2 Events per 0.4 MeV/c

0

FIG. 13 (color online). Results (curve) of the unbinned, extended likelihood fits for determining the numbers ofB⁰candidates: the hadronic modes (a)MD and (c)MD, and inclusive semileptonic modes (b)MKand (d) MKMK. The filled histograms indicate various backgrounds.

lation; in this simulation, theD^þ_s’s are forced to decay only to the final states, which can yield misidentified mass in the MKwindow. The number of theD^þs background events is constrained to the estimated number ofHb !D^þsX events in the data ðN_DsÞ as described below. First, the following decay mode is reconstructed in the data:Hb ! D^þ_sX, where D^þ_s !ð1020Þ^þ and ð1020Þ ! K^þK. The narrow ð1020Þ resonance provides a good handle for removing the combinatorial background ofD^þs. Second, the fraction from theð1020Þ^þmode relative to all contributing D^þs decays ðRÞ is extracted using the world averages of theD^þs branching ratios, and the accep-tance times efficiency determined from the full simulation.

Then,ND_sis simply the yield of theð1020Þ^þmode in data divided by R. The value of ND_s for the con-straint is 1812160. The systematic uncertainty is as-signed by independently varying the ratio of the branching fraction of one specific D^þs decay relative to that of the D^þ_s !ð1020Þ^þ decay by 1, since the branching fractions of allD_sdecays have been measured relative to that of theð1020Þ^þmode [7].

Figure13(c)shows the fit result for theMDspectrum.

TheB⁰ !Dð2010Þ^þyield returned by the fit is106 11. The analysis of the Dð2010Þ^þ signal and back-grounds is similar to that in the D^þ mode. The only difference is that extra constraints are imposed due to the small size of theDð2010Þ^þ sample. The width of the signal Gaussian D, the ratio ^N_N^DK

D, and the ratio of backgrounds ND=ðN_DþNHb!remainingDXÞ, are con-strained to0:02590:0012 GeV=c²,0:0710:019, and 0:2420:008, respectively. The systematic uncertainty is assessed in the same way as in the ⁰_b and the D^þ modes.

Figure13(d) shows the fit result for theM_KM_K spectrum for events with muons. The likelihood fit for the Dð2010Þ^þX mode is performed in the mass window M_KM_K ¼0:140:18 GeV=c², whereas Fig.13(d) shows a more restricted mass range near the signal peak.

The inclusiveDð2010Þ^þX yield returned by the fit is 105933. The signal peak at MKMK 0:145 GeV=c² is modeled by two Gaussian distributions with a common mean and different widths. The combina-torial background (light-gray filled region) is

parameter-ized by a constant, while the background from other b-hadron decays with misidentifiedc-hadron daughters is found to be negligible. The size of the combinatorial background is very small due to the requirement that MK is consistent with the world average D⁰ mass, the minimum requirement on the mass MD, and the mini-mum requirements on thepT and the number of SVX hits for the low-momentum pion from the Dð2010Þ^þ decay (Sec.IX A). The fitting function for this spectrum does not use any branching ratios and no systematic uncertainty is assigned.

Table XII summarizes the B⁰ hadronic and inclusive semileptonic yields and the ² probability of correspond-ing fits. Each model describes the data well, as indicated by the ²probability.

C. Compositions of the inclusive semileptonic data The procedures for estimating the backgrounds to the B⁰!D^þ and B⁰!Dð2010Þ^þ decays are similar to those described in Sec. VI. The following de-scribes the differences when estimating the feed-in back-groundNfeedin theB⁰system. Unlike the⁰_bsystem, many decays of band cmesons have been measured by other experiments [31–34], and serve as inputs to the EVTGEN

decay package. In addition, EVTGEN also includes esti-mates of branching fractions for decay modes that have not yet been measured. Therefore, all possible decays that may contribute to the Nfeed in theB⁰ control samples are studied using the PDG summary and the default EVTGEN

decay table [7,30].

The feed-in backgrounds to the B⁰!D^þ and B⁰!Dð2010Þ^þ signals fall into two categories:

(1) Semileptonic decays of B⁰=B=B⁰_s, which include either additional particles (e.g.,B⁰ !D^þ0) or a higher mass c meson with subsequent decay into the c-meson signal [e.g., B⁰! Dð2010Þ^þ,Dð2010Þ^þ!D^þ0].

(2) Hadronic decays of b mesons into two c mesons:

onecmeson decays hadronically in a reconstructed final state, the other c meson decays semileptoni-cally (e.g.,B⁰ !D^þD_s,D_s !ð1020Þ).

