THE SEARCH FOR PHYSICS BEYOND THE STANDARD MODEL WITH CDF

Pekka K. Sinervo^{∗} Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7, Canada

ABSTRACT

The results of searches for physics beyond the standard model undertaken by the CDF Collaboration are presented. Studies of ∼ 4 pb^{−1} of \overline{p} p Tevatron Collider data place the most stringent bounds on lepton and quark compositeness, the mass of the squark and gluino in the minimal supersymmetric standard model, additional gauge bosons and a first generation leptoquark. The measurement of the rare decay W^{±} → π^{±}γ and the study of events with unusual large depositions of energy in the CDF detector are also described.

1. Introduction

The success of the standard model^{2} as a description of the electroweak and strong forces is a compelling reason to believe that it is fundamentally a good approximation to physics at the subatomic scale. However, it has several well-known inadequacies: the large number of parameters, that it does not predict the structure of the Higgs sector, and the lack of an explanation for the number of lepton and quark generations are only three of the shortcomings of the model. Many extensions to the standard model have been proposed that attempt to address these issues. However, the only way to choose among these is to search for phenomena predicted by one or other of these new theories.

The study of high energy proton-antiproton (\overline{p} p) collisions provides a unique laboratory in which to search for much of this “new physics.” Essentially anything that couples to quarks and gluons will be produced in such collisions, including both mediators of a new force and new particles. The large centre-of-mass collision energies (\sqrt{ŝ}) and four-momentum transfer (Q) available in the parton-parton interactions gives access to mass scales of several hundred GeV/c^{2}, and probes parton substructure at the multi-TeV energy scale. Finally, the inherently high luminosity of a hadron collider makes it possible to perform searches that are quite sensitive to new phenomena.

The Collider Detector at Fermilab (CDF) has been used to study \overline{p} p collisions at a centre-of-mass energy of 1.8 TeV using the Tevatron Collider. In this article, I review the recent results of searches for new phenomena using a 4.2 pb^{−1} data set acquired during the 1988-89 Collider run. I will first briefly describe the CDF detector; further details can be found in Ref. 3. The following sections will then summarize the results on: searches for compositeness, supersymmetric particles, additional gauge bosons, leptoquarks, the rare decay W^{±} → π^{±}γ, and events with anomolously large amounts of transverse energy.

∗Representing the CDF Collaboration^{1}

2. The CDF Detector

The CDF is a general-purpose, solenoidal detector designed to detect and record \overline{p} p collisions that produce one or more high transverse-momentum (P_{T}) particles in the final state.^{3} The detector, shown in Fig. 1, consists of charged particle tracking devices in the solenoidal magnetic field, surrounded by finely-segmented electromagnetic and hadronic calorimeters that measure the energy flow from the collision over the pseudorapidity∗ interval |η| < 4.2. Charged particles are detected by a vertex time projection chamber (VTPC) instrumenting the inner region out to a radius of 23 cm and a central tracking chamber (CTC) that tracks particles out to a radius of 1.2 m. The momentum resolution of the tracking system is σ_{P} /P ≃ 0.0011P. The electromagnetic calorimeters surround the tracking volume and consist of plates of lead absorber interleaved with scintillator in the central pseudorapidity region |η| < 1.1 and lead plates interleaved with proportional gas counters over the remainder of the solid angle. The hadronic calorimeters consist of plates of steel absorber interleaved with scintillator in the central region and interleaved with proportional gas counters in the pseudorapidity interval |η| > 1.1.

A proportional wire chamber located at a depth of six radiation lengths in the central EM calorimeter measures the position of electromagnetic showers to a few millimeters in both the azimuthal and axial directions. This “strip chamber” is an important component of the CDF electron and photon identification system. Muons are identified in the region |η| < ∼ 0.6 using four layers of drift chambers located immediately outside the central hadronic calorimeter. This system measures the position and trajectory of muon candidates and is used in conjunction with the CTC to identify high-P_{T} muons. An energetic neutrino produced in a collision is detected by measuring the transverse momenta of the other charged and neutral particles in the event with the calorimeter system and inferring the neutrino transverse momentum magnitude and direction from the resulting missing transverse energy vector.

