Study of radially excited $D_s(2^1S_0)$ and $D^+_{sJ}(2632)$

0.16 MB·

by  Yu Tian

Study of radially excited Ds(21S0) and Ds+J(2632)
Yu Tian, Ze Zhao and Ailin Zhang∗
Department of Physics, Shanghai University, Shanghai 200444, China
The JP = 0− radial excitation Ds(21S0) is anticipated to have mass 2650 MeV (denoted with
Ds(2650)) though it has not been observed. Ds(2650) is anticipated to be observed in inclusive
e+e− and ppcollisions in D∗K channel. Ds(2650) can beproducedfrom hadronicdecaysof higher
excited resonances. In a 3P0 model, hadronic production of Ds(2650) has been studied, relevant
decaywidthshavebeenestimated. ThehadronicdecaysofDs(3P)havebeenexploredindetail,and
the dominant decay channels have been pointed out. Two hadronic decay channels of D+(2632)
sJ
were observed by SELEX, but have not been observed by any other experiment. Hadronic decays
ofD+(2632) indifferentassignmentshavebeenexploredinthe3P model. Inviewofthehadronic
sJ 0
7 decaymannerofD+(2632),weconcludethatD+(2632)cannotbeaconventionalcharmedstrange
sJ sJ
1 cs¯meson.
0
2 PACSnumbers: 13.25.Ft;12.39.-x
n Keywords: 3P0 model,Hadronicdecay, Ds(2650), Ds+J(2632)
a
J
I. INTRODUCTION
0 TABLEI:Tentativeassignment of2S and1D excitedD and
2 Ds resonances.
h] areTbheelileovweedstesltyainbglis1hSeda[n1d, 21]P. IenxrceitceedntDyeaanrsd,Dmsorsetaatneds \Dn2S+1LJ 2D1(S20550) 2D3∗S(12600) D11(,32D7520) D13∗D(21760) D13∗D(23760)
1 3
p more higher excited D and Ds resonances have been ob- Ds −− Ds∗1(2700) −− Ds∗1(2860) Ds∗3(2860)
- served though some of them have not been identified.
p
Study of their spectroscopy, production and decay will
e
h be helpful for their identification and quark dynamics. denoted as D (2650) and be studied. The JP = 2− D
[ For D resonances, D(2550), D∗(2600), D(2750) and s s
D∗(2760) were observed in inclusive e+e− and pp colli- resonance will not be addressed for an unclear mixing.
1 In 2600 2700 MeV energy region, a surprisingly
v sions by BaBar [3] and LHCb [4] collaborations, respec- narrow char∼med strange state, D+(2632), was first re-
8 tively. D∗(2760) was subsequently found consisting of ported by SELEX [21] in D+η ansdJ D0K+ decay chan-
7 D1∗(2760) and D3∗(2760) [5, 6]. nels: D+(2632) D0K+,sD+η. D (2632) was ob-
56 obFseorrveDdsbryesoBneallnece[s7,]Das∗n1d(27B0a0B)aarnd[8]Dcs∗oJl(l2a8b6o0r)atiwoenrse. sMerevVe.dIwnsiJptharmticauslsa→rM, it=ha2s63a2n.5se±xo1ti.c7 rMseJleaVtivaenbdraΓnc<hin1g7
0
1. DDs∗∗J((22886600))[w9,a1s0a].lsAocfcoournddingcotnosiRsteifnsg. [o1f1–D20s∗1],(2w8e60h)avaenda rsaeqtiuoenΓt(Dse0aKrc+h)f/oΓr(DD+s+η()26=320).b14y±Ba0B.0a6r.[2H2]o,wFeOveCr,UsSuobr-
0 s3 sJ
7 tentativeassignmentoftheseD andDs resonancesgiven BELLE has not found any evidence.
