Photons Interacting with Pions at COMPASS Jan M. Friedrich - - PowerPoint PPT Presentation
Photons Interacting with Pions at COMPASS Jan M. Friedrich Physik-Department, TU M unchen COMPASS collaboration June 18, 2015 ChPT & Resonances in + COMPASS Intro: Pions & ChPT COMPASS Pion polarisability Summary
Jan M. Friedrich
Physik-Department, TU M¨ unchen COMPASS collaboration
June 18, 2015
COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
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secondary π, K,
(−)
p : up to 2·107/s (typ. 5·106/s)
hadron spec. & Primakoff reactions tertiary muons: 4·107 / s 2002-04, 2006-07, 2010-11: spin structure of the nucleon
COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
lepton scattering at high momentum transfer → partonic structure of the nucleons
QCD αs(Mz) = 0.1185 ± 0.0006
Z pole fit 0.1 0.2 0.3
αs (Q)
1 10 100
Q [GeV]
Heavy Quarkonia (NLO) e+e– jets & shapes (res. NNLO) DIS jets (NLO)
Lattice QCD (NNLO)
(N3LO)
τ decays (N3LO) 1000 pp –> jets (NLO)
(–)
)
2
c System (GeV/
−
π
+
π
−
π Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
c Number of Events / (5 MeV/ 0.05 0.1 0.15 0.2 0.25 0.3 0.35
6
10 ×
(COMPASS 2008) p
−
π
+
π
−
π → p
−
π
diffractive dissociation of pions and kaons → meson spectrometry scattering of pions (and kaons) in nuclear Coulomb field → low-energetic meson-photon reactions πγ → πγ (pion polarisability), πγ → 3π (chiral dynamics, radiative couplings)
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
lepton scattering at high momentum transfer → partonic structure of the nucleons
QCD αs(Mz) = 0.1185 ± 0.0006
Z pole fit 0.1 0.2 0.3
αs (Q)
1 10 100
Q [GeV]
Heavy Quarkonia (NLO) e+e– jets & shapes (res. NNLO) DIS jets (NLO)
Lattice QCD (NNLO)
(N3LO)
τ decays (N3LO) 1000 pp –> jets (NLO)
(–)
)
2
c System (GeV/
−
π
+
π
−
π Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
c Number of Events / (5 MeV/ 0.05 0.1 0.15 0.2 0.25 0.3 0.35
6
10 ×
(COMPASS 2008) p
−
π
+
π
−
π → p
−
π
diffractive dissociation of pions and kaons → meson spectrometry
scattering of pions (and kaons) in nuclear Coulomb field → low-energetic meson-photon reactions (this talk) πγ → πγ (pion polarisability), πγ → 3π (chiral dynamics, radiative couplings)
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Experimental Setup
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Fixed-target experiment two-stage magnetic spectrometer high-precision, high-rate tracking, PID, calorimetry
COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Experimental Setup
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Fixed-target experiment two-stage magnetic spectrometer high-precision, high-rate tracking, PID, calorimetry Runs with Hadron Beams 2004, 2008/09, 2012 190 GeV π− beam on p and nuclear targets (C, Ni, W, Pb) Silicon microstrip detectors for “vertexing” recoil and (digital) ECAL triggers
COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
+ − − + − + απ
pion polarisabilities απ, βπ in units of 10−4 fm3 size of the pion ∼ 1 fm3 [cf. atoms: polarisability ≈ size ≈ 1 A
Theory: ChPT (2-loop) prediction: απ − βπ = 5.7 ± 1.0 απ + βπ = 0.16 ± 0.1 experiments for απ − βπ lie in the range 4 · · · 14 (απ + βπ = 0 assumed)
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
+ − − + − + απ
