Constraining interactions mediated by axion-like particles with ultracold neutrons

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Constraining interactions mediated by axion-like

particles with ultracold neutrons

S. Afach, G. Ban, G. Bison, K. Bodek, M. Burghoff, M. Daum, M. Fertl, B.

Franke, Z.D. Grujic, V. Helaine, et al.

To cite this version:

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Constraining

interactions

mediated

by

axion-like

particles

with

ultracold

neutrons

S. Afach

a

,

b

,

c

,

G. Ban

d

,

G. Bison

b

,

K. Bodek

e

,

M. Burghoff

f

,

M. Daum

b

,

M. Fertl

a

,

b

,

1

,

B. Franke

a

,

b

,

∗

,

2

,

Z.D. Gruji ´c

g

,

V. Hélaine

b

,

d

,

M. Kasprzak

g

,

Y. Kermaïdic

h

,

K. Kirch

a

,

b

,

P. Knowles

g

,

3

,

H.-C. Koch

g

,

i

,

S. Komposch

a

,

b

,

A. Kozela

j

,

J. Krempel

a

,

B. Lauss

b

,

∗

,

T. Lefort

d

,

Y. Lemière

d

,

A. Mtchedlishvili

b

,

O. Naviliat-Cuncic

d

,

4

,

F.M. Piegsa

a

,

G. Pignol

h

,

P.N. Prashanth

k

,

G. Quéméner

d

,

D. Rebreyend

h

,

D. Ries

a

,

b

,

S. Roccia

l

,

∗

,

P. Schmidt-Wellenburg

b

,

A. Schnabel

f

,

N. Severijns

k

,

J. Voigt

f

,

A. Weis

g

,

G. Wyszynski

a

,

e

,

J. Zejma

e

,

J. Zenner

a

,

G. Zsigmond

b

a_{ETHZürich,InstituteforParticlePhysics,CH-8093Zürich,Switzerland} b_{PaulScherrerInstitute(PSI),CH-5232Villigen-PSI,Switzerland}

c_{HansBergerDepartmentofNeurology,JenaUniversityHospital,D-07747Jena,Germany} d_{LPCCaen,ENSICAEN,UniversitédeCaen,CNRS/IN2P3,Caen,France}

e_{MarianSmoluchowskiInstituteofPhysics,JagiellonianUniversity,30-059Cracow,Poland} f_{PhysikalischTechnischeBundesanstalt,D-10587Berlin,Germany}

g_{PhysicsDepartment,UniversityofFribourg,CH-1700Fribourg,Switzerland} h_{LPSC,UniversitéGrenobleAlpes,CNRS/IN2P3,Grenoble,France}

i_{InstitutfürPhysik,Johannes–Gutenberg–Universität,D-55128Mainz,Germany} j_{HenrykNiedwodnicza´nskiInstituteforNuclearPhysics,31-342Cracow,Poland} k_{InstituutvoorKern–enStralingsfysica,UniversityofLeuven,B-3001Leuven,Belgium} l_{CSNSM,UniversitéParisSud,CNRS/IN2P3,OrsayCampus,France}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received9December2014

Receivedinrevisedform30March2015 Accepted14April2015

Availableonline20April2015 Editor:M.Doser

Keywords:

CPviolation

Shortrangespin-dependentinteraction Axion

Axion-likeparticle Ultracoldneutrons

Neutronelectricdipolemoment

We report a new limit on a possible short range spin-dependent interaction from the precise measurement of the ratio of Larmor precession frequencies of stored ultracold neutrons and 199Hg atoms confined inthe same volume. The measurement was performed ina ∼1μT vertical magnetic holding fieldwiththe apparatussearching forapermanentelectricdipole momentofthe neutronat the PaulScherrerInstitute.Apossible couplingbetweenfreelyprecessingpolarized neutronspinsand unpolarized nucleons ofthe wall materialcan be investigated by searching for atiny change of the precessionfrequenciesofneutronand mercuryspins.Suchafrequencychangecanbeinterpretedasa consequenceofashortrangespin-dependentinteractionthatcouldpossiblybemediatedbyaxionsor axion-like particles.The interactionstrengthis proportional tothe CPviolatingproductofscalarand pseudoscalarcouplingconstantsgSgP.Ourresultconfirmslimitsfromcomplementaryexperimentswith

spin-polarizednucleiinamodel-independentway.Limitsfromotherneutronexperimentsareimproved byuptotwoordersofmagnitudeintheinteractionrangeof10−6_{< λ<10}−4_m.

