I report results on the X(3872) from the Tevatron. Mass and other properties
have been studied, with a focus on new results on the dipion mass spectrum in X
-> J/PsiPi^+Pi^- decays. Dipions favor interpreting the decay as J/PsiRho,
implying even C-parity for the X. Modeling uncertainties do not allow
distinguishing between S- and P-wave decays of the J/PsiRho mode. Effects of
Rho-Omega interference in X decay are also introduced.Comment: Contribution to PANIC05, Santa Fe, 24-28 October 2005 (4 pages, 6
  plots

/MIT, LNS

Bauer, G.

English

arXiv

The author reports results on the X(3872) from the Tevatron. Mass and other properties have been studied, with a focus on new results on the dipion mass spectrum in X {yields} J/{psi}{pi}{sup +}{pi}{sup -} decays. Dipions favor interpreting the decay as J/{psi}{rho}, implying even C-parity for the X. Modeling uncertainties do not allow distinguishing between S- and P-wave decays of the J/{psi}-{rho} mode. Effects of {rho}-{omega} interference in X decay are also introduced

UNT (University of North Texas) Digital Library

FERMILAB-CONF-05-488-Ehep-ex/0511041PANIC‘05(24 Oct 2005)The X 3872 at the TeVatronG. Bauer(RepresentingtheCDF & DØ Collaborations)Laboratory of Nuclear Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue,Cambridge, MA 02139, USAAbstract. I reportresultson theX  3872 from theTevatron.Massandotherpropertieshave beenstudied,with afocusonnew resultsonthedipionmassspectrumin X  J  ψ π  π  decays.Dipionsfavor interpretingthe decayas J  ψ ρ , implying evenC-parity for the X . Modeling uncertaintiesdo not allow distinguishingbetweenS- and P-wave decaysof the J  ψ-ρ mode.Effectsof ρ-ωinterferencein X decayarealsointroduced.Keywords: X(3872),charmonium,exotic mesonsPACS: 14.40.Gx,13.25.G,12.39MkThecharmonium-like X  3872	 standsasa majorspectroscopicpuzzle.Its massandwhat is known of its decaysmakescc̄ assignmentsproblematic.Exotic interpretationshavebeenoffered,notablythattheX maybea D0-D  0 “molecule” [1].X  3872	 J  ψ π  π  was confirmedby CDF [2] and DØ [3], and is copiouslyproducedatFermilab’s p̄p collider—albeitwith highbackgrounds.Massmeasurementsarecomparedin Fig. 1, with an averageof 3871 2  0  4 MeV c2. DØ studiedotherXpropertiesby comparingthe fractionsof X yield in varioustypesof subsamplesto thecorrespondingfractionsfor theψ  2S 	 [3]. Theresultsfor 230pb 1 aresummarizedinFig. 1, wherethesubsamplesarethefractionof signalwhichhave:a) pT  J  ψππ 	 15GeV, b)  y  J  ψππ 	 1,c) cos θπ 	 0  4 (π helicity angle),d) properdecaylengthct 100µm, e) no trackswith ∆R  0  5 aroundthecandidate,f) cos θµ 	 0  4 (µ helicityangle).In all casestheX resultsarecompatiblewith thoseof theψ  2S 	 . CDF usedthe)2X(3872) Mass   (MeV/c3865387038753880 BaBarD0CDF II Belle Threshold*0D0D  Threshold*-D+D   [hep-ex/0507090]PRL 93, 162002 (2004)[hep-ex/0405004]PRL 93, 072001 (2004)[hep-ex/0312021]PRL 91, 262001 (2003)[hep-ex/0309032]+ X K→ +BS0 X K→ 0B 0.4±3871.2 00.10.20.30.40.50.60.70.80.91(2S)  ψ  X(3872)a! b c" d# e$ f%ComparisonFractionDØP (X)>15 GeVTθπcos(    )<0.4θ µcos(   )<0.4|y|<1Decay LengthIsolatedFIGURE 1. LEFT: Summaryof X-massmeasurementscomparedto theD0D & 0 andD  D &' thresholds.RIGHT: DØ’s comparisonof