Table Of ContentD∗±(2317) and KD scattering from B0 decay
s0 s
Miguel Albaladejo,1, Marina Nielsen,2, and Eulogio Oset1,
∗ † ‡
1 Departamento de F´ısica Te´orica and IFIC, Centro Mixto Universidad de Valencia-CSIC,
Institutos de Investigaci´on de Paterna, Aptdo. 22085, 46071 Valencia, Spain
2Instituto de F´ısica, Universidade de S˜ao Paulo, C.P. 66318, 05389-970, S˜ao Paulo, SP, Brazil
WestudytheB¯s0 →Ds−(DK)+ weakdecay,andlookattheDK invariantmassdistributionwith
the aim of obtaining relevant information on the nature of the D∗+(2317) resonance. We make a
s0
simulation of the experiment using the actual mass of the D∗+(2317) resonance and recent lattice
s0
QCD relevant parameters of the KD scattering amplitude. We then solve the inverse problem
of obtaining the KD amplitude from these synthetic data, to which we have added a 5% or 10%
error. We prove that one can obtain from these ”data” the existence of a bound KD state, the
5 KD scattering length and effective range, and most importantly, the KD probability in the wave
1 functionoftheboundstateobtained,whichwasfoundtobelargelydominantfromthelatticeQCD
0 results. ThismeansthatonecanobtaininformationonthenatureoftheD∗+(2317)resonancefrom
s0
2 the implementation of this experiment, in the line of finding the structure of resonances, which is
n oneof themain aims in hadron spectroscopy.
a
J PACSnumbers:
2
2
I. INTRODUCTION inRef. [28], goingbeyondthe effective rangeapproxima-
tion and making use of the three levels of Refs. [25, 27].
]
h As a consequence, one can be more quantitative about
p-p firsTthoebvseerryvendarinrotwhechDars+mπe0dcshcaanlanrelmbeysotnheDBs∗0+A(B23A1R7)Cwoals- tchoemnpaotnuernetoofftahbeouDts07(02%31,7w)i,thwihnicehrraoprsp.ears with a KD
e laboration [1] and its existence was confirmed by CLEO
In addition to these lattice results, and more precise
h [2], BELLE [3] and FOCUS [4] Collaborations. Its mass
ones that should be available in the future, it is very
[ wascommonlymeasuredas2317 MeV, whichisapproxi-
importantto havesome experimentaldatathatcouldbe
2 mately160 MeVbelowthepredictionoftheverysuccess- used to test the internal structure of this exotic state.
v ful quark model for the charmed mesons [5]. Due to its
55 leoxwtemnsaivsse,lythdeesbtartuecdt.urIetohfatshbeemenesinotneDrps∗r0±et(e2d31a7s)ahcas¯ssbteaetne maHsserdeiswtreibpurotpioonseoftothuesewethaekedxepcaeyrimofeBn¯ts0a→lKDDs−i(nDvaKri)a+n1t
4 [6–10],two-mesonmolecularstate[11–18],K D-mixing in order to obtain information about the internal struc-
501.03 [mtQ1hC9ees]D,omfnoosuialmernc-duqululafaoatruriokrinn-sqsttuea[ra2tpre5rks–e2[ts28at0a]t.–ito2eIns3n][c2opa4rrm]e.aveAimordueixdcsteitulnairtotelntyibac−lfeertsowsumtpeuepdnloaiertttstwictoooe-f itDemuvs∗ree+ern,Dtosafs∗iln−tcdheaaenttaDhdes∗Bf0¯+obs0r(r2a→t3nh1ce7hD)idns+segDtcaafs∗rty−ae.cB+t¯iTs0oDnh→ss∗e+rfeoDDras−rts−eha(eDnreodKterce)yas+epy.tseceBt¯xHis0vpoeew→lry--
the D (2317), it was treated as a conventional quark- 1.85% and 1.28%, we believe that the branching frac-
:1 antiqus∗a0rk state and no states with the correctmass (be- tion for the B¯s0 → Ds−Ds∗0+ decay, should not be so dif-
v lowtheKDthreshold)werefound. InRefs.[25,27],with ferent from that and it will be seen through the chan-
Xi theintroductionofKDmesonoperatorsandusingtheef- nel B¯s0 → Ds−(DK)+. This is why it is really impor-
fectiverangeformula,aboundstateisobtainedabout40 tant to have theoretical predictions for the DK invari-
r
a MeV below the KD threshold. The fact that the bound ant mass distribution that considers the formation of
state appears with the KD interpolator may be inter- the Ds∗0+(2317) state. At this point, it is worth stress-
preted as a possible KD molecular structure, but more ing that recently, in the reactions B0 D−D0K+ and
precise statements cannot be done. In Ref. [26] lattice B+ D¯0D0K+ studied by the BABA→R Collaboration
→
QCD results for the KD scattering length are extrapo- [31], an enhancement in the invariant DK mass in the
latedtophysicalpionmassesbymeansofunitarizedchi- range 2.35 2.50 GeV is observed, which could be asso-
ral perturbation theory, and by means of the Weinberg ciated with−this Ds∗0+(2317) state. It is also interesting
compositenesscondition [29,30]the amountofKD con- to quote that in a different reaction, Bs0 → D¯0K−π+,
tentintheD (2317)isdetermined,resultinginasizable theLHCbCollaborationalsofindsanenhancementclose
fractionofths∗e0orderof70%within errors. Areanalyisof to the KD threshold in the D¯0K− invariant mass dis-
thelatticespectraofRefs.[25,27]hasbeenrecentlydone tribution, which is partly associated to the Ds∗0(2317)
resonance [32].