pion polarisabilities απ, βπ in units of 10−4 fm3 size of the pion ∼ 1 fm3 [cf. atoms: polarisability ≈ size ≈ 1 A
Theory: ChPT (2-loop) prediction: απ = 2.93 ± 0.5 βπ = −2.77 ± 0.5 experiments for απ lie in the range 2 · · · 7 (απ + βπ = 0 assumed)
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
high-energetic pion beam on 4mm nickel disk
coincidence with produced hard photons study of cross-section shape
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Charged pions traverse the nuclear electric field
typical field strength at d = 5RNi: E ≈ 300 kV/fm
Bremsstrahlung process:
particles scatter off equivalent photons tiny momentum transfer Q2 ≈ 10−5 GeV2/c2 pion/muon (quasi-)real Compton scattering
Polarisability contribution
Compton cross-section typically diminished corresponding charge separation ≈ 10−5 fm · e
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Charged pions traverse the nuclear electric field
typical field strength at d = 5RNi: E ≈ 300 kV/fm
Bremsstrahlung process:
particles scatter off equivalent photons tiny momentum transfer Q2 ≈ 10−5 GeV2/c2 pion/muon (quasi-)real Compton scattering
Polarisability contribution
Compton cross-section typically diminished corresponding charge separation ≈ 10−5 fm · e
[GeV/c]
T
q 0.05 0.1 0.15 0.2 0.25 0.5 1 1.5 2 2.5 3
details: see later
photon exchange s t r
g i n t e r a c t i
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Q2 < <
2
m2
π
π π
(A,Z)
− −
γ
π π+ −
(A,Z) γ Primakoff processes
Radiative pion photoproduction
π π
Photon-Photon fusion
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Q2 < <
2
m2
π
π π
(A,Z)
− −
γ
π π+ −
(A,Z) γ
Primakoff processes
p n π+
Radiative pion photoproduction
π π
Photon-Photon fusion
year of publication
1980 1985 1990 1995 2000 2005 2010 2015
3
fm
/ 10
π
β
α
10 20 30 40 50 Z γ π → Z π Serpukhov Sigma n
+
π γ → p γ Lebedev PACHRA n
+
π γ → p γ MAMI
+
π → γ γ DM2, Mark II PLUTO, DM1 Babusci Mark II Donoghue
+
π → γ γ Kaloshin
+
π → γ γ Fil'kov GIS '06
3
fm
/ 10
π
β
α
5 10 15 20 25 30 35
2
χ Serpukhov 0.06 PACHRA 0.65 MAMI 0.10 0.81 (CL=0.67) 2.5 ± world avg.: 12.7 GIS (2006)
GIS’06: ChPT prediction, Gasser, Ivanov, Sainio, NPB745 (2006), plots: T. Nagel, PhD Fil’kov analysis objected by Pasquini, Drechsel, Scherer PRC81, 029802 (2010)
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Two kinematic variables, in CM: total energy √s, scattering angle θcm dσπγ dΩcm = α2(s2z2
+ + m4 πz2 −)
s(sz+ + m2
πz−)2 −
α m3
π (s − m2 π)2
4s2(sz+ + m2
πz−) · P
P = z2
−(απ − βπ)+ s2
m4
π
z2
+(απ + βπ) − (s − m2 π)2
24s z3
−(α2 − β2)
z± = 1 ± cos θcm
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
E B
+ − − + − + απ
βπ
Two kinematic variables, in CM: total energy √s, scattering angle θcm dσπγ dΩcm = α2(s2z2
+ + m4 πz2 −)
s(sz+ + m2
πz−)2 −
α m3
π (s − m2 π)2
4s2(sz+ + m2
πz−) · P
P = z2
−(απ − βπ)+ s2
m4
π
z2
+(απ + βπ) − (s − m2 π)2
24s z3
−(α2 − β2)
z± = 1 ± cos θcm
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
ECAL1 CEDARs SM1 SM2 ECAL2 silicon stations C/Ni/W targets 2009 RPD
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Identify exclusive reactions πγ{Ni→Ni′}→ πγ at smallest momentum transfer < 0.001 GeV2/c2 Assuming απ + βπ = 0, from the cross-section R = σ(xγ) σαπ=0(xγ) = Nmeas(xγ) Nsim(xγ) = 1 − 3 2 · m3
π
α · x2
γ