X production/decaypropertiesto thatof theψ  2S  [3]. Thefractionof theyield surviving thelistedcut is plotted(seetext for descriptions).0.3 0.4 0.5 0.62(2S) yield per 10 MeV/cψ0200(400)600800*1000-1         CDF II Preliminary, 360 pb]+2 Mass [GeV/cπ,π,-π,+π,ψ- J/→(2S) Ψ Multipole Expansion1S.3PRD 22, 1652 (1980)Prob = 6.9%Brown - Cahn/PRL 35, 1 (1975)0/ndf = 226/2712χ20.4 0.6 0.82X(3872) yield per 20 MeV/c-50050100150200250]32 Mass [GeV/cππ-π+4πψ J/→X(3872)  (L=0)ρ ψJ/ (L=1)ρ ψJ/15S36 x 51P15J7D36:c8Multipole Expansions for c-1            CDF II Preliminary   360 pbFIGURE 2. LEFT: The ψ  2S  dipion massspectrumwith fits of 3S1 multipole expansionand anoldercalculationof Brown andCahn.RIGHT: TheX  3872 dipionmassspectrumwith fits of multipoleexpansionpredictionsfor C-oddcharmonia,andof X  J  ψ ρ for L 9 0 and1 usinga relativistic Breit-Wignerwith Blatt-Weisskopf factors(Rρ 9 0 : 3 andRX 9 1 : 0 fm).properdecaylengthct to quantifythefractionof X ’s thatcomefrom b-hadrons,versusthosethatarepromptlyproduced.Using220pb 1, CDF findsthefractionof X ’s fromb-decaysis 16 1  4  9  2  0%, in contrastto 28 3  1  0  0  7% of ψ  2S 	 ’s [4]. The Xfractionis somewhatlower thantheψ  2S 	 ’s,but within ; 2σ . FromtheseperspectivestheX is compatiblewith theψ  2S 	 . ThelargeX -productionat theTevatronis indicativeto someof a charmoniumcharacter[5]. Naïvely one expectsproductionof a fragileD0-D  0 molecule,bound by anMeV or less, to be suppressed.It may, however, besufficient to accommodatethesefeaturesif theX merelyhasasignificantcc̄ “core.”Anotherpropertyis thedipion massspectrum.If theX hasevenC-parity, thedipionsare (to lowest L) in a 1 < isovectorstate,anddominatedby the ρ0. An odd-C stateproduces0< dipions,for which QCDmultipoleexpansionpredictionsexist for cc̄.CDF used360 pb 1 ( ; 1  3k X ’s) to measurethe ππ-spectrum[6, 7]. The sampleis divided into mππ “slices” and fitted for X  3872	 and ψ  2S 	 yields. After modestefficiency corrections,thespectraof Fig.2 wereobtained.Theψ  2S 	 is agoodreferencesignalandis well modeledby multipolepredictions[8]. Also in Fig. 2 aremultipolefitsto the X for theC-odd cc̄ states.The 1P1 and3DJ fits areunacceptable.The3S1 is anexcellentfit to theX , but no 3S1 cc̄ is availablefor assignmentin this massregion.Earlier this spring CDF provided J  ψ ρ fits using a simple non-relativistic Breit-Wignersculptedby phasespace[6]. Goodagreementwasobtained(36%probability).About the sametime Belle releasednew dipion datafit with a more sophisticatedρmodel[9], which includedthe effectsof angularmomentumL for the J  ψ-ρ system.The phase-spacefactorof the J  ψ momentumin the X rest-frame,k  , generalizesto k =	 2L  1, therebyturning off the massspectrumat the upperkinematiclimit (k > 0)fasterfor L ? 1 thanfor L ? 0. Belle obtaineda goodfit for S-wave decay, but onlya 0  1% probability for L ? 1. Thus, the latter casewas strongly disfavored, and inconjunctionwith angularinformation,Belle arguedfor a 1< assignmentfor theX [9].Theabove CDF fit for J  ψ ρ wasimplicitly for L ? 0. A CDF fit usingBelle’s L ? 1modelalsoyields0  1%probability. Theimplicationis, however, not robust.Breit-Wigner formulationsareoftenmodifiedby Blatt-Weisskopf form factors[10].The centrifugalmodification to  k @	 2L  1 tendsto be too strong,and for L ? 