The Proton Radius
Nuclear Physics' Newest Puzzle
Guy Ron
Hebrew University of Jerusalem
Joint Nuclear Physics Seminar, 22 Aug. 2012
Radii
The Proton Radius
Nuclear Physics' Newest Puzzle
Guy Ron
Hebrew University of Jerusalem
Joint Nuclear Physics Seminar, 22 Aug. 2012
Charge Radii
The Proton Radius
Nuclear Physics' Newest Puzzle
Guy Ron
Hebrew University of Jerusalem
Joint Nuclear Physics Seminar, 22 Aug. 2012
Outline
•
How to measure the proton size.
•
Elastic eP.
•
AMO-type measurements.
•
Evolution of measurements.
•
Recent results and the “proton size crisis”.
•
(Some) attempts at resolutions.
•
Looking forward.
How to measure the proton size
Bernauer et al., PRL105,
242001 (2010)
Chambers and Hofstadter,
Phys Rev 103, 14 (1956)
Hofstadter @ Stanford: 1950s electron scattering
Atomic physicists - precise
atomic transitions in
hydrogen
Zhan et al., PLB705, 59 (2011)
Ron et al., PRC84, 055204 (2011)
Hadronic physicists all over:
1960s-2010s - Form factors
Pohl et al., Nature 466, 213
(2010)
How to measure the proton size
Question:
Why should hadronic physicists care about
what atomic physicists
are
measuring?
Bernauer et al., PRL105,
242001 (2010)
Chambers and Hofstadter,
Phys Rev 103, 14 (1956)
Zhan et al., PLB705, 59 (2011)
Ron et al., PRC84, 055204 (2011)
Answer:
Hofstadter @ Stanford: 1950s Hadronic physicists all over:
electron scattering
1960s-2010s - Form factors
Because sometimes they can measure
things in NP more precisely than we can!
Atomic physicists - precise
atomic transitions in
hydrogen
Pohl et al., Nature 466, 213
(2010)
Scattering Measurements
ELECTRON SCATTERING CROSS-SECTION (1-γ)
2
d R
↵
= 2
d⌦
Q
✓
0
E
E
◆2
2 ✓e
cot 2
1+⌧

Q
2 ✓e
⌧=
, " = 1 + 2(1 + ⌧ ) tan
2
4M
2
2
Rutherford - Point-Like
1
e
e'
γ*
N
N'
ELECTRON SCATTERING CROSS-SECTION (1-γ)
2
d R
↵
= 2
d⌦
Q
✓
0
E
E
◆2
2 ✓e
cot 2
Rutherford - Point-Like
1+⌧

d M
d R
2 ✓
=
⇥ 1 + 2⌧ tan
d⌦
d⌦
2

Q
2 ✓e
⌧=
, " = 1 + 2(1 + ⌧ ) tan
2
4M
2
2
Mott - Spin-1/2
1
e
e'
γ*
N
N'
ELECTRON SCATTERING CROSS-SECTION (1-γ)
2
d R
↵
= 2
d⌦
Q
✓
0
E
E
◆2
2 ✓e
cot 2
1+⌧

d M
d R
2 ✓
=
⇥ 1 + 2⌧ tan
d⌦
d⌦
2
Rutherford - Point-Like
Mott - Spin-1/2
h
i
Rosenbluth
d Str
d M
⌧
2
2
2
2
=
⇥ GE (Q ) + GM (Q ) Spin-1/2 with
d⌦
d⌦
"
Structure

1
Q
2 ✓e
⌧=
, " = 1 + 2(1 + ⌧ ) tan
2
4M
2
p
n
GE (0) = 1 GE (0) = 0
p
GM = 2.793 GnM = 1.91
2
Sometimes
G E = F1 ⌧ F 2
written using: GM = F 1 + F2
e
e'
γ*
N
N'
ELECTRON SCATTERING CROSS-SECTION (1-γ)
2
d R
↵
= 2
d⌦
Q
✓
0
E
E
◆2
2 ✓e
cot 2
1+⌧

d M
d R
2 ✓
=
⇥ 1 + 2⌧ tan
d⌦
d⌦
2
Rutherford
- Point-Like
Everything
we don’t
know goes here!
Mott - Spin-1/2
h
i
Rosenbluth
d Str
d M
⌧
2
2
2
2
=
⇥ GE (Q ) + GM (Q ) Spin-1/2 with
d⌦
d⌦
"
Structure

1
Q
2 ✓e
⌧=
, " = 1 + 2(1 + ⌧ ) tan
2
4M
2
p
n
GE (0) = 1 GE (0) = 0
p
GM = 2.793 GnM = 1.91
2
Sometimes
G E = F1 ⌧ F 2
written using: GM = F 1 + F2
e
e'
γ*
N
N'
Form Factor Moments
Z
e
i~
k·~
r
⇢(~r)d r /
GE,M (Q ) = 1
2
3
Z
r ⇢(r)j0 (kr)dr
2
3d Fourier Transform
for isotropic density
1⌦ 2 ↵ 2
1 ⌦ 4 ↵ 4
rE,M Q +
rE,M Q
6
120
1 ⌦ 6 ↵ 6
rE,M Q + · · ·
5040
Non-relativistic assumption (only) = k=Q; G is F.T. of
density
dGE,M
6
dQ2
Q2 =0
⌦
↵
2
2
= rE,M
⌘ rE,M
Slope of GE,M at Q2=0 defines the radii. This is what FF
experiments quote.
