Search for chameleons with CAST

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Search

for

chameleons

with

CAST

V. Anastassopoulos

a

,

M. Arik

b

,

1

,

S. Aune

c

,

K. Barth

d

,

A. Belov

e

,

H. Bräuninger

f

,

G. Cantatore

g

,

J.M. Carmona

h

,

S.A. Cetin

b

,

F. Christensen

i

,

J.I. Collar

j

,

T. Dafni

h

,

M. Davenport

d

,

∗

,

K. Desch

k

,

A. Dermenev

e

,

C. Eleftheriadis

l

,

G. Fanourakis

m

,

E. Ferrer-Ribas

c

,

P. Friedrich

f

,

J. Galán

c

,

J.A. García

h

,

A. Gardikiotis

a

,

J.G. Garza

h

,

E.N. Gazis

n

,

T. Geralis

m

,

I. Giomataris

c

,

C. Hailey

o

,

F. Haug

d

,

M.D. Hasinoff

p

,

D.H.H. Hoffmann

q

,

F.J. Iguaz

h

,

I.G. Irastorza

h

,

J. Jacoby

r

,

A. Jakobsen

i

,

K. Jakovˇci ´c

s

,

J. Kaminski

k

,

M. Karuza

t

,

g

,

M. Kavuk

b

,

1

,

M. Krˇcmar

s

,

C. Krieger

k

,

A. Krüger

d

,

2

,

B. Laki ´c

s

,

J.M. Laurent

d

,

A. Liolios

l

,

A. Ljubiˇci ´c

s

,

G. Luzón

h

,

S. Neff

q

,

I. Ortega

h

,

d

,

T. Papaevangelou

c

,

M.J. Pivovaroff

u

,

G. Raffelt

v

,

H. Riege

q

,

M. Rosu

q

,

J. Ruz

u

,

I. Savvidis

l

,

S.K. Solanki

w

,

3

,

T. Vafeiadis

d

,

l

,

∗

,

J.A. Villar

h

,

J.K. Vogel

u

,

S.C. Yildiz

b

,

4

,

K. Zioutas

d

,

a

(CAST Collaboration)

and

P. Brax

x

,

I. Lavrentyev

y

,

A. Upadhye

z

a_{PhysicsDepartment,UniversityofPatras,Patras,Greece} b_{DogusUniversity,Istanbul,Turkey}

c_{IRFU,Centred’EtudesNucléairesdeSaclay(CEA-Saclay),Gif-sur-Yvette,France} d_{EuropeanOrganizationforNuclearResearch(CERN),Genève,Switzerland} e_{InstituteforNuclearResearch(INR),RussianAcademyofSciences,Moscow,Russia} f_{Max-Planck-InstitutfúrExtraterrestrischePhysik,Garching,Germany}

g_{IstitutoNazionalediFisicaNucleare(INFN),SezionediTriesteandUniversitàdiTrieste,Trieste,Italy} h_{InstitutodeFísicaNuclearyAltasEnergías,UniversidaddeZaragoza,Zaragoza,Spain}

i_{DanishTechnicalUniversity-Space(DTU),Copenhagen,Denmark}

j_{EnricoFermiInstituteandKICP,UniversityofChicago,Chicago,IL,UnitedStatesofAmerica} k_{PhysikalischesInstitut,UniversitätofBonn,53115Bonn,Germany}

l_{AristotleUniversityofThessaloniki,Thessaloniki,Greece}

m_{NationalCenterforScientificResearch“Demokritos”,Athens,Greece} n_{NationalTechnicalUniversityofAthens,Athens,Greece}

o_{ColumbiaUniversity(CU),NewYork,UnitedStatesofAmerica}

p_{DepartmentofPhysicsandAstronomy,UniversityofBritishColumbia,Vancouver,Canada} q_{TechnischeUniversitätDarmstadt,IKP,Darmstadt,Germany}

r_{J.W.Goethe-Universität,InstitutfúrAngewandtePhysik,FrankfurtamMain,Germany} s_{RudjerBoškovi´cInstitute,Zagreb,Croatia}

t_{PhysicsDepartmentandCenterforMicroandNanoSciencesandTechnologies,UniversityofRijeka,Croatia} u_{LawrenceLivermoreNationalLaboratory,Livermore,CA94550,UnitedStatesofAmerica}

v_{Max-Planck-InstitutfúrPhysik(Werner-Heisenberg-Institut),München,Germany} w_{Max-Planck-InstitutfürSonnensystemforschung,Göttingen,Germany}

x_{InstitutdePhysiqueThéorique,CEA,IPhT,CNRS,URA2306,F-91191Gif/YvetteCedex,France} y_{BostonUniversity,Boston,MA02215,UnitedStatesofAmerica}

z_{PhysicsDep.,UniversityofWisconsin-Madison,1150UniversityAvenue,Madison,WI53706,UnitedStatesofAmerica}

*

Correspondingauthor.

