Measurement of the charged pion mass using X-ray spectroscopy of exotic atoms

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Measurement of the charged pion mass using X-ray spectroscopy of exotic atoms

Martino Trassinelli, D. F. Anagnostopoulos, G. Borchert, A. Dax, J.P. Egger, D. Gotta, M. Hennebach, P. Indelicato, Y-W Liu, B. Manil, et al.

To cite this version:

Martino Trassinelli, D. F. Anagnostopoulos, G. Borchert, A. Dax, J.P. Egger, et al.. Measurement of

the charged pion mass using X-ray spectroscopy of exotic atoms. Physics Letters B, Elsevier, 2016,

759, pp.583-588. �10.1016/j.physletb.2016.06.025�. �hal-01314041v2�

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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Measurement of the charged pion mass using X-ray spectroscopy of exotic atoms

M. Trassinelli^a^,^∗,D.F. Anagnostopoulos^b, G. Borchert^c^,¹, A. Dax^d,J.-P. Egger^e,D. Gotta^c, M. Hennebach^c^,², P. Indelicato^f, Y.-W. Liu^d^,³, B. Manil^f^,⁴,N. Nelms^g^,⁵, L.M. Simons^d, A. Wells^g

aInstitutdesNanoSciencesdeParis,CNRS-UMR7588,SorbonneUniversités,UPMCUniv. Paris06,75005,Paris,France bDept.ofMaterialsScienceandEngineering,UniversityofIoannina,GR-45110Ioannina,Greece

cInstitutfürKernphysik,ForschungszentrumJülichGmbH,D-52425Jülich,Germany dLaboratoryforParticlePhysics,PaulScherrerInstitut,CH5232-VilligenPSI,Switzerland eInstitutdePhysiquedel’UniversitédeNeuchâtel,CH-2000Neuchâtel,Switzerland

fLaboratoireKastlerBrossel,UPMC-SorbonneUniversités,CNRS,ENS-PSLResearchUniversity,CollegedeFrance,4,placeJussieu,75005Paris,France gDept.ofPhysicsandAstronomy,UniversityofLeicester,LeicesterLEI7RH,England,UnitedKingdom

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received10May2016

Receivedinrevisedform10June2016 Accepted12June2016

Availableonline15June2016 Editor:V.Metag

Keywords:

Chargedpionmass Exoticatoms X-rayspectroscopy

The5g−⁴^f transitionsinpionicnitrogenandmuonicoxygenweremeasuredsimultaneouslybyusinga gaseousnitrogen–oxygenmixtureat1.4 bar.Duetothepreciseknowledgeofthemuonmassthemuonic lineprovidestheenergycalibrationfor thepionictransition.Avalue of(139.57077±0.00018) MeV/c² (±^{1.3 ppm)}îs ^derived ^for^the ^mass ôf^the ^negatively^charged ^pion,^whichîs ^{4.2 ppm} ^larger^than^the presentworldaverage.

©²⁰¹⁶^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

X-ray spectroscopy of exotic atoms allows the determination of the mass of captured negatively charged particle like muons, pions,and antiprotonsfrom the energies of the characteristic X- radiation.X-raytransitionsoccurduring thede-excitationcascade oftheexoticatomwhichisformedatprincipalquantumnumbers ofn≈^{16 in} ^the^case^of^pions^[1,2].^The ^precisedeterminationof the pion mass requires the use ofX-ray lines which are not affected either by strong-interaction effects nor by collisions with surroundingatoms.Such conditionsarefoundintheintermediate partofthecascadeforexoticatomsformedingases.

The most recent X-ray measurements were performed at the Paul Scherrer Institute (PSI) and used either a DuMond [3–5] or

* Correspondingauthor.

E-mailaddress:martino.trassinelli@insp.jussieu.fr(M. Trassinelli).

