Searches	  for	  T	  Viola/on	  with	  Neutrons	  	  	  Mike	  Snow	  Indiana	  University/CEEM	  IU	  Center	  for	  Space/me	  Symmetries	  The	  scien/ﬁc	  mo/va/on	  	  The	  value	  of	  “null	  tests”	  of	  /me	  reversal	  invariance	  	  Searches	  for	  the	  neutron	  electric	  dipole	  moment	  	  Polarized	  neutron	  op/cs	  test	  of	  T	  invariance	  	  T-­‐viola/ng	  poten/al	  from	  light	  boson	  exchange	  	  Thanks	  for	  slides	  from:	  D.	  Bowman,	  V.	  Gudkov,	  H.	  Shimizu,	  J-­‐C	  Peng,	  M.	  Kitaguchi,	  P.	  Schmidt-­‐Wellenburg,…	  	  P,	  CP,	  T,	  and	  CPT	  Detector• Parity	  viola/on	  (1956)	  – only	  in	  weak	  interac/on	  • CP	  viola/on	  (1964)	  60

– Parametrized	  (CKM!)	  but	  not	  understood	   Co– Seen	  in	  K0	  &	  B0	  systems	  – Doesn’t	  seem	  to	  be	  responsible	  for	  baryon	  asymmetry	  of	  universe	  • T	  viola/on	  (1999)	  π– CPT	  is	  good	  symmetry	  so	  far:	  T	  ↔	  CP	  π
KSπe-KLππMa0er/An2ma0er	  Asymmetry	  in	  the	  Universe	  in	  Big	  Bang,	  star2ng	  from	  zero	  Sakharov	  Criteria	  to	  generate	  ma0er/an2ma0er	  asymmetry	  from	  the	  laws	  of	  physics	  – Baryon Number Violation (not yet seen)– C and CP Violation (seen but too small by ~1010)– Departure from Thermal Equilibrium (no problem?)A.D.	  Sakharov,	  JETP	  Leb.	  5,	  24-­‐27,	  1967	  	  Searches for T violation with neutrons:	  	  Electric Dipole Moment Searches (E~0)
T-odd Polarized Neutron Optics (E~6 MeV)

“Time	  Reversal”	  -­‐>	  Mo/on	  Reversal	  V2(t=1)

V1(t=0)-V2(t=0)

V3(t=1)In	  QM:	  reversal	  of	  ini/al	  and	  ﬁnal	  states:	  	  <a|O|b>	  -­‐>	  <b|OT|a>	  Is the final state of the motion with time-reversed final conditions
V3(t=1) the same as the time-reversed initial condition -V1(t=0)?
This is an experimental question

Gotta reverse the spins tooNeutron	  decay:	  not	  mo/on	  reversal	  invariant	  Reversing	  the	  electron,	  neutrino,	  and	  proton	  to	  get	  the	  neutron	  is	  imprac/cal.	  	  	  S/ll	  look	  for	  formally	  T-­‐odd	  correla/ons	  of	  observables	  	  But	  one	  must	  worry	  about	  “ﬁnal	  state	  eﬀects”	  giving	  T-­‐odd	  correla/on	  even	  if	  no	  real	  T	  viola/on	  is	  presentElectric Dipole Moments:
P-odd/ T-odd Observable3d n = ∫ xρ ( x)d x = d n sˆNon-zero dn violates both P and T

Under a parity operation:

Under a time-reversal operation:sˆ → sˆ ,sˆ → − sˆ ,E → −E  d n ⋅ E → −d n ⋅ EE→E  d n ⋅ E → −d n ⋅ E

EDMs	  are	  “null	  tests”	  of	  /me	  reversal	  invariance	  	  (no	  “ﬁnal	  state	  eﬀects”	  can	  fake	  an	  EDM)	  |i>=|f>	  Experimental Limit on d (e cm)