1 in Table I Since the report of D+ (2632), there appear many in-
sJ
v: When these highly excited D and Ds resonances are terpretations of this state. In Refs. [23–25], Ds+J(2632)
i examined, it is interesting to note that the masses of was interpreted as the JP =1− first radial excitation of
X D∗ (2700),D∗ (2860)andD∗ (2860)areabout100MeV D∗(2112). The special decay manner was attributed to
r higs1her than ths1ose of D∗(2600s3), D∗(2760) and D∗(2760), thsenodestructureofthewavefunctionsinRef.[23]orto
1 3
a
respectively. Therefore,twomissingDswithmasses2650 the couple channels effect in Ref. [25]. However, the as-
MeV and 2850 MeV are expected to correspond to the signment of D+(2632)with 2+ D (3P ) or 1− D (23S )
± sJ s 2 s 1
observedD(2550)andD(2750). InRef.[16],DsJ(2850) was pointed out impossible in Refs. [26, 27], and the as-
h51a.s6bMeeenVpcroerdriecstpedonwdiitnhgΓtoto(taJlP==1225−.,1jMq =eV23a)nadndΓt(oJtaPl == sRigenfsm. e[2n7t,o2f8D].s+J(I2n63t2h)ewfritahmDeso(1f3hDe1a)vywaqsuaadrkvoecffateecdtivine
2−,j = 5), respectively. theory (HQET) sum rule [29], it was pointed out that
q 2
D(2550) was suggested as the JP = 0− radial exci- Ds+J(2632) was unlikely to be a conventional orbitally
tation D(21S ) [11, 12, 15, 16], and D(2750) was sug- higher excited cs¯resonance.
gested as the0 JP = 2− admixture of D(11D2) and Ds+J(2632) was alternatively interpreted as a four-
D(13D ) [12, 14, 16]. Therefore, the two missing D quarkstateinRefs.[30–32]. Thenarrowwidthandexotic
2 s
are expected to have JP = 0− and JP = 2−. In this decaymanner wereinterpretedinthis assignment. How-
paper,theD (21S )withmassaround2650MeVwillbe ever, the predicted partners and more decay channels of
s 0 D+(2632)have not been observed. In Refs. [24, 33], the
sJ
authors concluded that D+(2632) was an experimental
sJ
artefact.
∗Correspondingauthor: zhangal@staff.shu.edu.cn The 3P0 model is a phenomenological method first
2
put forth by Micu [34] and subsequently developed by where J~ = J~ + J~ , J~ = J~ + J~ +L~ and M =
B C A B C JA
Yaouanc et al. [35–37]. It has been employed suc- M +M . The helicity amplitude reads
JB JC
cessfully to explore Okubo-Zweig-Iizuka-allowed (OZI-
allowed) hadronic decays of hadrons. Hadronic decays δ3(p~B +p~C)MMJAMJBMJC
of the JP = 0− radial excitation D with M = 2673 = 8E E E γ L M S M J M
s A B C h A LA A SA| A JAi
MeV and M = 2650 MeV have been explored in the p MLAX,MSA,
3mPi0ssimngodDel([21625,03)8f]r,obmuthitghheerhaedxrcoitneidcrpersoodnuacntcieosnhoafstnhoist MMLLCB,M,MSSCB,m,
s
L M S M J M L M S M J M
been explored. As that in Refs. [18, 19], it is interest- ×h B LB B SB| B JBih C LC C SC| C JCi
ing to explorethe hadronicproductionof Ds(2650)from ×h1m;1−m|00ihχ1S3BMSBχ2S4CMSC|χ1S2AMSAχ314−mi
higher excited resonances.
