Search for muoproduction of X(3872) at COMPASS and indication of a new state (X)over-tilde(3872)

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Search

for

muoproduction

of

X

(

3872

)

at

COMPASS

and

indication

of

a

new

state

X

(

3872

)

.

COMPASS

Collaboration

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received6July2017

Receivedinrevisedform4July2018 Accepted6July2018

Availableonline11July2018 Editor:M.Doser Keywords: COMPASS X(3872) Photoproduction Tetraquark Exoticcharmonia

We have searched for exclusive production of exotic charmonia in the reaction

μ

+N→

μ

+(J/ψ

π

+

π

−)

π

±N usingCOMPASS datacollectedwithincomingmuonsof160 GeV/c and200 GeV/c momentum.Inthe J/ψ

π

+

π

− massdistributionweobserveasignal withastatistical signiﬁcanceof4.1

σ

.Itsmass and widthareconsistentwiththoseofthe X(3872).Theshapeofthe

π

+

π

−massdistributionfromthe ob-serveddecayinto J/ψ

π

+

π

−showsdisagreementwithpreviousobservationsforX(3872).Theobserved signal may be interpretedas a possible evidenceof anew charmoniumstate. It could be associated withaneutralpartnerof X(3872) withC= −1 predicted byatetraquarkmodel.Theproductofcross sectionandbranchingfractionofthedecayoftheobservedstateinto J/ψ

π

+

π

−isdeterminedtobe 71±28(stat)±39(syst) pb.

The exotic hadron X

(

3872

)

was ﬁrst discovered in 2003 by the BelleCollaboration [1] and constitutesthe ﬁrstin a long se-riesofnewcharmonium-likehadronsatmassesabove3.8 GeV/c2. The X

(

3872

)

was observed as a narrow peak in the J

/ψ

π

+

π

− mass spectrum originating fromthe decay B±

→

K±J

/ψ

π

+

π

−. Subsequently, thisstate hasalso been observed innumerous re-actionchannelsandﬁnalstates:ine+e− collisionsbyBelle[2–5], Babar [6–12] andBESIII [13] and inhadronicinteractions byCDF [14–17],D0[18],LHCb[19–21],ATLAS[22] andCMS[23].The cur-rentworld average forthe massof the X

(

3872

)

is 3871.69

±

0.17 MeV/c2 [24], which is very close to the D0D

¯

∗0 threshold at 3871.81

±

0.09MeV/c2_._However,_the_decay_width_of_this_state_was

not determined yet as in all experiments the measured widths were compatible withthe experimental resolution.Thus only an upperlimitforthenaturalwidth

X(3872)ofabout1.2MeV/c2 (CL

=

90%) exists [5]. The spin, parity andcharge-conjugation quan-tumnumbers JP C ofthe X

(

3872

)

weredeterminedbyLHCbtobe 1++ [20,25].Charged partnersofthe X

(

3872

)

havenot been ob-served[26].The X

(

3872

)

hadronispeculiarinseveralaspectsand itsnatureisstillnotwellunderstood.Inparticular,approximately equalprobabilities to decayinto J

/ψ

3

π

and J

/ψ

2

π

ﬁnal states

B(

X

(

3872

)

→

J

/ψ

ω

)/

B(

X

(

3872

)

→

J

/ψ

π

+

π

−

)

=

0

.

8

±

0

.

3 [27] indicatelarge isospin-symmetrybreaking.There areseveral inter-pretationsofthishadron:purecc-state,

¯

tetraquark,meson–meson molecule,cc g meson,

¯

glueball,orothers(seereviews[28–30]).In additiontoknowingmassandquantumnumbersofthisstate,the measurementofitswidthwouldprovideacrucialinputtonarrow down speculations on its nature. Currently such a measurement

canonlybedonebyperformingenergyscansin pp annihilations,

¯

asitisforeseenatFAIR[31,32].

InthisLetter, wereport ona search for X

(

3872

)

produced by virtualphotonsinthecharge-exchangereaction

γ

∗N

→

X0

π

±N (1)

at COMPASS. Here, N denotes the target nucleon, N the unob-served recoilsystemand X0 _an _intermediate _state _decaying _into

J

/ψ

π

+

π

−.The possibilitytoobserve theproductionof X

(

3872

)

inthisreactionwasﬁrstmentionedinRef. [33].

The COMPASS experiment [34] is situated at the M2 beam lineof theCERN SuperProton Synchrotron.The dataused inthe present analysis were obtained by scattering positive muons of 160 GeV/c or 200 GeV/c momentum off solid 6LiD or NH3

tar-gets.The totaldatasetaccumulatedbetween2003and2011was used. The target material was arranged intwo or three cylindri-cal cells placed along the beam direction. It was longitudinally or transversely polarized with respect to this direction. The po-larization isoppositeinconsecutivetarget cells,anditisreversed periodicallyduringdatataking.Aftercombiningdatawithopposite polarization,possibleeffectsfromresidualtargetpolarizationhave negligibleinfluenceonthisanalysis. Particletrackingand identifi-cationwereperformedusingatwo-stagespectrometer,coveringa wide momentumrangefromabout1 GeV/c up tothebeam mo-mentum. The eventtrigger was based on scintillator hodoscopes andhadron calorimeters.Differenttrigger schemeswere usedfor the different data sets. Possible differencesin trigger efficiencies areexpectedtocancelinthedeterminationofabsoluteproduction https://doi.org/10.1016/j.physletb.2018.07.008

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recordedinparallel,seebelow.Beamhalomuonswererejectedby vetocounterslocatedupstreamofthetarget.

