The Proton Radius - weizmann.ac.il

The Proton RadiusNuclear Physics' Newest Puzzle

Guy RonHebrew University of Jerusalem

Joint Nuclear Physics Seminar, 22 Aug. 2012




Radii




RadiiCharge

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

Chambers and Hofstadter, Phys Rev 103, 14 (1956)

Hofstadter @ Stanford: 1950s - electron scattering

Hadronic physicists all over: 1960s-2010s - Form factors

Bernauer et al., PRL105, 242001 (2010)

Zhan et al., PLB705, 59 (2011)Ron et al., PRC84, 055204 (2011)

Atomic physicists - precise atomic transitions in hydrogen

Pohl et al., Nature 466, 213 (2010)

How to measure the proton size

Chambers and Hofstadter, Phys Rev 103, 14 (1956)

Hofstadter @ Stanford: 1950s - electron scattering

Hadronic physicists all over: 1960s-2010s - Form factors

Bernauer et al., PRL105, 242001 (2010)

Zhan et al., PLB705, 59 (2011)Ron et al., PRC84, 055204 (2011)

Atomic physicists - precise atomic transitions in hydrogen

Pohl et al., Nature 466, 213 (2010)

Question:Why should hadronic physicists care about what atomic physicists are measuring?

Answer:Because sometimes they can measure things in NP more precisely than we can!

Scattering Measurements

ELECTRON SCATTERING CROSS-SECTION (1-γ)d�R

d⌦

=

↵2

Q2

✓E0

E

◆2cot

2 ✓e2

1 + ⌧

⌧ =Q2

4M2, " =

1 + 2(1 + ⌧) tan2 ✓e

2

��1

Rutherford - Point-Like

N N'

e e'

γ*


d⌦

=

↵2

Q2

✓E0

E

◆2cot

2 ✓e2

1 + ⌧

⌧ =Q2

4M2, " =

1 + 2(1 + ⌧) tan2 ✓e

2

��1


d�M

d⌦=

d�R

d⌦⇥

1 + 2⌧ tan2 ✓

2

�Mott - Spin-1/2

N N'

e e'

γ*


d⌦

=

↵2

Q2

✓E0

E

◆2cot

2 ✓e2

1 + ⌧

⌧ =Q2

4M2, " =

1 + 2(1 + ⌧) tan2 ✓e

2

��1

Sometimes written using:

GE = F1 � ⌧F2

GM = F1 + F2

GpE(0) = 1 Gn

E(0) = 0Gp

M = 2.793 GnM = �1.91


d�M

d⌦=

d�R

d⌦⇥

1 + 2⌧ tan2 ✓

2

�Mott - Spin-1/2

d�Str

d⌦=

d�M

d⌦⇥

hG2

E(Q2) +⌧

"G2

M (Q2)i Rosenbluth - Spin-1/2 with

Structure

N N'

e e'

γ*


d⌦

=

↵2

Q2

✓E0

E

◆2cot

2 ✓e2

1 + ⌧

⌧ =Q2

4M2, " =

1 + 2(1 + ⌧) tan2 ✓e

2

��1

Sometimes written using:

GE = F1 � ⌧F2

GM = F1 + F2

GpE(0) = 1 Gn

E(0) = 0Gp

M = 2.793 GnM = �1.91


d�M

d⌦=

d�R

d⌦⇥

1 + 2⌧ tan2 ✓

2

�Mott - Spin-1/2

d�Str

d⌦=

d�M

d⌦⇥

hG2

E(Q2) +⌧

"G2

M (Q2)i Rosenbluth - Spin-1/2 with

Structure

N N'

e e'

γ*

Everything we don’t know goes here!

Form Factor MomentsZ

e�i~k·~r⇢(~r)d3r /Z

r2⇢(r)j0(kr)dr

GE,M (Q2) = 1� 16

⌦r2E,M

↵Q2 +

1120

⌦r4E,M

↵Q4 � 1

5040⌦r6E,M

↵Q6 + · · ·

�6dGE,M

dQ2

��Q2=0

=⌦r2E,M

↵⌘ r2

E,M

3d Fourier Transform for isotropic density

Non-relativistic assumption (only) = k=Q; G is F.T. of density

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

• 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.