1 Presentaddress:TUMunich,D-85747Garching,Germany.

2 Presentaddress:DAHERNUCLEARTECHNOLOGIESGmbH,D-63457Hanau,Ger- many.

3 Presentaddress:Phys.Depart.,NationalTsingHuaUniv.,Hsinchu300,Taiwan.

4 Presentaddress:Lab.dePhysiquedesLasers,UniversitéParis13,SorbonneParis Cité,CNRS,France.

5 Presentaddress:ESA-ESTEC,POBox299,2200AG,Noordwijk,TheNetherlands.

a Johann-type crystal spectrometer [6]. In the case of the Du- Mond spectrometer, theenergy calibrationforthe pionic magne- sium (4f −^3d) transition was performed with a nuclear γ-ray, whilefortheJohannset-upKα ﬂuorescenceradiationfromcopper wasusedtodeterminetheenergyofthepionicnitrogen(5g−⁴^f) transition.

In the πMg experiment, electron refilling is unavoidable due to the use of a solid state target. Different assumptions on the Kelectron population lead todifferencesin thepion massup to 16 ppm [5].The previous πNexperiment, aswell asthe present one, useda nitrogengastarget atpressures around 1 bar, where electron refillingis unlikely [7,8], i.e.thede-excitation cascadeis decoupled from the environment. The absence of refilling ofthe electrons ejectedalreadyduring theupperpartofthecascadeby internalAugereffectmanifestsintheappearanceofX-raylinesat n≥^5,^whichôtherwise^would^be^convertedîntoÂugertransitions [9–11].Furthermore,alargeDopplerbroadeningwasmeasuredfor (5−⁴)transitions[12].ItoriginatesfromCoulombexplosiondur- ing theformationprocess oftheexoticatom withmoleculesand indicates that the velocity at the time of X-ray emission is es- sentiallyunchangedsince thebreakup ofthemolecule. Thus, the http://dx.doi.org/10.1016/j.physletb.2016.06.025

0370-2693/©²⁰¹⁶^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

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584 M. Trassinelli et al. / Physics Letters B 759 (2016) 583–588

Table 1

CalculatedcontributionstothetotalQEDtransitionenergyofμOandπN(5g−^4f)lines(ineV)[17].Forthepionictransition,theworldaveragepionmassvalueasgiven in[14]isused.TheμOlineconstitutesatripletduetothemuonspin.ThetotaluncertaintyoftheQEDcalculation(excludingtheuncertaintyofthepionmass)is±1 meV.

Transition μ¹⁶O π¹⁴N

(5g9/2−^4f7/2) (5g7/2−^4f7/2) (5g7/2−⁴^f5/2) (5g−^4f⁾

Coulomb 4022.8625 4022.6188 4023.4124 4054.1180

self energy −⁰.0028 −⁰.0013 −⁰.0013 −⁰.0001

vac. pol. (Uehling) 0.8800 0.8800 0.8807 1.2485

vac. pol. Wichman–Kroll −⁰.0007 −⁰.0007 −⁰.0007 −⁰.0007

vac. pol. two-loop Uehling 0.0003 0.0004 0.0004 0.0008

vac. pol. Källén–Sabry 0.0084 0.0084 0.0084 0.0116

relativistic recoil 0.0025 0.0025 0.0025 0.0028

hyperﬁne structure − − − −⁰.0008

Total 4023.7502 4023.5079 4024.2983 4055.3801

absenceofscreeningeffectsfromremainingelectronsintheinter- mediatepartoftheatomiccascadeleadstoaunique solutionfor themass[6].Inaddition,indilutetargetsthelineintensityisal- readymostlycollected inthecirculartransitions(n,=ⁿ−¹)→ (n−¹,=ⁿ−²),wherecorrectionsowingtothehadronicpoten- tialarestilltiny.