ϕ13ϕ24 ϕ12ϕ34 IMLA,m (p~) (4)
As for Ds+J(2632), its hadronic decay has not yet been ×h B C| A 0 i MLB,MLC
systematicallystudiedinthe3P0model. Inordertoiden- where ~pB and p~C (p~B=-p~C=p~) are the momenta of final
tify Ds+J(2632),it is requiredto explore the hadronic de- mesons B and C in A’s center-of-mass frame, respec-
cay features of D+ (2632) no matter whether D+ (2632) tively. γ is a phenomenological parameter, which indi-
sJ sJ
is an experimental artefact or not. cates the strength of the quark-pair creation from the
The paper is organized as follows. In the second sec- vacuum. IMLA,m (p~) is a momentum integral
tion, the 3P model and the parameters are briefly in- MLB,MLC
0
troduced. In Sec. III, the numerical results relevant to IMLA,m (p~)= d~k d~k d~k d~k
hadronicdecaysofDs(2650),Ds(3P)andDs+J(2632)are MLB,MLC Z 1 2 3 4
presented. The summaries and discussionsare presented δ3(~k +~k p~ )δ3(~k +~k )
1 2 A 3 4
in Sec. IV. × −
δ3(p~ ~k ~k )δ3(p~ ~k ~k )
B 1 3 C 2 4
× − − − −
Ψ∗ (~k )Ψ∗ (~k )
× nBLBMLB 13 ncLCMLc 24
II. 3P0 MODEL Ψ (~k )Y ~k (5)
× nALAMLA 12 1m(cid:16) 34(cid:17)
Among models for hadronic decays, the 3P model is with a relative momentum of quark i and quark j:
popularly known as a quark-paircreation (QP0C) model. ~k = mj~ki−mi~kj (i,j = 1,2,3,4). Ψ (~k) are simple
Since the propose of 3P0 model [34–37], it has been ex- hiajrmonimcoi+scmiljlator(SHO)wavefunctnioLnMsLforthemesons,
tensively applied to mesons and baryons with success. andy (~k)= ~k Y (Ω)isthesolidharmonicpolynomial
1m 1m
To proceed with a practical computation, the formula | |
of the created P-wave quark pair.
in Refs. [19, 39] are presented. In the 3P model, the
0 In terms of 9j symbols [37], the flavor matrix element
hadronic decay width of A BC is
reads
→
ϕ13ϕ24 ϕ12ϕ34 = I I3;I I3 I ,I3
Γ=π2M|p~|2 |MJL|2 (1) h B C| A 0 i XI,I3h C C B B| A Ai
A XJL [(2I +1)(2I +1)(2I +1)]1/2
B C A
×
where ~p is the momentum of the final mesons B and C I1 I3 IB
in the initial meson A’s center-of-mass frame I2 I4 IC (6)
× 
I 0 I
A A
p~ = [m2A−(mB −mC)2][m2A−(mB+mC)2] (2) whereIi(i=1,2,3,4)istheisospinofthefouru,d,sorc
| | p 2mA quark. IA,IB andIC aretheisospinsofthemesonsA,B
and C, respectively. I3, I3 and I3 are the third isospin
A B C
and MJL is the partial wave amplitude of A BC. components of the mesons, and I I3;I I3 I ,I3 is
The partial wave amplitude MJL is obtained fr→om the the isospin matrix element. h C C B B| A Ai
helicity amplitude MJAMJBMJC interms ofthe Jacob- The spin matrix element reads
M
Wick formula as follows
χ13 χ24 χ12 χ34
D SBMSB SCMSC| SAMSA 1−mE
JL(A BC)= √2L+1 =( 1)SC+1[3(2SB+1)(2SC +1)(2SA+1)]1/2
M → 2J +1 −
A
S M S M SM SM S M ;1, m
L0JM J M × h B SB C SC| Sih S| A SA − i
× X h JA| A JAi SX,MS
MJB,MJC 1/2 1/2 S
B
J M J M J,JM
×h B JB C JC| JAi 1/2 1/2 SC. (7)
MJAMJBMJC(p~) (3) ×SA 1 S 
×M
 
3
Withtheseformulainhand,weproceedwithourcalcu- D(2D)andD (2D)havebeenexploredinthe3P model
s 0
lation. In the practical calculation, the parameters have in Refs. [18, 19]. Hadronic decays of D (3P) have been
s
been employedas follows. The massesof the constituent studied in Ref. [12], where some decay channels were ig-
quarksaretakentobe,m =1628MeV,m =m =220 nored. In this subsection, hadronic decays of D (3P)
c u d s
MeV, and m = 419 MeV [12]. The masses and the resonances as an example are explored in detail.
s
effective scale parameters β of relevant mesons are pre- IntheD (3P)multiplets,D (33P )andD (31P )may
s s 1 s 1
sentedinTable II [1,12], wherea commonvalue β =0.4 mix with each other. For lack of information, the detail
GeV is employed for all light flavor mesons. For reso- of the mixing of D (33P ) with D (31P ) is not clear.
s 1 s 1
nances included in PDG, their masses in PDG are em- Therefore, the OZI-allowed hadronic decay channels of
ployed (unlike those in Ref. [12]), while for resonances D (33P ),D (31P ),D (33P )andD (33P )arestudied
s 0 s 1 s 1 s 2
not included in PDG or not observed by experiment, separately.
