Jpsi and psi(2S) Radiative Decays to eta_c

a r X i v :0805.0252v 1 [h e p -e x ] 2 M a y 2008

CLNS 08/2021

CLEO 08-05

J/ψand ψ(2S )Radiative Transitions to ηc

R.E.Mitchell,1M.R.Shepherd,1D.Besson,2T.K.Pedlar,3D.Cronin-Hennessy,4K.Y.Gao,4J.Hietala,4Y.Kubota,4T.Klein,https://www.360docs.net/doc/474966203.html,ng,4R.Poling,4A.W.Scott,4

P.Zweber,4S.Dobbs,5Z.Metreveli,5K.K.Seth,5A.Tomaradze,5J.Libby,6

A.Powell,6G.Wilkinson,6K.M.Ecklund,7W.Love,8V.Savinov,8A.Lopez,9

H.Mendez,9J.Ramirez,9J.Y.Ge,https://www.360docs.net/doc/474966203.html,ler,10I.P.J.Shipsey,10B.Xin,10G.S.Adams,11M.Anderson,11J.P.Cummings,11I.Danko,11D.Hu,11B.Moziak,11J.Napolitano,11Q.He,12J.Insler,12H.Muramatsu,12C.S.Park,12E.H.Thorndike,12F.Yang,12M.Artuso,13S.Blusk,13S.Khalil,13J.Li,13R.Mountain,13S.Nisar,13K.Randrianarivony,13N.Sultana,13T.Skwarnicki,13S.Stone,13J.C.Wang,13

L.M.Zhang,13G.Bonvicini,14D.Cinabro,14M.Dubrovin,14A.Lincoln,14P.Naik,15

J.Rademacker,15D.M.Asner,16K.W.Edwards,16J.Reed,16R.A.Briere,17

T.Ferguson,17G.Tatishvili,17H.Vogel,17M.E.Watkins,17J.L.Rosner,18

J.P.Alexander,19D.G.Cassel,19J.E.Duboscq,19R.Ehrlich,19L.Fields,19R.S.Galik,19L.Gibbons,19R.Gray,19S.W.Gray,19D.L.Hartill,19B.K.Heltsley,19D.Hertz,19J.M.Hunt,19J.Kandaswamy,19D.L.Kreinick,19V.E.Kuznetsov,19J.Ledoux,19H.Mahlke-Kr¨u ger,19D.Mohapatra,19P.U.E.Onyisi,19J.R.Patterson,19D.Peterson,19

D.Riley,19A.Ryd,19A.J.Sado?,19X.Shi,19S.Stroiney,19W.M.Sun,19

T.Wilksen,19S.B.Athar,20R.Patel,20J.Yelton,20P.Rubin,21B.I.Eisenstein,22I.Karliner,22S.Mehrabyan,22N.Lowrey,22M.Selen,22E.J.White,22and J.Wiss 22

(CLEO Collaboration)

1Indiana University,Bloomington,Indiana 47405,USA

2University of Kansas,Lawrence,Kansas 66045,USA

3Luther College,Decorah,Iowa 52101,USA

4University of Minnesota,Minneapolis,Minnesota 55455,USA

5Northwestern University,Evanston,Illinois 60208,USA

6University of Oxford,Oxford OX13RH,UK

7State University of New York at Bu?alo,Bu?alo,New York 14260,USA

8University of Pittsburgh,Pittsburgh,Pennsylvania 15260,USA

9University of Puerto Rico,Mayaguez,Puerto Rico 00681

10Purdue University,West Lafayette,Indiana 47907,USA

11Rensselaer Polytechnic Institute,Troy,New York 12180,USA

12University of Rochester,Rochester,New York 14627,USA

13Syracuse University,Syracuse,New York 13244,USA

14Wayne State University,Detroit,Michigan 48202,USA

15University of Bristol,Bristol BS81TL,UK

16Carleton University,Ottawa,Ontario,Canada K1S 5B6

17Carnegie Mellon University,Pittsburgh,Pennsylvania 15213,USA

18Enrico Fermi Institute,University of Chicago,Chicago,Illinois 60637,USA

19Cornell University,Ithaca,New York 14853,USA

20University of Florida,Gainesville,Florida 32611,USA

21George Mason University,Fairfax,Virginia 22030,USA

22University of Illinois,Urbana-Champaign,Illinois 61801,USA

(Dated:May 2,2008)

