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A New Measurement of $Bto D^{}pi$ Branching Fractions

A New Measurement of $Bto D^{}pi$ Branching Fractions
A New Measurement of $Bto D^{}pi$ Branching Fractions

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CLNS 97/1485

CLEO 97-11

A New Measurement of

B →D ?πBranching Fractions CLEO Collaboration (February 7,2008)Abstract The decays Υ(4S )→B B 0→D ?+π?)=(2.81±0.11±0.21±0.05)×10?3and B (B ?→D ?0π?)=(4.34±0.33±0.34±0.18)×10?3.

G.Brandenburg,1R.A.Briere,1Y.S.Gao,1D.Y.-J.Kim,1R.Wilson,1H.Yamamoto,1 T.E.Browder,2F.Li,2Y.Li,2J.L.Rodriguez,2T.Bergfeld,3B.I.Eisenstein,3J.Ernst,3 G.E.Gladding,3G.D.Gollin,3R.M.Hans,3E.Johnson,3I.Karliner,3M.A.Marsh,3

M.Palmer,3M.Selen,3J.J.Thaler,3K.W.Edwards,4A.Bellerive,5R.Janicek,5 D.B.MacFarlane,5K.W.McLean,5P.M.Patel,5A.J.Sado?,6R.Ammar,7P.Baringer,7

A.Bean,7D.Besson,7D.Coppage,7C.Darling,7R.Davis,7N.Hancock,7S.Kotov,7

I.Kravchenko,7N.Kwak,7S.Anderson,8Y.Kubota,https://www.wendangku.net/doc/5114396832.html,ttery,8S.J.Lee,8

J.J.O’Neill,8S.Patton,8R.Poling,8T.Riehle,8V.Savinov,8A.Smith,8M.S.Alam,9 S.B.Athar,9Z.Ling,9A.H.Mahmood,9H.Severini,9S.Timm,9F.Wappler,9

A.Anastassov,10S.Blinov,10,?J.E.Duboscq,10K.D.Fisher,10D.Fujino,10,?R.Fulton,10 K.K.Gan,10T.Hart,10K.Honscheid,10H.Kagan,10R.Kass,10J.Lee,10M.

B.Spencer,10 M.Sung,10A.Undrus,10,?R.Wanke,10A.Wolf,10M.M.Zoeller,10B.Nemati,11

S.J.Richichi,11W.R.Ross,11P.Skubic,11M.Wood,11M.Bishai,12J.Fast,12E.Gerndt,12 J.W.Hinson,12N.Menon,https://www.wendangku.net/doc/5114396832.html,ler,12E.I.Shibata,12I.P.J.Shipsey,12M.Yurko,12 L.Gibbons,13S.D.Johnson,13Y.Kwon,13S.Roberts,13E.H.Thorndike,13C.P.Jessop,14 K.Lingel,14H.Marsiske,14M.L.Perl,14S.F.Scha?ner,14D.Ugolini,14R.Wang,14

X.Zhou,14T.E.Coan,15V.Fadeyev,15I.Korolkov,15Y.Maravin,15I.Narsky,15

V.Shelkov,15J.Staeck,15R.Stroynowski,15I.Volobouev,15J.Ye,15M.Artuso,16

A.E?mov,16F.Frasconi,16M.Gao,16M.Goldberg,16D.He,16S.Kopp,16G.C.Moneti,16

R.Mountain,16S.Schuh,16T.Skwarnicki,16S.Stone,16G.Viehhauser,16X.Xing,16 J.Bartelt,17S.E.Csorna,17V.Jain,17S.Marka,17A.Freyberger,18R.Godang,18

K.Kinoshita,https://www.wendangku.net/doc/5114396832.html,i,18P.Pomianowski,18S.Schrenk,18G.Bonvicini,19D.Cinabro,19 R.Greene,19L.P.Perera,19G.J.Zhou,19B.Barish,20M.Chadha,20S.Chan,20G.Eigen,20 https://www.wendangku.net/doc/5114396832.html,ler,20C.O’Grady,20M.Schmidtler,20J.Urheim,20A.J.Weinstein,20