�R = (d�/d�)/(d�/d�)Mott = ⇥G2M + ⇤G2

E

Measurement TechniquesRosenbluth Separation

d�Str

d⌦=

d�M

d⌦⇥

hG2

E(Q2) +⌧

"G2

M (Q2)i

; ⌧ ⌘ Q2

4M2

1950s

Fit to RMS Radius

R.W. McAllister and R. Hofstadter, Phys. Rev. 102, 851 (1956)

Stanford 1956

hrEi = 0.74(24) fm

Low Q2 in 1974

Fit to GE(Q2) = a0+a1Q2+a2Q4

J. J. Murphy, Y. M. Shin, D. M. Skopik, Phys. Rev. C9, 2125 (1974)

Saskatoon 1974

hrEi = 0.810(40) fm

Q2 = 0.0389 GeV 2

Low Q2 in the 80s

G. G. Simon, Ch. Smith, F. Borkowski, V. H. Walther, NPA333, 381 (1980)

hrEi = 0.862(12) fm

GD =�1 + Q2/18.23fm2

��2

=�1 + Q2/0.71GeV 2

��2

From the dipole form get rE~0.81 fm

Recoil Polarization

2

tan2 )

(

2

tan)

1( 2

tan

)1(

2

'2

2

'

0

0

e

e

e

l

tM

E

e

M

e

el

e

ME

t

M

EE

P

PG

G

G

ME

EPl

GG

Pl

• Direct measurement of form

factor ratios by measuring the ratio

of the transferred polarization Pt

and Pl .

Advantages: • only one measurement is needed for

each Q2.• much better precision than a cross

section measurement.

• two-photon exchange effect small.

4

GHP 04/30/2009

I0Pt = �2�

⇤(1 + ⇤)GEGM tan⇥e

2

I0Pl =Ee + Ee�

M

�⇤(1 + ⇤)G2

M tan2 ⇥e

2Pn = 0 (1�)

R ⇥ µpGE

GM= �µp

Pt

Pl

Ee + Ee�

2Mtan

�e

2

• A single measurement gives ratio of form factors.• Interference of “small” and “large” terms allow measurement at practically all values of Q2.

Measurement Techniques

Polarized Cross Section: σ=Σ+hΔ∆

A =�+ � ��+ + ��

A = fPbPt

AT� ⌅⇤ ⇥a cos��G2

M +

ALT� ⌅⇤ ⇥b sin�� cos⇥�GEGM

cG2M + dG2

E

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.

Measurement Techniques

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 �6G0E(0) = r2

E

GE,Mdipole

(Q2) =✓

1 +Q2

aE,M

◆�2

GE,Mdouble dipole

(Q2) = aE,M0

1 +

Q2

aE,M1

!�2

+⇣1� aE,M

0

⌘ 1 +

Q2

aE,M2

!�2

GE,Mpolynomial, n(Q2) = 1 +

nX

i=1

aE,Mi Q2i

GE,Mpoly+dipole

(Q2) = GD(Q2) +nX

i=1

aE,Mi Q2i

GE,Mpoly x dipole

(Q2) = GD(Q2)⇥nX

i=1

aE,Mi Q2i

GE,Minv. poly.(Q

2) =1

1 +Pn

i=1

aE,Mi Q2i

G(Q2) =1

1 + Q2b1

1+

Q2b21+···

G(Q2) /Pn

k=0

ak⌧k

1 +Pn+2

k=1

bk⌧k

rE = 0.883 fmrM = 0.775 fmBernauer et al., PRL105, 242001 (2010)

rE = 0.863, rM = 0.848 fmKelly PRC70, 068202 (2004)

}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)

A multitude of Radii �6G0E(0) = r2

E

GE,Mdipole

(Q2) =✓

1 +Q2

aE,M

◆�2

GE,Mdouble dipole

(Q2) = aE,M0

1 +

Q2

aE,M1

!�2

+⇣1� aE,M

0

⌘ 1 +

Q2

aE,M2

!�2

GE,Mpolynomial, n(Q2) = 1 +

nX

i=1

aE,Mi Q2i

GE,Mpoly+dipole

(Q2) = GD(Q2) +nX

i=1

aE,Mi Q2i

GE,Mpoly x dipole

(Q2) = GD(Q2)⇥nX

i=1

aE,Mi Q2i

GE,Minv. poly.(Q

2) =1

1 +Pn

i=1

aE,Mi Q2i

G(Q2) =1

1 + Q2b1

1+

Q2b21+···

G(Q2) /Pn

k=0

ak⌧k

1 +Pn+2

k=1

bk⌧k

rE = 0.883 fmrM = 0.775 fmBernauer et al., PRL105, 242001 (2010)

rE = 0.863, rM = 0.848 fmKelly PRC70, 068202 (2004)

}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)

rM = 0.775 fm

rM = 0.868 fmrM = 0.867 fm

rM = 0.848 fm

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)