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

*

Correspondingauthor.

E-mailaddresses:[email protected](B. Franke),[email protected]

(B. Lauss),[email protected](S. Roccia).

1 _{NowatUniversityofWashington,SeattleWA,USA.}

2 _{NowatMax-Planck-InstituteofQuantumOptics,Garching,Germany.} 3 _{NowatLogrusData,Vienna,Austria.}

4 _{NowatMichiganStateUniversity,East-Lansing,USA.}

1. Introduction

Wepresentaninterpretationofourrecentmeasurementofthe ratio

γ

n

/

γ

Hg of theneutron and199Hg magnetic moments [1]in

terms of the strength of a possible short range spin-dependent neutron–nucleon interaction.Thisratiowas inferred froma com-parisonofthesimultaneouslyrecordedLarmorprecession frequen-ciesofthetwospeciescontainedinthesamestoragevolume.The

http://dx.doi.org/10.1016/j.physletb.2015.04.024

measurementwasperformedusingtheapparatusdedicatedtothe searchfortheneutronelectricdipole moment(nEDM)[2]bythe nEDMCollaboration atthesourceforultracoldneutrons[3]ofthe PaulScherrerInstitute,Switzerland.

Inthecentralstoragevesselofthe apparatus,thespinsofthe neutronsandmercuryatomsaremadeto precesssimultaneously inthesamevolume.Theratio

R

=

fn fHg

(1)

constitutes a sensitive tool for the control of systematic effects during the measurement ofthe nEDM. By correcting R properly

forknowndifferencesoftheLarmorprecessionofthetwospecies neutrons and199_{Hg, respectively, theratio ofmagnetic moments}

γ

n

/

γ

Hg can be extracted. A dataset of R taken in 2012was

in-dependentlyanalysedin[1]andin[4],whereweadditionally ex-amineditssensitivity tohypotheticalshortrange spin-dependent interactions.Possibleforcemediatorsareaxions,oraxion-like par-ticlesandtheinteractionstrengthisproportionaltotheproductof scalarandpseudoscalarcouplingconstants gSgP.Ithasbeen

pro-posedin[5,6] to usean nEDMapparatusforthe investigationof suchaforce.

A motivation to search for an interaction involving gSgP is

giveninSection 2.Theinfluenceofashortrangespin-dependent interactionon the observable R isexplained andderived in Sec-tion3, whereadditionallysome related details aboutthe experi-mentareshown.Ourresultiscomparedtoothercurrentlimitson theproduct gSgP inSection4.

2. Motivation

The investigation of CP violating processes is a major line of research in particle physics. In contrast to the weak interaction, thereissofarnoevidencethat thestronginteractionviolatesCP symmetry.The non-observationofan nEDMatcurrentsensitivity levelsconstrains theCPviolating term(

θ

-term) intheLagrangian ofthe stronginteraction to be nine orders of magnitudesmaller than naturally expected [7]. This fact is known as thestrongCP problem andasolutiontoitwasproposedin[8],wherethe spon-taneouslybrokenPeccei–Quinnsymmetrywasintroduced.

A new pseudoscalar boson emerges from this symmetry, the axion [9,10]. Anintrinsic feature ofthe Peccei–Quinn modelis a fixedrelationbetweenmassandinteractionstrengthoftheaxion. Theoriginallyassumedsymmetrybreakingscale(correspondingto theelectroweak scale)was ruled out, leavingonly higherenergy scalespossible. Fortheaxion one thusexpectsa smallmassand afeebleinteractionwithotherparticles.Thepossiblemassofthe axionisconstrainedbycosmologyandastro-particlephysics mea-surementstotheso-calledaxionwindow[11].

