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The physics potential of the electron-positron collider daφne

Wolfgang Kluge ^a

a Institut für Experimentelle Kernphysik, Universität Karlsruhe, Postfach, Karlsruhe, Germany

To cite this Article Kluge, Wolfgang(2001) 'The physics potential of the electron-positron collider daφne', Surveys in High Energy Physics, 16: 1, 13 — 37

To link to this Article: DOI: 10.1080/01422410108225683 URL: http://dx.doi.org/10.1080/01422410108225683

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Surveys in High Energy Physics, 2001, Vol. 16, pp. 13-37 Reprints available directly from the publisher Photocopying permitted by license only

0 2001 OPA (Overseas Publishers Association) N.V.

Published by license under the Hanvood Academic Publishers imprint, part of Gordon and Breach Publishing, a member of the Taylor & Francis Group.

THE PHYSICS POTENTIAL COLLIDER DAmNE

OF THE ELECTRON

-

POSITRON

WOLFGANG KLUGE*

Institut f iir Experimentelfe Kernphysik, Universitat Karlsruhe, Postfach 3640, 0-76021 Karlsruhe, Germany

(Received in final form 6 September 2000)

The physics to be pursued a t the electron-positron collider D A a N E in Frascati with the detectors DEAR, FZNUDA and KLOE is addressed, with particular emphasis on the test of discrete symmetries in the neutral kaon system, measurements of cross sections of hadron production following electron ^~ positron annihilation and tests of chiral perturbation theory to be carried out with KLOE and DEAR.

Keywords: Discrete symmetries; CP-violation; Kaon decays; Hadronic contribution to vacuum polarisation; Tests of chiral perturbation theory; Storage ring DAaNE;

Detectors DEAR; FZNUDA and KLOE

INTRODUCTION

The symmetric collider DAiDNE accelerates and stores electrons and positrons of 510 MeV to produce 4-mesons with the mass 1020 MeV/c2 and the quantum numbers J p c = 1 ^-via the reaction e+e- +

y* +

4.

The &mesons decay mainly into charged and neutral kaon pairs K + K - (branching ratio BR = 49.5%) and @Ko(K&) (BR = 34.3%), but also into p r and r+r-ro (BR ⁼15.5%), qy (BR= 1.3%), q'y (BR= 1.2

.

The neutral kaon pairs are produced in a well defined quantum and kinematical state with charge

*Tel.: ( + 7 247) 82-3537, Fax: (+ 7 247) 82-3414, e-mail: [email protected] karlsruhe.de

13

Downloaded By: [CERN Library] At: 22:57 25 March 2010

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parity C = - 1 :

The kaons are monochromatic (the momentum of the charged kaons is 127 MeV/c and that of the neutral ones 110 MeVjc) and are emitted back-to-back to be detected in an almost backgroundfree environment. Absolutely unique to DAQNE is the possibility to study interferometric patterns of neutral kaons and the tagging of Ks (or

KO)

by its KL (or

KO)

companion and vice versa as well as the tagging of Kt by K - (and vice versa) facilitating the investigation of rare KL and Ks as well as K + and K - decays.

-1 -1

s corresponding to an integrated luminosity of Jltechn.year Ldt =

1 0 7 s . 5 . 1 0 3 2 c m - 2 ~ - 1 = 5 ~ 1 0 6 n b - ’ (1 ‘technical’yearto betakenas 107s) 2 ^I10” +-mesons will be produced decaying into 10’’ charged kaon pairs and 0.7.10’0 neutral kaon pairs. In the light of those numbers it seems to be justified to call DAQNE [2] a ‘&factory’ or

‘strangeness producing factory’. DAQNE has two interaction regions.

At present DEAR [ 3 ] is located in one of them to be replaced by FINUDA [4] in a later stage. In the second one KLOE [5] has been installed. DEAR (DAQNE Exotic Atoms Research) has been designed to measure the shift and width of the 2p-1s X-ray transition of kaonic hydrogen and kaonic deuterium. FINUDA (FIsica NUcleare ar DAQNE) will investigate the production, weak decays, life times and spectroscopy of hypernuclei. KLOE ( K L o n g Experiment) is a universal detector to study all kinds of K , q5, p,

v,

7’ decays emphasis- ing tests of discrete symmetries (CP-, CPT-, T-invariance), measurements of hadronic cross sections and tests of chiral perturbation theory ( x P T ) . Due to the possibility to test xPT in a large number of decay modes DAQNE has also been called a ‘chiral’ machine [6].

With a design luminosity of

L

M 5

.

lo3’ cm-’ scl = 5 . lo2 pb

K-PHYSICS

Kaons played always a crucial role in particle physics and led to fundamental discoveries. The observation of the so called associated

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THE PHYSICS POTENTIAL OF D A a N E 15

production r - p -+ AK inspired the introduction of a third Cflavour) quantum number strangeness. Strange was the copious production of A hyperons (by the strong interaction) compared to their relatively long lifetime of 10-’os (driven by the weak interaction). For the first time particle - antiparticle oscillations K O #

I?

have been observed with neutral kaons. The ‘6 - T puzzle’ observed in the decays of K+

into 2 and 3 pions gave rise to the fall of parity and led finally to the discovery of the V-A structure of weak interactions. The quark model with the underlying group SUF(3) was formulated including the strange particles. The idea of chiral symmetry SUL(3) €$ SUR(3) was born (see below) and its spontaneous breaking into SUF(3). The light pseudoscalar particles r, K, 7, (7’) have been identified as the bosonic excitations (Goldstone bosons) of the spontaneous breaking of chiral symmetry. By comparing the strength of r and K decays the Cabibbo angle 6, has been defined and the first step was done of establishing the more complete Cabibbo-Kobayashi-Maskawa Matrix.

