La Fisica dei K a DAΦNE-2 · La Fisica dei K a DAΦNE-2 F. Bossi CSN1, Frascati 14-15 Ottobre 2005...

La Fisica dei K a DAΦNE-2

F. Bossi

CSN1, Frascati 14-15 Ottobre 2005

1

Summary of the talk

DAΦNE and KLOE 1999 − 2005

PHYSICS ISSUES AT DAΦNE−2:

• TESTS OF CPT• CHIRAL PERTURBATION THEORY

• SOME PREDICTION OF THE STANDARD MODEL

DETECTOR ISSUES

F. Bossi, CSN1, Frascati 14 Ottobre 2005 2

Some basic concepts (and numbers)

A Φ meson decaying at rest produces pairs of neutral or chargedkaons with branching ratios of ~34% and ~49%,respectively

Daughter particles are monochromatic, Pch ~ 125 MeV/c, Pneu ~ 110 MeV/c

Parity conservation imposes the neutral state to be KSKL

In resonant e+e− collisions, particles fluxes are:

1.5 x 106 K± pairs/pb−1

1. x 106 KS KL pairs/pb−1


A brief history of luminosity

2

DAΦNE performance up to April 2005

Peak Luminosity

Integrated Luminosity

Present day performance

Lpeak ~ 1.4 x 1032 cm−2s−1

Best ∫L dt ~ 200 pb−1/month

Total KLOE ∫L dt ~ 2200 pb−1

(2001,02,04,05) 4

F. Bossi, CSN1, Frascati 14 Ottobre 2005

KLOE papers on K physics

Ks → πeν PLB 535, 37 (02)Ks → ππ PLB 538, 21 (02)

KL → γγ PLB 566, 61 (03)

K± → π±π0π0 PLB 597, 49 (04)

Ks → 3π0 PLB 619, 61 (05)

KL lifetime PLB 626, 15 (05)

KL main BR, Vus Accepted by PLB

K± → µ±ν Accepted by PLB

Plus (at least) as many in preparation


A possible evolution of DAΦNE

The Laboratory is now studying the possibilty for an upgrade of the present facility

There are a few options under consideration. The one that I willdiscuss here, and refer to as DAΦNE-2 is:

A Φ-factory able to deliver 7-10 fb−1 in one year, i.e some 109 well tagged kaons of all species after 2-3 years of run

I will also assume that the detector to be used is some more or less conservative evolution of KLOE. Therefore almost all of the

figures about detection performances are based on measurements on real data


K Physics issues at DAΦNE-2

What studies can be performed using kaons at DAΦNE-2?:

• Tests of fundamental symmetries (CP, CPT)

• Tests of prediction of Chiral Perturbation Theory

• Tests of prediction of Standard Model

For each of these three topics I will discuss some examples of measurements that can be performed at DAΦNE−2. The list reflects my present personal knowledge of the matter and

must be considered as non-exhaustive


CPT


CPT

In the framework of quantum field theory (QFT), CPTconservation is a theorem. It is consequence of Lorentz

invariance, locality as well as quantum mechanics

The possibility of CPT violation is considered in several theoreticalcontexts that go beyond conventional QFT, for instance in models

of quantum gravity

CPT violation may manifest itself in many subtle ways differentfrom the inequality of particle-antiparticle masses. This is mostly

the realm of Φ-factories


CPT violation: the “standard” path

In the standard description of the neutral K system, a chargeasymmetry in semileptonic KL and KS decays is predicted due to

CP and (possibly) CPT violation

δL = 2Re(εK ) − ∆

δS = 2Re(εK ) + ∆CPT is violated if

δS ≠ δL

The most recent measurement are:

δL = (3322 ± 58 ± 47) x 10−6 KTeV, 02δS = (1.5 ± 10 ± 3) x 10−3 KLOE, ~400 pb−1


Potentialities of DAΦNE-2 for δS

Assuming present detection efficiencies and a modestimprovement in systematic studies, at DAΦNE-2 one could aim at

a total error on δS of order 10-3

B (kG)

