Rethinking the X(3872)

0.05 MB·

by  T. J. Burns

Rethinking the X(3872)
T. J. Burns 1
INFNRoma,PiazzaleA.Moro2,Roma,I-00185,Italy
Abstract. TheBaBaranalysiswhichfavours2 +quantumnumbersfortheX(3872)impliesthatitmaybenoneotherthan
−
1 the11D2 charmoniastate.Inthatcasetheisospinbreakinginclosedflavourmodesmaybetheresultofre-scatteringfrom
1 openflavour.However,theobservedproductioncrosssectioninproton-antiprotoncollisionsismuchlargerthanexpectations,
0 whilethemassofthestate,comparedtothepredictionsofastringmodel,istoohigh.The1D2 assignmentwouldimplya
2 3D2 partnernearbyinmass,whichmaybetheX(3875).Inthetetraquarkinterpretationthe2−+ assignmentimpliesarich
spectrumofpartnerstates,althoughtheX(3872)maybeamongthefewwhicharenarrowenoughtobeobservable.Thistalk
n
isbasedinpartonref.[1].
a
J ContributiontotheproceedingsofQuarkConfinementandtheHadronSpectrumIX,

5 UniversidadComplutensedeMadrid,30August–3September2010.
2
Keywords: X(3872),charmonium,tetraquarks

PACS: 12.39.Jh,12.40.Yx,14.40.Rt,14.40.Pq
]
h
p
INTRODUCTION to hidden light quark content uu, which is a state of
-
p mixedisospin:
e InarecentpapertheBaBarcollaborationclaims[2]that
h thequantumnumbersoftheX(3872)arenot1++,ashad 1 uu+dd 1 uu dd
[ ccuu = cc + cc − . (1)
generallybeenaccepted,but2−+.Althoughahighstatis- | i √2| √2 i √2| √2 i
1 tics analysis by CDF [3] allowed both possibilities, an
v earlier conference paper by Belle [4] favored 1++, and In the limit that the dd component is completely sup-
6 mosttheoreticalworkhasbeenbasedonthisassumption. pressed and that the r and w have equal mass and
1 ThenewresultfromBaBarthereforeprovokesarevision width, one thus predicts equal magnitude isospin one
8 oftheoreticalideasconcerningtheX(3872).Ifthisquan- and isospin zero J/yr and J/yw modes. Even if the
4
. tum numberassignmentis confirmed,the molecularin- X(3872)isastandardccmeson,however,anessentially
1 terpretationoftheX(3872)asalooselyboundstateofa verysimilarargumentmayexplaintheobservedisospin
0
D0andaD¯ 0mesonseemsunlikely.Whereasa1++state breaking.
1 ∗
1 canbeformedinrelativeS-wave,a2−+ statewouldre- Suppose that the X(3872) lies slightly above the
: quirearelativeP-wave,anditisunlikelythatp exchange D0∗D¯0threshold.ThestrongdecayX(3872) D0∗D¯0+
v couldbindsuchastate,giventhateveninS-waveitisnot c.c. is allowed, while X(3872) D±∗D∓ is→forbidden;
i →
X clearthattheattractionissufficientlystrong[5]. this is a maximal violation of isospin, which would re-
quireneutraland chargedmodesin equalmeasure.The
r
a producedD0 D¯0+c.c.couldthenre-scatterintoachar-
∗
THE 1D INTERPRETATION moniapluslightmeson,andtheflavourcontentofthelat-
2
terwouldthusbeanequaladmixtureofisospinzeroand
isospinone.Moreover,sincetheirthresholdsareremark-
Withthemolecularinterpretationrenderedlesslikely,the
BaBar result revives the possibility that the X(3872) is ably similar to the X(3872)mass, at 3872.41MeV and
a conventional11D charmoniumstate. The main chal- 3879.57 MeV respectively, the J/yr and J/yw pairs
2
havesmallmomenta,andthusthere-scatteringwouldre-
lengeisthestrongviolationofisospin:theX(3872)de-
caystoJ/yr andJ/yw withapproximatelyequalmag- quireverylittle momentumtransferfromthesmallmo-
nitude[6].Itwasnotedlongago[7]thatduetoitsprox- mentum D0∗D¯0+c.c. pair. A similar mechanism could