∗Electronicaddress: Miguel.Albaladejo@ific.uv.es
†Electronicaddress: [email protected] 1 Throughoutthiswork,thenotation(DK)+referstotheisoscalar
‡Electronicaddress: oset@ific.uv.es combinationD0K++D+K0.
2
D
s−
c¯
s
b c
D0, D+, D+
s
B¯0 u¯u+d¯d+s¯s+c¯c
s
s¯ K+, K0,η
s¯
FIG. 1: Mechanism for thedecay B¯s0 →Ds−(DK)+.
In Fig. 1 we show the mechanism for the decay B¯0 A. Elastic DK scattering amplitude
D (DK)+. Theideaistotakethedominantmechansis→m
s−
for the weak decay of the B¯s0 into Ds− plus a primary cs¯ Let us start by discussing the S-wave amplitude for
pair. The hadronization of the initial cs¯pair is achieved theisospinI =0DK elasticscattering,whichwedenote
by inserting a qq¯pair with the quantum numbers of the T. It can be written as
vacuum: uu¯+dd¯+ss¯+cc¯, as shown in Fig. 1. There-
fore,the cs¯pairishadronizedintoapairofpseudoscalar T−1(s)=V−1(s) G(s) T(s)=V(s)(1+G(s)T(s)) ,
mesons. Thispairofpseudoscalarmesonsisthenallowed − ⇒ (1)
tointeracttoproducetheDs∗0+(2317)resonance,whichis whereG(s)isaloopfunctionbearingtheunitaryorright
consideredhere as mainly a DK molecule [15]. The idea hand cut,
issimilartothe oneusedinRef.[33]forthe formationof
the f0(980) and f0(500) scalar resonances in the decays d4l 1 1
of B0 and Bs0. G(s)≡iZ (2π)4l2 m2 +iǫ(q l)2 m2 +iǫ, (2)
− K − − D
The paper is organized as follows. In Section II we
and s = q2 is the invariant mass squared of the DK
settle the formalism for our study. Namely, in Subsec-
tion IIA we study the (DK)+ elastic scattering ampli- system. This function needs to be regularized, and this
is accomplished in this work by means of a subtraction
tude, and in Subsection IIB we study the differential
decay width for the process B0 D (DK)+. As said constant,a(µ). Inthisway,theGfunctioncanbewritten
s → s− as:
before, there is not yet experimental information con-
cerning the differential decay width for this process. For m m ∆ m2
this reason, we will have to generate synthetic data for 16π2G(s)=a(µ)+log D K + log D
µ2 2s m2
this decay in order to explore if this reaction is suitable K
for the study of the (DK)+ final state interactions and ν s ∆+ν s+∆+ν
+ log − +log , (3)
the Ds∗0+(2317) bound state. The generation and analy- 2s(cid:18) −s+∆+ν −s−∆+ν(cid:19)
sis of these synthetic data, which constitutes the results ∆=m2 m2 , ν =λ1/2(s,m2 ,m2 ) ,
of the work, are done in Subsection III. Conclusions are D− K D K
delivered in Section IV. where λ(x,y,z)=x2+y2+z2 2xy 2yz 2zx is the
− − −
K¨allenortrianglefunction. InEq.(1),V(s)isthepoten-
tial, typically extracted from some effective field theory,
although a different approach will be followed here (see
below).