The CDF identifies collisions with one or more high-P_{T} particles using a threelevel trigger system. The recorded events have to satisfy one of several trigger conditions, such as the presence of an electron candidate with E_{T} > 12 GeV, a muon candidate with P_{T} > 9 GeV/c, a neutrino with Et > 25 GeV, or a jet with Et > 120

∗We define η ≡ − ln tan(θ/2), where θ is the polar angle with respect to the incoming proton beam direction.

Fig. 1. An elevation view of the CDF detector.

GeV. These trigger conditions typically have efficiencies in excess of 95% for correctly tagging candidate events.

3. Quark and Lepton Compositeness

The standard model assumes that the fundamental fermions (i.e. the quarks and leptons) are point-like particles. It is important to test this ansatz as evidence of substructure would place strong constraints on any extension to the standard model. Previous limits on quark and lepton substructure have been derived from studies of high transverse momentum lepton-lepton and quark-quark scattering.^{4} It is conventional to quote the limits set by these searches in terms of a generic scattering model^{5} that adds an effective 4-fermion contact interaction to the Lagrangian. The effective cross section is modified by a structure function of the form

1 + (Q/Λ)^{2} ,  (1)

where Q is the 4-momentum transfer in the interaction and Λ is a parameter that sets the compositeness scale, which depends on both the initial and final state fermions in the scattering process. The experimental signal is an excess of events at high Q^{2}.

3.1. Quark Compositeness Searches

CDF has searched for quark compositeness by measuring the inclusive jet E_{T} spectrum^{6} and comparing these data with the next-to-leading order perturbative QCD predictions.^{7} Events are selected that have at least one transverse energy cluster with E_{T} > 120 GeV in the central calorimeter. The detector resolution is deconvoluted from the observed jet energy distribution to determine the produced jet E_{T} spectrum, which is shown in Fig. 2(a) along with the result of the next-to-leading order QCD calculation. The plots in Fig. 2(b) show the difference between the data and the QCD predictions normalized to the theory values, and illustrate the consistency of the QCD calculation with the data. Although the very highest E_{T} points are somewhat above the QCD prediction, this effect is not statistically significant.

These data have been fit to the next-to-leading order QCD prediction including the 4-fermion interaction term, yielding a lower limit on the quark compositeness scale of

Λ_{qq} > 1.4 TeV at 90% C.L.  (2)

This result can be contrasted with the limits of Λ_{qq} > 0.41 TeV from the UA1 collaboration.^{4} A recent CDF analysis of the dijet angular distribution sets a comparable limit of Λ_{qq} > 1.0 TeV at 90% C.L.^{8}

3.2. Lepton-Quark Compositeness

Lepton-quark compositeness in hadron-hadron collisions would first be observed as an excess of high-mass dilepton events above the expected Drell-Yan production rate. CDF has searched for evidence of this substructure in both the dielectron^{9} and dimuon^{10} data sets.

The event selection requires two well-identified lepton candidates with P_{T} > 20 GeV/c. Each lepton candidate is required to be isolated with respect to other particles in the event as the signal is expected to have lepton candidates that are uncorrelated with the energy flow in the collision whereas most of the background sources result in at least one non-isolated lepton candidate. The isolation cut requires the additional calorimeter energy in a cone of radius R ≡ \sqrt{(Δη)^{2} + (Δϕ)^{2}} = 0.4 surrounding each lepton candidate be less than 10% of the lepton candidate E_{T}. The lepton ID cuts are sufficient to reduce all expected backgrounds to of order one event.

