Charged Kaon Mass Measurement using the Cherenkov Effect

0.96 MB·English

by  The MIPP Collaboration

ChargedKaonMassMeasurementusingtheCherenkovEffect
N.Graff A.Lebedevd R.J.Abramsk,n U.Akgunj G.Aydinj W.Bakerc P.D.Barnes,Jr. g
0 T.Bergfeld(cid:96) L.Beverlyc A.Bujakh D.Careyc C.Dukesm F.Duruj G.J.Feldmand A.Godley(cid:96)
1
0 E.Gu¨lmezj,o Y.O.Gu¨naydınj H.R.Gustafsonk L.Gutayh E.Hartounig P.Hanlete S.Hansenc
2M.HeffnergC.JohnstonecD.KaplaneO.KamaeveJ.KilmercJ.KlaygM.KostincD.LangegJ.Ling(cid:96)

n M.J.Longok L.C.Lum C.Materniakm M.D.Messierf H.Meyerc,p D.E.Millerh S.R.Mishra(cid:96)
a
K.Nelsonm T.Nigmanovk A.Normanm Y.Onelj J.M.Paleyf H.K.Parkk A.Penzoj R.J.Petersoni
J
R.Rajac D.Rajaramk D.Ratnikove C.Rosenfeld(cid:96) H.Rubine S.Seund N.Solomeye,p R.Soltzg
4
E.Swallowb R.Schmittc P.Subbaraok Y.Torune T.E.Topec K.Wilson(cid:96) D.Wrightg K.Wu(cid:96)

]
x aBrookhavenNationalLaboratory,UptonNY11973
e bElmhurstCollege,Elmhurst,IL60126
- cFermiNationalAcceleratorLaboratory,Batavia,IL60510
p dHarvardUniversity,Cambridge,MA02138
e eIllinoisInstituteofTechnology,Chicago,IL60616
h
fIndianaUniversity,Bloomington,IN47403
[
gLawrenceLivermoreNationalLaboratory,Livermore,CA94550
2 hPurdueUniversty,WestLafayette,IN47907
v iUniversityofColorado,Boulder,CO80309
1 jUniversityofIowa,IowaCity,IA52242
7 kUniversityofMichigan,AnnArbor,MI48109
9 (cid:96)UniversityofSouthCarolina,Columbia,SC29201
0 mUniversityofVirginia,Charlottesville,VA22904
. nCurrentlyatMuons,Inc.,Batavia,IL60510
9 oAlsoatBogaziciUniversity,Istanbul,Turkey
0 pCurrentlyatWichitaStateUniversity,Wichita,KS67260
9
0
:
v
iAbstract
X
rThetwomostrecentandprecisemeasurementsofthechargedkaonmassuseX-raysfromkaonicatomsandreportuncertaintiesof
a
14ppmand22ppmyetdifferfromeachotherby122ppm.Wedescribethepossibilityofanindependentmassmeasurementusing
the measurement of Cherenkov light from a narrow-band beam of kaons, pions, and protons. This technique was demonstrated
usingdatatakenopportunisticallybytheMainInjectorParticleProductionexperimentatFermiNationalAcceleratorLaboratory
which recorded beams of protons, kaons, and pions ranging in momentum from +37 GeV/c to +63 GeV/c. The measured value
is491.3±1.7MeV/c2,whichiswithin1.4σ oftheworldaverage.Animprovementoftwoordersofmagnitudeinprecisionwould
makethistechniqueusefulforresolvingtheambiguityintheX-raydataandmaybeachievableinadedicatedexperiment.
1. Introduction X-ray energies from kaonic atoms. While these measure-
ments report uncertainties of 14 and 22 ppm they differ
The charged kaon mass is an important input in deter- by 122 ppm (4.6σ). In this article we explore one possibil-
mining the CKM matrix element V from measurements ity to resolve this discrepancy using an independent tech-
us
of the branching ratio of K+ → π0e+ν. The value of the nique for measuring the charged kaon mass based on the
chargedkaonmassreportedbytheParticleDataGroupis Cherenkoveffect.Thewellknownpionandprotonmasses
493.677MeV/c2withanuncertaintyof26partspermillion are used as references. The technique is demonstrated us-
(ppm)[1].Thisvalueisaweightedaverageofsixmeasure- ing data taken opportunistically using the Ring Imaging
mentsbutisdominatedbythetwomostrecentandprecise Cherenkov (RICH) sub-detector of the Main Injector Par-
measurementsfromDenisov[2]andGall[3]whichmeasure ticleProduction(MIPP)experimentatFermilab[4].
