Physics Has a Core Problem

Physicists can solve many puzzles by taking more accurate and careful measurements. Randolf Pohl and his colleagues at the Max Planck Institute of Quantum Optics in Garching, however, actually created a new problem with their precise measurements of the proton radius, because the value they measured differs significantly from the value previously considered to be valid. The difference could point to gaps in physicists’ picture of matter.

Measuring with a light ruler: Randolf Pohl and his team used laser spectroscopy to determine the proton radius – and got a surprising result. PHYSICS & ASTRONOMY_Proton Radius

TEXT PETER HERGERSBERG

he atmosphere at the scientific conferences that Ran- dolf Pohl has attended in the past three years has been very lively. And the T physicist from the Max Planck Institute of Quantum Optics is a good part of the reason for this liveliness: the commu- nity of experts that gathers there is working together to solve a puzzle that Pohl and his team created with its measurements of the proton radius. Time and time again, speakers present possible solutions and substantiate them with mathematically formulated arguments. In the process, they some- times also cast doubt on theories that for decades have been considered veri- fied. Other speakers try to find weak spots in their fellow scientists’ explanations, and present their own calcula- tions to refute others’ hypotheses. In the end, everyone goes back to their desks and their labs to come up with subtle new deliberations to fuel the de- bate at the next meeting. In 2010, the Garching-based physicists, in collaboration with an international team, published a new value for the charge radius of the proton – that is, the nucleus at the core of a hydrogen atom. The charge radius describes the space in which the positive charge of the nucleus is concentrated. To determine this number, the researchers working with Randolf Pohl used a dif-

Photo: Axel Griesch ferent method than the one used pre- PHYSICS & ASTRONOMY_Proton Radius

viously, and obtained a result that dif- femtometers and 0.875 ± 0.011 fem- nover. Clearly, this is going to cause fers significantly from the figure that tometers, respectively. problems – it would be no different used to be considered valid. So signifi- In other words, the difference be- than if one were to suddenly look for cantly, in fact, that the difference can’t tween the measurements is 0.036 fem- Hamburg’s St. Michael’s church on Mu- be explained by the measurement accu- tometers, or 4 percent. That doesn’t nich’s main square, Marienplatz. racies of the two methods. And to keep sound like much, but in the context of To explain the great difference be- the tension from subsiding, Randolf the given uncertainty of the measuring tween the two measurements, physi- Pohl and his colleagues recently refined accuracy, it is actually a lot. The dis- cists initially scoured the two methods their measurement result further, thus crepancy corresponds to seven com- for systematic errors that might skew making it clear: more precise analyses bined error bars and is thus significant- the result. “It could, of course, be the don’t make the problem go away. ly larger than one would expect if case that we overlooked such an error, For years, Randolf Pohl and his col- different experiments merely yielded but we searched very carefully and leagues thought that their measuring slightly different results in the context found nothing,” says Randolf Pohl, instrument wasn’t sufficiently accu- of statistical fluctuations. whose team took a new approach to rate: they first conducted an experi- measuring the proton radius some 15 ment in 2003 to determine the size of NO SYSTEMATIC ERROR years ago, and published the first result a proton. However, they didn’t discov- WAS FOUND of this work in 2010. er the signal that would give them in- The researchers used laser spectros- formation about it. “But this wasn’t Just how great the difference is between copy to determine how high the ener- due to the inaccuracy of our method, the results and uncertainties of the two gy of a photon has to be to transport an but rather to the fact that we hadn’t different methods of measuring the exotic hydrogen atom from one special expected such a large deviation,” says proton radius can be illustrated by energy state to another. The energy of Randolf Pohl. The researchers had se- transferring them to a map of Germa- some of these states depends on the lected too small a window for their ny. Suppose one were to put the result proton radius, and that of others measurements. obtained by Randolf Pohl’s team in the doesn’t. If the atom is taken from one According to the latest measure- center of Munich, and the competing state that appears to be sensitive to the ments by Pohl’s team, the charge radi- measurement in the center of Ham- proton radius to one that is not sensi- us of the proton is 0.84087 femtome- burg. Then the uncertainty of the Mu- tive to it, then the radius can be calcu- ters (one femtometer is a millionth of a nich value would correspond to the dis- lated. However, this requires physicists millionth of a millimeter) and the mea- tance between the two Munich neigh- to know all the other effects that influ- suring uncertainty here is just ± 0.00039 borhoods Pasing and Trudering. The ence the position of the states. femtometers. With the previously com- Hamburg measurement, in contrast, In ordinary hydrogen, where one mon measuring method, two indepen- would be so imprecise that the actual electron whizzes around the proton, dent groups recently determined that value might very probably even lie the influence of the proton radius is the charge radius must be 0.879 ± 0.009 somewhere between Flensburg and Ha- very small because the lightweight elec- left: Final preparations for the measurement: Randolf Pohl calibrates the apparatus through which muons are directed into a vessel containing hydrogen. A superconducting magnet in the silver cylinder produces the strong magnetic field required for this. right: The green light produces intense red light in a titanium-sapphire crystal. This is subsequently converted to invisible infrared light and used to perform spectroscopy of muonic hydrogen. Photos: MPI of Quantum Optics

