pp and p K atoms as a tool to check precise low energy QCD

Trento, June 20, 2006 Leonid Nemenov, CERN (presented by L. Tauscher)

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and K atoms as a tool to check precise low energy QCD

International Workshop“Exotic hadronic atoms, deeply bound kaonic nuclear states

and antihydrogen: present results, future challenges”

Trento, June 19 to 23, 2006


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OutlineOutline

High-energy and low-energy QCD

Precise predictions of low-energy QCD

Experimental check of low-energy QCD predictions

First lifetime measurement of the π+π–-atom

The new experiment on the investigation of π+π–-atom and observation of πK-atoms at PS CERN

Potentials of the DIRAC setup at SPS CERN, GSI and J-PARC


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Theoretical motivationTheoretical motivation

QCD

Standard Model

Q>> Q<<

LOW energyHIGH energy

Spontaneous chiralsymmetry breaking (1967 – Weinberg)

perturbative QCD

QCD Lagrangian in presence of quark masses:

LQCD(q,g) = Lsym+ Lbreak-sym

high energy (small distance) “weak” interaction (asymptotic freedom) expansion in coupling

Leff( ,K,) = Lsym+ Lbreak-sym

low energy (large distance) strong interaction (confinement) expansion in momentum & mass

M, for large Q, depends only on: Lsym

Lsym and Lbreak-sym and q-condensate

M, for small Q, depends on both:

At low energies, QCD is replaced by an effective quantum field theory (ChPT) formulated in terms of asymptotically observable fields like , K, 1979,Weinberg 1984,Gasser & Leutwyler


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AA and Aand AKK observation and lifetime measurement observation and lifetime measurement

Main features of the DIRAC set-up

Thin targets: ~ 7 10–3 X0, Nuclear efficiency: 3 10−4

Magnetic spectrometerProton beam ~ 1011 proton/spill

Resolution on Q: Qx≈ Qy≈ QL≈ 0.5 MeV/c

(AπK) too small to be measured directly

e. m. interaction of AπK in the target

AπK π+K -

AKπ K+π-

Q < 3MeV/c, , lab< 3 mrad• Coulomb from short-lived sources• non-Coulomb from long-lived sources

“atomic pairs”

“free pairs”

Target Ni 98 m

AπK

p

24 GeV/c

p

π

p

K=

mK

m

p

24 GeV/c

π

K

KA−K+ → −K+

A +K− → +K−


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Theoretical limitations (Theoretical limitations (AA) ) 1. A2π lifetime

π+

ππ0

π0

002A→H. Jalloul, H.Sazdjian 1998

M.A. Ivanov et al. 1998

A. Gashi et al. 2002

J. Gasser et al. 2001

Current accuracy from the A2π lifetime calculation

2. A2π interaction with matter (break-up)L.Afanasyev, G.Baur, T.Heim, K.Hencken, Z.Halabuka, A.Kotsinyan, S.Mrowczynski, C.Santamarina, M.Schumann, A.Tarasov, D.Trautmann, O.Voskresenskaya from Basel, JINR and CERN

Current accuracy from break-up probability Pbr

To be reduced by factor 2

Δ |a0 −a2 ||a0 −a2 |

=0.6%

Γ( 0 0 ) =R (a0 −a2 )

2(1+δ )

Δ |a0 −a2 ||a0 −a2 |

=1.2%

→ δ =(5.8 ±1.2)⋅10−2


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Theoretical limitations (Theoretical limitations (AAKK) )

K+

πK0

π0

J. Schweizer (2004)

Γ(K )=RK |a1/ 2 −a3/ 2 |

2 (1+δK )

δK =(4.0 ±2.2)⋅10−2

AK− + and A

K+− lifetime

Current accuracy from the AKπ lifetime calculations

Δ |a1/ 2 −a3/ 2 ||a1/ 2 −a3/ 2 |

=1.1%

A−K+ → 0K 0

A +K− → 0K 0


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Energy splittingEnergy splitting

Energy Splitting between Energy Splitting between npnp - - nsns states in Astates in A22 atom atom

For n = 2 eV from QED calculations

eV estimate from ChPT

a0 = 0.220 ± 0.005, a2 = 0.0444 ± 0.0010 (2001) G. Colangelo, J. Gasser and H. Leutwyler

s

ΔE2 ≈ 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.