imitytothethreshold,theX(3872)oughttocouplemore beinplaceiftheX(3872)isslightlybelowthreshold,in
stronglytoD0 D¯0+c.c.thantoD D ,whichliessome whichcasethedominanceoftheneutralcharmedmesons
∗ ±∗ ∓
(and hence the maximal isospin violation) is due to the
8MeVhigher.Inthemolecularinterpretationthisleads
largeenergydenominator;thisisessentiallytheideapro-
posedinref.[5]inthecontextofthe1++X(3872).
Ashasbeenwidelydiscussedintheliterature poten-
1 [email protected]
tialmodelstypicallypredicta11D statelyingsome50-
2
100MeVlighterthantheX(3872)[8,9,10].Inastring some50and120timessmallerthantheestimatedexperi-
model one obtains a similar prediction; in the heavy mentalcrosssection.Itisdifficult,therefore,toreconcile
quark limit one finds an expression for the mass E of the observed production cross-section of the X(3872)
amesonintermsofitsorbitalangularmomentumL, withtheexpectationsfora11D state.Otherdifficulties
2
associatedwiththe1D interpretationoftheX(3872)are
3 LT 2/3 discussedinrefs.[17,218].
E =2m 1+ , (2)
2(cid:18)2m2(cid:19) ! Afeaturecommontomostpotentialmodels,ascanbe
seenbythecomparisonofmasspredictionspresentedin
wheremisthequarkmassandT thestringtension.The ref[8], isthatthe 1D is accompaniedbya 3D partner
2 2
correspondingresultforlightquarksyieldsthestandard
whosemassiswithinacoupleofMeV.Isitpossiblethat
ReggetrajectoriesE √TL[11].
thisstatehasalreadybeenobserved?BothBelle[19]and
∼
AssumingthattheL=0stateofthestringisdescribed
BaBar [20] have observed a second state, the X(3875),
by the spin-weightedaverage of the 1S and 3S states,
0 1 with a mass a few MeV higher than, and inconsistent
thereisalinearrelationamongthemasses,
with, that of the X(3872). The interpretation of the ex-
1 22/3 perimental data is a subtle issue [21] and it is possible
M(1D2)=22/3M(1P1)+ − M(1S0)+3(3S1) thatthetwostatesareoneandthesame[22].Supposing,
4
(3) however,thatthe two states are distinct:what is known
(cid:0) (cid:1)
and a parameter-independentprediction of the mass of aboutthe heavier one? Whereas the radiative decays of
the 1D state in termsof the masses ofthe h , J/y and thelighterX(3872)fixitschargeconjugationtobeposi-
2 c
h , tive,theheavierX(3875)isobservedonlyinD0D¯0p 0,a
c
M(1D )=3795MeV. (4) modeallowedforbothpositiveandnegativechargecon-
2
jugationstates.Thisraisestheintriguingpossibilitythat
In agreement with potential model predictions, this is
theX(3875)isthe2 state3D .
difficult to reconcile with the observed X(3872) mass. −− 2
Being above threshold, such a state ought to decay
The validity of the mass formula can be tested in the
dominantly to D0D¯0p 0, consistent with observations.
bottomonia spectrum, using as input the experimental
values for the h and ¡ masses, and for the h the Moreover the proposed mechanism for the enhanced
centre of gravitybof the c , c and c ; the forbmula closed flavour modes J/yr and J/yw in the X(3872)
b0 b1 b2 need not imply a large J/yh in the X(3875),since the
yields a predicted mass for the unobserved 1D state
M(h )=10168.72+1.4 MeV, to be compared w2ith the momentumtransferwouldbelarge,andthisisconsistent
spin-bw2eighted avera−ge1.8M(h ) = 10165.84 1.8MeV withthecurrent(weak)upperlimit[23].Acriticaltestof
oftherecentlyobserved[12]b32D statesof±theupsilon the3D2scenariowouldbetheobservationofX(3875)in
1,2,3 c g .The currentexperimentalupperlimitonthis mode
sector. 1