The invariant mass distribution for the dielectron data is shown in Fig. 3 (the dimuon data is similar). The expected contribution from Drell-Yan production (excluding the Z pole) is also illustrated. The data is dominated by the Z resonance but the tail of events at larger masses is consistent with the expected Drell-Yan contribution. The absence of an excess of events at large invariant mass is used to set limits on the left and right-handed electron-quark 4-fermion contact interaction, i.e. on the

Fig. 2. The inclusive jet energy spectrum is shown in (a), after corrections for detector resolution effects. The curve is the prediction from the next-to-leading order QCD calculation. The difference between the data and the QCD prediction scaled to the theoretical value is plotted in (b).

compositeness scales Λ_{−}^{LL} and Λ_{+}^{LL}, respectively:

Λ_{−}^{LL} > 2.2 TeV at 95% C.L.  (3)
Λ_{+}^{LL} > 1.7 TeV at 95% C.L.  (4)

The dimuon data has the same absence of events at large invariant mass, which sets muon-quark compositeness limits of

Λ_{−}^{LL} > 1.6 TeV at 95% C.L.  (5)
Λ_{+}^{LL} > 1.4 TeV at 95% C.L.  (6)

4. Supersymmetry Searches

Supersymmetry^{13} remains an attractive extension to the standard model for several reasons: it naturally explains the “heirarchy” problem where interactions at the grand unification (GUT) energy scale of 10^{16} GeV lead to large cancellations that bring the Higgs mass down to the electroweak scale of order 100 GeV/c^{2} to 1 TeV/c^{2}; it provides a framework for string theory in which the four fundamental interactions stem

Fig. 3. The dielectron invariant mass distribution for the CDF data set. The prediction from Drell-Yan production is also shown.

from one force, and predicts the unification of the electroweak and strong forces at the GUT scale. The theory requires the existence of a new set of matter fields that are in 1to-1 correspondence with the quarks, leptons and vector bosons of the standard model. However, there has been no direct experimental evidence for these supersymmetric partners, making their discovery an important test of the model.

The supersymmetric partners to the quark and gluon, the squark (q̃) and gluino (g̃), are predicted to couple strongly to ordinary quarks and gluons, so that they should be copiously pair-produced in hadron-hadron collisions. The interactions of the supersymmetric particles are predicted to conserve a new quantum number, R, so that the produced squarks and gluinos will eventually decay to the lightest supersymmetric particle (LSP), which is usually assumed to be the photino (γ̃). The LSP does not interact with ordinary matter and therefore generates a missing transverse energy (E̸_{T}) signature in SUSY pair production.

Searches at e^{+}e^{−} colliders have set limits of Mq̃ > 45,^{11} but the most stringent limits have come from searches at hadron colliders. The UA1 collaboration has published limits^{12} of Mq̃ > 45 and Mg̃ > 53 at 90% C.L. while the CDF collaboration has previously set limits^{14} of Mq̃ > 74 and Mg̃ > 73 at 90% C.L.

The CDF collaboration has recently reported the results of a new SUSY search

Fig. 4. The missing transverse energy distribution for the events in the SUSY candidate sample. The events are required to have E̸_{T} > 40 GeV and at least two jets. The dashed line shows the distribution expected from the standard model sources described in the text. The inset figures show the E̸_{T} distribution expected for two specific scenarios: (a) Mq̃ = 125 GeV/c^{2} and Mg̃ = 5000 GeV/c^{2}, and (b) Mq̃ = 225 GeV/c^{2} and Mg̃ = 225 GeV/c^{2}.

that considerably extends the previous limits. The recent CDF search focuses on the SUSY decay modes

g̃ → qq̄γ̃
q̃ → qg̃ for Mq̃ > Mg̃  (7)
q̃ → qγ̃ for Mg̃ > Mq̃,

which results in events with significant amounts of missing transverse energy and up to six jets. Events are selected by requiring E̸_{T} > 40 GeV and at least two energy clusters in the calorimeter with observed E_{T} > 15 GeV and with |η| < 3.5. The E̸_{T} distribution for the 93 events that survive this selection is shown in Fig. 4.

