Precision Measurement of the Mass of the $D^{*0}$ Meson and the Binding Energy of the $X(3872)$ Meson as a $D^0\overline{D^{*0}}$ Molecule

0.15 MB·English

by  A. Tomaradze

Precision Measurement of the Mass of the D∗0 Meson and the Binding Energy of the
X(3872) Meson as a D0D∗0 Molecule
A. Tomaradze,1 S. Dobbs,1 T. Xiao,1 and Kamal K. Seth1
1Northwestern University, Evanston, Illinois 60208, USA
(Dated: January 9, 2015)
A precision measurement of the mass differencebetween theD0 and D∗0 mesons has been made
using 316 pb−1 of e+e− annihilation data taken at √s = 4170 MeV using the CLEO-c detector.
We obtain ∆M M(D∗0) M(D0) = 142.007 0.015(stat) 0.014(syst) MeV, as the average
for the two deca≡ys, D0 K−−π+ and D0 K−±π+π−π+. Th±e new measurement of ∆M leads
to M(D∗0) = 2006.850 →0.049 MeV, and t→he currently most precise measurement of the binding
energyof the“exotic” m±eson X(3872) if interpretedas aD0D∗0 hadronicmolecule, Eb(X(3872))
5 M(D0D∗0) M(X(3872))=3 192 keV. ≡
− ±
1
0
2 Of all the claims and counterclaims for the so-called ∆M has remained fixed at the value, ∆M = 142.120
n “exotic” mesons, which do not fit in the pictures of 0.070 MeV as measured by CLEO in 1992 using dat±a
a conventional qq¯ mesons [1], the most intriguing one is taken at the Υ(4S) resonance [17]. To determine the
J X(3872). Its existence has been confirmed from nu- binding energy of X(3872)with the highest possible pre-

7 merous measurements, by Belle [2], CDF [3], D0 [4], cision, it has become imperative to make a new higher-
BaBar [5], LHCb [6] and CMS [7], and its mass, width, precision measurement of ∆M M(D∗0) M(D0).
] ≡ −
x and spin are respectively, M(X(3872)) = 3871.69 In this Letter we report on such a measurement us-
e 0.17 MeV, Γ(X(3872)) < 1.2 MeV, and JPC = 1++ [8±]. ing data taken at the ψ(4160) resonance, which decays
- Although many different suggestions for the structure of into D∗D∗, D∗D, and DD. We analyze D∗0 D0π0,
p
e X(3872) exist in the literature [9–12], the closeness of and D0 decays, D0 K−π+ (henceforth K→π), and
h the X(3872) mass to the sum of the masses of the D0 D0 K−π+π+π− (he→nceforth K3π).
[ and D∗0 mesons, and the smallness of its width have W→e use 316 pb−1 of e+e− annihilation data taken

1 made the suggestion that it is a weakly bound hadronic at √s = 4170 MeV with the CLEO-c detector. The
v molecule made of the D0 and D∗0 mesons extremely at- CLEO-c detector [19] consists of a CsI(Tl) electromag-
8
tractive [13]. To submit this provocative suggestion to neticcalorimeter,aninnervertexdriftchamber,acentral
5
6 experimentaltest it is important to measure the binding drift chamber, and a ring-imaging Cherenkov (RICH)
1 energy of X(3872), indeed to determine if it is bound at detector, all inside a superconducting solenoid mag-
0 all. ThisLetterreportsontheresultsofjustsuchamea- net providing a 1.0 Tesla magnetic field. The accep-
1. surement. Throughout this Letter we use the PDG [8] tance for charged and neutral particles is cosθ <
0 convention for units, with masses in MeV and momenta 0.93. Charged-particle momentum resolution |is σ /|p =
p
5 inMeV/c,andinclusionofcharge-conjugatestatesisim- 0.6% @ 1 GeV/c. Photon energy resolution is σ /E =
E
1 plied. 2.2% @ 1 GeV, and 5% @ 100 MeV. The detector re-
:
v A measurement of the binding energy of X(3872) sponse was studied using a GEANT-based [20] Monte
Xi requires the knowledge of three masses, M(X(3872)), Carlo simulation.
