proton radius puzzle

The radius of the proton is defined by a formula which can be calculated by quantum electrodynamics and be derived from either atomic spectroscopy or by electron–proton scattering. The formula involves a form-factor related to the two-dimensional parton diameter of the proton.{{Cite journal |last=Miller |first=Gerald A. |date=2019-03-07 |title=Defining the proton radius: A unified treatment |url=https://link.aps.org/doi/10.1103/PhysRevC.99.035202 |journal=Physical Review C |language=en |volume=99 |issue=3 |page=035202 |doi=10.1103/PhysRevC.99.035202 |issn=2469-9985|arxiv=1812.02714 |bibcode=2019PhRvC..99c5202M }}

Prior to 2010, the proton charge radius was measured using one of two methods: one relying on spectroscopy, and one relying on nuclear scattering.{{cite journal|url=http://www.nature.com/news/proton-size-puzzle-deepens-1.22760|title=Proton-size puzzle deepens|journal=Nature|date=5 October 2017|author=Davide Castelvecchi|doi=10.1038/nature.2017.22760}}

The spectroscopy method compares the energy levels of spherically symmetric 2s orbitals to asymmetric 2p orbitals of hydrogen, a difference known as the Lamb shift. The exact values of the energy levels are sensitive to the distribution of charge in the nucleus since the 2s levels overlap more with the nucleus.{{Cite journal |last1=Karr |first1=Jean-Philippe |last2=Marchand |first2=Dominique |last3=Voutier |first3=Eric |date=November 2020 |title=The proton size |url=https://www.nature.com/articles/s42254-020-0229-x |journal=Nature Reviews Physics |language=en |volume=2 |issue=11 |pages=601–614 |doi=10.1038/s42254-020-0229-x |bibcode=2020NatRP...2..601K |issn=2522-5820}} Measurements of hydrogen's energy levels are now so precise that the accuracy of the proton radius is the limiting factor when comparing experimental results to theoretical calculations. This method produces a proton radius of about {{val|0.8768|(69)|ul=fm}}, with approximately 1% relative uncertainty.

Similar to Rutherford's scattering experiments that established the existence of the nucleus, modern electron–proton scattering experiments send beams of high energy electrons into 20cm long tube of liquid hydrogen.{{cite journal |last1=Walker |first1=R. C. |last2=Filippone |first2=B. W. |last3=Jourdan |first3=J. |last4=Milner |first4=R. |last5=McKeown |first5=R. |last6=Potterveld |first6=D. |last7=Andivahis |first7=L. |last8=Arnold |first8=R. |last9=Benton |first9=D. |last10=Bosted |first10=P. |last11=deChambrier |first11=G. |last12=Lung |first12=A. |last13=Rock |first13=S. E. |last14=Szalata |first14=Z. M. |last15=Para |first15=A. |date=1994-06-01 |title=Measurements of the proton elastic form factors for {{nowrap|1 ≤ Q² ≤ 3 (GeV/c)²}} at SLAC |url=https://link.aps.org/doi/10.1103/PhysRevD.49.5671 |journal=Physical Review D |language=en |volume=49 |issue=11 |pages=5671–5689 |doi=10.1103/PhysRevD.49.5671 |issn=0556-2821}} The resulting angular distribution of the electron and proton are analyzed to produce a value for the proton charge radius.