PreprintsubmittedtoNuclearInstrumentsandMethods 4January2010
2. MeasurementConcept the differences in the Cherenkov angles are largest, while
stayingaboveprotonthreshold.
Cherenkov light is emitted when a relativistic charged In a RICH detector, the angle θ can be determined on
particle of mass m, momentum p, and speed β = atrack-by-trackbasisfromthepatternofCherenkovpho-
1/(cid:112)1+(m/p)2 travels through a radiator volume of in- tons recorded. However, the light for a single ring will be
dex of refraction n with β > 1/n. (As is customary in distributed about the central angle θ due to the variation
high energy physics we work in units in which the speed of the index of refraction of the radiator medium over the
of light, c, is 1.) Neglecting dispersive effects for the mo- wavelengths at which Cherenkov photons are produced.
ment, the light is emitted in a cone at an angle θ given by Thisgivesascontributiontotheuncertaintyintheaverage
cosθ =1/βn[5,6]whichisapproximately angleθ determinedfromasingletrackof
(cid:114) 1 1 (cid:18) 1 (cid:19)2
θ = 2(1− ) (1) σ(cid:48)2 = δ2, (7)
nβ θi Nh θin2βi n
for small angles. Now, consider two particles i and j with where δ is the amount of dispersion over the photomul-
n
identicalmomentapbutdifferentmassesm ,m andspeeds tiplier tube (PMT) wavelength acceptance and N is the
i j h
β ,β .TheywillemitCherenkovlightatanglesθ ,θ which numberofPMThitsinthering.
i j i j
arerelatedbytheexpression Inabeamline,particleswillbeacceptediftheirmomen-
tum lies in a narrow window about some central value p.
β θ2−β θ2 =2(β −β ). (2)
i i j j i j Thefinitesizeofthismomentumacceptancewindowintro-
duces an additional uncertainty in the average angle mea-
In the relativistic limit p (cid:29) m, β ≈ 1− m2. This, when
2p2 suredfromasingletrack.AveragingoverN rings,themo-
combinedwithEqn.2,gives r
mentumspreadcontributesanuncertainty
θ2−θ2 = m2j −m2i, (3) 1 (cid:34) (cid:18)m2β (cid:19)2 (cid:35)
i j p2 σ2 = σ(cid:48)2 + i i (σ /p)2 (8)
θi N θi θ np2 p
r i
where we have neglected the small difference between βθ
andθ.Iftheparticlesiandjarepions,protons,andkaons, to the measurement of θ, where σ is the spread in the
p
wehavetwoindependentangle-squareddifferencesthatcan beamparticlemomentaabouttheircentralvalue.Wetake
bemeasured the specific case of an experiment using CO as the radi-
2
ator (n = 1.00045, δ = 3×10−5) and a beam of central
m2 −m2 m2−m2 n
θ2 −θ2 = K π, and θ2 −θ2 = p π. (4) momentum 40 GeV/c with a width of σ /p=0.01. Under
π K p2 π p p2 p
these assumptions, σ values are in good agreement with
θi
Usingthese,thekaonmassisgivenby observed widths of ring radius distributions. This gives a
statisticaluncertaintyinthekaonmassof
θ2 −θ2
m2 =m2 +∆ π K, (5)
K π pπ θ2 −θ2 σ2 31.02 44.12 18.12
π p mK =0.62+0.92+ + + [ppm]2, (9)
m2 N N N
where ∆ ≡ m2 −m2. Notice that for a monochromatic K π K p
pπ p π
beam in the absence of dispersion the index of refraction where the first term results from uncertainties in the pion
n and momenta p drop out. The kaon mass can be deter- mass,thesecondfromuncertaintiesintheprotonmass,and
mined,inprinciple,throughmeasurementsofthepionand thefinalthreetermsresultfromuncertaintiesintheangles
proton masses and the Cherenkov angles of the three par- θ , θ , and θ with N , N , and N being the number
π K p π K p
ticles. The proton and pion masses are known to 0.9 ppm ofmillionsofpion,kaon,andprotonringsrecorded.Using
and 2.5 ppm respectively and will not be the limiting fac- Eqn.9wefindthattheuncertaintyisminimizedif32%of
torsintheexperiment. the data is collected using protons, 23% using pions, and
Using Eqn. 5 we can estimate the uncertainty in m2 45% using kaons. This result is only weakly dependent on
K
measuredusingthismethodas: momentumasshowninFigure1whichplotstheexpected
statisticalprecisionofthechargedkaonmassasafunction
(cid:18)θ2 −θ2 (cid:19)2 of momentum choice and total number of rings recorded.
