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Decays of doubly charmed meson molecules 4 1 0 2 n a R. Molina J ∗ ResearchCenterforNuclearPhysics(RCNP),OsakaUniversity, 7 1 Ibaraki,Osaka567-0047,Japan E-mail: [email protected] ] h A. Hosaka p - ResearchCenterforNuclearPhysics(RCNP),OsakaUniversity, p Ibaraki,Osaka567-0047,Japan e h E-mail: [email protected] [ H. Nagahiro 1 v DepartmentofPhysics,NaraWomen’sUniversity 9 E-mail: [email protected] 2 2 4 The interaction between pseudoscalarand/or vector mesons can be studied using hidden gauge . 1 Lagrangians. Inthisframework,theinteractionbetweencharmedmesonshasbeenstudied. Fur- 0 4 thermore,doublycharmedstatesarealsopredicted.ThesenewstatesareneartheD∗D∗andD∗D∗s 1 thresholds,andhavespin-parityJP=1+. Weevaluatethedecaywidthsofthesestates,namedas : v R (3970)andS (4100)(withstrangeness),andobtain44MeVforthenon-strangeness,and24 cc cc i X MeV for the doublycharm-strangestate. Essentially, the decaymodesare DD p andDD g , (s) (s) r beingtheDp andDg emittedbyoneoftheD mesonwhichformsthemolecule. a ∗ XVInternationalConferenceonHadronSpectroscopy-Hadron2013 4-8November2013 Nara,Japan Speaker. ∗ (cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ Decaysofdoublycharmedmesonmolecules R.Molina 1) 1.1) Rc+c D∗+ π0,η,η′ D+ D∗+ π+ D0 Rc+c D∗0 π0,η,η′ DD0+ D∗0 π− DD+0 DD∗∗00 DD∗+0 DD∗∗00 DD∗0+ 2) DD∗∗++ Dπ+∗+ γD0 3) DD∗∗++ D∗+ γD0 π+ π0,η,η′ π+ γ π− γ D∗+ D∗0 D∗+ D∗+ 3.1) D∗0 D+ 3.2) D∗0 D+ D∗+ D+ D∗+ D0 D∗+ D+ D∗0 D+ ρ0,ω,J/ψ ρ+ π0,η,η′ γ π+ γ DD∗∗00 DD∗+0 DD∗∗00 DD∗0+ 4) DD∗∗0+ D∗+ DD0+ 4.1) DD∗∗+0 D∗+ DD0+ ρ+ ρ0,ω,J/ψ ρ0,π0 γ ρ−,π− γ D∗+ D∗0 D∗+ D∗+ D∗0 D0 D∗+ D0 Figure 1: Left: Feynman diagrams evaluated in the decay R DD . Right: Diagrams for the R+ cc → ∗ cc → D0D+g decaythroughoneloop. 1. Introduction Recently, the LHCb has measured the quantum numbers of the X(3872) as 1++ [1]. This result rules out the X(3872) to be a charmonium state, favoring the molecular interpretation [2]. Inaddition, several authors havediscussed whether someoftheother observed XYZparticles can be described in terms of molecules [3, 4, 5]. Some of the reasons on why these states cannot be accomodated into cc¯ are the unusually high decay rates into (r ,w orf )J/y [2]. Also, charged statesZ anddecaysbetweenthemareobserved [6]. c Using hidden gauge Lagrangians combined with unitarity in coupled channels, some of the observed states which are near the open charm thresholds, are well described in terms of two- meson molecules [3, 4]. Moreover, two-meson bound states of D D or D D are dynamically ∗ ∗ ∗ ∗s generated [7]. Those doubly charmed mesons form a charged isospin singlet and doublet, they are called R+(3970) and S+(+)(4100), for the non-strangeness and strangeness one respectively. cc cc Doublycharmstateswiththesamequantumnumbershavealsobeenfoundin[8]fromsolvingthe scattering problem of two D-mesons with the interaction provided by the chiral constituent quark model. Theoretically, tetraquark structure hasbeenalsodiscussed [9,10,11]. Inthistalk,inorder toexplorefurthertheinternalstructureofthesestates,westudythedecaysofthesestatesindetail. 2. Decay modes ofdoubly charm states The two D mesons can form a molecular state of spin and parity JP = 1+ when they are ∗ dominatedbyans-wavestate. Duetothesequantumnumbers,itcannotdecayintoDD¯. Strongand radiative decays of the doubly charm states occur through DD (or D D ) which subsequently ∗(s) (s) ∗ go to three body states via D p D or Dg . Direct decays into three-body states, DDg , are also ∗ → evaluated,buttheyaresmallascomparedtotheaboveprocessesgoingthroughtwobodies. Theset ofFeynmandiagramsconsideredaredepictedinFig. 