M(D0), and M(D∗0), with the most accurately deter- We select events with well-measured tracks by requir-
r
a mined value of M(D∗0) obtainedby measuring the mass ing that they be fully contained in the barrel region
difference, ∆M M(D∗0) M(D0). Since the dis- ( cosθ < 0.8) of the detector, and have transverse mo-
≡ − | |
covery of X(3872) in 2003, the precision in the value menta >120 MeV/c.
of the mass of the X(3872) has steadily improved from In our previous article on the precision measurement
800 keV, originally, to the present average with error of the mass of the D0 meson [16], we made a precision
±
of 170keV[8] because ofnumerous improvedmeasure- recalibration of the CLEO-c solenoid magnetic field and
me±nts. Similarly, the precision of the value M(D0) has determined a correction of (2.9 0.4) 10−4 in the de-
improved, from 1000 keV, originally, to 180 keV by faultcalibrationoftheCLEO-cm±agnet×icfield. Thedata
a CLEO measur±ement of M(D0) in 2007±[14], and to we use in the present investigation were taken just after
40 keV due to two recent higher-precision measure- this recalibration. We use the same corrected field as
±ments of M(D0) by BaBar [15], and our recent pub- determined in our previous article in the present Letter.
lication [16]. As a consequence, the determination of
Chargedpionsandkaonswereidentifiedusinginforma-
the binding energy of X(3872) as a D0D∗0 molecule has
tion from both the drift chamber dE/dx and the RICH
changedfrom(600 600)keVin2007[14]to (126 204)
± ± detector. First, it was required that the dE/dx of the
keV in 2014 [16].
charged particle track be consistent within 3σ of the re-
Through all these improvements, the mass difference spective pion or kaon hypothesis. For tracks with mo-
2
V6000 V1400
e e
M M
nts/1 5000 (a) D0→ Kπ ents/2 1200 (a) D0→ Kπ
eve4000 of ev1000
of er 800
er 3000 mb
b u
m n 600
u
n2000
400
1000
200
0 0
1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 200 300 400 500 600 700 800 900 1000
M(Kπ), MeV p(Kπ), MeV
V8000 V1000
e e
M M 900
nts/1 67000000 (b) D0→ K3π ents/2 800 (b) D0→ K3π
of eve5000 er of ev 670000
er 4000 mb 500
b u
m n
u3000 400
n
300
2000
200
1000
100
0 0
1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 200 300 400 500 600 700 800 900 1000
M(K3π), MeV p(K3π), MeV
FIG. 1. Reconstructed mass spectra for the candidates for FIG. 2. Momentum spectra in data for (a) D0 Kπ and
the decays (a) D0 Kπ, (b) D0 K3π. The verti- (b)D0 K3π forthecandidatesidentified inFig→. 1. Asde-
cal dashed lines sho→w the regions in→which we accept D0 scribed→inthetext,theenhancementscorrespondtomomenta
mesons, M(D0 ) = 1850 1880 MeV, and M(D0 ) = forthedifferentexpectedfinalstateswithtwocharmmesons.
1855 1875 McaenVd, for D0 −Kπ and D0 K3π chcaanndnels, The vertical dashed lines define the intervals of p(D0 ) in
− → → cand
respectively. which the eventswere accepted for analysis.
menta>700MeV,forwhichinformationfromtheRICH
are defined as calorimeter showers with E (barrel)> 30
detector is available, the log-likelihood LRICH, as de- γ
i MeV and a transverse energy spread consistent with
scribed in Ref. [18], was constructed. For such tracks,
that of an electromagnetic shower. The photon candi-
the combined dE/dx information σidE/dx, and the log- dates from π0 decays are required to have a two-photon
likelihood LRi ICH are used to distinguish between parti- invariant-mass, M(γγ), within 15 MeV of the nomi-
cle hypotheses i and j, nal M(π0) = 135.0 MeV [8], an±d to have neither pho-
toncandidatecombinewithanotherphotoncandidatein
∆Li,j =(σidE/dx)2−(σjdE/dx)2+LRi ICH −LRjICH. (1) the event to obtain an invariant mass closer to M(π0).
ThesecandidateswerekinematicallyfitwithM(γγ)con-
For tracks with momenta < 700 MeV, for which RICH strained to the nominal π0 mass in order to improve the
information is not available,
energy resolution.