E-mailaddresses:Martyn.Davenport@cern.ch(M. Davenport),Theodoros.Vafeiadis@cern.ch(T. Vafeiadis). 1 _{Pr.addr.:BogaziciUniversity,Istanbul,Turkey.}

2 _{Pr.addr.:HochschuleKarlsruheTechnikundWirtschaft,Univ.ofAppliedSciences,Moltkestr.30,76133Karlsruhe,Germany.} 3 _{Sec.affiliation:SchoolofSpaceResearch,KyungHeeUniversity,Yongin,RepublicofKorea.}

4 _{Pr.addr.:Dep.ofPhysicsandAstronomy,UniversityofCaliforniaIrvine,Irvine,CA92697,UnitedStatesofAmerica.}

http://dx.doi.org/10.1016/j.physletb.2015.07.049

0370-2693/©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

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Articlehistory: Received25March2015

Receivedinrevisedform8July2015 Accepted21July2015

Availableonline28July2015 Editor:M.Doser Keywords: Chameleon CAST SDD X-ray Tachocline Darkenergy

Inthisworkwepresentasearchfor(solar)chameleonswiththeCERNAxionSolarTelescope(CAST).This novelexperimentaltechnique,inthefieldofdarkenergyresearch,exploitsboththechameleoncoupling to matter(βm)and tophotons (βγ) viathePrimakoffeffect. By reducingthe X-raydetectionenergy

thresholdusedforaxionsfrom1keVto400eVCASTbecamesensitivetotheconvertedsolarchameleon spectrumwhichpeaksaround600eV.Eventhoughwehavenotobservedanyexcessabovebackground, wecan providea95%C.L. limitforthe couplingstrengthofchameleonstophotons ofβγ1011 for

1< βm<106.

©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Thedarksectorofcosmologyrepresentsabigchallengein fun-damentalphysics.Inparticular,darkenergy[1,2],whichis respon-siblefortheacceleratedexpansionoftheUniverse,couldbedueto theexistenceofascalarfieldlikethepostulatedchameleon [3–5]

(for a comprehensive theoretical treatment we refer to [6]). Al-thougha highenergydescriptionof chameleonsderived froman ultraviolet completion such as string theory is still missing, this typeoflowenergymodelissuggestiveenoughtojustifynovel in-vestigationsliketheonepresentedinthiswork.

ChameleonscanbecreatedinthesunviathePrimakoffeffect. Like axions,creation could occur inthe nuclearcoulomb field of theplasma atthesolar core,butsuch a calculation doesnot ex-istasyet,thoughitwouldbe ofinterest.Additionallytheycanbe createdinregions of strongtransverse magneticfieldsin the so-larinterior.Thetachocline,aregioninsidetheSunatadistanceof around0.7R_ fromthecenter,iswidelybelievedtobethesource of intense magnetic fields. At presentonly the characteristics of chameleoncreationatthe tachoclinehavebeenstudiedindetail, togetherwiththeirpropagationinthesunandjourneytothe he-lioscope[7,8].

Chameleons have non-linear self-interactions and interactions withmatter which give them an “effective mass” dependent on theambientmass(energy)density.Theoutersolarmagneticfields cantransformchameleonstosoftX-rays.Thesamecouldalso hap-penwiththeintegratedtransversemagneticfieldallthewayfrom the Sun to the Earth, because the effective mass of chameleons decreases with lower and lower density in the free space be-tween the Sun and the Earth’s atmosphere. Taking into account thelimitof

β

γ whichsaturatesthesolarluminosity,the transfor-mation probability inany of the aforementioned magnetic fields isnegligibly smalland doesnot affectthe expectedflux arriving inCAST.TraversingtheEarth’satmospheremakesnodifferencein theintensity of the relatively energeticsolar chameleons we are consideringhere.

Theywouldhaveavery smalleffectivemassinouter spaceor in the evacuated magnet cold bores of CAST [9] but a large ef-fective massinside the detectormaterial of mostterrestrialdark matterexperiments.Theircorrespondingenergiesgenerallyexceed thechameleoneffectivemassinsidematterandthustheytraverse materialswithhardlyanyinteraction,makingdetectiondifficult.

Chameleondarkenergy isan effective field theory (EFT) with acutoffaround thedarkenergyscale, 2meV,abovewhich rigor-ouspredictionscannotbemadewithoutaUVcompletion.Asingle particlewitha3-momentummuchhigherthan thecutoffis per-fectly consistent withan EFT treatment, since the 3-momentum is not Lorentz invariant. However, we cannot rigorously quantify

two-particle interactions with center-of-mass energies far above thecutoff.Inonesuchprocess,fragmentation,twochameleons in-teracttoformagreaternumberoflower-energychameleons.The treatmentofchameleonfragmentationasacoherent,semiclassical processin[10]isinapplicabletotheSun.