It turned out that the mass eigenstates of the up and down quarks are not the eigenstates of the weak interaction, but rather the quark doublet

(

^:c) ⁼

(

dcos6c fssin6, U

The extremely small branching ratio of 7. observed for the decay KL + p + p - indicated that there exist no flavour changing neutral currents in nature. This could be understood by the GIM mechanism necessitating the existence of a second quark doublet and thus predicting the fourth (flavour) quantum number charm

(h)

⁼(-dsin6,+scos6, C

CP-violation finally required the existence of a third generation of fermions and in particular the fifth and sixth (flavour) quantum numbers bottom and top. The weak eigenstates are given by the Cabibbo-Kobayashi-Maskawa Matrix ( C K W V

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with

1

- p

^X AX3(p ^-iq)

v = (

-A 1 -;A2 AX2

0.9751 0.221 /0.00351 0.221 0.9743 0.041

4

10.0091 0.040 0.9991

AX3(l ^-p - iq) AX2 1

1

which is a very special unitary matrix with 4 real parameters (where the imaginary part q

#

0 is responsible for CP-violation). It is almost diagonal, almost symmetric, while the matrix elements get smaller moving away from the diagonal. The matrix connects intimately CP- violation to basic questions of the standard model SM: W h y there are families? W h y there are three? W h y there are so diferent fermion masses?

TESTS OF DISCRETE SYMMETRIES (CP-

,

T- AND CPT-INVARIANCE)

The main goal of the experiments at D A a N E are tests of discrete symmetries, i.e., tests of CP-, T- and CPT-invariance [1,7-lo]. CP- violation is the least tested corner of the S M and its potential source is the Yukawa sector, the interaction of the fermions with the Higgs particles. CP-violation might be a reflection of physics at much higher energies, at the Grand Unification scale of ^NNlOI5 GeV or even at the higher Planck scale of ^M1019GeV. It might also be the origin of the asymmetric distribution of matter and antimatter in the Universe.

The existence of CP-violation allows us to distinguish matter and antimatter, left and right without any convention and even defines an arrow of time, if CPT-invariance holds. The former is immediately seen remembering that the long living KL decay more frequently into positrons than into electrons. If T invariance is violated, the principle of detailed balance does no hold:

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THE PHYSICS POTENTIAL OF DA@NE 17

The neutral kaon system is a very peculiar one.

I?

and

KO

are not CP- eigenstates, but rather the linear combinations K1 =

&

^(KO

+ ^KO)

^MKs and K2 = -!-(KO -

KO)

^MKL, being the short and long living neutral kaons with exponential decay laws and CP-eigenvalues of

+

1 and - 1, respectively. With CP- and CPT-violation these wave functions are given by

4

cK and SK are small complex numbers characterising unequal admixtures of

I?

and K O to the Ks and KL states. CP-conservation would mean: cK = 0 and CPT-conservation: SK = 0.

If CP-conservation would hold the CP-even kaons K 1 rz Ks would decay exclusively into a CP-even state with two pions, while the CP- odd kaons K2 M KL would decay exclusively into a CP-odd state with three pions. A decay of KL into two pions obviously violates CP- invariance. This observation is known since more than 35 years. It has been found in hadronic and semileptonic decays: KL -+ r + r , KL ^-+

roro, KL + r

* P v ( !

= e , p ) . The only dynamical information, however, yielded after almost 4 decades of great efforts, are the moduli

Iv+ - 1

and

lvool

of the amplitude ratios

The values are

Iv+ - 1

⁼(2.285 f 0.019)

.

l o p 3 and

lvool=

(2.275 f 0.019).10-3. The phases $ + - =(43.5&0.6)' and q500=(43.4~ 1.0)' agree within the error bars and with the so called superweak phase q51;sw = arctan(2Am/Ar) = (43.44 f 0.09)', therefore not revealing new information on CP-violation (Am = mL - ms and A r =

rS

-

rL).

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The value for the charge asymmetry observed in semileptonic decays

= (3.27 0.12)

.

1 0 - ~

does not provide new information. The value of ^EK measures CP- violation in oscillations between KO and

KO

(traditionally called

‘indirect’ CP-violation): the oscillation probability KO

+ KO

is different from that of K O

+

@, being of 2nd order in the weak interaction with a total change of strangeness A S = 2 (Fig. l), while the value of ^E’ measures CP-violation in the decay amplitude with AS= 1 (‘direct’ CP-violation). Indirect CP-violation can be ascribed to an admixture of c K . K1 with the ‘wrong’ CP-eigenvalue to the K2 state (or E ~ K ~ to the K 1 state). Hence, A ( &

-

^mr)⁼E ~ A ( K ~ + nr) E

E K A ( K , -+ m) and 7 7 % ~ ~ . The direct CP-violation can be expressed e.g., as the direct decay of CP-odd K2 into a CP-even final state A(K2

+ m)

#

0 without preceding oscillations. In the SM it is described by so called electroweak and gluonic penguin graphs (Fig. 2). There need

S

FIGURE 1 Oscillations (mixing) of i? into Ro and vice versa occur due to 2nd order weak interactions. The complex matrix element VTd(6) i s responsible for ‘indirect’ CP- violation with a change of strangeness by two units A S = 2 .

-

ii, c, ^f

G, 2 O . y

- U

d d

n+

n -

FIGURE 2 Penguin graphs are responsible for ‘direct’ CP-violation in the amplitudes due to 1st order weak interaction with A S = 1.

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THE PHYSICS POTENTIAL OF DAQNE 19

to be two interfering amplitudes: in the case of two pions in t h e j n a l state an interference of two weak decay amplitudes A. and A2 with different CP-violating weak phases ^{4 0}and q52 is required where the indices denote the isospin I = 0 and I = 2 of the two pions.