Fromthe πNexperimentmπ⁻=(139.57071±⁰.00053)MeV/c² [6]is obtainedwhich suggests that both K electrons are present when the πMg(4f −^3d) transition occurs (solution B: mπ⁻ = (139.56995±⁰.00035)MeV/c² [5]). This is corroborated by the factthattheresult,assuming1 Kelectrononly(solutionA:mπ⁻= (139.56782±⁰.00037)MeV/c²), is in conﬂict withthe measurement of the muon momentum for charged pion decay at rest

π⁺→μ⁺νμ [13].ForsolutionA,themass squaredofthemuon neutrinobecomesnegativebysixstandarddeviations,whereasthe average of solution B and the result of the πN(5g−⁴^f) measurement(mπ⁻ =(139.57018±⁰.00035)MeV/c² [14]) yields the upperlimitmμν<190 keV/c² (90%c.l.).

Theexperimentdescribedhereresumesthestrategyofthegas target, but exploits (i) the high precision of 0.033 ppm for the massofthepositivelychargedmuonbeingmμ⁺=(105.6583715± 0.0000035)MeV/c²[14]and(ii)theuniquefeaturethatin πNand

μO transition energies almost coincide (Table 1). Using a N2/O2 gasmixtureinthetargetallowsthesimultaneousmeasurementof

πNand μOlines,withthemuonictransitionservingasanon-line calibration. Hence, systematic shifts during the unavoidably long measuringperiodsareminimised.

Inthecaseofnitrogenandoxygen, (6h−^5g),(5g−⁴^f),and (4f −^3d) transitions meet the operating conditions of the crys- talspectrometer. Finally,the(5g−⁴^f)transitionwaschosen because:(i)forthe(6h−^5g)lines(2.2 keV)absorptioninthetarget gas itself and windows significantly reduces the count rate and (ii) the 3d-level energy in πN requires a substantial correction because of the strong interaction. Electromagnetic transition energies(Tables 1 and2)werecalculatedusingamulti-configuration Dirac–Fockapproach[15,16]toaprecisionof±^{1 meV and}înclude relativisticandquantumelectrodynamicscontribution(relativistic recoil, self-energy, vacuum polarisation) as well as the hyperfine structureofpionicnitrogen[17].

Energyshiftsduetonuclearﬁnitesizearefoundtobeassmall as 4 aeV and 2 peV for the 5g and 4f levels in πN. Values for nuclearmasses,radii,andmomentsweretakenfromrecentcom- pilations [18–20]. The strong-interaction shifts of the πN levels wereestimatedfrominterpolatingthemeasuredhadronic2p-level shiftsin πCand πO[21]andbyusingscalingrelationsbasedon theoverlapofnucleusandahydrogen-likewave functionforthe pionorbit(seeTable 3).Detailsonthecalculationofthetransition energiesmaybefoundelsewhere[22].

The measurement was performed at the high-intensity pion beamlineπE5of thePaul Scherrer Institute(PSI)using aset-up

Table 2

TransitionenergiesEQED [17]andBragganglesBoftheμOandπNlinesused inthefittothe spectrum.Therelativeintensitieswithinthefinestructuremul- tiplets ofμO (FS int.)havebeen fixed inthe fit tothe statistical weight.The BraggangleincludestheindexofrefractionshiftcalculatedwiththecodeXOP[32].

Fortwicethelatticedistance2d=0.768062286(13)nm isassumedatatempera- tureof22.5^◦C[34].Theconversionconstantusedishc=1.239841930(28)nm keV [14].The πN(5g−⁴^f)andπN(5f−^4d)transitionenergiesincludethestrong- interactionshift(seeTable 3).

Transition FS int. EQED/eV B

μ¹⁶O(5g7/2−4f7/2) 1 4023.5079 53^◦2151.48 μ¹⁶O(5g9/2−4f7/2) 35 4023.7503 53^◦2134.77 μ¹⁶O(5g7/2−^4f5/2) 27 4024.2984 53^◦2057.01 μ¹⁶O(5f5/2−^4d⁵/2) 1 4025.3956 53^◦1941.47 μ¹⁶O(5f7/2−4d5/2) 20 4025.8031 53^◦1913.44 μ¹⁶O(5f5/2−^4d3/2) 14 4026.9922 53^◦1751.70 μ¹⁶O(5d5/2−^4p3/2) 9 4028.5625 53^◦163.90 μ¹⁶O(5d3/2−4p1/2) 5 4033.5273 53^◦1024.10 μ¹⁸O(5g7/2−4f7/2) 1 4026.6692 53^◦1813.90 μ¹⁸O(5g9/2−^4f7/2) 35 4026.9132 53^◦1757.13 μ¹⁸O(5g7/2−^4f⁵/2) 27 4027.4642 53^◦1719.28