In orderfor fragmentationin the Sunto be calculable within theEFT context,thecut-off ofthehigherorderinteractions lead-ing to fragmentationwould have to be increasedtowards a few keV from its nominal value of 2 meV. The wayof doing this is notknown,butchangingthecut-offscaleofchameleonmodelsis aprioriindependentfromthematter densitydependenceofboth the vevofthe chameleonandits mass.Hence one mayenvisage thatmodelswithahighercut-offandthesamedependenceofthe vevandthemassontheenvironmentcouldbeconstructed.Since aUVcompletionisbeyondthescopeofthispaper[11]our analy-sisismadeontheassumptionthatfragmentationatthetachocline isnegligible.

To investigate the existence of exotica like chameleons we present the first results witha new experimental technique [7], bytransforminganaxionhelioscopetoachameleonicone.

Chameleons, like axions, can be detected by the inverse Pri-makoffeffectinsideatransversemagneticfield,withtheir conver-sion efficiency being optimized in vacuum. Their expected spec-trumoriginatesfromthephotonthermalspectrumandismodified by thecreationprobability insuch anenvironment whichis pro-portionalto thesquare of thephoton energy(

ω

2_{) timesa factor}

of

ω

−1/2 _{which derives from the fact that the photonsperform}

a random walk in the Sun. Allin all, this shifts thepeak ofthe

spectrum of produced chameleons fromthe photon temperature

in the tachocline at around 200 eV to a much larger value of 600 eV.Itisinterestingtonotethatbelow

∼

1keVtheconversion probability fromchameleon to photon via the Primakoffeffect is quasi-constant[8].

Inthispaperwe discusstheupperlimit onthe chameleonto photon couplingstrength(βγ ) forawide rangeoftheir coupling tomatter. Ourresulton

β

γ iscomparablewiththeone obtained by theGammeV-CHASE (hereafterCHASE)experimentsin alaser cavity[12,13].Weexploreuncertaintiesinthetachoclinemagnetic field, the precise radius and width of this region and the frac-tionofsolarluminosity emitted aschameleons. Wealsoconsider higherpowersofthechameleonpotentialandshowthatourlimit,

β

γ



1011,standsalmostindependentofthetypeofinversepower lawpotentialused.

2. Theexperiment

The detection of solarchameleons can be performed withan axion helioscope like CAST via the inverse Primakoff effect. The

relevantchameleon-to-photoncouplingstrength



β

γ



replacesthe axion-to-photoncouplingconstant



gaγ



.TheexpectedX-ray spec-trumpeaks at600eV, whereas the X-raysfrom axionsfromthe solar core are expected to appear with energies in the multiple keVrange.Therefore tostudysolar chameleonsinCAST thecold boresshould bein vacuum,whilst thedetectorshould ideallybe sensitivetothe150–1500 eV energyrange.

Afterrunning withvacuum inthe magnet bores in2003 and

2004[14,15],andwithhelium-filledcoldboresbetween2005and 2012[16–18],CASTwasconfiguredonceagainforvacuumrunning in2013by removingthethinX-raywindows(which hadacutoff at1 keV). This produced an uninterruptedvacuum line, running fromthe vacuum port ofthe magnet cryostat atone end ofthe magnet,throughthecoldboresofthe10mprototypeLHCmagnet, totheexitportofthecryostatontheoppositesideofthemagnet. X-raydetectorsonCASTintheperiodfrom2003to2012have operated withenergy thresholds above 1 keV to cover the solar axion energyspectrum.The 2013vacuumsetupallowed sub-keV photonstoexitthemagnetcoldboreandreachtheX-raydetectors withoutabsorption.Sub-keVsensitivedetectorswerethen ableto explorethisenergyrange.

The experiment described here took place in a short running period before the installation of a powerful combination of the existing X-ray telescope (MPE-Abrixas flight spare) and a newly developed InGrid detector[19],capable of simultaneous sub-keV andmulti-keV operation.A sub-keV detectorsystem was assem-bledusingmostlycommerciallyavailableequipmenttoexploitthis firstperiodofvacuumrunning.Thedetectorwas installedonthe sunrisesideoftheexperimenttakingdataduringthemorning so-lar trackingof the magnet for

∼

90 min eachday. The magnetic field length was 9.26m, thecold borediameter 43mm andthe field9T.

3. Thedetectorsystem

The X-ray detector system comprised a Silicon Drift Detector (SDD) [20]anda preamplifier-readout card5 _{insidea vacuum}

en-closure. The1.1W dissipatedfromthepreamplifier was removed byacopperheatexchangerblock.TheSDDsignalwasroutedtoa DigitalPulseProcessor(DPP).6_{TheDPPwasoperatedwitha}

peak-ing timeof 5.6μsingated mode usingthegate providedby the preamplifier-readoutcard.Theenergythresholdofthedevicewas setto167eV.

