Tests of Chiral Perturbation Theory in Primakoff Reactions at COMPASS

Tests of Chiral Perturbation Theory in Primakoff Reactions at COMPASS Jan Friedrich Physik Department Technische Universität München for the COMPASS collaboration SPIN-PRAHA-010 July 0 supported by: Maier-Leibnitz-Labor München, Excellenzcluster: Origin and Structure of the Universe, BMBF

Outline Introduction: QCD and ChPT COMPASS at the CERN SPS Primakoff reactions chiral anomaly 3-pion final state [ pion polarisabilities dedicated talk by Alexey Guskov] J. Friedrich Tests of ChPT with COMPASS /50

The strong force, the pion and χpt Yukawa s particle of the strong force development of QCD: quarks and gluons running coupling parameter, confinement m q 0 chiral symmetry (spontaneously broken) SU() L SU() R SU() V series expansion of QCD in particle momenta, inner d.o.f. are condensed into Low Energy Constants π + π π (re-)appear as Goldstone bosons J. Friedrich Tests of ChPT with COMPASS 3/50

Yukawa s particle of the strong force m q? 0 chiral symmetry (spontaneously broken) The strong force, the pion and χpt development of QCD: quarks and gluons running coupling parameter, confinement SU() L SU() R SU() V series expansion of QCD in particle momenta, inner d.o.f. are condensed into Low Energy Constants π + π π (re-)appear as Goldstone bosons J. Friedrich Tests of ChPT with COMPASS 3/50

ChPT and Experiment Pion scattering lengths: -loop predictions a0 0m π + = 0.0 ± 0.005 confirmed in K + π + π e + ν e (E865) (a0 0 a 0 )m π + = 0.64 ± 0.006 confirmed in K + π + π π (NA48: 0.68 ± 0.010) Electromagnetic structure Form factor described by coupling to ρ(770) (resonance effect, VMD) Polarisability accessible as contribution to Compton scattering; prediction obtained by the LEC relation to π + e + ν eγ α π + β π = (0. ± 0.1) 10 4 fm 3 α π β π = (5.7 ± 1.0) 10 4 fm 3 [Gasser, Ivanov, Sainio, Nucl. Phys. B745, 006] π π π γ * ρ π π π γ γ π π J. Friedrich Tests of ChPT with COMPASS 4/50

COmmon Muon and Proton Apparatus for Structure and Spectroscopy J. Friedrich Tests of ChPT with COMPASS 5/50

COmmon Muon and Proton Apparatus for Structure and Spectroscopy CERN SPS: protons 400 GeV tertiary muons: 4 10 7 / s (5 s spills) 00-04, 006-07, 010-11: spin structure of the nucleon secondary π, K, ( ) p : 10 7 / s Nov. 004, 008-09: hadron spectroscopy J. Friedrich Tests of ChPT with COMPASS 5/50

COMPASS Experimental Setup Fixed-target experiment collaboration of 40 physicists two-stage magnetic spectrometer J. Friedrich Tests of ChPT with COMPASS 6/50

COMPASS Experimental Setup Fixed-target experiment collaboration of 40 physicists two-stage magnetic spectrometer Pilot Hadron Run 004 190 GeV π beam on nuclear targets Tracking: SMD for vertexing Trigger: Multiplicity trigger, ECAL trigger J. Friedrich Tests of ChPT with COMPASS 6/50

Weizsäcker-Williams Method Electric charge at rest J. Friedrich Tests of ChPT with COMPASS 7/50

Weizsäcker-Williams Method Electric charge moving J. Friedrich Tests of ChPT with COMPASS 8/50

Weizsäcker-Williams Method Electromagnetic field J. Friedrich Tests of ChPT with COMPASS 9/50

Weizsäcker-Williams Method (almost) real photons J. Friedrich Tests of ChPT with COMPASS 10/50

Key to ChPT: Primakoff reactions Access to π + γ reactions via the Primakoff effect: At small momentum transfer to the nucleus, high-energetic particles scatter predominantly off the el.mag. field quanta ( Z ) π + γ π + γ π + π 0 π + π 0 + π 0 π + π + π + π +... analogously: Kaon-induced reactions K + γ J. Friedrich Tests of ChPT with COMPASS 11/50