Notes
•
In NRQM, the FF is the 3d Fourier transform (FT) of the Breit frame
spatial distribution, but the Breit frame is not the rest frame, and
doing this confuses people who do not know better. The low Q2
expansion remains.
•
Boost effects in relativistic theories destroy our ability to determine
3D rest frame spatial distributions. The FF is the 2d FT of the
transverse spatial distribution.
•
The slope of the FF at Q2 = 0 continues to be called the radius for
reasons of history / simplicity / NRQM, but it is not the radius.
•
Nucleon magnetic FFs crudely follow the dipole formula, GD =
(1+Q2/0.71 GeV2)-2, which a) has the expected high Q2 pQCD behavior,
and b) is amusingly the 3d FT of an exponential, but c) has no
theoretical significance
Measurement Techniques
Rosenbluth Separation
h
i
2
d Str
d M
⌧ 2
Q
2
2
2
=
⇥ GE (Q ) + GM (Q ) ; ⌧ ⌘
d⌦
d⌦
"
4M 2
R
= (d /d )/(d /d )Mott =
2
⇥ GM
•
Measure the reduced cross section at
several values of ε (angle/beam energy
combination) while keeping Q2 fixed.
•
Linear fit to get intercept and slope.
+
2
⇤GE
1950s
hrE i = 0.74(24) f m
Fit to RMS Radius
Stanford 1956
R.W. McAllister and R. Hofstadter, Phys. Rev. 102, 851 (1956)
Low
2
Q
in 1974
hrE i = 0.810(40) f m
Q = 0.0389 GeV
2
Fit to GE(Q2) = a0+a1Q2+a2Q4
Saskatoon 1974
J. J. Murphy, Y. M. Shin, D. M. Skopik, Phys. Rev. C9, 2125 (1974)
2
Low
2
Q
in the 80s
hrE i = 0.862(12) f m
GD
= 1 + Q /0.71GeV
From the dipole form get
rE~0.81 fm
2
G. G. Simon, Ch. Smith, F. Borkowski, V. H. Walther, NPA333, 381 (1980)
2
2
2
2
= 1 + Q /18.23f m
2
mea
f
orm
s
rre
u
d po ring t
Pt 
he
lari
rat
zat
2
i
i
o
nP o
 (1

t
)
E
G
 e 
EG
E
M ta
e
e'
n
M

(
⇥
2
1
e
P

 It (P

= 2 ⇤)G(12 + ⇤ )GE GM tan
0 Eet 
Pl
M ta 2
E
2

n
e
2M e ' )
2
n ee
Ee +taE
2
2 ⇥e
esI:0 Pl =
⇤ (1 + ⇤ )GM tan
2
Pl .
m ea
nsf
e
M
Measurement Techniques
sur
eme
P
=
0
(1
)
nt i
n
s ne
r pr
ede
ecis
d fo
ion
rem
G
r E
tha
ent
n a⇥ µp
.
R
=
xch
c
r
oss G
ang
M
e ef
fec
t sm
all.
•
•
2
Pt E e + E e
e
µp
tan
Pl 2M
2
A single measurement gives ratio of form factors.
Interference of “small” and “large” terms allow
2
measurement at practically all values of Q .
Measurement Techniques
Polarized Cross Section: σ=Σ+hΔ∆
A=
+
+
+
AT
ALT
⌅⇤ ⇥
⌅⇤
⇥
2
a cos GM + b sin cos⇥ GE GM
A = f Pb Pt
cG2M + dG2E
Measure asymmetry at two different target settings, say θ*=0, 90.
Ratio of asymmetries gives ratio of form factors.
Functionally identical to recoil polarimetry measurements.
A multitude of fits
Better measurements, to higher
Q2 lead to a cornucopia of fits
J. J. Kelly, Phys. Rev. C70, 068202 (2004)
A multitude of Radii
2
GE,M
(Q
)
dipole
=
✓
2
Q
1 + E,M
a
2
GE,M
(Q
)
double dipole
=
◆
aE,M
0
2
GE,M
(Q
)=1+
polynomial, n
2
1+
n
X
2
Q
aE,M
1
2i
aE,M
Q
i
i=1
2
2
GE,M
(Q
)
=
G
(Q
)+
D
poly+dipole
2
2
GE,M
(Q
)
=
G
(Q
)⇥
D
poly x dipole
2
GE,M
(Q
)
inv. poly.
G(Q ) =
2
=
1+
1
Q2 b1
Pn
1
n
X
i=1
n
X
!
2
aE,M
0
}
2i
aE,M
Q
i
i=1
⇣
+ 1
2i
aE,M
Q
i
E,M 2i
a
Q
i=1 i
1 + Q2 b 2
1+ 1+···
Pn
k
a
⌧
k
k=0
G(Q2 ) /
P
n+2
1 + k=1 bk ⌧ k
2
6G0E (0) = rE
⌘
1+
2
Q
aE,M
2
!
