You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


---
abstract: |
    We have observed exclusive $\gamma\gamma$ production in proton-antiproton collisions at $\sqrt{s}=1.96$ TeV, using data from 1.11 $\pm$ 0.07 fb$^{-1}$ integrated luminosity taken by the Run II Collider Detector at Fermilab. We selected events with two electromagnetic showers, each with transverse energy $E_T > 2.5$ GeV and pseudorapidity $|\eta| <$ 1.0, with no other particles detected in $-7.4 <
    \eta < +7.4$. The two showers have similar $E_T$ and azimuthal angle separation $\Delta\phi \sim \pi$; 34 events have two charged particle tracks, consistent with the QED process $p \bar{p} \rightarrow p + e^+e^- + \bar{p}$ by two-photon exchange, while 43 events have no charged tracks. The number of these events that are exclusive $\pi^0\pi^0$ is consistent with zero and is $<$ 15 at 95% C.L. The cross section for $p\bar{p} \to
    p+\gamma\gamma+\bar{p}$ with $|\eta(\gamma)| < 1.0$ and $E_T(\gamma) > 2.5$ GeV is $2.48\,^{+0.40}_{-0.35}(\mathrm{stat})\,^{+0.40}_{-0.51}(\mathrm{syst})\,
    \mathrm {
    pb}$.
author:
- 'T. Aaltonen'
- 'M.G. Albrow'
- 'B. Álvarez González$^z$'
- 'S. Amerio'
- 'D. Amidei'
- 'A. Anastassov$^x$'
- 'A. Annovi'
- 'J. Antos'
- 'G. Apollinari'
- 'J.A. Appel'
- 'T. Arisawa'
- 'A. Artikov'
- 'J. Asaadi'
- 'W. Ashmanskas'
- 'B. Auerbach'
- 'A. Aurisano'
- 'F. Azfar'
- 'W. Badgett'
- 'T. Bae'
- 'A. Barbaro-Galtieri'
- 'V.E. Barnes'
- 'B.A. Barnett'
- 'P. Barria$^{hh}$'
- 'P. Bartos'
- 'M. Bauce$^{ff}$'
- 'F. Bedeschi'
- 'S. Behari'
- 'G. Bellettini$^{gg}$'
- 'J. Bellinger'
- 'D. Benjamin'
- 'A. Beretvas'
- 'A. Bhatti'
- 'D. Bisello$^{ff}$'
- 'I. Bizjak'
- 'K.R. Bland'
- 'B. Blumenfeld'
- 'A. Bocci'
- 'A. Bodek'
- 'D. Bortoletto'
- 'J. Boudreau'
- 'A. Boveia'
- 'L. Brigliadori$^{ee}$'
- 'C. Bromberg'
- 'E. Brucken'
- 'J. Budagov'
- 'H.S. Budd'
- 'K. Burkett'
- 'G. Busetto$^{ff}$'
- 'P. Bussey'
- 'A. Buzatu'
- 'A. Calamba'
- 'C. Calancha'
- 'S. Camarda'
- 'M. Campanelli'
- 'M. Campbell'
- 'F. Canelli$^{11}$'
- 'B. Carls'
- 'D. Carlsmith'
- 'R. Carosi'
- 'S. Carrillo$^m$'
- 'S. Carron'
- 'B. Casal$^k$'
- 'M. Casarsa'
- 'A. Castro$^{ee}$'
- 'P. Catastini'
- 'D. Cauz'
- 'V. Cavaliere'
- 'M. Cavalli-Sforza'
- 'A. Cerri$^f$'
- 'L. Cerrito$^s$'
- 'Y.C. Chen'
- 'M. Chertok'
- 'G. Chiarelli'
- 'G. Chlachidze'
- 'F. Chlebana'
- 'K. Cho'
- 'D. Chokheli'
- 'W.H. Chung'
- 'Y.S. Chung'
- 'M.A. Ciocci$^{hh}$'
- 'A. Clark'
- 'C. Clarke'
- 'G. Compostella$^{ff}$'
- 'M.E. Convery'
- 'J. Conway'
- 'M.Corbo'
- 'M. Cordelli'
- 'C.A. Cox'
- 'D.J. Cox'
- 'F. Crescioli$^{gg}$'
- 'J. Cuevas$^z$'
- 'R. Culbertson'
- 'D. Dagenhart'
- 'N. d’Ascenzo$^w$'
- 'M. Datta'
- 'P. de Barbaro'
- 'M. Dell’Orso$^{gg}$'
- 'L. Demortier'
- 'M. Deninno'
- 'F. Devoto'
- 'M. d’Errico$^{ff}$'
- 'A. Di Canto$^{gg}$'
- 'B. Di Ruzza'
- 'J.R. Dittmann'
- 'M. D’Onofrio'
- 'S. Donati$^{gg}$'
- 'P. Dong'
- 'M. Dorigo'
- 'T. Dorigo'
- 'K. Ebina'