Consistent with the spectroscopy method, this produces a proton radius of about {{val|0.8775|(5)|ul=fm}}.{{cite journal |vauthors=Sick I, Trautmann D |s2cid=118615444 |year=2014 |title=Proton root-mean-square radii and electron scattering |journal=Physical Review C |volume=89 |issue=1 |pages= 012201 |doi=10.1103/PhysRevC.89.012201|arxiv=1407.1676 |bibcode=2014PhRvC..89a2201S }}

In 2010, Pohl et al. published the results of an experiment relying on muonic hydrogen as opposed to normal hydrogen. Conceptually, this is similar to the spectroscopy method. However, the much higher mass of a muon causes it to orbit 207 times closer than an electron to the hydrogen nucleus, where it is consequently much more sensitive to the size of the proton. The resulting radius was recorded as {{val|0.842|(1)|u=fm}}, 5 standard deviations (5σ) smaller than the prior measurements. The newly measured radius is 4% smaller than the prior measurements, which were believed to be accurate within 1%. (The new measurement's uncertainty limit of only 0.1% makes a negligible contribution to the discrepancy.){{cite journal |vauthors=Carlson CE |s2cid=54915587 |date=May 2015 |title=The proton radius puzzle |journal=Progress in Particle and Nuclear Physics |volume=82 |pages=59–77 |arxiv=1502.05314 |bibcode=2015PrPNP..82...59C |doi=10.1016/j.ppnp.2015.01.002}}

A follow-up experiment by Pohl et al. in August 2016 used a deuterium atom to create muonic deuterium and measured the deuteron radius. This experiment allowed the measurements to be 2.7 times more accurate, but also found a discrepancy of 7.5 standard deviations smaller than the expected value.{{cite journal |vauthors=Pohl R, Nez F, Fernandes LM, Amaro FD, Biraben F, Cardoso JM, Covita DS, Dax A, Dhawan S, Diepold M, Giesen A, Gouvea AL, Graf T, Hänsch TW, Indelicato P, Julien L, Knowles P, Kottmann F, Le Bigot E, Liu Y, Lopes JA, Ludhova L, Monteiro CM, Mulhauser F, Nebel T, Rabinowitz P, dos Santos JM, Schaller LA, Schuhmann K, Schwob C, Taqqu D, Veloso JF, Antognini A |s2cid=206647315 |display-authors=1 |year=2016 |title=Laser spectroscopy of muonic deuterium |journal=Science |volume=353 |issue=6300 |pages=669–673 |doi=10.1126/science.aaf2468 |bibcode=2016Sci...353..669P |pmid=27516595 |hdl=10316/80061 |hdl-access=free }}{{cite news |title=Proton-radius puzzle deepens |journal=CERN Courier |date=16 September 2016 |url=https://cerncourier.com/a/proton-radius-puzzle-deepens/|quote=After our first study came out in 2010, I was afraid some veteran physicist would get in touch with us and point out our great blunder. But the years have passed, and so far nothing of the kind has happened.}}

The anomaly remains unresolved and is an active area of research. There is as yet no conclusive reason to doubt the validity of the old data. The immediate concern is for other groups to reproduce the anomaly.

The uncertain nature of the experimental evidence has not stopped theorists from attempting to explain the conflicting results. Among the postulated explanations are the three-body force,{{cite journal |last1=Karr |first1=J. |last2=Hilico |first2=L.|year=2012 |title=Why three-body physics does not solve the proton-radius puzzle |journal=Physical Review Letters |volume=109 |issue=10 |page=103401 |arxiv=1205.0633 |s2cid=12752418 |bibcode=2012PhRvL.109j3401K |doi=10.1103/PhysRevLett.109.103401 |pmid=23005286}} interactions between gravity and the weak force, or a flavour-dependent interaction,{{cite journal |last=Onofrio |first=R. |year=2013 |title=Proton radius puzzle and quantum gravity at the Fermi scale |journal=EPL |volume=104 |issue=2 |page=20002 |s2cid=119243594 |arxiv=1312.3469 |bibcode=2013EL....10420002O |doi=10.1209/0295-5075/104/20002}}{{cite news |last=Zyga |first=Lisa |date=November 26, 2013 |title=Proton radius puzzle may be solved by quantum gravity |url=http://phys.org/news/2013-11-proton-radius-puzzle-quantum-gravity.html |newspaper=Phys.org |access-date=September 2, 2016}} higher dimension gravity,{{cite journal |last1=Dahia |first1=F. |last2=Lemos |first2=A.S. |year=2016 |title=Is the proton radius puzzle evidence of extra dimensions? |journal=European Physical Journal |volume=76 |issue=8 |page=435 |arxiv=1509.08735 |s2cid=118672005 |bibcode=2016EPJC...76..435D |doi=10.1140/epjc/s10052-016-4266-7}} a new boson,{{cite journal |vauthors=Liu Y, McKeen D, Miller GA |year=2016 |title=Electrophobic Scalar Boson and Muonic Puzzles |journal=Physical Review Letters |volume=117 |issue=10 |page=101801 |s2cid=20961564 |arxiv=1605.04612 |bibcode=2016PhRvL.117j1801L |doi=10.1103/PhysRevLett.117.101801 |pmid=27636468}} and the quasi-free {{math|{{SubatomicParticle|link=yes|Pion+}}}} hypothesis.{{cite report |last=Lestone |first=J.P. |title=Muonic atom Lamb shift via simple means |series=Los Alamos Report |id=LA-UR-17-29148 |date=4 October 2017 |publisher=Los Alamos National Laboratory |url=https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-18-29699}}