Abstract

Using24.5millionψ(2S)decays collected with the CLEO-c detector at CESR we present the most precise measurements of magnetic dipole transitions in the charmonium system.We measure B(ψ(2S)→γηc)=(4.32±0.16±0.60)×10?3,B(J/ψ→γηc)/B(ψ(2S)→γηc)=4.59±0.23±0.64, and B(J/ψ→γηc)=(1.98±0.09±0.30)%.We observe a distortion in theηc line shape due to the photon-energy dependence of the magnetic dipole transition rate that prevents a precision measurement of theηc mass and width.

The spectrum of bound charm quarks provides an important testing ground for our un-derstanding of Quantum Chromodynamics(QCD)in the relativistic and non-perturbative regimes.Radiative transitions in particular have recently been the subject of both lattice QCD calculations[1]and e?ective?eld theory techniques[2].Key among these are the magnetic dipole(M1)transitions J/ψ→γηc andψ(2S)→γηc,which are among the most poorly measured transitions in the charmonium system.Not only are precision measure-ments needed to validate our theoretical understanding,precise measurements of these M1 transitions are critical for normalizingηc branching fractions,a key input to extracting other properties such asΓγγ(ηc).

In this Letter,we present the most precise measurements of B(J/ψ→γηc)(abbrevi-ated B1S),B(ψ(2S)→γηc)(abbreviated B2S),and their ratio using24.5millionψ(2S) decays collected with the CLEO-c detector[3].For the?rst time,we also clearly observe the distortion of theηc line shape in the photon energy spectrum due to phase space and energy-dependent terms in the transition matrix element.We suggest that this distortion may be responsible for the3.3σinconsistency in previousηc mass measurements from J/ψandψ(2S)→γηc(averaging2977.3±1.3MeV/c2)compared toγγor pˉp production (averaging2982.6±1.0MeV/c2)[4].

The CLEO-c detector operates at the Cornell Electron Storage Ring(CESR)[5],which provided symmetric e+e?collisions at theψ(2S)center-of-mass.The detector features a solid angle coverage of93%for charged and neutral particles.The charged particle tracking system operates in a1.0T magnetic?eld along the beam axis and achieves a momentum resolution of≈0.6%at p=1GeV/c.The cesium iodide(CsI)calorimeter attains photon energy resolutions of2.2%at Eγ=1GeV and5%at100MeV.Two particle identi?cation systems,one based on ionization energy loss(dE/dx)in the drift chamber and the other a ring-imaging Cherenkov(RICH)detector,are used together to separate K±fromπ±. Detection e?ciencies are determined using a GEANT-based[6]Monte Carlo(MC)detector simulation.

To extract B2S we use the≈640MeV photon transition line visible in the inclusive photon energy spectrum from multi-hadronic events collected at theψ(2S)resonance.A series of exclusive decay modes of theηc(where the background can be greatly suppressed)are used to constrain the line shape for the inclusive spectrum.To measure B1S/B2S,we take the ratio of events in the chains

ψ(2S)→π+π?J/ψ;J/ψ→γηc;ηc→X i(1)

ψ(2S)→γηc;ηc→X i,(2) where the X i are exclusive decay modes of theηc;we then adjust for e?ciencies and B(ψ(2S)→π+π?J/ψ).Rather than using the inclusive photon spectrum from J/ψde-cays,we minimize systematic errors by taking B1S to be the product of B2S with B1S/B2S.