ThemainsubjectofthisLetter isthestudyofmuoproduction ofan X0 _in_the_process

μ

+N

→

μ

+X0

π

±N

→

μ

+

(

J

/ψ

π

+

π

−

)

π

±N

→

μ

+

(

μ

+

μ

−

π

+

π

−

)

π

±N

,

(2) the diagram of which is schematically shown in Fig. 1. In order to select such events, we ﬁrst require a reconstructed vertex in thetarget regionwithan incomingbeammuon track, three out-going muon tracks (two

μ

+, one

μ

−) and three outgoing pions (

π

+

π

−

π

+or

π

+

π

−

π

−).Reconstructedparticlesareidentifiedas muonsifthey havemomentum above 8 GeV/c andhave crossed more than 15 radiation lengths of material. The muon identifi-cation efficiency for such energetic particles is higher than 90%. Otherchargedparticlesareassumedtobepions.Sincethedimuon massresolutionofthesetupforthe J

/ψ

peakisabout50MeV/c2

[35],candidatesfor J

/ψ

decayingintoapairofoppositelycharged muonsare acceptediftheir reconstructed mass liesin therange from3.02 GeV/c2 _to_{3.18 GeV/c}2_._With_two

_μ

+ _in_a _given_event, wemayreconstructtwo J

/ψ

candidatesinthe

μ

+

μ

− ﬁnalstate, inwhichcasetheeventis rejected(

∼

3% ofevents).Thenominal

J

/ψ

mass[24] isassignedtoaccepteddimuons.Inordertoselect exclusiveproductioninprocess(2), werequire

E tomatchthe energyEbeamofthebeamparticle,exceptforasmallrecoilenergy

to the target. Here,

E isthe sum ofenergies of the scattered muon,ofthe J

/ψ

,andofthethreepions intheﬁnal state.Since atCOMPASStheexperimentalresolutionfor

E

=

E

−

Ebeam is

about2 GeV,werequire

|

E

|

<

4 GeV inordertoselectexclusive productionofthe J

/ψ

3

π

ﬁnalstate.Thetotalnumberofselected exclusive

μ

+J

/ψ

2

π

+

π

−and

μ

+J

/ψ

π

+2

π

−eventsis72and49, respectively. The ratio (72/49) corresponds approximately to the ratiooftheaveragenumbersofprotonsandneutronsinthetarget materialthatis

∼

1

.

3.

Fig.2(a)showsthemassspectrum forthe J

/ψ

π

+

π

− subsys-teminreaction(2) fromthresholdto5 GeV/c2 afterthe aforemen-tioned selection criteria were applied. As there are two equally charged pions per event, this mass spectrum contains contribu-tionsfromthetwopossible

π

+

π

− combinations.Themass spec-trumexhibitstwopeakstructuresbelow4 GeV/c2_,_with_positions

andwidthsthatarecompatiblewiththeproductionanddecayof

ψ(

2S

)

and X

(

3872

)

. However, forreasons that will be described below,we prefer to namethe particle corresponding to the sec-ondpeak observedforthereaction(2) as

X

(

3872

)

.Wedetermine theresonanceparametersbyamaximumlikelihoodﬁttothemass spectrumfromthresholdto5 GeV/c2_,_using_a_sum_of_two_Gaussian

functionsforthetwosignalpeaksandthebackgroundterm

B

(

M

)

=

c1

(

M

−

m0

)

c2e−c3M

,

(3)

Fig. 2. (a) The J/ψπ+π− invariantmassdistributionforthe J/ψπ+π−π± final state(twoentriesperevent)forexclusiveevents(|E|<4 GeV).Thefittedcurve isshowninred.Thebluedashedlineshowsafitofthebackgroundcontribution [Eq. (3)]tothedataexcludingthesignalrange.(b)Theprobabilitytoobtainthe observedoralargernumberofeventsduetoastatisticalfluctuationofthe Poisso-nianbackgroundwithameanvaluedescribedbyEq. (4).(Forinterpretationofthe coloursinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)

whereM

=

MJ/ψπ+π− andm0

=

MJ/ψ

+

2mπ .Weignorepossible contributions from other stateslike

ψ(

3770

)

,

ψ(

4040

)

,

ψ(

4160

)

,

X

(

4260

)

,X

(

4360

)

andX

(

4660

)

sincetheirbranchingfractionsinto

J

/ψ

π π

are too small [24] to signiﬁcantly impact the shape of theobservedmassdistribution.Theﬁtfunctionhaseightfree pa-rameters: the resonancemass andthenumber ofevents ineach mass peak, the same width

σ

M for both peaks and the param-eters c1, c2, c3 describing the background shape. The yields for

ψ(

2S

)

and

X

(

3872

)

are determined to be Nψ (2S)

=

24

.

2

±

6

.

5 and N_X₍₃₈₇₂₎

=

13

.

2

±

5

.

2 events, andtheir massesare Mψ (2S)

=

3683

.

7

±

6

.

5 MeV/c2andM_X₍₃₈₇₂₎

=

3860

.

4

±

10

.

0 MeV

/

c2, respec-tively. The estimated mass values are consistent with the world average values for

ψ(

2S

)

and X

(

3872

)

[24]. The ﬁt yields

σ

M

=

22

.

8

±

6

.