Randolf Pohl, the original investigator of the puzzle, stated that while it would be "fantastic" if the puzzle led to a discovery, the most likely explanation is not new physics but some measurement artefact. His personal assumption is that past measurements have misgauged the Rydberg constant and that the current official proton size is inaccurate.{{cite news |last=Wolchover |first=Natalie |date=11 August 2016 |title=New measurement deepens proton puzzle |newspaper=Quanta Magazine |url=https://www.quantamagazine.org/20160811-new-measurement-deepens-proton-radius-puzzle/ |access-date=2 September 2016}}

In a paper by Belushkin et al. (2007), including different constraints and perturbative quantum chromodynamics, a smaller proton radius than the then-accepted 0.877 femtometres was predicted.{{cite journal |last1=Belushkin |first1=M.A. |last2=Hammer |first2=H.-W. |last3=Meißner |first3=Ulf-G. |year=2007 |title=Dispersion analysis of the nucleon form factors including meson continua |journal=Physical Review C |volume=75 |issue=3 |page=035202 |s2cid=42995123 |issn=0556-2813 |arxiv=hep-ph/0608337 |doi=10.1103/PhysRevC.75.035202 |bibcode=2007PhRvC..75c5202B}}

Papers from 2016 suggested that the problem was with the extrapolations that had typically been used to extract the proton radius from the electron scattering data{{cite journal |last1=Higinbotham |first1=Douglas W. |last2=Kabir |first2=Al Amin |last3=Lin |first3=Vincent |last4=Meekins |first4=David |last5=Norum |first5=Blaine |last6=Sawatzky |first6=Brad |date=31 May 2016 |title=Proton radius from electron scattering data |journal=Physical Review C |volume=93 |issue=5 |page=055207 |doi=10.1103/PhysRevC.93.055207 |arxiv=1510.01293 |bibcode=2016PhRvC..93e5207H }}{{cite journal |last1=Griffioen |first1=Keith |last2=Carlson |first2=Carl |last3=Maddox |first3=Sarah |title=Consistency of electron scattering data with a small proton radius |journal=Physical Review C |date=17 June 2016 |volume=93 |issue=6 |page=065207 |doi=10.1103/PhysRevC.93.065207 |arxiv=1509.06676 |bibcode=2016PhRvC..93f5207G }}{{cite journal |last1=Horbatsch |first1=Marko |last2=Hessels |first2=Eric A. |last3=Pineda |first3=Antonio |title=Proton radius from electron–proton scattering and chiral perturbation theory |journal=Physical Review C |date=13 March 2017 |volume=95 |issue=3 |page=035203 |doi=10.1103/PhysRevC.95.035203 |arxiv=1610.09760|bibcode=2017PhRvC..95c5203H |s2cid=119232774 }} though these explanation would require that there was also a problem with the atomic Lamb shift measurements.

