Expected Statistics for GlueX

• The expected statistics for GlueX in 1 year of running will depend on several crucial factors, summarized below.
• Initial studies for the expected data rates for GlueX were done in
  • GlueX PAC30 Documentation
  • Potential GlueX Physics During the First Two Years of 12 GeV Running
  • Talk:The First Two Years of GlueX Physics
• The experimental data input for the cross sections at 9 GeV come from SLAC, namely
  • H. H. Bingham et al. (SLAC) Phys. Rev. D8, 1277
  • J. Ballam et al. (SLAC) Phys. Rev. D7, 3150
  • and references therein
• SLAC photoproduction results

$\sigma _{{tot}}$	124.0$\pm$2.5 $\mu$b
$p\pi ^{{+}}\pi ^{{-}}$	14.7 $\pm$0.6 $\mu$b
$pK^{{+}}K^{{-}}$	0.58 $\pm$0.05 $\mu$b
$n2\pi ^{{+}}\pi ^{{-}}$	3.2 $\pm$0.7 $\mu$b

• Basic formula to calculate expected events: $N_{{raw}}=\sigma \times N_{{t}}\times N_{{\gamma }}\times T$ where
  • $N_{{raw}}$: expected raw events
  • $\sigma$: cross section for wanted reaction
  • $N_{{t}}$: density of target
  • $N_{{\gamma }}$: number of photons/s
  • $T$: integrated time
• The total number of events that we actually detect is then $n=N_{{raw}}\times \epsilon \times BR$ where
  • $\epsilon$: expected construction efficiency for this channel
  • $BR$: the branching fraction of the particular decay to this channel

so that $n=\sigma \times N_{{t}}\times N_{{\gamma }}\times T\times \epsilon \times BR$, and the number of events is the product of 6 factors.

• The target density, $N_{{t}}$ is the easiest to determine. With a 30cm $LH_{{2}}$ target, the density is $1.26b^{{-1}}$
• The photon rate is expected to start at $10^{{7}}\gamma /s$, with a gradual increase to the maximum of $10^{{8}}\gamma /s$
• For the integrated time $T$, we assume, as in the previous studies listed above, that we run for 1 year, of which 6 months is datataking, with 1/3 efficiency (effectively 2 months out of the first year), which gives us $5\times 10^{{6}}$ s (this efficiency also takes into account the tagging ratio)
• The most difficult estimates are the factors of $\sigma$ (the cross section), $\epsilon$ (the efficiency of reconstruction), and $BR$ (the branching ratio), all of which are dependent on the specific channel of interest. Here we take the channel $\pi \pi \pi (n)$, since this is one of the prime channels of interest, and Monte Carlo studies have been done on this channel. According to the SLAC data above, the cross section for $n2\pi ^{{+}}\pi ^{{-}}$ is $\sigma =3.2\mu b$, of which an unknown fraction will be our signal of interest, the $\pi _{{1}}(1600)$. Current (2011) efficiency studies by Jake Bennett at IU show that the reconstruction efficiency in the mass region of interest is around $20\%$, with hopefully an increase as the kinematic fitter is further developed. Taking $BR=1$, we come to our final estimate of

$n=3.2[\mu b]\times 1.26[b^{{-1}}]\times 10^{{7}}[s^{{-1}}]\times 5\times 10^{{6}}[s]\times 0.20\times 1=400M$ events.

• This number can be contrasted with the estimates given in the above references, for example, $p\pi ^{{+}}\pi ^{{-}}$ assuming $\sigma =20\mu b$ and $\epsilon =0.75$ and the same flux and integrated time as above gives $940M$ events in the 1st year.
• Also to be contrasted is the number of events in other analyses. These include:
  • Nozar et al. (CLAS) photoproduction of $\pi ^{{+}}\pi ^{{+}}\pi ^{{-}}(n)$: 83k events for PWA
  • Dzierba et al. (E852-IU) pionproduction of $\pi ^{{-}}\pi ^{{-}}\pi ^{{+}}p$: 2.6M events
  • Alekseev (COMPASS) pionproduction of $\pi ^{{-}}\pi ^{{-}}\pi ^{{+}}p$: 420k events
• In conclusion, even with the relatively pessimistic numbers of $T=$ 2 months effective running, $\epsilon =0.20$, $N_{{\gamma }}=10^{{7}}\gamma /s$, GlueX should accumulate on the order of several hundred million events in the channels of interest, which is at least 2-3 orders of magnitude higher than other experiments.