1 − xγ απ is derived, depending on xγ = Eγ(lab)/EBeam. Measuring R the polarisability απ can be concluded. Control systematics by µγ{Ni→Ni′}→ µγ and K − → π−π0 → πγγ
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Identify exclusive reactions πγ{Ni→Ni′}→ πγ at smallest momentum transfer < 0.001 GeV2/c2 Assuming απ + βπ = 0, from the cross-section R = σ(xγ) σαπ=0(xγ) = Nmeas(xγ) Nsim(xγ) = 1 − 3 2 · m3
π
α · x2
γ
1 − xγ απ is derived, depending on xγ = Eγ(lab)/EBeam. Measuring R the polarisability απ can be concluded. Control systematics by µγ{Ni→Ni′}→ µγ and K − → π−π0 → πγγ
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
E [GeV] ∆
10 20 counts / 250 MeV 500 1000 1500 2000 2500
Ni γ
−
π → Ni
−
π data simulation (normalised)
Energy balance ∆E = Eπ + Eγ − EBeam Exclusivity peak σ ≈ 2.6 GeV (1.4%) ∼ 63.000 exclusive events (xγ > 0.4) (Serpukhov ∼ 7000 for xγ > 0.5)
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
|Q| [GeV/c] 0.05 0.1 0.15 0.2 0.25 0.3 counts / 2.74 MeV/c 2000 4000 6000 8000
Ni γ
−
π → Ni
−
π data simulation (normalised)
∆QT ≈ 12 MeV/c (190 GeV/c beam → requires few-µrad angular resolution) first diffractive minimum on Ni nucleus at Q ≈ 190 MeV/c data a little more narrow than simulation → negative interference?
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
|Q| [GeV/c] 0.05 0.1 0.15 0.2 0.25 0.3 counts / 2.74 MeV/c 2000 4000 6000 8000
Ni γ
−
µ → Ni
−
µ data simulation (normalised) COMPASS 2009
muon control measurement: pure electromagnetic interaction e.m. nuclear effects well understood
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
ECAL1 CEDARs SM1 SM2 ECAL2 silicon stations C/Ni/W targets 2009 RPD
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
from: Th. Nagel, PhD thesis TUM 2012
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
0.4 0.5 0.6 0.7 0.8 0.9
data x2
−
µ simulation
−
µ data
−
π simulation
−
π
γ
π
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
γ
0.4 0.5 0.6 0.7 0.8 0.9 0.85 0.90 0.95 1 1.05 1.10 1.15
π
R pion beam
γ
0.90 0.95 1 1.05 1.10 1.15
µ
R muon beam
γ π γ
x 0.4 0.5 0.6 0.7 0.8 0.9
µ
απ = ( 2.0 ± 0.6stat ) × 10−4 fm3 (assuming απ = −βπ) “false polarisability” from muon data: ( 0.5 ± 0.5stat ) × 10−4 fm3
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
0.2 0.4 0.6 0.8 1 cosθcm
0.5 1 1.5 radiative correction [%] s
1/2 = 2m
s
1/2 = 3m
s
1/2 = 4m
s
1/2 = 5m
λ = 3.8 MeV
muon Compton scattering: µ
0.2 0.4 0.6 0.8 1 z = cosθcm
0.5 1 radiative correction [%]
s
1/2 = 2mπ
s
1/2 = 3mπ
s
1/2 = 4mπ
s
1/2 = 5mπ
λ = 5 MeV
pion Compton scattering: π
Nucl.Phys. A837 (2010) Eur.Phys.J. A39 (2009) 71
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
source of systematic uncertainty estimated magnitude CL = 68 % [10−4 fm3] determination of tracking-detector efficiencies 0.5 treatment of radiative corrections 0.3 subtraction of π0 background 0.2 strong interaction background 0.2 pion-electron elastic scattering 0.2 contribution of muons in the beam 0.05 quadratic sum 0.7
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
source of systematic uncertainty estimated magnitude CL = 68 % [10−4 fm3] determination of tracking-detector efficiencies 0.5 treatment of radiative corrections 0.3 subtraction of π0 background 0.2 strong interaction background 0.2 pion-electron elastic scattering 0.2 contribution of muons in the beam 0.05 quadratic sum 0.7 COMPASS result for the pion polarisability: απ = ( 2.0 ± 0.6stat ± 0.7syst ) × 10−4 fm3 with απ = −βπ assumed
