1 La Fisica dei K a DA NE-2 F. Bossi CSN1, Frascati 14-15 Ottobre 2005.

1

La Fisica dei K a DANE-2

F. Bossi

CSN1, Frascati 14-15 Ottobre 2005

2 F. Bossi, CSN1, Frascati 14 Ottobre 2005

Summary of the talk

DANE and KLOE 1999 2005

PHYSICS ISSUES AT DANE2:

DETECTOR ISSUES

• TESTS OF CPT

• CHIRAL PERTURBATION THEORY

• SOME PREDICTION OF THE STANDARD MODEL


Some basic concepts (and numbers)

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

Daughter particles are monochromatic,

Pch ~ 125 MeV/c, Pneu ~ 110 MeV/c

In resonant e+e collisions, particles fluxes are:

1.5 x 106 K± pairs/pb1

1. x 106 KS KL pairs/pb1

Parity conservation imposes the neutral state to be KSKL


A brief history of luminosity

2

DANE performance up to April 2005

Peak Luminosity

Integrated Luminosity

Present day performance

Lpeak ~ 1.4 x 1032 cm2s1

Best L dt ~ 200 pb1/month

Total KLOE L dt ~ 2200 pb1 (2001,02,04,05)


KLOE papers on K physics

Ks e PLB 535, 37 (02)

Ks PLB 538, 21 (02)

KL PLB 566, 61 (03)

K± ±00 PLB 597, 49 (04)

Ks 30 PLB 619, 61 (05)

KL lifetime PLB 626, 15 (05)

KL main BR, Vus Accepted by PLB

K± ± Accepted by PLB

Plus (at least) as many in preparation


A possible evolution of DANE

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 will discuss here, and refer to as DANE-2 is:

A -factory able to deliver 7-10 fb1 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 DANE-2

• Tests of fundamental symmetries (CP, CPT)

• Tests of prediction of Chiral Perturbation Theory

• Tests of prediction of Standard Model

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

For each of these three topics I will discuss some examples of measurements that can be performed at DANE2. 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), CPT conservation is a theorem. It is consequence of Lorentz

invariance, locality as well as quantum mechanics

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

of quantum gravity

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

the realm of -factories


CPT violation: the “standard” path

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

CP and (possibly) CPT violation

L = 2Re(K )

S = 2Re(K ) +

CPT is violated ifS ≠ L

The most recent measurement are:

S = (1.5 ± 10 ± 3) x 103 KLOE, ~400 pb1

L = (3322 ± 58 ± 47) x 106 KTeV, 02


Potentialities of DANE-2 for S

Assuming present detection efficiencies and a modest improvement in systematic studies, at DANE-2 one could aim at

a total error on S of order 10-3

B (kG)

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

53 4

0.05

0.1

0.15

0.2

A

ccep

tanc

e

However it has already been shown that one can obtain an increase in acceptance up to a factor of 2 just by lowering the B field to 3

kGauss

With some optimism one can hope to reach a

sensitivity on S below the 103 level


CPT and decoherence

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

together with CPT violation

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

standard QM


CPT and decoherence: the EHNS model

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

CPT violating parameters ,, with dimensions of energy

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

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

framework

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

parameters by proper fitting

14

Fixing the EHNS parameters

The EHNS parameters have already been constrained by CPLEAR results

= ( 0.5 ± 2.8) x 1017 GeV

= ( 2.5 ± 2.3) x 1019 GeV

= ( 1.1 ± 2.5) x 1021 GeV

KLOE can reach equal sensitivity on , with present data sample

just with the ++ channel

F. Bossi, CSN1, Frascati 14 Ottobre 2005

15

(/S) (/S) (/S)

fb1 fb1 fb1

• Present KLOE

• KLOE + VDET

Fixing the EHNS parameters

With 20 fb1 one can dramatically improve, especially on and

In the plots below the horizontal line is CPLEAR, VDET means vert = ¼ S


16

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 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()>) + ( І KS(+)> І KS()> І KL(+)>І KL()>)}

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

is still described by the equations of standard QM


Naively, ІІ ~ O(MK2 / MPlank )1/2 ~ 10-3 104

17

Measuring the parameter


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

Arg() = 0,

ІІ = 1,2,3 x 103

t (S units)

fb1

• Present KLOE• KLOE + VDET

A. Di Domenico

A. Di Domenico

18

A note on the previous slides

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

channels, to be studied in more detail.