Ashortrangespin-dependent interaction whichcould be me-diated by an axion was proposed in [12]. There, three classes of interactions were presented, involving either g2

S-, gSgP-, or

g2_P-couplings,whereasgSgP-couplingsareconsideredofparticular

interest,sincetheyviolateCPsymmetry.A gSgP-couplingdiagram

isshowninFig. 1(a)andtakesplacebetweenanunpolarized par-ticle



(whereunpolarized meansrandomlypolarizedwithrespect to any quantizationaxis) anda polarized particle



. The sym-bol  is used to denote properties of the particle interacting at thepseudoscalar vertexwitha strength proportional to the cou-plingconstant g_P oftheparticle



.Thepotentialcausedbysuch a gSgP-couplingbetweenanunpolarizedparticleandapolarized

particlewithmassmandspin

σ

isderivedas[12]:

V

(

r

)

=

gSgP

(

hc

¯

)

2 8

π

mc2

(

σ

ˆ



_{· ˆ}

_r

₎



1 r

λ

+

1 r2



e−r/λ

,

(2)

Fig. 1. (a)Interactiondiagramofascalar-pseudoscalarcouplingbetweenparticles

and.isunpolarizedandinteractsatthescalarvertexwiththecoupling con-stantgS,whereasispolarizedandinteractsatthepseudoscalarvertexwiththe

couplingconstantgP.Thetotalinteractionstrengthisproportionaltotheproduct

gSgP.(b)Apolarizedneutronnwithspinσ interactswithanunpolarizednucleon

Natdistancer withinbulkmattershapedasaplateofthicknessd.Aviewofthe

–z planeinacylindricalcoordinatesystem(,φ,z)isshown.

where

σ

ˆ

 istheunitvectorofthespin,r is

ˆ

theunitvectoralong thedistancer betweentheparticles,and

λ

theinteractionrange. Theproduct

(

σ

ˆ



· ˆ

r

)

alsoviolatesparityPandtimereversal sym-metryT.

gSgP-couplings can also be mediated by other hypothetical

spin-zeroparticleswhichare generictotheaxion andusually re-ferredtoasaxion-likeparticles.However,forthesegenericbosons no relation between mass and interaction strength is given, as compared to the genuine axion. The originof such particles can besymmetriesotherthanPeccei–Quinnsymmetry,whichare bro-kenatveryhighenergiesandoftenpostulatedintheoriesbeyond theStandardModelofparticlephysics,suchase.g. StringTheory. Thus,bothaxionsandaxion-likeparticles,areintriguingdark mat-tercandidatesandbeyondStandardModelphysicsprobes[13–15]. However,duetothenon-observationofthenEDMashortrange spin-dependent interaction mediated by an axion is constrained to gSgP

<

10−40

. . .

10−34 [16].Onthe otherhand,ifthe force is

mediated by an axion-like particle, gS and gP are not related to

aspecificsymmetrybreakingscale.Thus,nosignificantconstraint (i.e. comparable to experimental sensitivity ranges) on gSgP can

bededucedfromcurrentEDMlimits[16]forthecaseofageneric bosonbeingtheinteractionmediator.

Our measurement withultracold neutrons is particularly sen-sitive to axion-likeparticles witha mass intherange ofroughly 10 meVto100 meVcouplingtofermions.Italsomatchesthemass rangetargetedby helioscopessuch asCAST[17] whichwouldbe sensitivetoaxion-likeparticlescouplingtophotons.

3. ThemeasurementwiththenEDMapparatus

The experiment is performedby confining ultracold neutrons (UCN) ofenergies below 160 neV [18,19] in a cylindrical storage chamber withvertical axisat thecenter ofthe nEDMapparatus. Thedimensionsofthestoragechamberandsomespecificfeatures areshowninFig. 2.A homogeneousverticalmagneticholdingfield of

∼

1μT is appliedwith a cos

θ

-coilwound around the horizon-tally cylindricalvacuumtank. This vacuumtank isenclosed by a four-layermagneticshielding[20]andanactivemagneticfield sta-bilisationsystemfortheexternalmagneticfield[21].

Spin-polarizedUCNarefilledintothestoragechamber approx-imatelyevery340 swheretheyprecessfreelyfor180 sduring the described measurements.Theprecessionfrequencyisinferred us-ingRamsey’smethod[2].Thespinsofpolarized199Hg atoms pre-cess simultaneously in the same volume allowing to correctthe Larmor precession frequency of the neutrons for potential, small magnetic field fluctuations whichcan occur inside thefour-layer magneticshieldingmadeofμ-metal.

