VILLARS 2004 CERN SPS and PS Committee L. Nemenov 25 September 2004

Creation of an intense source of ππ, πK and other exotic atoms at

SPS proton beam and using them for accurate measurements of ππ, πK scattering length and other low energy parameters to check the

precise low energy QCD predictions

VILLARS 2004 CERN SPS and PS CommitteeL. Nemenov 25 September 2004


perturbative QCD: LQCD (q,g)

interaction „weak“ (asympt. freedom): expansion in coupling

Check only Lsym

chiral sym. & break: Leff (GB: ,K,)

interaction „strong“ (confinement) - but: expansion in energy

Check Lsym as well as Lbreak-sym

q-condensate

QFD

QCD

QED

Standard Model

Q>> Q<<

LOW energy(large distance)

HIGH energy(small distance)


ChPT predicts s-wave scattering lengths:

0

2

0 2

0.220 0.005(2.3%)

0.0444 0.0010(2.3%)

0.265 0.004(1.5%)

a

a

a a

Chiral expansion of the mass:

22 32 2

3

32

( )

u d u d

u d

lM m m B m m B

F

O m m

(1)2where | 0 | | 0 |

is the reflectinga pr

operty of the

, .

quark condensateQCD vacu

u

u

BF u

m

0 2 3

0 3(BNL)

e.g.: 0.260 3% 1 11 or 1.00 / 1.06

E865: 0.216 6% 12 or .98 / 1.06

a a l M M

a l M M

3SchPT 0 5l

(1)

3Measurement of estimate of | 0 | | 0 |:u dl m m uu

scatteringscattering

4( )e eK e K

Rosselet et al. CERN, 1977

0 0.216 0.013 (stat)0.004 (sys) 0.002 (th),

a

Pislak et al. E865/BNL,2001/03

0 0.26 0.05,a 1) using Roy eq.

2a) 0

2

0.203 0.0330.055 0.023

aa

0 1 2 20 1

measurement of the phase difference (s) (s)- (s) for 4 KM s M

2b)

using Roy eq. & 2 ChPT 0( )a f a

DIRAC after analysis of all collected data

0 2( ) 5%( ) 3% ( ) 2% ( )a a stat syst theor

preliminary



I. ChPT predicts s-wave scattering lengths:

( 2 ) ( 4 )

1/ 2 3/ 20 00.19 0.2 0.05 0.0

1

2

,L L

a a

and loop

K scatteringK scattering

1/ 2 3/ 20 0 0.23 0.01 a a

( 2 ) ( 4 ) ( 6), , 2 -L L L and loop

1/ 2 3/ 20 0 0.269 0.015 a a

V. Bernard, N. Kaiser, U. Meissner. – 1991

J. Bijnens, P. Talaver. – April 2004

A. Rossel. – 1999

II. Roy-Steiner equations:

III. AK lifetime:0 0 0 0

0 0 1/ 2 3/ 2 20 0

15(3.7

( )

( ) ~ | prec

0.4)

issio

1

~ %

0

n 1|

K K

A K A K

K a a

s

J. Schweizer. – 2004

1. A2π time of life

2. AK+

π- and AK+π

- time of life

π+

ππ0

π0

K+

πK0

π0

20 2

1( )R a a

0 0

2A

0 2

0 2

| |4% ( ), 2%( ) 1%( ) 1%( )

a astat stat syst theor

a a

(*)1%R

R

(*) A. Gall et al. PR(2001)DIRAC ADDENDUM

00

KA K

2

1/ 2 3/ 2

1| |KR a a

(**)2%K

K

R

R

DIRAC ADDENDUM

1/ 2 3/ 2

1/ 2 3/ 2

| |20% ( ), 10%( ) 1%( ) 1.5%( )

a astat stat syst theor

a a

0 0

KA K

(**) J. Schweizer (2004)



Energy Splitting between Energy Splitting between npnp - - nsns states in ( states in ( ++ - - ) atom ) atom

For n = 2

E2 ≈ 0.56 eV

(1979) A. Karimkhodzhaev and R. Faustov (1999) A. Gashi et al.(1983) G. Austen and J. de Swart (2000) D. Eiras and J. Soto(1986) G. Efimov et al. A. Rusetsky, priv. comm.