The detector chosen was a single channel, non-imaging SDD,

without a vacuum window, in this case a commercial research

grade device,7 with a large surface of 89 mm2 effectively

cover-ing 6.13% of the magnet cold bore (diameter 43 mm). The

de-vicewasmadefrom450μmthick polysilicontechnologywithan entrance window optimized for light elements. The energy

res-olution of the device is 39 eV FWHM at 277 eV. Due to the

sharply rising noise profile at low energies, the threshold used inthe analysiswas set at400eV. The typicalquantum response is shown in Fig. 1; the quantum efficiency(

ε

q) exceeds 80% for

photon energies above 400 eV.The background level forthe de-vicewas

∼

10−3_cts/keV/cm2

_{/s in}

_{therange400–1500 eV andwas}

independentof thedetectortemperatureover therange

−

25◦ to

−

45◦C.TheSDDwasoperatedat

−

30◦C usinganintegrated dou-ble Peltier cooling element; the 1.0 W from the SDD was also removed bythecopper heatexchanger. Thedetectortemperature remainedconstantwhentiltingthemagnetduringsolartracking.

5 _{ReadoutElectronicsBoard(pulsedreset)fromPNDetector,Munich,Germany.} 6 _{PX5-DigitalPulseProcessorAMPTEK,Bedford,UnitedStatesofAmerica.} 7 _{SDD-100-130pnW-OM-icPremiumLinefromPNDetector,Munich,Germany.}

Fig. 1. Quantum efficiency of the SDD.

The detector system inside the vacuumvessel was connected directly to the cold bore vacuumport gate valve (on the left in

Fig. 2).Thevacuumvesselwasmadefroman iso-KDN100 stain-lesssteeltubeconnectedtoacustom-builtcopperendflange.

Shielding inside the vacuum vessel was provided by the OFE

copper back flange plus an OFE copper inner cylinder and

up-stream collimator; the vacuum vessel was surrounded by 6 cm

thick lead rings, and lead plates with thickness between 1 and 3 cm. Theturbo-pumped dryvacuumsystemoperatedata pres-sureof 1.2

×

10−6mbar with thecryostat gate valve openedfor datataking.

4. Laboratorytests

Prior to installationon CAST,the SDD was testedin a labora-tory atCERN ona variable energyX-rayvacuumbeamline [21]. Thesystemprovidedcalibrationenergiesbetween0.28and10keV. Usingthecharacteristicemissionlineswiththebeststatistics,the energy resolution (FWHM) of the detectorwas defined for vari-ous energies. In

Fig. 3

the measuredFWHMversus the energyis shown.

During the first run of the detector on the X-ray beam line,

a noticeable drop in the count rate with time was observed

in the energy range 300–800 eV with the detector operated at

−

46◦C and in a relatively poor vacuum of 4

×

10−5 _{mbar. To}

quantify this phenomenon further, measurements were taken at the nominaldetector operatingtemperatureof

−

30◦C,using the bremsstrahlungspectrum oftheAg target inthe X-raygenerator. After a few hours at room temperature, the detectorwas cooled to

−

30◦C at a vacuum pressure of 2.5

×

10−6 _{mbar. Then}

sev-eral5 minmeasurements ofthesame spectrumwere takenover the course of the next 25 h to determine the loss of efficiency withtime.Returningthedetectortoroomtemperaturefor1hwas enoughtofullyrecoveritsefficiency.

The loss of efficiencywas attributedto substances outgassing fromthematerialsinsidethevacuumsystemandthenbeing

cryo-pumped on to the cold entrance window surface. Both the

ex-perimentalandthe laboratorytest setupsusedstandard,

surface-cleaned stainless steel High Vacuum (HV) components and dry

Vitonjoints.TheSDDpreamplifiercard,whilstintentionedfor vac-uumuse,wasnotconstructedfromHVmaterialsandcomponents. ThewiringandconnectorsbetweenSDD,preamplifiercardandthe electrical vacuumfeed-throughs were not HV standard. As these componentswerecommontobothsystems(laboratoryand exper-imental),theresultinglossofefficiencymeasuredinthelaboratory isbelievedtohavealsobeenpresentintheexperiment.

Monte-Carlo simulations verified that the loss in efficiencyof theSDD couldbeexplainedbyafilmdepositionwithathickness

Fig. 2. SDD detector vacuum and shielding system.

Fig. 3. Measured FWHM of the SDD versus energy.

thatincreasesuniformlywithtime.Moreovertheabsorption spec-trumofa simplehydrocarbonfilm(C3H6) provedtobe sufficient

whenfoldedwiththeresolutionofthedetectortoreproducethe measuredabsorption.In

Fig. 4

thecomparisonofthespectrataken after3,7,21and25h ofoperationofthe detector,withthe ini-tialone(directly aftercool down)is displayed,together withthe simulated values. A chi-squared fit was performed between the simulatedandreal data todetermine the evolution ofthe thick-nessofthehydrocarbonfilm.Theresultisshownin

Fig. 5

,where theevolutionofthetransmissionofthehydrocarbonfilmisshown foreachbinof100eV.Thesedatawereusedforthe parameteriza-tionofthetransmissionofthehydrocarbonfilm,versustime and energy,inorderto calculatetheoverall efficiencyofthe detector tophotonsintherange400–1500 eV.Ourcorrectionforthiseffect tothetrackingdataislessthan3%.OurSDD provedtobe signifi-cantlymoreefficientthananSDDfittedwithavacuumwindow. 5. Datataking