2. TheR DD transitioncanbereached cc→ ∗(s) throughanomalouscouplingsVVPwithpseudoscalarorvectormesonexchange. TheLagrangians needed toevaluatethedecaywidthtoDD are[12], ∗(s) LPPV = ig Vm [P,¶ m P] , L3V =ig (Vm ¶ n Vm ¶ n Vm Vm )Vn ) − h i h − i 2 Decaysofdoublycharmedmesonmolecules R.Molina LVVP= √G2′ e mnab h¶ m Vn ¶ a Va Pi , (2.1) with e the unit electronic charge, G′ =3g′2/(4p 2f), g′ = GVMr /(√2f2), GV = f/√2 and g= − M /2f. Theconstant f isthepiondecayconstant f =93MeV,Q=diag(2, 1, 1,1)/3 andM V V − − is the mass ofthe vector meson. TheP andV matrix contain the 15-plet of the pseudoscalars and vectorsrespectivelyinthephysicalbasis. In[7]theuncertaintiesrelatedwiththeSU(4)breakingof thecouplinggarestudied,consideringbothheavyandlightcouplings. Thesedecayscomethrough oneloopwhichinvolves anintegralwhichislogarithmically divergent, howeverthisdivergence is related to the vertex that couples the resonance to the two-meson molecular states, and is also presentinthetwo-mesonloopfunction, G,whenthosestatesaredynamicallygenerated[7]. Thus, thesamevalueofthecutoffneeded toobtainthesestatesattheirmasses[7]isusedtoevaluatethe integral involved in the decays in the one-loop diagrams of Fig. 2. Once set the cutoff, one has a fixed mass and coupling of the bound state to the two-meson component, g . Since these three R magnitudes are related, there is only one free parameter in the calculation, the cutoff q , and max performing variations of this parameter one has an idea of the uncertainties in the decay widths. This is reflected in the errors of the widths, where 15% variations around its central value, 750 MeV,havebeenconsidered. The diagrams included in the evaluation of the radiative decay of doubly charmed meson molecules,R DDg aredepictedinFig. 2(rightpanel),whereonlynon-vanishing diagramsare cc → shown. 3. Results The results are shown in Table 4. We observe that the total widths of the doubly charmed states are (44 12), (24 8), and (24 8) MeV for the R+, S+ and S++ respectively, giving cc cc cc ± ± ± both channels (ex. D0D + and D+D 0 for the R+) the same contribution to the width. The direct ∗ ∗ cc diagramswiththree/fourpropagatorsofFig. 2,type1),2)and3),leadtoaverysmallwidthofthe order offewKeVinthe case oftheR+(3970) and S+(4100) and 0.13 KeVforthe doubly charge cc cc state, S++(4100). cc 4. Conclusions We have considered the possible decay modes of the doubly charmed molecules, R (3970) cc and S (4100), and evaluated partial decay widths to DD p and DD g . We find that the main cc (s) (s) source ofthesedecayscomefromthedecayofaD mesonintoD p orD g . Thesedecaysare ∗(s) (s) (s) mediated by the exchange of one meson, vector or pseudoscalar, between the D D pair of the ∗ ∗(s) molecule. Thelargestwidthcomesfromr ,p andw exchange(decreasingorder)fortheR (3970). cc Since they are not qq¯, having a pair of cc and doubly charged, these mesons are under challenge forexperiments. Hopefully, theycouldbeobserved bytheLHCborBelle. References [1] R.Aaijetal.(LHCbCollaboration),Phys.Rev.Lett.110,222001(2013). 3 Decaysofdoublycharmedmesonmolecules R.Molina State Channelk G k [MeV] Channelj G k [MeV] G [MeV] j tot R+(3970) Hadronicdecays cc D0D + 22 6 D0(D+p 0) 7 2 44 12 ∗ ± ± ± D0(D0p +) 15 4 ± D+D 0 22 6 D+(D0p 0) 14 4 ∗ ± ± Radiativedecays D+D 0 D+(D0g ) 8 2 ∗ ± D0D + D0(D+g ) 0.4 0.2 ∗ ± D0D+g (2 1) 10 3 − ± × D 0D+g (0.03 0.01) 10 3 ∗ − ± × D +D0g (0.5 0.2) 10 3 ∗ − ± × S+(4100) Hadronicdecays cc D+D 0 12 4 D+(D0p 0) 7 2 24 8 s ∗ s ± ± ± D0D + 12 4 - - ∗s ± Radiativedecays D0D + D0(D+g ) 11 4 ∗s s ± D+D 0 D+(D0g ) 5 2 s ∗ s ± D0D+g (2 1) 10 3 s − ± × D 0D+g (0.3 0.1) 10 3 ∗ s − ± × D +D0g (4 1) 10 3 ∗s − ± × S++(4100) Hadronicdecays cc D+D + 12 4 D+(D+p 0) 4 1 24 8 s ∗ s ± ± ± D+(D0p +) 8 3 s ± D+D + 12 4 - - ∗s ± Radiativedecays D+D + D+(D+g ) 11 4 ∗s s ± D+D + D+(D+g ) 0.2 0.1 s ∗ s ± D+D+g (1.3 0.1) 10 4 s − ± × D +D+g (0.3 0.1) 10 3 ∗ s − ± × D +D+g (0.3 0.1) 10 3 ∗s − ± × Table1: Totalandpartialdecaywidthsofthedifferentdecaymodesofthedoublycharmedstates. 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