Measurement of the direct photon momentum spectrum in ${\rm Y}(1\mathrm{S})$, ${\rm Y}(2\mathrm{S})$, and ${\rm Y}(3\mathrm{S})$ decays

Using data taken with the CLEO III detector at the Cornell Electron Storage Ring, we have investigated the direct photon spectrum in the decays ${\rm Y}(1\mathrm{S})\to \gamma gg$, ${\rm Y}(2\mathrm{S})\to \gamma gg$, ${\rm Y}(3\mathrm{S})\to \gamma gg$. The latter two of these are first measurements. Our analysis procedures differ from previous ones in the following ways: (a) background estimates (primarily from ${\pi }^0$ decays) are based on isospin symmetry rather than a determination of the ${\pi }^0$ spectrum, which permits measurement of the ${\rm Y}(2\mathrm{S})$ and ${\rm Y}(3\mathrm{S})$ direct photon spectra without explicit corrections for ${\pi }^0$ backgrounds from, e.g., ${\chi }_{bJ}$ states, (b) we estimate the branching fractions with a parametrized functional form (exponential) used for the background, and c) we use the high-statistics sample of ${\rm Y}(2\mathrm{S})\to \pi \pi {\rm Y}(1\mathrm{S})$ to obtain a tagged sample of ${\rm Y}(1\mathrm{S})\to \gamma +X$ events, for which there are no QED backgrounds. We determine values for the ratio of the inclusive direct photon decay rate to that of the dominant three-gluon decay ${\rm Y}\to ggg(R_{\gamma }=B(gg\gamma )/B(ggg))$ to be $R_{\gamma }(1\mathrm{S})=(2.70\pm 0.01\pm 0.13\pm 0.24)\%$, $R_{\gamma }(2\mathrm{S})=(3.18\pm 0.04\pm 0.22\pm 0.41)\%$, and $R_{\gamma }(3\mathrm{S})=(2.72\pm 0.06\pm 0.32\pm 0.37)\%$, where the errors shown are statistical, systematic, and theoretical model dependent, respectively. Given a value of $Q^2$, one can estimate a value for the strong coupling constant ${\alpha }_s(Q^2)$ from $R_{\gamma }$.

Figure 1

Comparison of the direct photon spectral shapes for the two theoretical models used in this analysis.

Figure 2

Efficiency for an event containing a fiducially contained direct photon to pass both event selection and shower selection requirements for ${\rm Y}(1\mathrm{S})\to \gamma gg$ using our default photon selection requirements and our default charged-multiplicity requirement ($\ge 4$ charged tracks observed in a candidate event; solid line); ${\rm Y}(1\mathrm{S})\to \gamma gg$ showing the efficiency if the multiplicity requirement was relaxed to $\ge 2$ charged tracks (dashed line); ${\rm Y}(1\mathrm{S})$ direct photon daughters, for ${\rm Y}(1\mathrm{S})$ produced in ${\rm Y}(2\mathrm{S})$ dipion decays (dotted line, and discussed later in this document). Efficiencies are derived from full GEANT-based CLEO III detector simulations.

Figure 3

Comparison of shower-reconstruction efficiency for direct photons, compared to well-separated photons resulting from ${\pi }^0$ decays, based on full GEANT-based CLEO III simulations. The former efficiency is used to determine final direct photon signal branching fractions in the data itself; the latter is used to determine the fraction of generated pseudophotons which are expected to contribute to the background showers observed in data. The difference between the two is attributed to the typically greater isolation of direct photons.

Figure 4

${\pi }^0/({\pi }^{+}+{\pi }^{-})$ ratio, as a function of charged pion momentum, including tracking efficiency, particle identification efficiency, and event selection requirements (from GEANT-based CLEO III Monte Carlo simulations). The loss of efficiency at large $p_{\pi }$ is largely due to the bias introduced by the minimum charged-particle multiplicity requirement.

Figure 5

Estimate of the momentum-dependent contribution from various background sources to the observed below-${\rm Y}(4\mathrm{S})$ inclusive photon spectrum, based on the JETSET 7.4 event generator plus a full CLEO III GEANT-based detector simulation. Initial state radiation contributions are not included.