The?rst half of this Letter describes three samples of events:exclusive decays of the J/ψ(Eq.(1));exclusive decays of theψ(2S)(Eq.(2));and the inclusive photon spectrum fromψ(2S)decays.We investigate the photon-energy dependence of theηc line shape and ?t the photon energy spectra with various hypotheses.In the second half,our measurement techniques,guided by our line shape investigations,are more fully developed.

Twelve exclusiveηc decay modes are used:X i=2(π+π?),3(π+π?),2(π+π?π0),π?K±K0S,π0K+K?,π?π+π?K±K0S,π+π?π0K+K?,2(K+K?),2(π+π?)K+K?,π+π?K+K?,π+π?η,and2(π+π?)η,where theηis detected in either itsγγorπ+π?π0 decay mode.These include all previously reported decay modes of theηc(except p

has a comparatively small rate)[4]in addition to new decay modes observed here with comparable raw yields.

The reconstruction of the J/ψandψ(2S)→γηc exclusive decay chains share several selection criteria.In addition to standard?ducial requirements,photons must have energy greater than30MeV and must not align with the projection of any track into the calorimeter. Forπ0andηdecays toγγ,the mass of the pair of daughter photons is required to be within 3σof the nominal mass.We require?tted tracks of charged particles to haveχ2/d.o.f.<50 and be located in the central region of the detector(|cosθ|<0.93,whereθis the polar angle with respect to the e+direction).All charged tracks must be positively identi?ed by a combination of dE/dx and the RICH detector.To reconstructη→π+π?π0all three decay products must pass the above criteria and must have an invariant mass within30MeV/c2 of the nominalηmass.The K0S candidates are selected from pairs of oppositely charged and vertex-constrained tracks with invariant mass within15MeV/c2of the K0S mass.A four-constraint kinematic?t of all identi?ed particles to the initialψ(2S)four-momentum is performed and aχ24C/d.o.f<5is required.This both sharpens the measured momenta and reduces backgrounds due to missing particles or particle misidenti?cation.The hypothesis with the best?t quality is accepted per decay mode;less than0.5%of events enter multiple modes.

For the selection of exclusive J/ψdecays,the recoil mass of theπ+π?pair is used to select the processψ(2S)→π+π?J/ψand to select J/ψsidebands.A sideband subtraction is used to account for non-J/ψdecays.Theπ+π?recoil momentum is used to boost the photon energy into the J/ψrest frame.

Fits to the resulting photon energy spectrum for the sum of allηc decay modes are shown in Fig.1.The background shape has two essential features:(i)background that falls with energy from J/ψ→X i,where a spurious cluster is found in the calorimeter,and whose shape is modeled by MC simulation and(ii)a rising background from both J/ψ→π0X i and non-signal J/ψ→γX i that is freely?t to a polynomial.These two contributions and their total are shown as dot-dashed and dashed curves.A?t using an unmodi?ed Breit-Wigner resonance(dotted line),with the amplitude,mass,and width as free parameters, fails on both the low and high sides of the signal.A?t using a Breit-Wigner modi?ed by a factor of E3γimproves the?t around the peak but leads to a diverging tail at higher energies (not shown).To damp the E3γan additional factor of exp(?E2γ/β2)is added,inspired by the overlap of two ground state wave functions.The resulting?t has a25%con?dence level (solid line),withβ=65.0±2.5MeV.In all cases the signal shapes used are convolved with a resolution function determined from MC simulation.The resolution is4.8MeV after the kinematic?t.

The uncertainty associated with the line shape prohibits precision mass and width mea-surements.It is interesting to note,however,that the resultingηc mass in the unmodi?ed Breit-Wigner?t is2976.7±0.6MeV/c2(statistical error only),consistent with previous measurements from J/ψandψ(2S)→γηc,while the modi?ed Breit-Wigner?t returns an ηc mass of2982.2±0.6MeV/c2(statistical error only),consistent with that determined from γγfusion and p

FIG.1:Fits to the photon spectrum in exclusive J/ψ→γηc decays using Breit-Wigner(dotted) and modi?ed(solid)signal line shapes convolved with a4.8MeV wide resolution function.Total background is given by the dashed line.The dot-dashed curves indicate two major background components described in the text.