Measurement of and ΔE allows one to obtain a0 and a2 separately

Lifetime: ALifetime: A22 00 00

1

=W

A+−

→ 0 0 ∝ a0 −a22

ΔEn ≡ Ens − Enp ≈ ΔEnvac + ΔEn

strong ΔEnstrong ∝ 2a0 + a2

ΔE2vac = − 0.107

ΔE2strong ≈ − 0.45


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Metastable atomsMetastable atoms

A2* is a metastable atom

small angle ∂∂ EE+−≅

+

Externalbeam

p

For pA = 5.6 GeV/c and = 201s = 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 mm

Br (l ≥1)

2p0 3p0 4p0 (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: (l ≥1)


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Atomic pairsAtomic pairs


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DIRAC analysisDIRAC analysisImprovements on systematics in PBr

CC background no improvement ± 0.007signal shape no improvement ± 0.002Multiple scattering measured to ±1% (DONE) + 0.002 /-0.002

K+K

/ppbar admixtures to be measured* + 0.000 /-0.023

Finite size effects to be measured** + 0.000 /-0.017Total + 0.008 /-0.030 * To be measured in 2007/2008 with new PID** To be measured in 2006/2008 with new trigger for identical particles at low Q

Improvements on data quality by fine tuning•Adjustments of drift characteristics almost run-by-run•B-field adjustment and alignment tuning with -mass New pre-selection for all runs (DONE)

Comments on analysis strategiesUsing only downstream detectors (Drift chambers) and investigating only QL causes less sensitivity to multiple scattering and to the signal shape. Studies are under way and very promising.

K+K − / p %p


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Finite-size effectsFinite-size effects characteristic scale |a| = 387 fm (Bohr radius of system) average value of r* ~ 10 fm range of ~ 30 fm range of ' ~ 900 fm critical region of r* ~ |a| is formed by and ' pairs

UrQMD simulation pNi 24 GeV:● ~15% pairs ● < 1% ' pairs shift in Pbr mainly due to pairs

'


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Finite-size effectsFinite-size effects

Simulation vs fit of DIRAC CF simulation N( ) = 19.2% fit result N( ) = 21±7% good description of pairs by UrQMD

In π+π system finite-size effect induces shift in Pbr

UrQMD simulation N (π+π) = 15% δPbr ~ 2% δ ~ 5%

upper limit at 1 of fit N (π+π) = 20% δPbr ~ 3% δ ~ 7.5%

Systematic shift in measurement from finite-size effect < 10% i.e. less then present DIRAC statistical error in . Expected shift with multi-layer target in future DIRAC five times less

corr. Function (CF), arbitrary units


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Dual Target MethodDual Target Method

• Single/Multilayer target comparison:

– Same amount of multiple scattering

– Same background (CC, NC, ACC)

– Same number of produced A2 , but lower number of dissociated pairs


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ππππ scattering lengths scattering lengths

Results from E865/BNL (S.Pislak et al., Phys. Rev. Lett. 87 (2001) 221801) : K π+πe+ve(Ke4)

Present low energy QCD predictions:

using Roy eqs. using Roy eqs. and ChPT constraints a2 = fChPT(a0)

Upgraded DIRAC (DIRAC II)

Results from NA48/2 (J.R.Batley et al., Phys. Lett. B633 (2006) 173): K+ π0π0π+

First result (L. Rosselet et al., Phys. Rev. D15 (1977) 574):

DIRAC, 2001data (Phys. Lett. B 619 (2005) 50)

(a

0−a2 )m =0.264 ±7.5%(stat)

+3%−8%

(syst)

DIRAC expected results, 2001–2003 data

δ(a0 −a2 ) =±5%(stat)

+3%−8%

(syst)

δ(a0 - a2 ) =±2%(stat) ±1%(syst) ±1%(theor)

a0=0.28±0.05(18%) using Roy eqs

(a0−a2 )m =0.268±0.010(stat) ±0.004(syst) ±0.013(ext)

δ(a0 −a2 ) =±3.7%(stat) ±1.5%(syst) ±5%(theor)

a0= 0.216 ±0.013 (stat) ±0.004(syst) ±0.002 (theor)

δa0 =±6% (stat) ±2%(syst) ±1% (theor)

a0=0.203±0.033(16%)

a2 =−0.055±0.023(42%)

a0=0.220 ±0.005(2.3%) a2 =−0.0444 ±0.0010(2.3%)

a0 −a2 =0.265±0.004(1.5%)


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Trajectories of πTrajectories of π−− and K and K++ from the A from the AπKπK break-upbreak-up

π and K+ momenta in GeV/c

AπK, π- and K+

momenta

Patom

(GeV/c)

Pπ

(GeV/c)

PK

(GeV/c)

5.13 1.13 4.0

5.77 1.27 4.5

6.41 1.41 5.0

10.26 2.26 8.0


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Upgraded DIRAC experimental set-up Upgraded DIRAC experimental set-up descriptiondescription