Chiral anomaly π γ π π ε µ γ π π π q 1 q q 3 e ɛ 4π fπ 3 µναβ ε µ q1 ν q α q β 3 F χpt 3π = 9.7 GeV 3 F Serpukhov 3π = 1.9 ± 1.4 (10.7±1.) GeV 3 (theory: real photons) (data: quasi-real) 10 σ tot (γπ - ->π - π 0 ) counts 700 COMPASS 004 hadron data 600 σ [µb] 1 0.1 tree + loops + ρ resonance + loops + lec 500 400 300 00 100 - beam K - ρ 0.01.5 3 3.5 4 4.5 5 5.5 6 s 1/ [m π ] 0 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 m π [GeV] π 0 J. Friedrich Tests of ChPT with COMPASS 1/50

Chiral anomaly - analysis of 004 data counts 700 600 COMPASS 004 hadron data 500 400 300 00 100 - beam K - ρ 0. 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 m π [GeV] - π 0 J. Friedrich Tests of ChPT with COMPASS 13/50

Chiral anomaly - analysis of 004 data counts 4 10 full π - π 0 mass range low π - π 0 mass - beam K decay 3 10 10 COMPASS 004 hadron data -0.01-0.009-0.008-0.007-0.006-0.005-0.004-0.003-0.00-0.001 0 q [GeV /c ] J. Friedrich Tests of ChPT with COMPASS 14/50

Low-t production mechanisms Production via photon and strong (pomeron) exchange separable by different t dependence e.g. resonance a (130) is produced both ways radiative width phase between the photon and strong amplitudes low-mass region ChPT J. Friedrich Tests of ChPT with COMPASS 15/50

004 Primakoff results (diffractive trigger) π Pb Pb π π π + Number of Events 5 10 10 4 3 10 COMPASS 004 - π - Pb π π - π + Pb 10 0 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Momentum Transfer t (GeV /c ) Low t : 10 3 (GeV/c) < t < 10 (GeV/c) 000 000 events Primakoff region : t < 10 3 (GeV/c) 1 000 000 events J. Friedrich Tests of ChPT with COMPASS 16/50

004 Primakoff results (diffractive trigger) π Pb Pb π π π + Number of Events 5 10 10 4 3 10 COMPASS 004 - π - Pb π π - π + Pb PWA of a1(160), a(130) contributions in t slices 10 0 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Momentum Transfer t (GeV /c ) Low t : 10 3 (GeV/c) < t < 10 (GeV/c) 000 000 events Primakoff region : t < 10 3 (GeV/c) 1 000 000 events J. Friedrich Tests of ChPT with COMPASS 16/50

PWA: a 1, a and Φ in separated t regions ) Intensity / (40 MeV/c ) Intensity / (40 MeV/c 6 10 0.16 ++ + 1 0 ρπ S COMPASS 004 0.14 π Pb π π π + Pb 0.0015 < t < 0.01 GeV /c 0.1 t < 0.0005 GeV /c 0.1 0.08 0.06 0.04 0.0 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + System (GeV/c ) 3 10 4.5 ++ + 1 ρπ D COMPASS 004 4 π Pb π π π + Pb 3.5 0.0015 < t < 0.01 GeV /c t < 0.0005 GeV /c 3.5 1.5 1 0.5 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + System (GeV/c ) Phase (degrees) 50 0 50 100 150 00 50 COMPASS 004 π Pb π π π + Pb 0.0015 < t < 0.01 GeV /c t < 0.0005 GeV /c ++ + ++ + Φ ( 1 ρπ D 1 0 ρπ S) 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + System (GeV/c ) J. Friedrich Tests of ChPT with COMPASS 17/50

Phase a a 1 in detail: t dependence Intensity (a. u.) Intensity (a.u.) 9 10 0.16 ++ + 1 0 ρπ S COMPASS 004 0.14 π Pb π π π + Pb t < 0.0 GeV /c 0.1 1.6 < m 3π < 1.38 GeV/c 0.1 0.08 0.06 0.04 0.0 0 0 4 6 8 10 1 14 16 18 3 10 0 Momentum Transfer t (GeV /c ) 6 10 0 ++ + 1 ρπ D COMPASS 004 π Pb π π π + Pb 18 16 14 1 10 8 6 4 0 t < 0.0 GeV /c 1.6 < m 3π < 1.38 GeV/c 3 10 0 4 6 8 10 1 14 16 18 0 Momentum Transfer t (GeV /c ) Phase (degrees) 0 0 40 60 80 100 ++ + ++ + Φ ( 1 ρπ D 1 0 ρπ S) COMPASS 004 π Pb π π π + Pb t < 0.0 GeV /c 1.6 < m 3π < 1.38 GeV/c 10 10 0 4 6 8 10 1 14 16 18 0 Momentum Transfer t (GeV /c ) 3 J. Friedrich Tests of ChPT with COMPASS 18/50

