Measurement of the π 0 Lifetime: QCD Axial Anomaly and Chiral Corrections INT Sept, 2009 A.M. Bernstein MIT spontaneous chiral symmetry breaking pions π 0 γ γ : axial anomaly, chiral corrections ~m d -m u previous experiments PrimEx experiment at Jefferson Lab Possible extensions with 12 GeV low energy photo-pion physics: πn physics, IS conclusions 1
meson mass gap: QCD chiral symmetry breaking meson mass (MeV) η η η K K large η mass due to gluon axial anomaly Λ x 1 GeV m s 140 MeV π m π 2 = B(m u + m d ) 0 m u 5 MeV, m d 9 MeV S=0 S=1 S=2 2
Opportunity to perform a precision π 0 lifetime measurement π 0 is the lightest hadron spontaneous chiral symmetry hiding: m(π) 140 MeV EM: m(π ± )- m(π 0 ) = 4.6 MeV EM decay π 0 γ γ (BR =98.8 ± 0.032%) axial anomaly dominant 3
History: π 0 Lifetime Experiments 1947 π + discovered in cosmic rays 1950 π 0 discovered, cosmic rays, Berkeley cyclotron π 0 γ γ decay mode observed lifetime too short for electronic measurement τ < 10-15 sec established by 1957 K + π + π 0 emulsion experiment (d < 0.5µ) 1951: Primakoff effect γ γ π 0 : experiments 1970-5 PDB data base established by 1988 4
History: π 0 Lifetime Theory PCAC predicts A πγγ = 0 in the chiral limit 1968 Adler, Bell, Jackiw discover the axial anomaly A πγγ = α /π F π Γ(π 0 γ γ) = (m π 3 /64π)A πγγ 2 = 7.725 ev ± 0.5% τ(π 0 ) = 0.807 10-16 sec c τ(π 0 ) = 0.0253 µ 5
Chiral calculations Γ(π 0 > γγ): π,η,η ChPT: Goity, AB, Holstein: O(p 6 ), O(p 4 1/Nc) sum rules: Ananathanarayan, Moussallam ChPT(2 flavor): Kampf, Moussallam 4.6% ChPT average(lec errors) Anomaly, O(p 4 ) 0.3% exp. error in F π 6
σ(γa π 0 X) Primakoff + nuclear σ prim (θ π ) Γ γγ Z 2 E γ 4 sin 2 (θ π )/Q 4 Q= mom.trans. σ (θ π ) = A prim + e iφ A nc 2 + σ incoherent fit data with 4 parameters; Γ γγ, φ, scale factors for nuclear coherent and incoherent 7
Improvements tagged photons:0.1% beam emittance duty factor detector resolution 8
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C and Pb cross sections relative values of Prim and NC differ greatly obtain consistent values of Γ from both! σ P Z 2 σ P Z 2 σ NC A 0.9 σ int σ incoh σ NC A 0.9 σincoh σ int 11
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Compton Cross Section Experiment and theory agree within the 0.6% statistical and 1.8% systematic errors 2.4 5.5 GeV 13
PrimEx result Γ(π 0 γ γ)=7.82ev± 2.2%(stat) ± 2.1%(sys) [3.0% total error] 1970 Primakoff 1985 1974 1970 PrimEX 2009 1988 14
PrimEx Collaboration Future Projects 6 GeV: PAC approved run 2 to reduce error by ~50% in the next few years 12 GeV program under development: Γ(η γγ), Γ(η γγ) transition form factors F γγ* at low Q 2 (0.001 0.5 GeV2) 15
Conclusions We have concluded a modern Primakoff measurement Γ(π 0 γ γ)=7.82ev± 2.2%(stat) ± 2.1% (syst) [3.0% total error] The systematic error was checked by measurements of the Compton and pair production cross sections to ~ 1.8% The results agree with the predictions of the axial anomaly + chiral corrections~m d -m u Primex 2: to reduce error to ~1.5% in the next few years 12 GeV Jlab η γ γ, η γ γ ; transition form factors at low Q 2 π 0,η, η γ γ 16
AB: Outlook: Experiment and Theory A modern ( ~ 1%) e + e - experiment is needed! preferably for π 0, η, η γ γ measurement of π 0 momentum spectrum for direct experiment reduction of ~1% theoretical error for π 0 γ γ lattice-chiral extrapolation - calculation of low energy constants? QCD predictions for η, η γ γ 17
Ph.D. students, postdocs A. Ambrozewicz(NCAT), E. Clinton(U. Mass),I. Larin(ITEP), D. McNulty (MIT), I. Nakagawa (U. Kentucky), Y. Prok(MIT, A. Teymarazyan(U. Kentucky), M. Wood (U. Mass) 18
Can the 12 GeV upgrade at Jlab help to use the Chew-Low method? pion pole: proton target photon pole: proton or nuclear target neutron pole: D target 19
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Near threshold γp π 0 p: Chiral Symmetry Tests new review article; Annual Rev. AB et al ChPT in good agreement with past experiments new Mainz experiment A2/10-09; transverse polarized target measures time reversal odd observables sensitive to πn phase shifts, scattering lengths 22
Mainz 23
γ p π 0 p Mainz data, ChPT 24
Polarized γ p photon π 0 p Mainz asymmetry data <k>=159.5 MeV ChPT: ChPT: O(p O(p 4 ) 4 ) ChPT: O(p 3 ) DR 25
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Projected results: γp πn Mainz Exp A2/10-09 T = transverse pol. target asymmetry 27
Unitary Cusp γp π 0 p β = E 0+ ( γ p π + n) a cex ( π 0 p π + n) cusp sign and magnitude 28
Surprisingly large effects of D-Waves in Near Threshold Pion Photoproduction C.Fernandez-Ramrez, A.B., T.W.Donnelly circularly polarized photons transverse target polarization spd sp 29
Conclusions: γp π 0 p more stringent chiral symmetry tests coming isospin conservation neutron target : a cex ( π + n π 0 p ) New method to get at π N sigma term? observe surprisingly large d wave effect near threshold? 30
CERN: Direct lifetime measurement: PL 1985 31
π 0 spectrum derived from measured π +, π - π + π 0 Largest systematic error statistical ± 2.45% systematic ± 1.9% total ± 3.1% π - π 0 β + 32