Fig. 2. VerticalcutviewoftheUCNstoragechamberwithimportantparts schemat-ically indicated(not toscale). The biggrey arrowindicates the main magnetic holdingfieldB0.Theblueshadedregionistheinsideofthechamberandindicates

theinhomogeneousUCNdensitydistribution.TheredshapesdepictCs magnetome-ters[22]whicharemountedaboveandbelowthestoragechamber:fourontopand sevenatthebottom.TheseconsistofaCs-vapourfilledglassbulbinsideashielded housingandservetomeasuretheverticalmainmagneticfieldB0andalsovertical

magneticfieldgradientsG.Themeasuresarethethicknessd ofthetopandbottom platesofthevessel (coatedwithdiamond-likecarbonforimprovedUCNstorage properties[18]),distanceD betweentopandbottomCsmagnetometers,heightH

ofthevessel,andradiusC ofthevessel.UCNarefilledthroughaguidefrom be-low.Thelateralwallofthevesselisapolystyreneringwithadeuteratedcoating forimprovedUCNstorageproperties[19].Thevacuumtank(VT)oftheapparatus isenclosedbyafour-layermagneticshielding(MS)made fromμ-metal [20]and asurroundingfieldcompensation(SFC)whichactivelystabilisestheexternal mag-neticfield[21].(Forinterpretationofthereferencestocolorinthisfigurelegend, thereaderisreferredtothewebversionofthisarticle.)

by thepotential ofEq.(2) andanexample isshownin Fig. 1(b). Integratingtheinteractionoverallthenucleonspresentinuniform bulkmatterresultsinaneffectivefieldnormaltothesurface.

Sincethepotentialisspin-dependent,itcanalsoberegardedas a pseudomagneticfield b which can affectthe Larmor frequency of precessing spins. For a symmetric setup withidentical mate-rialfor thebottomandtop ofthestorage vessel,thefield atthe vesselsurfacespointsinoppositedirections.Therefore,weexpect no shiftin theLarmor frequencyof the Hg atomswhich sample the volume homogeneously. However, UCNs havesuch low ener-giesthattheyaresignificantlyaffectedbygravityandtheirdensity increasestowardsthebottomofthestoragevessel.Thus,thevessel isinhomogeneously sampled andthe effectof apseudomagnetic fieldatthebottomofthechamberwillnotcanceloutcompletely. Dependingon thesign ofthe verticalmagnetic field,the preces-sion frequency ofthe UCN spins will be increasedor decreased. Consequently, R will beshifted by a constant withopposite sign fortheupwardordownwardorientedmagneticholdingfield B0:

R↑↓

=

γ

n

γ

Hg



1

±

b B0



,

(3)

wherethe

±

signappliestotheupward/downwardoriented mag-neticholdingfield,respectively.

3.1. Derivationofthepseudomagneticfield

IntegratingthepotentialgiveninEq.(2)overbulkmatter,e.g. a plateofthicknessd,radiusC ,andnucleonnumberdensityN, re-sultsinatotalpotential Vtot atheight z abovethesurfaceofthe

plate(cylindricalcoordinatesr

= (



,

φ,

z

)

areused)[4]:

Vtot

(

z

)

=

−d



0 2π



0 C



0 N V

(

r

)



d



d

φ

dz (4)

=

gSgP

¯

h2N

λ

4m



e−λz

−

_e−z+λd

−

_e−  C 2+z2 λ

+

_e−  C 2+(z+d)2 λ



(5)

≈

gSgP

¯

h2N

λ

4m

1

−

e−d/λ

e−z/λ

.

(6)

TheapproximationfromEq.(5)to(6)neglectsthethirdandfourth terms intheroundbracketsandiswelljustifiedduetothe dimen-sionsofthechamber(d



C ),andtherangeofinterestof

λ

andz

(

λ,

z



C ).Italsocorresponds to simplifyingtheintegration over theradialcomponent



toaninfiniteplane.

Thepseudomagneticfieldb normaltothesurfacecanbe writ-tenasafunctionofheight z:

b

(

z

)

=

2Vtot

(

z

)

γ

h

¯

≈

gSg  P

¯

h

λ

N 2

γ

m

1

−

e−d/λ



e−z/λ



,

(7)

where

γ

isthegyromagneticratioofthepolarizedparticle.This resultagreeswiththeonederivedin[5].

InordertocalculatethefieldpresentinthenEDMsetupbnedm,

boththebottomandthetopofthestoragevesselhavetobetaken intoaccount.Thevessel’sinnerhorizontalsurfacesare perpendic-ulartoz,withthebottomsurfaceatz

= −

H

/

2 andthetopsurface atz

= +

H

/

2,asshowninFig. 2.UsingEq.(7)onefinds

bnedm

(

z

)

=

bbottome−

z+H/2

λ

−

_btope−− z+H/2

λ

_.