Time evolution of the Radius from eP data

1960 1970 1980 1990 2000 2010

0.80

0.85

0.90

0.95

Year

r Ch@fmD

CODATAZhan et al. (JLab)Bernauer et al. (Mainz)Older eP Data

Spectroscopic Measurements

n=1

n=2n=3

1S1/2

2S1/2, 2P1/2

2P3/2

2S1/2

2P1/2

F=1

F=0

F=1

F=0

0.15MHz

1.2 MHz-43.5 GHz

Bohr Dirac QEDDarwin TermSpin-OrbitRelativity

QED HFSProtonSize

Components of a calculationHydrogen Energy Levels

1.4 GHz8.2 Ghz

n=1

n=2n=3

1S1/2

2S1/2, 2P1/2

2P3/2

2S1/2

2P1/2

F=1

F=0

F=1

F=0

0.15MHz

1.2 MHz-43.5 GHz

Bohr Dirac QEDDarwin TermSpin-OrbitRelativity

QED HFSProtonSize


1.4 GHz8.2 Ghz

n=1

n=2n=3

1S1/2

2S1/2, 2P1/2

2P3/2

2S1/2

2P1/2

F=1

F=0

F=1

F=0

0.15MHz

1.2 MHz-43.5 GHz

Bohr Dirac LambDarwin TermSpin-OrbitRelativity

QED HFSProtonSize


1.4 GHz8.2 Ghz

n=1

n=2n=3

1S1/2

2S1/2, 2P1/2

2P3/2

2S1/2

2P1/2

F=1

F=0

F=1

F=0

0.15MHz

1.2 MHz-43.5 GHz


QED HFSProtonSize


1.4 GHz8.2 Ghz

n=1

n=2n=3

1S1/2

2S1/2, 2P1/2

2P3/2

2S1/2

2P1/2

F=1

F=0

F=1

F=0

0.15MHz

1.2 MHz-43.5 GHz


QED HFSProtonSize


1.4 GHz8.2 Ghz

n=1

n=2n=3

1S1/2

2S1/2, 2P1/2

2P3/2

2S1/2

2P1/2

F=1

F=0

F=1

F=0

0.15MHz

1.2 MHz-43.5 GHz


QED HFSProtonSize


1.4 GHz8.2 Ghz

0.014% of the Lamb

Shift!

"for their contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique".

The Nobel Prize in Physics 2005Roy J. Glauber, John L. Hall, Theodor W. Hänsch

“Since Galileo Galilei and Christiaan

Huygens invented the pendulumclock, time and frequency have been the quantities that we can measure

withthe highest precision.”

H-Like Lamb Shift CalculationsDeviation from unperturbed energy level:

E(0)(nlj) = mR [f(nj)� 1]� m2R

2(M + m)[f(nj)� 1]2

f(nj) =

0

BBB@1 +

(Z↵)2✓

n� j � 12 +

q�j + 1

2

�2 � (Z↵)2◆2

1

CCCA

�1/2

Lamb shift is mostly QED with nuclear size corrections:

�E = �EQED + �ENucl

�E = h�0|�V |�0i +X

n

0 h�0|�V |�ni h�n�V |�0iE0 � En

|�0i =X

n

|�ni h�n|�V |�0iE0 � En

�V = �↵

Zd3r1⇢E(r1)

✓1

|~r � ~r1| �1~r

◆

� (r) =mr↵3

n3⇡

�1/2

e�mr↵r ' �(0) [1�mr↵r + · · · ]

�E1 = �↵�(0)2Z

d3r1⇢E(r1)Z

d3r⇥(r � r1)✓

1r1� 1

r

◆

R2p ⌘

Zr2d3r⇢E (r)

) �E1 =2⇡↵

3�(0)2R2

p

To Lowest order

Non Relativistically

H-Like Lamb Shift Nuclear Dependence

�ENucl(nl) =23

(Z↵)4

n3(mRN )2 �l0

✓1 + (Z↵)2 ln

1Z↵mRN

◆

�ENucl(2p1/2)116

(Z↵)6m (mRN )2

�ENucl(2p3/2) = 0

!ELamb(1S) = 8172.582(40) MHz

!ELamb(2S) = 1057.8450(29) 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!ENucl(2S) = 0.1254 MHz for rp = 0.8 fm

LHyd1S (rp) = 8171.636(4) + 1.5645

⌦r2p

↵MHz

(some of) The Lamb Shift Diagrams

Time evolution of the Radius from H Lamb Shift

CODATAH-Lamb Data

1960 1970 1980 1990 2000 2010

0.80

0.85

0.90

0.95

Year

r Ch@fmD

1960 1970 1980 1990 2000 2010

0.80

0.85

0.90

0.95

Year

r Ch@fmD

Time evolution of the Radius from H Lamb Shift + eP

CODATAZhan et al. (JLab)Bernauer et al. (Mainz)Older eP DataH-Lamb Data

Why atomic physics to learn proton radius?Why μH?