Branching fractions of theB !DD decays relative to the signal are all below 3%. A generator-level study indicates that they are further suppressed after a minimum require-ment on the four-track invariant massM_DðDÞ, and there-fore, contribute less than 1% to the signal. Backgrounds frombmesons decaying semileptonically to more particles or higher masscmesons are also reduced or eliminated by the same minimum mass requirement.

Tables XIII and XIV summarize the feed-in back-grounds that contribute1%to theB⁰ !D^þ and the B⁰!Dð2010Þ^þ decays. The definition of quantities listed in each column follows Table V. Only TABLE XII. Observed number of events in each decay mode

determined from the unbinned, extended likelihood fit, ²=NDF, and the corresponding probability computed to indicate quality of the fit.

Mode Yield ²=NDF Prob (%)

B⁰!D^þ 57930 80=91 78.9 D^þX 4720100 47=31 3.40 B⁰!Dð2010Þ^þ 10611 21=12 5.40 Dð2010Þ^þX 105933 108=93 14.1

these decays are subtracted from the inclusive semileptonic yield. The leading background toB⁰!D^þisB⁰ ! Dð2010Þ^þ, where Dð2010Þ^þ !D^þ0. The leading background to B⁰!Dð2010Þ^þ

is B!D1ð2420Þ⁰, where D1ð2420Þ⁰ ! Dð2010Þ^þ. Combining information compiled in the PDG, backgrounds from B!D^ð;ÞX, which are not considered in Tables XIII and XIV contribute less than 2% to the signal. The estimates ofNfalse andN_bb;c c

for theB⁰ are identical to those for the⁰_b. TableXVlists the results. Figure14shows theMK andMKMK

distributions weighted with muon-misidentification proba-bilities and the results of the ² fit.

The compositions of the inclusive D^þ and Dð2010Þ^þ samples are summarized in Table XVI.

The dominant signal contamination is from the feed-in background. The second largest background arises from false muons. The smallest background source is from bb=c c.

D. Systematic uncertainties

Figure 15 shows a summary of internal-consistency checks. The fractional systematic and statistical uncertain-ties on theB⁰relative branching fractions are summarized in TableXVII. The leading sources of internal systematic uncertainties are the mass fitting models and the shape of TABLE XIII. The feed-in backgrounds to theB⁰!D^þsignal. For theB⁰s !D^þK⁰decay, theðB⁰sÞ=½ðBÞ þðB⁰Þ from the PDG is used to obtainNfeed=Nhad[69,70]. Numbers in parentheses are estimated uncertainties for the unmeasured branching fractions [71]. The definition of quantities listed in each column follows TableV.

Mode B(%) ⁱ

B0!Dþ

Nfeed Nhad

_i

Nfeed Nexclsemi

_i

Nevent

B⁰!D^þ 0:2680:013 1.000 – – 57930

D^þX – – – – 4720100

B⁰!D^þ 2:170:12 0:4550:004 3.688 1.000 –

B⁰!Dð2010Þ^þ 5:160:11 0:3720:004 2.314 0.627 134069 ,!D^þ0= 32:300:64

B⁰!D^þ0 0:30 ð0:30Þ 0:1650:003 0.185 0.050 1076

B⁰!D^þ 1:000:40 0:1000:004 0.065 0.018 372

,! 17:360:05

B!D1ð2420Þ⁰ 0:400:07 0:2780:005 0.134 0.036 784 ,!Dð2010Þ^þ

,!D^þ0= 32:300:64

B!D⁰1ð2430Þ⁰ 0:37 ð0:37Þ 0:2730:005 0.081 0.022 472 ,!Dð2010Þ^þ 66:67 ð3:33Þ

,!D^þ0= 32:300:64

B!D^þ 0:420:05 0:1650:003 0.259 0.070 1508

B⁰s !D^þK⁰ 0:30 ð0:30Þ 0:1370:004 0.064 0.017 372

TABLE XIV. The feed-in backgrounds to theB⁰!Dð2010Þ^þsignal.