2
rE = 0.883 fm
rM = 0.775 fm
Bernauer et al., PRL105, 242001 (2010)
rE = 0.901, rM = 0.868 fm Arrington&Sick, PRC76, 035201 (2007)
rE = 0.875, rM = 0.867 fm Zhan et al., PLB705, 59 (2011)
rE = 0.863, rM = 0.848 fm
Kelly PRC70, 068202 (2004)
A multitude of Radii
2
GE,M
(Q
)
dipole
=
✓
2
Q
1 + E,M
a
2
GE,M
(Q
)
double dipole
=
◆
aE,M
0
2
GE,M
(Q
)=1+
polynomial, n
2
1+
n
X
2
Q
aE,M
1
2i
aE,M
Q
i
i=1
2
2
GE,M
(Q
)
=
G
(Q
)+
D
poly+dipole
2
2
GE,M
(Q
)
=
G
(Q
)⇥
D
poly x dipole
2
GE,M
(Q
)
inv. poly.
G(Q ) =
2
=
1+
1
Q2 b1
Pn
1
n
X
i=1
n
X
!
2
aE,M
0
}
2i
aE,M
Q
i
i=1
⇣
+ 1
2i
aE,M
Q
i
E,M 2i
a
Q
i=1 i
1 + Q2 b 2
1+ 1+···
Pn
k
a
⌧
k
k=0
G(Q2 ) /
P
n+2
1 + k=1 bk ⌧ k
2
6G0E (0) = rE
⌘
1+
2
Q
aE,M
2
!
2
rE = 0.883 fm
rM = 0.775 fm
Bernauer et al., PRL105, 242001 (2010)
rE = 0.901, rM = 0.868 fm Arrington&Sick, PRC76, 035201 (2007)
rE = 0.875, rM = 0.867 fm Zhan et al., PLB705, 59 (2011)
rE = 0.863, rM = 0.848 fm
Kelly PRC70, 068202 (2004)
A flavor of the data
GR et al., PRC84, 055204(2011)
Bernauer et al, PRL105, 242001 (2010)
A flavor of the data
GR et al., PRC84, 055204(2011)
Bernauer et al, PRL105, 242001 (2010)
rCh @fmD
Time evolution of the Radius
from eP data
0.95
0.90
0.85
CODATA
Zhan et al. (JLab)
Bernauer et al. (Mainz)
Older eP Data
0.80
1960
1970
1980
1990
Year
2000
2010
Spectroscopic Measurements
Components of a calculation
Hydrogen Energy Levels
n=3
n=2
2P3/2
2S1/2, 2P1/2
-43.5 GHz
0.15MHz
2S1/2
F=1
2P1/2
F=0
8.2 Ghz
1.4 GHz
F=1
1.2 MHz
F=0
HFS
Proton
Size
n=1
1S1/2
Bohr
Dirac
QED
Darwin Term
Spin-Orbit
Relativity
QED
Components of a calculation
Hydrogen Energy Levels
n=3
n=2
2P3/2
2S1/2, 2P1/2
-43.5 GHz
0.15MHz
2S1/2
F=1
2P1/2
F=0
8.2 Ghz
1.4 GHz
F=1
1.2 MHz
F=0
HFS
Proton
Size
n=1
1S1/2
Bohr
Dirac
QED
Darwin Term
Spin-Orbit
Relativity
QED
Components of a calculation
Hydrogen Energy Levels
n=3
n=2
2P3/2
2S1/2, 2P1/2
-43.5 GHz
0.15MHz
2S1/2
F=1
2P1/2
F=0
8.2 Ghz
1.4 GHz
F=1
1.2 MHz
F=0
HFS
Proton
Size
n=1
1S1/2
Bohr
Dirac
Lamb
Darwin Term
Spin-Orbit
Relativity
QED
Components of a calculation
Hydrogen Energy Levels
n=3
n=2
2P3/2
2S1/2, 2P1/2
-43.5 GHz
0.15MHz
2S1/2
F=1
2P1/2
F=0
8.2 Ghz
1.4 GHz
F=1
1.2 MHz
F=0
HFS
Proton
Size
n=1
1S1/2
Bohr
Dirac
Lamb
Darwin Term
Spin-Orbit
Relativity
QED
Components of a calculation
Hydrogen Energy Levels
n=3
n=2
2P3/2
2S1/2, 2P1/2
-43.5 GHz
0.15MHz
2S1/2
F=1
2P1/2
F=0
8.2 Ghz
1.4 GHz
F=1
1.2 MHz
F=0
HFS
Proton
Size
n=1
1S1/2
Bohr
Dirac
Lamb
Darwin Term
Spin-Orbit
Relativity
QED
Components of a calculation
Hydrogen Energy Levels
n=3
n=2
2P3/2
2S1/2
2S1/2, 2P1/2
-43.5 GHz
0.014%
0.15MHz
F=1of the Lamb
Shift!
2P1/2
F=0
8.2 Ghz
1.4 GHz
F=1
1.2 MHz
F=0
HFS
Proton
Size
n=1
1S1/2
Bohr
Dirac
Lamb
Darwin Term
Spin-Orbit
Relativity
QED
The Nobel Prize in Physics 2005
Roy J. Glauber, John L. Hall, Theodor W. Hänsch
“Since Galileo
Galilei and Christiaan
Huygens invented the pendulum
clock, time and frequency have been
the quantities that we can measure
with
the highest precision.”
"for their contributions to the development of laser-based precision
spectroscopy, including the optical frequency comb technique".