Fig.3a.Several small nonlinear backgrounds below560MeV are apparent and are due to a combination of(i)ψ(2S)→π0h c;h c→γηc;(ii)ψ(2S)→γχcJ;χcJ→γJ/ψ;and (iii)ψ(2S)→π0J/ψ.Based on detailed MC studies,all other backgrounds are linear,the largest beingψ(2S)→π0X i.

Fits to theψ(2S)→γηc photon energy spectrum with a Breit-Wigner convolved with an experimental resolution function(with a resolution of5.1MeV after the kinematic?t)were unsuccessful.For a hindered M1transition the matrix element acquires terms proportional to E2γ,which,when combined with the usual E3γterm for the allowed transitions,lead to contributions in the radiative width proportional to E7γ[2].We?nd that if we assume a linear background,as indicated by MC simulations,we are not able to obtain a good?t to our Eγspectrum for the sum of exclusiveψ(2S)→γηc modes with a pure E7γdependence. We therefore use the empirical procedure described below to extract theψ(2S)→γηc yield.

Extensive cross-checks have been performed to prove that the line shape asymmetry is not an experimental artifact.Events selected without the aid of a kinematic?t indicate an asymmetric line shape independently in both the photon energy and the hadronic mass. The asymmetric line shape is not correlated withηc decay modes that includeπ0,K0S,or ηcandidates.No indication of either asymmetry or peaking background has been found in detailed MC studies,where all known decays in the charmonium and light quark systems are simulated and unknown decays are modeled with the EvtGen generator[7].The photon

FIG.2:The kinematically ?tted photon energy spectra from ψ(2S )→γηc for individual ηc decay modes.

angular distribution from ψ(2S )→γηc ?ts the 1+cos 2θdistribution expected for M1tran-sitions,whether using symmetric or asymmetric signal shapes to extract yields in di?erent regions of cos θ.

For the selection of the third sample of events,the inclusive photon spectrum from ψ(2S )decays,the photon is required to pass the same requirements and ψ(2S )→π+π?J/ψis suppressed in the same manner as the exclusive ψ(2S )→γηc .To suppress the π0background,each signal photon candidate is paired with all other photons in the event and is rejected if the pair is consistent with a π0.Backgrounds due to e +e ?QED processes are substantially reduced by requiring one or more charged tracks in an event in combination with requirements on total energy and track momenta [8].The inclusive photon spectrum is shown in Fig.3c.The rise at lower energies is from χcJ →γJ/ψ.All other backgrounds are smooth and are dominated by π0decays.

FIG.3:(a)The kinematically?tted photon spectrum from the sum of exclusiveψ(2S)→γηc modes with a polynomial?t to the background(solid line for the regions included in the?t;dotted line elsewhere).(b)The photon energy spectrum that has not been adjusted by the kinematic?t with the same background shape as(a)overlaid.(c)The?t to the inclusive photon spectrum in ψ(2S)decay.The signal shape(solid line)is described in the text.The background is given by the dashed line.(d)The background subtracted inclusive photon spectrum with the signal shape overlaid(solid line).

Our?nal results are obtained from:

B2S=N INC 2S

B2S =

N EXC

εINC

(εEXC

/εEXC

)Nψ(2S)Bππ

(5)

where N and?represent the observed yields and the calculated e?ciencies ofψ(2S)and J/ψin inclusive(INC)and exclusive(EXC)ηc channels.The B(ψ(2S)→π+π?J/ψ),

TABLE I:Final yields and e?ciencies.

N INC 2S 59510±2145

N EXC

5376±199

N INC 2S /N EXC

11.07±0.33

N EXC

5638±187

εINC

56.37%

εEXC 1S /εEXC

0.6515

TABLE II:Summary of systematic errors(in percent). Systematic Error(%)B2S B1S B1S/B2S

signal shape present in the inclusive photon spectrum.