σ2 =σ2 + π K σ2 +
m2K m2π θπ2 −θp2 ∆pπ With 10 million rings at 40 GeV/c, we expect a statistical
(cid:34) (cid:35) precisionof30ppmusingthistechnique.
∆2 ∆2
4p4 θ2 pKσ2 +θ2 σ2 +θ2 Kπσ2 . (6)
π ∆2 θπ K θK p ∆2 θp
pπ pπ 3. RICHdetectoroverview
Thefirsttwotermsareduetotheuncertaintiesinthepion
and proton masses and are small. The third term grows The RICH detector used by MIPP was built by the SE-
with momentum and suggests that it is best to conduct LEXCollaboration[7]foruseinthatexperiment.Wesum-
themeasurementataslowamomentumaspossiblewhere marize here only the most important features of the de-
2
m] 30 pion
p
p
Error [200 1200
Mass 150 M E vents -100
1
-20
-30
100 3M Events
50 10M Events 30 kaon
30M Events 20
10
m
0 c0
35 40 45 50 55 60 65
-10
Momentum [GeV/c]
-20
-30
Fig.1.Expectedstatisticaluncertaintyforkaonmassmeasurement.
30 proton
tector as deployed for the MIPP experiment and refer the
20
readerto[8–11]fordetails.
10
0
Phototube
Array -10
-20
-30
Beam -80 -60 -40 -20 c0m 20 40 60 80
BWeinadmow Rings 105
Fig.2.Schem1amticoftheRICHdetecMft =oir r1ro0[rm8]. Reconstructed 110034

ThegeometryoftheRICHcounterisshowninFigure2. 102
Thedetectorwasconstructedfromalowcarboncylindrical
10
steel vessel 10.22 m in length and 93 in. in diameter with
a wall thickness of 1 in. The ends were sealed with 1.5 in. 1
2 10 15 20 25 30 35
thickaluminumflangesthatwerecutouttoholdthinbeam
Radius [cm]
windows at each end and a photomultiplier tube holder
plate at the upstream end. The vessel was wrapped by a Fig. 3. Sample event displays of 40 GeV pion (top), kaon (second
water line carrying chilled water and 15 cm of building from top), and proton (second from bottom) rings in the RICH
counter. Small circles indicate hit PMTs. The large dashed circles
insulationtoregulatethetemperature.
show the rings reconstructed from the PMT hits. The bottom plot
A2.4m×1.2marrayof16mirrorsmountedatthedown-
isthedistributionofreconstructedringradiifor40GeV.
streamendofthecounterfocusedCherenkovlightonanar-
rayof1/2in.photomultipliertubes.Onaveragethemirrors of PMTs were used: Hamamatsu R760 and Russian made
had a radius of curvature of 1980 cm with variations less FEU60. The FEU60 tubes were coated with a wavelength
than5cmandareflectivityofmorethan85%at160nm. shifter to match the acceptance region of the R760’s. The
MIPPusedCO2gasheldatjustaboveatmosphericpres- R760(FEU60)tubeshaveamaximumquantumefficiency
sure as the radiator. At STP, CO2 has an index of refrac- of about 25% (11%) at 350 nm. Of the available 89 PMT
tion of 1.00045 at λ = 300 nm giving thresholds of p = columns,68wereused,withR760’sinstalledin15columns
4.5GeV/cforpions,17GeV/cforkaons,and31GeV/cfor and FEU60’s installed in 53 columns. The front-end elec-
protons. The gas temperature and pressure were continu- tronics of the RICH detector was re-designed and rebuilt
ouslymonitoredenablingcalibrationoftheindexofrefrac- bytheMIPPcollaboration.