₍₈₎

Becauseoftheirinhomogeneousdensitydistribution

ρ

(

z

)

,theUCN experienceaneffectivefieldgivenby

bUCN

=

H 2



−H 2 bnedm

(

z

)

ρ

(

z

)

dz

.

(9)

ThefirstorderestimatefortheUCNdensitydistributionis

ρ

(

z

)

=

1 H



1

+

12h H2z



,

(10)

whereh

= −

2

.

35

(

5

)

mm isthemeasuredcenter-of-massoffset be-tweenUCNandHgatomdistributions(seealsoSection3.2).

Since the pseudomagnetic field isexpected to be of short in-teraction range

λ

given by the limits which have already been imposed on gSgP, the UCNdensity distribution can be

approxi-mated witha constantvalue within adistance

∼λ

to thebottom andtopsurfaces.Asaconsequence,Eq.(9)canbesimplifiedinthe followingway: bUCN

≈

H 2



−H 2

ρ

bottombbottome− z+H/2 λ

−

ρ

_topbtope−− z+H/2 λ

dz

,

(11)

where

ρ

bottom

=

ρ

(

−

H

/

2

)

and

ρ

top

=

ρ

(

+

H

/

2

)

.Thusthe integral

canbesolvedanalyticallyandthescalarandpseudoscalarcoupling constantscanbeisolatedasfollows:

gSgP

=

bUCN H2

γ

m 6hhN

¯

λ

2

1

−

e−H/λ

₋1

1

−

e−d/λ

₋1

.

(12)

The bottom and top of theUCN storage vessel are madeof alu-minumandhaveathicknessofd

=

2

.

5cm each.WeuseN

≡

NAl

=

1

.

62

·

1024_cm−3 _and

_γ



_≡

_γ

_n

₌

_2π

_·

₂₉

_.

_1646943MHz

_/

_T[23].The

issimilartothatofaluminum.Thus thecoatingisdisregardedin thecalculation butforthefact thatwerestrictthevalidityofour derivedlimitto

λ

>

1μm.

The center-of-mass offset h contributes to the denominator of Eq. (12) and depends on the energy spectrum of the UCN. Hence, a changeinthe energy spectrum,or alsoa different ves-sel height H ,will influence the sensitivityof our apparatusto a pseudomagneticfield.

3.2.DetailsonthemeasurementoftheratioR andthecenter-of-mass offseth

In [1], the measurement of R and its experimental setup are thoroughlydescribed.Herewebrieflyrecapitulateselectedaspects of the experiment and related systematics relevant to our mea-surement.

Taking into account systematicshifts on the UCN or mercury spinprecessionfrequency,theratioR canberewrittenas:

R

=

fn fHg

=

γ

n

γ

Hg



1

+ δ

Grav

+ δ

Trans

+ δ

Light

+ δ

Earth



.

(13)

Alinear, G-dependent fit of the form x

+

G y, where G

= ∂

B

/∂

z

istheverticalmagneticfield gradient,wasperformedtothedata listedinTable 2 of[1].Thefirst twoterms inEq.(13)constitute thetermsofthefit.Theothertermsshifttheconstantfit parame-terandaddtothesystematicerror.Thedifferentcontributionsto Eq.(13)arediscussedinthefollowing.

Firstlywewanttofocusontheshifts

δ

Gravand

δ

Transwhichare

bothrelatedtotheverylowkineticenergiesoftheUCN.

The gravitation-induced systematic effect is described at first orderby

δ

↑↓_Grav

= ±

h

B0

G

,

(14)

where the plus-sign refers to B0↑ and the minus-sign to B0↓.

Eq.(14)is derived assuming a UCNdensitydistribution asgiven in Eq. (10) and thus the common slope in both equations cor-responds to the center-of-mass offset h of the UCN. The linear gradient dependenceis assumed to hold for small G. Measuring

R asafunctionofvaryingverticalmagneticfieldgradientsenables usextractthecenter-of-massoffseth fromtheslopeofR vs. G.

Twocorrectioncoils(woundassaddlecoilsontopandbottom ofthe vacuumtank) were powered in an anti-Helmholtz config-uration to superimpose a vertical magnetic field gradient to B0.

