Proton radius puzzle
Jan C. Bernauer
COFI workshop - San Juan - May 2018 100 years of protons! Proton is a composite system. It must have a size! How big is it?
What is ”stuff”?
The matter around us is described by non-perturbative quantum chromodynamics. npQCD is hard. Simplest QCD system to study: Protons
2 Proton is a composite system. It must have a size! How big is it?
What is ”stuff”?
The matter around us is described by non-perturbative quantum chromodynamics. npQCD is hard. Simplest QCD system to study: Protons
100 years of protons!
3 What is ”stuff”?
The matter around us is described by non-perturbative quantum chromodynamics. npQCD is hard. Simplest QCD system to study: Protons
100 years of protons! Proton is a composite system. It must have a size! How big is it?
4 Two transitions for two unknowns: Rydberg constant R 1S Lamb shift = radius∞ ⇒ Direct Lamb shift 2S 2P →
Motivation: ”Normal” Hydrogen Spectroscopy
8S 4S 3S 3D
2S 2P
R∞ L1S EnS u 2 + 3 − n n
2 1S L1S = 8171.626(4) + 1.5645 rp MHz
5 Direct Lamb shift 2S 2P →
Motivation: ”Normal” Hydrogen Spectroscopy
8S 4S 3S 3D 2S 8S 2S 8D → → 2S 2P
R∞ L1S EnS u 2 + 3 − n n Two transitions for two unknowns: Rydberg constant R ∞ 1S 2S 1S Lamb shift = radius → ⇒
2 1S L1S = 8171.626(4) + 1.5645 rp MHz
6 Motivation: ”Normal” Hydrogen Spectroscopy
8S 4S 3S 3D 2S 2P 2S → 2P
R∞ L1S EnS u 2 + 3 − n n Two transitions for two unknowns: Rydberg constant R 1S Lamb shift = radius∞ ⇒ Direct Lamb shift 2S 2P →
2 1S L1S = 8171.626(4) + 1.5645 rp MHz
7 ”Normal” Hydrogen Spectroscopy Results
8 Elastic lepton-proton scattering
Method of choice: Lepton-proton scattering Point-like probe No strong force Lepton interaction ”straight-forward”
Measure cross sections and reconstruct form factors.
9 Cross section for elastic scattering
dσ dΩ 1 = εG2 Q2 + τG2 Q2 dσ ε (1 + τ) E M dΩ Mott h i with:
2 1 Q θ − τ = , ε = 1 + 2 (1 + τ) tan2 e 4m2 2 p Rosenbluth formula Electric and magnetic form factor encode the shape of the proton Fourier transform (almost) gives the spatial distribution, in the Breit frame
10 How to measure the proton radius
dG d (G /µ ) r2 6 2 E r2 6 ² M p E = ~ 2 M = ~ 2 − dQ 2 − dQ 2 Q =0 Q =0 D E D E
1 0.995
. 0.99 dip
. 0.985
std 0.98
/G 0.975 E dGE G 0.97 dQ2 → Q2=0 0.965
0.96 0 0.05 0.1 0.15 0.2 0.25 0.3 Q2 [(GeV/c)2]
11 History of unpolarized electron-proton scattering
100
10 2 )
/c 1
(GeV 0.1 / 2 Q 0.01
0.001 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year Andivahis Borkowski Janssens Rock Walker Bartel Bosted Litt Sill Berger Christy Price Simon Bernauer Goitein Qattan Stein
12 Mainz Microtron cw electron beam 10 µA polarized, 100 µA unpolarized MAMI A+B: 180-855 MeV MAMI C: 1.6 GeV
A1 3-spectrometer facility 28 msr acceptance angle resolution: 3 mrad 4 momentum res.: 10−
High-precision p(e,e’)p measurement at MAMI
13 A1 3-spectrometer facility 28 msr acceptance angle resolution: 3 mrad 4 momentum res.: 10−
High-precision p(e,e’)p measurement at MAMI
Mainz Microtron cw electron beam 10 µA polarized, 100 µA unpolarized MAMI A+B: 180-855 MeV MAMI C: 1.6 GeV
14 High-precision p(e,e’)p measurement at MAMI
Mainz Microtron cw electron beam 10 µA polarized, 100 µA unpolarized MAMI A+B: 180-855 MeV MAMI C: 1.6 GeV
