University of Santiago de Compostela, Spain

|a|a00-a-a22|| MeasurementMeasurement from from

Pionium Lifetime by DIRACPionium Lifetime by DIRAC

Oton Vázquez Doce on behalf of DIRAC collaboration

9thInternational Workshop on Meson Production, Properties and Interaction KRAKÓW, POLAND

9 - 13 June 2006

90 Physicists from 18 Institutes

Basel Univ., Bern Univ., Bucharest IAP, CERN, Dubna JINR, Frascati LNF-INFN, Ioannina Univ., Kyoto-Sangyo Univ., Kyushu Univ. Fukuoka,

Moscow NPI, Paris VI Univ., Prague TU, Prague FZU-IP ASCR, Protvino IHEP, Santiago de Compostela Univ., Tokyo Metropolitan Univ., Trieste

Univ./INFN, Tsukuba KEK.

Lifetime Measurement of +- atoms to test low energy QCD predictionswww.cern.ch/DIRAC

DImeson Relativistic Atomic Complexes

DIRACDIRAC

Pionium lifetimePionium lifetime

The lifetime of + atoms is dominated by charge exchange process into 00:

3

2

222 104

1

0

0

a0 and a2 are the S-wave scattering lengths for isospin I=0 and I=2.

Pionium is a hydrogen-like atom consisting of + and - mesons

EB=-1.86 keV, rB=387 fm, pB≈0.5 MeV

π+

ππ0

π0

220

3π2 )a(apα

9

2Γ

0at lowest order :

Pionium lifetime in QCDPionium lifetime in QCD

2π

220

3

s1s1 Mδ)(1|aa|pα

9

2

τ

1Γ 2

π22

0π2π Mα

4

1MMp

= (5.8 ± 1.2) × 10-2 significant correction non-singular relativistic amplitude at threshold

At next-to-leading order in α and (md – mu )2 :

Measurement of (10%) |a0-a2| (5%)

J. Gasser et al , Phys. Rev. D62 (2001) 016008

Pionium lifetime in QCDPionium lifetime in QCD

The scattering lengths have been calculated in the framework of Chiral Perturbation Theory (ChPT):

A self-consistent representation of the amplitudes also exists:

004.0265.0

0010.00444.0005.0220.0

20

20

aa

aa

fss 1.09.21

G. Colangelo, J. Gasser and H. Leutwyler, Nucl. Phys. B603 (2001) 125.

J. R. Peláez, F. J. Ynduráin, Phys. Rev. D69 114001 (2004)

Experimental resultsExperimental results

K+→+-e+e (Ke4) decay

New measurement at BNL (E865)

S.Pislak et al., Phys.Rev. D 67 (2003) 072004

a0=0.216±0.013 ±0.003(syst)

a2=-0.0454±0.0031

±0.0013(syst)

L. Rosselet et al., Phys. Rev. D 15 (1977) 574a0=0.26±0.05

N→N near threshold

M. Kermani et al., Phys. Rev. C 58 (1998) 3431a0=0.204±0.014

±0.008(syst)

C.D. Froggatt, J.L. Petersen, Nucl. Phys. B 129 (1977) 89a0=0.26±0.05

N.Cabibbo, Phys. Rev. Lett. 93, 121801 (2004)

N.Cabibbo, G.Isidori, hep-ph/0502130|a0-a2|= 0.281 ± 0.007 (stat.) ±0.014 (syst.)

K+→+00 and KL→30 NA48

The pionium is a Coulomb bound state:

MeV1fm387)(

0keV858.1

2

B

PCB

PAR

JE

+ and - originating from short lived sources (, K*, ,...) and resonance decays may form a pionium atom. The differential cross section is:

Lorentz Center of Mass to Laboratory factor.

Wave function at origin (accounts for Coulomb interaction).

Pion pair production from short lived sources.

Production of pioniumProduction of pionium

Method of pionium detectionMethod of pionium detection

Pionium is created in nS states then it interacts with target material:

decay 15 for 17c m

L.Nemenov, Sov.J.Nucl.Phys. 41 (1985) 629

Annihilation: A2→00

Excitation: transitions between atomic levels

Break-up(ionisation): characteristic “atomic” pairs nA

• Qcms<3MeV/c

• → in laboratory system E+≈E-, small opening angle θ<3mrad

Coulomb and atomic pairs are detected simultaneously:

Niforμmλ S 201int

C

Ath

A

ABr N

n

KN

nP

1

Production of pioniumProduction of pionium

Atoms are Coulomb bound state of two pions produced in one proton-nucleus collision

Background processes:Coulomb pairs. They are produced in one proton nucleus collision from fragmentation or short lived resonances resonances (, K*, ,...) and exhibit Coulomb interaction in the final state:

Non-Coulomb pairs. They are produced in one proton nucleus collision. At least one pion originates from a long lived resonance. No Coulomb interaction in the final state

Accidental pairs. They are produced in two independent proton nucleus collision. They do not exhibit Coulomb interaction in the final state

α/q)Mπ2exp(1

α/qMπ2(q)A

dpdp

σd(q)A

dpdp

σd

π

πC

0S

2

CC

2

DIRAC SpectrometerDIRAC Spectrometer

Upstream detectors: MSGCs, SciFi, IH.