I /Zoorphotonpenguin = tan& gluonpenguin = tan&

To summarise, there exist various ways to violate CP-invariance: the indirect CP-violation in oscillations (or mixing) with AS = 2, the direct CP-violation in the decay amplitudes with A S = 1 and mixing induced CP-violation as an interference between mixing and decay

. ZmAO

E = & K + z - = EK

+

itan

40

%eAo

The measurement of E’ has a long history, yielding in a first round of experiments (CERN NA31 and Fermilab E73 1) contradictory results which only recently have been better converging (Fermilab KTeV and

CERN N A 48):

Re&’& = (23.0 f 6.5)

.

lop4 CERN - NA311993[11]

XeE’E = (7.4 f 5.9)

.

!Re&’& = (15.0 f 8.0)

.

l o p 4

!Re&’/& = (28.0 f 4.1)

.

%E’/E = (12.2 f 4.9)

.

low4

FermilabE73 1 1993 [ 121 world average value before 1999[13]

FermilabKTeV 1999 [ 141

CERN - NA48,Junuary2000[15]

= (18.5 f 7.3)

.

^10-4 CERN - NA48 [ 151

KLOE intends to measure Re&‘/& with the same accuracy of a few l o p 4 as is the goal of the CERN and Fermilab experiments, but with a completely different experimental set-up and consequently different systematic errors. A jinite value of ^E‘ is indicative for CP-violation within the SM (i.e., in the Cabibbo-Kobuyashi-Maskawa matrix). It rules out the superweak model of CP-violation with an one-step A S = 2 transition between K O and KO in which the value ^E’ would be

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zero by definition. The method (as used by the CERN and Fermilub experiments) to measure E' is the determination of the double ratio

KLOE has been designed to use this method as well as kaon interferometry to be discussed below based, of course, on the same data sample.

KAON INTERFEROMETRY [1,7-10]

At DAQNE a novel phenomenon can be studied for the first time:

interference patterns which arise due to the existence of two amplitudes in the initial quantum state of the neutral K system being produced in the &decay with the charge parity C = - 1 :

- 0 - 0 1 L - s

KpK-a)

=

- (K@K-- -

Jz

P

The interference patterns depend on the various final states

fi

of K s and KL decays and on the difference of the proper times A t = tl - t 2 at which the two kaons decay. The amplitude ratios ql = ( & ~ K L ) /

&

IK,)) = lqjle-'di contain all relevant parameters which describe CP- violation and possible CPT-violation and parameters like Am,

rS, rL

as well. In principle also possible effects of quantum gravitation or a violation of the validity of quantum mechanics would reveal in these patterns. With the given initial neutral kaon state the amplitude for the decay of Ks at time tl into the final statefi and of KL at time t2 intofZ (and vice versa) is

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THE PHYSICS POTENTIAL OF DAaNE Examples of Kaon Interferences:

21

With identical final states (fl =f2 = 7 r f 7 r - ) precise values

rL, rs,

Am, $sw are determined. For equal proper times (At=O) the amplitude Acfi, t l ; fi, t l ) = 0 and the rates are zero at At = 0 and symmetrical around At = 0 (destructive interference):

In this case no information on CP-violation is obtained, but tests of quantum mechanics (in the spirit of the Einstein-Podolski-Rosen paradoxon) are possible.

With almost identical final states

cfi

⁼^{T + T -}^{and f 2}⁼^ro7ro)^XeE'^is

obtained for large time differences At and Zm& for /At[

<

5 ~the ~ , latter determining r$+- - 400

=

3Zrnd/~. The interference is con- structive (Fig. 4).

For semileptonic decays f i =n-C+u and f2 =

r+B-v

the CPT violating parameters XeSK and ZmSK are determined for large time differences and for lAtl

<

5r8, respectively. The interference is destructive (Fig. 5).

For f i = 7r7r and fz = r+C-v or ?r-C+u small time differences yield Am, lqnxl and $,,, while for large time differences tests of T- and CPT-invariance are possible.

&'(AS = I)

KO

* f

R"

. 3 m A ,

& = & K

+

^I^-

m e A,

FIGURE 3 There are three ways of CP-violation: 'indirect' CP-violation in mixing described by EK with AS = 2, 'direct' CP-violation in the amplitudes described by E' with AS = 1, and mixing induced CP-violation as an interference between oscillations and direct decay.

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1.2

1 0.8

0.4

0.2

0

~ * I - t & ,

FIGURE 4 Interference pattern of almost identical final states as to be observed in the decay of neutral kaon pairs which have arisen from the decay of &mesons, where one kaon decays into the final statefi = ? T + B - and the other into the final statef2=?ya?ya.

35

3 2.5 2 1.5

1 0.5

0

*4tftp)lctl

FIGURE 5 Interference pattern of semileptonic decays as to be observed in the decay of neutral kaon pairs which have arisen from the decay of &mesons, where one kaon decays into the final statefi =n-!+v and the other into the final statef2 = a+!-P.

CP-VIOLATION IN K s AND CHARGED KAON DECAYS The production of about 5 . lo9 Ks/year in an almost backgroundfree environment is absolutely unique to DAQNE. Hence, for the first time

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THE P H Y S I C S POTENTIAL OF D A @ N E 23

the CP-violating decay Ks -+ 7r07r07ro with a branching ratio BR ^M2

.

can be observed. The expected rate is about 15 events per year.

The present limit is BR

<

1.9

.

l o p 5 . Also the ‘direct’ CP-violation in charged kaon decays K * -+ T 7 r + C (T -mode decays) or K * + 7r

*

^7r07ro

(7’ *

-mode decays) revealed by an asymmetry like

7rP7r’r-)) can be investigated. Theoretically it is expected, however, to be of the order of lo-’, beyond the sensitivity of KLOE which is l o p 3 . . .

A=

( r ( K + -+r+.iT+q -r(K- -+K-r+r- ) / r ( K + t.iT+.iT+.iT- )

+ r ( r

^-+

SUMMARY

In Table I CP- and CPT-violating and other parameters of the neu- tral K system to be determined with KLOE are summarised together with the present values. An integrated luminosity per year of SLdt = 5 . 1039cm-2 has been assumed. Possible highlights are printed in bold letters.