- 'A. Elagin'
- 'A. Eppig'
- 'R. Erbacher'
- 'S. Errede'
- 'N. Ershaidat$^{dd}$'
- 'R. Eusebi'
- 'S. Farrington'
- 'M. Feindt'
- 'J.P. Fernandez'
- 'R. Field'
- 'G. Flanagan$^u$'
- 'R. Forrest'
- 'M.J. Frank'
- 'M. Franklin'
- 'J.C. Freeman'
- 'Y. Funakoshi'
- 'I. Furic'
- 'M. Gallinaro'
- 'J.E. Garcia'
- 'A.F. Garfinkel'
- 'P. Garosi$^{hh}$'
- 'H. Gerberich'
- 'E. Gerchtein'
- 'S. Giagu'
- 'V. Giakoumopoulou'
- 'P. Giannetti'
- 'K. Gibson'
- 'C.M. Ginsburg'
- 'N. Giokaris'
- 'P. Giromini'
- 'G. Giurgiu'
- 'V. Glagolev'
- 'D. Glenzinski'
- 'M. Gold'
- 'D. Goldin'
- 'N. Goldschmidt'
- 'A. Golossanov'
- 'G. Gomez'
- 'G. Gomez-Ceballos'
- 'M. Goncharov'
- 'O. González'
- 'I. Gorelov'
- 'A.T. Goshaw'
- 'K. Goulianos'
- 'S. Grinstein'
- 'C. Grosso-Pilcher'
- 'R.C. Group$^{53}$'
- 'J. Guimaraes da Costa'
- 'S.R. Hahn'
- 'E. Halkiadakis'
- 'A. Hamaguchi'
- 'J.Y. Han'
- 'F. Happacher'
- 'K. Hara'
- 'D. Hare'
- 'M. Hare'
- 'R.F. Harr'
- 'K. Hatakeyama'
- 'C. Hays'
- 'M. Heck'
- 'J. Heinrich'
- 'M. Herndon'
- 'S. Hewamanage'
- 'A. Hocker'
- 'W. Hopkins$^g$'
- 'D. Horn'
- 'S. Hou'
- 'R.E. Hughes'
- 'M. Hurwitz'
- 'U. Husemann'
- 'N. Hussain'
- 'M. Hussein'
- 'J. Huston'
- 'G. Introzzi'
- 'M. Iori$^{jj}$'
- 'A. Ivanov$^p$'
- 'E. James'
- 'D. Jang'
- 'B. Jayatilaka'
- 'E.J. Jeon'
- 'S. Jindariani'
- 'M. Jones'
- 'K.K. Joo'
- 'S.Y. Jun'
- 'T.R. Junk'
- 'T. Kamon$^{25}$'
- 'P.E. Karchin'
- 'A. Kasmi'
- 'Y. Kato$^o$'
- 'W. Ketchum'
- 'J. Keung'
- 'V. Khotilovich'
- 'B. Kilminster'
- 'D.H. Kim'
- 'H.S. Kim'
- 'J.E. Kim'
- 'M.J. Kim'
- 'S.B. Kim'
- 'S.H. Kim'
- 'Y.K. Kim'
- 'Y.J. Kim'
- 'N. Kimura'
- 'M. Kirby'
- 'S. Klimenko'
- 'K. Knoepfel'
- 'K. Kondo'
- 'D.J. Kong'
- 'J. Konigsberg'
- 'A.V. Kotwal'
- 'M. Kreps'
- 'J. Kroll'
- 'D. Krop'
- 'M. Kruse'
- 'V. Krutelyov$^c$'
- 'T. Kuhr'
- 'M. Kurata'
- 'S. Kwang'
- 'A.T. Laasanen'
- 'S. Lami'
- 'S. Lammel'
- 'M. Lancaster'
- 'R.L. Lander'
- 'K. Lannon$^y$'
- 'A. Lath'
- 'G. Latino$^{hh}$'
- 'T. LeCompte'
- 'E. Lee'
- 'H.S. Lee$^q$'
- 'J.S. Lee'
- 'S.W. Lee$^{bb}$'
- 'S. Leo$^{gg}$'
- 'S. Leone'
- 'J.D. Lewis'
- 'A. Limosani$^t$'
- 'C.-J. Lin'
- 'M. Lindgren'
- 'E. Lipeles'
- 'A. Lister'
- 'D.O. Litvintsev'
- 'C. Liu'
- 'H. Liu'
- 'Q. Liu'
- 'T. Liu'
- 'S. Lockwitz'
- 'A. Loginov'
- 'D. Lucchesi$^{ff}$'
- 'J. Lueck'
- 'P. Lujan'
- 'P. Lukens'
- 'G. Lungu'
- 'J. Lys'
- 'R. Lysak$^e$'
- 'R. Madrak'
- 'K. Maeshima'
- 'P. Maestro$^{hh}$'
- 'S. Malik'
- 'G. Manca$^a$'
- 'A. Manousakis-Katsikakis'
- 'F. Margaroli'
- 'C. Marino'
- 'M. Martínez'
- 'P. Mastrandrea'
- 'K. Matera'
- 'M.E. Mattson'
- 'A. Mazzacane'
- 'P. Mazzanti'
- 'K.S. McFarland'
- 'P. McIntyre'
- 'R. McNulty$^j$'
- 'A. Mehta'
- 'P. Mehtala'
- 'C. Mesropian'
- 'T. Miao'
- 'D. Mietlicki'
- 'A. Mitra'
- 'H. Miyake'
- 'S. Moed'
- 'N. Moggi'
- 'M.N. Mondragon$^m$'
- 'C.S. Moon'
- 'R. Moore'
- 'M.J. Morello$^{ii}$'
- 'J. Morlock'
- 'P. Movilla Fernandez'
- 'A. Mukherjee'
- 'Th. Muller'
- 'P. Murat'
- 'M. Mussini$^{ee}$'