Systematic errors due to this?t procedure are determined by varying the orders of the background polynomials,the ranges of the?ts,and the range of the signal that is excluded

in the exclusive?t.We?nd8%variations for N INC

2S and N EXC

,but only4%variations in

their ratio.In addition,since we integrate our signal between560MeV and1100MeV,our uncertainty in the line shape a?ects the signal e?ciency.We take a conservative systematic

error of7%forεINC

2S to cover the two extreme cases that the signal shape has a Breit-Wigner

tail and the case that the entire signal lands within the signal region.The systematic error

is smaller forεEXC

2S (3%)because the kinematic?t pulls more of the signal within the signal

region.These errors are correlated resulting in an error of4%in the ratio.

The measurement of N EXC

1S is from the modi?ed Breit-Wigner?t shown in Fig.1,which

results in anηc width of31.5±1.5MeV/c2(statistical error only).A?t using an unmodi?ed Breit-Wigner with theηc width?xed to the current PDG value(26.5MeV/c2)gives a

smaller value of N EXC

1S by10%.A10%systematic error covers this extreme minimum,

as well as variations using a Breit-Wigner modi?ed only by an E3γterm and variations of the background parametrization.The signal is integrated above40MeV,which introduces

an additional1%systematic error into the e?ciency estimate(εEXC

1S )due to signal shape

uncertainty.

Because only≈25%of allηc decays are known,our estimate ofεINC

2S depends on mod-

eling the unknown decays of theηc.We use two di?erent hadronization models,but then weight the e?ciencies for di?erent track multiplicities according to multiplicities observed in data.We perform conservative variations of this weighting technique to account for our limited sensitivity to events with no tracks.We also simultaneously vary the event selection requirements,keeping and removing theπ0suppression,and using several QED suppression schemes.All variations are covered with an8%systematic error.

The ratio of exclusive e?ciencies,εEXC

1S /εEXC

,is calculated by weighting the e?ciency

ratio for eachηc decay mode individually using the number ofψ(2S)→γηc events observed in each mode.The ratio of e?ciencies has a slight dependence on decay mode.Varying the number of events in each mode by30%,we?nd a2%systematic error due to the composition of decay modes.

Many systematic errors,such as those due to tracking orπ0reconstruction e?ciencies,

cancel in the ratio of exclusive e?ciencies,εEXC

1S /εEXC

.To estimate any possible dependence

of the?nal numbers on the exclusive event selection,a wide range of requirements on the quality of the kinematic?t are imposed,and photons are required to be in di?erent regions of the calorimeter,resulting in variations of less than3%.We conservatively assume that systematic uncertainties for the reconstruction e?ciencies of the≈110MeV and≈640MeV transition photons do not cancel in the ratio and assign2%uncertainties for each.We also assign a2%uncertainty for the e?ciency of theπ+π?fromψ(2S)→π+π?J/ψ.

We?nd B2S=(4.32±0.16±0.60)×10?3,B1S/B2S=4.59±0.23±0.64,and B1S=(1.98±0.09±0.30)%.Both M1transitions B1S and B2S are larger than previous measurements[8,10] (56%and44%higher than the PDG averages[4],respectively)due to a combination of a largerηc width and an accounting for the asymmetry in the line shapes.These new measurements will renormalize manyηc branching fractions,includingΓγγ(ηc).We also ?nd that a thorough theoretical understanding of theηc line shape in M1transitions in the charmonium system will be crucial if the mass and width of theηc are to be extracted from these processes.

We gratefully acknowledge the e?ort of the CESR sta?in providing us with excellent

luminosity and running conditions.We also thank Jozef Dudek and Nora Brambilla for useful discussions.This work was supported by the A.P.Sloan Foundation,the National Science Foundation,the U.S.Department of Energy,the Natural Sciences and Engineering Research Council of Canada,and the U.K.Science and Technology Facilities Council.

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