Thetestsinthelaboratoryindicatedthatthedetectorrequired 1h atambient temperature inorder to fully recover its lost ef-ficiency.Toensuremaximumefficiencyofthedetectorduringthe sunrisesolartracking,thedetectorwassettoambienttemperature 2hbefore datatakingandsetto

−

30◦C only30min beforethe sunrisesolartrackingstarted.Attheendofthesunrisesolar track-ing thedetector was againset to ambienttemperature andthen

set back to

−

30◦C about 30min before theevening solar track-ing.Thedetectorthenremainedatnominaloperatingtemperature untilthenextday,2hbeforesunrisesolartracking,whenthe cy-clewas repeated.The datatakingtook placeover9 sunrisesolar trackings amounting to 15.2h of exposure.The background data consistedof13.8hofsunsetsolartrackingand94.2hofovernight backgroundrunswiththemagnetstationary(108hintotal).

The operational energy threshold for the SDD was 167 eV

whichproducedanacquisitionrateof

∼

5 mHz overtherangeup to 10 keV. This rate was quasi-constant andindependent of the magnetmotion.Overthe wholedata takingperiodof9daysthe SDDratebetween400and1500eVwas1.40

±

0.16 mHz (15.2 h sunrise tracking) corresponding to 1.43

×

10−3 cts/keV/cm2

/s.

The rate obtainedduring background runswas 1.42

±

0.06 mHz (108 h).Thespectraofthesunrisetrackingandbackgroundrates areshownin

Fig. 6

.

Theeffectoftheinternalcopperandexternalleadshieldingin

the background can be gauged by the comparison between data

taken in the X-ray laboratory (unshielded) and from CAST (both internal copperandexternallead shielding).The backgroundrate in the range1.5–10 keV ofthe SDD in the X-raybeam linewas 3.86

±

0.34 mHz (comparedto1.42

±

0.06 mHz onCAST)andfor 400–1500 eV was2.31

±

0.26 mHz (comparedto1.42

±

0.06 mHz onCAST),indicating thepresenceofelectronicnoise atlow ener-gies. Analysisoftheenergyspectraforallbackgroundrunstaken over typically 13.5h each dayshowed no statisticallysignificant decrease withtime in the spectra atlow energies (300–600 eV), asshownin

Fig. 7

.

6. Theoreticalchameleonspectrum

Chameleons can be producedby mixing withthephoton flux

emanatingfromtheSun’score[7,8].Theconversionprobabilityof photonsintochameleonsin amagnetizedregion withaconstant magneticfield B overadistancel isgivenby[8]

pγ→φ

(

l

)

=

β

2 γB2l2ω 4m2 Pl sin2 l lω

,

(1)

wherethePlanckmassismPl

∼

2

×

1018GeV,thecoherencelength

isgivenbylω

=

_m4ω2 eff

andtheeffectivemassofthechameleonis

m_eff2

= β

m(n+2)/(n+1)

ω

ρ2

−

ω

2pl

,

(2)

Fig. 4. Comparisonofthespectrumthatwastakenimmediatelyafterthecool-downoftheSDD,withtheonestaken3,7,21 and25 h later.Theformofthehistograms clearlyindicatesaprogressivedepositionofanabsorptionlayeronthedetectorsurface.Thesimulateddata(continuousline)correspondtothedepositionofaC3H6filmon thesurfaceofthedetector.

Fig. 5. Thedropintransmissionduetotheincreasingdepositionofthehydrocarbon filmonthesurfaceofthe detector,foreach energybin,at theenergyrangeof interest(400–1500 eV).

ω

2_ρ

=

(

n

+

1

)

ρ

mPl

(

ρ

n mPl



n+4

)

1/(n+1) (3)

andtheplasma frequencyis

ω

2 pl

=

4π αρ

memp.Wehaveintroducedthe

fine structure constant

α

∼

1/137 and the proton and electron massesmp andme.The massof the chameleon dependson the

density

ρ

andthecouplingtomatter

β

m.Theindexn

>

0 defines

the chameleon model and comes from the scalar potential _φn+4n

where



∼

10−3eV is the dark energy scale. We have assumed thatthemixingangle

θ

=

ωBβγ

mPlm2 eff



1.

Photonsinthesolarplasmaperformarandomwalk.Whenthey havemovedbyaradialdistanced

(

l

)

inonesecond,theyhave un-dergone N

(

l

)

collisions with the plasma where l is the distance betweentwocollisions

Fig. 6. Combinedspectraoftherateduringsunrisetrackingandduringbackground measurements.

N

(

l

)

=

c

d

(

l

)

,

d

(

l

)

=

l



N

(

l

) .

