Measurement of the direct photon spectrum from Y ( 1 S ) decays

A. Bizzeti a, j. Schiitte b, D. Antreasyan c, Ch. Bieler d, J.K. Bienlein e, E.D. Bloom f, I. Brock g, K. BrockmiJller e, A. Cartacci a, M. Cavalli-Sforza h, A. Compagnucci ~, G. Conforto a, S. Cooper i.1, D. Coyne h, K.H. Fairfield r, G. Folger b, A. Fridman f, G. Glaser b, G. Godfrey f, K. Graaf d, F.H. Heimlich a, F.H. Heinsius d, R. Hofstadter i,2, j. Irion c, Z. Jakubowski J, H. Janssen i, K. Karch f, S. Keh k, T. Kiel o, H. Kilian k, I. Kirkbride f M. Kobel b, W. Koch e, A.C. K/Snig i, K. K/Snigsmann f,3, S. KriJger d, G. Landi ~, R. Lekebusch d, S. Lowe r, B. Lurz b, H. Marsiske J, W. Maschmann d, p. McBride c, W.J. Metzger i, B. Monteleoni ~, B. Muryn ~,4, B. Niczyporuk f, G. Nowak J, P.G. Pelfer ~, M. Reidenbach i, M. Scheer k, p. Schmitt k, J. Schotanus i, D. Sievers d, T. Skwarnicki e, V. Stock d, K. Strauch c, U. Strohbusch d, J. Tompkins f, B. van Uitert f, R.T. Van de Walle i, A. Voigt ~, U. VoUand b, K. Wachs e, H. Wegener b and D.A. Williams d a INFNandUniversi tyofFlorence, l-50125Florence, Italy b Universitgit Erlangen-Niirnberg 5, W-8520 Erlangen, FRG c Harvard University 6, Cambridge, MA 02138, USA d L InstitutJ~r Experimentalphysik 7, Universitiit Hamburg, I4:-2000 Hamburg, FRG e Deutsches Elektronen Synchrotron DES)', W-2000 Hamburg, FRG f Department o f Physics s, HEPL, andStanfordLinearAccelerator Center 9, Stanford University, Stanford, CA 94305, USA g Carnegie-Mellon University 1o, Pittsburgh, PA 15213, USA h University o f California at Santa Cruz 1 i, Santa Cruz, CA 95064, USA i University o f Nijmegen and NIKHEF 12, NL-6525 ED Nijmegen, The Netherlands i Cracow Institute o f Nuclear Physics, PL-30055 Cracow, Poland k Universitiit Wiirzburg 13, W-8700 Wiirzburg, FRG


Introduction
According to the QCD theory of strong interactions, the Y ( 1 S) decays predominantly into hadrons via a three-gluon intermediate state [ l ]. The decay into one photon and two gluons is also allowed [ 2 ], but is suppressed by a factor O(aem/Ots) compared to the dominant decay, where Ogem and ors are the electromagnetic and the strong coupling constants, respectively.
A perturbative QCD calculation in next-to-leading order in ors gives for the ratio Rv of the partial decay widths [ 3 ] Rv-e(Y---,ggg) 2 36C~em(~) (1+(2.2+0.6)~) (1) 5 O~s where eb= --~e is the electric charge of the b-quark and the MS renormalization scheme at Q2= (0.157 Mr) 2= 2.2 GeV 2 is used. The large QCD corrections affecting the "/gg and ggg decay widths nearly cancel in this ratio, so that a measurement of R r should allow a reliable determination of ot~.
In addition, the shape of the direct photon energy spectrum contains information on the non-abelian structure of QCD. In fact, the lowest order perturbative calculation predicts [ 2 ] an almost linearly rising spectrum in z=Ev/EBeam with a sharp decrease at z= 1, in analogy to the decay of ortho-positronium [ 4 ]. A summation of leading logarithmic contributions to all orders in perturbation theory performed by Photiadis [ 5 ] yields a slight softening of the spectrum compared to ref. [ 2 ]. This spectrum, however, is still quite similar to that obtained by lowest order QCD and peaks close to z= 1.
A calculation by Field [ 6 ] predicts a much softer spectrum using a parton-shower Monte Carlo approximation to perturbative QCD that estimates the effect of the self-coupling of gluons. The two gluons recoiling against the direct photon acquire a non-zero invariant mass by radiating further bremsstrahlung gluons. This leads to a suppression of direct photons with energies close to the beam energy, yielding a spectrum with a maximum at z~ 0.7.