- 'J. Nachtman$^n$'
- 'Y. Nagai'
- 'J. Naganoma'
- 'I. Nakano'
- 'A. Napier'
- 'J. Nett'
- 'C. Neu'
- 'M.S. Neubauer'
- 'J. Nielsen$^d$'
- 'L. Nodulman'
- 'S.Y. Noh'
- 'O. Norniella'
- 'L. Oakes'
- 'S.H. Oh'
- 'Y.D. Oh'
- 'I. Oksuzian'
- 'T. Okusawa'
- 'R. Orava'
- 'L. Ortolan'
- 'S. Pagan Griso$^{ff}$'
- 'C. Pagliarone'
- 'E. Palencia$^f$'
- 'V. Papadimitriou'
- 'A.A. Paramonov'
- 'J. Patrick'
- 'G. Pauletta$^{kk}$'
- 'M. Paulini'
- 'C. Paus'
- 'D.E. Pellett'
- 'A. Penzo'
- 'T.J. Phillips'
- 'G. Piacentino'
- 'E. Pianori'
- 'J. Pilot'
- 'K. Pitts'
- 'C. Plager'
- 'L. Pondrom'
- 'S. Poprocki$^g$'
- 'K. Potamianos'
- 'F. Prokoshin$^{cc}$'
- 'A. Pranko'
- 'F. Ptohos$^h$'
- 'G. Punzi$^{gg}$'
- 'A. Rahaman'
- 'V. Ramakrishnan'
- 'N. Ranjan'
- 'I. Redondo'
- 'P. Renton'
- 'M. Rescigno'
- 'T. Riddick'
- 'F. Rimondi$^{ee}$'
- 'L. Ristori$^{42}$'
- 'A. Robson'
- 'T. Rodrigo'
- 'T. Rodriguez'
- 'E. Rogers'
- 'S. Rolli$^i$'
- 'R. Roser'
- 'F. Ruffini$^{hh}$'
- 'A. Ruiz'
- 'J. Russ'
- 'V. Rusu'
- 'A. Safonov'
- 'W.K. Sakumoto'
- 'Y. Sakurai'
- 'L. Santi$^{kk}$'
- 'K. Sato'
- 'V. Saveliev$^w$'
- 'A. Savoy-Navarro$^{aa}$'
- 'P. Schlabach'
- 'A. Schmidt'
- 'E.E. Schmidt'
- 'T. Schwarz'
- 'L. Scodellaro'
- 'A. Scribano$^{hh}$'
- 'F. Scuri'
- 'S. Seidel'
- 'Y. Seiya'
- 'A. Semenov'
- 'F. Sforza$^{hh}$'
- 'S.Z. Shalhout'
- 'T. Shears'
- 'P.F. Shepard'
- 'M. Shimojima$^v$'
- 'M. Shochet'
- 'I. Shreyber-Tecker'
- 'A. Simonenko'
- 'P. Sinervo'
- 'K. Sliwa'
- 'J.R. Smith'
- 'F.D. Snider'
- 'A. Soha'
- 'V. Sorin'
- 'H. Song'
- 'P. Squillacioti$^{hh}$'
- 'M. Stancari'
- 'R. St. Denis'
- 'B. Stelzer'
- 'O. Stelzer-Chilton'
- 'D. Stentz$^x$'
- 'J. Strologas'
- 'G.L. Strycker'
- 'Y. Sudo'
- 'A. Sukhanov'
- 'I. Suslov'
- 'K. Takemasa'
- 'Y. Takeuchi'
- 'J. Tang'
- 'M. Tecchio'
- 'P.K. Teng'
- 'J. Thom$^g$'
- 'J. Thome'
- 'G.A. Thompson'
- 'E. Thomson'
- 'D. Toback'
- 'S. Tokar'
- 'K. Tollefson'
- 'T. Tomura'
- 'D. Tonelli'
- 'S. Torre'
- 'D. Torretta'
- 'P. Totaro'
- 'M. Trovato$^{ii}$'
- 'F. Ukegawa'
- 'S. Uozumi'
- 'A. Varganov'
- 'F. Vázquez$^m$'
- 'G. Velev'
- 'C. Vellidis'
- 'M. Vidal'
- 'I. Vila'
- 'R. Vilar'
- 'J. Vizán'
- 'M. Vogel'
- 'G. Volpi'
- 'P. Wagner'
- 'R.L. Wagner'
- 'T. Wakisaka'
- 'R. Wallny'
- 'S.M. Wang'
- 'A. Warburton'
- 'D. Waters'
- 'W.C. Wester III'
- 'D. Whiteson$^b$'
- 'A.B. Wicklund'
- 'E. Wicklund'
- 'S. Wilbur'
- 'F. Wick'
- 'H.H. Williams'
- 'J.S. Wilson'
- 'P. Wilson'
- 'B.L. Winer'
- 'P. Wittich$^g$'
- 'S. Wolbers'
- 'H. Wolfe'
- 'T. Wright'
- 'X. Wu'
- 'Z. Wu'
- 'K. Yamamoto'
- 'D. Yamato'
- 'T. Yang'
- 'U.K. Yang$^r$'
- 'Y.C. Yang'
- 'W.-M. Yao'
- 'G.P. Yeh'
- 'K. Yi$^n$'
- 'J. Yoh'
- 'K. Yorita'
- 'T. Yoshida$^l$'
- 'G.B. Yu'
- 'I. Yu'
- 'S.S. Yu'
- 'J.C. Yun'
- 'A. Zanetti'
- 'Y. Zeng'
- 'C. Zhou'
- 'S. Zucchelli$^{ee}$'
date: 'September 21, 2011'
title: ' Observation of Exclusive [$\gamma\gamma$]{} Production in [$p\bar{p}$]{} Collisions at [$\sqrt{s}=1.96$]{} TeV '
---