TheamplitudeT(s)canalsobewrittenintermsofthe
II. FORMALISM phase shift δ(s) and/oreffective rangeexpansionparam-
eters,
In this work the influence of the presence of the
8π√s 8π√s
Dgas∗t0+ed(2.3T17h)eiDns∗t0+h(e23p1r7o)ceissscoB¯ns0sid→ereDds−m(DaiKnly)+asisainbvoeusntid- T(s)=−pKctgδ−ipK ≃−a1 + 21r0p2K −ipK, (4)
state of the DK system, so we address the elastic DK
scatteringamplitudeinSubsectionIIA.Then,thediffer- with
ential decay width for the B¯0 D (DK)+ reaction in
terms of the DK invariantmsas→s is cs−onsideredin Subsec- λ1/2(s,M2,M2)
p (s)= K D , (5)
tion IIB. K 2√s
3
themomentumoftheK mesonintheDK centerofmass In this way, the quantity αg2 represents the probabil-
system. Above, a and r are the scattering length and ity of finding other components beyond DK in the wave
0
the effective range, respectively. function of Ds∗0+(2317). The following relation can also
In this channelandlinkedto it we find the Ds∗0+(2317) be deduced from Eqs. (13) and (9):
resonance, the object of study of this paper, below the
1 P ∂G(s)
DK threshold, the latter being located roughly above α= − DK . (14)
2360 MeV. This means that the amplitude has a pole at − PDK ∂s (cid:12)(cid:12)s=s0
the squaredmass ofthis state, M2 s , so that, around (cid:12)
≡ 0 We can now link this formalism (cid:12)with the results of
the pole,
Ref. [28], where a reanalysis is done of the energy levels
g2 found in the lattice simulations of Ref. [27]. In Ref. [28],
T(s)= +regular terms, (6) thefollowingvaluesfortheeffectiverangeparametersare
s s
− 0 found:
being g the coupling of the state to the DK channel.
a = 1.4 0.6 fm , r = 0.1 0.2 fm . (15)
0 0
FromEqs.(1)and (6), we see that (the followingderiva- − ± − ±
tives are meant to be calculated at s=s0): Also, in studying the Ds∗0+(2317) bound state, a binding
1 ∂T 1(s) ∂V 1(s) ∂G(s) energyB =MD+MK−MDs∗0+ =31±17MeVisfoundin
− − Ref. [28]. The probability P is also studied, and the
= = . (7) DK
g2 ∂s ∂s − ∂s valueP =0.72 0.12isfound. Hence,forouranalysis,
DK
inwhichsynthetic±dataforthereactionB¯0 (DK)+D
We have thus the following exact sum rule, s → s−
will be generated, we can start from the hypothesis that
a bound state exists in the DK channel, with a mass
∂G(s) ∂V 1(s)
1=g2(cid:18)− ∂s + ∂−s (cid:19) . (8) MDs∗0+ =2317 MeV (the nominal one), and with a prob-
ability P = 0.75. This implies, from Eq. (14), the
DK
In Ref. [34] it has been shown, as a generalizationof the valueα=2.06·10−3 GeV−2. Finally,forthe subtraction
constant in the G function, Eq. (3), we shall take, as in
Weinbergcompositenesscondition[29](seealsoRef.[35]
Ref. [15], the value a(µ) = 1.3 for µ = 1.5 GeV. Note
andreferencestherein), thatthe probabilityP offinding −
that ∂G(s)/∂s does not depend on µ or a(µ).
the channel under study (in this case, DK) in the wave
function of the bound state is given by:
B. Decay amplitude and invariant DK mass
∂G(s)
P = g2 , (9) distribution in the B¯0 →D−(DK)+ decay
s s
− ∂s
whiletherestofther.h.s. ofEq.(8)representstheprob- We now discuss the amplitude for the decay B0
abilityofotherchannels,andhencetheprobabilitiesadd Ds−(DK)+ decay,anditsrelationtotheDK elasticssca→t-
upto1. Finally,ifonehasanenergyindependentpoten- teringamplitudestudiedabove. Thebasicmechanismfor
tialthe secondtermofEq.(8)vanishes,andthenP =1, this process is depicted in Fig. 1, where, from the s¯b ini-
that is, the bound state is purely given by the channel tial pair constituting the B0, a c¯s pair and a s¯c pair are
s
under consideration. In Ref. [34], these ideas are gener- created. The first pair produces the Ds−, and the DK
alized to the coupled channels case. state arises from the hadronization of the second pair.