TABLE I C P -, CPT-violating K L O E ‘highlights’.

CP- and CPT-violating parameters to be measured with DAiPNE- KLOE (integrated luminosity per year of JLdt= 5 . 1039cm-2) and the present values (possible highlights are printed in bold letters)

Ouantitv Present values PDG 1998 Exvected at DA@NE (1.1193 f 0.001)

(0.001 934 f 0.000 015) (0.5301 f 0.0014)

(43.49 f 0.08)”

(2.285 f0.019).10-3 (2.275 f 0.019).

(43.5 f 0.6)”

(3.50 f 14.0). lOW3 (2.282 f 0.014).10-3

(21.2 f 2.8). 1 0 - ~ (-0.1 f 0.8)”

( 3 . 2 7 ~ 0 . 1 2 ) . 1 0 - ~ (1.652 f 0.026).

(-0.3 f 0.35). lo--’

(0.24f0.28).10-3’

(1.5 f 2.3 4~ 2.3 f 0.3).

(0.024 f 0.050).

‘global information (1.4 f 5.6).10-’9*

f 0.000 010 f 0.000 001 f 0.0012 f 0.000 6

-

f 0.000 9 *

f i.6.10-~

f 1.2.10-~

f 0.000 6.1y-3 f 0.04.10- f 0.25.10-3 f 0 . 0 1 . 1 0 - ~ f 0.06.10-~

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CLOSING REMARKS ON CP-VIOLATION

KLOE is part of a worldwide venture to find an answer to the question of CP-violation. Other efforts regard very rare decays of neutral kaons: K f + .rr+vV [order O(l0-")I, KL + .rrovV [order O(lO-'o)]

(Fermilub-KTe V , Brookhaven-AGS, KEK), the decay of B-mesons (SLAC - BABAR, KEK - BELLE, Cornell - CLEO, DESY - HERA B, and future projects Fermilab-BTeV, LHC-ATLAS, C M S , LHC B) and of charmed particles ( B factories, Fermilub), hyperons (Fermilab) and r leptons (CERN, B-factories, BES-Beijing). Also searches for non SM origins of CP-violation are pursued, e.g., in the investigation of the transverse polarisation of muons in K* + p

*

vn0 (KEK, AGS), in measurements of the electric dipole moment of neutrons (ILL) and electrons (Seattle, Berkeley and Amherst).

WHERE DO WE STAND WITH CP-VIOLATION?

The violation of CP-symmetry is clearly established, because the long living neutral kaons decay into two pions: KL -+ mr. The origin of CP- violation is unclear. If the parameters E and E' measured in the decay K L + m are to be described within the SM (i.e., within the CKM matrix) there must be large CP-violating effects in B decays because quarks of the third generation are already involved in first order. The predictions for B decays (e.g., B: + J / $ K , ) are very precise in the S M . If no CP-violation will be found in B decays, the S M will be clearly in trouble. 'New physics' then drives the decay KL + mr. But which one?

The measurements of E' has given an important hint (KTeV, NA48), but B decays will be finally decisive.

MORE KLOE PHYSICS

Besides tests of discrete symmetries KLOE will address a wide field of important questions in particle physics. Among them are tests of chiral symmetry breaking schemes in K,

4

p, 7, 7' decays, and measurements of cross sections of e+e- annihilation into hadrons. Tests of the breaking of chiral symmetry will comprise measurements of form

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THE PHYSICS POTENTIAL OF D A @ N E 25

factors in Ke, decays, the determination of m p h a s e shifts in Ke4 decays ( K

*

^-+ ^n-+x-e

*

^v,, K

*

⁴xOroe

*

^u,, KL -+

*

e f u ) , radiative K decays etc. The data can be compared with existing predictions of chiral perturbation theory [l]. These problems are discussed in more detail in a dedicated Section below.

Hadronic Cross Sections

Cross sections for the production of hadrons after the annihilation of electrons and positrons at energies between 0.3 and 1.4GeV ( e + e - -+

y* + hadrons) will be measured with a precision below 1

YO.

They are of great relevance mainly for two reasons [16]. They are needed to determine with better accuracy the hadronic correction of the vacuum polarisation according to (e'e- +)y* -+ qq (see Fig. 6) and, hence, are important for the interpretation of a new measurement of the anomalous magnetic moment of the muon a, as a precision test of the SM (going on in Brookhaven [17]) and for the determination of the value of the running fine structure constant at the

2

resonance a(rn;) which is presently one of the limiting factors for further precision tests of the SM [18].

The various terms contributing to a, are given in the following sum together with the present values and corresponding errors

atheor - - aQED ⁺ahadr ⁺aweak + anew phys.

P fl fl fl

,

= (1 1658470 f _0.5

+

⁷⁰³^f¹⁷

+

²⁰^f1

+

^?)

.

lo-''

FIGURE 6 The hadronic correction to the vacuum polarisation of muons

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The first and by far largest contribution comes from QED, the second term denotes the virtual hadronic (quark) contribution, a r k sum- marizes the weak effects due to virtual W ,

9

and Higgs particle ex- changes and aFw phys. stands for contributions from possible extensions of the S M . Within the present experimental accuracy of u F P =

(1 1 659 192 f 18)

.