1 it ismultiplied by f1i  k @	 ∝  1 A R2i k  2 	  12 , whereRi is a “radius” of meson-i. Specifically,CDF’s J  ψ ρ model is: dN  dmππ ∝  k  	 2L  1 f 2LX  k  	BBρ  2 for angularmomentumL.Theρ propagatorBρ ∝ C mππΓρ  mππ 	DFE m2ρ G m2ππ G imρ Γρ  mππ 	IH , whereΓρ  mππ 	J?Γ0 K q @ q 0 L 3 M E mρ  mππ HNE f1ρ  q @	O f1ρ  q 0 	IH 2, q  is theπ momentumin theππ rest-frame,andq 0 P q  mρ 	 . Theρ parametersmρ andΓ0 aretakenfrom thePDG.TheL ? 0 factoris f0i  x 	Q? 1. The f1i factorsrequiretwo uncertainparameters,RX and Rρ . For lightmesons,like theρ , values; 0  3 fm areusuallyfound,whereasfor charmmesonslargerradii ; 1 fm areoften used[11]. Choosingthesevaluesfor Rρ andRX , CDF obtainsthefits in Fig. 2 (Right). The L ? 0 fit hasan excellentprobability of 55%.While theL ? 1 probabilityis not quantitatively asgood,it is a respectable7.7%.This P-wave fitis sensitive to theRi’s,wherebytheprobabilitycanbeincreasedby loweringRρ and/orraisingRX . Weconcludethatflexibility in thefit modelcanaccommodateitherL.Othermodelinguncertaintiesmayarise,for example,theeffectsof ρ-ω interference.Belle reportedX  J  ψ π  π  π0, andinterpretsit asdecayvia a virtual ω. As such,they find theratio of J  ψ ω to J  ψ ρ branchingratios R 3S 2 is 1  0  0  5 [12]. Althoughω  π  π  is nominallynegligible here,its interferenceeffectsmaynot be.dN2π  dmππ is generalizedby replacing Bρ  2 with AρBρ A eiφ AωBω2π  2 whereAρand Aω are X -decayamplitudesvia ρ and ω, and φ is the relative phase.The formfor Bω2π is identical to Bρ exceptρ quantitiesarereplacedby ω ones,including theω  ππ branchingratio. Theratio Aω  Aρ  is establishedby therelationshipbetweenR 3S 2 andtheintegralsof dN2π  dmππ anddN3π  dm3π for X  J  ψ π  π  π0, wherethelatter is ∝ AωBω3π  2. TheBω3π follows Bω2π exceptthenumeratorcontainsΓω3π  m 	 .While Γω2π  m 	 follows Γρ  m 	 , a differentform for Γω3π  m 	 is adaptedfrom theSNDexperimentstudyinge  e   π  π  π0 [13]. They modelω  π  π  π0 asvirtual ρπdecaysandusetheω matrix-elementUTqπ V M Tqπ W  2, where Tqπ VYXZW areπ  S  momenta.The integral of dN2π  dmππ dependsupon the phase,which is a priori unknown.As an illustration, Aω  Aρ  is determinedassumingthatφ arisescompletelyfrom ρ-ωmixing, i.e.φ ? 95[ [14]. ThedN2π  dm2π decomposesinto threeparts:“pure” ρ andωterms,andaninterferencecross-term.In thismodelwith R 3S 2 ? 1  0, thesefractionsare,respectively, 71.0,6.2,and22.8%for S-wave decay, and67.4,8.7,23.9%for P-wave.Fits with thesefractionsimposedare shown in Fig. 3 (Left). The S-wave probabilityhasdeclinedasthe modelpeakstoo muchat high mass,but is still very goodat 19%.Increasingtheamountof highmasseswith interferenceimprovestheP-wavefit to 53%.TheL ? 