=2 =3

[^1]

[^2]

In proton-(anti)proton collisions, two direct high-$E_T$ photons can be produced at leading order by $q\bar{q}$$\,\rightarrow\,$${\gamma}{\gamma}$ and by $gg$$\,\rightarrow\,$${\gamma}{\gamma}$ through a quark loop. In the latter case it is possible for another gluon exchange to cancel the color of the fusing gluons, allowing the (anti)proton to emerge intact with no hadrons produced. For $p\bar{p}$ collisions, this is the “exclusive" process $p\bar{p}$$\,\rightarrow\,$$p$$\,+\,$$\gamma\gamma$$\,+\,$$\bar{p}$, for which the leading order diagram is shown in Fig. \[fig:cepDiagrams\]a [@cdfloi; @exclgg1]. The outgoing (anti)proton has nearly the beam momentum, and transverse momentum $p_T \lesssim 1$ GeV/c, having emitted a pair of gluons in a color singlet. There is a pseudorapidity gap $\Delta\eta >$ 6 adjacent to the (anti)proton. In Regge theory this is diffractive scattering via pomeron [@forshawross; @donnachie], $\rm I\kern +0.53em\llap P$, exchange. The cross section for $|\eta(\gamma)| < 1.0$ and transverse energy $E_T(\gamma)
> 2.5$ GeV is predicted [@KMRgg; @KMRgg2] to be $\sigma({\gamma}{\gamma})_{\mathrm{exclusive}} \sim$ 0.2 - 2 pb, depending on the low-$x$ (unintegrated) gluon density. Additional uncertainties come from the cross section for $g+g$$\,\rightarrow\,$${\gamma}+{\gamma}$, the probability that no hadrons are produced by additional parton interactions (rapidity gap survival factor and Sudakov suppression [@sudakov]), and the probability that neither proton dissociates (e.g., $p$$\,\rightarrow\,$$p\
\pi^+\pi^-$) [@KMRgg]. The calculation is also imprecise because of the low $Q^2$, the squared 4-momentum transfer. The total theoretical uncertainty on the cross section can be estimated to be a factor $^{\times{3}}_{\div{3}}$ [@exchiggs]. Apart from its intrinsic interest for QCD, the process tests the theory of exclusive Higgs boson production [@cdfloi; @exclgg1; @KMRgg; @bialaslandshoff; @schafer; @exchiggs; @harland; @forshaw; @acf] $p+p$$\,\rightarrow\,$$p+H+p$, Fig. \[fig:cepDiagrams\]b, which may be detectable at the LHC. The leading order processes $gg$$\,\rightarrow\,$$\gamma\gamma$ and $gg$$\,\rightarrow\,$$H$ are calculable perturbatively, but the more uncertain elements of the exclusive processes (mainly the unintegrated gluon densities, the Sudakov suppression, and the gap survival probability) are common to both (see Fig. \[fig:cepDiagrams\]). For a 120 GeV standard model Higgs boson the exclusive cross section at $\sqrt{s} = 7$ TeV is 3 fb with a factor $^{\times{3}}_{\div{3}}$ uncertainty [@exchiggs].

![Leading order diagrams for central exclusive production in $p(\bar{p})-p$ collisions: a) exclusive $\gamma\gamma$ production in $\bar{p}-p$ collisions; b) exclusive Higgs boson production in $p-p$ collisions. Note the screening gluon that cancels the color flow from the interacting gluons. \[fig:cepDiagrams\] ](figure1.eps){width="38.00000%"}

Processes other than $gg$$\,\rightarrow\,$$\gamma\gamma$ can produce an exclusive $\gamma\gamma$ final state. Contributions from $q\bar{q}$$\,\rightarrow\,$$\gamma\gamma$ and $\gamma\gamma$$\,\rightarrow\,$$\gamma\gamma$ are respectively $<$ 5% and $<$ 1% of $gg$$\,\rightarrow\,$$\gamma\gamma$ [@KMRgg]. Backgrounds to exclusive $\gamma\gamma$ events to be considered are $\pi^0\pi^0$ and $\eta\eta$, with each meson decaying to two photons, of which one is not detected. We also consider events where one or both protons dissociate, e.g., $p$$\,\rightarrow\,$$p\,\pi^+\pi^-$, to be background. These backgrounds are small.