Mode B(%) ⁱ

B0!Dð2010Þþ

Nfeed Nhad

_i

Nfeed Nexclsemi

_i

Nevent

B⁰!Dð2010Þ^þ 0:2760:013 1.000 – – 10611

Dð2010Þ^þX – – – – 105933

B⁰!Dð2010Þ^þ 5:160:11 0:4470:006 8.361 1.000 – B⁰!D1ð2420Þ^þ 0:81 ð0:32Þ 0:3490:008 0.341 0.041 364

,!Dð2010Þ^þ0 33:33 ð1:67Þ

B⁰!D⁰1ð2430Þ^þ 0:37 ð0:37Þ 0:3360:008 0.150 0.018 162 ,!Dð2010Þ^þ0 33:33 ð1:67Þ

B⁰!Dð2010Þ^þ0 0:10 ð0:10Þ 0:2390:006 0.086 0.010 91

B⁰!Dð2010Þ^þ 1:600:50 0:1360:005 0.137 0.016 142

,! 17:360:05

B!D1ð2420Þ⁰ 0:400:07 0:3560:008 0.516 0.062 556 ,!Dð2010Þ^þ

B!D⁰1ð2430Þ⁰ 0:37 ð0:37Þ 0:3510:008 0.314 0.038 333 ,!Dð2010Þ^þ 66:67 ð3:33Þ

B!Dð2010Þ^þ 0:610:06 0:2420:006 0.534 0.064 576

the measuredB⁰ pT spectrum. The dominant PDG uncer-tainties come fromBðB⁰!D^þÞfor theD^þmode, and BðB⁰ !D1ð2420Þ^þÞfor theDð2010Þ^þ mode. The dominant uncertainties on the estimated branching frac-tions come fromBðB⁰ !D^þ0Þfor theD^þ mode andBðB!D⁰1ð2430Þ⁰Þfor theDð2010Þ^þ mode.

The B⁰ relative branching fractions with complete

uncer-tainties are found to be BðB⁰ !D^þÞ

BðB⁰!D^þÞ ¼9:91:0ðstatÞ 0:6ðsystÞ 0:4ðPDGÞ 0:5ðEBRÞ;

BðB⁰ !Dð2010Þ^þÞ

BðB⁰ !Dð2010Þ^þÞ ¼16:52:3ðstatÞ 0:6ðsystÞ 0:5ðPDGÞ 0:8ðEBRÞ:

The uncertainties are from stat, internal syst, world aver-ages of measurements published by the PDG or subsidiary measurements in this analysis, and unmeasured branching fractions EBR, respectively.

X. RESULTS

The⁰_bandB⁰relative branching fractions are measured to be:

Bð⁰_b !^þ_cÞ

Bð⁰_b!^þ_cÞ ¼16:63:0ðstatÞ 1:0ðsystÞþ2:6

3:4ðPDGÞ 0:3ðEBRÞ;

BðB⁰ !D^þÞ

BðB⁰!D^þÞ ¼9:91:0ðstatÞ 0:6ðsystÞ 0:4ðPDGÞ 0:5ðEBRÞ;

BðB⁰ !Dð2010Þ^þÞ

BðB⁰ !Dð2010Þ^þÞ ¼16:52:3ðstatÞ 0:6ðsystÞ 0:5ðPDGÞ 0:8ðEBRÞ:

2

) (GeV/c

π π

M

K

1.80 1.85 1.90 1.95

2

Events per 5 MeV/c

0 20 40 60 80 100

120 D

⁺

h

^-

X

π

+

π

+

K

-→

(a)

2

) (GeV/c

π

-M

K π π

M

K

0.140 0.145 0.150 0.155

2

Events per 0.4 MeV/c

0 2 4 6 8 10 12

14 D

^*

(2010)

⁺

h

^-

X π

+

D

0

→ → K

^-

π

+

(b)

FIG. 14 (color online). The invariant mass distributions produced from data with a hadron track (h) and ac-meson candidate in the final state, after weighting the hadron track with an average muon-misidentification probability (Pavg): (a) MK and (b)MKMK. The curves indicate the results of the ²fit.

TABLE XV. The estimated sizes of the false-muon, bb, cc, and feed-in background contribution to theB⁰!D^þand B⁰!Dð2010Þ^þsignals and the observed yields in data.

Uncertainties on thebb,cc, and feed-in backgrounds are statis-tical only.

D^þ Dð2010Þ^þ

Nfalse 23019 443

Nbb=Nhad 0:080:01 0:080:01 Ncc=Nhad 0:050:01 0:050:01 Nfeed=Nhad 3:100:03 2:080:02

Nhad 57930 10611

Ninclsemi 4720100 105933

TABLE XVI. The composition of the inclusive D^þ and Dð2010Þ^þ data samples.

N=Ninclsemi(%)

D^þ Dð2010Þ^þ

Signal 55.5 73.7

False muon 4.9 4.2

bb=c c 1.6 1.3

Feed-in 38.0 20.8

The uncertainties are from statistics (stat), internal system-atics (syst), world averages of measurements published by the Particle Data Group or subsidiary measurements in this analysis (PDG), and unmeasured branching fractions esti-mated from theory (EBR), respectively. The control sam-ple results are consistent with the ratios published by the -

)

FIG. 15 (color online). Internal-consistency checks of the relative branching fractions measured in the two B⁰ control samples:

(a)B⁰!D^þdecays and (b)B⁰!Dð2010Þ^þdecays. The uncertainty on each point is a statistical only. Each independent group is separated by a horizontal dashed line. The solid bands indicate the relative branching fractions with their statistical uncertainties from the complete, undivided samples.