Present analysis, MC with detailed field map400 pb−1 MC with LSF=0.5, with uniform axial B field

53 4

0.05

0.1

0.15

0.2

Acc

epta

nce

However it has already beenshown that one can obtainan increase in acceptanceup to a factor of 2 just bylowering the B field to 3

kGauss

With some optimism one can hope to reach a

sensitivity on δS below the 10−3 level

11F. Bossi, CSN1, Frascati 14 Ottobre 2005

CPT and decoherence

It has been suggested that quantum gravity could give rise tomodification of standard QM, observed in decoherence effects

together with CPT violation

This can be observed in deviation of the behaviour of entagledsystems (like KSKL from Φ decays) from the one predicted by

standard QM


CPT and decoherence: the EHNS model

Ellis, Hagelin, Nanopoulos and (independently) Srednicki set up anevolution equation of the neutral K system containing three new

CPT violating parameters α,β,γ with dimensions of energy

Naively, one expects α,β,γ ~ O(MK2 / MPlank) ~ 10-20 GeV

Peskin and Huet worked out the expression of the usual doubledecay intensity of the KSKL pair from Φ decays in the EHNS

framework

There appear new bizarre terms in the distribution which allow toextract experimentally limits (or measurements) of these new

parameters by proper fitting


Fixing the EHNS parameters

The EHNS parameters have already been constrained byCPLEAR results

α = ( −0.5 ± 2.8) x 10−17 GeVβ = ( 2.5 ± 2.3) x 10−19 GeVγ = ( 1.1 ± 2.5) x 10−21 GeV

KLOE can reach equal sensitivityon β,γ with present data samplejust with the π+π−π+π− channel


Fixing the EHNS parameters

With 20 fb−1 one can dramatically improve, especially on βand γ

In the plots below the horizontal line is CPLEAR, VDETmeans σvert = ¼ τS

δ(α/ΓS) δ(β/ΓS) δ(γ/ΓS)

fb−1 fb−1 fb−1

• Present KLOE• KLOE + VDET


CPT and Bose statistics: the BMP model

Bernabeu, Mavromatos and Pavassiliou argued that in presence of CPT violation induced by quantum gravity the concept of

antiparticle has to be modified. In this case the KSKL state from Φ decays does not strictly obey

Bose statistics, thus modifying the final state wave function

І i > = C {( І KS(+)> І KL(−)> − І KL(+)>І KS(−)>) + ω ( І KS(+)> І KS(−)> − І KL(+)>І KL(−)>)}

The complex parameter ω quantifies the departure from Bosestatistics, in a formalism in which the time evolution of the state

is still described by the equations of standard QM

Naively, ІωІ ~ O(MK2 / MPlank ∆Γ)1/2 ~ 10-3 ÷ 10−4


Measuring the ω parameter

The parameter ω can be measured by a fit to the decay time distribution of the KSKL pair to 4π

Arg(ω) = 0, ІωІ = 1,2,3 x 10−3

∆t (τS units)

fb−1

• Present KLOE• KLOE + VDET

A. Di Domenico

A. Di Domenico

δ(ω)


A note on the previous slides

All our estimates refer to the π+π−π+π− channel only. Further information can be obtained by other decay

channels, to be studied in more detail.


Some fundamental bibliography

1. Hawking, PR D14 (1975) 2460, Comm. Math. Phys. 87 (1982) 395

2. Wald, PR D14 (1975) 2460, Comm. Math. Phys. 87 (1982) 395

3. Ellis et. al, NP B241 (1984) 381; MPL A10 (1995) 425; PRD53 (1996) 3846

4. Huet, Peskin, NP B434 (1995) 3

5. Bernabeu, et al. PRL 92 (2004) 131601, hep-ph/0506025

6. Benatti, Floreanini, NP B511 (1998) 550

7. Bertlmann, Durstberger, Hiesmayr, PR A68 (2003) 012111


Chiral Perturbation Theory


Chiral Perturbation Theory

In the limit in which u,d,s are massless the QCD lagrangian isinvariant under SUL(3)xSUR(3). The left-handed world is separate

from the right-handed one: this is chiral symmetry.