EDM	  limits:	  the	  ﬁrst	  50	  years	  10-20

10-20

neutron:electron:Electromagnetic

10-22
10-24
Multi
Higgs

SUSY
φ∼1
Left-Right

10-30

1960

1970

1980

1990

Factor ~10 per 8 years

2000

10-30
10-32
10-34
10-36

Barr: Int. J. Mod Phys. A8208 (1993)φ ∼ α/π10-38Standard ModelEDM	  Measurement	  Principle/Sensi/vity	  B0B0 EB0 Ehν(↑↑)

hν(↑↓)<Sz> = + h/2hν(0)<Sz> = - h/2ν(↑↑)	  –	  ν(↑↓)	  =	  	  –	  4	  E	  d/	  h	  	  assuming	  B	  unchanged	  when	  E	  is	  reversed.	  
EDM	  limits	  -­‐>	  ra/o	  (T-­‐odd	  amplitude	  in	  nucleon/strong	  amplitude)~10-­‐11	  	  T	  viola/on	  from	  CKM	  phases	  smaller	  by	  ~5	  orders	  of	  magnitude	  here	  	  EDMs	  are	  ground	  state	  proper/es	  of	  the	  system:	  excita/on	  energy	  ~0	  nEDM	  	  apparatus	  at	  ILL	  using	  UCN	  Best	  limit:	  d<2.9×10-­‐26ecm	  Baker	  et	  al.,	  PRL97(2006)	  • Use 199Hg comagnetometer tosample the variationof B-field in the UCN
storage cell
• Limited by low UCN
flux of ~ 5 UCN/cm3• Figure–of-merit ~E(NΤ)1/2

Four-layer mu-metal shield

High voltage lead

Quartz insulating
cylinderCoil for 10 mG
magnetic field

Main storage cellUpperelectrode

Hg u.v.
lamp
PMT todetect Hg
u.v. light

Vacuum wall

Mercury
prepolarisingcell
RF coil to flip spins
MagnetUCN polarising foil

UCN detector

Hg u.v. lamp
SN

UCN guidechangeover
Ultracold
neutrons(UCN)

The	  nEDM	  spectrometer	  at	  PSI	  Neutron	  EDM	  sensi/vity	  σ=h2αTE NRAL/Sussex/ILL*

PSI 2013

best

avg

best

avg

E-field

8.8

8.3

12

10.3

Neutrons

14 000

14 00010 500

6 500

Tfree

130

130

200

180

Tduty

240

240

340

340

Α

0.68

0.51

0.62

0.57

~0.75	  (10-25ecm)

2.0

2.8

1.5

2.8

<2	  ~7500	  2013	  data	  taking:	   	  3266	  cycles	  	  	  25	  days	  	  	  Stopped	  by	  switch	  break	  down	  	  	  2013	  accumulated	  sensi/vity	  6×10-­‐26	  e.cm	  	  *	  Best	  nedm	  limit:	  Baker	  et	  al.,	  PRL97(2006)	  “We	  expect	  with	  300	  data-­‐days	  un/l	  2016	  a	  sta/s/cal	  sensi/vity	  of	  	  	  σ	  ≲10-26 e⋅cm” PSI2016

T	  viola/on	  Searches	  with	  EDMs	  and	  Compound	  Nuclei	  complicated	  theore/cal	  landscape	  important	  to	  perform	  experiments	  in	  many	  systems	  Compound	  nuclei?	  What	  is	  this?	  Low	  energy	  neutrons	  can	  access	  a	  dense	  forest	  	  of	  highly	  excited	  states	  in	  the	  compound	  nucleus.	  	  	  Large	  ampliﬁca/on	  of	  discrete	  symmetry	  viola/on	  	  (P	  and	  T)	  is	  possible.	  Very	  large	  ampliﬁca/ons	  	  of	  P	  viola/on	  were	  observed	  long	  ago	  Apparatus	  to	  Measure	  σ	  .k	  Parity	  Viola/ng	  Asymmetry	  TRIPLE	  collabora/on	  measured	  ~60	  parity-­‐odd	  asymmetries	  in	  p-­‐wave	  resonances	  in	  heavy	  nuclei	  G.	  M.	  Mitchell,	  J.	  D.	  Bowman,	  S.	  I.	  Penrla,	  and	  E.	  I.	  Sharapov,	  Phys.	  Rep.	  354,	  157	  (2001).	  	  Quan/ta/ve	  analysis	  of	  distribu/on	  of	  parity-­‐odd	  asymmetries	  conducted	  using	  nuclear	  sta/s/cal	  spectroscopy	  S.	  Tomsovic,	  M.	  B.	  Johnson,	  A.	  Hayes,	  and	  J.	  D.	  Bowman,	  Phys.	  Rev.	  C	  62,	  054607	  (2000).	  