F.W¨u rthwein,20D.M.Asner,21D.W.Bliss,21W.S.Brower,21

G.Masek,21

H.P.Paar,21

V.Sharma,21J.Gronberg,22T.S.Hill,22R.Kutschke,https://www.wendangku.net/doc/5114396832.html,nge,22S.Menary,22 R.J.Morrison,22H.N.Nelson,22T.K.Nelson,22C.Qiao,22J.D.Richman,22D.Roberts,22

A.Ryd,22M.S.Witherell,22R.Balest,23

B.H.Behrens,23K.Cho,23W.T.Ford,23

H.Park,23P.Rankin,23J.Roy,23J.G.Smith,23J.P.Alexander,24C.Bebek,24

B.E.Berger,24K.Berkelman,24K.Bloom,24D.G.Cassel,24H.A.Cho,24

D.M.Co?man,24D.S.Crowcroft,24M.Dickson,24P.S.Drell,24K.M.Ecklund,24

R.Ehrlich,24R.Elia,24A.D.Foland,24P.Gaidarev,24B.Gittelman,24S.W.Gray,24

D.L.Hartill,24B.K.Heltsley,24P.I.Hopman,24J.Kandaswamy,24N.Katayama,24

P.C.Kim,24D.L.Kreinick,24T.Lee,24Y.Liu,24G.S.Ludwig,24J.Masui,24

J.Mevissen,24N.B.Mistry,24C.R.Ng,24E.Nordberg,24M.Ogg,24,?J.R.Patterson,24 D.Peterson,24D.Riley,24A.So?er,24C.Ward,24M.Athanas,25P.Avery,25C.D.Jones,25

M.Lohner,25C.Prescott,25J.Yelton,25and J.Zheng25

1Harvard University,Cambridge,Massachusetts02138

2University of Hawaii at Manoa,Honolulu,Hawaii96822

3University of Illinois,Champaign-Urbana,Illinois61801

4Carleton University,Ottawa,Ontario,Canada K1S5B6

and the Institute of Particle Physics,Canada

5McGill University,Montr′e al,Qu′e bec,Canada H3A2T8

and the Institute of Particle Physics,Canada

6Ithaca College,Ithaca,New York14850

7University of Kansas,Lawrence,Kansas66045

8University of Minnesota,Minneapolis,Minnesota55455

9State University of New York at Albany,Albany,New York12222

10Ohio State University,Columbus,Ohio43210

11University of Oklahoma,Norman,Oklahoma73019

12Purdue University,West Lafayette,Indiana47907

13University of Rochester,Rochester,New York14627

14Stanford Linear Accelerator Center,Stanford University,Stanford,California94309 15Southern Methodist University,Dallas,Texas75275

16Syracuse University,Syracuse,New York13244

17Vanderbilt University,Nashville,Tennessee37235

18Virginia Polytechnic Institute and State University,Blacksburg,Virginia24061 19Wayne State University,Detroit,Michigan48202

20California Institute of Technology,Pasadena,California91125

21University of California,San Diego,La Jolla,California92093

22University of California,Santa Barbara,California93106

23University of Colorado,Boulder,Colorado80309-0390

24Cornell University,Ithaca,New York14853

25University of Florida,Gainesville,Florida32611

The study of B decays to exclusively hadronic?nal states has been limited because samples in available data are small.In this paper we employ a technique,a“partial re-construction,”that can increase the acceptance of the sequenceΥ(4S)→B

B0→D?+π?decays were

reconstructed;in this letter,we report the reconstruction of~2600

B0→D?+π?decays[2].

Both the CLEO[1,3]and ARGUS[4]collaborations reported measurements of B→D?πbased on the full reconstruction technique.In the analysis of data presented in this letter,all kinematic quantities that describe the decay chain B→D?πf,D?→Dπs are reconstructed from measurements of the three-momenta of the two pions,one fast(πf)and one slow(πs), p f and p s;the D from D?decay is undetected,which yields an order of magnitude increase in acceptance over full reconstruction,and removes systematic uncertainty introduced by D branching fractions.