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
year of publication
1980 1985 1990 1995 2000 2005 2010 2015
3
fm
/ 10
π
β
α
10 20 30 40 50 Z γ π → Z π Serpukhov Sigma n
+
π γ → p γ Lebedev PACHRA n
+
π γ → p γ MAMI Z γ π → Z π COMPASS
+
π → γ γ DM2, Mark II PLUTO, DM1 Babusci Mark II Donoghue
+
π → γ γ Kaloshin
+
π → γ γ Fil'kov GIS '06
3
fm
/ 10
π
β
α
5 10 15 20 25 30 35
2
χ Serpukhov 2.70 PACHRA 0.91 MAMI 1.43 COMPASS 3.09 8.14 (CL=0.04) 1.6 ± world avg.: 7.5 GIS (2006)
The new COMPASS result is in significant tension with the earlier measurements of the pion polarisability The expectation from ChPT is confirmed within the uncertainties
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Planned measurements at ALICE and JLab σtot(s) = 2πα2 ˆ s3m2
π
s + ˆ s|C(ˆ s)|2 ˆ s(ˆ s − 4) +8
s + ˆ s ReC(ˆ s)
√ˆ s + √ˆ s − 4 2
C(ˆ s) = −βπ m3
π
2α ˆ s − m2
π
(4πfπ)2 ˆ s 2 + 2
√ˆ s + √ˆ s − 4 2 − iπ 2 2
2 2.5 3 3.5 4 4.5 5 s
1/2 [mπ]
0.1 0.2 0.3 0.4 0.5 0.6 σtot(s) [µb]
tree approx. polarizability pion-loops
total cross section γγ --> π
+π
limited sensitivity to the polarisability contribution
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
π
/m s 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Born
σ / σ 0.85 0.9 0.95 1 1.05
=2.00 β =- α LEX =2.85 β =- α LEX LEX + chiral loops DR [B. Pasquini]
=
=2)+chiral loops α LEX( =0)+chiral loops α LEX( =0.00 α chiral loops, =2.7
π
/m s
Polarisability and Loop Contributions z=-1.0 DR calculations: Barbara Pasquini (Pavia)
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
mπ(sea)=306 MeV mπ(sea)=227 MeV Detmold 390 MeV 200 250 300 350 400
1 2 3 4 5 mπ[MeV] απ +[10-4 fm3] lattice QCD fit model 10 20 30 40 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 t/a a meff
FIGURE 3. Left: electric polarizability for the charged pions as a function of the valence quark mass. The data for mπ = 390MeV is taken from [5]. Right: effective mass for a charged pion correlator together with the scalar particle correlator determined from the
Alexandru et al., Pion electric polarizability from lattice QCD, arXiv:1501.06516
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Access to π + γ reactions via the Primakoff effect: At smallest momentum transfers to the nucleus, high-energetic particles scatter predominantly off the electromagnetic field quanta (∼ Z 2) π− + γ → π− + γ π− + π0 / η π− + π0 + π0 π− + π− + π+ ⇐ = π− + π− + π+ + π− + π+ π− + ... analogously: Kaon-induced reactions K − + γ → · · ·
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
π− Pb → Pb π− π− π+
)
2
System (GeV/c
+
π
Mass of 0.5 1 1.5 2 2.5 3 )
2
Events / (5 MeV/c 5 10 15 20 25 30 35
3
10 × COMPASS 2004 Pb
+
π
→ Pb
)
2
/c
2
Ranges in t’ (GeV all t’
t’ < 10
< t’ < 10
10
< t’ < 10
10 0.1 < t’ < 1 t’ > 1 [x5]
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”Low t′”: 10−3 (GeV/c)2 < t′ < 10−2 (GeV/c)2 ∼ 2 000 000 events ”Primakoff region”: t′ < 10−3 (GeV/c)2 ∼ 1 000 000 events
COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
3 4 5 6 7 s
1/2 [mπ]
1 2 3 4 5 6 7 σtot [µb]
tree approximation with chiral loops+cts
total cross section: π
+π
2
[GeV/c
π 3
m 0.45 0.5 0.55 0.6 0.65 0.7 b] µ [
γ