π¹⁴N(5g−4f) 4055.3802 52^◦4546.76

π¹⁴N(5f−^4d) 4057.6984 52^◦4311.81

π¹⁴N(5d−^4p) QED only 4061.9460 52^◦3828.76

π¹⁵N(5g−4f) 4058.2394 52^◦4235.67

π¹⁵N(5f−^4d) 4060.5605 52^◦400.95

similar to the one used by Lenz et al.[6]. Major improvements are: (i) The use ofcyclotron trap II [23] having a larger gap be- tween the magnet coils yielding a substantially increased muon stop rate, (ii) a Bragg crystalofsuperiorquality and(iii)a large- areaX-raydetectorinordertosimultaneouslycoverthereﬂections of themuonicandpionictransitions (seeFig. 1).In addition,the averageprotoncurrentoftheacceleratorwasabout1.4 mA,which is40%higherthaninthepreviousexperiment.

TheN2/O2gasmixturewasenclosedinacylindricaltargetcell placedatthecentreofthecyclotrontrap.Thecellwallwasmade ofa50 μmthick Kapton^® foil.Towardsthecrystalspectrometer a circular7.5 μmMylar^® windowwasusedsupportedby astainless steelhoneycombstructurewithafreeareaof90%.Thetargetwas operatedat1.4 barandroomtemperature.

The muons used originate from the decay of slow pions in- sidethecyclotrontrap,becausethestopdensityformuonsatthe high-intensity pion beam is still superior to the one at a dedi- catedmuonchannel.Forthesimultaneousmeasurementcompara- blecountratesarerequiredforthe πNandthe μOline.Thiswas achievedwithaN₂/O₂ mixtureof10%/90%byadaptingthesetof polyethylene degraders inside the magnetgap and optimised by

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Table 3

Correctionstothemeasuredangledifferencebetweentheπ¹⁴N(5g−⁴^f)andtheμ¹⁶O(5g9/2−^4f⁷/2)transitionsandassociateduncertainties.A1 ppmchangeinthepion masscorrespondsto4.055 meVintransitionenergy,to0.27arcsecindiffractionangle,ortoadisplacementof3.2 μminthedetectorplane.Contributionstothemass uncertaintyfromlatticeandconversionconstantcancelinleadingorderbecausethemeasurementprincipleisbasedontheangulardifference.Formoredetailsseetext.

Typeofuncertainty μO

/ arcsec

πN / arcsec

Total / arcsec

Uncertainty /ppb

index of refraction shift 13.22 12.94 −⁰.28 ±²⁰

silicon lattice constant ±2

bending correction 14.01 13.71 0.30 ±²⁰

penetration depth correction −⁰.07 −⁰.07 0 ±⁴

focal length ±670

temperature correction ±30

CCD alignment ±³⁴⁰

pixel distance ±¹²⁰

alignment of detector normal ₋⁺₃₀⁰

detector height offset ₋⁺₃₅⁰

shape of target window ±¹⁰⁰

shape of reﬂection ±225

individual curvature correction ±¹⁵⁰

response function and Doppler broadening ⁺₋²⁹⁰₃₅₀

line pattern modelling ⁺₋¹⁹⁰₂₉₀

ﬁt interval ±15

muon mass ±³⁰

QED energy ±³⁵⁰

conversion constanthc ±2

4f strong interaction 45 μeV 0.003 −⁰.003 ±¹⁰

5gstrong interaction 0.2 μeV 0.000 0.000 ±⁰

K electron screening ±0

total systematic error ₋⁺₁₀₀₀⁹⁶⁰

statistical error ±⁸²⁰

meansofanX-raymeasurementusingaSi(Li) semiconductorde- tector.