Let us now apply these ideas to the case of DK scat- Let us consider in some more detail the hadronization
tering. From Eq. (1) it can be seen that the existence of mechanism. To construct a two meson final state, the cs¯
a pole implies pair has to combine with another q¯q pair created from
the vacuum. We introduce the following matrix,
V 1(s) G(s )+α(s s )+ , (10)
− 0 0
≃ − ··· u
α ∂V−1(s) , (11) M =vv¯= d u¯ d¯ s¯ c¯
≡ ∂s (cid:12) s
(cid:12)(cid:12)s=s0 c (cid:0) (cid:1)
(cid:12)
in the neighbourhood of the pole. If we assume that the
uu¯ ud¯ us¯ uc¯
energydependenceissmoothenoughtoallowustoretain
du¯ dd¯ ds¯ dc¯
onlythelineartermins,wecannowwritetheamplitude = , (16)
su¯ sd¯ ss¯ sc¯
as
cu¯ cd¯ cs¯ cc¯
T 1(s)=G(s ) G(s)+α(s s ) , (12)
− 0 − − 0 which fulfils:
and the sum rule in Eq. (8) becomes: M2 =(vv¯)(vv¯)=v(v¯v)v¯
P =1 αg2 . (13) = u¯u+d¯d+s¯s+c¯c M . (17)
DK
− (cid:0) (cid:1)
4
The firstfactorinthe lastequalityrepresentstheq¯q cre- Central Value 5 % 10 %
ation. This matrix M is in correspondence with the me- 103 α (GeV−2) 2.06 +0.17 +0.10
−0.40 −1.09
son matrix φ:
η + π0 + η′ π+ K+ D¯0 MDs∗a0(µ(M) eV) −2311.370 ++−0124.415 +−+2071.327
√3 √2 √6 −0.37 −0.49
φ= KDπ−−0 √η3 −DK√π¯0+20+ √η′6 √√23ηDK′ −s+0 √η3 DDη(cs−−18) . |gar|00P(D((GffKmmeV))) −−100.117...10504 +−++−−+−10000000........000260026736 +−++−−+−20001000........211410156641
The hadronizationof the cs¯pair proceeds then through
the matrix element M2 , which in terms of mesons TABLE I: Fitted parameters (α, MD∗+ and a(µ)) and pre-
43 s0
reads: (cid:0) (cid:1) dicted quantities (|g|, a0, r0, PDK) for µ = 1.5 GeV. The
secondcolumnshowsthecentralvalueofthefit,whereasthe
(φ2)43 =K+D0+K0D++ , (19) third(fourth)columnpresentstheerrors(estimatedbymeans
···
ofMC simulation) when theexperimentalerror is5% (10%).
where only terms containing a KD pair are retained,
since coupled channels are not considered in this work.
We note that this KD combination has I = 0, as it
should, since it is produced from a cs¯, which has I = 0, explore the sensitivity of the decay B¯0 (DK)+D
andthestronginteractionhadronizationwhichconserves to the presence of this bound state, wse→generate syns−-
isospin(theq¯q withthequantumnumbersofthevacuum thetic data from our theory for the differential decay
has I =0). width for the process with Eqs. (22) and (12). We gen-
Ds−L(eDt Kt )b+e, twhheicfhulallraemadpylittuadkeesfoirntotheaccporuoncetssthBes0fin→al einrgatefro1m0 sythnrtehsehtoicldp.oinTtos einacahrcaenngterooidf,10w0eMasesVignstatrhte-
state interaction of the DK pair. Also, let us denote by value obtained with the central values explained in Sub-
v the bare vertex for the same reaction. To relate t and section IIA (103α = 2.06 GeV−2, a(µ) = 1.3, and
vof, tthhaetDisK, topatiark,easinstkoetacchceoduninttFhieg.fi2n,awl setawtreitien:teraction MDs∗0+ =2317 MeV). We shall study two differ−ent cases,
in which each experimental point is given an error of a
5% or a 10% of the highest value of the differential de-
t=v+vG(s)T(s)=v(1+G(s)T(s)) . (20)
cay width. Taking these synthetic data as experiment-
From Eq. (1), the previous equation can also be written given data, we perform the inverse problem of analysing
as: them with our theory. Obviously, the reproduction of
T(s) the data must be perfect, but we recall that the scope
t=v . (21) here is to investigate the experimental accuracy that is
V(s)
actually needed to obtain reliable values for the quanti-
Boledc,atuhsiesporfotcheessprweislelndceepeonfdthsetrboonugnlydosntasteinbtehloewkitnhermesaht-- ties fitted or predicted from our theory (MDs∗0+, a0, r0,
and P ). The analysis of these synthetic data goes as
DK
icalwindowrangingfromthresholdto100MeVaboveit, follows. Wegeneratearound2 103 setsofrandomexper-
sowecansafelyassumethattdependsonlyons. Hence, ·
imental points, in which each centroid is varied around
thedifferentialwidthforthe processunderconsideration
itstheoreticalvalueaccordingtoaGaussiandistribution
is given by:
withthe errorgivento eachpoint. For eachofthese sets
2 of random points, the parameters are fitted to the data.