Parity	  Viola/on	  in	  n+	  139La	  at	  0.734	  eV	  	  	  	  	  Δσ/σ =0.097±.005.	  	  	  	  Larger	  than	  dimensional	  analysis	  es/mate	  by	  ~106	  	  How?	  (1)	  Admixture	  of	  (large)	  s-­‐wave	  amplitude	  into	  (small)	  p-­‐wave	  ~1/kR~1000	  (2)	  Weak	  amplitude	  dispersion	  for	  106	  Fock	  space	  components	  ~sqrt(106)=1000	  	  Idea	  is	  to	  use	  the	  observed	  enhancement	  of	  PV	  to	  search	  for	  a	  TRIV	  asymmetry.	  ⇥n · (k⇥n⇥I)

The	  enhancement	  of	  P-­‐odd/T-­‐odd	  amplitude	  on	  p-­‐wave	  resonance	  (σ.[K	  X	  I])	  is	  (almost)	  the	  same	  as	  for	  P-­‐odd	  amplitude	  (σ.K).	  	  
PT=Experimental	  observable:	  ra/o	  of	  P-­‐odd/T-­‐odd	  to	  P-­‐odd	  amplitudes	  	   P TP	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  λ	  can	  be	  measured	  	  with	  a	  sta/s/cal	  uncertainty	  of	  ~1	  10-­‐5	  in	  107	  sec	  at	  MW-­‐class	  spalla/on	  neutron	  sources.	  	  	  Ra/o	  (T-­‐odd	  amplitude	  in	  nucleon/strong	  amplitude)~10-­‐12	  	  Forward	  scabering	  neutron	  op/cs	  limit	  is	  null	  test	  for	  T	  (no	  ﬁnal	  state	  eﬀects)	  EDITORS’ SUGGESTION Phys. Rev. C (2015)
Search for time reversal invariance violation in neutron transmission
J. David Bowman and Vladimir Gudkov

NOPTREX	  collabora/on	  (Nagoya	  U	  +…)	  is	  becoming	  serious	  New	   interac/ons	   with	   ranges	   from	   millimeters	  to	  microns…	  “Who	  ordered	  that?”
1. Weakly-coupled, long-range interactions fromexchange of light particles are a genericconsequence of spontaneously broken continuous
symmetries (Goldstone theorem)
2. Specific theoretical ideas (axions, extra dimensionsfor gravity) imply new interactions at ~mm-µm scales
3. Dimensional analysis: dark energy->100 microns
Comptes	  Rendus	  Physique	  12,	  755-­‐778	  (2011)	  	  J.	  Jaeckel	  and	  A.	  Ringwald,	  Ann.	  Rev.	  Nucl.	  Part.	  Sci.	  60,	  405	  (2010).	  P-ODD AND T-ODD SPIN-DEPENDENT INTERACTIONS
mf2! g s g p ⎛ 1
1 ⎞ − r / λa⎜⎜
U (r ) =+ 2 ⎟⎟e(σˆ ⋅ rˆ)
8 π m f ⎝ rλa r ⎠σNon-­‐Rela/vis/c	  Limit,	  	  	  posi/on	  space	  J.	  E.	  Moody,	  F.	  Wilczek,	  	  Phys	  .	  Rev.	  D,	  30,	  130	  (1984))	  Induces an interaction between polarized and unpolarized matter
Violates both P and T symmetry
Poorly constrained over “mesoscopic” ranges(millimeters to microns)
From axions or “axion-like particles”

SIMPLE MEASUREMENT CONCEPT• Use a sensitive NMR magnetometer consisting of spin polarized nuclei• Oscillate a low magnetic susceptibility, unpolarized mass near and far
from the ensemble• Look for changes in the NMR frequency of the magnetometer induced by
the change in the potential energy• Any magnetic effects from the oscillating mass would appear as asystematic error