(4)

The distancel is distributed accordingto a Poissonlaw with av-erage

λ

given by the meanfree path.In a solar region ofwidth

R wherethemeanfreepathandthemagneticfieldare(nearly) constant,theconversionprobabilityintochameleonsisgivenby

d

P

(

l

)

=

R

d

(

l

)

N

(

l

)

pγ→φ

(

l

)

e

−l/λdl

λ

.

(5)

Summingoverthetotalnumberofcellsdefinedby R_

/

R weget theconversionrateperunitlength

d

P

dx

=



c lω

(

r

)

β

_γ2B2

(

r

)

l2_ω

(

r

)

R_ 4m2 Pl

λ(

r

)

∞



0 sin2y y3/2 e −lω(r)y/λ(r)_dy

_,

₍₆₎

Fig. 7. Evolution of low energy background (300–600 eV) with time.

which dependson the radius r from the center ofthe Sun. The conversion probability is obtained by integrating the conversion rateoverx

=

r

/

R_.

In the tachocline, and for the range ofenergies of interest it turnsoutthatlω

(

r

)

 λ(

r

),

implyingthattheconversionrate sim-plifiesgreatly d

P

dx

=

C



c l_ω

(

r

)

β

_γ2B2

₍

_r

₎

_l2 ω

(

r

)

R 4m2_Pl

λ(

r

)

,

(7)

whereC

=



₀∞sin_y3/22ydy.Noticethatthespectrumdependson

ω

3/2

and not

ω

2 _{due to the random walk of the photons in the}

so-larplasma,andthe

√

N

(

l

)

excursions ofthephotonscoveringthe distanced

(

l

)

inone second. In practice and in the absence of a resonancewherem2

effvanishes somewhereinthetachoclinefora

large value of

β

m, the effectivemass ofthe chameleon is

essen-tiallyindependentofthecouplingtomatter

β

m.Thisimpliesthat

theconversion probability dependsonly onthe couplingto pho-tons,

β

γ .

ThechameleonfluxleavingtheSunissimplygivenby



cham

(

ω

)

=

1



0 n_γp_γd

P

dxdx

,

(8)

where the integrand vanishes outside the tachocline. It depends onthephotonfluxnγ andthephoton spectrum pγ .The spectral dependenceofthisfluxisin

ω

3/2

pγ

(

ω

)

∼

_eωω/T7/2₋₁,whereT isthe

photon temperature in the tachocline, with a maximum around

ω

max

∼

600 eV. The total luminosity of the Sunin chameleonsis

givenby Lcham

=

∞



0

ω



cham

(

ω

)

d

ω

,

(9)

which depends on

β

_{γ .}2 We calibrate

β

γ in such a way that the chameleonluminosity doesnot exceed10% ofthesolar luminos-ity.Forn

=

1 andatachoclineofwidth0.01R_ locatedataradius 0.7R_ andamagneticfield of10T,thechameleonssaturatethe solarluminosity bound for

β

sun

γ

=

1010.81. As the numberof re-generatedphotonsintheCASTdetectorisproportionalto

β

_{γ ,}4 this givesan upperlimitto thenumberofphotonsthat one may ex-pectto detect. Inthe following, we shall seehow the likelihood analysistakesintoaccount thesolarbound onthechameleon lu-minosity.

Fig. 8. ExpectednumberofphotonsarrivingattheSDD,forβγsun=1010.81,

assum-ingallchameleonspassthroughthefullmagneticlengthoftheCASTmagnetand assumingnoabsorbingmaterialupstreamofthecoldbore.

7. Analysisandresults

The coldborediameterof43mm attheupstream endofthe magneticregionofL0

=

9.26 m resultsinanapertureof3.5mrad

asseenbytheSDD.Chameleonsemittedfromlargeranglesupto thetachocline(6.5mradforaspherediameterof0.7R_)traverse lessthanthefull magneticlength ofthemagnet.A simulation of theCASTgeometrywascarriedoutandtheresultswerethat15.7% of emitted chameleons passed through the full field length, the remainderpassthroughvaryinglengths(L)whichwhenintegrated andscaledbythe

(

L

/

L0

)

2 factorareequivalent toafurther23.2%

passingthroughthefulllength.Intotalascalefactor(F )of38.9% hasto be appliedto theexpectednumberof photonstoaccount forthe fact that not all chameleons that reach thedetector pass throughthefullmagneticlength.

Allchameleonsfromthe tachoclineincident onthe SDDmust passviatheleadshieldingonthesunsetsideofthemagnetbefore entering the magnetcold bores. The 400 eV energythreshold in theanalysisiswellabovethemaximumchameleoneffectivemass inlead (meff

=

135 eV forn

=

1,

β

m

=

106), hencenoabsorption

effectsoccurwithinourregionofinterest.