The basic idea was described in[5]:a B fromΥ(4S)decay is nearly at rest and the energy release in the D?→Dπdecay is small,so the decay products,πs andπf,are nearly back to back.The smearing introduced in[5]by neglect of the detailed kinematics of the decay sequence is much larger than the smearing caused by errors in either the measurement of the pion momenta,or by the error in knowledge of the magnitude of the initial B momentum. Complete evaluation of the detailed kinematics leads to a signi?cant improvement in the description of the shape of the signal,the shape of the background,and rejection of the background.

To fully describe the kinematics of the decay,twenty parameters are required:four for each four-vector of the?ve particles:B,D?,πf,D,andπs.Energy-momentum conservation can be applied twice,in the B→D?πf and D?→Dπs decays,yielding eight equations; the masses of the?ve particles can be assumed;and the center-of-mass energy of the e+e?collisions can be used to obtain the magnitude of the three-momentum of the initial B.The six free parameters that remain describe the kinematics of the decay sequence.These can be thought of as six angles:two that describe the B direction,two angles(θ?f,φ?f)that describe the direction of theπf in the B rest frame,and two angles(θ?s,φ?s)that describe the direction of theπs in the D?rest frame.We evaluate those six angles from the measurement of the three components of theπf momentum and the three components of theπs momentum.

The angles that provide e?ective discrimination between signal and background areθ?f andθ?s,for which the explicit expressions are:

cosθ?f=?βB(E?f?E?D?)

2γ2BβB M B P?f

and(1)

cosθ?s=?βD?(E?s?E?D)

2γ2D?βD?M D?P?s

,(2)

where E?f,E?D?and P?f are the energy and momentum of theπf and D?in the B center of

mass;E?s,E?D and P?s are the energy and momentum of theπs and D in the D?center of mass;γB(D?),βB(D?)and M B(D?)are the Lorentz factor,the velocity and the mass of the B(D?)in the lab frame.The magnitude of the D?and D momenta in the lab frame,|P D?|and|P D|, are determined by applying energy-momentum conservation in the decay chain.For signal, the magnitudes of these cosines will tend to fall into the‘physical’region;less than one. The signal distribution will be uniform in cosθ?f(because the B has spin0),and as cos2θ?s (because the D?has helicity0),before consideration of detector acceptance,e?ciency,and resolution.Detector resolution sometimes pushes signal events into the‘non-physical’region, where the magnitude of one or both of the cosines exceeds unity.Backgrounds usually fall into the non-physical region.The variables cosθ?f and cosθ?s tend to depend linearly on| p f| and| p s|once the dependence of|P D?|and|P D|on these variables is included.

The angle between the plane of the B→D?πf decay and the plane of the D?→Dπs decay,φ=φ?f?φ?s,is reconstructed in the following manner.In the lab frame,the D?direction must lie on a small cone of angleαf around the direction opposite to theπf. Simultaneously,the D?must also lie on a second small cone of angleαs around the direction of theπs.The expressions for these angles are:

cosαf=M2B?M2D??M2π

βD?βf

and cosαs=?

M2D?+M2π?M2D

βD?βs

,(3)

where the momenta and velocities are measured in the lab frame.The decay kinematics limitαf≤0.14andαs≤0.28.Intersection of these two cones determines the D?directions, of which in practice there are two:a so-called quadratic ambiguity.For both D?directions:

cosφ=

cosδ?cosαf cosαs

B pairs(referred to as‘o?-resonance’).The on-resonance data correspond to(3.27±

0.06)×106B B decays.

Charged pions that are consistent with production at the e+e?annihilation position and that penetrate all layers of the CLEO II tracking system are identi?ed by means of time-of-?ight,speci?c ionization,and shower development in the CsI calorimeter and surrounding muon identi?er.Neutral pions are reconstructed primarily from information in the CsI calorimeter[6].