TABLE XVII. Summary of statistical and systematic uncer-tainties for the B⁰ modes. The R is uncertainty on the B⁰ relative branching fraction,R.

_R

Simulation sample size 1.6 1.7

B⁰ p_T spectrum 3.0 2.4

XFT/CMU efficiency scale factor 0.5 0.4

Detector material 1.7 1.3

Sum of internal 6.3 3.7

PDG 4.1 2.8

Estimated branching fractions 4.7 4.9

Statistical 9.7 14.1

TABLE XVIII. TheB⁰relative branching fractions measured in this analysis and those published in the 2008 PDG [7]. The measurements of this analysis include both the statistical and the systematic uncertainties.

2008 PDG [7] at the 1:3 and 0:8 level, respectively, (see Table XVIII). The measured ratio of ⁰_b branching fractions is compared with the predicted value based on HQET. The prediction has a 30% uncertainty and is obtained by combining the results of Huang et al. [9]

and Leibovich et al.[10,72]. Figure16shows the

consis-tency between this measurement and the theoretical prediction.

The branching fractions of the four new⁰_bsemileptonic decays relative to that of⁰_b!^þ_care measured to be

Bð⁰_b!_cð2595Þ^þÞ

Bð⁰_b!^þ_cÞ ¼0:1260:033ðstatÞþ0:047 0:038ðsystÞ;

Bð⁰_b!_cð2625Þ^þÞ

Bð⁰_b!^þ_cÞ ¼0:2100:042ðstatÞþ0:071 0:050ðsystÞ;

1 2

Bð⁰_b !_cð2455Þ^0þÞ

Bð⁰_b!^þ_cÞ þBð⁰_b!_cð2455Þ^þþÞ Bð⁰_b!^þ_cÞ

¼0:0540:022ðstatÞþ0:021 0:018ðsystÞ:

XI. CONCLUSION

Using data from an integrated luminosity of172 pb¹ collected with the CDF II detector, 123797 ^þ_cX and 17919 ⁰_b!^þ_c signal events are recon-structed. The large ⁰_b sample enables the measurement of Bð⁰_b!^þ_cÞ=Bð⁰_b!^þ_cÞ and the

com-parison to the predictions of heavy quark effective theory.

The uncertainty is dominated by the size of the data sample, the world average ofBð^þ_c !pK^þÞ, and the CDF I measurement of ⁰_b=B⁰. Ratios for the control modesBðB⁰ !D^þÞ=BðB⁰ !D^þÞandBðB⁰! Dð2010Þ^þÞ=BðB⁰!Dð2010Þ^þÞ are found to be in good agreement with the world averages [7]. For the first time, the semileptonic decay ⁰_b! _cð2625Þ^þhas been observed, and three other semi-leptonic decays ⁰_b!_cð2595Þ^þ, ⁰_b! _cð2455Þ^0þ, ⁰_b!_cð2455Þ^þþ have been reconstructed, using data from an integrated luminos-ity of 360 pb¹. Measurements of the ratios of their branching fractions to the branching fraction of ⁰_b! ^þ_c have been performed. Finally, the transverse-momentum distribution of the⁰_b baryon produced inpp collisions is found to be softer (moreb hadrons at lower p_T) than that of theB⁰meson; this results in a new estimate for Bð⁰_b !^þ_cÞ in better agreement with the theory than the PDG evaluation.

ACKNOWLEDGMENTS

We thank the Fermilab staff and the technical staff of the participating institutions for their vital contributions. This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada;

the National Science Council of the Republic of China; the Swiss National Science Foundation; the A. P. Sloan Foundation; the Bundesministerium fu¨r Bildung und Forschung, Germany; the Korean Science and Engineering Foundation; and the Korean Research Foundation; the Science and Technology Facilities Council and the Royal Society, UK; the Institut National de Physique Nucleaire et Physique des Particules/CNRS;

-

) π

+

Λ

c

→

0

Λ

b µ

)/B(

ν µ

-+

Λ

c

→

0

Λ

b

B(

10 15 20 25

Theory

Dans le document First measurement of the ratio of branching fractions B(Λ_b⁰→Λ_c⁺μ⁻ν_μ)/B(Λ_b⁰→Λ_c⁺π⁻) (Page 25-30)