In one of the attempts to resolve the puzzle without new physics, Alarcón et al. (2018) of Jefferson Lab have proposed that a different technique to fit the experimental scattering data, in a theoretically as well as analytically justified manner, produces a proton charge radius from the existing electron scattering data that is consistent with the muonic hydrogen measurement.{{cite journal |last1=Alarcón |first1=J.M. |last2=Higinbotham |first2=D.W. |last3=Weiss |first3=C. |last4=Ye |first4=Zhihong |date=5 April 2019 |title=Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory |journal=Physical Review C |volume=99 |issue=4 |page=044303 |doi=10.1103/PhysRevC.99.044303 |doi-access=free |arxiv=1809.06373 |bibcode=2019PhRvC..99d4303A}} Effectively, this approach attributes the cause of the proton radius puzzle to a failure to use a theoretically motivated function for the extraction of the proton charge radius from the experimental data. Another recent paper has pointed out how a simple, yet theory-motivated change to previous fits will also give the smaller radius.{{cite journal |last1=Barcus |first1=Scott K. |last2=Higinbotham |first2=Douglas W. |last3=McClellan |first3=Randall E. |date=10 July 2020 |title=How analytic choices can affect the extraction of electromagnetic form factors from elastic electron scattering cross section data |journal=Physical Review C |volume=102 |issue=1 |page=015205 |doi=10.1103/PhysRevC.102.015205 |arxiv=1902.08185|bibcode=2020PhRvC.102a5205B |s2cid=146808413 }}

In 2017 a new approach using a cryogenic hydrogen and Doppler-free laser excitation to prepare the source for spectroscopic measurements; this gave results ~5% smaller than the previously accepted spectroscopic values with much smaller statistical errors.{{cite journal |doi=10.1126/science.aah6677 |title=The Rydberg constant and proton size from atomic hydrogen |year=2017 |last1=Beyer |first1=Axel |last2=Maisenbacher |first2=Lothar |last3=Matveev |first3=Arthur |last4=Pohl |first4=Randolf |last5=Khabarova |first5=Ksenia |last6=Grinin |first6=Alexey |last7=Lamour |first7=Tobias |last8=Yost |first8=Dylan C. |last9=Hänsch |first9=Theodor W. |last10=Kolachevsky |first10=Nikolai |last11=Udem |first11=Thomas |s2cid=206652697 |journal=Science |volume=358 |issue=6359 |pages=79–85 |pmid=28983046 |bibcode=2017Sci...358...79B |doi-access=free }} This result was close to the 2010 muon spectroscopy result. These authors suggest that the older spectroscopic analysis did not include quantum interference effects that alter the shape of the hydrogen lines.

In 2019, another experiment for the spectroscopy Lamb shift used a variation of Ramsey interferometry that does not require the Rydberg constant to analyze. Its result, 0.833 fm, agreed with the smaller 2010 value once more.{{cite journal |last1=Bezginov |first1=N. |last2=Valdez |first2=T. |last3=Horbatsch |first3=M. |last4=Marsman |first4=A. |last5=Vutha |first5=A. C. |last6=Hessels |first6=E. A. |s2cid=201845158 |title=A measurement of the atomic hydrogen Lamb shift and the proton charge radius |journal=Science |date=5 September 2019 |volume=365 |issue=6457 |pages=1007–1012 |doi=10.1126/science.aau7807 |pmid=31488684 |bibcode=2019Sci...365.1007B |doi-access=free }}