10-l' theory and experiment are in best agreement:

- (-38 =t 85)

.

lo-", but the electroweak corrections are still hidden in the uncertainties of both experiment and theory. This situation will change, if the Brookhaven experiment will succeed to achieve its goal of an experimental error of f 4 . 1 0 - " and if the hadronic correction can be determined with an error of 3 1.5. lo-'' using mainly new data from KLOE. Low energy experimental data are indispensible because the hadronic vacuum polarisation at low energies cannot be calculated by using perturbative QCD. One rather has to rely on a semiphenomenological approach using a dispersion integral which allows to compute the hadronic contribution as an integral over experimental data from electron ^-positron annihilation into hadronic state

atheor - aexp -

P P

gtot(e+e- -+ y* -+ hadrons) gtot(e+e- -+ y* --+ p f p - ) R(s) =

where K(s) is a smooth function. The energy denominator l/s2 ^Ml / E 4 of the integral enhances dramatically the low energy (non perturbative) contributions. Actually 90% of the total hadronic contribution can be derived from hadronic cross section measurements below

1.4 GeV accessible at DABNE.

Hadronic data of electron ^-positron annihilation cross sections will also contribute to improve the accuracy of the shift Aa(mg) of the running fine structure constant at the

9

resonance. The value of a (s) plays a crucial role in precision tests of the S M . Most of the S M predictions depend on Aa(s) including the prediction of the Higgs mass. Like in the case of the anomalous magnetic moment of the muon the low energy hadronic contribution to Aahadr can only be obtained by a dispersion integral and is also limited nowadays by the unsufficient knowledge of the hadronic cross sections. It turned out

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THE PHYSICS POTENTIAL OF DAQNE 27

recently that perturbative QCD calculations can be performed down to M 2.5 GeV [19]. Therefore the need of precise hadronic cross sections at lower energies is even more mandatory than before.

In recent years the energy dependence of the hadronic cross sections has been measured by changing (scanning) the energy of the accelerator [20]. DA@iVE will, however, be operated at the

4-

resonance for any foreseeable time. Therefore, it has been suggested [21] to use the emission of real photons in the initial state (initial state radiation ISR’) to measure the energy dependence of the dominant hadronic final states (see Fig. 7). ISR reduces the c.m. energy s = Q2 = m$ - 2Errn$ of the annihilating electrons and positrons and consequently of the final hadronic state from the energy of the 4(1020) resonance down to the two pion threshold. Both methods to measure the energy dependence of hadronic cross sections (ISR and the energy scan) are totally complementary due to different systematic errors [22].

Using the ISR method has the advantage that the errors of the measured luminosity and of the energy of the electrons and positrons enter the photon spectrum and consequently the hadronic (Q2) spectrum only once. The very good energy resolution to be obtained for the photon spectrum results most of all from the precise measurements of the momenta of the charged pions in the KLOE drift chamber E7 =

F(T-)

^+p’(r+))

.

c. As a consequence the overall normalisation error is the same for all energies of the hadronic system, if energy dependent efficiencies and cuts can be controlled reliably.

Another advantage is that the data are taken as a by-product of the

e+ e- ^--i,y

+

hadrons 2mn2 < s,+,-

.=

me 2

FIGURE 7 Graphs showing the initial state radiation from electrons and positrons.

‘At LEP the ZSR leads to a ‘radiative return’ to the 2-resonance, at DACJNE it is observed as the return to the p- and w-resonances.

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standard experimental program of KLOE without changing any details of the set up. Clearly the ISR method is restricted to energies below the &resonance and the analysis has to take into account radiative corrections and the emission of photons in the final state (FSR).

Hadron Spectroscopy

The structure of the two scalar mesons a. and fo with Jpc = O + ⁺and masses lighter than the $-meson which are generated in the radiative decays

4 -

^ao/foris still puzzling. They might be e.g., qqqq states or K K ‘molecules’. The decays of ~ ~ ( 9 8 0 ) into “q and K K have been observed (ao being an isovector?), also the decays offo(980) into mr and K K dfo being an isoscalar 3s state?). Measurements of ratios like B R ( 4 -+ ao~)/BR(q5

-for)

would help to clarify those questions. G- parity violating (isospin breaking) decays as q5 + row, p

*

-+ ^T q and

q’ ^---fp ^7rT will be investigated. Radiative decays of &mesons into

pseudoscalar mesons (4-77, 45-77’) might help to constrain the glue content of the q’ and reveal possible q - q’ mixing. The q’ does not seem to be a pure l S ( q q ) but to have admixtures of 2S(qq) and/or gluonic contents. The interest in the coupling of gluons to q’ has been renewed by the abundance of q’ in B-decays. The results should be compared with the decays q

-

^p/w^yprobing the uzi

+

dd contents of q and 7’. In addition the branching ratios BR(4

-

^yq)/BR(4^-+^yq’)

might probe the 3s content of q and 7’.

CHIRAL SYMMETRY AND ITS BREAKING IN QCD (DEAR AND KLOE PHYSICS)2

The strong interaction is successfully described by Quantum Chromo- dynamics (QCD), by the interaction of coloured quark and gluon fields, qq and Gtv, respectively. The interaction Lagrangian contains among many other terms a quark mass term which is most relevant at low Lagrangian is invariant under the locul colour gauge transformations energies as available at DA@NE : LQCD = LQcD 0 - Cq=u,d,smqq.ij. This

’This Section is indebted largely to J. Gasser and G. Colangelo.

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THE PHYSICS POTENTIAL OF DAQNE 29

SUc(3) by construction. Furthermore it would also be invariant under the global SUf(3) flavour transformation if the three light quark masses would be equal in nature (m, = md= m,y). The quark fields transform then according to q' = exp(iO"Xu/2)q. The indices run over the flavour quantum numbers isospin up, isospin down and strangeness. If the light quark masses would even be zero (which is called the chiral limit defined by m,=0) the Lagrangian would be invariant under separate left and right handed flavour transformations SUL(3) @

SUR(3) and the left and right handed quark fields would transform independently

This chiral transformation can be written analogously to the transformation S U f ( 3 ) as

q' = exp(iy5P~"/2)q.