∆L =(σdE/dx)2 (σdE/dx)2. (2) We reconstruct single D∗0 candidates through the de-
i,j i − j cays D∗0 π0D0, D0 Kπ and D0 K3π, by first
Toidentifypions,itwasrequiredthat∆L <0. For reconstruc→ting the D0 d→ecay and then→looking for the
π,K
kaons, it was required that ∆L >0. corresponding π0 to make D∗0.
π,K
We reconstruct π0 γγ decays using photons only WeselectD0 candidatesusingthestandardCLEOD–
→
in the barrel region, cosθ 0.80. Photon candidates tagging criteria, which impose very loose requirements
| | ≤
3
on the beam-energy-constrained D0 mass, as described
V 800
in Ref. [21]. e
k
In Fig. 1, we show the reconstructed invariant-mass 50 700
speActtra√fsor=D041→70KMπeaVn,dDD00 →meKso3nπs ccaanndibdeatpesr.oduced s / 2 600 (a) D0 → Kπ
through several different decays: e+e− D∗D∗, D∗D, ent
and DD. As illustrated in Fig. 2, the→se different de- ev 500
of
cays have different yields, and they populate different r 400
ranges of D0 momenta. The enhancement in D0 mo- be
m
menta at 500 MeV arises from e+e− D∗0D∗0, and u 300
decays of≈both D∗0 and D∗0 to the co→rresponding D0 N
200
and D0. The enhancement at 720 MeV arises from
e+e− D∗0D0, and D∗0 dec≈aying to D0. The en-
100
hancem→ent at 950 MeV arises from e+e− D0D0.
≈ →
GEANT-based[20]genericMonteCarloisfoundtofaith- 1035 140 145 150 155 160
fully reproduce both the observedenhancement, andthe M(Kππ0) - M(Kπ), (MeV)
background, which arises from the other decays of D
mtmheoosmsoeeninsn.tuwmEhvicdehnistatstriolbefuatisnitotonenrseeosDtf Ff∗o0irg(.othr2e,Dtp∗h0re)ersieesnifstoraamnneaedlny.hsIiansntachreee- NormalizedResiduals -022
135 140 145 150 155 160
mentcenteredatp(D0 ) 520MeV,whicharisesfrom
cand ≈
eventswith bothD∗0 andD∗0,whichdecayinto D0 and V
e
D0, respectively,andanenhancementatp(D0 ) 720 k 450
MeVwhicharisesfromeventswithonlyoneDca∗n0dor≈D∗0. 50 (b) D0 → K3π
2 400
Tasheexypieecldteidn,tnheeaernlyhaanfcaecmtoerntfoautrpl(aDrgc0earndt)h≈an5t2h0aMt ienVthise, nts / 350
e
enhWaencreemcoennsttrautctp(DD∗c00an(do)r≈D∗702)0cManedVid.atesfortheevents of ev 300
r 250
pin(Dt0he )enha7n20ceMmeeVnt,sanadt cpo(nDstc0raundct)th≈e d5is2t0ribMuteiVonsafnodr mbe 200
∆McandM≈(D∗0 ) M(D0 ). These are shown sepa- Nu 150
rately≡forthecdaencday−sD0 caKndπandD0 K3πinFig.3.
→ → 100
Since most of the instrumental uncertainties cancel in
50
the measurement of the mass difference ∆M, the resolu-
tionwidthof∆M isapproximatelyafactorofsixsmaller 0
135 140 145 150 155 160
(FWHM 2.7MeV)thanthatfortheindividualD0 and M(K3ππ0) - M(K3π), (MeV)
D∗0 mass≈es (FWHM 17 MeV).
≈
tmoiFabolarcaknbgdortoshuignKndasπlppaaanrradammKeet3terπrii,zzeewddeabfisyttahtesheescuoumnndb-oionfrndaeedGrpaspoulesycsnitarona- NormalizedResiduals -022
135 140 145 150 155 160
andanother Gaussianwith the same mean,but different
widths oneachsideofthe mean. Goodfits areobtained.
FIG. 3. The ∆M spectra and fits for the decays (a) D0
(FFigo.r3c(laa)r)itay,ndweDs0howKth3eπ∆(MFig.sp3e(cbt)r)a, faonrdDth0e→corKreπ- Kthπe,uannbdinn(be)dDda0ta→diKst3riπb.utTiohnes,fibtust(sfeoer tcelaxrti)tywtehree dfiotsnean→tdo
→
spondingplotsofresidualsforthedatabinnedin250keV corresponding residuals are shown for 250 keVbins.
bins. The results of the fits are listed in Table I. As is
customary, the peak values from the unbinned fits are
assumed to be measures of the corresponding mass dif-
agree with those in Eqs. 3 and 4 within 20 50 keV,
ferences, which are −
consistent with their statistical uncertainties.