σ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 COMPASS 2004
+
π
→ γ
Pb
+
π
→ Pb
from
Fitted ChPT Intensity Leading Order ChPT Prediction
Full Systematic Error Luminosity Uncertainty
published in PRL 108 (2012) 192001
3 4 5 6 7 s
1/2 [mπ]
1 2 3 σtot [µb]
tree approximation with chiral loops+cts tree approx. mπ
0 < mπtotal cross section: π
0π
normalization: analysis ongoing
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
)
2
(GeV/c
π 3
m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
2
Intensity / 40MeV/c 2 4 6 8 10 12
3
10 × D π ρ 1
++
2 = 0.97
all
σ /
prim
σ ) γ π →
2
(a Γ = 293 keV COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
t' < 0.001 GeV
)
2
(GeV/c
π 3
m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
2
Intensity / 40MeV/c 0.2 0.4 0.6 0.8 1 1.2 1.4
3
10 × S π
2
1 f
2 = 0.95
all
σ /
prim
σ ) γ π →
2
π ( Γ = 153 keV COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
t' < 0.001 GeV
⇔ meson w.f.’s: Γi→f ∝ | Ψ
f| e−i q·
ǫ · p |Ψ
i |2, VMD
normalization via beam kaon decays large Coulomb correction published in EPJ A50 (2014) 79
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
Measurement of the pion polarisability at COMPASS
Via the Primakoff reaction, COMPASS has determined απ = ( 2.0 ± 0.6stat ± 0.7syst ) × 10−4 fm3 assuming απ + βπ = 0 most direct access to the πγ → πγ process Most precise experimental determination Systematic control: µγ → µγ, K − → π−π0
COMPASS measures more aspectes of chiral dynamics in π−γ → π−π0 and πγ → πππ reactions High-statistics run 2012
separate determination of απ and βπ s−dependent quadrupole polarisabilities First measurement of the kaon polarisability
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COMPASS Intro: Pions & ChPT COMPASS Pion polarisability ChPT & Resonances in π−π−π+ Summary and Outlook
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[GeV/c]
T
q 0.05 0.1 0.15 0.2 0.25 ]
[GeV
2
FF
T
q 0.5 1 1.5 2 2.5 3
Photon density squared form factor
calculation following G. F¨ aldt (Phys. Rev. C79, 014607) eikonal approximation: pions traverse Coulomb and strong-interaction potentials
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0.1 0.2 0.3 0.4
0.2 0.4 0.6 s = m
2
s = 4 m
2
θ = 0 θ = 1 8 0o t = 4 m2 u = m
2
u = 4 m
2
ν (GeV) t (GeV2) s = m
2
s = 4 m
2
θ = 0 θ = 1 8 0o t = 4 m2 u = m
2
u = 4 m
2
ν (GeV) t (GeV2)
0.1 0.2 0.3 0.4
0.2 0.4 0.6
red hatched:
two-pion thresholds
π, u = 4m2 π,
t = 4m2
π
DR integration paths
π, s = m2 π, . . .
from: D. Drechsel, talk at IWHSS 2011 Paris
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beam
γ
P = z2
−(απ − βπ) + s2
m4
π
z2
+(απ + βπ)−(s − m2 π)2
24s z3
−(α2 − β2)
z± = 1 ± cos θcm
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CM
θ cos
0.2 0.4 0.6 0.8 1 b] µ [
CM
Ω /d σ d 0.02 0.1 0.2 0.3 0.4
< 20 GeV
Primakoff
γ
E
2 π
s=3m
2 π
s=5m
2 π
s=8m
2 π
s=15m
= -3.00
π
β = 3.00,
π
α
loop effects not shown
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CM
θ cos
0.2 0.4 0.6 0.8 1 b] µ [
CM
Ω /d σ d 0.02 0.1 0.2 0.3 0.4
< 20 GeV
Primakoff
γ
E
2 π
s=3m
2 π
s=5m
2 π
s=8m
2 π
s=15m
= -2.86
π
β = 3.00,
π
α
loop effects not shown
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CM
θ cos
0.2 0.4 0.6 0.8 1 b] µ [
CM
Ω /d σ d 0.02 0.1 0.2 0.3 0.4
< 20 GeV
Primakoff
γ
E
2 π
s=3m
2 π
s=5m
2 π
s=8m
2 π
s=15m
= -3.14
π
β = 3.00,
π
α