0 2~ 2snE a a

-n ns np

vac sn n n

E E E

E E E

2

2

0

2

0.107

0.45

0.220 0.005 0.0444 0.0010

vac

s

E eV from QED calculations

E eV numerical estimated value from ChPT

aa

. , . (200 1) . G Colangelo J Gasser and H Leutwyler


Method of AMethod of A22ππ Observation Observation

(A2π) too small to be measured directly

“atomic pairs”

“free pairs”Coulomb from short-lived sourcesnon- Coulomb from long-lived sources

e.m. interation of A2π in the target

A2π π+π

Q < 3MeV/c E+ E

lab < 2.5 mrad


PBr=0.447±0.023stat

+0.44stat=2.85 [fs] 0.38stat

A2* is a metastable atom

small angle

π πE E

+

Externalbeam

p

For pA = 5.6 GeV/c and = 20

1s = 2.9 × 10 15 s , 1s = 1.7 × 10 3 cm2s = 2.3 × 10 14 s , 2s = 1.4 × 10 2 cm2p = 1.17 × 10 11 s , 2p = 7 cm 3p 23 cm 4p 54 cm

TargetZ

Thickness Μm

Br Σ(l ≥1)

2p0 3p0 4p0 Σ(l =1, m = 0)

04 100 4.45% 5.86% 1.05% 0.46% 0.15% 1.90%

06 50 5.00% 6.92% 1.46% 0.51% 0.16% 2.52%

13 20 5.28% 7.84% 1.75% 0.57% 0.18% 2.63%

28 5 9.42% 9.69% 2.40% 0.58% 0.18% 3.29%

78 2 18.8% 10.5% 2.70% 0.54% 0.16% 3.53%

Probabilities of the A2π breakup (Br) and yields of the long-lived states for different targets provided the maximum yield of summed population of the

long-lived states: Σ(l ≥1)


Yields of the long-lived states 2p (m = 0) as a function of the A2π lifetime for Beryllium targets (Z = 04). Target thicknesses are given in microns on the right side of the picture.

2( ) 4.5 /p A GeV c 2( ) 10 /p A GeV c



External magnetic and electric fieldsExternal magnetic and electric fields

≡ relative distance between + and mesons in A2 atom

r

≡ laboratory magnetic field

≡ electric field in the CM system of an A2 atom

F

BLab

LabLab BγBγβF

Atoms in a beam are influenced by external magnetic fieldand the relativistic Lorentz factor

F

LabB

p

A

+

r

A2 , c

vβ

z


2

2

2

2

2

2eff

ξ2011

τ

τ

τ

4

ξ1

τ

p

s

p

p

where:

222

22

EE

Fξ

sp

BLab = 4 Tesla

2eff

2eff

τγ 20 , ξ 0.1 τ

2.2τ

γ 40 , ξ 0.2 τ6

p

p

The dependence of AThe dependence of A22ππ life time in 2p-states life time in 2p-states effeff

from a strength of the electric field Ffrom a strength of the electric field F


Schematic top view of the updated DIRAC spectrometer.

Downstream of the

magnet, in each spectrometer arm: drift chambers (DC), vertical and horizontal scintillation hodoscopes (VH, HH), gas Cherenkov counters (Ch), preshower detector (PSh) and, behind the iron absorber, muon detector (Mu).

In the left arm: Aerogel

Cherenkov counters.

Upstream of the spectrometer magnet: microdrift chambers (MDC) , scintillating fiber detectors (SFD) , ionization hodoscopes (IH).

(Addendum to DIRAC/PS212 (CERN) (13/04/04): CERN-SPSC-2004-009 (SPSC-P-284 Add.4))

AA2π2π and A and AπKπK productionproduction0

2

1 2 1 2

23 ( )

1 2

2

1 2

1

v

(

v v , v

. .

2 ) (0)A

Cnlm sn m

K

l

for atoms where velocities of

particles in the L S for al

for A production p p

for A production

l types of atoms

d dE d d

M dp dp dp dpdP

��

KK

mp p

m

��


450 0p LE GeV

InclusiveInclusive cross-sections for cross-sections for ππ++, , ππ - mesons generation - mesons generation


450 0p LE GeV

InclusiveInclusive cross-sections for cross-sections for KK++,, KK - - mesons generationmesons generation


5.7 1.3 24L pE GeV 5.7 1.3 450L pE GeV

AA22ππ momentum distributionsmomentum distributions


2 1.3 450L pE GeV 0 1.3 450L pE GeV

AA22ππ momentum distributionsmomentum distributions


Yield of A2π and π± into the aperture of 1.7·10-3 sr per one proton interaction

L 5.7º±1.3º 5.7º±1.3º 2º±1.3º 0º±1.3º

Ep 24 GeV 450 GeV 450 GeV 450 GeV

WA 0.46·10-8 0.53·10-7 0.47·10-6 0.18·10-5

WAN 1. 12. 103. 389.