LABORATORY SEARCH FOR A LONG-RANGE,SCALAR-PSEUDOSCALAR INTERACTION USING
DUAL-SPECIES NMR WITH POLARIZED 129XE AND
131XE GAS
M. Bulatowicz, R. Griffith, M. Larsen, J. Mirijanian, and J. Pavell
Northrop Grumman Corporation, Woodland Hills, California 91367, USA
C.B. Fu, E. Smith, W. M. Snow, and H. Yan
Indiana University, Bloomington, Indiana 47408, USA andCenter for Exploration of Energy and Matter, Indiana University,Bloomington, IN 47408
T. G. Walker
University of Wisconsin, Madison, Wisconsin 53706, USA
Supported By:
NSF grants PHY-1068712 and PHY-0116146, IU Faculty Research Support program, the Indiana University Center for Spacetime
Symmetries, NGC IRAD funding, and the DoE

PHYS. REV. LETT. 111, 102001 (2013)

Experimental	  Setup	  	  	  The experimental system
uses a85Rb-129Xe-131Xe
co-magnetometer
configuration with a zirconia
rod as the unpolarized
sourceThe Rb magnetometermeasures the Free Induction
Decay (FID) of the two xenon
isotopes as an amplitude
modulation of the Rb spin
projection.
This signal is read by optical
Faraday rotation anddemodulated to give the sumof the two Xe Larmour
precession signals

Results	  from	  Northrop/Grumman	  	  γ 129δΩ129 +δΩ131 = −8 ± 23 × 10 −6 Hzγ 131

3.37350
Rod out
Rod in3.37345!1/!

2€
3.37340

3.37335

3.37330
050

100

150
Run #200

250

300

Frequency shift zero at 2E-5 Hz level in ~3-day experiment on their “test” apparatus
Apparatus improvements can achieve ~1E-9 Hz precision

Constraints	  on	  Monopole-­‐Dipole	  Interac/ons	  	  A. Pethkhov	  et	  al,	  PRL	  105,	  	  170401	  (2010)	  S. Afach et al,arXiv 1412.3679

M. Bulatowicz et al,arXiv 1301.5224
PRL 111, 102001 (2013)

K. Tullney et al,
PRL 111, 100801 (2013)

Constraints on general P-odd Note: neutron/atom EDM limits are lessT-odd interactions in mm range stringent for generic light scalars in this range(S. Mantry et al, PRD 90, 054016 (2014)

The	  Axion	  Resonant	  InterAc/on	  Detec/oN	  Experiment	  (ARIADNE)ARIADNE	  Collabora/on:

A.Arvanitaki	  and	  AG.,	  Phys.	  Rev.	  Le1.	  113,161801	  (2014).

NSF	  PHY-­‐1306942	  Asimina	  Arvanitaki	  (Perimeter)
Aharon	  Kapitulnik	  (Stanford)
Eli	  Levenson-­‐Falk	  (Stanford)
Josh	  Long	  (Indiana)
Chen-­‐Yu	  Liu	  (Indiana)
Mike	  Snow	  (Indiana)
Erick	  Smith	  (Indiana)	  Jus/n	  Shor/no	  (Indiana)
Yannis	  Semertzidis	  (CAPP)
Yunchang	  Shin	  (CAPP)
Andrew	  Geraci	  (UNR)
Suyesh	  Koyu	  (UNR)
Jordan	  Dargert	  (UNR)MEOP (Metastability Exchange Optical Pumping) Works on
Arbitrary 3He/4He Mixtures
pure 3He or 3He-4He Mixtures

σ+23P01083 nmRF dischargeOPTICAL PUMPING
of METASTABLE 3He•••

RF discharge excites metastable
1083 nm light pumps metastable
Hyperfine interaction polarizes nucleus

METASTABILITYEXCHANGE
Excitation exchanged in fast collision
Nuclear spins unperturbed

1083 nmσ+23S1mF = -1/2

mF= + 1/2

electron spin
nuclear spinpolarized
metastable
3He atomground state
3He atompolarized
ground state
3He atommetastable
3He atomConceptual Drawing of Apparatus

Use	  laser	  polarized
3He	  gas	  at	  4KLarmor	  frequency:	  	  ωRota/ng	  tungsten	  massoscillates	  force
in	  resonance	  at	  nωSuperconduc/ng
B	  shield
Ellipsoidal	  sample
SQUID	  magnetometry