As a consequence of this flavour symmetry eight vector and axial vector currents and the corresponding vector and axial vector charges are conserved

(the former is known as the theorem of Conserved Vector Current CVC). The chiral symmetry would cause a doubling of hadron multiplets, the existence of baryon partners with J" = 1/2- and scalar meson partners with O + and equal masses which are not observed in nature. This led to the idea of the spontaneous breaking of chiral symmetry. The combined transformation SUL(3) @ SUR(3) is broken down to SUf(3). The Lagrangian is symmetric under the symmetry group but the ground state (the QCD vacuum) is not and the vacuum expectation value is unequal zero (Ol@lO) # O . The spontaneously broken (hidden) global chiral symmetry results in the excitation of eight massless pseudoscalar bosons. These Goldstone bosons acquire their finite and different masses from those of the light quarks and appear in nature as real (the light) pions, kaons and 7-mesons with m,

#

mK

#

m,

#

0. The quark mass term in the Lagrangian is thus

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responsible for the explicit symmetry breaking. Low energy theorems (previously derived in the chiral limit m, = 0 by means of Current Algebra and Partially ConservedAxial vectorcurrent) have become inte- gral constituents of QCD. In spite of its breaking chiral symmetry is the most important guide in the realm of low energy (nonperturba- tive) QCD and follows in a unique way from the structure of the Lagrangian and explains many observations (meson nucleon scattering, hadronic mass spectrum, decays). At low energies energies we do not deal, however, with quarks and gluons but rather with hadrons (mesons and baryons). Chiralperturbntion theory

(x

P T ) is the tool to bridge this gap [23,24]. It is a well defined effective quantum field theory and allows to derive unambiguously the consequences of the approximate chiral symmetry of the strong interactions for any observable by searching for the most general effective Lagrangian which is compatible with chiral symmetry. Since pions, kaons, and q interact weakly at low energies the vertices can be expanded in powers of 4-momenta and quark masses in the neighbourhood of the chiral limit. Within this perturbative expansion all the good properties of a quantum field theory (like unitarity and analyticity) are automatically respected. All possible graphs are calculated and the parameters of the theory (effective coupling constants, masses) are renormalised order by order. At low energies (< 1 GeV) this framework allows to make in some cases very precise predictions (of the order of a few percent).

At each order, however, appear parameters which are not constrained by chiral symmetry, but have to be determined by experiments. In the sector of strong interactions the lowest order Lagrangian

,d2)

^contains

2 constants, at the next-to-leading order

d4)

contains 7(10) constants if the numbers of flavours N f = 2 (Nf= 3), and at the next-to-next-to leading order 53 (90). In the weak sector the Lagrangian ,C$Jak contains also 2 constants, while at the next-to-leading order L:Jak contains 37. A guide through the forest of 0 ( p 4 ) constants in the weak sector is shown in Figure 8 [25].

DABNE and Tests of the Breaking of Chiral Symmetry

DAQNE, as mentioned above, has been baptised a ‘chiral’ machine [6]

because it allows a wealth of investigations and tests in the realm of chiral symmetry. In preparation of the forthcoming data taking with

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THE PHYSICS POTENTIAL OF D A @ N E 31

opaamrs

1

9 opaaton with an erplicity &Id (F t-)

J

13 meratom without

J I

Y

! I

j

I 1 1

ⁱ

i

K * Z n r + r - K-Jny

I

^K-^{x 1-}

1

^t- K + - n ' y y

K - 2 n y K - n n y y

i

K - Z n y

+ K - 3 n y

K- x

IattiFsQCD K-r ' x i K - 2 1

K-33%

(quad slopes) K - 3 x

1

FIGURE 8 A guide through the forest of 0(p4) constants (courtesy G. Isidori) [25]. In the weak sector the Lagrangian L!2a of chiral perturbation theory contains 2 constants, while at the next-to-leading order L!Jak contains 37.

DEAR, FINUDA and KLOE enormous theoretical efforts [I] have been undertaken to calculate cross sections, scattering lengths, decay rates etc.

m Scattering (KLOE Physics) [24]

A 'golden' testing ground of x P T is the determination of the TT

isospin I=O and 1 = 2 5'-wave scattering lengths u! and u;. It will be an important challenge for KLOE to determine those numbers in the Ke4 decays of K' ⁺z f K e v,, Ki ⁴zozoe

'

^u,^and

KO-+

TOT

*

eFu. The expansion parameter is small (m:/l GeV2 x 0.02) and a tree level calculation is already relatively accurate. But it turned out that one-loop and two-loop calculations present substantial corrections confirmed by a preliminary analysis of a recent experiment

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by means of dispersion relations (Roy equations):

857

Log+-Log2+... 42 with L o g = m ~ / ( 4 . i r f , ) 2 1 n ( m ~ / ~ 2 )

tree 1-loop 2-loop

---

at =0.156+0.039+0.005+0.013+0.003+0.001 =0.217

"

0.201

/I being the scale parameter.

MESON-NUCLEON (KN AND KN) o-TERMS

AND THE STRANGE CONTENT OF THE NUCLEON (DEAR PHYSICS)

During recent years the determination of the 7rN a-term has received much attention [23,26]. It appears as one of the most important numbers of non perturbative QCD because it determines not only the size of the explicit breaking of chiral symmetry but provides also hints as to the size of the nucleon matrix element (Nl3slN) of the scalar operator 3s that is on the content of the strange sea quark pairs in the nucleon. A non vanishing value of (NISslN)

#

0 would determine the contribution of strange sea quark pairs to the mass of the nucleon. Similarly non zero matrix elements of the axial vector operator (NISysypslN) and of the vector operator (NISy,slN) would contribute to the spin and magnetic moment of the nucleon. Within the naive quark model with explicit chiral symmetry breaking (m4

#

mu

#

md

#

m,) the 7rN a-term is given by

?TI (Nluu

+

^ddlN)

a,N = - with

m = (m,

+

md) and mN the nucleon mass 2 m ~ 1 - y

1

where an unknown contribution of strange sea quarks is para- metrised by

2 ( N 15s IN) (Nluu

+

d d l N ) . Y =

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THE PHYSICS POTENTIAL OF DAQNE 33

In K N scattering two a-terms can be determined

where It = 0 , l are the isospins in the t-channel. The factor (1 +y)/

( 1 - y ) indicates a higher sensitivity to changes of the parameter y than in the 7rN case. In the chiral limit (m4 = 0) the a-terms would all be zero proving that they are a direct measure of the explicit breaking of chiral symmetry. In first order perturbation theory the .rrN and KNa-terms can be expressed by hadron masses

yielding M 275 MeV and

air')

^M65 MeV. By means of heavy baryon chiral perturbation theory approximate values of

&To)

^M

493.