Theory: Phase a (strong+coulomb)-a 1 (strong) phase [deg] 150 100 50 0-50 -100 Coulomb + strong πa strong πa interaction difference -150 0 0.003 0.006 0.009 0.01 0.015 q t [GeV ] Glauber model G. Fäldt and U. Tengblad, Phys. Rev. C79, 014607 (009) Plot: N. Kaiser (TU München) Phase (degrees) 0 0 40 60 80 100 ++ + ++ + Φ ( 1 ρπ D 1 0 ρπ S) COMPASS 004 π Pb π π π + Pb t < 0.0 GeV /c 1.6 < m 3π < 1.38 GeV/c 3 10 10 0 4 6 8 10 1 14 16 18 0 Momentum Transfer t (GeV /c ) indicates confirmation of interference Coulumb-interaction - strong interaction detailed studies of the nature of resonances J. Friedrich Tests of ChPT with COMPASS 19/50

Primakoff contribution at t < 10 3 (GeV/c) Primakoff: σ(t ) e b Prim t, b Prim 000 (GeV/c) (mainly resolution) Diffractive: σ(t ) e b diff t, b diff 400 (GeV/c) for lead target Events 5 10 COMPASS 004 π Pb π π π + Pb t < 0.01 GeV /c 4 10 10 0 1 3 4 5 6 7 8 9 10 Momentum transfer t (GeV /c ) (Mass) spectrum of this Primakoff contribution? Statistical subtraction of diffractive background (for bins of m 3π ) 3 J. Friedrich Tests of ChPT with COMPASS 0/50

Basic features of the statistical subtraction Fit of t spectrum with sum of both exponentials for 0 < t < 0.006 (GeV/c) (0.5 < m 3π <.5 GeV/c ) Subtraction of diffractive exponent from t spectrum Events 5 10 4 10 COMPASS 004 π Pb π π π + Pb t < 0.01 GeV /c 3 10 0 1 3 4 5 6 7 8 9 10 Momentum transfer t (GeV /c ) Events after statistical subtraction 10 8 6 4 3 10 COMPASS 004 π Pb π π π + Pb 0 3 10 0 1 3 4 5 6 Momentum transfer t (GeV /c ) Fit and subtraction in 3π mass bins: b Prim = 050 (GeV/c) fixed b diff as fit parameter Primakoff contribution J. Friedrich Tests of ChPT with COMPASS 1/50

Mass spectrum from statistical subtraction Events after statistical subtraction Statistical subtraction separately in 40 MeV/c mass bins Integrate Primakoff contribution of the t spectra for t < 10 3 (GeV/c) 10 5 4 3 1 0 3 COMPASS 004 π Pb π π π + Pb t < 0.001 GeV /c Selex, Phys. Lett. B 51(001), 171-180 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + system (GeV/c ) J. Friedrich Tests of ChPT with COMPASS /50

Another look at the mass spectrum: threshold region Events after statistical subtraction 10 5 4 3 1 0 3 COMPASS 004 π Pb π π π + Pb t < 0.001 GeV /c σ tot [µb].5 1.5 1 0.5 (sample graph) π - π + π - π - π 0 π 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + system (GeV/c ) 0 3 4 5 6 s 1/ [m π ] Simple approach: look at Primakoff mass spectrum by statistical subtraction Chiral Perturbation Theory prediction: tree diagrams calculation 008 Formula for (absolute) total cross section: N. Kaiser, JF, EPJA 36 (008) 181 J. Friedrich Tests of ChPT with COMPASS 3/50

Chiral anomaly - contribution of loop graphs new calculation (N. Kaiser, TUM) J. Friedrich Tests of ChPT with COMPASS 4/50

Diffraction 004: π Pb π π π + Pb Momentum Transfer Distributions 4-pion vertex in Pb target Exclusive in the energy within resolution Momentum transfer: t = Q (p beam p (π π π + )) Number of Events 5 10 10 4 3 10 COMPASS 004 - π - Pb π π - π + Pb Number of Events 3 10 10 COMPASS 004 - π - Pb π π - π + Pb 10 0 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Momentum Transfer t (GeV /c ) 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Momentum Transfer t (GeV /c ) J. Friedrich Tests of ChPT with COMPASS 5/50