1 fit is sensitive to φ andRX asis seenin the insetof Fig. 3. Thedependenceon Rρ is relatively weakfor bothL. Theoverall picturefrom thesefits is insensitive tothe  1σ spanof R 3S 2, asis seenin Fig. 3 (Right).In summary, propertiesof X  3872	\ J  ψ π  π  studiedat the Tevatronarequitesimilar to thoseof the ψ  2S 	 . Thereis no viable C-odd charmoniumassignmentac-cording to QCD multipole expansionfits to the ππ-massspectrum.Decayto J  ψ ρprovidesgoodfits, irrespective of thecc̄ structure.This impliestheX is C-even,in-linewith Belle’s reportof X  J  ψ γ [12]. Theeffectsof ρ-ω interferenceareintroduced,0.6 0.72X(3872) yield per 20 MeV/c050100150200250]2] Mass [GeV/cππ^Total_ρ`IntrfωaL=1 L=0 Phase  [degrees]ω-ρb-100 0 100 200 300  [fm]Xc R 0.20.40.60.81Probability [%]01020304050ρψd J/→P-Wave X  -1              CDF Preliminary, 360 pbInterference Phase [Degrees]0e100 200 300fFit Probability (%)0e102030f4050g60h70i 0.5j±k = 1.0)lρmψnJ/o→B(X )lωpψnJ/o→qB(X r = 1.0 fmXR = 0.3 fmρRL=0 FitL=1 Fit-1         CDF Preliminary, 360 pbFIGURE 3. LEFT: Blow-up of the dipion spectrumwith J  ψ ρ fits for L 9 0 (lines) and1 (shaded)including ρ-ω interferencewith 95s phaseandsub-componentsetby t 3u 2 9 1 : 0. The decompositioninto ρ , interference,andω termsis given.The insetshows L 9 1 fit probabilitiesasa functionof φ andRX in 5% contours.RIGHT: J  ψ ρ fit probabilitiesfor L 9 0 (shaded)and1 (hatched)asa functionofphase.Thebandsspanthe v 1σ rangeof t 3u 2.andcanbequiteimportant.This typeof ρ-ω modelinghighlightsthat R 3S 2 ; 1 impliesthe intrinsic amplitudefor X  J  ψ ρ is actually significantlysuppressedrelative toJ  ψ ω by virtue of the muchgreaterphasespacefor J  ψ ρ decayover J  ψ ω. Giventhemodelinguncertaintiesgoverningthe tails of theBreit-Wigners—especiallyif ρ-ωinterferenceis in play—theCDF spectrumcanbewell describedby J  ψ ρ decayof ei-therL ? 0 or 1: suchasfrom C-evencharmonia(e.g.1< or 2 F ) or from a1< exoticaspreferredfor a D0-D  0 molecule.REFERENCES1. Seefor example:E.J.Eichten,K. Lane,andC. Quigg,hep-ph/0511179;andreferencestherein.2. D. Acostaet al. (CDF),Phys.Rev. Lett. 93, 072001(2004).3. V.N. Abazov et al. (DØ), Phys.Rev. Lett. 93, 162002(2004).4. G. Bauer(CDF),DPF ’04, RiversideCA, 25-31August2004[hep-ex/0409052].5. K.-T. Chao, 2nd Workshop on Heavy Quarkonium, FNAL, 20-22 Sep. 2003 [www.qwg.to.infn.it/WS-sep03/WS2talks/prod/chao.ppt]; G. Bauer, hep-ex/0505083;C. Meng,Y.-J.Gao,K.-T. Chao,hep-ph/0506222;M. Suzuki,hep-ph/0508258.6. CDF Note 7570 (7 April 2005) [www-cdf.fnal.gov/physics/new/bottom.html];S. Nahn, APS/DPF Meeting, TampaFL, 16-19 April 2005 [www-cdf.fnal.gov/physics/talks_transp/2005/aps_bphys_nahn.pdf]; A. Rakitin,Ph.D.Thesis,MIT (2005).7. A. Abulenciaet al. (CDF), to besubmittedto PRL.8. T.M. Yan,Phys.Rev. D 22, 1652(1980);Y.-P. Kuanget al., ibid D 37, 1210(1988).9. S. Olsen (Belle), APS/DPF Meeting, TampaFL, 16-19 April 2005 [belle.kek.jp/belle/talks/aps05/olsen.pdf]; K. Abe et al. (Belle),Lepton-Photon’05 [hep-ex/0505038].10. J.M.Blatt andV.F. Weisskopf, Theoretical Nuclear Physics, JohnWiley & Sons(1952).11. For example:S. Koppet al. (CLEO),Phys.Rev. D 63, 092001(2001);H. Albrechtet al. (ARGUS),Phys.Lett. B 308, 435(1993);D. Astonet al. (LASS),Nucl. Phys.B 296, 493(1988).12. K. Abe et al. (Belle),Lepton-Photon’05, Uppsala,Sweden,30 June-5July2005[hep-ex/0505037].13. M.N. Achasov et al. (SND),Phys.Rev. D 68, 052006(2003).14. Γρ wYx mρ y mω z|{ 2tanx 95} z [A.S. Goldhaber, G.C.Fox, andC. Quigg,Phys.Lett. B 30, 249(1969)].

The X(3872) at the Tevatron

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The X(3872) at the Tevatron

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