tion.Aβ =1particleproducedaringofradius29.5cmand
an average of 30 PMT hits providing 3σ π/K separation
up to 80 GeV/c and 3σ p/K separation up to 120 GeV/c. 4. DataAnalysis
Figure3showssampleeventdisplaysforeachbeamspecies
showingPMThitsandreconstructedrings. In outlining the measurement concept, we made several
The PMTs were mounted in a hexagonal array behind simplifyingassumptionswhichmustbeaccountedfordur-
a 2 mm thick quartz window which provided a gas-tight ing analysis. Due to dispersion, Cherenkov light is not ob-
sealbetweenthephototubesandtheradiatorvolume.They servedatasingleangle,butasadistributionacrossseveral
were read out in threshold (on/off) mode. Two models angles.Inouranalysis,wemeasuredtheaveragePMToc-
3
cupanciesforpion,proton,andkaonringsasafunctionof
Cherenkovangleindataandcomparedthemtocalculations absorption in radiator
1
which incorporated the kaon mass as a free parameter. In quartz efficiency
total 12 million rings were recorded for this measurement mirror reflectivity
usingpositivelychargedbeamsofpions,kaons,andprotons cone reflectivity
rangingfrom37GeV/cto63GeV/cinmomentum.
In the data, wire chambers upstream and downstream
of the RICH counter were used to reconstruct the particle nor
m
ttwarhaaPasjtMeacpsTtrsoeirgdtynoiceatfidnirodtenopwferoaaerscdhtichcoPtemMtchpeTeunttcaeeendrndptaeotsrhsaieotfiafoutvnhne,ercaatRigoCeInChpeHorrofebrnCiankhbogeiv.lrieUtanynskigfnoolvger 0.5 PMT efficiaelinzecd yphotoelectrons
angle. This procedure was done separately for each PMT
twyapse,mmaidrerowr,itahndbemaommpenatrutimclesse,ttliignhgt.Astsruthckemonelaysutrheemtewnot normalized photons
0
centralmirrors,labeled8and9.
200 400 600
To compare to the data, we calculated the expected oc-
Wavelength [nm]
cupancyofeachPMTintheRICHarrayforpion,proton,
and kaon rings. The calculation starts with the number of
Fig.4.Overlayofallefficiencyfunctionsincorporatedintothecalcu-
Cherenkovphotonsproducedperunitpathlengthbetween lationofdetectorphotoelectronsasafunctionofangle.Alsoshown
wavelengthsλandλ+dλ[5,6]: aretheinitialCherenkovphotonproductionspectrumandfinalpho-
toelectronyieldnormalizedtopeakat1forinclusionintheplot.
d2N 2πα
dλdpxh = λ2 sin2θC, (10) P =1−exp(−Npe−b), (13)
where α is the fine structure constant. These photons wherebaccountsforthePMTdarknoiserate.
travel through the radiator medium, reflect off mirrors, The measured and calculated PMT occupancies were
pass through a quartz window, and are collected by a re- comparedusingaχ2statistic.Inthecomparisonseveralpa-
flectiveconebeforetheyareincidentonthephotodetector. rameterswereallowedtovarytominimizeχ2.Thesewere:
The transmission probability for a Cherenkov photon of i. Intrinsicdetectorsmearingwidth,σ
0
wavelength λ for each of these steps is plotted in Figure 4 ii. Dispersivesmearingwidth,σ
N
along with the photodetector efficiency. Combining these iii. Densityratioscalingfactor
factors, the average number of photoelectrons detected by iv. Densityratiooffset
PMTiisgivenby v. LevelofaircontaminationinCO
2
vi. Centralpionmomentum
(cid:90)L(cid:90)θ2(cid:90)λ22πα(cid:18) 1 (cid:19) vii. Widthofmomentumdistribution
Npie= λ2 1− n2(λ)β2 e−µ(λ)(FL+x)⊗ viii. Kaonmass
The density ratio is defined as the gas density inside the
0 θ1 λ1
S(θ,θ (λ))(cid:15)(λ)G (θ)dλdθdx (11) RICHdividedbydensityatSTPandwasvariedtoaccount
C i
foruncertaintiesinthecalibrationofthepressureandtem-
where(cid:15)(λ)istheproductofallwavelength-dependenteffi- peraturemonitorsinstalledinthecounter.