Data sample and detector
The data used for this analysis were collected with the Crystal Ball detector at the e+e -storage ring DORIS I1 and represent an integrated luminosity of 17.1 +0.4 pb -~ taken on the "f(1S) resonance, corresponding to 153.5× 103 observed "f(1S) decays, and 19.2 _+ 0.5 pb-~ taken in the continuum.
The Crystal Ball detector, described in detail elsewhere [ 7 ], is a non-magnetic calorimeter designed to measure precisely the energies and directions of electromagnetically showering particles. Its main part (the Ball) is a spherical shell, consisting of 672 optically isolated NaI (T1) crystals. The Ball covers 93% of the entire solid angle, two holes being left for the beam pipe. Each crystal has the shape of a truncated triangular pyramid pointing to the e+e -interaction region and projects a radial distance of 16 radiation lengths (corresponding to about one nuclear interaction length).
Showers produced by high energy ( > 1 GeV) electrons and photons in the Ball deposit about 94% of their energy in 13 adjacent crystals in an almost symmetric pattern, resulting in an energy resolution aE/E = (2.7 + 0.2 ) %/~x/~/GeV and an angular resolution of about 2 °.
Muons and charged hadrons that do not undergo a strong interaction deposit energy by ionization only. Minimum ionizing particles deposit typically 200 MeV in one or two crystals. If an energetic hadron interacts strongly while traversing the Ball, the deposited energy is in general much larger than 200 MeV and the pattern of the hadronic shower is quite irregular compared to that of an electromagnetic shower. The directions of charged particles emerging from the e+e -interaction region are measured by a set of pro-portional wire chambers located inside the Ball. The chambers consist of 800 aluminum tubes, assembled in four cylindrical double-layers around the beam pipe.

Event and photon selection
The selection ofygg events is designed to suppress background from QED processes, cosmic rays, beamgas and beam-wall interactions. We require a total energy deposited in the Ball of gBall > 0.3EcMs, where ECMs=2EBeam (=9.46 GeV on the Y(IS) resonance). We also require a minimum transverse energy ET .... = Yi Ei sin 0i> 0.25EcMs, where we sum over all crystals; here Ei is the energy deposited in the ith crystal and 0i is the angle between the beam axis and the center of that crystal. These cuts mainly reject beam-related background events, which deposit most of their energy at small angles with respect to the beam axis.
Background events from the QED processes e+e --~e+e -(y) and e+e -~yy(y) generally contain two high energy particles depositing almost their entire energy in the Ball; (Y) here denotes additional radiative photons. In contrast, it is very unlikely in Ygg events that a particle other than the direct photon deposit a large amount of energy in the Ball, since the two gluons fragment into several hadrons, most of which deposit only part of their energy. We therefore require a multiplicity Npa~c,~s/> 3 and an energy deposited by the second most energetic particle to be less than 0.65EcMs-0.5EBR.. These cuts reject almost all QED background events, while maintaining a high efficiency for Ygg events up to the highest T energies. The small QED background still left after this selection is subtracted at a later stage of the analysis using continuum data.
Photon candidates are selected from energy clusters in the calorimeter by requiring z = Ev/Eaeam > 0.3, a direction within the geometrical acceptance of the tube chambers (lops0[ <0.80), no tube chamber track associated with the cluster direction, and a lateral energy distribution consistent with that expected for a single electromagnetically showering particle. The last cut is chosen rather loose as the lateral energy distribution of the photon candidates will be used to discriminate the ~o background in a later stage; it is, however, effective in removing interacting hadrons and most of the overlapping showers. The resulting spectrum of photon candidates is shown in fig. l as the solid histogram.
The efficiency of the event and photon selection is determined using Ygg Monte Carlo events produced with the Lund 6.3 generator [8]. The generated events are passed through a complete detector simulation, which uses the EGS 3 program [ 9 ] for electrons and photons and the GHEISHA 6 program [ 10 ] for hadronic interactions. The Monte Carlo events are then analyzed exactly like the real data. The efficiency, shown in fig. 2, is smooth and rather flat with values of at least 50% in the range 0.35 < z < 1.