The dynamical breaking of this (approximate) symmetry produces8 massless Goldstone bosons to be identified with the π, K, η

One then writes down the most general lagrangian consistent withthe chiral symmetry, and expands it in terms of the momentum of

the involved particles. If momenta are low enough, then: M(p2) > M(p4) > M(p6) …

…and one can perform calculations perturbatively

This is the basic idea of Chiral Perturbation Theory


ChPT: the pros and the cons

Thus chiral symmetry is:

• A true/direct consequence of QCD

• A rigorous way to calculate in the low energy region

On the other hand, the effective ChPT lagrangian leaves a number of free parameters to be determined experimentally, that

increase with the order to which the lagrangian is computed

Thus, the higher you go with the power of p, the higher is the number of the number measurement you need to fix the theory

2 at orderd p2, 12 at order p4…


KS → γγ : a test for ChPT

NA48/1 has measured BR(KS → γγ) = (2.78 ±0.06±0.04)x10−6

This result differs from predictions of ChPT at O(p4) by 30%

A preliminary analysis shows that KLOE can reach a statisticalaccuracy of ~ 4% with the present data sample.

A projection to 20 fb−1 would give an accuracy better than 1%


KS → π+π −π0 : another test for ChPT

ChPT predicts B(Ks → π+π−π0) = (2.4 ± 0.7)x10−7

The present experimental value (3.3 +1.1−0.9 ) x10−7 is the average

of three different measurement each individually precise at ~ 40%A preliminary KLOE analysis obtains εsig ~ 1.3%, S/B ~ 2

AssumingError on BR @ 2 fb−1 (%)

Error on BR @ 20 fb−1 (%)

No further effort madeto reduce background ~ 60% ~ 20%

Further effortscompletely removebackground

~ 40% ~ 12%


KS → π+π −π0 as a pedagogical example

This is the typical case where analysis would greatly benefit fromsimple detector upgrades

At least one of the two tracks has low momentum: 65% of signallost only due to acceptance

Acceptance can be increased by the use of a lower B field. Alsothe use of a vertex chamber could definitely help

Both can be useful also for the rejection of the background due topathological charged kaon events


Study of KS → π+π −γ spectrum

Spectrum is distorted wrt topure I.B.

Calculations at O(p4) can lead either to an excess or toa lack of events wrt prediction

at O(p2), BR O(10−6)

Toy MC fit: sensitivity to BR at 10−6 level with 106 events

with Eγ > 20 MeV

Events with 20 fb−1: 107 withEγ > 20 MeV


A digression in the η world

It is known that a good Φ-factory is also a reasonable η-factory.

Actually, at present KLOE has the largest η statistics in the world

The η world is largely complementary with the K one in that itaddresses most of the same physics issues.

Tests of C, CP, CPT Tests of ChPT

η → γγγη → π0l+l−

η → ππγ

η → π0γγη → 3πη → ππγ

More on C. Bini’s talk


Predictions of the SM


KS → π0π 0π0 : a genuine CP violating decay

MCEff. Stat. =5.3× data

This decay violates CP. SM branching ratio is 2x10−9 χ2

2π

Analysis based on γ countingand kinematic fit on 2π0 and 3π0

hypothesis χ23π

450 pb−1

’01+’02 dataKLOE with 450 pb−1

χ22πB(KS → 3π0) < 1.2 x 10−7 90% CL

based on 2 observed events with anexpected background of 3.1

29

χ23π

F. Bossi, CSN1, Frascati 14 Ottobre 2005

KS → π0π 0π0 : perspectives

Background mostly due to photon clusters double splittings

Preliminary studies show that there is room for “algorithmic” improvements in background rejection without losses in

signal efficiency

Study of the entire KLOE data set crucial for a betterassessment of the real potentialities of the analysis but…