Probability for lepton to be inside the proton:proton to atom volume ratio

⇠✓

rp

aB

◆3

= (rp↵)3m3

Lepton mass to the third power!

0.001 0.1 10 1000 10510-27

10-22

10-17

10-12

10-7

0.01

r @fmD

f 2S@abu

D

electron

muon

Why atomic physics to learn proton radius?Why μH?

Probability for lepton to be inside the proton:proton to atom volume ratio

⇠✓

rp

aB

◆3

= (rp↵)3m3

Lepton mass to the third power!Muon to electron mass ratio ~205 ➙ factor of about 8 million!

0.001 0.1 10 1000 10510-27

10-22

10-17

10-12

10-7

0.01

r @fmD

f 2S@abu

D

electron

muon

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)• 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.

�E(2PF=23/2 � 2SF=1

1/2 ) = 209.9779(49)� 5.2262r2p + 0.0347r3

p [meV]

1960 1970 1980 1990 2000 2010

0.80

0.85

0.90

0.95

Year

r Ch@fmD


CODATAZhan et al. (JLab)Bernauer et al. (Mainz)Older eP DataH-Lamb Data

1960 1970 1980 1990 2000 2010

0.80

0.85

0.90

0.95

Year

r Ch@fmD


CODATAZhan et al. (JLab)Bernauer et al. (Mainz)Older eP DataH-Lamb DataPohl et al.

1960 1970 1980 1990 2000 2010

0.80

0.85

0.90

0.95

Year

r Ch@fmD


CODATAZhan et al. (JLab)Bernauer et al. (Mainz)Older eP DataH-Lamb DataPohl et al.

# 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 2-4

0.8764±0.0047

6 Muonic Hydrogen 0.842±0.001

X. Zhan et al., PLB705, 59 (2011)GR et al., PRC84, 055204(2011)

Proton Radius PuzzleMuonic hydrogen disagrees with atomic physics and electronscattering 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 2-4

0.8764±0.0047

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 valueProton 11-12% smaller (volume), 11-12% denser than previously believed

Particle Data Group: “Most measurements of the radius of the proton involve electron-proton 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.



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

R. Pohl et al., Nature 466, 213 (2010).

Systematics: 300 MHzStatistics: 700 MHz

Discrepancy:5.0σ = 75GHz → Δν/ν=1.5x10-3

“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 (Lamb shift) measurements?

Experimental Error in the electron scattering measurements?

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.

0.00 0.01 0.02 0.03 0.04 0.050.9860.9880.9900.9920.9940.9960.9981.000

Q2 @GeV2D

GEP

Theory Error?

Theory Error?

Theory Error?

Theory Error?Checked, Rechecked,and Checked againNo Error Found

Theory Error?Checked, Rechecked,and Checked againNo Error Found

Third Zemach Moment�E(2PF=2

3/2 � 2SF=11/2 ) = 209.9779(49)� 5.2262r2

p + 0.0347r3p [meV]


3/2 � 2SF=11/2 ) = 209.9779(49)� 5.2262r2

p + 0.0347r3p [meV]


3/2 � 2SF=11/2 ) = 209.9779(49)� 5.2262r2

p + 0.0347r3p [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)).


3/2 � 2SF=11/2 ) = 209.9779(49)� 5.2262r2

p + 0.0347r3p [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)

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 multi-photon terms.

Miller et al., Phys. Rev. A84, 020101 (2011)Paz & Hill, Phys. Rev. Lett. 107, 160402 (2011)

Essentially proton polarizability terms.

m4 term, negligible for electrons

This is in an interesting idea, but almost certainly wrong since these terms are constrained from accurate measurements of, for example, inclusive electron scattering.

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.


• 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

�ELepto

Lamb

= |�nS

(0)|2�2

Lµd

m2L

=m3

r

↵3

⇡n3

�2Lµd

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

�ELepto

Lamb

0.0044 meVln(m2

L

/m2d

) ⇠ 10

Measurement deviation is about 300 μeV with an error about 4 μeV!Possible Leptoquark effect 4.4 μeV.

Clearly leptoquarks are out!