3π Data in the range 0.3 < t /(GeV /c ) < 1 π π π + Mass Distributions and Acceptance ) Events / (5 MeV/c 3 10 3.5 3.5 1.5 1 0.5 a (130) a 1 (160) π (1670) COMPASS 004 - π - Pb π π - π + Pb 0.1 < t < 1.0 GeV /c 0 0 0.5 1 1.5.5 3 Mass of π - π - π + System (GeV/c ) BNL-E85, Phys. Rev. D65, 07001, 00 Acceptance 1 0.9 0.8 0.7 0.6 0.5 0.4 COMPASS 004 MC π - Pb π - π - π + Pb 0.1 < t < 1.0 GeV /c 0.3 0. 0.1 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π - π - π + System (GeV/c ) J. Friedrich Tests of ChPT with COMPASS 6/50

PWA Results 1 ++ 0 + ρπs and + 0 + f πs Intensity / (40 MeV/c ) 3 10 16 ++ + 1 0 ρπ S 14 1 10 8 6 4 COMPASS 004 - π - Pb π π - π + Pb 0.1 < t < 1.0 GeV /c 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π - π - π + System (GeV/c ) Intensity / (40 MeV/c ) 3 10 3.5 COMPASS 004 3 - π - Pb π π - π + Pb 0.1 < t < 1.0 GeV /c.5 1.5 1 0.5 -+ + 0 f π S 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π - π - π + System (GeV/c ) Phase (degrees) 350 300 50 00 150 100 50 - π - Pb π π - π + Pb 0.1 < t < 1.0 GeV /c COMPASS 004 -+ + ++ + φ ( 0 f π S - 1 0 ρπ S) BW for a 1 (160) + background: M = (1.56 ± 0.006 +0.007 0.017 ) GeV Γ = (0.366 ± 0.009 +0.08 0.05 ) GeV BW for π (1670): M = (1.659 ± 0.003 +0.04 0.008 ) GeV Γ = (0.71 ± 0.009 +0.0 0.04 ) GeV 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 J. Friedrich Tests of ChPT with Mass COMPASS of π - π - π + System (GeV/c ) 7/50

PWA Results Exotic 1 + 1 + ρπp Wave Intensity / (40 MeV/c ) -+ + 800 1 1 ρπ P 700 600 500 400 300 00 100 COMPASS 004 - π - Pb π π - π + Pb 0.1 < t < 1.0 GeV /c 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π - π - π + System (GeV/c ) BNL E85 signal: Phase (degrees) -50-100 -150-00 -50-300 -350 - π - Pb π π - π + Pb 0.1 < t < 1.0 GeV /c -+ + ++ + φ (1 1 ρπ P - 1 0 ρπ S) COMPASS 004-400 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π - π - π + System (GeV/c ) Significant 1 + amplitude consistent with resonance at 1.6 GeV No leakage observed BW for π 1 (1600) + background: M = (1.660 ± 0.010 +0.000 0.064 ) GeV Γ = (0.69 ± 0.01 +0.04 0.064 ) GeV J. Friedrich Tests of ChPT with COMPASS 8/50

COMPASS Setup 008 CEDARs J. Friedrich Tests of ChPT with COMPASS 9/50

COMPASS Setup 008 Target region: Recoil Proton Detector J. Friedrich Tests of ChPT with COMPASS 30/50

COMPASS Setup 008 Target region: RPD Signals Ring A RingB J. Friedrich Tests of ChPT with COMPASS 31/50

COMPASS Setup 008 Target region: Silicon detectors J. Friedrich Tests of ChPT with COMPASS 3/50

COMPASS Setup 008 Target region: Pixel GEM detectors J. Friedrich Tests of ChPT with COMPASS 33/50

COMPASS Setup 008 Calorimetry: J. Friedrich Tests of ChPT with COMPASS 34/50

Compton scattering and polarisability π + γ π + γ Leading deviation from pointlike particle e.m. polarisability E + + α + B β γ π s t γ π for α π β π [10 4 fm 3 ]: (α π β π) ChPT: 5.7±1.0 experiments: 4 14 J. Friedrich Tests of ChPT with COMPASS 35/50