9 MeV/c2 for the width. As this value is dominated by theexperimental resolution,itappears suﬃcienttousethe same widthparameterforeachGaussian.Inordertoestimatethe statis-ticalsigniﬁcanceoftheobservedsignals, thebackgroundfunction

B

(

M

)

inEq. (3) wasﬁttedtothemassspectrumshowninFig.2(a) in the region below 5 GeV/c2_, _excluding _the _signal _range _from

3.62 GeV/c2 to3.90 GeV/c2.Theprobability p

(

M

)

toﬁnda num-ber ofevents equalorlarger than observedin themass window

M

±

M,where

M

=

30MeV

/

c2_,_due_to_a_statistical_{ﬂuctuation,}

isshowninFig.2(b).Inordertocalculatep

(

M

)

weassumea Pois-sonianbackgroundwiththemeanvalue

¯

N

(

M

)

=

M

+M

M−M

B

(

M

)

dM

.

(4)

The statistical signiﬁcance for

ψ(

2S

)

and

X

(

3872

)

, expressed in terms of the Gaussian standard deviation, is 6.9

σ

and 4.5

σ

, respectively. A possible contribution of systematic effects is not taken into account here and will be discussed later. We have repeated the ﬁt keeping the mass separation of the two Gaus-sians ﬁxed to the mass difference between

ψ(

2S

)

and X

(

3872

)

fromRef. [24], whichdid not signiﬁcantlyalter neither the mass value for the

ψ(

2S

)

nor the number of observed events for ei-therstate:Mψ (2S)

=

3680

.

9

±

5

.

7 MeV/c2,Nψ (2S)

=

24

.

9

±

5

.

7 and

(3)

Fig. 3. The J/ψπ+π−invariantmassdistributionfortheexclusive J/ψπ+π−ﬁnal statefromreaction(5).

Inorderto selectanon-exclusive datasample forprocess (2), werequirealargermissingenergy,i.e.

−

12 GeV

<

E

<

−

4 GeV. TheresultinginvariantmassdistributionisshowninFig.4(a). Ex-cept for

ψ(

2S

)

, we observe no statistically signiﬁcant signal of charmonium(-like)production.

Inparalleltoreaction(2),weinvestigatethereactionwith neu-tralexchange,

μ

+N

→

μ

+X0N

→

μ

+

(

J

/ψ

π

+

π

−

)

N

→

μ

+

(

μ

+

μ

−

π

+

π

−

)

N

,

(5) byrequiringintheﬁnalstate onlytwochargedpionswith oppo-sitecharge.Hence the schematic representationofreaction(5) is similartotheone showninFig.1,butwithoutthebachelorpion. Theinvariant mass distributionfortheexclusive J

/ψ

π

+

π

− ﬁnal state is shown in Fig. 3. The parameters of the

ψ(

2S

)

peak are determined fromaﬁt usingthe modeldescribed above withthe massof the X

(

3872

)

Gaussian ﬁxed to thenominal value ofthe

X

(

3872

)

mass.TheyareNψ (2S)

=

314

±

18,Mψ (2S)

=

3687

.

1

±

0

.

8 MeV/c2 and

σ

M

=

13

.

3

±

0

.

7 MeV/c2.The X

(

3872

)

yieldobtained fromtheﬁtis

−

2

.

9

±

2

.

5 events,i.e.nostatisticallysigniﬁcant evi-denceforanX

(

3872

)

signalwasfoundinreaction(5).Astatistical simulation was used to determine the upper limit for NX(3872). Sampleswere generatedaccordingtotheﬁtresultsforthe

ψ(

2S

)

peak and the background continuum, while the strength of the

X

(

3872

)

Gaussian signal was varied.Theupperlimit NU L X(3872) for thenumberofeventsNX(3872),whichisrequiredtoobtainthe re-sultof

−

2.9 eventsor lower, is 0.9 eventsat a conﬁdence level of 90%. Similar studies were performed for the exclusive reac-tionwiththeﬁnalstate

μ

+J

/ψ

2

π

+2

π

−N.Itwasfoundthatthe massspectrumofthe J

/ψ

π

+

π

−subsystemdoesnotexhibit any glimpseofX

(

3872

)

.

Inordertoinvestigatetheoriginsof

X

(

3872

)

and

ψ(

2S

)

in re-action(2),we add the bachelor pionto bothstates todetermine theinvariantmassesofthe

X

(

3872

)

π

±and

ψ(

2S

)

π

±systems.For thisstudy,weconsideronlythetwo narrowmassregionsof

±

30 MeV/c2 _around_the_estimated_mass_values_of

_X

₍

₃₈₇₂

₎

_and

_ψ(

_2S

₎

_.

The fraction of background events in the samples is 40% and 25%, respectively. Although no signiﬁcant structure can be seen in the mass distribution shown in Fig. 5(a), some enhancement of

ψ(

2S

)

π

± eventsmaybespottedatmassesofabout4 GeV

/

c2, wheretheZ_c±(4020)charmonium-likestatewasobservedbyBESIII [36–39].Fig.5(b)showsdistributionsforthemissingmass,deﬁned asM2_miss

= (

Pμ

+

PN

−

Pμ

−

PX0

)

2,forreactions(5) and(2).Note that accordingtothisdeﬁnition,thebachelor pioncontributesto the missing mass of reaction (2). The mean value of the miss-ingmassfor

ψ(

2S

)

producedinreaction(5) isabout1.4 GeV

/

c2_.

Fig. 4. (a) The J/ψπ+π−invariantmassdistributionsforthe J/ψπ+π−π±ﬁnal state(twoentriesperevent)fornon-exclusiveevents(−12 GeV<E<−4 GeV) and (b)forexclusiveevents(−4 GeV<E<4 GeV)with missingmass Mmiss

above3 GeV/c2_(see_text_for_the_deﬁnition_of_M miss).