48 MaxPlanckResearch 3 | 13 Graphic: MPI of Quantum Optics/CREMA Collaboration are around200timesheavier. a negativechargebut electrons, carry periments, aswell,becausemuons, like measuring theproton,andfor otherex- pays off:muonichydrogen is idealfor only onemicrosecond.But thehaste they needfortheirexperiments onic hydrogenremainsinthestate reveal theenergiesofstates,asmu- pace withtheirlaserexperimentsthat form muonichydrogenatoms. molecules, displacetheirelectronsand Some muonsarecapturedbyhydrogen particles. halts theexoticelementary sel containinghydrogengas,which searchers directthemuonsintoaves- erator. Usingmagneticfields,there- shot atacarbondiskinparticleaccel- muons comeaboutwhenprotonsare the world’s strongestmuonbeam.The ligen, Switzerland,wheretheycanuse gen atthePaulScherrerInstituteinVil- cleus, theeffectisfargreater. rather thananelectron,orbitsthenu- element, incontrast,whichamuon, the nucleus.Inanexoticvariantof tron usuallyhangsoutfarawayfrom Now physicistshavetostepupthe Physicists producemuonichydro- Water cell Muon beam amplifier Titanium-sapphire magnet andhydrogen vessel Superconducting iklsrDisklaser Disk laser Raman cell scientists shootelectronsathydrogen tering measurements.Forthelatter, of normalhydrogenandelectronscat- mately 0.88femtometers:spectroscopy had puttheprotonradiusatapproxi- vious experimentspermitted,which in anycasemoreaccuratelythanpre- charge radiuswithgreataccuracy–or makes itpossibletodeterminethe us thanarenormalelectrons.This thus moresensitivetotheprotonradi- located closertothenucleusandare Due totheirgreatermass,muonsare some ofthepotentialsystematic errors have sincediscussed–and excluded – considered tobe.Moreover, physicists ment is,themorereliable itis ing. Andthemoreprecisea measure- mal hydrogenandtheelectron scatter- the resultsofspectroscopyonnor- more thantentimesprecise onic hydrogenisthefactthattheyare What favorsthemeasurementsonmu- DISREGARD EXOTIC SPECIMENS THE MUONEXPERIMENTS flected bytheprotons. howtheyarede- nuclei andobserve Diode laser Pion beam Cyclotron trap laser Titanium-sapphire Titanium-sapphire oscillator Proton beam is found,onecanimaginethe magnet- describes thespaceinwhich thecharge the samesize.Whilecharge radius magnetic radiusneedn’t necessarilybe rotating aboutitself.Theelectrical and that thechargedparticleis constantly of theproton–thatis,fromfact distributed. Thisresultsfromthespin region inwhichthemagnetizationis us. Themagneticradiusindicatesthe the proton,butalsomagneticradi- measure notonlythechargeradiusof spectroscopy ofmuonichydrogento with theMaxPlanckphysicistsused permit examination. don’t remainstablelongenoughto these exoticentitiesarecreated,they basis forthissuspicion:evenifbothof lations thathavesinceunderminedthe physicists fromParisperformedcalcu- two protonsandamuon.However, an electron,ormoleculescomposedof drogen ionsthatcontainamuonand negativelychargedmuonichy- served might, withoutrealizingit,haveob- for example,whetherPohl’s team drogen. Someskepticshadspeculated, of theexperimentswithmuonichy- the Raman cell, the laser’s pulses are are pulses laser’s the cell, Raman the in Finally, laser. a titanium-sapphire pump to inorder isdoubled frequency Their pulses. light intense emit to laser than 200 nanoseconds, causes the disk inless that, asignal produce muons with energy. lasers disk ytterbium-YAG parallel two muon beam. There, diode lasers pump the from isshielded which hut,” “laser duce this beam a few meters away pro- in the researchers The vessel. hydrogen the into isdirected beam laser intense extremely The room. living a spacious magnet. inasuperconducting located is which