their masses and β are taken from Ref. [12]. γ = 6.95 The masses of D (3P) are employed as fol-
s
is employed in this paper, where γ is √96π times as the lows [12]: M(D (33P )) = 3412 MeV, M(D (31P )) =
s 0 s 1
γ = 0.4 adopted in Ref. [12] for a different definition. M(D (33P )) = 3425 MeV, M(D (33P )) = 3439 MeV.
s 1 s 2
The meson flavor follows the convention [12]: D0 = cu¯, ThemassesofD (31P )andD (33P )areassumedequal
s 1 s 1
D+ = cd¯, D+ = cs¯, K+ = us¯, K− = su¯, φ = ss¯, to the mean mass value of D (3P ) and D (3P′) in
and η =−(uu¯ sdd¯)/−2 ss¯/√2.− − Ref. [12]. The final decay widthssare1given in Tsable1s IV-
− −
VII. All the four D (3P) resonances have large total de-
s
cay widths, which are larger than those in Ref. [12].
III. HADRONIC DECAYS From Table IV, Γ (D (33P )) = 162.3 MeV
total s 0
and the dominant decay channels of D (33P ) are:
s 0
A. Ds(2650) (11D2)D(2750)K, DK, D(2550)K and D1(2420)K∗.
From Table V, Γ (D (31P ))=260.4 MeV and the
total s 1
Two possible hadronic decay channels and partial de- dominant decay channels of Ds(31P1) are: D2∗(2460)K,
cay widths of the JP = 0− radial excitation D with D∗(2760)K , DK∗(1410) and D∗(2460)K∗.
s 3 2
M = 2650 MeV (Ds(2650)) were calculated in the 3P0 FromTableVI,Γtotal(Ds(33P1))=204.8MeVandthe
model [38]: dominant decay channels of Ds(33P1) are: D1(2430)K∗,
D∗(2760)K, D(2600)K and D∗(2460)K.
Γ(Ds(21S0) D∗K)=78 MeV, 3From Table VII, Γ (D2(33P )) = 307.9 MeV
→ total s 2
Γ(D (21S ) D∗η)=0. and the dominant decay channels of D (33P ) are:
s 0 → s D∗K∗(1410), D∗(2460)K∗, DK∗(1410) andsD(26200)K.
Once the JP =0− radial excitation D has a mass M = 2
s
2673 MeV, the partial decay widths become [38]:
Γ(D (21S ) D∗K)=94 MeV, C. D+(2632)
s 0 → sJ
Γ(D (21S ) D∗η)=0.6 MeV.
s 0 → s In Table I, D∗ (2700) and D∗ (2860) are tentatively
s1 s3
In Ref. [12], the results were improved as follows identified with D (23S ) and D (13D ), respectively.
s 1 s 1
Γ(D (21S ) D∗K)=73.6 MeV, However, as introduced in the first section, Ds+J(2632)
s 0Γ(D→(21S ) D∗η)=0. was once regardedas a Ds(23S1), Ds(13D1) or their ad-
s 0 → s mixture if its lower mass is ignored. In order to have a
D∗K decay channel is the dominant hadronic decay of look at these possibilities, let’s explore the hadronic de-
cayofD+(2632). ThemixingofD (23S )andD (13D )
D (2650), which may be used as a typical evidence to sJ s 1 s 1
s
identify the JP =0− radial excitation D . D(2550) was will not be taken into accountfor its unclear mixing fea-
observed in inclusive e+e− and pp collissions, D (2650) ture.
s In D (23S ) or D (13D ) assignment, D+(2632) may
is naturally anticipated to be observed in these inclusive s 1 s 1 sJ
e+e− and pp collisions in D∗K channel. decayintoD0K+,D+K0,Dsη,D∗0K+andD∗+K0final
states. The partial and total decay widths are given in
In other ways, D (2650) can be produced from the
s
Table VIII.
hadronic decays of higher excited D and D mesons
s
InthecaseofaD (23S ),wehavethefollowingratios:
throughD (2650)K orD (2650)ηchannels,respectively. s 1
s s
Relevant hadronic partial decay widths have been esti-
mated and presented in Table III. Γ(DK) =0.79; Γ(Ds+η) =0.08. (8)
Γ(D∗K) Γ(D∗K)
B. Hadronic decay of Ds(3P) resonances InthecaseofaDs(13D1),wehavethefollowingratios:
D (2650) can be produced from hadronic decays of Γ(DK) Γ(D+η)
s =3.95; s =0.25. (9)
higher excited D and Ds mesons. Hadronic decays of Γ(D∗K) Γ(D∗K)
4
TABLE II: Masses and β values of mesons (MeV).