When

ψ(

2S

)

and

X

(

3872

)

are produced together witha bache-lor pionin reaction (2), the mean value for the missingmass is 2.7 GeV

/

c2 _and_{4.3 GeV}

_/

_c2_,_{respectively.} _The _apparent _difference

thatcanbeseenbetweenthemissingmassdistributionsfor

ψ(

2S

)

and

X

(

3872

)

producedinreaction(2) mayindicatedifferent pro-duction mechanisms. The J

/ψ

π

+

π

− invariant mass distribution for exclusive J

/ψ

π

+

π

−

π

±N eventsfromreaction (2) using the additionalrequirementMmiss

>

3 GeV

/

c2isshowninFig.4(b).By

thisrequirement the

ψ(

2S

)

peak andthebackgroundcontinuum are reducedinrespectto the

X

(

3872

)

signal whilethestatistical signiﬁcanceofthelatterdecreasesto4

σ

.

Reactions(2) and(5) are characterizedby twokinematic vari-ables:thenegativesquaredfour-momentumtransferQ2

= −(

Pμ

−

Pμ

)

2 andthe centre-of-mass (CM) energy of the virtual-photon – nucleon system,

√

sγN. The distributions of these two vari-ables are shown in Figs. 6(a) and 6(b). Most events occur at smallvaluesof Q2.TheCMenergyisdistributedbetween8 GeV and 18 GeV, while the kinematic limit for beam momenta of 160 GeV/c and 200 GeV/c is17.3 GeV and19.4 GeV, respectively. We testedthe hypothesis that the observed

X

(

3872

)

peak is an artiﬁcialstructure appearinginthereaction

γ

∗ N

→ ψ(

2S

)

N∗

→

(

J

/ψ

π

+

π

−

)(

N

π

±

)

, where one mixed up the pion from

ψ(

2S

)

decay withthe pion from N∗ decay inthe reconstruction of the

J

/ψ

π

+

π

− mass.TheresultsofatoyMonte-Carlosimulation dis-favourthishypothesis.

Themassspectrumofthetwopionsresultingfromthedecayof the X

(

3872

)

waspreciselystudied,e.g. bytheBelle[5],CDF[15], CMS[23] and ATLAS [22] collaborations.Theyfound apreference forhigh

π

+

π

−massesandadominanceofthe X

(

3872

)

→

J

/ψ

ρ

0

decaymode.Themeasuredtwo-pionmassspectraforevents pro-ducedinreaction(2) withina

±

30MeV/c2 _mass_window_around

the

ψ(

2S

)

(blue) and the

X

(

3872

)

(red) are shown in Fig. 7(a). The result for

ψ(

2S

)

is in a good agreementwith former obser-vations,whiletheshapeofthe

π π

massdistributionfor

X

(

3872

)

looksverydifferentfromthewell-knownresultsfor X

(

3872

)

.The comparisonofthetwo-pionmassdistributions from

X

(

3872

)

de-cay obtainedby COMPASS and from X

(

3872

)

decay obtained by ATLAS [22] (the ATLAS resultis takenasa typical high-precision example)ispresentedinFig.7(b).ThecutMmiss

>

3 GeV/c2 is

ap-pliedforFig.7(b)toreduceunderlyingbackgroundcontributionin the

X

(

3872

)

sample. Our studies show that the observed

(4)

differ-Fig. 5. (a) InvariantmassspectraforX(3872)π±(red)andψ(2S)π±(blue)ofreaction(2).(b)Missingmassdistributionsfortheexclusivereactions(2) and(5).Theyellow histogramshowstheeventsintherange±30 MeV/c2_around_the_ψ(_2S₎_peak_of_reaction₍₅_)._Blue_circles_and_red_squares_show_the_events_in_the_range_±_{30 MeV/c}2_around

theψ(2S)andX(3872)peaksofreaction(2).

Fig. 6. Kinematic distributionsforQ2_(a)_and√_s

γN(b)forreactions(2) and(5).Theyellowhistogramscorrespondtotheeventsintherange±30 MeV/c2aroundtheψ(2S)

peakofreaction(5).Bluecirclesandredsquaresshowtheeventsintherange±30 MeV/c2_around_the_ψ(_2S₎_and_X₍₃₈₇₂₎_peaks_of_reaction₍₂_). encecannot be explainedbyacceptanceeffects. Withinstatistical

uncertainties, the shape of the COMPASS

π π

mass distribution is in agreement with a three-body phase–space decay andwith the expectation for a state with quantum numbers JP C

₌

₁+− [40], while the quantum numbers previously determined for the

X

(

3872

)

are1++.Apossibledistortionofthetwo-pionmass spec-trumbynon-resonant backgroundunderthe peakwas estimated usingthe sPlot procedure [43] and was found to be unlikely for reaction (2). The statistical signiﬁcance of the disagreement be-tween the observed two-pion mass spectrum and the expected onefromtheknowndecay X

(

3872

)

→

J

/ψ

ρ

0 _was _estimated

us-ing the maximum likelihood approach andwas found to be be-tween4.7

σ

and7.3

σ

depending onthetreatmentoftheresidual backgroundunder the

X

(

3872

)

peak. We investigated the possi-bilityto obtain the observed two-pion spectrum fromthe decay

X

(

3872

)

→

J

/ψ

ω

→

J

/ψ

π

+

π

−

π

0 _where _the

_π

0 _has _been_lost,

and excluded it. A possibility to have visible contribution from the

χ

c0,1,2

→

J

/ψ

γ

decay,followedbythephotonconversioninto

e+e− misidentiﬁedas

π

+

π

−,wasalsoinvestigatedandexcluded. A possible interpretation of the observed

X

(

3872

)

signal is that it is not the well-known X

(

3872

)

but a new charmonium state withsimilarmass.Thiswouldbeinagreementwiththetetraquark modelofRefs. [41,42] whichpredictsaneutralpartnerofX