loop effects not shown
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CM
θ cos
0.2 0.4 0.6 0.8 1 b] µ [
CM
Ω /d σ d 0.02 0.1 0.2 0.3 0.4
< 20 GeV
Primakoff
γ
E
2 π
s=3m
2 π
s=5m
2 π
s=8m
2 π
s=15m
= -6.10
π
β = 6.10,
π
α
loop effects not shown
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Pion Polarisability: Experimental Techniques
Radiative π+ production on the proton: γ π∗ − → π γ [via γ p → n π+ γ] Mainz (2005) measurement: απ − βπ = 11.6 ± 1.5 ± 3.0 ±0.5 “±0.5”: model error only within the used ansatz, full systematics not under control Primakoff Compton reaction: γ∗ π − → π γ [via π Z → Z π γ] tiny extrapolation γ∗ → γ O(10−3m2
π)
fully under theoretical control
[N. Kaiser, J.F., Nucl. Phys. A 812 (2008) 186]
42/32
[GeV/c]
T
p 0.1 0.2 0.3 counts / 2.5 MeV/c 500 1000 1500 2000 2500 3000
Ni γ
−
π → Ni
−
π data simulation (normalised)
43/32
]
2
[GeV/c
γ π
m 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2
counts / 5 MeV/c 500 1000 1500 2000 2500
Ni γ
−
π → Ni
−
π data simulation (normalised)
ρ contribution from πγ → ππ0
44/32
]
2
[GeV/c
γ π
m 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 [GeV]
π
γ
+E
π
E'
10 20 30 500 MeV ) ×
2
events / ( 10 MeV/c 20 40 60 80 100 120 140 160 Ni γ
→ Ni
COMPASS 2009
ρ contribution from πγ → ππ0
45/32
for πγ → πγ
CM
θ cos
0.2 0.4 0.6 0.8 1
π
/m s 1 2 3 4 5 6 7
20 GeV 40 GeV 60 GeV 80 GeV 100 GeV 120 GeV 140 GeV 160 GeV 180 GeV 0.4 mrad . 7 m r a d 1.0 mrad 1.5 mrad 2 . 5 m r a d 5 . m r a d 8 . m r a d
46/32
47/32
M.R. Pennington in the 2nd 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 mπ. Thus the polarisabilities cannot be determined accurately from γγ experiments in a model-independent way and must be measured in the Compton scattering region.
48/32
π− Pb → Pb π− π− π+
)
2
/c
2
Momentum Transfer t’ (GeV 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Number of Events
2
10
3
10
4
10
5
10 COMPASS 2004 Pb
+
π
→ Pb
49/32
”Low t′”: 10−3 (GeV/c)2 < t′ < 10−2 (GeV/c)2 ∼ 2 000 000 events ”Primakoff region”: t′ < 10−3 (GeV/c)2 ∼ 1 000 000 events
π− Pb → Pb π− π− π+
)
2
/c
2
Momentum Transfer t’ (GeV 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Number of Events
2
10
3
10
4
10
5
10 COMPASS 2004 Pb
+
π
→ Pb
PWA of a1(1260), a2(1320) contributions in t slices
49/32
”Low t′”: 10−3 (GeV/c)2 < t′ < 10−2 (GeV/c)2 ∼ 2 000 000 events ”Primakoff region”: t′ < 10−3 (GeV/c)2 ∼ 1 000 000 events
)
2
System (GeV/c
+
π
Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 20 40 60 80 100 120 140 160
3
10 × S π ρ
+ ++
1 COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
0.0015 < t' < 0.01 GeV
2
/c
2
t' < 0.0005 GeV
)
2
System (GeV/c
+
π
Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 1 2 3 4 5 6 7
3
10 × D π ρ
+
1
++
2 COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
0.0015 < t' < 0.01 GeV
2
/c
2
t' < 0.0005 GeV
)
2
System (GeV/c
+
π
Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Phase (degrees)
50 100 S ) π ρ
+ ++
D - 1 π ρ
+
1
++
( 2 Φ ∆ COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
0.0015 < t' < 0.01 GeV
2
/c
2
t' < 0.0005 GeV
50/32
)
2
/c
2
Momentum Transfer t’ (GeV 2 4 6 8 10 12 14 16 18 20
−3
10 × 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
9
10 × S π ρ
+ ++
1 COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
t’ < 0.02 GeV
2
< 1.38 GeV/c
π 3