∆M(Kπ)=142.007 0.018 MeV(stat), (3) Weestimatesystematicuncertaintiesinourresultsfor
±
∆M(K3π)=142.008 0.027 MeV(stat). (4) ∆M from the following sources. The results are listed
± in Table II. The CLEO energy calibration for photons is
We have analyzed the ∆M spectra for events in the basedonthe knownπ0 mass,andonphotonenergiesex-
enhancements at p(D0 ) 520 MeV, and p(D0 ) tracted in the radiative decays ψ(2S) γχ (J =1,2),
cand ≈ cand ≈ → cJ
720 MeV, separately, and find that the results for ∆M all of which are known with high precision. The uncer-
4
TABLE I. The results of the fits.
Fit D0 Kπ (Fig. 3(a)) D0 K3π (Fig. 3(b))
→ →
Numberof signal events 6344 178 3697 134
± ±
FWHM of ∆M distribution (MeV) 2.7 2.6
χ2/d.o.f of 250 keV binnedfit ≈1.10 ≈1.02
∆M from unbinnedfit (MeV) 142.007 0.016(stat) 142.008 0.024=7(stat)
± ±
TABLE II.Systematic errors in ∆M M(D∗0 ) M(D0 ) in keV.
≡ cand − cand
Source D0 Kπ D0 K3π
→ →
Photon energy calibration ( 0.4%) 10 10
Charged particle momentum±calibration (B-field 0.4 10−4) 3 3
± ×
Signal shape (default vs. single Gaussian) 10 7
Background shape (polynomial order +1) 1 7
K± mass ( 16 keV) 3 3
Cut variati±ons in M(D0 ), Fig. 1, ( 2.5 MeV) 4 1
Cut variations in p(D0can)d, Fig. 2, ( ±10 MeV) 4 1
cand ±
Cut variations in M(γγ) ( 2MeV) 4 6
±
Total 16 16
taintyinthiscalibrationisestimatedtobeto 0.4%. By The PDG2014 [8] average of ∆M based on the 1992
rescalingtheπ0 photonenergiesby 0.4%,we±determine measurement of Ref. 17 is ∆M = 142.12 0.07 MeV
± ±
the resulting uncertainty in ∆M. In Ref. [16], we made based on a total of 1176 counts in Kπ and K3π decays.
a precision determination of the CLEO solenoid B-field Our measurement, based on 10,041 counts, has factor
with an uncertainty of factor 0.4 10−4. This results 3.5 smaller overall uncertainty, and has 113 keV smalle≈r
×
in 3 keV uncertainty in ∆M. The uncertainty in sig- value of ∆M.
±
nal shape is estimated using making alternate fits of the The present measurement (Eq. 7), ∆M = 142.007
∆M spectra by a single Gaussian in the restricted range 0.021MeV,andthelatestaverageofD0 mass,M(D0)±=
of ∆M =141 143 MeV. The systematic error in back- 1864.843 0.044 MeV, [16] lead to
− ±
groundshapewasobtainedbyincreasingtheorderofthe
M(D∗0)=2006.850 0.049 MeV. (8)
polynomial used in the fit by one unit. The PDG2014
±
±
mass of the K has an uncertainty of ±16 keV [8]. This compares with the value M(D∗0) = 2006.96
It leads to 3 keV uncertainty in ∆M. Contributions ±
± 0.10 MeV obtained by the PDG2014 [8] from a simul-
to the systematic uncertainties derived from variations taneous fit of four masses, M(D∗+), M(D∗0), M(D+),
of event selection requirements in M(Dc0and) (Fig. 1), and M(D0).