(

3872

)

thathasasimilarmass,negativeC -parity,anddecaysinto J

/ψ

σ

. In order to estimate the Breit–Wigner width of the

X

(

3872

)

statetheﬁttingprocedureforthe J

/ψ

π

+

π

−invariantmass

distri-butionshowninFig.2(a)wasredone. AGaussianshapewasused toﬁtthe

ψ(

2S

)

peakwhiletheconvolutionofaGaussian distribu-tionofthesamewidthasfor

ψ(

2S

)

andaBreit–Wignerfunction havingthesamemassastheGaussianonewasusedfor

X

(

3872

)

. The obtained resultfor the width of

X

(

3872

)

is the upperlimit

X(3872)

<

51MeV/c2CL

=

90%.

Thepreviouslymentionedstatisticalsigniﬁcanceofthe

X

(

3872

)

signal was evaluated without including systematic effects. As a resultofthecomprehensivestudiesofsystematiceffects,we con-cludethat thesystematicuncertaintyrelatedtoourchoice ofthe backgroundshape [Eq. (3)]andthe ﬁttingrangeisthe dominant one. Weestimate thisuncertainty tobe equivalent to15% ofthe Gaussianuncertaintyofthe N value

¯

[Eq. (4)].Takingintoaccount thissystematicuncertaintybyusingthefrequentistapproach pro-posedinRef. [46],thesigniﬁcanceofthe

X

(

3872

)

signalshownin Fig.2(b)isreducedfrom4.5

σ

to 4.1

σ

.We quotethelattervalue astheestimateofsigniﬁcanceofthe

X

(

3872

)

signal.

In order to determine the cross section of exclusive

X

(

3872

)

productioninreaction(2),weusetheexclusiveproductionof J

/ψ

offthetargetnucleon,

μ

+N

→

μ

+J

/ψ

N

,

(6)

asnormalization.The samedataareusedandthesameselection criteriaareappliedasforreactions(2) and(5).Themethodusedto determinethecrosssectionforreaction(2) reliesonthe

(5)

assump-Fig. 7. (a) Invariantmassspectrafortheπ+π−subsystemfromthedecayofX(3872)(redsquares)andψ(2S)(bluecircles)producedinreaction(2).Thecorresponding distributionsforthree-bodyphase–spacedecaysareshownbythecurves.(b)Invariantmassspectrafortheπ+π− subsystemfromthedecayofX(3872)measuredby COMPASSwiththeappliedcutMmiss>3 GeV/c2(redsquares)andfromthedecayofX(3872)observedbyATLAS[22] (bluepoints).Bothdistributionsarenormalisedto

thesamearea.

tionthattheﬂuxesofvirtualphotonsforreactions(2) and(6) are the same.Thisassumption is supported by thesimilar shapes of the Q2 _and

√

_sγ

N distributions in both cases. We can therefore relatethephoto- andleptoproductioncrosssectionsasfollows:

σ

_μ_N_→_μ_X₍₃₈₇₂₎_π_N

σ

μN→μJ/ψN

=

σ

_γ_N_→_X₍₃₈₇₂₎_π_N

σ

γ N→J/ψN

.

(7)

Thecrosssectionofthereaction

γ

N

→

J

/ψ

N isknownforour range of

√

sγN; it is 14

.

0

±

1

.

6

(

stat

)

±

2

.

5(syst) nb at

√

sγN

=

13

.

7 GeV [44].Sincethisvaluewasobtainedfortheproductionby areal-photonbeam,wereduceitbyafactorof0.8inordertotake intoaccountthe Q2 _dependence_of_the_cross_section_by_using_the

parameterisationofRef. [45] andtheaverage photonvirtualityin oursamplesofabout1

(

GeV

/

c

)

2.Sincethethreechargedpions ap-pearonlyintheﬁnalstateofreaction(2),theratioofacceptances of the two reactions is in ﬁrst approximation equal to the pion acceptanceaπ cubed.Based onprevious COMPASSmeasurements andMonteCarlosimulations,weestimate aπ

=

0

.

6

±

0

.

1

(

syst

)

as averageover thegeometricaldetectoracceptance andboth target conﬁgurations.Thusweset

σ

_γ_N_→_X₍₃₈₇₂₎_π_N

×

B

X(3872)→J/ψπ π

σ

γN→J/ψN

=

N_X₍₃₈₇₂₎ a3_πNJ/ψ

,

(8)

whereNX(3872) andNJ/ψ aretherespectivenumbersofobserved

X

(

3872

)

and J

/ψ

eventsfromexclusiveproductiononquasi-free nucleons.ThenumberNJ/ψ isdeterminedas9

.

6

×

103,witha sys-tematicuncertaintyofabout10%duetonon-exclusivebackground in our data sample. The amount of COMPASS data used in this analysisisequivalenttoabout14 pb−1_of_the_integrated

luminos-ity,whenconsideringa real-photonbeamofabout100 GeV inci-dentenergy scatteringofffree nucleons. Usingthe normalization procedure described in Ref. [35], we determine thecross section forthereaction

γ

N

→

X

(

3872

)

π

±N multipliedbythebranching fractionforthedecay

X

(

3872

)

→

J

/ψ

π

+

π

−tobe

σ

_γ_N_→_X₍₃₈₇₂₎_π_N

×

B

X(3872)→J/ψπ π

=

71

±

28

(

stat

)

±

39

(

syst

)

pb

.