Also in 2019 W. Xiong et al. reported a similar result using extremely low momentum transfer electron scattering.{{cite journal |last1=Xiong |first1=W. |last2=Gasparian |first2=A. |last3=Gao |first3=H. |last4=Dutta |first4=D. |last5=Khandaker |first5=M. |last6=Liyanage |first6=N. |last7=Pasyuk |first7=E. |last8=Peng |first8=C. |last9=Bai |first9=X. |last10=Ye |first10=L. |last11=Gnanvo |first11=K. |last12=Gu |first12=C. |last13=Levillain |first13=M. |last14=Yan |first14=X. |last15=Higinbotham |first15=D. W. |last16=Meziane |first16=M. |last17=Ye |first17=Z. |last18=Adhikari |first18=K. |last19=Aljawrneh |first19=B. |last20=Bhatt |first20=H. |last21=Bhetuwal |first21=D. |last22=Brock |first22=J. |last23=Burkert |first23=V. |last24=Carlin |first24=C. |last25=Deur |first25=A. |last26=Di |first26=D. |last27=Dunne |first27=J. |last28=Ekanayaka |first28=P. |last29=El-Fassi|first29=L.|last30=Emmich|first30=B.|last31=Gan|first31=L.|last32=Glamazdin|first32=O.|last33=Kabir|first33=M. L.|last34=Karki|first34=A.|last35=Keith|first35=C.|last36=Kowalski|first36=S.|last37=Lagerquist|first37=V.|last38=Larin|first38=I.|last39=Liu|first39=T.|last40=Liyanage|first40=A.|last41=Maxwell|first41=J.|last42=Meekins|first42=D.|last43=Nazeer|first43=S. J. |last44=Nelyubin|first44=V.|last45=Nguyen|first45=H.|last46=Pedroni|first46=R.|last47=Perdrisat|first47=C.|last48=Pierce|first48=J.|last49=Punjabi|first49=V.|last50=Shabestari|first50=M.|last51=Shahinyan|first51=A.|last52=Silwal|first52=R.|last53=Stepanyan|first53=S.|last54=Subedi|first54=A.|last55=Tarasov |first55=V. V. |last56=Ton|first56=N.|last57=Zhang|first57=Y.|last58=Zhao|first58=Z. W. |s2cid=207831686 |display-authors=5 |title=A small proton charge radius from an electron–proton scattering experiment |journal=Nature |volume=575|issue=7781 |year=2019 |pages=147–150 |issn=0028-0836 |doi=10.1038/s41586-019-1721-2|pmid=31695211 |bibcode=2019Natur.575..147X |osti=1575200 }}

Their results support the smaller proton charge radius, but do not explain why the results before 2010 came out larger. It is likely future experiments will be able to both explain and settle the proton radius puzzle.{{cite journal |last1=Karr |first1=Jean-Philippe |last2=Marchand |first2=Dominique |title=Progress on the proton-radius puzzle |journal=Nature |volume=575 |issue=7781 |year=2019 |pages=61–62 |issn=0028-0836 |doi=10.1038/d41586-019-03364-z|pmid=31695215 |bibcode=2019Natur.575...61K |doi-access=free }}

A re-analysis of experimental data, published in February 2022, found a result consistent with the smaller value of approximately 0.84 fm.{{Cite journal|last1=Lin|first1=Yong-Hui|last2=Hammer|first2=Hans-Werner|last3=Meißner|first3=Ulf-G.|date=2022-02-03|title=New Insights into the Nucleon's Electromagnetic Structure|url=https://link.aps.org/doi/10.1103/PhysRevLett.128.052002|journal=Physical Review Letters|language=en|volume=128|issue=5|pages=052002|doi=10.1103/PhysRevLett.128.052002|pmid=35179940|arxiv=2109.12961|bibcode=2022PhRvL.128e2002L|s2cid=237940595|issn=0031-9007}}{{Cite web|title=Protons are probably actually smaller than long thought|url=https://www.uni-bonn.de/en/news/020-2022|access-date=2022-02-15|website=Universität Bonn|language=en}}

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Category:2010 in science

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Category:Proton

Category:Unsolved problems in physics

Category:Radii