A1 3-spectrometer facility 28 msr acceptance angle resolution: 3 mrad 4 momentum res.: 10−
15 Measured settings
A 1 B C
0.8 ] 2 )
/c 0.6 (GeV [ 2
Q 0.4
0.2
0 0 0.2 0.4 0.6 0.8 1
1422 settings JCB et al., Phys. Rev. Lett. 105 (2010) 242001, M. O. Distler, JCB, Th. Walcher, Phys. Lett. B 696, 343 (2011) JCB et al., Phys. Rev. C90 (2014) 015206
16 Cross sections
100 100
10
10
1 ] ] 1 µb µb [ [ 0.1 exp exp σ σ
0.1 180 0.01 MeV 315 585 MeV MeV 0.01 720 450 0.001 MeV MeV 855 MeV
0.001 0.0001 0◦ 20◦ 40◦ 60◦ 80◦ 100◦ 120◦ 140◦ 0◦ 20◦ 40◦ 60◦ 80◦ 100◦ 120◦ 140◦ Central angle of spectrometer Central angle of spectrometer
Polynomial Inv. poly. Friedrich-Walcher Poly. + dip Spline Double dipole Poly. dip Spline dip Extended G.K. × ×
17 Muonic Hydrogen Spectroscopy
Replace electron with muon 200 times heavier = 200 times smaller orbit ⇒ Probability to be ”inside” 2003 higher!
18 PSI setup (CREMA)
19 Result Two semi-independent measurements Consistent results
Muonic Hydrogen Spectroscopy Results
20 Muonic Hydrogen Spectroscopy Results
Result Two semi-independent measurements Consistent results
21 From the 2017 Review of Particle Physics Until the difference between the e p and µ p values is understood, it does not make sense to average the values together. For the present, we give both values. It is up to the workers in this field to solve this puzzle.
The proton radius puzzle
7.9 σ µp 2013 electron avg.
scatt. JLab
µp 2010 scatt. Mainz
H spectroscopy
0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] ch
22 The proton radius puzzle
From the 2017 Review of Particle Physics Until the difference between the e p and µ p values is understood, it does not make sense to average the values together. For the present, we give both values. It is up to the workers in this field to solve this puzzle.
23 seems solid ep experiments wrong? both scattering and H-spectroscopy wrong? Theory wrong? checked thoroughly ...but maybe framework is wrong? Everybody is right? New physics! ”Naive” dark matter models essentially excluded But can play cancelation games E.g.: Electrophobic force (Liu, Cloët, Miller arXiv:1805.01028) WE NEED MORE DATA
Solutions?
µp experiment wrong?
24 Theory wrong? checked thoroughly ...but maybe framework is wrong? Everybody is right? New physics! ”Naive” dark matter models essentially excluded But can play cancelation games E.g.: Electrophobic force (Liu, Cloët, Miller arXiv:1805.01028)
WE NEED MORE DATA
Solutions?
µp experiment wrong? seems solid ep experiments wrong? both scattering and H-spectroscopy wrong?
25 Everybody is right? New physics! ”Naive” dark matter models essentially excluded But can play cancelation games E.g.: Electrophobic force (Liu, Cloët, Miller arXiv:1805.01028)
WE NEED MORE DATA
Solutions?
µp experiment wrong? seems solid ep experiments wrong? both scattering and H-spectroscopy wrong? Theory wrong? checked thoroughly ...but maybe framework is wrong?
26 WE NEED MORE DATA
Solutions?
µp experiment wrong? seems solid ep experiments wrong? both scattering and H-spectroscopy wrong? Theory wrong? checked thoroughly ...but maybe framework is wrong? Everybody is right? New physics! ”Naive” dark matter models essentially excluded But can play cancelation games E.g.: Electrophobic force (Liu, Cloët, Miller arXiv:1805.01028)