ciencyfactors,µ(λ)istheabsorptioncoefficientofCO2,FL Themomentumacceptanceofthebeamlinewasmodeled
is the mirror focal length, and Gi is the geometric accep- as a Gaussian and uncertainties in the mean and width of
tanceoftheith PMT.Scatteringoflightfromangularbin thisacceptancewereincorporatedintothecalculation.The
θC to bin θ is accounted for by the function S(θ,θC). The average proton and kaon momenta accepted by the beam-
lightscatteringwasmodeledasaGaussianofwidthσwith linedifferslightlyfromtheaveragepionmomentumdueto
threecomponents.Theseincludeanintrinsictermindepen- variations in particle production at the secondary target.
dentofwavelengthandawavelength-dependentdispersive Thiseffectwasincorporatedusingasimulationofthecop-
term[12].Athirdtermaccountsformultiplescatteringof persecondarytargetusingtheFLUKA[13,14]production
thebeamparticleintheRICHradiator: model.
After all known effects were accounted for there were
σ2
σ2 =σ2+ N +σ2 (12) O(10%) differences between the measured and calculated
0 tan2θ ms
C PMT occupancies, due presumably to our incomplete un-
where σ is the intrinsic scattering width and σ is the derstandingofthefactorswhichcontrolCherenkovphoton
0 n
dispersivescatteringwidth. Thecalculatedshapesareim- production and transport in our detector. To account for
plicitly functions of the particle masses through β. Using these differences, the uncertainties in the PMT occupan-
Poisson statistics, the probability for a PMT seeing N cies were increased until χ2/ndf = 1 was achieved at the
pe
photoelectronstobeonis: minimum.Thescalingfactorrangedfromabout25to100
4
for the different combinations of PMT type, mirror, and
beammomentum.Systematicuncertaintiesoverwhelmthe
Occupancy0.4 DPraetadiction Occupancy0.15 DPraetadiction s4t0aGtisetVic/aclduantcaeristasihnotwiens fionrFtihgiusrdea5t.aPseertc.eAntsdaimffeprleencfietbfoer-
Mirror 9 Hamamatsu 0.2 Mirror 9 FEU 0.00.51 tTnlawahretgeeeeydnradtbghyarateankeaatowhnniedthrspitinnragetds5is.i-tc1Tit5ceha%dilsouodcnvciecffureeprrttaheanneinccyateyniigssinustlhyeaoaprwcirchnaanalilnngyugF1uei5lgailurtluirmbemien6is-..
V]
0 0.028 0.03 0.032 0 0.028 0.03 0.032 Me Fit Result
Pion Ring Angle [rad] Pion Ring Angle [rad] s [ World Avg.
s
a
M
Occupancy0.2 DPraetadiction Occupancy0.1 DPraetadiction Kaon 500
Mirror 9 Hamamatsu 0.1 Mirror 9 FEU 0.05
450
0 0 40 50 60
0.015 0.02 0.015 0.02
Proton Ring Angle [rad] Proton Ring Angle [rad] Momentum [GeV]
Occupancy 0.4 DPraetadiction Occupancy0.15 DPraetadiction Fbeiga.m7.mSoummenmtaaraynodfmkairornorsm.aAstseraecshultmsofmorendtautma sseetttsinugs,inrgesuvaltrsiofuosr
Mirror 9 Hamamatsu 0.2 Mirror 9 FEU 0.00.51 mmtfrhoiierrmrrfioontrrha98elakParaerDoenpGlpom.ltoattestdsedrsehssiufhtlietfd,teasdnlidgshltitghlhyetdtlyootttthoeedtrhliigenhetle.isfTt,thheweshaoiclleicderpleitnseuedlstvhsaolfwuoesr
KaonmassresultsforeachdatasetareshowninFigure7.