Compton cross section dσ πγ = α (s z+ + mπz 4 ) dω cm s(sz + + mπz α m3 π (s mπ) ) 4s (sz + + mπz P ) with (quadrupole polarisability α β ) (z ± = 1 ± cos θ cm) P = z (α π β π) + s z+(α mπ 4 π + β π) (s m π) z (α 3 β ) 4s Measuring the differential cross section with high statistics allows to determine all three polarisability contributions J. Friedrich Tests of ChPT with COMPASS 36/50

Polarisability effect (LO ChPT values) loop effects not shown [µb] dσ /dω CM 0.4 0.3 0. s=3m π Primakoff E γ < 0 GeV 0.1 s=8m π s=5m π s=15m π - - - α π = 3.00, β = -3.00 π 0.0-1 -0.8-0.6-0.4-0. 0 0. 0.4 0.6 0.8 1 cos θ CM J. Friedrich Tests of ChPT with COMPASS 37/50

Polarisability effect (NLO ChPT values) loop effects not shown [µb] dσ /dω CM 0.4 0.3 0. s=3m π Primakoff E γ < 0 GeV 0.1 s=8m π s=5m π s=15m π - - - α π = 3.00, β = -.86 π 0.0-1 -0.8-0.6-0.4-0. 0 0. 0.4 0.6 0.8 1 cos θ CM J. Friedrich Tests of ChPT with COMPASS 38/50

Polarisability measurements at COMPASS Nov. 004 recorded statistics (eff. 3 days) competitive to the Serpukhov measurement problems with the calorimeter (stability, trigger logic) large estimated systematic error Nov. 009 major upgrade of calorimeter readout, new digital trigger fine tuning / offline corrections ongoing 01 http://wwwcompass.cern.ch New proposal COMPASS-II proposal for a high-statistics Primakoff run increase statistics by a factor > 30, uncertainty on α π β π: ±0.66 (ChPT: 5.7) First measurement of polarisability sum α π + β π expected uncertainty ±0.05 (ChPT: 0.16) J. Friedrich Tests of ChPT with COMPASS 39/50

Summary and Outlook COMPASS 004 hadron run (few days) using a 190 GeV π beam Primakoff: calorimetry problems diffractive: spin-exotic π 1 observation (PRL104), more results coming π Pb π π π + Pb at (very) low momentum transfer Production phase of a (130) dependent on t shows interference of contributions from Coulomb and strong interaction Test of chiral diagrams in threshold mass region coming up 009 data with extended spectrometer diffractive on H, Pb, Ni Primakoff on Ni High-statistics run 01 J. Friedrich Tests of ChPT with COMPASS 40/50

BACKUP: 3π Data Sample (004) π π π + mass distribution ) Events / (5 MeV/c 35 30 5 0 15 10 5 3 10 - π - Pb π π - π + Pb Different t ranges: COMPASS 004 Ranges in t (GeV /c ) all t 0 0 0.5 1 1.5.5 3 Mass of π - π - π + System (GeV/c ) -3 t < 10-3 - 10 < t < 10-10 < t < 10 0.1 < t < 1 t > 1 [x5] -1 J. Friedrich Tests of ChPT with COMPASS 41/50

BACKUP: Partial Wave Analysis Formalism Mass-independent PWA (narrow mass bins): σ indep (τ, m, t ) = N r / Tir ɛ fi ɛ (t )ψi ɛ (τ, m) f ɛ i (t ) dt ψ ɛ i (τ, m) dτ ɛ=±1 r=1 i Production strenght assumed constant in single bins Decay amplitudes ψi ɛ(τ, m), with t dependence fi ɛ (t ) Production amplitudes Tir ɛ Extended log-likelihood fit Acceptance corrections included Spin-density matrix: ρ ɛ ij = r Physical parameters: Intens ɛ i = ρ ɛ ii, relative phase Φ e ij Coh ɛ i,j = Tir ɛ Tjr ɛ ( Re ρ ɛ ij ) + ( Im ρ ɛ ij ) / ρ ɛ ii ρ ɛ jj Mass-dependent χ -fit (not presented here): X parameterized by Breit-Wigner (BW) functions Background can be added J. Friedrich Tests of ChPT with COMPASS 4/50

Mass dependence of the diffractive slope ) ((GeV/c) diff Diffractive slope b 500 400 300 00 100 0 COMPASS 004 π Pb π π π + Pb 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + system (GeV/c ) J. Friedrich Tests of ChPT with COMPASS 43/50