States Mass β States Mass β
(11S )K± 493.677 400 (1P )K (1270)0(±) 1272 400
0 1 1
(11S )K0 497.614 400 (1P′)K (1400)0(±) 1403 400
0 1 1
(13S )K∗± 891.66 400 (13P )K∗(1430)0 1432.4 400
1 2 2
(13S )K∗0 895.81 400 (13P )K∗(1430)± 1425.6 400
1 2 2
(11S )η 547.862 400 (13P )K∗(1430)0(±) 1425 400
0 0 0
(13S )φ 1019.461 400 (1P )D (2430)0(±) 2427 475
1 1 1
(11S )D± 1869.61 601 (1P′)D (2420)0 2421.4 475
0 1 1
(11S )D0 1864.84 601 (1P′)D (2420)± 2423.2 475
0 1 1
(13S )D∗± 2010.26 516 (13P )D (2400)0 2318 516
1 0 0
(13S )D∗0 2006.96 516 (13P )D (2400)± 2403 516
1 0 0
(11S0)Ds 1968.30 651 (13P2)D2(2460)± 2464.3 437
(13S )D∗ 2112.1 562 (13P )D (2460)0 2462.6 437
1 S 2 2
(21S )K(1460)0(±) 1460 400 (23S )D∗(2600)0 2608.7 434
0 1
(23S )K∗(1410)0(±) 1414 400 (23S )D∗(2600)+ 2621.3 434
1 1
(21S )D(2550)0(±) 2539.4 450 (13D )D∗(2760)0 2763.3 456
0 1 1
(13P0)Ds0(2317) 2317.7 542 (13D1)D1∗(2760)+ 2769.7 456
(1P1)Ds1(2460) 2459.5 498 (13D3)D3∗(2760)0 2763.3 407
(1P1′)Ds1(2536) 2535.10 498 (13D3)D3∗(2760)+ 2769.7 407
(13P2)Ds2(2573) 2571.9 464 (11D2)D(2750)0 2752.4 428
(23S )D∗ (2700) 2708.3 458 (11D )D(2750)+ 2752.4 428
1 s1 2
(13D )D∗ (2860) 2859 469 (13D )D(2750)0 2752.4 428
1 s1 2
(13D )D∗ (2860) 2860.5 426 (13D )D(2750)+ 2752.4 428
3 s3 2
TABLEIII: Hadronic partial decay widthsof Ds(2650) from highly excited resonances (MeV)
Mode Width Mode Width
D(43S1)→Ds(2650)K 0.1 Ds(43S1)→Ds(2650)η 0.0
D(53S1)→Ds(2650)K 0.0 Ds(53S1)→Ds(2650)η 0.0
D(33P0)→Ds(2650)K 1.8 Ds(33P0)→Ds(2650)η 0.1
D(33P2)→Ds(2650)K 2.8 Ds(33P2)→Ds(2650)η 2.4
D(43P0)→Ds(2650)K 0.2 Ds(43P0)→Ds(2650)η 0.0
D(43P2)→Ds(2650)K 0.0 Ds(43P2)→Ds(2650)η 0.2
D(23D1)→Ds(2650)K 6.1 Ds(23D1)→Ds(2650)η 4.7
D(23D3)→Ds(2650)K 0.0 Ds(23D3)→Ds(2650)η 0.1
D(33D1)→Ds(2650)K 0.0 Ds(33D1)→Ds(2650)η 0.5
D(33D3)→Ds(2650)K 1.4 Ds(33D3)→Ds(2650)η 1.0
D(13F2)→Ds(2650)K −− Ds(13F2)→Ds(2650)η 0.0
D(23F2)→Ds(2650)K 4.5 Ds(23F2)→Ds(2650)η 3.0
D(23F4)→Ds(2650)K 0.6 Ds(23F4)→Ds(2650)η 0.8
D(13G3)→Ds(2650)K 0.6 Ds(13G3)→Ds(2650)η 0.6
D(13G5)→Ds(2650)K 0.0 Ds(13G5)→Ds(2650)η 0.0
D(23G3)→Ds(2650)K 1.6 Ds(23G3)→Ds(2650)η 1.0
D(23G5)→Ds(2650)K 0.7 Ds(23G5)→Ds(2650)η 1.0
Obviously,the decay manner ofD+(2632)is differentin IV. CONCLUSIONS AND DISCUSSIONS
sJ
different assignments. In fact, this decay manner can be
employed to distinguish D (23S ) from D (13D ).