A measurementofthemagnitudeofG isprovidedbycesium mag-netometers[22]whicharelocatedaboveandbelowtheUCN stor-agevessel(seeFig. 2).Asecondorderpolynomialparametrization ofthemagneticfieldisusedtoextractG fromthemagnetometers’ readingsandtheirpositions.

Thesystematiceffectduetopossibletransversecomponentsof

B0 reads

δ

↑↓_Trans

=

B_⊥2



↑↓ 2B02

,

(15)

where

B_⊥2



↑↓ is the storage chamber volume average of trans-versemagneticfieldcomponentsB_⊥forthecaseofthemain mag-neticfield B0beingorientedupwardsordownwards,respectively.

Thiscorrectionresultsfromthefactthat,givenbytheirlow veloci-ties,theneutronsareintheadiabaticregime(Larmorfrequency

>

wallcollision rate)andtheir precessionfrequency isproportional totheaveragemagneticfieldmodulus fn

∝ |

B

|

.Whereasforthe

mercuryatomswiththermalvelocities(Larmor frequency

<

wall collisionrate), fHg

∝ |



B

|

.

Table 1

Relativecontributionstotheoverallerrorlistedbytheeffectwhichcontributesto themagneticfield.

Effect B0↑ B0↓ Statistics ±0.5·10−6 _±0 .5·10−6 Gravitational shift (−8.9±2.3)·10−6 _{(−1.8±2.7)·10}−6 Transverse shift (3.7±0.8)·10−6 _{(3.0±1.2)·10}−6 Light shift (1.3±0.7)·10−6 _{(0.8±0.6)·10}−6

Earth rotation shift −5.3·10−6 _+5.3·10−6

A magnetic field mapping was performed inside the vacuum tank with a sophisticated non-magnetic robot using a custom-madehighsensitivitytriaxialfluxgate magnetometer.Thevolume oftheprecessionchamberhasbeenmapped.Thefollowingresults forthetwomagneticfieldorientationswereobtained:



B_⊥2



_↑

= (

2

.

1

±

0

.

5

)

nT2

;



B_⊥2



_↓

= (

1

.

7

±

0

.

7

)

nT2

.

(16)

These numbers have to be regarded in relation to the absolute value of the magnetic field of

∼

1μT.Comparing the two values for

↑

and

↓

witheach other also demonstrates how well a po-laritychangeof B0 resemblesa perfectinversion ofthemagnetic

field.

δ

Lightresultsfromashiftof fHgduetolight-intensity-dependent

effectsduring theoptical read-outofthemercuryprecession fre-quencyasexplainedin[24].Thecorresponding correction factors aregiveninTable 1(fourthrow).

The remaining

δ

Earth is a consequence of the Earth being a

rotatingframeofreference.Inthiscontextitisofparticular inter-estthatneutronsandmercuryatomshavedifferentsignsoftheir gyromagnetic ratios,i.e. they precess in differentdirections with respectto themagneticfield. Thiscanbe correctedforby apply-ingthetermsinTable 1(fifthrow).

Allsystematicerrorcontributionsaresummarizedintheerror budget for the measurement of the ratio R in Table 1. We can derive two independent valuesfor R using the datafor B0↑ and

B0↓,respectivelyandtheerrorcontributionsfromTable 1:

R↑

=

3

.

8424583

(

26

)

(17)

R↓

=

3

.

8424562

(

30

).

(18)

FromthedifferenceofR↑ andR↓(asgiveninEq.(3))andthesum

R↑

+

R↓

=

2γn

/

γ

Hgwecanextract bUCN

=



R↑

−

R↓





R↑

+

R↓



B0

= (

0

.

28

±

0

.

53

)

pT

.

(19) 4. Resultandcomparisontootherexperiments

UsingEq.(12),themeasuredpseudomagneticfieldbUCNcanbe

convertedtoa95 %confidencelevellimitongSgP

gSgP

λ

2

<

2

.

2

·

10−27m2 (20)

for1μm

< λ

<

5mm.Attheupperendofthisrange,thelastfactor inEq.(12)departs from

∼

1 andthe relation gSgP

∝

1

/λ

2 isnot

fulfilledanymore. Asa consequencethe sensitivityofour experi-mentto gSgP decreases whichresultsina flatteningofthelimit

inthe gSgP vs.

λ

-plane(seeFig. 3).Thelowerendofthisrangeis

constrainedby thewavelengthofultracold neutrons andaffected bysurfacepropertiessuchascoating,roughness,etc.