H-Like Lamb Shift Calculations
Deviation from unperturbed energy level:
E
(0)
(nlj) = mR [f (nj)
1]
0
B
B
f (nj) = B1 + ✓
@
m2R
[f (nj)
2(M + m)
(Z↵)
q
+
j+
2
n
j
1
2
1 2
2
(Z↵)2
2
1]
C
C
◆2 C
A
Lamb shift is mostly QED with nuclear size corrections:
E=
EQED +
EN ucl
1
1/2
E=h
|
0i
=
V =
0|
X|
n
↵

Z
V|
0i
+
ni h n|
E0
X0 h
0|
V | ni h n V |
E0 E n
n
V|
En
d r1 ⇢E (r1 )
3
3 1/2
mr↵
(r) =
n3 ⇡
e
Non Relativistically
0i
✓
0i
1
|~r
mr ↵r
~r1 |
1
~r
◆
' (0) [1
mr ↵r + · · · ]
To Lowest order
Z
E1 = ↵ (0)
d r1 ⇢E (r1 )
Z
2
2 3
Rp ⌘ r d r⇢E (r)
2
)
3
2⇡↵
2 2
E1 =
(0) Rp
3
Z
3
d r⇥(r
r1 )
✓
1
r1
1
r
◆
H-Like Lamb Shift Nuclear Dependence
✓
2 (Z↵)4
1
2
2
EN ucl (nl) =
(mR
)
1
+
(Z↵)
ln
N
l0
3 n3
Z↵mRN
1
2
6
EN ucl (2p1/2 ) (Z↵) m (mRN )
16
EN ucl (2p3/2 ) = 0
Hyd
L1S (rp )
◆
⌦ 2↵
= 8171.636(4) + 1.5645 rp MHz
!ELamb(1S) = 8172.582(40) MHz
!ENucl(1S) = 1.269 MHz for rp = 0.9 fm
!ENucl(1S) = 1.003 MHz for rp = 0.8 fm
!ENucl(2S) = 0.1586 MHz for rp = 0.9 fm
!ELamb(2S) = 1057.8450(29) MHz
!ENucl(2S) = 0.1254 MHz for rp = 0.8 fm
(some of) The Lamb Shift Diagrams
rCh @fmD
Time evolution of the Radius
from H Lamb Shift
0.95
0.90
0.85
0.80
CODATA
H-Lamb Data
1960
1970
1980
1990
Year
2000
2010
rCh @fmD
Time evolution of the Radius
from H Lamb Shift + eP
0.95
0.90
0.85
CODATA
Zhan et al. (JLab)
Bernauer et al. (Mainz)
Older eP Data
H-Lamb Data
0.80
1960
1970
1980
1990
Year
2000
2010
Why atomic physics to learn proton radius?
Why μH?
Probability for lepton to be inside the proton:
✓ ◆3
proton to atom volume ratio
⇠
rp
aB
= (rp ↵) m
3
3
Lepton mass to the third power!
0.01
muon
f2 S @abuD
10-7
10-12
10-17
electron
10-22
10-27
0.001
0.1
10
r @fmD
1000
105
Why atomic physics to learn proton radius?
Why μH?
Probability for lepton to be inside the proton:
✓ ◆3
proton to atom volume ratio
⇠
rp
aB
= (rp ↵) m
3
3
Lepton mass to the third power!
Muon to electron mass ratio ~205 ➙ factor of about 8 million!
0.01
muon
f2 S @abuD
10-7
10-12
10-17
electron
10-22
10-27
0.001
0.1
10
r @fmD
1000
105
Lamb shift in eP and μP
T. Nebel, PhD Thesis
Lamb shift in eP and μP
T. Nebel, PhD Thesis
Courtesy of R. Pohl
μP Lamb Shift Measurement
μP Lamb Shift Measurement
•
μ from πE5 beamline at PSI (20 keV)
μP Lamb Shift Measurement
•
μ from πE5 beamline at PSI (20 keV)
μP Lamb Shift Measurement
•
μ from πE5 beamline at PSI (20 keV)
μP Lamb Shift Measurement
•
•
•
μ from πE5 beamline at PSI (20 keV)
μ’s with 5 keV kinetic energy after carbon foils S1-2
Arrival of the pulsed beam is timed by secondary electrons in PM1-3
μP Lamb Shift Measurement
•
•
•
•
μ from πE5 beamline at PSI (20 keV)
μ’s with 5 keV kinetic energy after carbon foils S1-2
Arrival of the pulsed beam is timed by secondary electrons in PM1-3
μ’s are absorbed in the H2 target at high excitation followed by decay to the 2S
metastable level (which has a 1 μs lifetime)
μP Lamb Shift Measurement
•
•
•
•
•
•
μ from πE5 beamline at PSI (20 keV)
μ’s with 5 keV kinetic energy after carbon foils S1-2
Arrival of the pulsed beam is timed by secondary electrons in PM1-3
μ’s are absorbed in the H2 target at high excitation followed by decay to the 2S
metastable level (which has a 1 μs lifetime)
A laser pulse timed by the PMs excites the 2S1/2F=1 to 2P3/2F=2 transition
The 2 keV X-rays from 2P to 1S are detected.
F =2
E(2P3/2
F =1
2S1/2
) = 209.9779(49)
5.2262rp2 + 0.0347rp3 [meV]
rCh @fmD
Time evolution of the Radius
from H Lamb Shift + eP
0.95
0.90
0.85
CODATA
Zhan et al. (JLab)
Bernauer et al. (Mainz)
Older eP Data
H-Lamb Data
0.80
1960
1970
1980
1990
Year
2000
2010
rCh @fmD
Time evolution of the Radius
from H Lamb Shift + eP
0.95
0.90
0.85
CODATA
Zhan et al. (JLab)
Bernauer et al. (Mainz)
Older eP Data
H-Lamb Data
Pohl et al.