The expected number of photons fromchameleon conversion

insidetheCASTmagnet,thatwillreachtheSDDiscalculatedfrom the theoretical photon spectrum (Fig. 8) arriving at our detector takingintoaccountthetotaltrackingtime,thequantumefficiency of the detector, the magnetic length that the chameleons travel insideCAST,theabsorptionphenomenaonthesurfaceoftheSDD andtheareaofthedetector:

N_ich

=

f



Ei

, β

γ4

×

ASDD

×

t

×

F

×

ε

q

×

ε

abs

×

dE

,

(10)

wheretheindexi runsovertheenergybins, f

(

Ei

)

istheexpected

numberofphotonsgivenincts/100eV/mm2

_{/s in}

_frontofour

de-tector,calculatedwith

β

_γsun

=

1010.81_{andhavingtravelledthefull}

length of the CAST magnet, ASDD the area of the detector, t the

total tracking time in seconds,

ε

q the quantum efficiency of the

detector,

ε

absthetransmissionofthethinabsorbinglayer,thathas

accumulatedafter2h onits surface,anddE theenergybinsize. Theresultingspectrumisshownin

Fig. 9

.

Theanalysisofthedatahasbeenperformedbyusingthe like-lihoodmethod.FordatathatfollowaPoissondistributionthe like-lihoodfunctioncanbeexpressedas

log

(

L

)

= 

i

(

−λ

i

+

tilog

(λ

i

)

−

log

(

ti

!)) ,

(11)

whereti isthenumberoftrackingcountsintheenergybini and

Fig. 9. Expectednumberofphotons(βγsun=1010.81)tobedetectedbythe SDD

takingintoaccountthetotaltrackingtime.

Fig. 10. Subtractedcounts, expectednumberofcounts duringthesolar tracking (red)andbestfittothedatafromthemaximisationoftheLikelihood(blue).

λ

i

=

bi

+

NiC

,

(12)

withbi theexpectedbackgroundinenergybini andNiC the

ex-pected number ofphotons fromchameleon conversion,which is proportionaltothequantity

β

_{γ (eq.}4 (10)).Forsimplicitywechoose thefreeparameterasC

=



β

γ

/β

sunγ

4

toevaluatethedata. The maximum of log(L

)

will be achieved by tuning the pa-rameterC .Theobtainedvalue CBest fit iscompatiblewiththenull

hypothesiswithin1sigma.In

Fig. 10

thesubtractedcounts, track-ingminusbackground(normalizedtotrackingtime),togetherwith the expected photon signal fromchameleon conversion, andthe bestfittoourdataareshown.

The upper limit on

β

γ is then obtained by integrating the Bayesianprobability withrespectto C from 0up to95%, consid-eringonlythenon-negativepartofthedistribution.Theresulting boundon

β

γ is

β

γ

≤

9

.

26

×

1010at 95% CL

.

(13)

Our resultcan be modulated depending on the type of solar modelconsidered.Indeed,we havefocusedon the B

=

10 T case in the tachocline. The uncertainty on the tachocline field is be-lieved tobe in the range4 to25–30 T[22–24]. Hence the CAST limit onthe photon couplingcan be shiftedby a factorof about plusorminus 2.51/2 _{ascanbeseenin}

_{Fig. 11}

_{.Thelimitobtained}

withtheSDDisactuallylowerthanthesolarluminosityboundfor valuesoftachoclinemagneticfieldsbelow4.9T.

Additionally, we have shifted the position of the tachocline downto0.66R_andincreaseditswidthfrom0.01R_to0.04R_.

Fig. 11. TheCASTlimitonβγ fordifferentvaluesofmagneticfieldinthetachocline.

Table 1

Upperlimitonβγ derivedfromourmeasurementsfordifferentsolarmodels,all

for10%solarluminositybound.

Tachocline [] Width [] βγ at 95% CL βsunγ

0.66 0.04 5.69×1010 ₂

.95×1010

0.66 0.01 8.9×1010 ₅

.89×1010 0.7 0.1 linear 7.29×1010 _3.47×1010

Wehavealsoconsideredalinearlydecreasingmagneticfield(10 T at 0.7R_ down to0 T at0.8R_). The changes to the bound on

β

γ canbefoundin

Table 1

.Onthewholeandirrespectivelyofthe astrophysicsofthetachocline,wehavefoundthatthecouplingof photonstochameleonssatisfies

β

γ

≤

1011.

8. Discussion

The parameterspaceofchameleonsisdeterminedbythe cou-pling constants to matter and radiation, and a discrete index n which specifies the type of dark energymodel under considera-tion.Ourresultfortheupperlimiton

β

γ ispresentedin

Fig. 12

, together with other experimental bounds. A number of experi-mentsaretotallyinsensitivetothecouplingtophotonsresultingin verticallinesinthefigure.Thetorsionpendulumtestsofthe pres-enceofnew scalarforceslead toa lower boundon thecoupling to matter(in green)[25].Neutroninterferometry testsleadtoan upperbound (lilac) [26]. Presently,the atom-interferometry tech-nique ispromisingthe largestreductionin theupperbound[27]

onthecouplingtomatter.Precisiontestsofthestandardmodelare onlysensitivetothecouplingtogaugefields,i.e.heretophotons, and provide a large upper bound. From astrophysics, an analysis of thepolarisationof thelight comingfrom astronomicalobjects providesaboundof

β

γ

>

1.1

×

109 [28].