Events with two pions are classi?ed according to the net charge,which is0or±1for signal.The fast pion is charged,but the slow pion can be either charged(π?fπ+s)or neutral (π?fπ0s).Only D?±decays yield slow charged pions,but slow neutral pions are produced from both D?0and D?±decays,and so theπ?fπ0s sample will contain contributions from

both

B events.The distribution of decay products in these events tends to be jet-like,while in B

B events,each candidate event must satisfy R2<0.275,where R2is the ratio of the second Fox-Wolfram moment to the zeroth moment[7].We also reject events where the momentum of any charged track exceeds the maximum possible from a B decay,2.45GeV/c.

To extract the branching fractions we perform a two-dimensional?t in cosθ?f and cosθ?s, where the?t region is|cosθ?f|<1.65and?1.6

B background shape and rate is determined from a sample of o?-resonance data,that has been scaled for the relative luminosities and cross-sections between the on-resonance and o?-resonance data samples.The cosθ?f and cosθ?s distributions in non-B

B events shows that this background is dominated by modes that are able to produce a fast pion candidate,such as B→D(±,0)X,where the X system is predominantlyπ,ρorμνμ,and the D(±,0)can be in an excited state.The background distribution in cosθ?f is determined by the kinematics of the fast pion from the B decay.Slow pions are plentiful in these B

B distribution.When both candidates come from the same B decay,the distribution inθ?s andθ?f is distinctive,but unlike that of the signal:the branching ratios of modes that enter the?nal sample in this manner are allowed to?oat in the?nal?t,either constrained by a Gaussian to the central value and error in[9],or left unconstrained,if no measurement is available.The branching fractions used in theπ?fπ+s and theπ?fπ0s samples are constrained to be equal.

One B decay background mode is handled di?erently.The Cabibbo-suppressed mode B→D?K is essentially indistinguishable from B→D?πin the partial reconstruction. We assume that the ratio of branching fractions,B(B→D?K)/B(B→D?π),is given by the ratio of the decay constants for kaons and pions,f K/fπ,the ratio of the CKM matrix elements,V us/V ud,and the ratio of form factors.The product of these ratios is determined to be(7.69±0.08)%[10,11].The assumed B→D?K rate is subtracted,with adjustment

for acceptance.

The projections of the data and the?tting function in cosθ?f and cosθ?s are shown in Fig.1 for theπ?fπ+s?t and in Fig.2for theπ?fπ0s?t.The sidebands outside the signal region tend to determine the background normalization,and are?tted well by the background functions. The sharp turn-on of signal at±1can be seen while the background distribution in cosθ?s shows the expected peaking in the signal region due to the D?cone overlap requirement. The con?dence level for theπ?fπ+s(π?fπ0s)?t alone is29%(2%).No structure is observed in the residuals of the?t and con?dence level for the combined?t is3%.The?tted number of signal events is given in Tab.I along with the product of acceptance and e?ciency and the relevant D?branching fraction.The background subtracted plots for theπ?fπ+s andπ?fπ0s ?ts for the cosθ?s projection are shown in Fig.3.The peaks are asymmetric because the acceptance functions for charged and neutral slow pions have momentum dependences.

The systematic uncertainty was determined to be7.5%for

B pairs produced,signal shape smearing, Monte Carlo statistics and the simulation of cosδ.

To convert from?tted yields to branching fractions we use the value of(3.27±0.06)×106 B B0production(f+?/f00) is one.This is in agreement with the current CLEO measurement of f+?τB±/f00τB0= 1.15±0.17±0.06[12]and the value[9]for the ratio of lifetimesτB±/τB0=1.03±0.06.We ?nd:

B(

B events, the R2requirement,and the fast pion reconstruction cancel.The ratio is measured to be r=1.55±0.14±0.15.

An implementation of the factorization hypothesis[14]predicts that r is equal to(1+ 1.29a2/a1)2.The coe?cient a1≈1describes the‘external spectator amplitude,’where the W hadronizes to a single pion,and a2describes the internal,color-suppressed amplitudes,and is expected to be rather smaller than1.The measurement of r yields a2/a1of0.19±0.04±0.05. Another ratio,B(B0→D?+π?)is given by0.84×(a2/a1)2using the same model.From the results quoted above,the factorization hypothesis predicts,in the absence of?nal state interactions,B(

the superior background rejection of the full reconstruction technique[15]leads to better sensitivity,except in the case of B0→D?0η′)<14×10?4 at90%con?dence level.The con?dence level of the?t was10%.