0.80
1960
1970
1980
1990
Year
2000
2010
rCh @fmD
Time evolution of the Radius
from H Lamb Shift + eP
0.95
0.90
0.85
CODATA
Zhan et al. (JLab)
Bernauer et al. (Mainz)
Older eP Data
H-Lamb Data
Pohl et al.
0.80
1960
1970
1980
1990
Year
2000
2010
Proton Radius Puzzle
Muonic hydrogen disagrees with atomic physics and electron
scattering determinations of slope of FF at Q2 = 0
#
Extraction
<rE>2 [fm]
1
Sick
0.895±0.018
2
CODATA 0.8768±0.0069
3
Mainz
0.879±0.008
4
This
Work
0.875±0.010
5
Combined 0.8764±0.004
2-4
7
6
Muonic
Hydrogen
0.842±0.001
X. Zhan et al., PLB705, 59 (2011)
GR et al., PRC84, 055204(2011)
Proton Radius Puzzle
Muonic hydrogen disagrees with atomic physics and electron
scattering determinations of slope of FF at Q2 = 0
#
Extraction
<rE>2 [fm]
1
Sick
0.895±0.018
2
CODATA 0.8768±0.0069
3
Mainz
0.879±0.008
4
This
Work
0.875±0.010
5
Combined 0.8764±0.004
2-4
7
6
Muonic
Hydrogen
0.842±0.001
X. Zhan et al., PLB705, 59 (2011)
GR et al., PRC84, 055204(2011)
Huh?
Muonic Hydrogen: Radius 4% below previous best value
Proton 11-12% smaller (volume), 11-12% denser than
previously believed
Particle Data Group:
“Most measurements of the radius of the proton involve electronproton interactions, and most of the more recent values agree with
one another... However, a measurement using muonic hydrogen finds
rp = 0.84184(67) fm, which is eight times more precise and seven
standard deviations (using the CODATA 10 error) from the
electronic results... Until the difference between the ep and μp
values is understood, it does not make much sense to average all
the values together. For the present, we stick with the less precise
(and provisionally suspect) CODATA 2010 value. It is up to workers
in this field to solve this puzzle.”
Huh?
Muonic Hydrogen: Radius 4% below previous best value
Proton 11-12% smaller (volume), 11-12% denser than
previously believed
Particle Data Group:
“Most measurements of the radius of the proton involve electronproton interactions, and most of the more recent values agree with
one another... However, a measurement using muonic hydrogen finds
rp = 0.84184(67) fm, which is eight times more precise and seven
standard deviations (using the CODATA 10 error) from the
electronic results... Until the difference between the ep and μp
values is understood, it does not make much sense to average all
the values together. For the present, we stick with the less precise
(and provisionally suspect) CODATA 2010 value. It is up to workers
in this field to solve this puzzle.”
Directly related to the strength of QCD in the non perturbative
region.
Huh?
Muonic Hydrogen: Radius 4% below previous best value
Proton 11-12% smaller (volume), 11-12% denser than
previously believed
Particle Data Group:
“Most measurements of the radius of the proton involve electronproton interactions, and most of the more recent values agree with
one another... However, a measurement using muonic hydrogen finds
rp = 0.84184(67) fm, which is eight times more precise and seven
standard deviations (using the CODATA 10 error) from the
electronic results... Until the difference between the ep and μp
values is understood, it does not make much sense to average all
the values together. For the present, we stick with the less precise
(and provisionally suspect) CODATA 2010 value. It is up to workers
in this field to solve this puzzle.”
Directly related to the strength of QCD in the non perturbative
region.
Which would be really important if we actually knew how to
extract “strength of QCD” in the non perturbative region.
?
?
Experimental Error?
R. Pohl et al., Nature 466, 213 (2010).
Experimental Error?
Water-line/laser wavelength:
300 MHz uncertainty
water-line to resonance:
200 kHz uncertainty
Systematics: 300 MHz
Statistics: 700 MHz
Discrepancy:
5.0σ = 75GHz → Δν/ν=1.5x10-3
R. Pohl et al., Nature 466, 213 (2010).
Experimental Error in the electron
(Lamb shift) measurements?
“The 1S-2S transition in H has been measured to
34 Hz, that is, 1.4 × 10−14 relative accuracy. Only
an error of about 1,700 times the quoted
experimental uncertainty could account for our
observed discrepancy.” - R. Pohl
Experimental Error in the electron
scattering measurements?
GE P
Essentially all (newer) electron scattering results
are consistent within errors, hard to see how one
could conspire to change the charge radius without
doing something very strange to the FFs.
1.000
0.998
0.996
0.994
0.992
0.990
0.988
0.986
0.00
0.01
0.02
0.03
Q2 @GeV2 D
0.04
0.05
Theory Error?
Theory Error?
Theory Error?
Theory Error?
Checked,
Rechecked,
and Checked again
No Error Found
Theory Error?
