violation and CP T tests,with a few historical reminders,to place the present measurements in perspective.The kaons were discovered around 1947,as a surprise,and since then,they have been a cornucopia for particle physics.We owe to them the ideas of “?avor”,“quark”,and “?avor mixing”.Parity violation ?rst showed up in the “τ?θ”puzzle.From semi-leptonic decays we learnt of the ?S =?Q rule and obtained the ?rst value of sin θC .The kaons’two pion decays taught us the dominance of ?I =1/2transitions,whose explanation is still being

labored over by lattice and chiral perturbation physicists.Finally,of course,CP violation,C

\P \in the following.Indirect CP violation had been discovered long ago and direct CP violation has only just been de?nitively established,in the neutral kaon system.

Just for nostalgia,I list some “recent”historical dates:(1)1964C \P \in |?S |=2seen.(2)1967-1973A L ?～

√

K 0)|<4.5×10?10eV.

2Other C\P\Kaon Physics

In the near future,three experiments in Europe,NA48/11,NA48/22,and KLOE,are set to do the?rst?ve measurements listed below.The sixth needs such high intensity kaon beams that given the?scal stringency at CERN(so that its proposed high-intensity proton driver3is not likely to be built),probably can only be realized in the U.S.,if KOPIO at BNL is funded.(1) K S→π0π0π0,BR～2×10?9:NA48/1,KLOE2004.(2)Odd pion slopes from K+-K?:NA48/2, KLOE2004.(3)K±→π±π0γ,NA48/2,KLOE2004.(4)Γ(K+→π+π+π?)?Γ(K?→π?π?π+):KLOE2004.(5)K S→π0e+e?:NA48/1,KLOE2004.(6)K L→π0νˉν:BR～3×10?11,

KOPIO20??.The above list is in order of experimental di?culty and descending branching ratios,BR’s.The expected signals are quite predictable theoretically for items1and item6, while the situation is di?erent for items2,3and4.Item5is an ancillary measurement,useful for isolating the direct CP violating component in K L→π0e+e?.

2.1K S→π0π0π0

Since there has been some confusion in what this BR should be lately,I will write down a couple of lines on its derivation.

Let:|K S =|K1 +?|K2 ;K L=|K2 +?|K1 ;ηi= i|K L / i|K S ;?=(2η+?+η00)/3.Then:

η000= 3π0|K L

ΓS

=|?|2×BR(K L→3π0)×τS

2Γ=

Γ(K+→3π)?Γ(K?→3π)

2g =

g(K+→3π)?g(K?→3π)

?b?

?a

where α0and β0are small rescattering phases,and sin(α0?β0)～0.1.From Maiani and Paver 4:

A g ,τ=(?2.3±0.6)×10?6

A g ,τ′=(1.3±0.4)×10?6A Γ,τ=(?6±2)×10?8A Γ,τ′=(2.4±0.8)×10?8

But where things are small,big surprises might hide.D’Ambrosio,Isidori,and Martinelli 5

state that large C

\P \e?ects,A g of O (10?4),could be triggered by a misalignment of quark and squark mass matrices through the chromomagnetic operator -CMO:possible only if several conditions conspire in the same direction .Fine tuning becomes then necessary for explaining the experimental value of ?(?′/?).3

K S →π?ν

From this reaction one can learn about ?S =?Q and T CP violation by measuring (a)the rate Γ(K S →π?ν)and (b)the leptonic asymmetry A S ?.3.1

?S =?Q

There is no ?S =??Q in the SM.We only have s →W ?u ,ˉs →W +ˉu .The diagram illustrates a fake ?S =??Q process,if we were just to look at the ?nal lepton sign.At the su vertex ?S =?Q .

d

n u

K 0

u

s W

-

d

p -e +

W

+

Fig.1.

K 0)states,tagged by strong interactions.One needs eg ,e +e ?→φ→K +K ?.

One K ±

tags the other.Charge exchange,in any material,gives K 0(or

If c=d=0,then A S??A L?=4?δ.A limit from the above improves the determination of M(K0)?M(

J12=6%⊕

δη

Table 1.DAΦNE parameters.Parameter Design

2004

45

Current (A)5

5×1031

Beam τ(m)

?100

～190

K 0,?p ?|

√

K 0 and |K L ≡p |K 0 ?q |

K 0beams.From unitarity and σ(γγ→

K 0

t 1

t 2

K S ,K L

K L ,K S

f 1

f 2

φ

Fig.4.The decay φ→KK →f 1,f 2.