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

ππKK scattering scattering I. ChPT predicts s-wave scattering lengths:

a01/ 2 =0.19 ±0.2 a0

3/ 2 =−0.05±0.02

a01/ 2 −a0

3/ 2 =0.23±0.01

a01/ 2 −a0

3/ 2 =0.269 ±0.015

J. Bijnens, P. Talaver. – April 2004

A. Rossel. – 1999

II. Roy-Steiner equations:

III. AK lifetime:

A +K− → 0K 0 (A

K +− → 0K 0 )

Γ( 0K 0 ) ~ |a01/ 2 −a0

3/ 2 |2 precision~1%

=(3.7 ±0.4)⋅10−15 s J. Schweizer. – 2004

L (2), L (4) and 1-loop

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


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What new will be known whenWhat new will be known whenK scattering length will be measured?K scattering length will be measured?

The measurement of s-wave πK scattering length would test our understanding of chiral SU(3)L SU(3)R symmetry breaking of QCD

(u, d and s), while the measurement of ππ scattering length checks only SU(2)L

SU(2)R symmetry breaking (u, d).

This is the main difference betweenππ and πK scattering!


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Time scale for the ATime scale for the A2π2π and A and AπKπK experiment experiment

=6%,

(a0 −a2 )a0 −a2

=3%

=20%,

(a1/ 2 −a3/ 2 )a1/ 2 −a3/ 2

=10%

2006

Manufacture and installation of new detectors and electronics: 6 months

Test of the Upgraded setup and calibration: 3

months

2007 and 2008Measurement of A2π lifetime: 12 months

In this time 86000 ππ atomic pairs will be collected to measure A2π lifetime with precision of:

At the same time we also should observe AπK and, if so, detect 5000 πK atomic pairs to estimate AπK lifetime with precision of:

This estimation of the beam time is based on the A2π statistics collected in 2001 and on the assumption of having 2.5 spills per supercycle during 20

hours per day.


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Expected accuracy for Expected accuracy for ππππ-scattering-scatteringEstimates of relative errors (Δ|a0 - a2| / |a0 - a2| ) based on data taken with the upgraded DIRAC

setup during 12 months (20h/day), single-layer target

Number of atomic pairs

nA

Statistical

error

Theoretical error from

= f (a0 - a2)

Theoretical errorfrom

Pbr = ()(*)

Error fromnon point-like

production

PS CERN 24 GeV/c

85000 2% 0.6% 1.2% 1%

J-PARC50 GeV/c

4.1105 0.9% 0.6% 1.2%

GSI90 GeV/c

1.2 106 0.6% 0.6% 1.2%

SPS CERN450 GeV/c

1.26 106 0.5% 0.6% 1.2%

(*) Precision on Pbr = () can be increased and the error will be less than 0.6% private communication by D. Trautmann


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Expected accuracy for Expected accuracy for ππKK-scattering-scatteringEstimates of relative errors (Δ|a1/2 - a3/2| / |a1/2 - a3/2| ) based on data taken with the upgraded

DIRAC setup during 12 months (20h/day), single-layer target

Number of atomic pairs

nA

Statistical

error

Theoretical error from

= f (a1/2 - a3/2)

Theoretical errorfrom

Pbr = ()(*)

Error fromnon point-like

production

PS CERN 24 GeV/c

7000 10% 1.1% 1.2% 1%

J-PARC50 GeV/c

1.7104 7% 1.1% 1.2%

GSI90 GeV/c

1.4 105 2.5% 1.1% 1.2%

SPS CERN450 GeV/c

1.26 105 2.5% 1.1% 1.2%

(*) Precision on Pbr = () can be increased and the error will be less than 0.6% private communication by D. Trautmann


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DIRAC collaborationDIRAC collaboration 75 Physicists from 18 Institutes75 Physicists from 18 Institutes

INFNLaboratori Nazionali di FrascatiFrascati, ItalyTrieste University and INFN-Trieste Trieste, ItalyUniversity of Messina Messina, Italy

Basel University Basel, SwitzerlandBern University Bern, SwitzerlandZurich University Zurich, Switzerland

Santiago de Compostela UniversitySantiago de Compostela, Spain

SINP of Moscow State UniversityMoscow, RussiaIHEP Protvino, Russia

JINR Dubna, Russia

IFIN-HH Bucharest, Romania

Czech Technical UniversityPrague, Czech RepublicInstitute of Physics ASCR Prague, Czech Republic

KEK Tsukuba, JapanKyoto Sangyou University Kyoto, JapanTokyo Metropolitan University Tokyo, Japan

CERN Geneva, Switzerland

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pp and p K atoms as a tool to check precise low energy QCD

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