Since we investigatedan interactionbetween unpolarized nu-cleons andpolarized neutrons, we can state that we probed the scalarcouplingconstantgenerallyvalidfornucleons gS

≡

gN_S and

the pseudoscalar coupling constant specific to the neutron g_P

≡

gn

Fig. 3. Overviewofcurrentlimitsontheproductofscalarandpseudoscalar cou-plingconstantsgSgP asfunctionoftheinteractionrangeλofashortrange

spin-dependentforceat95 %confidencelevel.Onthetop,thecorrespondingmassrange ofthemediatingparticle,i.e. axionoraxion-likeparticle,isshown.Theshaded re-gionisexcludedbydifferentexperiments.Solidlinelimitswereobtainedusingcold orultracoldneutrons.Dashedlinelimitswereobtainedusing3_He,129_Xe,or131_Xe

precessionexperiments.A[30];B[31],assuminganattractiveinteraction;C[32]; D[6];E[29];F[26];G[27];andH (redinthewebversion)thiswork.ThelineI (dotted)depictstheachievablelimitbyasimplemodificationofourapparatus(see text).

Fig. 3comparesourlimitongSgP toresultsfromother

exper-iments.Itcoverstheinteractionrangeof1μm

< λ

<

0

.

1m,which isnotyetstronglyexcludedbyastrophysicalorcosmological con-straints.

Experiments using free neutrons are depicted by solid lines. Experiments with precessing atoms, such as e.g. 3He, 129Xe, or

131_{Xe, are depicted by dashed lines. According to the Schmidt}

Model [25], polarized atoms ofodd isotopes (with one unpaired nucleon) can roughly be considered asa probe forthe magnetic properties ofthis unpaired nucleon, regardless ofthe other con-stituents of the nucleus. Under this assumption, both types of experimentsprobegN

SgnP.Whiletheseapproachesare

complemen-tary, the direct neutron measurements are model independent. The moststringentlimitsfor

λ

>

10−4m havebeenimposed re-centlyin[26]and[27] (curveslabelledFandG inFig. 3, respec-tively) which improved the recent limits from [28]. For shorter interactionranges,the moststringentlimitwas givenin[29] (E), whererelaxationofspinpolarized3He gas was investigated.This limit has been model independently confirmed and slightly im-proved by the measurements presented in this work (H). Lim-its derived from experiments with neutrons (A,B,C,D) [30–32,6] were improved by one order ofmagnitude for

λ

<

10−5 _andby

two orders of magnitude for

λ

>

10−5. In [33] a stronger but indirectlimit on gSgP was imposed by combininglaboratory

re-sults with stellar energy loss arguments. Such limits might be reached with dedicated future laboratory searches e.g. proposed in[34].

Already our present result constitutes a new direct limit on

gSgP.Replacing inourexperimentthe centralvesselbottom and

top with copper, a material with higher density and good UCN reflecting surface properties,would resultina sensitivity gain of

∼

3, corresponding to the density ratio betweencopper and alu-minum. Replacing either only the bottom ortop would createa trueasymmetric potentialandincrease the sensitivityby one or-der ofmagnitude[4].The consequentlyachievable limit depicted bythedottedcurve (I)inFig. 3wouldbean important contribu-tion toreduce the allowed parameter spaces ofbeyondStandard Modeltheories.

Acknowledgements

We are grateful to the PSI staff (the accelerator operating team and the BSQ group) forproviding excellent running condi-tions andacknowledge theoutstanding support ofM. Meier and F. Burri.SupportbytheSwissNationalScienceFoundationProjects 200020-144473(PSI),200021-126562(PSI), 200020-149211(ETH) and200020-140421(Fribourg)isgratefullyacknowledged.TheLPC Caen and the LPSC Grenoble acknowledge the support of the French Agence Nationale de la Recherche (ANR) under reference ANR-09–BLAN-0046.ThePolishcollaboratorsacknowledgethe Na-tional Science center, Poland, forthe grant No. UMO-2012/04/M/ ST2/00556 andthe support by the Foundation for PolishScience – MPD program, co-financed by the European Union within the European Regional DevelopmentFund. Thisworkwas partly sup-ported by the Fund for Scientific Research Flanders (FWO), and ProjectGOA/2010/10oftheKULeuven.Theoriginalapparatuswas fundedbygrantsfromtheUK’sPPARC.

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