We previously published a search for exclusive $\gamma\gamma$ production, finding three candidate events with $E_T({\gamma}) >$ 5 GeV and $|\eta|
<$ 1.0, using data from 532 pb$^{-1}$ of integrated luminosity [@cdfgg1]. The prediction of Ref. [@KMRgg] was 0.8$^{+1.6}_{-0.5}$ events. Two events had a single narrow electromagnetic (EM) shower on each side, as expected for ${\gamma}{\gamma}$, but no observation could be claimed. This Letter reports the observation of 43 events with a contamination of $< 15 \:
\pi^0\pi^0$ events (at 95% C.L.), after we lowered the trigger threshold on the EM showers from 4 GeV to 2 GeV and collected data from another 1.11 fb$^{-1}$ of integrated luminosity. We used the QED process $p$$\,+\,$$\bar{p}$$\,
$$\rightarrow$$\,$$p\,$$+$$\,\gamma^*\gamma^*$$+$$\,\bar{p}$$\,
$$\rightarrow$$\,$$p$$\,+\,$$e^+e^-$$+\,$$\bar{p}$ in the same data set, for which the cross section is well known, as a check of the analysis.

The data were collected by the Collider Detector at Fermilab, CDF II, at the Tevatron, with $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV. The CDF II detector is a general purpose detector described elsewhere [@cdf]; here we give a brief summary of the detector components used in this analysis. Surrounding the beam pipe is a tracking system consisting of a silicon microstrip detector, a cylindrical drift chamber (COT) [@cot], and a solenoid providing a 1.4 Tesla magnetic field. The tracking system is fully efficient at reconstructing isolated tracks with $p_T \geq$ 1 GeV/c and $|\eta|<1$. It is surrounded by the central and end-plug calorimeters covering the range $|\eta|<3.6$. Both calorimeters have separate EM and hadronic compartments. A proportional wire chamber (CES) [@balka], with orthogonal anode wires and cathode strips, is embedded in the central EM calorimeter, covering the region of $|\eta| < 1.1$, at a depth of six radiation lengths. It allows a measurement of the number and shape, in both $\eta$ and azimuth $\phi$, of EM showers (clusters of wires or strips). The anode-wire pitch (in $\phi$) is 1.5 cm and the cathode-strip pitch varies with $\eta$ from 1.7 cm to 2.0 cm. The CES provides a means of distinguishing single photon showers from $\pi^0 \rightarrow
\gamma\gamma$ up to $E_T(\pi^0) \sim$ 8 GeV. The region $3.6<|\eta|<5.2$ is covered by a lead-liquid scintillator calorimeter called the Miniplug [@miniplug]. At higher pseudorapidities, $5.4<|\eta|<7.4$, scintillation counters, called beam shower counters (BSC-1/2/3), are located on each side of the CDF detector. Gas Cherenkov detectors, with 48 photomultipliers per side, covering 3.7 $<|\eta|<$ 4.7, detect charged particles, and were also used to determine the luminosity with a 6% uncertainty [@clc].

The data were recorded using a three-level on-line event selection system (trigger). At the first level we required one EM cluster with $E_T >$ 2 GeV and $|\eta| < 2.1$ and no signal above noise in the BSC-1 counters ($|\eta| = 5.4 - 5.9)$. This rapidity gap requirement rejected a large fraction of inelastic collisions as well as most events with more than one interaction (pileup). A second EM cluster with similar properties was required at level two. A level three trigger selected events with two calorimeter showers consistent with coming from electrons or photons: i.e., passing the requirement (cut) that the ratio of shower energy in the hadronic (HAD) calorimeter to that in the EM (HAD:EM) be less than 0.125, and that the signal shape in the CES is consistent with a single shower.

We now describe the offline selection of events, with two isolated EM showers and no other particles except the outgoing $p$ and $\bar{p}$, which were not detected. Two central, $|\eta|<1$, EM showers were required with $E_T >$ 2.5 GeV to avoid trigger threshold inefficiencies. The energy resolution is $dE/E \sim 8\%$ from test beam studies and *in situ* $p/E$ matching for electrons. A refined HAD:EM ratio cut of $< 0.055+0.000\:45E$ was applied, as well as an acoplanarity cut of $|\pi-\Delta\phi|<0.6$. The trigger selection efficiency for single photons was measured using data collected with an interaction trigger (minimum bias). The BSC-1 gap trigger was taken to be 100% efficient as the BSC-1 trigger threshold was clearly above the noise level and the offline selection criteria. We measured an overall trigger efficiency of $\varepsilon_{\mathrm{trig}}=92\%\pm2\%$(syst). A weighting process was necessary due to the different slope in $E_T$ of the minimum bias probe data compared to the signal. The trigger efficiency did not show any $\eta$ or $\phi$ dependence for $|\eta|<1$. Monte Carlo signal simulation data samples were generated using the <span style="font-variant:small-caps;">superchic</span> program (version 1.3) [@harland; @superchic] based on recent developments of the Durham KMR model [@exclgg1]. The Monte Carlo samples were passed through a simulation of the detector, <span style="font-variant:small-caps;">cdfsim</span> 6.1.4.m including <span style="font-variant:small-caps;">geant</span> version 3.21/14 [@geant]. The systematic error was estimated by using the binwise uncertainty of the efficiency in the weighting process of the signal Monte Carlo sample. Taking into account a combined detector and offline reconstruction efficiency of $\varepsilon_{\mathrm{rec}}=55\%\pm3\%$(syst), and a photon identification efficiency of $\varepsilon_{\mathrm{id}}=93\%\pm1\%$(syst), we obtained a photon-pair efficiency $\varepsilon_{\mathrm{pho}}=\varepsilon_{\mathrm{trig}}^2*\varepsilon_{\mathrm{
rec } }*\varepsilon_{\mathrm{id}}^2=40\%\pm3\%$(syst). The systematic uncertainties of the reconstruction and identification efficiency were estimated by shifting kinematical input parameters over a reasonable interval motivated by the dominating EM-energy-scale uncertainty [@escale]. The offline selection then required that no activity other than these two showers (or clusters of showers) occurred in the entire detector, $|\eta| < 7.4$. We used the same procedure as in our earlier study of exclusive $e^+e^-$ events [@cdfee], searching all the calorimeters for any signal above noise levels, determined using noninteraction events; 99.2% of such events have no tower (out of 480) with $E_T > 125$ MeV. We also required the CLC counters and the more forward BSC counters to have signals consistent with only noise. Events triggered only on a bunch crossing (zero bias) showed that the exclusive efficiency, $\varepsilon_{excl}$, defined as the factor to be applied to the delivered luminosity to account for the requirement of no pileup, is $\varepsilon_{excl} = 6.8\%\pm0.4\%$(syst). The probability $P(0)$ of a zero-bias event satisfying all the exclusivity cuts, i.e., having no detected inelastic interaction, is $P(0)=A\exp(-\bar{n})=A\exp(-L_{\mathrm{x}} \sigma_{\mathrm{vis}})$,where $L_{\mathrm{x}}$ is the single bunch crossing luminosity (cm$^{-2}$) and $\sigma_{\mathrm{vis}}$ is the visible cross section; $\sigma_{\mathrm{vis}}=\sigma_{\mathrm{inel}}$ if everyinelastic collision is detected. We find $\sigma_{\mathrm{vis}}=67 \pm 6$ mb. In the absence of noise (above our chosen thresholds) $A = 1.0$; we find $A = 0.98 \pm 0.02$. We checked that the rate of candidate events, corrected for the exclusive efficiency, was constant during data taking (one year). The systematic uncertainty was estimated using the spread in slope parameters from fits to data in different time periods.