Figure 6

Estimate of the momentum-dependent percentage of showers produced by ${\overline{n}}^0$’s and $K_L^0$’s that passed our shower selection, based on a sample of $1\times {10}^6$ MC continuum events. There are no entries for $x>0.5$.

Figure 7

Angular distribution of the inclusive photons from continuum data compared with our pseudophoton estimate, based on isospin invariance, for showers with $x_{\gamma }>0.45$, and including a Monte Carlo-based estimate of the ISR background. The normalization is absolute.

Figure 8

Comparison of $x_{\gamma }$ spectra, obtained using below-${\rm Y}(4\mathrm{S})$ data, with the sum of ISR Monte Carlo simulations plus a pseudophoton spectrum obtained using identified data charged pions as input.

Figure 9

The ${\pi }^0$ and $\eta$ yields for data (dashed line) and simulated photons (solid line). The yields agree at the 2%–3% level.

Figure 10

Photon energy spectrum (minimal cuts) for data taken at the ${\rm Y}(1\mathrm{S})$ resonance energy, with continuum contribution (using CLEO data taken off the resonance, including ISR) and ${\rm Y}$ nondirect simulated pseudophotons (PP) resulting from decays of neutral hadrons overlaid.

Figure 11

${\rm Y}(2\mathrm{S})$ photon energy spectrum (minimal cuts), with nondirect pseudophotons, continuum background photons, and the cascade contribution from ${\rm Y}(1\mathrm{S})$ decays overlaid.

Figure 12

${\rm Y}(3\mathrm{S})$ photon energy spectrum (minimal cuts), with nondirect pseudophotons, continuum background photons, and the cascade contributions from ${\rm Y}(2\mathrm{S})$ and ${\rm Y}(1\mathrm{S})$ decays overlaid.

Figure 13

Subtraction of backgrounds using an exponential (below-${\rm Y}(4\mathrm{S})$ continuum data), with floating normalization to estimate the nondirect photon spectrum. The exponential, plus initial state radiation, gives a fair match to the observed spectrum, although the background is clearly underestimated in the intermediate region of the momentum spectrum.

Figure 14

Photon angular distribution for background-subtracted direct photon data (histogram) vs the Koller-Walsh prediction, modified for the experimental efficiency as a function of $x_{\gamma }$ and $\cos {\theta }_z$.

Figure 15

Fit to background-subtracted ${\rm Y}(1\mathrm{S})$ data, using explicit continuum data subtraction. The Garcia-Soto model is used for spectral shape (modified for efficiency and experimental resolution), either using a ${\chi }^2$ fit in the region where the direct photon contribution dominates, or normalizing the model to the experimental data in the same interval, as shown. The two fits very nearly overlay with each other.

Figure 16

Fit to background-subtracted ${\rm Y}(2\mathrm{S})$ data, using explicit continuum data subtraction and explicit subtraction of ${\rm Y}(1\mathrm{S})$ cascade contributions. Direct spectrum fit using the Garcia-Soto model.

Figure 17

Fit to background-subtracted ${\rm Y}(3\mathrm{S})$ data, using explicit continuum data subtraction and explicit subtraction of ${\rm Y}(1\mathrm{S})$ and ${\rm Y}(2\mathrm{S})$ cascade contributions.

Figure 18

Subtraction of backgrounds using an exponential [${\rm Y}(1\mathrm{S})$ data], with floating normalization to estimate the nondirect photon spectrum. Direct spectrum fit using the Field model.

Figure 19

Subtraction of backgrounds using an exponential [${\rm Y}(2\mathrm{S})$ data], with floating normalization to estimate the nondirect photon spectrum. Direct spectrum fit using the Field model.

Figure 20

Subtraction of backgrounds using an exponential [${\rm Y}(3\mathrm{S})$ data], with floating normalization to estimate the nondirect photon spectrum. Direct spectrum fit using the Field model.

Figure 21

Mass recoiling against oppositely signed charged pion pairs, ${\rm Y}(2\mathrm{S})$ data.

Figure 22

Contour plot illustrating dependence of ${\alpha }_s$ on the QCD scale parameter ${\Lambda }_{\overline{MS}}$ and the momentum scale $f_{\mu }$.

Figure 23

Contour plot illustrating the relationship between $R_{\gamma }$, the QCD scale parameter ${\Lambda }_{\overline{MS}}$, and the momentum scale $f_{\mu }$.