…there are hints that @ 20 fb−1 one can reach ~ 5 x 10−9

With KLOE as it is now. Can we do better than that? see laterdiscussion


KS → πeν decays and the ∆S = ∆Q rule

The relevant parameter here is:

Re (x+) ~<e+π−ν | Hwk | K0 >

<e+π−ν | Hwk | K0 >~ 10−6 S.M.

1 + 4 Re(x+) =ΓSΓL

BR(KS → πeν) τL

BR(KL → πeν) τS=

6 10−3

1 10−3 4 10−3

=

These are KLOE measurements

PresentUncertainties20 10−3

@ 20 fb−1 one can reach ~ 2 10−3 in BR(KS → πeν)


Play the same game with muons

Muon semilptonic channel is more difficult:• Lower expected BR ~ 4 x 10−4

• High pollution from ππ events with π decays in flight • More difficult to separate charge states

• 2002 data− MC µ+π− ν− MC ππγ− MC ππ

However, it has never beenmeasured before

KLOE has already a clearsignal and can reach 3%

accuracy with present data

This channel clearly begs formore luminosity

Emiss − Pmiss (πµ hyp) (MeV)32F. Bossi, CSN1, Frascati 14 Ottobre 2005

R = Γ(K± → e± ν) / Γ(K± → µ±ν ) and new physics

This ratio is a sensitive probe for new physics effects(see G. Isidori’s talk)

Standard Model Prediction: R = (2.472 ±0.001) x 10−5

NA48/2 Preliminary 05: R = (2.416 ±0.049) x 10−5

NA48/2 can reach ~ 1% precision with present data

Scaling from measured efficiencies for Ke3 decays KLOE can aim at ~ 0.5% @ 20 fb−1

Use of a vertex chamber could greatly improve efficiency


Detector Issues


The ingredients of KLOE success

E.M: Calorimeter: Drift Chamber:

Full angular coverageExceptional timing capabilitiesLarge lever arm

Good momentum resolutionLarge tracking volumeMinimization of materials

Excellent e/π separation based on t.o.f.

Good π0 reconstruction capabilities

Full kinematical reconstruction of events

Maximization of efficiency for long-lived particles (K± ,KL)


There can be improvements

Still, based on our experience, some possible modificationscan improve KLOE performance

• Use of a lower magnetic field. This can increase acceptancefor several of the above mentioned channels and easepattern recognition

• Insertion of a vertex chamber. At present, first tracking layeris at 30 cm (i.e. 50 τS) from the I.P.

• Try some z coordinate reconstruction in the drift chamber. Pattern recognition would benefit of it.

• Increase calorimeter’s readout granularity. Can improvephoton counting, as well as particle identification.


An explicative example from K+K−

Split track Split track, no VTX reconstructed


Summary (I)

A high luminosity Φ−factory is a perfect tool to study a widevariety of relevant physics topics in several distinct and

complementary ways

With KLOE we have learned a lot on how to perform thesemeasurements and have solid ideas on the potentialities of our

detector

We have also several ideas on the potential improvements thatcan be done and intend to study in detail the feasibility and

relevance of all of them in the coming months


Summary (II)

Upgrades of the detector can likely be of importance for otherimportant studies, which I did not mention previously because

of lack of time and/or because real potentialities have to beunderstood yet:

KS → π0e+e− (π0µ+µ−)

KS → π0 γγ

KS → e+e− (µ+µ−)

KL → γγ

KS lifetimeImproved Vus measurement


La Fisica dei K a DAΦNE-2 · La Fisica dei K a DAΦNE-2 F. Bossi CSN1, Frascati 14-15 Ottobre 2005...

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