  -------------------------------------------------- --------------------------------------------------------
  Integrated luminosity $\mathcal{L}_\mathsf{int}$                   $1.11\pm0.07$ fb$^{-1}$

  Exclusive efficiency                                           $0.068\pm0.004\,\mathrm{(syst)}$

  Exclusive $\gamma\gamma$                           

  Events                                                                        43

  Photon-pair efficiency                              $0.40\pm0.02\,\mathrm{(stat)}\pm0.03\,\mathrm{(syst)}$

  Probability of no conversions                                        $0.57\pm0.06$ (syst)

  $\pi^0\pi^0$ b/g (events)                                           0.0, $< 15$ (95% C.L.)

  Dissociation b/g (events)                                       $0.14\pm0.14\,\mathrm{(syst)}$

  Exclusive $e^+e^-$                                 

  Events                                                                        34

  Electron-pair efficiency                            $0.33\pm0.01\,\mathrm{(stat)}\pm0.02\,\mathrm{(syst)}$

  Probability of no radiation                                     $0.42\pm0.08\,\mathrm{(syst)}$

  Dissociation b/g (events)                                $3.8\pm0.4\,\mathrm{(stat)}\pm0.9\,\mathrm{
                                                                             (syst)}$
  -------------------------------------------------- --------------------------------------------------------

  :  Summary of parameters used for the measurement of the exclusive photon-pair cross section for $E_{T}(\gamma)>$ 2.5 GeV and $|\eta(\gamma)| <
  1.0$. Values for the $e^+e^-$ control study are also given. Note that b/g stands for background.\[summarystatgg\]

  -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   ![The $e^+e^-$ candidates: invariant mass distribution (a). The two-photon candidates: invariant mass distribution (b), $|\pi-\Delta\phi|$ distribution (c), and $p_T$ distribution of the two photons (d). All error bars are statistical. The MC predictions for $\gamma\gamma$ are normalized to data. The QED prediction for $e^+e^-$ is normalized to the delivered luminosity and efficiencies. The MC samples for the QED process were generated with the <span style="font-variant:small-caps;">lpair</span> program [@lpair]. \[fig:kinGGEE\] ](figure2a.eps "fig:"){width="24.00000%"}   ![The $e^+e^-$ candidates: invariant mass distribution (a). The two-photon candidates: invariant mass distribution (b), $|\pi-\Delta\phi|$ distribution (c), and $p_T$ distribution of the two photons (d). All error bars are statistical. The MC predictions for $\gamma\gamma$ are normalized to data. The QED prediction for $e^+e^-$ is normalized to the delivered luminosity and efficiencies. The MC samples for the QED process were generated with the <span style="font-variant:small-caps;">lpair</span> program [@lpair]. \[fig:kinGGEE\] ](figure2b.eps "fig:"){width="24.00000%"}
   ![The $e^+e^-$ candidates: invariant mass distribution (a). The two-photon candidates: invariant mass distribution (b), $|\pi-\Delta\phi|$ distribution (c), and $p_T$ distribution of the two photons (d). All error bars are statistical. The MC predictions for $\gamma\gamma$ are normalized to data. The QED prediction for $e^+e^-$ is normalized to the delivered luminosity and efficiencies. The MC samples for the QED process were generated with the <span style="font-variant:small-caps;">lpair</span> program [@lpair]. \[fig:kinGGEE\] ](figure2c.eps "fig:"){width="24.00000%"}   ![The $e^+e^-$ candidates: invariant mass distribution (a). The two-photon candidates: invariant mass distribution (b), $|\pi-\Delta\phi|$ distribution (c), and $p_T$ distribution of the two photons (d). All error bars are statistical. The MC predictions for $\gamma\gamma$ are normalized to data. The QED prediction for $e^+e^-$ is normalized to the delivered luminosity and efficiencies. The MC samples for the QED process were generated with the <span style="font-variant:small-caps;">lpair</span> program [@lpair]. \[fig:kinGGEE\] ](figure2d.eps "fig:"){width="24.00000%"}
  -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