(9) Thestatisticaluncertaintyisgivenbytheuncertaintyinthe num-berof

X

(

3872

)

signalevents,whilethemaincontributionstothe systematicuncertainty are: (i) 36 pb from the estimation ofa3

π ,

(ii) 14 pbfrom thecross section forreaction (6), (iii)7 pbfrom theestimationofNJ/ψ.

Also, an upper limit is determined for the production rateof

X

(

3872

)

inthereaction

γ

N

→

X

(

3872

)

N,mentionedinRef. [33], using the same procedure for normalization as described above. Theresultis

σ

γN→X(3872)N

×

B

X(3872)→J/ψπ π

<

2

.

9 pb (CL

=

90%

).

(10)

In summary, in our study of the process depicted in Fig. 1

we observedthemuoproductionofthestate

X

(

3872

)

witha sta-tistical signiﬁcance of 4.1

σ

. The absolute production rateof this statein J

/ψ

π

+

π

−modewasalsomeasured.Itsmass MX(3872)

=

3860

.

0

±

10

.

4 MeV/c2_and_width

X(3872)

<

51MeV/c2CL=90%and decaymode

X

(

3872

)

→

J

/ψ

π π

areconsistentwiththe X

(

3872

)

. Our observedtwo-pion mass spectrumshowsdisagreement with previousexperimentalresultsfortheX

(

3872

)

.Apossible explana-tioncouldbethattheobservedstateistheC

= −

1 partnerofthe

X

(

3872

)

aspredictedbyatetraquarkmodel.Thepresentedresults demonstratethephysicspotentialofstudyingexotic charmonium-like statesin(virtual) photoproduction.However, an independent conﬁrmation of the nature of the observed

X

(

3872

)

signal from high-precision experiments withhigh-energy virtual orreal pho-tonsisrequired.

We gratefully acknowledge the support of theCERN manage-ment andstaff aswell astheskillsandeffortsofthetechnicians ofthecollaboratinginstitutions.WearealsogratefultoDmitry De-dovich,SimonEidelman,ChristophHanhart,LucianoMaiani, Sebas-tian Neubert,MikePennington, EricSwansenandAdam Szczepa-niakforfruitfuldiscussions.

References

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(6)

PANDA:arXiv:0903.3905 [hep-ex].