dΓ 1 T(s)
d√s = 32π2M2 pDs−pK|t|2 =CpDs−pK(cid:12)V(s)(cid:12) , (22) After the whole run, a central range, containing a 68%
B¯s0 (cid:12)(cid:12) (cid:12)(cid:12) ofthevaluesoftheconsideredquantities(thedifferential
(cid:12) (cid:12) decay width, the fitted parameters, and the predicted
where the barevertexv has beenabsorbedin ,a global
C values) is retained. It is worth stressing here that, since
(but otherwise not relevant) constant, and where p is
K the centroidofthe experimentalpointin eachsetofran-
given in Eq. (5) and pDs− is the momentum of the Ds− dom experimental points is varied, a good reproduction
meson in the rest frame of the decaying B¯0, given by:
s of the random synthetic data is quite natural but not
λ1/2(M2 ,M2 ,s) completely trivial.
pDs− = 2BM¯s0B¯s0 Ds− . (23) expTlhaeingeedn,etrhaetyedhasvyentthweotidciffdearteanatreerrsohrowbanrsi,ntFheigs.m3.alAlesr
one corresponding to a 5% experimental error and the
larger one to a 10%. As commented above, they exactly
III. RESULTS matchthecentralcurve(dash-dottedline)producedwith
thecentralparametersofthetheory. Asolelyphasespace
We want to investigate the presence of the Ds∗0+(2317) distribution (i.e., a differential decay width proportional
state in the (DK)+ scattering amplitude. In order to to pDs−pK, but with no other kinematical dependence
5
D D D
s− s− s−
D
B¯0 D B¯0 D B¯0 D
s s s
= +
K K K
K
t v v T
G
FIG. 2: Diagrammatical interpretation of Eq. (20), in which DK final state interaction is taken into account for the decay
B¯s0 → Ds−(DK)+. The dark square represents the amplitude t for the process, in which the final state interaction is already
takenintoaccount. Thelight squarerepresentsthebarevertexfortheprocess, denotedbyv. Finally,thecirclerepresentsthe
hadronic amplitude for theelastic DK scattering.
0.016 2317+14 MeV, and if the error is increased to 10%, the
24
00..001124 B¯0s →D−s(DK)+ vcoanlucee−rinsedMwDis∗t0+ht=he2u3p1p7e+−r27e13rrMore,Vin. thHeesreensweethaarteitmiasitnhlye
0.01 one that defines if the bound state is clearly below the
s
√
d 0.008 DK threshold(whichisslightlyabove2360MeV)ornot.
/
Γ phasespace Considering this error, we see that the mass obtained is
d 0.006
10% well below the threshold, at the level of 2σ (3σ) for the
0.004 5%
case of a 5% (10%) experimental error. This is a good
centralfit
0.002 syntheticdata information: experimental data with a 10% error,which
0 is clearly feasible with nowadays experimental facilities,
2360 2380 2400 2420 2440 2460 canclearlydeterminethepresenceofthisbelowthreshold
√s(MeV) state Ds∗0+(2317).