Background subtraction
The background due to continuum processes (e + e-~qft (7) and remaining QED events ) is determined from data taken in the nearby continuum, which are analyzed exactly like the on-resonance data. The continuum data, scaled by the luminosity ratio and corrected for the energy dependence of the continuum cross section, are shown in fig. 1 as the dotted histogram. This continuum spectrum is then subtracted from the on-resonance spectrum of photon candidates.
The background remaining after the continuum subtraction is mainly due to high energy n°'s where the two decay photons are so close to each other that the showers overlap and appear as a single energy cluster in the calorimeter ("merged" s°'s). Two methods are used to correct for this background, which dominates the spectrum for z<0.5 (solid points in fig. 1 ): a statistical analysis of the shower shape (method 1 ) and a Monte Carlo calculation of the background (method 2). Note that previous investigations [11][12][13] of the direct photon spectrum have essentially followed the second approach; thus our first method provides an independent check on the shape of the photon spectrum.

Statistical analysis of shower shape (method 1)
This method [ 14 ] utilizes the different distributions of the squared angular width 0 2 of the lateral energy distribution of photon and merged n o showers [ 15 ]. In order to calculate the second moment 0 2, we first determine the center of gravity c of the shower from c= (l/E)~.i niEi, where the sum includes all crystals of the shower. E denotes the total shower energy, Et is the energy in the ith crystal and ni is the unit vector pointing to its center. The value of 0 2 is where the sum again is over all crystals of the shower.
The lateral shower extension of a high energy n ° is on average larger than the corresponding value for a single photon of the same energy. Since the two photons from a n ° come closer with increasing n ° energy, the reliability of a statistical differentiation between photons and n°'s is energy dependent: while the average (0 2) value for n°'s is about twice as large as that for photons at E= 2 GeV, the difference shrinks to about 20% at E=5 GeV. For each z bin (Az= 0.05 ), the 02 distribution for on-resonance data is calculated, and the corresponding distribution for continuum data is subtracted. Due to the sensitivity of this method to the absolute n o energy, only that part (7.9 pb -1) of the continuum data, which was taken just below the ~( 1 S) resonance, is used for this subtraction.
The resulting 02 distribution for T ( 1 S) decays are then fitted with Monte Carlo 02 distributions for photons and merged pions. The expected distributions for direct 7% have been extracted using photons in Monte Carlo 7gg events, whereas those for n°'s have been obtained by analyzing neutral shower depositions in Monte Carlo three-gluon and q~l events. All Monte Carlo events have been passed through the complete detector simulation described above. Note that the 0 2 distributions for n°'s from Monte Carlo and data also contain small contributions from accidental overlap of energy depositions and from single photons from well-separated n ° decays; the latter contribute a tail towards small values of 02. Thus separated n o decays are also included in this analysis.
The fit result for the 0 2 distribution of photon candidates with scaled energies between z= 0.60 and 0.65 is shown in fig. 3. By repeating this fitting procedure for all energy bins, we can split the continuum-subtracted spectrum of photon candidates on a statistical basis into a photon spectrum and a n o background spectrum. To minimize the effect of statistical fluctuations, we fit the n ° spectrum with an exponential function, shown as the solid curve in fig. l, and subtract the fit result from the spectrum of photon candidates to get the photon spectrum. After correcting for the efficiency, we obtain the final photon spectrum shown in fig. 4. This method is effective in the region z~> 0.35; at lower energies the background of well-separated photons from n ° decays prevents a good measurement of the number of direct photons. spectrum, corrected for efficiency, is shown in fig. 5. This method allows for a measurement of the direct photon spectrum in the region z~>0.30; we prefer, however, to use for the fits described below only the data points in the region z~> 0.50, where we are less sensitive to the evaluation of the Monte Carlo n ° background.