1.26 < m
)
2
/c
2
Momentum Transfer t’ (GeV 2 4 6 8 10 12 14 16 18 20
−3
10 × 2 4 6 8 10 12 14 16 18 20
6
10 × D π ρ
+
1
++
2 COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
t’ < 0.02 GeV
2
< 1.38 GeV/c
π 3
1.26 < m
)
2
/c
2
Momentum Transfer t’ (GeV 2 4 6 8 10 12 14 16 18 20
−3
10 × Phase (degrees) −120 −100 −80 −60 −40 −20 S) π ρ
+ ++
D − 1 π ρ
+
1
++
(2 Φ ∆ COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
t’ < 0.02 GeV
2
< 1.38 GeV/c
π 3
1.26 < m
transition of πγ to πIP → a2 production work in progress interference can be used to map details of resonances and production mechanisms
51/32
)
2
System (GeV/c
+
π
Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 1 2 3 4 5 6 7
3
10 × S π ρ
+
1
++
1 COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
t' < 0.001 GeV
)
2
System (GeV/c
+
π
Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Phase (degrees) 50 100 150 200 250 300 350 S ) π ρ
+ ++
S - 1 π ρ
+
1
++
( 1 Φ ∆ COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
t' < 0.001 GeV
No evidence for a1(1260) → πγ
)
2
System (GeV/c
+
π
Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Phase (degrees)
50 100 150 200 250 S ) π ρ
+
1
++
D - 1 π ρ
+
1
++
( 2 Φ ∆ COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
t' < 0.001 GeV
52/32
Mass-independent PWA (narrow mass bins): σindep(τ, m, t′) =
ǫ=±1 Nr
T ǫ
ir f ǫ i (t′)ψǫ i (τ, m)
i (t′)|2dt′
i (τ ′, m)|2dτ ′
Production strenght assumed constant in single bins Decay amplitudes ψǫ
i (τ, m), with t′ dependence f ǫ i (t′)
Production amplitudes T ǫ
ir → Extended log-likelihood fit
Acceptance corrections included
Spin-density matrix: ρǫ
ij = r
T ǫ
ir T ǫ∗ jr
→ Physical parameters: Intensǫ
i = ρǫ ii,
relative phase Φe
ij
Coh ǫ
i,j =
ij)2 + ( Im ρǫ ij)2
ρǫ
iiρǫ jj
Mass-dependent χ2-fit (not presented here):
X parameterized by Breit-Wigner (BW) functions Background can be added
53/32
)
2
system (GeV/c
+
π
−
π
−
π Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
−2
((GeV/c)
diff
Diffractive slope b 100 200 300 400 500 COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
54/32
Isobar Model S J PCM ε
target recoil
ε = +: natural ε = parity exchange parity exchange −: unnatural
X
L 1 2
Rππ π π π π
+ − − −(beam)
(bachelor) Isobar model: Intermediate 2-particle decays Partial wave in reflectivity basis: JPCMǫ[isobar]L Mass-independent PWA (40 MeV/c2 mass bins): 38 waves Fit of angular dependence of partial waves, interferences Mass-dependent χ2-fit (Not presented here)
55/32
)
2
System (GeV/c
+
π
Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 20 40 60 80 100 120
3
10 × M=0 Spin Total COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
t' < 0.001 GeV
)
2
System (GeV/c
+
π
Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 2 4 6 8 10 12 14 16 18
3
10 × M=1 Spin Total COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
t' < 0.001 GeV
)
2
System (GeV/c
+
π
Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 10 20 30 40 50 60 70 80 90
3
10 × S π ρ
+ ++
1 COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
t' < 0.001 GeV
)
2
System (GeV/c
+
π
Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 2 4 6 8 10 12
3
10 × 1 Spin Total
++
2 COMPASS 2004 Pb
+
π
→ Pb
2
/c
2
t' < 0.001 GeV
a2(1320) a1(1260)
56/32
Intensity of selected waves: 0−+0+f0(980)πS, 1++0+ρπS, 2++1+ρπD, 2−+0+f2(1270)πS