vessel, hydrogen the to channel acurved through directed and down slowed are muons The trap). (cyclotron tle bot- inamagnetic muons into decay that disk,a carbon producing negative pions strikes beam Aproton design: Experiment one microsecond. than less lasts process entire The ined. atom in the hydrogen vessel to be exam- hydrogen muonic the allow to color appropriate the of light into converted Upon entering the hydrogen vessel, vessel, hydrogen the entering Upon fill would apparatus the of part This In themeantime,teamworking 3 | 13 MaxPlanckResearch MaxPlanckResearch 49 50 right: The magnetcontainsthedumbbell-shapedhydrogen vessel, flankedabove andbelowby detectorsandelectronics. left: The muonspassthrough channeltoastrong thecurved magnet(leftofcenter). magnetic radiusisn’t causingsucha netic radius,aswell. than electronscatteringforthemag- er theirmethodyieldsadifferentvalue the researchers beable todecidewheth- increase theaccuracy.” Onlythenwill will becomeinterestingwhenwelater the firstplace,”saysRandolfPohl.“It spectroscopy ofmuonichydrogenin determined themagneticradiususing “What isimportantthatweactually values ofthechargeradiusfitwithit. imprecise thatthetwocontroversial tometers. Thisvalueiscurrentlystillso searchers nowobtain 0.87±0.06fem- ton itsmagneticmoment. culating currentsflowthatgiveapro- ic radiusastheregioninwhichcir- PHYSICS & ASTRONOMY for this great discrepancy. great this for found been yet has explanation No scattering. all measurements obtained with electron of average the than lower 4percent are ters, femtome- 0.84 at values, their but bars, error obtained in 2010 and 2013 have (μp) much hydrogen smaller muonic for results spectroscopic measurements of normal hydrogen. The spectroscopic the of value average the with well very fits value This lines). (horizontal bars large error with relatively 0.88 femtometers, about at nucleus ahydrogen of radius charge the US establish the and (Germany) Mainz with the elastic electron scattering from measurements New puzzle: radius proton The MaxPlanckResearch MaxPlanckResearch In anycase,forthetimebeing, For themagneticradius,re- 3 | 13 _Proton Radius other atomswithmoreelectrons,they scribe bestinmathematicalterms.In is, infact,theatomthattheycande- of justoneprotonandelectron,it know themostabout.Sinceitconsists drogen istheonequantumphysicists piquant because,ofalltheelements,hy- atoms inhydrogen.Thisisparticularly mental gapsinourunderstandingofthe measurements couldindicatefunda- one considersthatthecontradictory gether raisesfundamentalquestions. put theradiusinadifferentrangealto- periments. However, thefactthatthey radius asindicatedbylessaccurateex- ther narrowedtherangeofcharge issue ifthenewmeasurementshadfur- Even thelatterwouldn’t havebeenan great stir–unlikethechargeradius. 0.83 0.84 0.85 0.86 0.87 0.9 0.89 0.88 The story takes on added zest when takesonaddedzestwhen The story μp μp 2010 2013 4 % discrepancy have torelyonapproximations.That’s theories, andalsowhymanygroups why theyusehydrogentotesttheir substantiated. Still,itseemed,atfirst, is consideredtobeexceptionallywell ample, atoms–interactwithlight,and QED describeshowmatter–so,forex- AS-YET-UNKNOWN PHYSICS OF ROOM FOR PLENTY (QED), forinstance. discoveries –quantumelectrodynamics have continuallymadefundamental bition butbecause,indoingso,they They don’t do thisoutofasportingam- increasingly precisemeasurements. atom moreandaccuratelywith peting toseewhocancharacterizethis around theworldareconstantlycom- Proton charge radius [femtometers] Electron scattering Average value spectroscopy Hydrogen USA Electron scattering, Mainz Electron scattering,