ARIADNE SCIENTIFIC REACH FOR ALPSConclusions	  Any	  discovery	  of	  a	  new	  source	  of	  T	  viola/on	  is	  of	  fundamental	  importance	  for	  physics,	  	  and	  possibly	  also	  for	  cosmology	  	  EDMs	  and	  T	  viola/on	  in	  epithermal	  neutron	  resonances	  are	  both	  true	  “null	  tests”	  	  for	  T	  viola/on	  and	  are	  sensi/ve	  searches	  for	  T	  in	  strongly	  interac/ng	  systems	  	  ra/o	  (T-­‐odd	  amplitude	  in	  nucleon/strong	  amplitude)~10-­‐11-­‐10-­‐12	  	  Excita/on	  energy	  (EDMs)~0	  	  	  	  	  	  Excita/on	  energy	  (n	  resonances)~few	  MeV	  	  We	  usually	  think	  that	  the	  new	  physics	  should	  come	  from	  small	  virtual	  	  eﬀects	  from	  high	  energy,	  but	  be	  careful:	  it	  could	  be	  a	  very	  weakly-­‐coupled	  eﬀect	  at	  low	  energy	  as	  well.	  	  Neutron	  Time-­‐of-­‐Flight	  spectrum	  in	  transmission	  through	  Indium	  Excited	  state	  energies=~6	  MeV	  +(eV-­‐>keV)	  Narrow	  resonances	  (~100	  meV)	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  High	  density	  of	  levels	  per	  unit	  energy	  	  	  	  	  N- N Weak Interaction: Size and Mechanism~1 fm

NN repulsive core → 1 fm range for NN strong force= valence + sea quarks + gluons + …
interacts through NN strong force, mediated by mesons
QCD possesses only vector quark-gluon couplings → conserves parity
Both W and Z exchange possessmuch smaller range [~1/100 fm]
weakRelative strength of weak / strong amplitudes:
Use parity violation to isolate the weak contribution to the NN interaction.
NN strong interaction at low energy largely dictated by QCD chiral symmetry.
Can be parametrized by effective field theory methods.

Parity	  Viola/on	  in	  139La	  .734	  eV	  	  	  	  	  Δσ/σ =0.097±.005.	  	  	  	  	  	  	  	  	  	  106	  ampliﬁca/on!	  