Wπ 0.032 0.1 1.1 6.6

WπN 1. 3.1 34. 206.

WA /Wπ1.4·10-7 5.3·10-7 4.3·10-7 2.7·10-7

WAN

/WπN 1. 3.7 3. 1.9


Yield of A2π per one proton interaction, detectable by DIRAC setup at L=5.7º

Ep 24 GeV (old)

450 GeV (old)

450 GeV (new)

WA 0.96·10-9 0.11·10-7 0.13·10-7

WAN 1. 12. 13.

WA /Wπ3·10-8 1.1·10-7 1.3·10-7

WAN

/WπN

1. 3.7 4.3

A multiplier due to different spill duration ~4

Total

gain1. 15. 17.

, /Momentum of A GeV c

24 GeV/c

L=5.7º

(old)

450 GeV/c

L=5.7º

(old)

AA22ππ momentum distributions momentum distributions


— - red curve A2π spectra in channel the aperture - green curve A2π spectra registered by the set-up

Yield of AK+π- and AK-π+ into the aperture of 1.7·10-3 sr

per one proton interaction

AK+π- AK-π+

L 5.7º±1.3º 5.7º±1.3º 2º±1.3º 0º±1.3º 5.7º±1.3º 5.7º±1.3º 2º±1.3º 0º±1.3º

Ep 24GeV 450GeV 450GeV 450GeV 24GeV 450GeV 450GeV 450GeV

WA 0.11·10-8 0.13·10-7 0.16·10-6 0.65·10-6 0.60·10-9 0.10·10-7 0.11·10-6 0.54·10-6

WA N 1. 12. 146. 610. 1. 17. 192. 897.

WA /Wπ3.4·10-8 1.3·10-7 1.5·10-7 9.8·10-8 1.9·10-8 1.·10-7 1.·10-7 8.2·10-8

WA N

/Wπ N 1. 3.8 4.2 2.9 1. 5.3 5.3 4.4


Yield of AK+π- per one proton interaction, detectable by DIRAC setup at L=5.7º

Ep 24 GeV (old)

450 GeV (old)

450 GeV (new)

WA 0.20·10-10 0.34·10-9 0.10·10-8

WAN 1. 17. 49.

WA /Wπ6.2·10-10 3.4·10-9 1·10-8

WAN/Wπ

N

1. 5.4 16


Total

gain1. 22. 64., /

KMomentum of A GeV c

450 GeV/c

L=5.7º

(old)

450 GeV/c

L=5.7º

(new)

24 GeV/c

L=5.7º

(old)

AAKK++ππ- momentum distributionsmomentum distributions


— - red curve A2π spectra in the channel aperture - green curve A2π spectra registered by the set-up

Yield of Aπ+K- per one proton interaction, detectable by DIRAC setup at L=5.7º

Ep 24 GeV (old)

450 GeV (old)

450 GeV (new)

WA 0.11·10-10 0.23·10-9 0.71·10-9

WAN 1. 21. 63.

WA /Wπ3.4·10-10 2.3·10-9 7.1·10-9

WAN

/WπN

1. 6.7 20.6


Total

gain1. 27. 82., /

KMomentum of A GeV c

450 GeV/c

L=5.7º

(old)

450 GeV/c

L=5.7º

(new)

24 GeV/c

L=5.7º

(old)

AAππ++KK momentum distributions momentum distributions


— - red curve A2π spectra in the channel aperture - green curve A2π spectra registered by the set-up

Present low energy QCD predictions for ππ and πK scattering lengths

Expected results of DIRAC ADDENDUM at PS CERN

DIRAC at SPS CERN

0 2 0 22.3% 2.3% ( ) 1.5% a a a a 1/ 2 3/ 2( ) 10%a aK

1/ 2 3/ 2( ) 10%( ) ..........( 1.5%) ( )K a a stat theoA r 02 2( ) 2%( ) 1% ( ) 1% ( )( ) a a stat syst tA heor

22 0( ) 0.5%) (( )a a tA s at

1/ 2 3/ 2( ) 2( ) .5%( )K a a tA s at

0 2( ) (2 ) 2.5%( )np ns aE E a stat

1/ 2 3/ 2( () 2 )np ns KE a aE

( )( ) .

Possibility of the observation atomsand K K atoms will be studied

2 Observation of metastable A


VILLARS 2004 CERN SPS and PS Committee L. Nemenov 25 September 2004

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Transcript of VILLARS 2004 CERN SPS and PS Committee L. Nemenov 25 September 2004