The selection of 81 events passing all cuts was made without reference to the track detectors. We found that 34 have exactly two oppositely charged tracks, 43 have no tracks in the COT, and four are in neither class. Visual inspection of the latter showed that two had photon conversions, and two were likely to be $e^+e^-$ events with bremsstrahlung. These numbers are consistent with expectations from the detector simulation. The tracks in the 34 two-track events agree in all aspects with the QED process $p+\bar{p} \rightarrow p + e^+e^- + \bar{p}$ via two virtual photons, previously observed in CDF [@cdfee; @cdfz]. The calorimeter shower energies are consistent with the momenta measured from the tracks. Kinematic distributions, after detector simulation, are as expected. The mass $M(e^+e^-)$ distribution is presented in Fig. 2a, together with the QED prediction normalized to the delivered luminosity and efficiencies, showing that the cross section agrees with the QED prediction in both magnitude and shape. We measured a cross section of $\sigma_{e^+e^-,\mathrm{exclusive}}(|\eta(e)|<1,\,E_T(e)>2.5\,\mathrm{GeV}) =
2.88\,^{+0.57}_{-0.48}(\mathrm{stat})\pm0.63(\mathrm{syst})$ pb, compared to $3.25\pm0.07$ pb (QED, [@lpair]). The systematic uncertainties for the QED study are mostly identical to the photon case. Distinct from photons, electrons leave tracks in the tracking detectors and may radiate. The systematic uncertainty on the radiation probability was estimated by varying the exclusivity cuts by $\pm10$%. This $e^+e^-$ sample provides a valuable check of the exclusive $\gamma\gamma$ analysis.

The 43 events with no tracks have the kinematic properties expected for exclusive $\gamma\gamma$ production [@superchic]. In particular the $M(\gamma\gamma)$ distribution \[Fig. 2b\] extending up to 15 GeV/c$^2$ is as expected, as well as the acoplanarity $\pi - \Delta \phi(\gamma\gamma)$ \[Fig. 2c\] and the 2-vector sum of $p_T$ \[Fig. 2d\]; in these plots \[unlike Fig. 2a\] the <span style="font-variant:small-caps;">superchic</span> Monte Carlo prediction is normalized to the same number of events as the data. An important issue is whether some of these events could be $\pi^0\pi^0$, rather than $\gamma\gamma$. Note that $\gamma\pi^0$ events are forbidden by *C* parity. The CES chambers give information on the number of EM showers. The minimum opening angle $\Delta\theta_{min}$ between the two photons from $\pi^0$ decay is $2\tan^{-1}\left(\frac{m(\pi)}{p(\pi)}\right)$ = 3.1$^\circ$ for $p(\pi)$ = 5 GeV, well separated in the CES chambers, which have a granularity $< 0.5^\circ$. A $\pi^0$ can fake a $\gamma$ only if one photon ranges out before the CES, or falls in an inactive region (8%) of the detector. All of the 68 $e^{\pm}$ events in our sample, with similar energies, had matching showers in the CES chambers. A <span style="font-variant:small-caps;">geant</span> [@geant] simulation predicts the probability that a photon in our energy range produces a shower to be $\gtrsim98.3$%. We summed the number of reconstructed CES showers in the event, mostly 2 or 3 as shown in Fig. \[fig:pi0BG\] (left).

  -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   ![Estimate of $\pi^0\pi^0$ background fraction in the candidate sample. Distribution of reconstructed CES showers per event for data compared to $\gamma\gamma$ and $\pi^0\pi^0$ Monte Carlo simulations (a). Background fraction estimate using Pearson’s $\chi^2$ test to fit the composition hypothesis to the data distribution (b). \[fig:pi0BG\] ](figure3a.eps "fig:"){width="24.00000%"}   ![Estimate of $\pi^0\pi^0$ background fraction in the candidate sample. Distribution of reconstructed CES showers per event for data compared to $\gamma\gamma$ and $\pi^0\pi^0$ Monte Carlo simulations (a). Background fraction estimate using Pearson’s $\chi^2$ test to fit the composition hypothesis to the data distribution (b). \[fig:pi0BG\] ](figure3b.eps "fig:"){width="24.00000%"}
                                                                                                                                                                                                  a)                                                                                                                                                                                                                                                                                                                                                                                                 b)
  -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