How?	  (1)	  Admixture	  of	  (large)	  s-­‐wave	  amplitude	  into	  (small)	  p-­‐wave	  ~1/kR~1000	  (2)	  Weak	  amplitude	  dispersion	  for	  106	  Fock	  space	  components	  ~sqrt(106)=1000	  Idea	  is	  to	  use	  the	  observed	  enhancement	  of	  PV	  to	  search	  for	  a	  TRIV	  asymmetry.	  	  Apparatus	  to	  Measure	  σ	  .k	  Parity	  Viola/ng	  Asymmetry	  TRIPLE	  collabora/on	  measured	  ~80	  parity-­‐odd	  asymmetries	  in	  p-­‐wave	  resonances	  in	  heavy	  nuclei	  G.	  M.	  Mitchell,	  J.	  D.	  Bowman,	  S.	  I.	  Penrla,	  and	  E.	  I.	  Sharapov,	  Phys.	  Rep.	  354,	  157	  (2001).	  	  Quan/ta/ve	  analysis	  of	  distribu/on	  of	  parity-­‐odd	  asymmetries	  conducted	  using	  nuclear	  sta/s/cal	  spectroscopy	  S.	  Tomsovic,	  M.	  B.	  Johnson,	  A.	  Hayes,	  and	  J.	  D.	  Bowman,	  Phys.	  Rev.	  C	  62,	  054607	  (2000).	  Apparatus	  for	  PV	  at	  a	  spalla/on	  neutron	  source	  	  Polarized	  proton	  target	  to	  make	  polarized	  neutrons	  (S.	  Penrla,	  using	  cryostat	  now	  at	  UVA!)	  	  	  Look	  for	  σ.k	  dependence	  of	  total	  cross	  sec/on	  	  	  Study	  of	  Parity	  Viola/on	  in	  the	  Compound	  Nucleus	  A	  Paradigm	  for	  Time	  Reversal	  Comparison	  of	  experimental	  CN	  matrix	  elements	  with	  Tomsovic	  theory	  using	  DDH	  “best”	  meson-­‐nucleon	  couplings:	  agreement	  within	  a	  factor	  of	  2	  The	  enhancement	  of	  PVTR	  (σ.[K	  X	  I])	  is	  (almost)	  the	  same	  as	  for	  PV	  (σ.K).	  
PT
Sensi/vity	  expressed	  as	  a	  ra/o	  of	  P-­‐odd/T-­‐odd	  to	  P-­‐odd	  amplitudes	  	   P T =	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  P	  λ	  can	  be	  measured	  	  with	  a	  sta/s/cal	  uncertainty	  of	  ~1	  10-­‐5	  in	  107	  sec	  at	  MW-­‐class	  spalla/on	  neutron	  source	  like	  SNS/JSNS.	  	  	  sensi/vity	  ~	  100	  /mes	  beber	  than	  present	  n	  EDM	  limit,	  completely	  diﬀerent	  system.	  T	  viola/on	  in	  Neutron	  Op/cs	  • T	  –	  odd	  term	  in	  FORWARD	  scabering	  amplitude	  (a	  null	  test,	  like	  EDMs)	  with	  polarized	  n	  beam	  and	  polarized	  nuclear	  target	  	  ⇥• P-­‐odd/T-­‐odd	  (most	  interes/ng)	  	   ⇥n · (k⇥n I)• Ampliﬁed	  on	  select	  P-­‐wave	  epithermal	  neutron	  resonances	  by	  ~5-­‐6	  orders	  of	  magnitude	  • Es/mates	  of	  stat	  sensi/vity	  at	  SNS/JSNS	  look	  very	  interes/ng:	  Exis/ng	  technology/sources-­‐>ΔσPT/ΔσP~1E-­‐5	  • The	  nuclei	  of	  interest,	  resonance	  energies,	  and	  P-­‐odd	  asymmetry	  ampliﬁca/ons	  are	  measured	  Nucleus	   Resonance	  Energy	  PV	  asymmetry	  131Xe	  3.2	  eV	  0.043	  139La	  0.748	  eV	  0.096	  81Br	  0.88	  eV	  0.02	  Why	  is	  a	  pulsed	  spalla/on	  neutron	  source	  important	  for	  TREX?	  
resonance	  energy	  ~eV,	  	  resonance	  width	  ~meVs	  	  Short	  pulse-­‐>	  resonance	  can	  be	  resolved	  using	  neutron	  /me-­‐of-­‐ﬂight	  	  The	  rest	  of	  the	  neutrons	  in	  the	  beam	  can	  be	  used	  to	  characterize	  possible	  systema/c	  eﬀects	  !	  	  >~104	  more	  of	  these	  “oﬀ-­‐
resonance”	  neutrons	  	  Reality	  check	  If	  neutron	  were	  the	  size	  of	  the	  Earth...	  

+eδx-e... current EDM limit on neutron would
correspond to charge separation ofδx ≈ 10 µUCN	  produc/on	  in	  liquid	  helium	  Dispersion curve for freeneutrons

Landau-Feynman
dispersion curve for 4He
excitations

R. Golub and J.M. Pendlebury
Phys. Lett. 53A (1975),
Phys. Lett. 62A (1977)

λn = 8.9 Å; E = 1.03 meV• 1.03	  meV	  (11	  K)	  neutrons	  downscaber	  by	  emission	  of	  phonon	  in	  liquid	  helium	  at	  0.5	  K	  • Upscabering	  suppressed:	  Boltzmann	  factor	  e-­‐E/kT	  is	  small	  if	  T<<11K	  nEDM	  experiment	  at	  SNS	  	  GOAL:	  ~1E-­‐28	  e-­‐cm	  	  Figure–of-merit ~ E(NΤ)1/2
New approach aims at N à 100 N, T à 5 T, E à 5 E

APPARATUS DETAIL

4 mm

Experimental parameters:
11 segments
100 Hz nuclear spin precession frequency
2 x 1021 / cc 3He density
10 mm x 3 mm x 150 µm volumeSeparation 200 µm
Tungsten source mass (high nucleon density)

QCD AXION PARAMETER SPACEmAfA	  ≈	  6	  MeV	  	  -­‐	  Allows	  for	  a	  nice	  1D	  plot:	  Energy	  loss	  from	  stars	  puts	  strict	  upper	  limits	  on	  Axion	  coupling	  excluded“axion window” corresponds to~mm-micron interaction ranges

Lab and Astrophysicalbounds