COMPASSCollaboration

M. Aghasyan

y

,

R. Akhunzyanov

g

,

M.G. Alexeev

z

,

G.D. Alexeev

g

,

A. Amoroso

z

,

aa

,

V. Andrieux

ac

,

u

,

N.V. Anﬁmov

g

,

V. Anosov

g

,

A. Antoshkin

g

,

K. Augsten

g

,

s

,

W. Augustyniak

ad

,

A. Austregesilo

p

,

C.D.R. Azevedo

a

,

B. Badełek

ae

,

F. Balestra

z

,

aa

,

M. Ball

c

,

J. Barth

d

,

R. Beck

c

,

Y. Bedfer

u

,

J. Bernhard

m

,

j

,

K. Bicker

p

,

j

,

E.R. Bielert

j

,

R. Birsa

y

,

M. Bodlak

r

,

P. Bordalo

l

,

1

,

F. Bradamante

x

,

y

,

A. Bressan

x

,

y

,

M. Büchele

i

,

V.E. Burtsev

ab

,

W.-C. Chang

v

,

C. Chatterjee

f

,

M. Chiosso

z

,

aa

_,

_{I. Choi}

ac

_,

_{A.G. Chumakov}

ab

_,

S.-U. Chung

p

,

2

,

A. Cicuttin

y

,

3

,

M.L. Crespo

y

,

3

,

S. Dalla Torre

y

,

S.S. Dasgupta

f

,

S. Dasgupta

x

,

y

,

O.Yu. Denisov

aa

,

∗

,

L. Dhara

f

,

S.V. Donskov

t

,

N. Doshita

ag

,

Ch. Dreisbach

p

,

W. Dünnweber

4

,

R.R. Dusaev

ab

,

M. Dziewiecki

af

,

A. Efremov

g

,

21

,

P.D. Eversheim

c

,

M. Faessler

4

,

A. Ferrero

u

,

M. Finger

r

,

M. Finger jr.

r

,

H. Fischer

i

,

C. Franco

l

,

N. du Fresne von Hohenesche

m

,

j

,

J.M. Friedrich

p

,

∗

,

V. Frolov

g

,

j

,

E. Fuchey

u

,

5

,

F. Gautheron

b

,

O.P. Gavrichtchouk

g

,

S. Gerassimov

o

,

p

,

J. Giarra

m

,

F. Giordano

ac

,

I. Gnesi

z

,

aa

,

M. Gorzellik

i

,

16

,

A. Grasso

z

,

aa

,

A. Gridin

g

,

M. Grosse Perdekamp

ac

,

B. Grube

p

,

T. Grussenmeyer

i

,

A. Guskov

g

,

∗

_,

_{D. Hahne}

d

_,

_{G. Hamar}

y

_,

_{D. von Harrach}

m

_,

_{F.H. Heinsius}

i

_,

_{R. Heitz}

ac

_,

F. Herrmann

i

,

N. Horikawa

q

,

6

,

N. d’Hose

u

,

C.-Y. Hsieh

v

,

7

,

S. Huber

p

,

S. Ishimoto

ag

,

8

,

A. Ivanov

z

,

aa

,

Yu. Ivanshin

g

,

21

,

T. Iwata

ag

,

V. Jary

s

,

R. Joosten

c

,

P. Jörg

i

,

E. Kabuß

m

,

A. Kerbizi

x

,

y

,

B. Ketzer

c

,

G.V. Khaustov

t

,

Yu.A. Khokhlov

t

,

9

,

Yu. Kisselev

g

,

F. Klein

d

,

J.H. Koivuniemi

b

,

ac

,

V.N. Kolosov

t

,

K. Kondo

ag

,

K. Königsmann

i

,

I. Konorov

o

,

p

,

V.F. Konstantinov

t

,

A.M. Kotzinian

z

,

aa

,

O.M. Kouznetsov

g

,

Z. Kral

s

,

M. Krämer

p

,

P. Kremser

i

,

F. Krinner

p

,

Z.V. Kroumchtein

g

,

29

,

Y. Kulinich

ac

,

F. Kunne

u

,

K. Kurek

ad

,

R.P. Kurjata

af

,

I.I. Kuznetsov

ab

,

A. Kveton

s

,

A.A. Lednev

t

,

29

,

E.A. Levchenko

ab

,

M. Levillain

u

,

S. Levorato

y

,

Y.-S. Lian

v

,

11

_,

_{J. Lichtenstadt}

w

_,

_{R. Longo}

z

,

aa

_,

_{V.E. Lyubovitskij}

ab

,

12

_,

_{A. Maggiora}

aa

_,

A. Magnon

ac

,

N. Makins

ac

,

N. Makke

y

,

3

,

G.K. Mallot

j

,

S.A. Mamon

ab

,

B. Marianski

ad

,

A. Martin

x

,

y

,

J. Marzec

af

,

J. Matoušek

x

,

r

,

13

,

H. Matsuda

ag

,

T. Matsuda

n

,

G.V. Meshcheryakov

g

,

M. Meyer

ac

,

u

,

W. Meyer

b

,

Yu.V. Mikhailov

t

,

M. Mikhasenko

c

,

E. Mitrofanov

g

,

N. Mitrofanov

g

,

Y. Miyachi

ag

,

A. Nagaytsev

g

,

F. Nerling

m

,

D. Neyret

u

,

J. Nový

s

,

j

,

W.-D. Nowak

m

,

G. Nukazuka

ag

,

A.S. Nunes

l

,

A.G. Olshevsky

g

,

I. Orlov

g

,

M. Ostrick

m

,

D. Panzieri

aa

,

14

,

B. Parsamyan

z

,

aa

,

S. Paul

p

,

J.-C. Peng

ac

,

F. Pereira

a

,

M. Pešek

r

,

M. Pešková

r

,

D.V. Peshekhonov

g

,

N. Pierre

m

,

u

,

S. Platchkov

u

,

J. Pochodzalla

m

,

V.A. Polyakov

t

,

J. Pretz

d

,

10

_,

_{M. Quaresma}

l

_,

_{C. Quintans}

l

_,

_{S. Ramos}

l

,

1

_,

_{C. Regali}

i

_,

_{G. Reicherz}

b

_,

_{C. Riedl}

ac

_,

N.S. Rogacheva

g

,

D.I. Ryabchikov

t

,

p

,

A. Rybnikov

g

,

A. Rychter

af

,

R. Salac

s

,

V.D. Samoylenko

t

,

A. Sandacz

ad

,

C. Santos

y

,

S. Sarkar

f

,

I.A. Savin

g

,

21

,

T. Sawada

v

,

G. Sbrizzai

x

,

y

,

P. Schiavon

x

,

y

,

K. Schmidt

i

,

16

,

H. Schmieden

d

,

K. Schönning

j

,

15

,

E. Seder

u

,

A. Selyunin

g

,

L. Silva

l

,

L. Sinha

f

,

S. Sirtl

i

,

M. Slunecka

g

,

J. Smolik

g

,

A. Srnka

e

,

D. Steffen

j

,

p

,

M. Stolarski

l

,

O. Subrt

j

,

s

,

M. Sulc

k

,

H. Suzuki

ag

,

6

,

A. Szabelski

x

,

ad

,

13

,

T. Szameitat

i

,

16

,

P. Sznajder

ad

,

M. Tasevsky

g

,

S. Tessaro

y

,

F. Tessarotto

y

,

A. Thiel

c

,

J. Tomsa

r

,

F. Tosello

aa

,

V. Tskhay

o

,

S. Uhl

p

,

B.I. Vasilishin

ab

,

A. Vauth

j

,

J. Veloso

a

,

A. Vidon

u

,

M. Virius

s

,

S. Wallner

p

,

T. Weisrock

m

,

M. Wilfert

m

,

J. ter Wolbeek

i

,

16

_,

_{K. Zaremba}

af

_,

_{P. Zavada}

g

_,

_{M. Zavertyaev}

o

_,

E. Zemlyanichkina

g

,

21

,

N. Zhuravlev

g

,

M. Ziembicki

af

a_University_of_Aveiro,_Dept._of_Physics,_3810-193_Aveiro,_Portugal

b_Universität_Bochum,_Institut_für_{Experimentalphysik,}₄₄₇₈₀_Bochum,_Germany17,18

c_Universität_Bonn,_{Helmholtz-Institut}_für_{Strahlen- und}_Kernphysik,₅₃₁₁₅_Bonn,_Germany17

(7)