Checked,
Rechecked,
and Checked again
No Error Found
Third Zemach Moment
F =2
E(2P3/2
F =1
2S1/2
) = 209.9779(49)
5.2262rp2 + 0.0347rp3 [meV]
Third Zemach Moment
F =2
E(2P3/2
F =1
2S1/2
) = 209.9779(49)
5.2262rp2 + 0.0347rp3 [meV]
Third Zemach Moment
F =2
E(2P3/2
F =1
2S1/2
) = 209.9779(49)
5.2262rp2 + 0.0347rp3 [meV]
Prefactor determined using functional form of the FF.
Perhaps it’s wrong? (A. De Rújula, Phys. Lett. B 693, 555 (2010))
But the change suggested by de Rujula is very much in contrast to
experimental data. (I. Cloet & G. A. Miller, Phys. Rev. C83 12201 (2011)).
Third Zemach Moment
F =2
E(2P3/2
F =1
2S1/2
) = 209.9779(49)
5.2262rp2 + 0.0347rp3 [meV]
Prefactor determined using functional form of the FF.
Perhaps it’s wrong? (A. De Rújula, Phys. Lett. B 693, 555 (2010))
But the change suggested by de Rujula is very much in contrast to
experimental data. (I. Cloet & G. A. Miller, Phys. Rev. C83 12201 (2011)).
Off Shell Protons (2-photon)
Miller et al., Phys. Rev. A84, 020101 (2011)
Paz & Hill, Phys. Rev. Lett. 107, 160402 (2011)
Bound proton is off mass shell p2 ≠ mp2 - But usually this is not taken into
account (SIFF - Sticking In Form Factors).
Cannot use Dirac equation for proton propagator, need to include multiphoton terms.
Essentially proton polarizability
terms.
This is in an interesting idea,
but almost certainly wrong
since these terms are
constrained from accurate
measurements of, for example,
inclusive electron scattering.
m4 term,
negligible for electrons
μ≠e
(essentially beyond SM physics)
Beyond standard model physics or QED incorrect.
The 5 (now 7) σ difference is much greater than any other difference discussed
as evidence for physics beyond the standard model, such as the NuTeV result for
sin2θW or g-2 for the μ.
μ≠e
(essentially beyond SM physics)
μ≠e
(essentially beyond SM physics)
•
B. Marciano: massive photon (also solves muon g-2), violate mu-e universality, matter effects
in neutrino oscillations too big by 10000
•
Barger et al “We consider exotic particles that among leptons, couple preferentially to muons,
and mediate an attractive nucleon-muon interaction. We find that the many constraints from
low energy data disfavor new spin-0, spin-1 and spin-2 particles as an explanation.” Phys.
Rev. Lett. 106, 153001 (2011).
•
Brax, Burrage “Combining these constraints with current particle physics bounds we find
that the contribution of a scalar field to the recently claimed discrepancy in the proton radius
measured using electronic and muonic atoms is negligible.” Phys. Rev. D83, 035020(2011).
•
Brian Batell, David McKeen, Maxim Pospelov “The recent discrepancy between proton
charge radius measurements extracted from electron-proton versus muon-proton systems is
suggestive of a new force that differentiates between lepton species. We identify a class of
models with gauged right-handed muon number, which contains new vector and scalar
force carriers at the 100 MeV scale or lighter, that is consistent with observations. Such forces
would lead to an enhancement by several orders-of-magnitude of the parity-violating
asymmetries in the scattering of low-energy muons on nuclei.” Phys. Rev. Lett. 107,
011803(2011).
Example - Leptoquarks
Spin-0 or Spin-1 particles that couple to quarks and gluons.
Can contribute to H-atom via
Lepto
ELamb
=|
2
2 Lµd
nS (0)|
m2L
=
m3r ↵3
⇡n3
2
Lµd
m2L
Can use aμ=(g-2)μ/2 with the well known discrepancy to constrain.
Possible contribution from -
Example - Leptoquarks
So aμ=(g-2)μ/2 limits to leptoquark coupling to mass ratio, giving us
Lepto
ELamb  0.0044
2
2
ln(mL /md ) ⇠ 10
meV
Measurement deviation is about 300 μeV with an error about 4 μeV!
Possible Leptoquark effect 4.4 μeV.
Clearly leptoquarks are out!
μ≠e
(essentially beyond SM physics)
•
B. Marciano: massive photon (also solves muon g-2), violate mu-e universality, matter effects
in neutrino oscillations too big by 10000
•
Barger et al “We consider exotic particles that among leptons, couple preferentially to muons,
and mediate an attractive nucleon-muon interaction. We find that the many constraints from
low energy data disfavor new spin-0, spin-1 and spin-2 particles as an explanation.” Phys.
Rev. Lett. 106, 153001 (2011).
•
Brax, Burrage “Combining these constraints with current particle physics bounds we find
that the contribution of a scalar field to the recently claimed discrepancy in the proton radius
measured using electronic and muonic atoms is negligible.” Phys. Rev. D83, 035020(2011).
•
Brian Batell, David McKeen, Maxim Pospelov “The recent discrepancy between proton
charge radius measurements extracted from electron-proton versus muon-proton systems is
suggestive of a new force that differentiates between lepton species. We identify a class of
models with gauged right-handed muon number, which contains new vector and scalar
force carriers at the 100 MeV scale or lighter, that is consistent with observations. Such forces
would lead to an enhancement by several orders-of-magnitude of the parity-violating
asymmetries in the scattering of low-energy muons on nuclei.” Phys. Rev. Lett. 107,
011803(2011).