Downstream detectors: DCs, VH, HH, C, PSh, Mu.

Tracking principles Tracking principles •Precison time-of-flight to reduce accidental and proton background

•Strong e+e- rejection by Čerenkov counters

•Unambiguous transverse momentum QT by upstream tracking (MSGC+SFD)

•Longitudinal momentum QL measured by fast drift chambers and upstream tracks

DIRAC Spectrometer DIRAC Spectrometer High high irradiation

Downstream detectors:Drift chambersCherenkovTime-of-Flight

Upstream detectors:MSGC/GEMSFDIonisation Hodoscope

Pre-Shower and Muon Counters unseen

Nucl. Inst. Meth. A515 (2003) 467.

DIRAC Spectrometer DIRAC Spectrometer

Trigger performanceTrigger performance

CalibrationsCalibrations

Time difference spectrum at VH with e+e- T1 trigger.

Mass distribution of p- pairs from decay. =0.39 MeV/c2

Positive arm mass spectrum, obtained by TOF difference, under - hypothesis in the negative arm.

Accidental pairs, different proton interactions in the target

Coulomb pairs. From short lived sources.r < 3 fm, < R(A2

Non Coulomb pairs. From long lived sources.r ~ 1000 fm.

t= 174 ps +- pairs

Time-of-Flight spectrumTime-of-Flight spectrum

Analysis based on MCAnalysis based on MCAtoms are generated in nS states using measured momentum distribution for short-lived sources. The atomic pairs are generated according to the evolution of the atom while propagating through the target

Background processes:

Coulomb pairs are generated according to AC(Q)Q2 using measured momentum distribution for short-lived sources.

Non-Coulomb pairs are generated according to Q2 using measured momentum distribution for long-lived sources.

Monte Carlo simulation is restricted to detector response only withoutrelying on specific asumptions from proton-nucleus collision models

Qd

dn

Qd

dn

Qd

dn

Qd

dn

Qd

dnATACNCCCp

22322212

Qd

dn

NQd

dn i

i

i22

1 LT dQdQQd 2

2D 2 FIT TO (QT, QL) SPECTRUM

3 (accidentals fraction) measured from TOF

1 and free parameters in 10 independent 600 MeV/c +- momentum bins

Atom signal defined as difference between prompt data and Monte Carlo with = 0

1321

PIONIUM BREAK-UP SIGNAL IN +- SPECTRUM

LongitudinalTransverse

· cos

6761 atoms

Pionium signal in Q =√ QL2+ QT

2

PIONIUM TRANSVERSE SIGNAL

QL > 2 MeV/c

QL < 2 MeV/c

PIONIUM LONGITUDINAL SIGNAL

)(K

1

)(N

)(NP

expCC

ATBr

Qd(Q)A

/n1

π

)παM(2)(K

2C

33πth

)(K)(ε

)(εK th

AT

CCexp

)Q(0,)Q(0,Ω CL

CT

DETERMINATION OF BREAK-UP PROBABILITY

Different extrapolation domains:

QM analytical factor:

Coulomb-pair background NCC determined from fit 1 parameter:

Acceptance factors i determined by Monte Carlo simulation

Standard choice is QLC = 2 MeV/c and QT

C = 5 MeV/c

fs0.260.22S1 2.58τ

Break-up probability as function of pionium momentum

PBr

PBr as function of QL upper cut

Fraction of Coulomb pairs as function of momentum

1

Coulomb pairs 1/40

Atom pairs

Long-lived pairs (2)

Coulomb pairs

/(0.6 GeV/c)

Spectrum consistent with+- bound stateformation

Softer spectrum (, ..)expected from Monte Carlo

Breakup probabilityBreakup probability

018.0432.0)(009.0)(016.0432.0 syststatPBr

Summary of systematic uncertainties:

Source

QL trigger acceptance Multiple scattering angle (± 1.5 %)MSGC background Atom signal shape Finite size correction (± 25 % )Double-track resolution simulation

± 0.007± 0.003± 0.006± 0.002± 0.003± 0.003

Total ± 0.009

Results from DIRACResults from DIRAC• DIRAC collaboration has built up a double arm spectrometer which

provides a pair relative momentum (Q) resolution of 0.5 MeV/c for Q<30MeV/c

• More than 15000 of + - pairs from pionium break-up were observed• The analysis of Ni 2001 data provides a lifetime measurement which

translates into an S-wave amplitude measurement at rest :

fssyststat )()(2.58τ 15.014.0

0.260.22S1

π

π016.0014.020

M015.0280.0

M280.0||

aa

fs30.026.0S1 58.2τ