19

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 is invariant 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 produces 8 massless Goldstone bosons to be identified with the , K,

One then writes down the most general lagrangian consistent with the 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) …

This is the basic idea of Chiral Perturbation Theory

…and one can perform calculations perturbatively


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…


NA48/1 has measured BR(KS ) = (2.78 ±0.06±0.04)x106

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

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

A projection to 20 fb1 would give an accuracy better than 1%

KS : a test for ChPT


KS + 0 : another test for ChPT

ChPT predicts B(Ks +0) = (2.4 ± 0.7)x107

The present experimental value (3.3 +1.1 0.9 ) x107 is the average of three different measurement each individually precise at ~ 40%

A preliminary KLOE analysis obtains sig ~ 1.3%, S/B ~ 2

AssumingError on BR @ 2 fb1 (%)

Error on BR @ 20 fb1 (%)

No further effort made to reduce background ~ 60% ~ 20%

Further efforts completely remove background

~ 40% ~ 12%


KS + 0 as a pedagogical example

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

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

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

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


Study of KS + spectrum

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

at O(p2), BR O(106)

Spectrum is distorted wrt to pure I.B.

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

with E > 20 MeV

Events with 20 fb1: 107 with E > 20 MeV

27

A digression in the world

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

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

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

Tests of C, CP, CPT Tests of ChPT

0l+l

0 3

More on C. Bini’s talk



Predictions of the SM


KS 0 00 : a genuine CP violating decay

MCEff. Stat. =5.3 data

450 pb1

’01+’02 data

2 22 2

23

23

This decay violates CP. SM branching ratio is 2x109

Analysis based on counting and kinematic fit on 20 and 30

hypothesis

KLOE with 450 pb1

B(KS 30) < 1.2 x 107 90% CL

based on 2 observed events with an expected background of 3.1


KS 0 00 : 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 better assessment of the real potentialities of the analysis but…

…there are hints that @ 20 fb1 one can reach ~ 5 x 109

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


KS e decays and the S = Q rule

The relevant parameter here is:

Re (x+) ~<e+ | Hwk | K0 >

<e+ | Hwk | K0 > ~ 106 S.M.

1 + 4 Re(x+) = S

L

BR(KS e) L

BR(KL e) S

=

6 103

1 103 4 103

=

These are KLOE measurements

Present Uncertainties 20 103

@ 20 fb1 one can reach ~ 2 103 in BR(KS e)


Play the same game with muons

Muon semilptonic channel is more difficult:• Lower expected BR ~ 4 x 104

• High pollution from events with decays in flight

• More difficult to separate charge states

• 2002 data MC MC MC

Emiss Pmiss ( hyp) (MeV)

However, it has never been measured before

KLOE has already a clear signal and can reach 3%

accuracy with present data

This channel clearly begs for more luminosity


R = (K± e± ) / (K± ± ) 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 105

NA48/2 Preliminary 05: R = (2.416 ±0.049) x 105

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

Scaling from measured efficiencies for Ke3 decays KLOE can aim at ~ 0.5% @ 20 fb1

Use of a vertex chamber could greatly improve efficiency


Detector Issues


E.M: Calorimeter:

Full angular coverage

Exceptional timing capabilities

Large lever arm

Drift Chamber:

Good momentum resolution

Large tracking volume

Minimization of materials

Good 0 reconstruction capabilities

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

Full kinematical reconstruction of events

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

The ingredients of KLOE success


There can be improvements

Still, based on our experience, some possible modifications can improve KLOE performance

• Use of a lower magnetic field. This can increase acceptance for several of the above mentioned channels and ease pattern recognition

• Insertion of a vertex chamber. At present, first tracking layer is at 30 cm (i.e. 50 S) 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 improve photon counting, as well as particle identification.


An explicative example from K+K

Split track Split track, no VTX reconstructed


Summary (I)

A high luminosity factory is a perfect tool to study a wide variety of relevant physics topics in several distinct and

complementary ways

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

detector

We have also several ideas on the potential improvements that can 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 other important studies, which I did not mention previously because

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

KS 0e+e (0+)

KS 0

KS e+e (+)

KS lifetime

Improved Vus measurement

KL

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1 La Fisica dei K a DA NE-2 F. Bossi CSN1, Frascati 14-15 Ottobre 2005.

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