27 Solutions?
µp experiment wrong? seems solid ep experiments wrong? both scattering and H-spectroscopy wrong? Theory wrong? checked thoroughly ...but maybe framework is wrong? Everybody is right? New physics! ”Naive” dark matter models essentially excluded But can play cancelation games E.g.: Electrophobic force (Liu, Cloët, Miller arXiv:1805.01028)
WE NEED MORE DATA
28 Deuteron (arxiv:1607.03165)
In CODATA, rd is correlated strongly to rp because it uses ”isotope shift” from 1s-2s in both systems. But: Can built independent value from deuteron 1s-2s and 2s-8s/8d/12d. This gives a difference to muonic deuterium! another puzzle. → Rydberg from electric Hydrogen and Deuterium in perfect agreement. The muonic deuterium R is in slight disagreement with the muonic hydrogen∞ R (<3 sigma) ∞
29 New hydrogen results: MPQ (A. Beyer et al., Science 358, 79 (2017))
30 New results: Paris (Fleurbaey et al., Phys. Rev. Lett. 120, 183001 (2018))
31 Timeline of proton radius results
0.92 0.9 0.88 0.86 [fm] 0.84 >
E 0.82 0.8 < r 0.78 0.76 0.74 Paz ’10 Sick ’03 Pohl ’10 Zhan ’11 Hand ’63 Wong ’94 Udem ’97 Simon ’80 Lorenz ’12 Mergell ’96 Akimov ’72 McCord ’91 Blunden ’05 Eschrich ’01 Melnikov ’00 Bernauer ’10 CODATA ’06 CODATA ’02 Belushkin ’06 Antognini ’13 Borkowski ’75 Rosenfelder ’00 Frerejacque ’66
32 Comments on some newer scattering results 2010: >0.870 Hill, Paz: old data, z expansion with disp. bounds Bounds on infinite exp. bounds for truncated exp.? → 2012: 0.840(10) Lorenz, Hammer, Meissner: Disp. relation fit. Same value but a lot more data. Probably model dominated. 2014: 0.84 Lorenz, Meissner: z expansion without bounds Fit did not converge. In real minimum, large radius is found. 2014: 0.8989(1) Gracyk/Juszczak: Bayesian estimation Interesting technique, unbelievable? small errors 2016: 0.84? Higinbotham: F-Test to select max. order Misunderstood F-test. Absence of proof = proof of absence. 6 2016: 0.84? Horbatsch/Hessels/Griffioen/Carlson/Maddox... Low-Q Low-Q fits with low order don’t work. 2018: XXX Yan/Higinbotham/... Small radius fraction finally does bias testing
33 Volume of Mainz data set
7
2 6 σ σ ∆ 5 P q 4
3
2
Relative statistical weight 1
0 All others Mainz
Mainz data will dominate any fit. Need similar data set to validate!
34 Extrapolation to Q2 = 0
Have to extrapolate form factor to Q2 = 0. Mainz lowest Q2 = 0.0033 (GeV/c)2. We use a 10th order polynomial to fit data up to 1 (GeV/c)2. This gets people scared.
Can we fit just a linear term?
35 dσ But: Need to measure A to 1%, so measure dΩ to 6 0.002 0.01 = 0.012%. Good luck. · ·
Can a linear fit work?
dσ 1 A Q2 + B Q4 + ... dΩ ∝ − · · (6) (30) O O (Q in units of GeV/c) |{z} |{z} We want to measure the radius (~√A) to within 0.5%, without knowingB. So:
B/A Q2 0.01 Q2 0.002 (GeV/c)2 · −→
36 Can a linear fit work?
dσ 1 A Q2 + B Q4 + ... dΩ ∝ − · · (6) (30) O O (Q in units of GeV/c) |{z} |{z} We want to measure the radius (~√A) to within 0.5%, without knowingB. So:
B/A Q2 0.01 Q2 0.002 (GeV/c)2 · −→
dσ But: Need to measure A to 1%, so measure dΩ to 6 0.002 0.01 = 0.012%. Good luck. · ·
37 Why do low Q2 then?
Test / fix normalization Similar arguments apply, but helpful when dataset contains also higher Q2. Test for new physics / ultra long range structure Signal can easily, but doesn’t have to be undetectable small and still change the radius!