Using just the low momentum data sets results in a kaon
0 0 massmeasurementof491.9±1.1MeV;usingjustthehigh
0.024 0.026 0.028 0.03 0.024 0.026 0.028 0.03
Kaon Ring Angle [rad] Kaon Ring Angle [rad] momentumdatasetsgives486.7±3.0MeV.Theseresults
agreewithinuncertaintiesandarecombinedtogiveafinal
Fig. 5. Comparison of measured PMT occupancies to best-fit pre- resultforthechargedkaonmassof491.3±1.7MeV(3500
dictions for 40 GeV data set [15]. Pions are shown in the top row, ppm).Theconventionofscalingerrorbarswhencombining
protons in the middle row, and kaons in the bottom row. In each measurements so that χ2/ndf = 1 is followed resulting in
row,theleftpanelshowstheresultsforR760PMTswhiletheright
a larger final uncertainty. This result is within 1.4σ of the
panelshowstheresultsforFEU60PMTs.
PDGvalue[1].
See[15]foradetaileddiscussionoftheanalysispresented
inthispaper.
% Difference 1105 % Difference 105 5. SuggestionsforImprovement
matsu 5 FEU 0 In the analysis above we achieved an understanding of
ma 0 the PMT occupancies as a function of Cherenkov angle at
Ha -5 -5 the 10% level resulting in a final uncertainty in the kaon
-10 -10 mass of 3500 ppm. If the uncertainties in the PMT occu-
pancies could be reduced to 1% the contribution of this
-15
-15 source of uncertainty in the kaon mass would be reduced
0.026 0.027 0.028 0.029 0.026 0.027 0.028 0.029
Kaon Ring Angle [rad] Kaon Ring Angle [rad] to the level of the statistical uncertainties and make this
technique useful for resolving the 122 ppm discrepancy in
theX-raymeasurements.
Fig.6.Percentdifferencebetweendataandpredictedoccupancyfor
40 GeV/c kaons. Hamamatsu tubes are on the left, FEU tubes are The largest uncertainty in our calculation of the PMT
ontheright. occupancyasafunctionofangleresultsfromknowledgeof
the acceptance of the PMT array which was complicated
5
by cross-talk in the readout electronics – a problem which sure the charged kaon mass with 3500 ppm precision us-
manifesteditselfduringthehighrateconditionsthedetec- ing an existing RICH detector. We believe that there are
torwasoperatedunderforthismeasurement.Occasionally, significantopportunitiesforafutureexperimentdedicated
a single PMT hit would cause all 16 channels sharing the to the kaon mass measurement to reduce systematic un-
samereadoutboardtoregisterahit.Inouranalysiswere- certainties to the level where this technique may be useful
jectedPMThitsthatappearedtobeduetocross-talk.As to resolve the 122 ppm discrepancy in the X-ray measure-
thecross-talkwasdifficulttomodel,itsaffectonthePMT mentsofthechargedkaonmass.
acceptances has large uncertainties accountingfor most of
the ∼10% uncertainty in PMT occupancy as a function of Acknowledgments
angle.
Additional uncertainties in the occupancies result from
Fermilab is operated by Fermi Research Alliance, LLC
our treatment of the detector response as a function of
underContractNo.DE-AC02-07CH11359withtheUnited
wavelength. A measurement of the PMT response on a
StatesDepartmentofEnergy.
tube-bytubebasiswouldhaverequireddis-assemblyofthe
detector and was not undertaken, rather we used a single
averageresponseforallPMTs.Astheresponseofindivid- References
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thisintroducesanuncertaintyof∼6%inthecalculationof
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Cherenkov counter with a GEM-based photo-cathode [16]
which would afford 30 micron resolution of the Cherenkov
rings in a device with is 45.7 cm in diameter and 22.9 m
long. A complete assessment of the performance of such a
devicewouldrequireasignificantresearcheffortandawaits
an experimental proposal. We hope that this initial work
willinspirethesefutureinvestigations.
Inconclusion,wehaveusedtheCherenkoveffecttomea-
6