s 1 s 1 The missing JP = 0− radial excitation D (2650) is
s
anticipated to have mass 2650 MeV. D∗K channel is
the dominant hadronic decay channel of D (2650), and
s
D (2650)is anticipated to be observedin inclusive e+e−
s
∗
and pp collisions in D K channel. D (2650) can be pro-
s
In particular, the estimated ratios ΓΓ(D(D0s+Kη+)), 5.02 and dorucfreodmfroDmhmigehsoenretxhcriotuedghDDth(r2o6u5g0h)ηDcsh(2a6n5n0e)lK. channel
7.90,aremuchlargerthan the observed0.14 0.06. Ob- s s
viously, D+(2632) cannot be a convention±al charmed Hadronic decays of D (3P) have been studied. All
sJ s
strange cs¯meson. the hadronic decay channels are given, and the decay
5
TABLE IV:Hadronic decay widths of Ds(33P0) (MeV).
Channels Width Channels Width
D0K+ 10.5 D (2420)+K0 0.1
1
D+K0 10.3 Ds1(2536)η 0.3
Dsη 0.2 D1(2430)0K+ 7.8
D(2550)0K+ 9.8 D (2430)+K0 7.6
1
D(2550)+K0 9.7 Ds1(2460)η 0.2
D0K(1460)+ 5.5 D (2420)0K∗+ 8.1
1
D+K(1460)0 6.9 D (2420)+K∗0 8.2
1
D∗0K∗+ 3.2 D (2430)0K∗+ 5.7
1
D∗+K∗0 2.8 D (2430)+K∗0 5.7
1
D∗φ 4.0 D∗0K (1270)+ 1.1
s 1
D∗(2400)0K∗+ 0.6 D∗+K (1270)0 1.1
0 1
D∗(2400)+K∗0 2.2 D∗0K (1400)+ 0.3
0 1
D∗ (2317)φ 2.0 D∗(2460)0K∗+ 3.0
s0 2
D0K (1270)+ 0.8 D∗(2460)+K∗0 2.5
1 2
D+K (1270)0 0.6 D(2750)0K+ 19.3
1
D0K (1400)+ 1.5 D(2750)+K0 18.8
1
D+K1(1400)0 1.7 (21S0)Ds(2650)η 0.1
D (2420)0K+ 0.1 Γ 162.3
1 total
widthshavebeenestimated. ThefourD (3P)resonances which is much smaller than the predicted ones in these
s
havelargetotaldecaywidths. Thedominantdecaychan- possibilities. In short, D+(2632) cannot be a conven-
sJ
nels ofD (33P ) are: (11D )D(2750)K, DK, D(2550)K tional charmed strange cs¯meson, which keeps rooms for
s 0 2
and D (2420)K∗. The dominant decay channels of D (2650), D∗ (2700) and D∗ (2860).
1 s s1 s1
D (31P ) are: D∗(2460)K, D∗(2760)K , DK∗(1410)
s 1 2 3
∗ ∗
and D (2460)K . The dominant decay channels of
2
D (33P ) are: D (2430)K∗, D∗(2760)K, D(2600)K Acknowledgments
s 1 1 3
∗
and D (2460)K. The dominant decay channels of
2
D (33P ) are: D∗K∗(1410), D∗(2460)K∗, DK∗(1410)
s 2 2 This work is supported by National Natural Science
and D(2600)K.