We gratefully acknowledge the e?ort of the CESR sta?in providing us with excellent luminosity and running conditions.This work was supported by the National Science Foun-dation,the U.S.Department of Energy,the Heisenberg Foundation,the Alexander von Humboldt Stiftung,Research Corporation,the Natural Sciences and Engineering Research Council of Canada,and the A.P.Sloan Foundation.

REFERENCES

[1]B.Barish et al.,contribution to the1997European Physical Society meeting,Jerusalem

(preprint CLEO CONF97-01,August1997)(unpublished).

[2]R.G.Sachs,Report No.EFI-85-22,Chicago,1985(unpublished);R.G.Sachs,The

Physics of Time Reversal(The University of Chicago Press,Chicago,IL,1987),pp.257-261;I.I.Bigi and A.I.Sanda,Nucl.Phys.B281,41(1987);I.Dunietz and R.G.Sachs, Phys.Rev.D37,3186(1988).

[3]CLEO Collab.,M.S.Alam et al.,Phys.Rev.D50,43(1994).

[4]ARGUS Collab.,H.Albrecht et al.,Z.Phys.C48,543(1990).

[5]CLEO Collab.,R.Giles et al.,Phys.Rev.D30,2279(1984).

[6]CLEO Collab.,Y.Kubota et al.,Nucl.Instr.and Meth.A320,66(1992).

[7]G.C.Fox and S.Wolfram,Phys.Rev.Lett.41,1581(1978).

[8]I.Brock,A Fitting and Plotting Package Using MINUIT,CLEO/CSN Note245-B,

Revised(1992)(unpublished);F.James,MINUIT,Function Minimization and Error Analysis,CERN Program Library Long Writeup D506,Mar.1994(unpublished).

[9]R.M.Barnett et al.,Phys.Rev.D54,488-506(1996).

[10]R.M.Barnett et al.,Phys.Rev.D54,94,319(1996).

[11]M.Neubert and B.Stech,preprint hep-ph/9705292,to appear in:the Second Edition

of Heavy Flavours,edited by A.J.Buras and M.Linder(World Scienti?c,Singapore).

[12]CLEO Collab.,C.S.Jessop et al.,Phys.Rev.Lett.79,4533(1997).

[13]M.Bauer,B.Stech,and M.Wirbel,Z.Phys.C29,637(1985).

[14]M.Neubert,V.Rieckert,B.Stech and Q.P.Xu in Heavy Flavours,edited by A.J.Buras

and H.Lindner(World Scienti?c,Singapore,1992).

[15]CLEO Collab.,B.Nemati et al.,CLNS97/1503(submitted to Phys.Rev.D).

1000

4000

30002000

1000

++

I

I

I I E v e n t s / 0.55E v e n t s / 0.2*FIG.1.The projections of the data histogram in cos θ?f and cos θ?s with the ?tting function for the π?f π+s ?t.

cos s I I I I I

E v e n t s / 0.55E v e n t s / 0.22000

1500

1000

500

0400020000

*

*FIG.2.The projections of the data histogram in cos θ?f and cos θ?s with the ?tting function for the π?f π0s ?t.

TABLE I.The yield of signal events from the?ts.The D*branching fractions are not included in the calculation of acceptance times e?ciency.

Mode Yield Acc.×E?.B(D?→Dπ) B0→D?+π?;D?+→D+π0513±210.1830.6%

B?→D?0π?;D?0→D0π01560±1150.1861.9%

职场演讲英语口语展示PPT时常用的英语衔接口语完整版

职场演讲英语口语展示P P T时常用的英语衔接 口语 Document serial number【NL89WT-NY98YT-NC8CB-NNUUT-NUT108】

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