Photos and graphic: MPI of Quantum Optics/CREMA Collaboration Photo: Axel Griesch decreases moreslowly?Or has acusp oftheproton. Butwhatifit boundary proximately exponentially atthe sumed thatthechargedecreases ap- the proton.Thepreviousmodels as- cept ofhowthechargeisdistributed in icists, forinstance,questionedthecon- such explanations.Somenuclearphys- tionships. Thereisplentyofroomfor point toas-yet-unknownphysicalrela- hope thattheirmeasurementswill bility, RandolfPohlandhiscolleagues since beennearlydiscardedasapossi- overlooked uptonow.” likely thatsuchalargeeffecthasbeen Randolf Pohl.“Anditisextremelyun- large,”says effect wouldhavetobevery than inelectronichydrogen.“Butthis impact ontheenergystatesinmuonic nore aneffectthathasamuchstronger muonic hydrogenifQEDweretoig- differing protonradiiinelectronicand ofthe be possibletoresolvethemystery lenge thistheory. Specifically, itwould ments oftheprotonradiusmightchal- as ifthenew, moreprecisemeasure- toredof thetitanium-sapphire light. laserisconverted whichisenclosedintherectangular deviceinthecenterofimage,green Inthecrystal, light Light colorconverter: Even ifashortcomingofQEDhas DISTORTS THE PROTON AN ELECTRICALCHARGE proximately exponentialdecrease. the establishedassumptionofanap- reliably–andconfirmed bution very electrons characterizethechargedistri- ton puzzle.Experimentswithscattered tions, buttheyhaven’t solvedthepro- somewhere? Thesearelegitimateques- in muonichydrogen. larization, thiswillbemost noticeable ly don’t correctlyaccountforthepo- If thecorrespondingformulas current- from theirlaserspectroscopic analyses. when calculatingtheproton radius pulls onit.Physicistsfactorthisin more theheavierparticleisthat cloud oftheproton,anddoessoall electrical chargedistortsthe the muon,”saysRandolfPohl: it seesthenegativeelectricalchargeof ently thanpreviouslyassumedwhen “Perhaps theprotonispolarizeddiffer- quite populartakesasimilardirection. Another suggestionthatiscurrently PHYSIK & ASTRONOMIEPHYSIK & aware oftheparticleanddon’t know than assumed.Butifphysicists aren’t about atcloserrangetothe nucleus Randolf Pohl.Themuonthen moves to theprotonthanweassume,” says for themuonbeingmoretightly bound as-yet-unknown particleisresponsible dard model:“It’s conceivablethatan erally contributetoexpandingthestan- the mysterioussubstance,itcouldgen- directly beofanyhelpinthesearch for been identifiedeither. noticeable andthereforehasn’t yet practicallyun- of starsbutisotherwise ter, whichacceleratesthemovements it answerthequestionaboutdarkmat- doesn’t explaingravitation.Nordoes some weaknesses.Forinstance,it well,butitalsohas very observations forces between them.Itcoversmost particlesandmostofthe elementary model ofparticlephysicsdescribesall el,” saysRandolfPohl.Thestandard to aphysicsbeyondthestandardmod- however, isifourresultweretopoint “What wouldbemostinteresting, Although theshrunkenprotoncan’t 3 | 13 MaxPlanckResearch MaxPlanckResearch _Protonenradius 51 PHYSICS & ASTRONOMY_Proton Radius