Foundation of China under the grants: 11475111 and
D+(2632) has a mass comparable to those of pre-
sJ 11075102. ItisalsosupportedbytheInnovationProgram
dicted D (21S ), D (23S ) and D (13D ). However,
s 0 s 1 s 1 ofShanghaiMunicipalEducationCommissionunder the
D+(2632) has an exotic ratio Γ(D0K+) = 0.14 0.06, grant No. 13ZZ066.
sJ Γ(Ds+η) ±
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TABLE V:Hadronic decay widths of Ds(31P1) (MeV).
Channels Width Channels Width
D0K∗+ 3.9 Ds1(2460)η 0.0
D+K∗0 3.7 D (2420)0K∗+ 7.9
1
Dsφ 0.1 D1(2420)+K∗0 8.1
D0K∗(1410)+ 13.0 D (2430)0K∗+ 9.3
1
D+K∗(1410)0 12.4 D (2430)+K∗0 9.3
1
D∗0K+ 7.7 D∗0K (1270)+ 8.1
1
D∗+K0 7.6 D∗+K (1270)0 8.4
1
D∗η 0.2 D∗0K (1400)+ 2.6
s 1
D∗0K∗+ 2.7 D∗+K (1400)0 1.8
1
D∗+K∗0 2.4 D0K∗(1430)+ 3.1
2
D∗φ 2.0 D+K∗(1430)0 3.2
s 2
D∗0K∗(1410)+ 15.9 D∗(2460)0K+ 14.6
2
D∗+K∗(1410)0 4.5 D∗(2460)+K0 14.4
2
D∗(2400)0K+ 2.5 D∗ (2573)η 3.9
0 s2
D∗(2400)+K0 1.3 D∗(2460)0K∗+ 13.0
0 2
D∗ (2317)η 0.2 D∗(2460)+K∗0 12.4
s0 2
D0K∗(1430)+ 1.4 D∗(2600)0K+ 11.9
0
D+K∗(1430)0 1.6 D∗(2600)+K0 12.0
0
D∗(2400)0K∗+ 0.0 D(2750)0K+ 0.0
0
D∗(2400)+K∗0 0.0 D(2750)+K0 0.0
0
D∗ (2317)φ 0.0 D∗(2760)0K+ 0.7
s0 1
D0K (1270)+ 0.0 D∗(2760)+K0 0.7
1 1
D+K (1270)0 0.0 D∗(2760)0K+ 14.4
1 3
D0K (1400)+ 0.0 D∗(2760)+K0 13.1
1 3
D+K (1400)0 0.0 D∗ (2860)η 0.5
1 s1
D (2420)0K+ 0.0 D∗ (2860)η 0.0
1 s3
D (2420)+K0 0.0 D∗ (2700)η 3.5
1 s1
Ds1(2536)η 0.0 Γtotal 260.4
D (2430)0K+ 0.0
1
D (2430)+K0 0.4
1
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7
TABLE VI:Hadronic decay widths of Ds(33P1) (MeV).
Channels Width Channels Width
D0K∗+ 4.1 Ds1(2460)η 0.0
D+K∗0 3.8 D (2420)0K∗+ 4.5
1
Dsφ 0.2 D1(2420)+K∗0 4.6
D0K∗(1410)+ 7.2 D (2430)0K∗+ 11.9
1
D+K∗(1410)0 6.6 D (2430)+K∗0 12.0
1
D∗0K+ 8.5 D∗0K (1270)+ 7.6
1
D∗+K0 8.3 D∗+K (1270)0 8.0
1
D∗η 0.1 D∗0K (1400)+ 2.3
s 1
D∗0K∗+ 3.7 D∗+K (1400)0 1.7
1
D∗+K∗0 3.3 D0K∗(1430)+ 2.5
2
D∗φ 2.0 D+K∗(1430)0 2.8
s 2
D∗0K∗(1410)+ 0.0 D∗(2460)0K+ 9.1
2
D∗+K∗(1410)0 0.0 D∗(2460)+K0 9.0
2
D∗(2400)0K+ 0.0 D∗ (2573)η 2.6
0 s2
D∗(2400)+K0 0.0 D∗(2460)0K∗+ 3.6
0 2
D∗ (2317)η 0.0 D∗(2460)+K∗0 3.2
s0 2
D0K∗(1430)+ 0.0 D∗(2600)0K+ 9.8
0
D+K∗(1430)0 0.0 D∗(2600)+K0 9.3
0
D∗(2400)0K∗+ 0.3 D(2750)0K+ 6.7
0
D∗(2400)+K∗0 1.7 D(2750)+K0 6.5
0
D∗ (2317)φ 1.8 D∗(2760)0K+ 0.1
s0 1
D0K (1270)+ 0.0 D∗(2760)+K0 0.1
1 1
D+K (1270)0 0.0 D∗(2760)0K+ 12.0
1 3
D0K (1400)+ 1.2 D∗(2760)+K0 11.0
1 3
D+K (1400)0 1.4 D∗ (2860)η 0.3
1 s1
D (2420)0K+ 1.7 D∗ (2860)η 0.0
1 s3
D (2420)+K0 1.6 D∗ (2700)η 2.3
1 s1
Ds1(2536)η 0.2 Γtotal 204.8
D (2430)0K+ 1.8
1
D (2430)+K0 1.8
1
8
TABLE VII:Hadronic decay widths of Ds(33P2) (MeV).