No beyond SM effect seems to reliably
explain the discrepancy and remain
consistent with other results.
Where to now?
Zemach radius and Hyperfine splitting.
Actually properly called “Proton Structure Corrections of Order
"5” (Martynenko, Phys. Rev. A71, 022506 (2005))
EHF S = (1 +
S
=
Z
=
rZ =
Z
+
QED +
p
R
+
p
h⌫p
+
p
µ⌫p
+
p
W eak
+
p
)E
S
F
P ol
2↵mR rZ

Z
4
dQ GE (Q2 )GM (Q2 )
⇡
Q2
µp
1
2S,eP
EHF S
2S,µP
EHF
S
⇠ 177.555 MHz = 0.734 µeV
⇠ 5.5 THz = 22meV
Data for muonic hydrogen exists from combinations of measured
transitions but not released yet.
Can test consistency using both electric and magnetic proton FFs
(remember the discrepancy with the magnetic radius?).
Actually much more complicated when done relativistically
but still contains F1 and F2
Where to now?
Where to now?
What did they use
for GM? Unclear yet.
Where to now?
More and better theory calculations.
But it seems like we’ve reached a dead end - nothing obvious has been
discovered so far.
Another look at experimental systematics.
Done over and over - again, nothing obvious so far and it’s hard to think
of something that would cause this.
Where to now?
Lamb shift measurements on #3He+, #4He+ - New
experiment planned for PSI (already funded).
•
Helium radius known from electron scattering to better precision than
proton radius.
•
If effect comes from muonic sector it should scale with Z.
•
No hyperfine corrections needed in #4He+
E(2P1/2
µ4 He+
2S1/2 )
= 1670.370(600)
= 403.893(145)
2
3
105.322rHe
+ 1.529rHe
meV
2
3
25466rHe
+ 370rHe
GHz
A. Antognini et al, Can. J. Phys. 89, 47 (2011)
Where to now?
Where to now?
E08007 - Part II
•
High precision (< 1%) survey of the
FF ratio at Q2=0.01 - 0.16 GeV2.
•
Beam-target asymmetry
measurement by electron scattering
from polarized NH3 target.
•
Electrons detected in two matched
spectrometers.
•
Ratio of asymmetries cancels
systematic errors → only one
target setting to get FF ratio.
•
Ran Feb-May 2012 - Moshe
Friedman (HUJI) Thesis project.
elastic scattering
from heavy elements
pay attention to
the fine splitting
between different elements
elastic scattering
from hydrogen
● left arm
● right arm
Pr
el
im
in
ar
y
E08007 - Part II
Projected uncertainties
1.10
1.05
ÊÊÊÊ Ê
X
Ï
Ï
mP GE êGM
1.00
Ï
Ï
Ï
Ï
Ï
X
X
0.95
Û
ÊÛ X
Ê
Û
X
0.90
X
X
X
Ê
Û
Ê
Û
Ê
Ï
Ê
Ê
Ê
0.85
Mp2 4Mp2
0.80
0.0
0.1
0.2
0.3
0.4
Q2 @GeV2 D
0.5
0.6
0.7
Unfortunately
Low
2
Q
Measurements in eP scattering have been
pushed about as far as they can go
1-GE P @%D
1.5
1.0
0.5
0.0
0.000
0.001
0.002
0.003
Q2 @GeV2 D
0.004
0.005
Where to now?
Newest Idea
μP Scattering
•
Why μp scattering?
•
It should be relatively easy to determine if the
μp and ep scattering are consistent or different,
and, if different, if the difference is from novel
physics or 2γ mechanisms:
•
If the μp and ep radii really differ by 4%,
then the form factor slopes differ by 8%
and cross section slopes differ by 16% - this
should be relatively easy to measure.
•
2γ affects e+ and e-, or μ+ and μ-, with
opposite sign - the cross section difference is
twice the 2γ correction, the average is the
cross section without a 2γ effect. It is hard
to get e+ at electron machines, but relatively
easy to get μ+ and μ- at PSI.
μP Collaboration
J Arrington
Argonne National Lab
F Benmokhtar, E Brash
Christopher Newport University
A Richter
Technical University of Darmstadt
M Meziane
Duke University
A Afanasev, W. Briscoe, E. J. Downie
George Washington University
M Kohl
Hampton University
G Ron
Hebrew University of Jerusalem
D Higinbotham
Jefferson Lab
S Gilad, V Sulkosky
MIT
V Punjabi
Norfolk State University
L Weinstein
Old Dominion University
K Deiters, D Reggiani
Paul Scherrer Institute
L El Fassi, R Gilman, G Kumbartzki,
K Myers, R Ransome, AS Tadepalli
Rutgers University
C Djalali, R Gothe, Y Ilieva, S Strauch
University of South Carolina
S Choi
Seoul National Univeristy
A Sarty
St. Mary’s University
J Lichtenstadt, E Piasetzky
Tel Aviv University
E Fuchey, Z-E Meziani, E Schulte
Temple University
N Liyanage
University of Virginia
C Perdrisat
College of William & Mary
e-µ Universality
In the 1970s / 1980s, there were several experiments that tested
whether the ep and µp interactions are equal. They found no
convincing differences, once the µp data are renormalized up about
10%. In light of the proton ``radius’’ puzzle, the experiments are
not as good as one would like.
e-µ Universality
The 12C radius was determined with ep scattering and μC atoms.