Partial Wave Analysis Formalism Isobar Model π (beam) J PC M ε π (bachelor) ε = +: natural parity exchange X 1 R ππ L π π + Isobar model: Intermediate -particle decays ε = : unnatural parity exchange S Partial wave in reflectivity basis: J PC M ɛ [isobar]l target recoil Mass-independent PWA (40 MeV/c mass bins): 38 waves Fit of angular dependence of partial waves, interferences Mass-dependent χ -fit (Not presented here) J. Friedrich Tests of ChPT with COMPASS 44/50

Summary of Extracted States Comparison with PDG values ) Particle Mass (GeV/c 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1. COMPASS 004 PDG 006 a 1 (160) a (130) π 1(1600) π (1670) π (1800) a 4 (040) J. Friedrich Tests of ChPT with COMPASS 45/50

) Intensity / (40 MeV/c ) Intensity / (40 MeV/c.5 1.5 1 0.5 PWA of data with low t Intensity of selected waves: 0 + 0 + f 0 (980)πS, 1 ++ 0 + ρπs, ++ 1 + ρπd, + 0 + f (170)πS 3 10 COMPASS 004 3.5 π Pb π π π + Pb 3 0.001 < t < 0.01 GeV /c + + 0 0 f 0 (980)π S 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + System (GeV/c ) 3 10 3.5 3 ++ + 1 ρπ D COMPASS 004 π Pb π π π + Pb 0.001 < t < 0.01 GeV /c.5 1.5 1 0.5 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + System (GeV/c ) ) Intensity / (40 MeV/c ) Intensity / (40 MeV/c 0. 0.18 0.16 0.14 0.1 0.1 0.08 6 10 ++ + 1 0 ρπ S COMPASS 004 π Pb π π π + Pb 0.001 < t < 0.01 GeV /c 0.06 0.04 0.0 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + System (GeV/c ) 3 10 COMPASS 004 10 π Pb π π π + Pb 0.001 < t < 0.01 GeV /c 8 6 4 + + 0 f π S 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + System (GeV/c ) J. Friedrich Tests of ChPT with COMPASS 46/50

Spin Totals for t < 10 3 (GeV/c) Spin Totals : Sum of all contributions for given M (i.e. z-projection of J) t -dependent amplitudes: Primakoff production: M=1: σ(t ) e b Primt arises at t 0 (resoluted shape!) Diffractive production: M=0: σ(t ) e b diff(m)t ) Intensity / (40 MeV/c 10 0.1 0.1 0.08 0.06 0.04 0.0 6 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + System (GeV/c ) M=1: σ(t ) t e b diff(m)t vanishes for t 0 COMPASS 004 π Pb π π π + Pb t < 0.001 GeV /c M=0 Spin Total ) Intensity / (40 MeV/c 14 1 10 8 6 4 3 10 COMPASS 004 π Pb π π π + Pb t < 0.001 GeV /c M=1 Spin Total 0 0.6 0.8 1 1. 1.4 1.6 1.8..4 Mass of π π π + System (GeV/c ) M=0 M=1 J. Friedrich Tests of ChPT with COMPASS 47/50

004 Primakoff results (diffractive trigger) Momentum Transfer Momentum transfer to target: t = (p beam p (π π π + )) t = t t min Number of Events 5 10 10 4 3 10 COMPASS 004 - π - Pb π π - π + Pb with t min = (m 3π m π ) 4 p beam lab Diffraction pattern: Pb nucleus acts like black disc in optics 10 0 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Momentum Transfer t (GeV /c ) J. Friedrich Tests of ChPT with COMPASS 48/50

πγ scattering: embedding the process wanted: e e π π π e π e π π π + Q < m π p n (A,Z) (A,Z) J. Friedrich Tests of ChPT with COMPASS 49/50

γγ ππ and the pion polarisability M.R. Pennington in the nd DAΦNE Physics Handbook, What we learn by measuring γγ ππ at DAΦNE : All this means that the only way to measure the pion polarisabilities is in the Compton scattering process near threshold and not in γγ ππ. Though the low energy γγ ππ scattering is seemingly close to the Compton threshold (...) and so the extrapolation not very far, the dominance of the pion pole (...) means that the energy scale for this continuation is m π. Thus the polarisabilities cannot be determined accurately from γγ experiments in a model-independent way and must be measured in the Compton scattering region. J. Friedrich Tests of ChPT with COMPASS 50/50