ThecrystalspectrometerissetupinJohanngeometry[24]us- ingasphericallybentBraggcrystalandoptimisedtotheneedsof exotic-atom X-rayspectroscopy [25]. Such a conﬁguration allows the simultaneous measurement of two different energies within anenergyinterval,thelimitsofwhicharegivenby theextension ofthetargetinthedirectionofdispersionandcorrespondinglyby thesizethe detector.Sphericalbendingleads toa partialvertical focusing[26]whichincreasesthecountrate.

The Bragg crystal was made from a silicon crystal disk of 290 μm thickness and of a diameter of 100 mm. The disk is at- tached to a high-quality polished glass lens defining a spherical segment.Theaverageradiusofcurvatureofthecrystalsurfacewas measured to Rc=(2981.31±⁰.33)mm by sampling 500 points atthe surface witha mechanicalprecision sensor (performed by CarlZeissAG,D-73447Oberkochen,Germany). Anupperlimit for thecutangle(angle betweencrystalsurface andreflecting lattice planes) was determined in a dedicated measurement to be 120 secondsofarc[27].Hence,thefocalcondition correspondstothe symmetricBraggcasebeingRc·^sinB.Themeasurementusesthe secondorderreflectionatthe(110)planes.Analuminiumaperture of90 mm diametercovered theboundaryregionoftheSidiskin ordertoavoidedgeeffects.Forsourcegeometryasgivenhere,the overallefficiencyofthecrystalset-up is≈⁵·¹⁰⁻⁸^.Âbout^85%ôf thereflected intensityiscovered bythe sensitivearea ofthe detector.

The detectorwith a total sensitive area of about 48×^{72 mm}² (width×^height) ^was ^built ûp ^by â ²×³ ârray ôf charge-coupled

devices (CCDs) of 24 mm×^{24 mm} ⁽⁶⁰⁰×⁶⁰⁰ ^pixels) ^with ^frame storageoption[28].Havingadepletiondepthofabout30 μmthese CCDsreachtheirmaximumindetectioneﬃciencyofalmost90%at 4 keV.The detectorsurface isorientedperpendiculartothedirec- tion ofthe incoming X-rays.Excellent background conditionsare achieved (i) by using an especially tailoredconcrete shielding of atleast 1 mthickness betweenthe X-raydetectorandthe target region and (ii)by exploitingthe different pixeltopology oflow- energyX-raysandbackgroundevents,whicharemainlycausedby neutroninducedhighenergeticnuclear γ rays[2,6].

TheBraggangleforthe πN(5g−⁴^f)transitionandtherebyits energyisdeterminedfromthepositiondifferencetothe μO(5g− 4f)line.The positionsaredeterminedfromtheprojection ofthe patternon theCCD ontothe directionofdispersion aftercorrec- tion for curvature by means of a parabola ﬁt (Fig. 1). The main transitions μO(5g−⁴^f)and πN(5g−⁴^f)areseparatedbyabout 25 mm.

About9000eventsforeach elementwere collectedineach of the(5g−⁴^f)transitionsduring5 weeksofdatataking.Thecount ratesforthe πNand μOtransitionswereabout15eventsperhour each. Onlya commonsmalldrift wasobserved forthe lineposi- tions oflessthan onepixel intotal.Because ofthesimultaneous measurement the position difference is not affected. Bragg angle dependentcorrectionsaresmallbecausetheleadingordercancels insuchadifferencemeasurementperformedinthesameorderof reﬂection.

In fourthorder, the Bragg anglesof the Cu Kα linesare very closetotheonesofthe μO(5g−⁴^f)transitions.Therefore,inaddition Cu X-rays were repeatedly recorded asa stability monitor