We canalsodetermineP ,theprobabilityoffinding
DK
DFIs−G(.D3K:)+D.iffTehreenstyinatlhdeteiccadyatwai(dgtehnefroartetdheasreexapcltaioinnedB¯ins0 t→he tshheowDnKincthhaennlaesltinrowtheofDTs∗a0+b(l2e3I1.7A) swastvaetefudn,ctthieonc.enIttraisl
text)areshown with black points. Thesmaller (larger) error value P = 0.75 is the same as the initial one, but we
DK
barscorrespondtoa5%(10%)experimentalerror. Thedash-
are here interested in the errors,which are small enough
dottedlinerepresentsthetheoreticalpredictionobtainedwith
eveninthecaseofa10%experimentalerror. Thismeans
the central values of the fit. The light (dark) bands corre-
that with the analysis of such an experiment one could
spond totheestimation of theerror (bymeansof aMC sim-
addresswithenoughaccuracythe questionofthe molec-
ulation) when fitting the data with 5% (10%) experimental
error. Thedashedlinecorrespondstoaphasespacedistribu- ular nature of the state (Ds∗0+(2317), in this case).
tion normalized tothe same area in the range examined. Finally, it is also possible to determine other parame-
ters related with DK scattering, such as the scattering
length (a ) and the effective range (r ). They are also
0 0
of dynamical origin) is also shown in the figure (dashed shown in Table I. They are compatible with the lattice
line). The first important information to be extracted QCD studies presented in Refs. [27, 28]. Namely, the
from the figure is that the data are clearly incompatible results from Ref. [28] are shown in Eqs. (15), and their
with this phase space distribution. This points to the mutual compatibility is clear.
presence of a resonant or bound state or, at least, to
some strong final state interactions. Two error bands
are shown in the same figure, the lighter and smaller
IV. CONCLUSIONS
(darker and larger) one corresponding to a 5% (10%)
experimental error. The fitted parameters (a(µ), MDs∗0+, In the present work we have selected a reaction which
and α) are shown in Table I, together with their errors.2 isbothCabbiboandcolorfavored,theB¯0 D (DK)+
Notethat,witha5%experimentalerror,wegetMDs∗0+ = weak decay, and have looked at the DKsin→varisa−nt mass
distribution from where we expect to obtain relevant
information on the nature of the Ds∗0+(2317) resonance
whenactualdataareavailable. Forthispurposewehave
2 To avoid unphysical values of the fitted parameters a(µ) and performedasimulationoftheexperimenttakinginforma-
αge,nwerhaitcehdceoxuplderinmumenetrailcaplolyintrse,ptrhoedyucaereearecshtrsiectteodfttohevarraynwdoitmhilny tion from experiment about the mass of the Ds∗0+(2317)
resonance and from a recent QCD lattice analysis on
asensiblerange, but making surethat this range islarger than
theerrorobtainedforthesetwoparametersandshowninTableI. ananalyticalrepresentationoftheKD scatteringampli-
6
tude. Thisinformationhasservedustomakepredictions tionoftheexperiment,forwhichwehavemadeestimates
ontheshapeoftheKD invariantmassdistributionclose of a relatively large branching fraction.
to the KD threshold. After that we have taken these
resultsandwehaveassumedtheyareactual”experimen-
taldata”,associatingtotheman”experimentalerror”of Acknowledgments
5% or 10%. Then we havemade a fit to these ”synthetic
data” in order to extract from there the KD scattering This work is partly supported by the Spanish
amplitude, above and below threshold. We prove that Ministerio de Economia y Competitividad and Eu-
with both errors,typical of present experimental data of ropean FEDER funds under the contract number
spectra in B decays, one can obtain the KD scattering FIS2011-28853-C02-01 and FIS2011-28853-C02-02, and
amplitude with enough precision to predict that there the Generalitat Valenciana in the program Prometeo II-
is a KD bound state. We also predict the scattering 2014/068. We acknowledgethe support of the European
lenght and effective range of the KD interaction and, Community-ResearchInfrastructureIntegratingActivity
very important, we show that we can predict, with rel- Study of Strongly Interacting Matter (acronym Hadron-
atively small error, the probability of the mesonic KD Physics3, Grant Agreement n. 283286) under the Sev-
component in the wave function of the Ds∗0+(2317) reso- enth Framework Program of the EU. M. A. acknowl-
nance. From the QCD lattice results one induces about edgesfinancialsupportfromthe“JuandelaCierva”pro-
70% probability and we show that this number can be gram (reference 27-13-463B-731)from the Spanish Gov-
obtained from the analysis of the B decay spectra with ernmentthroughthe Ministeriode Econom´ıay Compet-
sufficient precission to make the number significative of itividad. M.N.acknowledgesthe IFIC for the hospitality
the main nature of the Ds∗0+(2317) resonance as a basi- andsupportduringherstayinValenciaandalsosupport
callyKDmolecularstatewithasmallermixtureofother from CNPq and FAPESP.
components.
Thestudydonehereshouldstimulatetheimplementa-
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