Channels Width Channels Width
D0K+ 1.0 D∗0K∗(1430)+ 0.3
0
D+K0 1.1 D∗+K∗(1430)0 0.2
0
Dsη 0.3 D1(2420)0K∗+ 4.1
D(2550)0K+ 2.6 D (2420)+K∗0 4.3
1
D(2550)+K0 2.7 D (2430)0K∗+ 3.1
1
D0K(1460)+ 5.3 D (2430)+K∗0 3.0
1
D+K(1460)0 5.0 D∗0K (1270)+ 3.1
1
D0K∗+ 2.3 D∗+K (1270)0 3.2
1
D+K∗0 2.2 D∗0K (1400)+ 1.8
1
Dsφ 0.0 D∗+K1(1400)0 1.6
D0K∗(1410)+ 11.1 D0K∗(1430)+ 1.1
2
D+K∗(1410)0 10.9 D+K∗(1430)0 1.0
2
D(2550)0K∗+ 0.0 D∗(2460)0K+ 6.5
2
D(2550)+K∗0 0.0 D∗(2460)+K0 6.5
2
D∗0K+ 3.8 D∗ (2573)η 1.8
s2
D∗+K0 3.8 D∗0K∗(1430)+ 1.6
2
D∗η 0.3 D∗(2460)0K∗+ 25.0
s 2
D∗0K∗+ 4.8 D∗(2460)+K∗0 24.9
2
D∗+K∗0 4.4 D∗(2600)0K+ 7.1
D∗φ 1.7 D∗(2600)+K0 7.6
s
D∗0K∗(1410)+ 45.2 D(2750)0K+ 2.0
D∗+K∗(1410)0 44.5 D(2750)+K0 2.0
D∗(2400)0K∗+ 0.1 D(2750)0K+ 0.4
0
D∗(2400)+K∗0 1.1 D(2750)+K0 0.4
0
D∗ (2317)φ 1.3 D∗(2760)0K+ 0.2
s0 1
D0K (1270)+ 2.9 D∗(2760)+K0 0.2
1 1
D+K (1270)0 2.7 D∗(2760)0K+ 4.7
1 3
D0K (1400)+ 1.6 D∗(2760)+K0 4.3
1 3
D+K1(1400)0 1.5 Ds(2650)η 2.4
D (2420)0K+ 1.9 D∗ (2860)η 0.0
1 s1
D (2420)+K0 1.8 D∗ (2860)η 0.0
1 s3
Ds1(2536)η 0.1 Ds∗1(2700)η 3.0
D (2430)0K+ 4.9 Γ 307.9
1 total
D (2430)+K0 4.9
1
Ds1(2460)η 2.7
TABLEVIII:Partial and total widths of D+(2632) (MeV) and Γ(D0K+)/Γ(D+η) in different assignments.
sJ s
Assignment D0K+ D+K0 Dsη D∗0K+ D∗+K0 Γtotal ΓΓ(D(D0s+Kη+))
D+(2632)(23S ) 17.8 17.5 3.5 22.9 21.6 83.2 5.02
sJ 1
D+(2632)(13D ) 34.2 33.4 4.3 8.8 8.3 88.9 7.90
sJ 1