Measure rM Low Q2 at = 1 means lowish Q2 at = 0
38 Three ways to get to lower Q2
θ Q2 = 4EE sin2 0 2 Smaller scattering angle PRad −→ Lower beam energy MESA −→ Initial State Radiation
39 Status Data taken successfully Analysis ongoing
JLAB: PRoton RADius
High resolution, large acceptance hybrid calorimeter Windowless target Simultaneous measure ep ep and Møller scattering → Q2 range: 2 10 4 to 2 10 2 (GeV/c)2 × − × −
40 JLAB: PRoton RADius
High resolution, large acceptance hybrid calorimeter StatusWindowless target SimultaneousData taken successfully measure ep ep and Møller scattering → QAnalysis2 range: ongoing 2 10 4 to 2 10 2 (GeV/c)2 × − × −
41 ISR method
2 QReconstruct
2 QVertex
Use initial state radiation to reduce effective beam energy Have to subtract FSR
42 Status Published: PLB 771:194-198 Radiative correction correct on the 1% level deep in the tail! Radius extraction not competitive in precision
ISR at MAMI
Simulation Data at 195 MeV + 7 Elastic Settings H(e, e′)n π and 10 0 Data at 495 MeV H(e, e′)p π Contributions Data at 330 MeV Background
106
5 MeV) 105 ·
4 ISR small E (0.1 mC 10 −→ 2 −→ 3 small Q Counts / 10
21 19 6 4 2 Extract F.F. from 102 22 20 18 7 5 3 1 17 15 13 11 9 radiative tail 16 14 12 10 8 3%
Or: test radiative tail 2% 1 − description 1% 0% Simulation / -1%
Data -2% Systematic uncertainty
-3% 100 150 200 250 300 350 400 450 500 Electron energy E ′ [MeV] See: arXiv:1612.06707
43 ISR at MAMI
Simulation Data at 195 MeV + 7 Elastic Settings H(e, e′)n π and 10 0 Data at 495 MeV H(e, e′)p π Contributions Data at 330 MeV Background
106
5 MeV) 105 ·
4 ISR small E (0.1 mC 10 −→ 2 −→ 3 small Q Counts / 10
21 19 6 4 2 Extract F.F. from 102 22 20 18 7 5 3 1 Status 17 15 13 11 9 radiative tail 16 14 12 10 8 Published: PLB 771:194-1983% Or: test radiative tail 2% 1 − descriptionRadiative correction correct1% on the 1% level deep in the tail! 0% Simulation / -1%
Radius extraction not competitiveData -2% in precisionSystematic uncertainty
-3% 100 150 200 250 300 350 400 450 500 Electron energy E ′ [MeV] See: arXiv:1612.06707
44 point-like no walls but less density
Electron- beam 49.5 mm 11.5 mm liquid hydrogen
10 µm Havar
Target cell Heat Ventilator exchanger
"Basel-Loop"
Background from target walls Scattering chamber Acceptance correction for extended target Eliminate with jet target ⇓
Rinse, repeat with D,3He,4He, ...
Target dominant source of uncertainty
For Mainz data, systematic errors dominate
45 point-like no walls but less density
Eliminate with jet target ⇓
Rinse, repeat with D,3He,4He, ...
Electron- beam 49.5 mm 11.5 mm liquid hydrogen
10 µm Havar Target dominant source of uncertainty
Target cell Heat Ventilator exchanger
For Mainz data, systematic errors dominate "Basel-Loop"
Background from target walls Scattering chamber Acceptance correction for extended target
46 Electron- beam 49.5 mm 11.5 mm liquid hydrogen
10 µm Havar Target dominant source of uncertainty
Target cell Heat Ventilator exchanger
For Mainz data, systematic errors dominate "Basel-Loop"
Background from target walls Scattering chamber Acceptance correction for extended target Eliminate with jet target point-like ⇓ no walls but less density Rinse, repeat with D,3He,4He, ...
47 Mainz future plans
Repeat ISR with new target Use new target also for classic approach
1 108 1 × MAGIX at E=50 MeV MAMI at E=180 MeV MAGIX at E=50 MeV MAMI at E=180 MeV 1 107 MAGIX at E=75 MeV MAMI at E=240 MeV MAGIX at E=75 MeV MAMI at E=240 MeV × MAGIX at E=100 MeV MAMI at E=300 MeV MAGIX at E=100 MeV MAMI at E=300 MeV 1 106 1 week × 0.1 100000 1 day ] 2 )
10000 /c 1 hour 0.01
1000 (GeV) [ 2 100 1 minute Q 0.001 10 Time to 0.1% statistical error [s] 1 1 second
0.1 0.0001 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ε ε
Took first data in April! Full MAMI experiment next year, MESA 2021.