NagoyaUniversity,464Nagoya,Japan

r_Charles_University_in_Prague,_Faculty_of_Mathematics_and_Physics,₁₈₀₀₀_Prague,_Czech_Republic19

s_Czech_Technical_University_in_Prague,₁₆₆₃₆_Prague,_Czech_Republic19

t_NRC_«Kurchatov_Institute_»_–_IHEP,₁₄₂₂₈₁_Protvino,_Russia u_IRFU,_CEA,_Université_{Paris-Saclay,}₉₁₁₉₁_{Gif-sur-Yvette,}_France18

v_Academia_Sinica,_Institute_of_Physics,_Taipei_11529,_Taiwan24

w_Tel_Aviv_University,_School_of_Physics_and_Astronomy,₆₉₉₇₈_Tel_Aviv,_Israel25

x_University_of_Trieste,_Dept._of_Physics,₃₄₁₂₇_Trieste,_Italy y_Trieste_Section_of_INFN,₃₄₁₂₇_Trieste,_Italy

z_University_of_Turin,_Dept._of_Physics,₁₀₁₂₅_Turin,_Italy aa_Torino_Section_of_INFN,₁₀₁₂₅_Turin,_Italy

ab_Tomsk_Polytechnic_University,₆₃₄₀₅₀_Tomsk,_Russia26

ac_University_of_Illinois_at_{Urbana-Champaign,}_Dept._of_Physics,_Urbana,_IL_61801-3080,_USA27

ad_National_Centre_for_Nuclear_Research,_00-681_Warsaw,_Poland28

ae_University_of_Warsaw,_Faculty_of_Physics,_02-093_Warsaw,_Poland28

af_Warsaw_University_of_Technology,_Institute_of_{Radioelectronics,}_00-665_Warsaw,_Poland28

ag_Yamagata_University,_Yamagata_992-8510,_Japan23

*

Correspondingauthors.

E-mailaddresses:oleg.denisov@cern.ch(O.Yu. Denisov),jan@tum.de(J.M. Friedrich),alexey.guskov@cern.ch(A. Guskov).

1 _Also_at_Instituto_Superior_Técnico,_Universidade_de_Lisboa,_Lisbon,_Portugal.

2 _Also_at_Dept._of_Physics,_Pusan_National_University,_Busan_609-735,_Republic_of_Korea_and_at_Physics_Dept.,_Brookhaven_National_Laboratory,_Upton,_NY_11973,_USA. 3 _Also_at_Abdus_Salam_ICTP,₃₄₁₅₁_Trieste,_Italy.

4 _Supported_by_the_DFG_cluster_of_excellence_‘Origin_and_Structure_of_the_Universe’₍_www.universe_-cluster.de₎_(Germany). 5 _Supported_by_the_Laboratoire_{d’excellence}_P2IO_(France).

6 _Also_at_Chubu_University,_Kasugai,_Aichi_487-8501,_Japan.

7 _Also_at_Dept._of_Physics,_National_Central_University,₃₀₀_Jhongda_Road,_Jhongli_32001,_Taiwan. 8

AlsoatKEK,1-1Oho,Tsukuba,Ibaraki305-0801,Japan.

9 _Also_at_Moscow_Institute_of_Physics_and_Technology,_Moscow_Region,_141700,_Russia. 10 _Present_address:_RWTH_Aachen_University,_III._{Physikalisches}_Institut,₅₂₀₅₆_Aachen,_Germany. 11 _Also_at_Dept._of_Physics,_National_Kaohsiung_Normal_University,_Kaohsiung_County_824,_Taiwan. 12 _Also_at_Institut_für_Theoretische_Physik,_Universität_Tübingen,₇₂₀₇₆_Tübingen,_Germany. 13 _Also_at_Trieste_Section_of_INFN,₃₄₁₂₇_Trieste,_Italy.

14 _Also_at_University_of_Eastern_Piedmont,₁₅₁₀₀_Alessandria,_Italy. 15 _Present_address:_Uppsala_University,_Box_516,₇₅₁₂₀_Uppsala,_Sweden.

16 _Supported_by_the_DFG_Research_Training_Group_Programmes₁₁₀₂_and₂₀₄₄_(Germany). 17 _Supported_by_BMBF_–_{Bundesministerium}_für_Bildung_und_Forschung_(Germany). 18 _Supported_by_FP7,_{HadronPhysics3,}_Grant₂₈₃₂₈₆_(European_Union).

19 _Supported_by_MEYS,_Grant_LG13031_(Czech_Republic). 20 _Supported_by_SAIL_(CSR)_and_B._Sen_fund_(India). 21 _Supported_by_CERN-RFBR_Grant_12-02-91500.

22 _Supported_by_FCT_–_Fundação_para_a_Ciência_e_Tecnologia,_COMPETE_and_QREN,_Grants_CERN/FP_116376/2010,_123600/2011_and_{CERN/FIS-NUC/0017/2015}_(Portugal). 23 _Supported_by_MEXT_and_JSPS,_Grants_18002006,_20540299,_18540281_and_26247032,_the_Daiko_and_Yamada_Foundations_(Japan).

24 _Supported_by_the_Ministry_of_Science_and_Technology_(Taiwan). 25 _Supported_by_the_Israel_Academy_of_Sciences_and_Humanities_(Israel).

26 _Supported_by_the_Russian_Federation_program_“Nauka”_(Contract_No._{0.1764.GZB.2017)}_(Russia). 27 _Supported_by_the_National_Science_Foundation,_Grant_no._PHY-1506416_(USA).

28 _Supported_by_NCN,_Grant_{2017/26/M/ST2/00498}_(Poland). 29 _Deceased.

Search for muoproduction of X(3872) at COMPASS and indication of a new state (X)over-tilde(3872)

Search

for

muoproduction

of

X

(

3872

)

at

COMPASS

and

indication

of

a

new

state

X

(

3872

)

.

COMPASS

Collaboration

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

μ

μ

π

π

π

π

π

σ

π

π

π

π

π

π

(

)

(

)

/ψ

π

π

→

/ψ

π

π

(

)

±

¯

±



=

(

)

(

)

(