.

.703 MeV and

a(j!F1)

^M^73.

.

.216 MeV have been obtained [27].

All meson-nucleon a-terms are defined in an unphysical kinematic region unaccessible to a direct measurement. Generations of theore- ticians and experimentalists have worked on the problem of the ^7rN 0-term the only one which has been established with reasonable confidence. Its history has not come to an end even until today due to still some contradictory experimental data and also due to unfin- ished theoretical work.

To determine the 7rN a-term input is required both from experiment and theory. On the experimental side precise data on .rrN scattering (scattering lengths, cross sections, polarisation data) are needed in a wide energy range (theoretically up to infinity) to determine the physical scattering amplitudes. These amplitudes have to be continued analytically by means of dispersion relations into the unphysical region. A low energy theorem states that the isospin even 7rN on-shell

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amplitude C =f:D+(0.2m:) at the unphysical Cheng Dashen point v = (s ^-u/4mN) = 0, t = 2m: (the bar denotes that the Born term has been subtracted) is related to the T N a-term a(0,O) at v = O , t = 2m: = 0. More exactly it is given by

C = a(0,O)

+

A,

+

O(m:lnmE).

The term A, has been obtained by dispersion relations A, = a(2m:) -

a(0) x 15 MeV [28], and O(m: lnm:) x 0.35.. .2.0MeV [29] has been calculated within chiral perturbation theory yielding the relation between the 'experimentally' determined amplitude C and the theoretical value of the .irN a-term as C ^M(a+ 15) MeV. By com- parison of C(0.2m:) = (64 f 8) MeV [26] and o(0,O) = (50 f 8) MeV a value of the parameter y ^FZ 0.2 f 0.2 was deduced, a result compatible with zero.

The determination of the KN a-terms has to follow the same route as in the T N case, but is an even more ambitious task due to the present lack of data and also due to theoretical complications involving the larger breaking of SUf(3) flavour symmetry, and a Cheng Dashen point located much farther from the physical region.

Recently it has been argued, however, that DEAR could determine the KN a-terms with an accuracy of about 20% [30].

EXPERIMENT DEAR

DEAR [3] has been designed to measure the isospin dependent K N scattering lengths by a measurement of the shiji ^E(with an accuracy of 1

YO)

and of the width I? (to a few

YO)

of the K, line of kaonic hydrogen ( K - p ) and kaonic deuterium ( K - d ) . This would be an order of magnitude improvement over recent results [3 11

E =

ep"+I,

^-Z $ ~ ~ l , = -327 f 63(stat.) f 1 l(syst.) eV

r

⁼⁴⁰⁷^f208(stat.) f 100(syst.) eV

and represent an important contribution to low energy KN scattering, and insofar to the determination of the KN a-terms and to information on the strangeness content of the nucleon. The scattering lengths Q ~ - ~

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THE PHYSICS POTENTIAL OF DAQNE 35

and aK-d are obtained from ^Eand

r

by i

E

+

2

-r

⁼2a3p&,a~-, = (412eVfm-')

.

aK-, and

with P K - d being the reduced mass and a the fine structure constant, while the isospin dependent scattering lengths a. for 1 = 0 and al for I = 1 can be obtained by aK-p = ( 1 / 2 ) ( a o

+

^{a l )}^and^aK-d⁼2 ( r n ~ +

~ K / ( W I N

+

r n ~ / 2 ) ) a ( ' )

+

^C,^where

do)

is the isoscalar scattering length

do)

= ( 1 / 2 ) ( f + - p + a ~ - , ) = (1/4)(ao

+

3 q ) , and the constant C takes into account higher-order scattering effects.

EXPERIMENT FZNUDA

FINUDA [4] represents a fixed target experiment at a collider. The main goals are the production, weak decays, life time measurements and spectroscopy of hypernuclei, and in a later phase the investigation of low energy K N and kaon nucleus scattering. Hypernuclei are produced by stopped negative kaons K - according to

Ksiop

+*

Z

+An

^Z

+

^r-

which are tagged by their positive companions K + . There are impor- tant improvement of FINUDA over previous experiments which have been carried with extracted (secondary) K - beams. Very thin targets can now be used (0.2 g/cm2), the energy resolution of hypernuclear levels is of the order of 700 keV, the event rates will be of the order of 400/hour at the design luminosity of

C =

5

.

cmP2 s-', almost forty times more than previously, also due to the large acceptance of the detector. Hypernuclei can decay weakly in various ways, in

mesonic decay modes t Z

+*

^(Z

+

1 )

+

^{T -} and $Z +A Z

+

no, nonmesonic ones +A-2 Z + n + n , t z - A - 2 ( 2 - l ) + n + p , where the basic processes are A + n +ro, A + p + ~ - , A + n -+ n+n, A +p + n +p, respectively. Measuring the corresponding partial decay rates

r,-,

I?#,

r,, r,

the lifetime T = of hypernuclei can be

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determined by

rtot

⁼

+r+ +I‘,+r,,

while the ratio I’,/I’, might allow conclusions on the isospin structure of the weak decays, e.g., on a possible violation of the AI= 1/2 rule.

High resolution spectroscopy of hypernuclei will be pursued by detecting the rTT- of the production reaction. There is a long list of hypernuclei, the production, decays and lifetimes of which will be studied, low mass nuclei i L i , :Be, ioB, ;He, f;Li as well as medium heavy and heavy mass nuclei i7Al, i 8 S i , i’V, i 9 Y , X3Cs ’ A (j5Ho, io9Bi.

Acknowledgements

I am grateful to my colleagues and friends of the DEAR, FINUDA and KLOE colaborations at DAQNE in Frascati for many discussions and for providing material for this talk.