The results agree:
Cardman et al. eC: 2.472 ± 0.015 fm
Offermann et al. eC: 2.478 ± 0.009 fm
Schaller et al. μC X rays: 2.4715 ± 0.016 fm
Ruckstuhl et al. μC X rays: 2.483 ± 0.002 fm
Sanford et al. μC elastic: 2.32 ± 0.13 fm
Perhaps carbon is right, e’s and μ’s are the same.
Perhaps hydrogen is right, e’s and μ’s are different.
Perhaps both are right - opposite effects for proton and neutron
cancel with carbon.
But perhaps the carbon radius is insensitive to the nucleon radius,
and μd or μHe would be a better choice.
μP Scattering
How well can we do?
Technical review - Test Beam awarded.
Beam test scheduled for Oct 2012.
Examining funding options.
σ0.84/σ0.88 vs. Q2
WCs +
Scintillators
160 MeV/c μ’s incident on protons
cross section uncertainties for
2.6x1011 μ on 4 cm LH2 (30 days)
SciFi
+ GEMs
SciFi
The Real Bottom Line
Charge radius extraction
limited by systematics, fit
uncertainties
Comparable to existing e-p
extractions, but not better
Many uncertainties are common to all
extractions in the experiments:
Cancel in e+/e-, m+/m-, and m/e
comparisons
Precise tests of TPE in e-p and m-p
or other differences for electron,
muon scattering
Comparing e/mu gets rid of most of the
systematic uncertainties as well as the
truncation error.
Projected uncertainty on the difference
of radii measured with e/mu is 0.0045.
Test radii difference to the
level of 7.7σ (the same level as
the current discrepancy)!
Relative
Other Possible Ideas
(w/o Elaborating)
•
•
•
•
•
High energy proton beam (FNAL? J-PARC?) on
atomic electrons, akin to low Q2 pion form
factor measurements - difficult - only goes
to 0.01 GeV2.
Very low Q2 eP scattering on collider (with
very forward angle detection) - MEIC/EIC.
Very low Q2 JLab experiment, near 00 using
``PRIMEX’’ setup: A. Gasparian, D. Dutta, H.
Gao et al.
Accurate Lamb shift measurement on
metastable C5+.
μ scattering on light nuclei (proposal being
written - GR).
Final words
The Rydberg Constant
The Rydberg constant represents the limiting value of the highest wavenumber (the inverse
wavelength) of any photon that can be emitted from the hydrogen atom, or, alternatively, the
wavenumber of the lowest-energy photon capable of ionizing the hydrogen atom from its ground
state. The spectrum of hydrogen can be expressed simply in terms of the Rydberg constant, using
the Rydberg formula.
1
V ac
= R1
✓
1
2
n1
1
2
n2
◆
This is the best determined physical constant!
Final words
The Rydberg Constant
Final words
The Rydberg Constant
It is possible (thought perhaps not correct yet?) to assume that the
muonic hydrogen result for the proton radius is correct and also assume
that the best measured Lamb shift (1S-2S in electronic hydrogen) is also
correct and use this to extract a new value of the Rydberg constant.
Final words
The Rydberg Constant - another surprise
New value of the Rydberg constant,
R=10,973,731.568160(16) m-1 (1.5 parts in 10-12). This is
-110 kHz/c or 4.9sigma away from the CODATA value, but 4.6
times more precise.
What does this mean
?????
Conclusions
Conclusions
Summary
Conclusions
Summary
•
Proton radii have been measured very accurately over the last 50
years.
Conclusions
Summary
•
•
Proton radii have been measured very accurately over the last 50
years.
Major discrepancy has now arisen (between electron and muon
results).
•
Ideas abound on how too fix this, either the muonic side, the
electronic side, or by inventing fancy new physics.
•
But none currently seem to solve the puzzle completely.
•
But remember that we also have another puzzle with the muon
in pure QED.
Conclusions
Summary
•
•
•
Proton radii have been measured very accurately over the last 50
years.
Major discrepancy has now arisen (between electron and muon
results).
•
Ideas abound on how too fix this, either the muonic side, the
electronic side, or by inventing fancy new physics.
•
But none currently seem to solve the puzzle completely.
•
But remember that we also have another puzzle with the muon
in pure QED.
Common thinking seems to be:
•
Theorists - “it’s an experimental problem, some systematic issue”
•
Experimentalists I - “Theorists have forgotten some obscure
correction”
•
Experimentalists from PSI/CREMA - “Problem with electron
results”
•
Fringe - “Exciting new physics”
Conclusions
Summary
•
•
•
•
Proton radii have been measured very accurately over the last 50
years.
Major discrepancy has now arisen (between electron and muon
results).
•
Ideas abound on how too fix this, either the muonic side, the
electronic side, or by inventing fancy new physics.
•
But none currently seem to solve the puzzle completely.
•
But remember that we also have another puzzle with the muon
in pure QED.
Common thinking seems to be:
•
Theorists - “it’s an experimental problem, some systematic issue”
•
Experimentalists I - “Theorists have forgotten some obscure
correction”
•
Experimentalists from PSI/CREMA - “Problem with electron
results”
•
Fringe - “Exciting new physics”
Several new experiments, both approved and planned, may help shed
(some) light on the issue.
The spectrum of hydrogen atom has proved to be the Rosetta
stone of modern physics.
T.W. Hänsch, A. L. Schalow, G.W. Series