The results we have presented herefor solar chameleons are only valid for values of the matter coupling below the reso-nance threshold in the production mechanism at the tachocline (βm

<

106).Forlargervaluesofthemattercoupling,thelarge

val-uesofthemassofthechameleoninsidethetachoclinecompared to the plasma mass lead to a large suppression. The CHASE ex-perimentissensitivetothephotoncouplinguptolargevaluesof themattercoupling(βm

∼

1014).Theregionabove

β

m

=

1.9

×

107

is already excluded by the neutron experiments. At low

β

m, our

resultsextendtheCHASEcoveragebyoverthreeordersof magni-tude tobelow

β

m

=

10 intoa region alreadyexcludedby torsion

Fig. 12. Theexclusionregionforchameleonsintheβγ–βmplane,achievedbyCAST in2013(purple).Weshowtheboundssetbytorsionpendulumtests(ingreen)[25], neutroninterferometrymeasurements(lilac)[26], CHASE(paleorange) [12]and colliderexperiments(yellow)[30].Theforecastsoftheatom-interferometry tech-nique[27]andtheastronomicalpolarisation[28]arerepresentedwithlines.

Table 2

Upperlimitonβγ derivedatCASTfordifferent

val-ues ofthe index n which definesthe chameleon model. index n βγ at 95% CL 1 9.26×1010 2 9.21×1010 4 9.20×1010 6 9.19×1010

Higher values of n could be envisaged but would not alter

the physical picture discussed here (see [7] for a discussion of then

=

4 case). Ourresultsare toa large extentinsensitive ton (Table 2),providedweareonlyinterestedintheregionof param-eterspacebelowtheresonanceinthemattercoupling.

Westudied theuncertainties intheassumptions for thesolar modelandtheireffectontheCASTresult.Ifforexamplethesolar luminosity bound is reduced by a factor 10,

β

sun_γ is reduced by afactor 101/2_,whilst

_β

γ remains constant, resultingina weaker limitrelativetothesolarluminositybound.Ratherconservatively, thedetails ofthe radial field strength andits distributionat the tachocline may affect the

β

γ limit by a factor of 1.6 (Table 1). Fortheuncertaintyonthemagnitudeofthemagneticfield atthe tachoclinewehaveconsidered arange from4 to25–30T,which producesanuncertaintyin

β

γ ofafactorofabout1.6upanddown respectively(Fig. 11).

Allinall,wefindthatthechameleonparameterspacehasbeen significantly reduced. Additional CAST data with the InGrid de-tector and an X-ray telescope will improve the photon coupling sensitivitybeyondthe solarbound in thenear future.In parallel CASTisdevelopingadetectiontechnique whichexploitsthe cou-plingofchameleonstomatter.Chameleonsofsolarorigin,focused byanX-raytelescopeonCAST,canbedirectlydetected bya radi-ationpressuredevice[29].

9. Conclusions

CAST has made a first dedicated sub-keV search for solar

chameleonsbasedonthePrimakoffeffect.Thissearch,runningin avacuumconfigurationusingareadily-availableapparatus,didnot observean excess above background and has set a limit for the couplingstrengthto photonswhichforn

≥

1 excludes anew re-gionofparameterspacecovering3ordersofmagnitudeinmatter

coupling and reachesdown to the level of photon coupling cor-responding to boththe 10% solar luminosity bound andalsothe limitderivedbyCHASE.

Acknowledgments

WethankCERNforhostingtheexperimentandforthe techni-cal support tooperate themagnet andthecryogenics. We thank CERNPH-DTandTE-CRGgroupsfortechnicalsupporttobuildthe X-raydetectorsystemandA.Niculae(PNDetector)fortechnical ad-vice.

We acknowledge support from NSERC (Canada), MSES

(Croa-tia), CEA (France),BMBF (Germany) underthe grant numbers 05

CC2EEA/9and05CC1RD1/0andDFG(Germany)undergrant

num-bers HO 1400/7-1 and EXC-153, GSRT (Greece), NSRF: Heraclei-tus II,RFFR(Russia),theSpanishMinistryofEconomyand Compet-itiveness(MINECO)underGrantsNo.FPA2008-03456,No. FPA2011-24058 andEIC-CERN-2011-0006. This work was partially funded

by the European Regional Development Fund (ERDF/FEDER), the

European Research Council (ERC) under grant

ERC-2009-StG-240054 (T-REX), Turkish Atomic Energy Authority (TAEK), NASA underthe grantnumberNAG5-10842.Part ofthisworkwas per-formed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. P. Brax acknowledges partial support from the European Union FP7 ITN INVISIBLES (Marie Curie Actions, PITN-GA-2011-289442)andfromtheAgenceNationaledelaRecherche undercontractANR2010BLANC041301.

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