Searching for the decisive data: Randolf Pohl (left) and Marc Diepold discuss the results of a measurement campaign that acquired enormous amounts of data, of which, however, only a fraction is based on signals from muonic hydrogen.

low them to test once again whether the QED models are actually complete. “Helium is better suited for this, because it is easier to observe weaker QED effects in heavier nuclei,” explains Pohl. For another, the measurements on muonic helium are better suited for comparison with the results of electron scattering. “The electron scattering data for helium is more precise,” says Pohl. A new elementary particle would also have to be noticeable in muonic helium. Then, in helium, there would that it forces the muon closer to the In the meantime, Randolf Pohl and his likewise have to be a discrepancy be- nucleus, the proton of muonic hydro- team are also continuing their experi- tween the two different measure- gen will appear to them to be smaller ments with muonic atoms at the Paul ments of its nuclei. Otherwise, the than that of electronic hydrogen. As Scherrer Institute. The researchers will door to a physics beyond the standard attractive as Pohl finds the thought of soon perform spectroscopy of muonic model would close again before it re- having found a door to the world be- helium ions. For one thing, this will al- ally even opened. yond the standard model, he remains realistic: “That isn’t very likely,” says the researcher. TO THE POINT

RYDBERG CONSTANT MUST BE ● An international team working with researchers from the Max Planck Institute DETERMINED MORE ACCURATELY of Quantum Optics measured the charge radius of the proton very precisely for the first time. To do so, the scientists performed spectroscopy of the energy states of muonic hydrogen. While theoretical physicists are busy ● The results of the measurements on muonic hydrogen differ significantly from formulating possible explanations, the the results of the spectroscopy of normal hydrogen and the results of electron experimenters are not sitting idly scattering, the method that was previously commonly used to determine the about. “A more precise determination proton radius – indicating that the proton is smaller than had been thought. of the Rydberg constant would allow us ● The difference between the results of the two measuring methods could indicate to verify whether our measurement is that the picture that physicists had of the proton is incomplete. But it could also correct,” explains Pohl. Physicists use point to an as-yet-unknown elementary particle. this constant to calculate the different energy levels of atoms and molecules. GLOSSARY If Randolf Pohl and his colleagues are right about the smaller proton radius, Electron scattering: When an electron is fired at a positive charge, such as a nucleus, then also this constant would change – the positive charge deflects it. Electron scattering uses this to advantage: the distribution of the charge, and thus its radius, can be deduced from an analysis of the electron paths. and perhaps a few other physical con- stants, as well. No other physical con- Charge radius: Quantum particles aren’t as precisely delimited as billiard balls – their boundaries are rather fuzzy. The same is true for the charge radius of the proton. It is stant is known as precisely as the defined as the radius within which about two-thirds of the positive charge of the proton Rydberg constant. If one could use elec- is concentrated. tronic hydrogen to determine it even Muon: This elementary particle has the same negative charge as an electron. It can more precisely, then it would be possi- thus replace an electron in hydrogen, or also in a helium ion. But since a muon is about ble to indirectly verify the result of the 200 times as heavy as an electron, it comes much closer to the nucleus, and certain proton measurement. Several research- effects more readily come to light in muonic atoms. ers around the world are working on Quantum electrodynamics (QED): This theory describes how matter – atoms, for this, including a group at the Max example – interacts with light. It is considered to be exceptionally well substantiated.

Planck Institute of Quantum Optics. Photo: Axel Griesch

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