The distribution agrees very well with the $\gamma\gamma$ simulation, and strongly disagrees with the $\pi^0\pi^0$ simulation. Fitting to the sum of the two components gives a best fit to the fraction $F(\pi^0\pi^0)$ = 0.0, with a 95% C.L. upper limit of 15 events. Since obtaining this result, a new calculation of exclusive $\pi^0\pi^0$ production [@hkms] predicts $\sigma_{excl}(\pi^0\pi^0)$ = 6 - 24 fb for $E_T(\pi^0) > 2.5$ GeV and $|\eta|
< 1.0$, $\lesssim0.01$ of our measured exclusive $\gamma\gamma$ cross section. In the cross section calculation we take this background to be zero. Exclusive $\eta\eta$ production is also expected to be negligible. The only other significant background could be undetected proton dissociation, about 10% for the QED $e^+e^-$ process but $<$1% for $\pom \:
+\,\pom\,\rightarrow {\gamma}+ {\gamma}$ [@KMRgg; @KMRchi; @vkpriv]. The cross section for both photons with $E_T(\gamma) > 2.5$ GeV and $|\eta(\gamma)| < 1.0$ and no other produced particles is given by: $$\sigma_{\gamma\gamma,\mathrm{exclusive}}= \frac{N(candidates)
- N(background)}{\mathcal{L}_\mathsf{int} . \varepsilon .
\varepsilon_{excl}}\mathrm{,}$$ where $\varepsilon$ is the product of the trigger, reconstruction, identification, and conversion efficiencies (22.8%) in Table \[summarystatgg\]. The systematic uncertainty on the conversion probability was estimated by varying the exclusivity cuts by $\pm10$%. We find $\sigma_{\gamma\gamma,\mathrm{excl}}\,(|\eta(\gamma)|<1,E_T(\gamma)>2.5~
\mathrm{GeV}) =
2.48\,^{+0.40}_{-0.35}(\mathrm{stat})\,^{+0.40}_{-0.51}(\mathrm{syst})$ pb. The theoretical prediction [@harland] is strongly dependent on the low-$x$ gluon density, having central values 1.42 pb (<span style="font-variant:small-caps;">mstw08lo</span>) or 0.35 pb (<span style="font-variant:small-caps;">mrst99</span>), with other uncertainties estimated to be a factor of about $^{\times3}_{\div3}$ [@vkpriv]. A comparison of our measurement with the only theoretical prediction available to date is shown in Fig. \[fig:expvsth\]. The rates of $e^+e^-$ and $\gamma\gamma$ events with $E_T(e/\gamma) > 5$ GeV are consistent with those in our earlier studies [@cdfee; @cdfgg1].

![Comparison of the measured cross section for the exclusive $\gamma\gamma$ production in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV with theoretical predictions [@harland].\[fig:expvsth\]](figure4.eps){width="36.00000%"}

In conclusion, we have observed the exclusive production of two high-$E_T$ photons in proton-antiproton collisions, which constitutes the first observation of this process in hadron-hadron collisions. The cross section is in agreement with the only theoretical prediction, based on $g+g \rightarrow
\gamma+\gamma$, with another gluon exchanged to cancel the color and with the $p$ and $\bar{p}$ emerging intact. If a Higgs boson exists, it should be produced by the same mechanism (see Fig. \[fig:cepDiagrams\]), and the cross sections are related.

We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions. This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A.P. Sloan Foundation; the Bundesministerium für Bildung und Forschung, Germany; the Korean World Class University Program, the National Research Foundation of Korea; the Science and Technology Facilities Council and the Royal Society, UK; the Institut National de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Ministerio de Ciencia e Innovación, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; the Academy of Finland; and the Australian Research Council (ARC). We also thank V.A. Khoze, M.G. Ryskin, and L.A. Harland-Lang for many valuable discussions.

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[^1]: Deceased

[^2]: With visitors from $^a$Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy, $^b$University of CA Irvine, Irvine, CA 92697, USA, $^c$University of CA Santa Barbara, Santa Barbara, CA 93106, USA, $^d$University of CA Santa Cruz, Santa Cruz, CA 95064, USA, $^e$Institute of Physics, Academy of Sciences of the Czech Republic, Czech Republic, $^f$CERN, CH-1211 Geneva, Switzerland, $^g$Cornell University, Ithaca, NY 14853, USA, $^h$University of Cyprus, Nicosia CY-1678, Cyprus, $^i$Office of Science, U.S. Department of Energy, Washington, DC 20585, USA, $^j$University College Dublin, Dublin 4, Ireland, $^k$ETH, 8092 Zurich, Switzerland, $^l$University of Fukui, Fukui City, Fukui Prefecture, Japan 910-0017, $^m$Universidad Iberoamericana, Mexico D.F., Mexico, $^n$University of Iowa, Iowa City, IA 52242, USA, $^o$Kinki University, Higashi-Osaka City, Japan 577-8502, $^p$Kansas State University, Manhattan, KS 66506, USA, $^q$Korea University, Seoul, 136-713, Korea, $^r$University of Manchester, Manchester M13 9PL, United Kingdom, $^s$Queen Mary, University of London, London, E1 4NS, United Kingdom, $^t$University of Melbourne, Victoria 3010, Australia, $^u$Muons, Inc., Batavia, IL 60510, USA, $^v$Nagasaki Institute of Applied Science, Nagasaki, Japan, $^w$National Research Nuclear University, Moscow, Russia, $^x$Northwestern University, Evanston, IL 60208, USA, $^y$University of Notre Dame, Notre Dame, IN 46556, USA, $^z$Universidad de Oviedo, E-33007 Oviedo, Spain, $^{aa}$CNRS-IN2P3, Paris, F-75205 France, $^{bb}$Texas Tech University, Lubbock, TX 79609, USA, $^{cc}$Universidad Tecnica Federico Santa Maria, 110v Valparaiso, Chile, $^{dd}$Yarmouk University, Irbid 211-63, Jordan.