p(Dc0and) (Fig. 2), and M(γγ) are seperately listed in Our measured masses lead to M(D∗0) + M(D0) =
Table II. Adding all systematic uncertainties in quadra-
3871.693 0.090 MeV. Using M(X(3872)) = 3871.69
ture, the total systematic uncertainty is estimated to be ± ±
0.12MeV[8]weobtainthebindingenergyofX(3872)as
±16 keV in ∆M(Kπ) and ∆M(K3π). a proposed D0D∗0 molecule,
Our final results for ∆M, including systematic errors,
are: Eb (3871.693 0.090) (3871.69 0.17) MeV=
≡ ± − ±
=3 192 keV. (9)
∆M(Kπ)=142.007 0.018(stat) 0.016(syst)MeV,(5) ±
± ±
The largest contribution to the uncertainty in the above
∆M(K3π)=142.008 0.027(stat) 0.016(syst)MeV.(6)
± ± resultisdueto 170keVuncertaintyinthePDG2014[8]
±
The results of the two D0 decay final states are in good average value of the mass of X(3872).
agreement (the agreement of the central values within The negative limiting value of the binding energy Eb
1 keV is fortuitous). The weighted average of the two impliesthatD0D∗0systemcouldbeunboundbyasmuch
determinations,takingproperaccountofthecorrelations as 189 keV. The positive limiting value Eb = 195 keV
in the systematic errors in the two decay modes, is impliesthattheproposedD0D∗0 molecule,withreduced
mass µ, has a minimum radius R=1/√2µE of 9.9 fm.
b
∆M =142.007 0.015(stat) 0.014(syst) MeV. (7) Hopefully,ournewresultforthebindingenergywillshed
± ±
5
light on the continuing saga of the D0D∗0 molecule and 189 (2004); C.E. Thomas and F.E. Close, Phys. Rev. D
other models of the structure of X(3872). 78, 034007 (2008); X. Liu, Z.-G. Luo, Y.-R. Liu, and
This investigation was done using CLEO data, and as S.-L. Zhu,Eur. Phys.J. C 61, 411 (2009).
[10] T. Barnes and S. Godfrey, Phys. Rev. D 69, 054008
members of the former CLEO Collaborationwe thank it
(2004); M. Suzuki, Phys. Rev. D 72, 114013 (2005);
for this privilege. This research was supported by the
C.MengandK.T.Chao,Phys.Rev.D75,114002(2007).
U.S. Department of Energy.
[11] L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer,
Phys. Rev.D 71, 014028 (2005).
[12] B.A. Li, Phys.Lett. B 605, 306 (2005).
[13] Forreviewsofmolecularmodelsee,forexample,E.Swan-
son,Phys.Reports429,243(2006),andN.Brambillaet
[1] See,forexample,S.Godfrey andN.Isgur,Phys.Rev.D aol., Euro. Phys. J. C71 ,1534 (2011).
32, 189-231 (1985). [14] C. Cawlfield et al., (CLEO Collaboration), Phys. Rev.
[2] S.K. Choi et al. (Belle Collaboration), Phys. Rev. Lett. Lett. 98, 092002 (2007).
91, 262001 (2003). [15] P. Lees et al. (BaBar Collaboration), Phys. Rev. D 88,
[3] D.Acostaetal.(CDFIICollaboration),Phys.Rev.Lett. 071104 (2013).
93, 072001 (2004). [16] A. Tomaradze, S. Dobbs, T. Xiao, K. K. Seth, G. Bon-
[4] V.M.Abazovetal.(D0Collaboration), Phys.Rev.Lett. vicini, Phys.Rev.D 89, 031501 (2014).
93, 162002 (2004). [17] D. Bortoletto et al. (CLEO Collaboration), Phys. Rev.
[5] B. Aubert et al. (BaBar Collaboration), Phys. Rev. D Lett. 69, 2046 (1992).
71, 071103 (2005). [18] Kamal K. Seth et al., Phys. Rev. Lett. 110, 022002
[6] R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. (2013).
110, 222001 (2013). [19] See,forexample,S.Dobbsetal.(CLEOCollaboration),
[7] S. Chatrchyan et al. (CMS Collaboration), JHEP 04 Phys. Rev.D 76, 112001 (2007).
(2013) 154. [20] R. Brun et al., CERN Long Writeup W5013 (1994), un-
[8] K. A. Olive et al. (Particle Data Group), Chin. Phys. C published.
38, 090001 (2014). [21] Q.Heet al.(CLEOCollaboration), Phys.Rev.Lett.95,
[9] N.A. Tornqvist, Z. Phys. C 61, 525 (1994); Phys. Lett. 121801 (2005).
B 590, 209 (2004); E.S. Swanson, Phys. Lett. B 588,