References

[I] The Second DA@NE Handbook Vols. I, 11, Eds. Maiani, L., Pancheri, G. and Paver, N., ZNFN-Laboratori Nazionali di Frascati 1995: http://www.lnf.infn.it/

theory/dafne.html

[2] DAaNE: http://www.lnf.infn.it/acceleratori/

[3] DEAR: (1999). Riv. Nuovo Cim., 22(11) http://www.lnf.infn.it/esperimenti/dear/

[4] FZNUDA: http://www.lnf.infn.it/esperimenti/flnuda/finuda.html [S] KLOE: http://www.lnf.infn.it/kloe/

[6] Gasser, J., private communication.

[7] Buchanan, C. et al. (1992). Phys. Rev., D45,4088.

[8] Bigi, I. I. and Sanda, A. I., “CP-violation”, Cambridge University Press, 2000.

[9] BeluSviC, R., “Neutral Kaons” Springer Tracts in Modern Physics 153, Springer- Verlag Berlin, Heidelberg, New York, 1999.

[lo] Kluge, W., Lectures given at the XXIXth Arbeitstreffen ‘Kernphysik‘, Schleching/

Obb., February 25 - March 5 , 1998: http://www.physik.uni-karlsruhe.de/

N gcataldi/phys.html

[ l l ] Barr, G. B. et al. (1993). Phys. Lett., 317, 233.

[I21 Gibbons, L. K. et al. (1993). Phys. Rev. Lett., 70, 1203.

[13] Particle Data Group (1998). Eur. Phys. J., C3(1).

[14] KTeV Collaboration (1999). Phys. Rev. Lett., 83, 22 http://kpasa.fnal.gov: SOSO/

[15] NA48 Collaboration (1999). Phys. Lett., B465: http://www1.cern.ch/NA48/

[16} Eidelman, S. and Jegerlehner, F. (1995). Z. Phys., C67,585: Jegerlehner, F., invited [ 171 Brookhaven Experiment: http://www.phy.bnl.gov/g2muon/home.html

[18] LEP Electroweak Working Group 1999 http://lepewwg.web.cern.ch/LEPEWWG/

[19] Eidelman, S., Jegerlehner, F., Kataev, A. L. and Veretin, 0. (1999). Phys. Lett., public/ktev _. results.html#epsp

Welcome.htm1 “January 2000: Re€’/€ = (12.2 k 4.9). 10 - 4 ’ 7 .

talk LNF Spring School, April 12- 17, 1999: http://www.ifh.de/ N fjeger/

plots/summer99/

B454, 369.

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THE PHYSICS POTENTIAL OF DAQNE 37 [20] Budker Institute of Nuclear Physics Novosibirsk: http://www.inp.nsk.su/detector.

html CMD2 - Cryogenic Magnetic Detector SND - Spherical Neutral Detector [21] Kiihn, J. H., private communication; Binner, S., Kiihn, J. H. and Melnikov, K.

(1999). Phys. Lett., B459, 279.

[22] Melnikov, K., Nguyen, F., Valeriani, B. and Venanzoni, G . (2000). Phys. Lett., B477, 114A. Denig Dissertation Universitt Karlsruhe, May, 1999, unpublished Cataldi, G., Denig, A , , Kluge, W. and Venanzoni, G., KLOE Memo 195, August, 1999; Cataldi, G., Denig, A., Kluge, W., Miiller, S. and Venanzoni, G., Workshop on 'Physics and Detectorsfor DAQNE', Frascati, November 16- 19, 1999, Frascati Physics Series XVI (2000), p. 569.

[23] Gasser, J. and Leutwyler, H. (1982). Phys. Rep., 87C, 77; Ann. Phys. (NU, ^{158, 142}

(1984). Nucl. Phys., B250, 465 (1985).

[24] see for References Colangelo, G., Invited talk at DAFNE99, Workshop on Physics and Detectors for DAQNE, Frascati, November 16- 19, 1999: http://wwwsis.lnf.

infn.it/talkshow/dafne99. htm

[25] Isidori, G., private communication, quoted in Ref. 24.

[26] Koch, R. (1982). 2. Physik, C15, 161; Hhler, G. In: Landoldt-Bornstein, Group 1, Vol. 9b, Ed. by Schopper, H., Springer-Verlag Berlin, 1983; Gasser, J., Leutwyler, H., Locher, M. P. and Sainio, M. E. (1988). Phys. Lett., B213, 85; Kluge, W.

(1991). Rep. Prog. Phys., 54, 1251.

[27] Borasoy, B. and MeiDner, U.-G. (1997). Ann. Phys. ( N Y ) , 254, 192.

[28] Gasser, J., Leutwyler, H. and Sainio, M. (1991). Phys. Lett., B253, 252, 260;

Bernard, V., Kaiser, N. and MjBner, U.-G. (1993). Z. Phys., C60, 144.

[29] Gasser, J., Leutwyler, H. and Svarc, A. (1988). Nucl. Phys., B307, 779.

[30] Seki, R., Frascati preprint LNF-981039.

[31] Ito, T. M. et al. (1997). Phys. Rev., C58, 2366.

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The physics potential of the electron-positron collider daφne

THE PHYSICS POTENTIAL COLLIDER DAmNE

OF THE ELECTRON

POSITRON

4.

.

KO)

KO)

v,

L

.

I?

(

(

(h)

- p

v = (

4

1

#

,

I?

KO

&

+ KO)

KO)

+

I?

* P v ( !

Iv+ - 1

lvool

Iv+ - 1

.

lvool=

rS

rL).

.

KO

+ KO

+

-

#

+

40

.

.

.

.

.

.

=

Jz

fi

&

rS, rL

rL, rs,

cfi

<

=

r+B-v

<

* f

R"

+

.

<

.

*

(7’ *

A=

+ r ( r

-

*

4

*

*

*

+ ^KO)