Monte Carlo calculation (method 2)
In this analysis [ 16 ] the background from other r(IS) decays is estimated by modelling the decays "l'(1S)~ggg~hadrons and ~'(IS)--,q~l~hadrons with the Lund generator [8], and ~'( 1S)~x+x -decays with a QED generator [ 17 ]. Detector response is again simulated as for the Monte Carlo events discussed above. In this analysis we use harder cuts on the lateral shape of the shower of photon candidates. This suppresses the n ° background by about an order of magnitude, thus decreasing our reliance on the Monte Carlo estimate, but also reducing our efficiency for direct photons by about 40%.
The energy spectrum of photon candidates from Monte Carlo events is scaled to the appropriate luminosity and, together with the continuum spectrum, is subtracted from the on-resonance spectrum of photon candidates. The resulting direct photon The two direct photon spectra obtained above agree well with each other with a confidence level (CL) of 58%. The spectra are compared to the predictions from lowest order QCD [ 2 ], Photiadis' model [ 5 ] and Field's model [ 6 ]. Fits with free overall normalization yield the X 2 values given in table 1. Both spectra are in good agreement with Field's model with CLs of 61% and 91% for the spectra from Method 1 and 2, respectively. The hard spectrum predicted by lowest order QCD is clearly ruled out (CL< 1.4× l0 -4 for both spectra), as can be seen in figs. 4 and 5. The fits to Photiadis' model yield CLs of 0.9% and 0.14%, respectively. We conclude that Field's model is strongly preferred over that of Photiadis. We use Field's prediction to extrapolate the spectra to z= 0 and obtain the number of direct photons stated in table 1, where the first error is statistical and the second is systematic. The systematic error for the first method is estimated by repeating the complete Table 1 Results of fits of the photon spectra to theoretical models.  [ 14 ]. For the second method the dominant systematic error results from the subtraction of the n o background modelled by Monte Carlo. We determined the error [ 16 ] by varying the photon selection cuts and modifying Monte Carlo parameters (e.g., the Px of the gluon jets). For both methods smaller contributions are included due to the omission of final state bremsstrahlung from the process Y(1S)~Tq~-~7+hadrons [14,18], and the uncertainty in the extrapolation of the photon spectra to Z~0.
Although the systematic errors for both methods are nearly independent and a weighted mean for Nv could be calculated (excluding the common statistical error), we chose the conservative approach of averaging both results and taking the larger of both systematic errors. We thus obtain for the total number of photons N v = (4.0 _+ 0.3 + 0.5 ) × 103. Correcting the number of observed hadronic Y decays for hadronic efficiencies and subtracting the contribution of T-~q(t, x+x-, 7gg decays, we obtain for the number of'f-~ggg decays [ 14 ] N~ = ( 147 _+ 1 + 6 ) X 103 and therefore a ratio Rv = Nv/Ng ~ = (2.7 -+ 0.2 + 0.4)%. Inserting R~ in ( 1 ) yields for the strong coupling constant in the MS renormalization scheme at Q2 = 2.2 GeV 2 a value as=0.25 + 0.02-+ 0.04.
The results of this analysis are compared to those obtained by previous experiments in table 2. The shape of our spectrum is consistent with those of ARGUS [ 11 ] and CLEO [ 12 ], but in disagreement with that measured by CUSB [13 ]. Our spectrum confirms with better energy resolution ARGUS' result that lowest order QCD does not describe the experimental photon spectrum. Our values of R v and as (2.2 GeV 2 ) are also consistent with the results from the other experiments. Excluding the CUSB measurement, we obtain an average of Rv=(2.77+ 0.15)% and as(2.2 GeV2)=0.24_+0.02, where the errors include the statistical and systematic errors.
In conclusion, a new analysis of the direct photon energy spectrum from "I'(1S) decays by the Crystal Ball experiment rules out the hard spectra predicted by lowest order QCD, but is in good agreement with the softer spectrum predicted by Field, who includes an estimate of the self-coupling of gluons. This suggests substantial contributions by higher order QCD corrections. Our value of Rv= (2.7 _+ 0.2 _+ 0.4)% results in as(2.2 GeV 2) =0.25+0.02_+0.04. This value of as is consistent with the results of other as measurements at higher Q2 values [19][20][21].

Acknowledgement
We would like to thank the DESY and SLAC directorates for their support. This experiment would not have been possible without the dedication of the DORIS machine group as well as the experimental Table 2 Comparison with other experiments. The energy resolutions of the respective calorimeters are given for a photon energy of 4.5 GeV.