48 The missing piece
rE [fm] ep µp Spectroscopy 0.8758 0.077 0.84087 0.00039 ± ± Scattering 0.8770 0.060 ???? ±
Measure radius with muon-proton scattering!
49 MUSE - Muon Scattering Experiment at PSI
World’s most powerful low-energy e/π/µ-beam: Direct comparison of ep and µp!
+ + + Beam of e /π /µ or e−/π−/µ− on liquid H2 target Species separated by ToF, charge by magnet Absolute cross sections for ep and µp Ratio to cancel systematics Charge reversal: test TPE Momenta 115-210 MeV/c Rosenbluth G ,G ⇒ E M 50 Experiment layout
Scattered Particle Beam-Line Scintillator (SPS) Monitor
Straw-Tube Tracker (STT) Secondary beam = track beam particles ⇒
Target Low flux (5 MHz)= large Chamber acceptance ⇒
3 GEM Detectors Mixed beam = PID in ⇒ Beam trigger Hodoscope Veto Scintillator pM1 Beam-Line
~ 100 cm
R. Gilman et al., arXiv:1303.2160 [nucl-ex]
51 Difference: Common uncertainties cancel! factor two more −→sensitivity
MUSE can verify 7σ effect with similar significance!
Predicted performance
Absolute radius extraction uncertainties similar to current exp’s.
52 Predicted performance
Absolute radius extraction uncertainties similar to current exp’s. Difference: Common uncertainties cancel! factor two more sensitivity−→
MUSE can verify 7σ effect with similar significance!
53 Summary
Proton radius puzzle persists since 2010 We need new data to resolve it A lot of data incoming in the next years, but pretty hard limit on achievable errors MUSE, with electron and muon scattering, will test existing radius value lepton universality two photon exchange / proton polarizability
The most exciting phrase to hear in science, the one that heralds new discoveries, is not “Eureka!” but “That’s funny . . . ” — Isaac Asimov
54 8Be is special
Many images from arXiv:1707.09749 8Be is special: two narrow, highly energetic states which can decay to ground state via E/M
55 Decay modes of 8Be(18.15)
Hadronic, electromagnetic and through internal pair conversion
56 The Atomkin experiment
θ
ATOMKI PAIR SPECTROMETER
1.04 MeV proton beam on 7Li to 8Be(18.15) + γ. Followed by decay. Looked at e± pairs from internal conversion.
57 The beryllium anomaly
58 Why believe it?
This model has χ2/d.o.f . of 1.07, significance of 6.8σ Bump, not last bin effect Rises/falls when scanning through proton energies around resonance Excess only happens for symmetric-energy pairs Preliminary reports of same excess in 8Be(17.6) (same group)
59 Why not believe it?
Group has a history of finding peaks IIUC, the detector acceptance has a minimum at 140◦ DM boson interpretation is proto-phobic to evade NA48/2 limits Actually: p coupling below 8%. Z 0 is 7% n ± ∼
60 Best kinematics: highest production rate if X takes all electron energy. CS rise beats all with limited out-of-plane acceptance, symmetric angle optimal
We can measure it!
In DarkLight, production is via Bremsstrahlung, predominantly ISR off the electron. We can look at e Ta e TaX, followed by X e e+ − → − → − Irreducible background: e Ta e Taγ? e Tae+e − → − → − −
61 We can measure it!
In DarkLight, production is via Bremsstrahlung, predominantly ISR off the electron. + We can look at e−Ta e−TaX, followed by X e−e → ? → + Irreducible background: e−Ta e−Taγ e−Tae e− Best kinematics: → → highest production rate if X takes all electron energy. CS rise beats all with limited out-of-plane acceptance, symmetric angle optimal
62 Reach
4 10−
-preferred 5 2) 10− (gµ −
6 10− -1c-1c 45 MeV 150 µA @ 10 µm 2000 hh-1c 5th force 10 7 − MESA APEX
2 Mu3e HPS 8 VEPP-3 10−
LHCb 9 10−
10 10 − SeaQuest SHIP 11 10− 101 102 103 mA [MeV]
63