)
2
System (GeV/c
+
π
−
π
−
π Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 0.5 1 1.5 2 2.5 3 3.5
3
10 × S π (980) f
+ −+
COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
0.001 < t’ < 0.01 GeV
)
2
System (GeV/c
+
π
−
π
−
π Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
6
10 × S π ρ
+ ++
1 COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
0.001 < t’ < 0.01 GeV
)
2
System (GeV/c
+
π
−
π
−
π Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 0.5 1 1.5 2 2.5 3 3.5
3
10 × D π ρ
+
1
++
2 COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
0.001 < t’ < 0.01 GeV
)
2
System (GeV/c
+
π
−
π
−
π Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 2 4 6 8 10
3
10 × S π
2
f
+ −+
2 COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
0.001 < t’ < 0.01 GeV
57/32
”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−bPrimt′ → arises at t′ ≈ 0 (resoluted shape!) Diffractive production: M=0: σ(t′) ∝ e−bdiff(m)t′ M=1: σ(t′) ∝ t′e−bdiff(m)t′ → vanishes for t′ ≈ 0
)
2
System (GeV/c
+
π
−
π
−
π Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 0.02 0.04 0.06 0.08 0.1 0.12
6
10 × M=0 Spin Total COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
t’ < 0.001 GeV
)
2
System (GeV/c
+
π
−
π
−
π Mass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
Intensity / (40 MeV/c 2 4 6 8 10 12 14
3
10 × M=1 Spin Total COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
t’ < 0.001 GeV
M=0 M=1
58/32
0.003 0.006 0.009 0.012 0.015 qt
2 [GeV 2]
50 100 150 phase [deg]
Coulomb + strong πA strong πA interaction difference
)
2
/c
2
Momentum Transfer t’ (GeV 2 4 6 8 10 12 14 16 18 20
−3
10 × Phase (degrees) −120 −100 −80 −60 −40 −20 S) π ρ
+ ++
D − 1 π ρ
+
1
++
(2 Φ ∆ COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
t’ < 0.02 GeV
2
< 1.38 GeV/c
π 3
1.26 < m
Glauber modell
aldt and U. Tengblad, Phys. Rev. C79, 014607 (2009) Plot: N. Kaiser (TU M¨ unchen)
⇒ indicates confirmation of interference Coulomb-interaction - strong interaction ⇒ detailed studies of the nature of resonances
59/32
60/32
Primakoff: σ(t′) ∝ e−bPrimt′, bPrim ≈ 2000 (GeV/c)−2 (mainly resolution) Diffractive: σ(t′) ∝ e−bdifft′, bdiff ≈ 400 (GeV/c)−2 for lead target
)
2
/c
2
Momentum transfer t’ (GeV 1 2 3 4 5 6 7 8 9 10
−3
10 × Events
4
10
5
10 COMPASS 2004 Pb
+
π
−
π
−
π → Pb
−
π
2
/c
2
t’ < 0.01 GeV
(Mass) spectrum of this Primakoff contribution? ⇒ Statistical subtraction of diffractive background (for bins of m3π)
3 4 5 6 7 s
1/2 [mπ]
1 2 3 4 5 6 7 σtot [µb]
tree approximation with chiral loops+cts
total cross section: π
+π
4 5 6 7 s
1/2 [mπ]
1 2 3 σtot [µb]
tree approximation with chiral loops+cts tree approx. mπ
0 < mπtotal cross section: π
0π
Chiral loops, e.g. (N. Kaiser, NPA848 (2010) 198)
π π− γ π Pb π− Pb π− π− π+ γ Pb Pb π− π π π
ρ terms:
π− π+ π− π− γ Pb Pb π− ρ0
61/32
γ π− π− π− π− π+ π γ π− π π π γ π− π− π− π+
Measured absolute cross-section of π−γ → π−π−π+
]
2
[GeV/c
π 3
m 0.45 0.5 0.55 0.6 0.65 0.7 b] µ [
γ
σ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 COMPASS 2004
+
π
→ γ
Pb
+
π
→ Pb
from
Fitted ChPT Intensity Leading Order ChPT Prediction
Full Systematic Error Luminosity Uncertainty
published in PRL 108 (2012) 192001
62/32
Partial Wave Analysis
Isobaric Model – Chiral Wave
63/32
Partial Wave Analysis
Chiral Model - Amplitudes
64/32