• 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))

EHFS = (1 + �QED + �pR + �p

h⌫p + �pµ⌫p + �p

Weak + �S)EpF

�S = �Z + �Pol

�Z = �2↵mRrZ

rZ = � 4⇡

ZdQ

Q2

GE(Q2)GM (Q2)

µp� 1

� E2S,ePHFS ⇠ 177.555 MHz = 0.734 µeV

E2S,µPHFS ⇠ 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 relativisticallybut still contains F1 and F2

Where to now?

Where to now?

What did they usefor 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+

A. Antognini et al, Can. J. Phys. 89, 47 (2011)

�E(2P1/2 � 2S1/2)µ4He+= 1670.370(600)� 105.322r2

He + 1.529r3He meV

= 403.893(145)� 25466r2He + 370r3

He GHz

Where to now?

• 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.

E08007 - Part IIWhere to now?

elastic scattering from heavy elements pay attention to

the fine splitting between different elements

elastic scattering from hydrogen

● left arm ● right arm

Preliminary

E08007 - Part IIProjected uncertainties

Ê

ÊÊ Ê Ê Ê

Ê Ê

ÛÛ Û

Û Û

ÏÏ

Ï

Ï ÏÏ

Ï

Ï

X

X

XX

X

X

X

X

ÊÊÊÊ Ê

Mp2 4Mp2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.80

0.85

0.90

0.95

1.00

1.05

1.10

Q2 @GeV2D

m PGEêG M

0.000 0.001 0.002 0.003 0.004 0.0050.0

0.5

1.0

1.5

Q2 @GeV2D

1-GEP@%DUnfortunately

Low Q2 Measurements in eP scattering have been pushed about as far as they can go

Newest IdeaμP Scattering

Where to now?• 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.

J ArringtonArgonne National LabF Benmokhtar, E Brash

Christopher Newport UniversityA Richter

Technical University of DarmstadtM Meziane

Duke UniversityA Afanasev, W. Briscoe, E. J. Downie

George Washington UniversityM Kohl

Hampton UniversityG Ron

Hebrew University of JerusalemD HiginbothamJefferson Lab

S Gilad, V SulkoskyMIT

V PunjabiNorfolk State University

L WeinsteinOld Dominion UniversityK Deiters, D Reggiani

Paul Scherrer InstituteL El Fassi, R Gilman, G Kumbartzki,K Myers, R Ransome, AS Tadepalli

Rutgers UniversityC Djalali, R Gothe, Y Ilieva, S Strauch

University of South CarolinaS Choi

Seoul National UniveristyA Sarty

St. Mary’s UniversityJ Lichtenstadt, E Piasetzky

Tel Aviv UniversityE Fuchey, Z-E Meziani, E Schulte

Temple UniversityN Liyanage

University of VirginiaC Perdrisat

College of William & Mary

μP Collaboration

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

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 neutroncancel with carbon.But perhaps the carbon radius is insensitive to the nucleon radius,and μd or μHe would be a better choice.

The 12C radius was determined with ep scattering and μC atoms.

The results agree:Cardman et al. eC: 2.472 ± 0.015 fmOffermann et al. eC: 2.478 ± 0.009 fmSchaller et al. μC X rays: 2.4715 ± 0.016 fmRuckstuhl et al. μC X rays: 2.483 ± 0.002 fmSanford et al. μC elastic: 2.32 ± 0.13 fm

μP Scattering How well can we do?

σ0.84/σ0.88 vs. Q2

160 MeV/c μ’s incident on protons cross section uncertainties for 2.6x1011 μ on 4 cm LH2 (30 days)

Technical review - Test Beam awarded.Beam test scheduled for Oct 2012.Examining funding options.

SciFi

SciFi+ GEMs

WCs +Scintillators

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 �

Relative

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)! �

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).

The Rydberg ConstantFinal wordsThe 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

✓1n2

1

� 1n2

2

◆

This is the best determined physical constant!

http://en.wikipedia.org/wiki/Wavenumber

http://en.wikipedia.org/wiki/Wavenumber

http://en.wikipedia.org/wiki/Rydberg_formula

http://en.wikipedia.org/wiki/Rydberg_formula

The Rydberg ConstantFinal words

The Rydberg ConstantFinal wordsIt 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.

The Rydberg Constant - another surpriseFinal words

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

ConclusionsSummary

ConclusionsSummary

• Proton radii have been measured very accurately over the last 50 years.

ConclusionsSummary


• 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.

ConclusionsSummary





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”

ConclusionsSummary





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

The Proton Radius - weizmann.ac.il

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