The decay intensity is given by:

I (f 1,f 2,t 1,t 2)=| f 1|K S |2| f 2|K S |2e ?ΓS t/2×

[|η1|2e

ΓS ?t/2

+|η2|2e

?ΓS ?t/2

?2|η1||η2|cos(?m t +φ1?φ2)]

.

Integrating over t 1and t 2,for ?t =t 1?t 2constant we ?nd:

I (f 1,f 2;?t )=

1

6.2Interference examples

0.2

0.40.60.81.0

1.2-15-10-5051015

I t ()

D D t t t t =()/12-S

1

2

3

-30-20-100102030

I t ()

D D t t t t =()/12-S

Fig. 5.Interference patterns.Left f 1,2=π+π?

,π0π0,sensitive to ?(?′/?)and ?(?′/?).Right f 1,2=??,?+yielding ?and ?of A ?±

6.3

Γ(K S →π+π?)/Γ(K S →π0π0),KLOE 2001

After all these years,chiral “perturbationists”are still trying to reach some accuracy in post-dicting the ?I =1/2rule.Its understanding would allow a more reliable calculation of ?(?′/?).Experimentally KLOE will measure the BR’s for K S decays (and K L )into various channels with high accuracy.The ratio R =Γ(K S →π+π?)/Γ(K S →π0π0)is not well known,only to a couple of %,even though the double ratio (K L →+?K L →00)/(K S →+?/K S →00)is known to ～0.1%.

KLOE would like to reach 0.1%on the former.Corrections are background sensitive.Luckily,K L interacting in the KLOE calorimeter gives an ideal K S tag,almost independent of K S

decay mode.For our ?rst measurement of this ratio we obtain:R =2.239±0.003(stat .)±0.015(syst .)6.Not only is this determination far more accurate than Particle Data Group’compilation,it is very important to note that KLOE includes all K S →π+π?γ,whereas the other previous exper-iments include unknown fractions,making comparison with theoretical calculations ambiguous.The above measurement is based on only 16pb ?1.KLOE in 2002has about 30times that amount of data to improve the accuracy of the measurement.6.4

K S →πeν,KLOE 2001

Fig.6.The signal for K S →e ±π?νin KLOE.

In the KLOE measurement of this process in 2001,we use only non spiraling tracks,time-of-?ight,TOF,for electron identi?cation and compare the missing energy,E miss ,with the missing momentum,|p miss |,thus achieve an almost completely rejection of π+π?backgrounds,as seen ?g.6.We ?nd:BR=(6.91±0.37)×10?47.By end of 2002,KLOE will improve this measurement

with 30times more statistics,and will have the ?rst measurement of A S ?.7Expectations from the coming experiments 7.1

?(?′/?)via the double ratio method

A review of the status of direct CP violation experiments has been given by B.Peyaud at this Rencontre,all references for NA48and KTEV are in his article in this proceedings.Fig.7shows the luminosity that KLOE needs to reach various accuracies on ?(?′/?)by measuring the double ratio.KLOE’s measurement will be performed at a φ–factory,with totally di?erent systematics from the ?xed target experiments.Furthermore,it will be charming,if nothing else,to see the interference patterns done with high accuracy.

?e /e ('′10 )

-3

Fig.7.KLOE expectations vs NA48and KTeV.

7.2

K ±Decays

Details and expectations of NA48/2are given in Gianmaria Collazuol’s paper.Table 2,is a summary of results expected from NA48/2and KLOE (Acc.stands for acceptance).

Table 2.K ±decays.

Mode

BR

Events Events NA48/2K ±→π+π?π±0.0561.26×1082×109K ±→π0π0π±0.0171.22×1081.2×108K ±→π±π0γ2.8×10?42×1061×106

K ±→π±γγ5×10?7

3750

those expected from KLOE(Acc.stands for acceptance).

Table3.K S and K L decays.

Mode BR Events Events

NA48/1 K S→π+π?0.675×109

K S→π0π00.312.5×109

K S→πeν7.4×10?42×106

K S→π0e+e?5.2×10?9137

K S→3π02×10?9164

K S→π0γγ4×10?8300114

K S→π+π?γ1.8×10?31.35×107

K S→π+π?π03.2×10?72500

K L→π+π?π00.121×109

K L→π+π?0.0021.1×107

K L→π0π00.0014×106

K L→π+π?γ4.6×10?53.7×105