Photo-‐Pion Produc-on: Tests of Chiral Symmetry A.M. Bernstein, MIT
PEB Workshop March 15,2013
Physics Opportuni-es Photo pion produc-on: charged and neutral Proton and neutron γN -‐> πN amplitudes
test isopsin conserva-on π produc-on on D, 3He
use/test few body calcula-ons
elas-c ep scat -‐> Rp Compton ScaSering
Few body hadronic reac-ons
Forward Electron ScaSering
γp -‐. πop Forward Proton Detector Near Threshold
Mainz photon tagger and detector
0
200
400
600
800
1,000
0 1 2 3 4 5 6 7
Moller Scattering
p'(MeV/c):E=1000p'(MeV/c):E=300
p'(M
eV/c
)
theta e (deg)
100,000
1,000,000
0 1 2 3 4 5 6 7
Moller count rate L =1032
cts/(10mrad):E=1000cts/(10mrad):E=300ct
s/(1
0mra
d)
theta e (deg)
Moller background
Forward Electron ScaSering
• measures electrons that have interacted in target • higher efficiency than conven-onal taggers • high currents, pure, thin targets • observe low energy par-cles
γp -‐> π0p, π+n γn –> π0n, π-‐p γD -‐> π0D • coherent p0 produc-on in D, 3He measure rela-ve signs of γp -‐> π0p, γn –π0n amplitudes • low Q2, virtual photons almost real (transverse) • small transverse beam spot
Tagged Photon Experiments Real: limited by rates in tagger need thick targets, limits energy region Virtual: I ≈ 1 mA can u1lize thin, unpolarized targets p ≈ 1 mm Hg can measure low energy π+, p recoil Virtual: I ≈ 100 mA E ≈ 1 GeV can u-lize polarized targets
-19.5
-19
-18.5
-18
-17.5
-17
-16.5
-16
nD-Duke nD-Bonn piD-LAMF a_pp
a_nn
a (f
m)
Is ann = app ? charge symmetry viola-on measure with γD -‐> nn π+ check anp with γD -‐> np π0
π-‐ D-‐> nn π0
γD → nnπ+
γ(�k)D → n( �p1) + n( �p2) + π+( �pπ)
�pr(θr,φr) = ( �p1 − �p2)/2
θr=0
θr=90
ann
polarized photon asymmetry → p wave amplitudes
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
145 150 155 160 165 170 175 180
(90
o)
E (MeV)
EMPIRICALHBCHPT
BCHPT
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
145 150 155 160 165 170 175 180
d/d
(92
.87
o)
(!b
/sr)
E (MeV)
EMPIRICALHBCHPT
BCHPT
cross sec1on → s, p wave amplitudes
γ p -‐> π0 p
ChPT works to ≤ 170 MeV
1
1.5
2
2.5
3
3.5
4
155 160 165 170 175 180 185 190 195Emax (MeV)
2/dof
EmpiricalHBCHPT
BCHPT
100127
154181
208237
266297
328359
390421
452483
514
Amount of experimental data
Unitary Cusp γp → π0p
β = E0+( γ p → π+n) acex( π0p ↔ π+n)
cusp sign and magnitude
Re E 0+
→ Im E 0+
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
140 150 160 170 180 190
Re E
0+ (
10
-3/m
+)
E (MeV)
EmpiricHBChPT
RChPT
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*+ ,--./0123456)!!7%#!!8----9315:;:/43<
=>?13:;1/0@:0
./01
23401A
-*+
,
B-+C1D,
Testing Isospin ConservationγN → πN
There are 3 isospin matrix elements,4 reaction channels.
The test of isospin conservation is:
A(γp → π+n) +A(γn → π−p)
=�(2)[A(γn → π0n)−A(γp → π0p)]
A = multipole matrix elementss wave (E0+), 3 p wave)
LQCD = L0 (mq → 0) + Lm (quark mass term)"" L0 has chiral symmetry; spontaneously broken " ⇒ Nambu-Goldstone Bosons (π, η, K)" ⇒ ChPT: effective theory of QCD"" Lm =A(mu+ md) + B (mu- md) ""explicitly breaks chiral symmetry"
" isospin symmetry broken: EM interaction " (md-mu)/ΛQCD ≈ 2%" exp. tests needed"""" "
tes1ng isospin symmetry
0.75
0.8
0.85
0.9
0.95
1
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
G_D(dipole) G_E:q^2 = 1- q2Rp2/6
G_D G_E:q^2
G_Ep
q^2(GeV^2)
0.1
1
10
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
elastic ep cts(Hz/msr)E= 300 MeV, L = 1032
cts(Hz/msr)
cts(
Hz/m
sr)
q^2(GeV^2)
elas-c ep -‐> Rp measure protons in coincidence
Physics Possibili-es
• Photo pion produc-on: charged and neutral • Proton and neutron amplitudes I spin checks • Coherent reac-ons on D, 3He
• elas-c ep scaSering : Rp • Polarized Compton ScaSering • Few body hadronic reac-ons
γ p → π0 p Mainz data: Hornidge..; HBChPT: BKM O(p4): Fernandez-‐Ramirez, AB, rela1vis1c BCHPT Hilt, Scherer, Tiator
0.00
0.005
0.010
0.015
0.020
0.025
d/d
(!b/
sr)
E = 146.95 MeV
0.00
0.02
0.04
0.06
E = 149.35 MeV
0.02
0.04
0.06
0.08
E = 151.68 MeV
HBCHPTBCHPT
0.02
0.05
0.08
0.11
d/d
(!b/
sr)
E = 154.03 MeV
0.05
0.10
0.15
E = 156.38 MeV
0.05
0.10
0.15
0.20
E = 158.72 MeV
0.10
0.15
0.20
0.25
-1 -0.5 0 0.5 1
d/d
(!b/
sr)
cos
E = 161.08 MeV
0.1
0.2
0.3
-1 -0.5 0 0.5 1
cos
E = 163.44 MeV
0.1
0.2
0.3
0.4
-1 -0.5 0 0.5 1
cos
E = 165.78 MeV