isnotyetstrongenoughtoexcludethepossibility,ascan
In addition to its discovery mode in B decays, the
bededucedfromtheargumentsofref[8]inthecontext
X(3872) has been observed in proton-antiproton colli-
ofthelighterX(3872).
sions by both CDF [13] and D0 [14]. Ref [15] consid-
eredthe hypothesisthattheX(3872)isalooselybound
molecule of D0 and D¯ 0, and found that the predicted
∗ THE TETRAQUARKINTERPRETATION
cross section is considerably smaller than that which is
observed,consistentwith expectationsthatitisdifficult
The 2 + assignment also changes the outlook for the
to produce a loosely-bound S-wave molecule in a high −
tetraquarkinterpretationof the X(3872),since it would
energyhadroncollisionenvironment.IftheX(3872)isa
haveaunitoforbitalangularmomentum.Theexistence
11D standardcharmonium,theproductioncrosssection
2 of such a state would imply the existence of a rich
isalsoexpectedtobesmall.Thefragmentationfunction,
spectrum of partner states, formed of combinations of
which describes the probability that quarks and gluons
spin1(axialvector)andspin0(scalar)diquarkscoupled
hadronise into bound states, can be expressed as a per-
to the L=1 orbital angular momentum to give various
turbative expansion in the quark velocity v. For a 11D
2 totalangularmomentaJ.Thisleadstooneeachof0
state the functionbeginsat orderO(v7), and so one ex- −−
and3 ,twoeachof2 ,0 +,1 + and2 +,andfour
pectsasmallercrosssectionthanfor1Pstates,forwhich −− −− − − −
1 .Thereoughtpresumablyalsotoexistasetoflighter
the function is O(v5), which are themselves suppressed −−
S-wave states, two each of 0++ and 1+ , and one each
withrespectto1Sstates,O(v3). −
of 1++ and 2++. Moreover for each JPC there would
Using fragmentationfunctionsof Cho and Wise [16]
be various flavour combinations: two neutral and two
and recent gluon distribution functions we find a pre-
chargedstatesformedoutof[cu]and[cd]buildingblocks
dictedcrosssection
and the corresponding antidiquarks, and a further four
s (pp¯ 11D +all)=0.6nb, (5) strangestatesifoneconsidersstrangediquarks.
2
→
Intheabsenceofexperimentalevidenceforthemany thereoughttoexistaseriesofS-wavestateswithmasses
predicted partner states a tetraquark explanationfor the comparabletoP-wavecharmonia,andthisisdifficultto
X(3872)isonlytenableifonecanexplainwhyit,among reconcilewithdata.
allthepossibleconfigurations,isunique.Onepossibility
isthatmostofthestatesaresobroadastobeeffectively
unobservable,whiletheX(3872)isamongthefewwhich REFERENCES
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∗
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−
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−−
3 andJPC-exotic1 + stateshavemanydecaymodes 10. E.J.Eichten,K.Lane,andC.Quigg,Phys.Rev.D73,
−− −
014014(2006),hep-ph/0511179.
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−−
hep-ex/0405004.
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−
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CONCLUSIONS
The BaBar result which favours2 + quantumnumbers
−
fortheX(3872)impliesaseriousrevisionoftheoretical
interpretationsisrequired.IftheX(3872)isa11D state
2
bothitsmassandproductioncrosssectionattheTevatron
are larger than expected. In any case, the 3D partner
2
state should exist within a few MeV and may be the
X(3875).IftheX(3872)is,instead,aP-wavetetraquark,