There are several potential standard model sources of events with large E̸_{T}, with

Table 1. The estimated rate of E̸_{T} + ≥ 2 jet events from the largest standard model sources.

Background Source Number of Events
Z → νν̄  23 ± 8
W → τν̄  41 ± 15
W → μν̄  18 ± 6
W → eν̄  9 ± 3
Heavy Quarks  4 ± 4

the largest being the production and leptonic decay of W bosons and the production of Z bosons following by the decay into neutrino pairs. These background rates have been estimated using the measured boson cross sections and the ISAJET Monte Carlo programme^{15} to model the kinematics of the W and Z boson daughters. The other significant potential source of large E̸_{T} events are from pair production of top or bottom quarks. These rates have been estimated assuming a top quark with a mass of 91 GeV/c^{2}, which gives the most conservative estimate for this background. The estimated background event rates are listed in Table 1. The total background estimate is 91 ± 17 events, which agrees well with the observed rate.

A limit on the pair production of q̃’s and g̃’s is derived by fitting the observed E̸_{T} distribution to contributions from the background sources and from SUSY production for various choices of Mq̃ and Mg̃. Both the fraction of SUSY and background events are allowed to vary in the fit. The likelihood distribution for the number of SUSY events in the data is then used to set an upper limit on the SUSY pair production cross section as a function of the squark and gluino mass. The region in the Mq̃-Mg̃ plane where this upper limit is below the predicted cross section is shown in Fig. 5. The mass limits obtained when either the q̃ or g̃ is not present (or very massive) are

Mg̃ > 141 GeV/c^{2} at 90% C.L.  (8)
Mq̃ > 126 GeV/c^{2} at 90% C.L.  (9)

It has been pointed out that for such large q̃ and g̃ masses, the simple decay scenario assumed in establishing these limits is unlikely.^{16} More complex “cascade” decays of squarks and gluinos are expected involving additional supersymmetric particles that change the expected signature by increasing the number of daughter particles and softening their P_{T} spectra. This would tend to reduce the efficiency of the event selection and accordingly lower the mass bounds shown in Fig. 5(a). The size of this effect depends on several parameters of the model making it difficult to summarize the mass limits; however, the mass limits are typically reduced by 20-30 GeV/c^{2} for most parameter choices. The excluded region of squark and gluino masses for a specific set

Fig. 5. The region of squark and gluino masses excluded at 90% C.L. by the CDF search for large E̸_{T} and multijet events assuming the naive decay scenario is shown. The dashed line reflects the previous CDF limits. The excluded region when assuming a specific example of cascade decays is shown in (b). The cascade scenario assumes μ = −250, M_{H^{+}} = 500 GeV/c^{2} and tan β = 2.

of parameters (μ = −250, M_{H^{+}} = 500 GeV/c^{2} and tan β = 2) is shown in Fig. 5(b).

5. W′ and Z′ Searches

Numerous extensions to the standard model predict the existence of additional gauge symmetries beyond the SU(3)×SU(2)×U(1) symmetry of the standard model.^{17} These symmetries would require additional gauge bosons that in general would be produced in quark-antiquark collisions, although the masses of these bosons and the strength of their couplings to the quark and lepton generations are generally modeldependent. The CDF collaboration has searched for such bosons decaying leptonically into either a charged lepton and neutrino (W′) or into a lepton-antilepton pair (Z′).^{18}

The CDF search identified candidate events by requiring at least one high-P_{T} charged lepton candidate and a large E̸_{T} signature or by requiring two oppositely charged, high-P_{T} lepton candidates. A signal for a heavy W′ would be an excess of events at large transverse mass, while a signal for a heavy Z′ would be an excess of events at large invariant dilepton mass. These searches are insensitive to a W′ or Z′ degenerate with the standard model W or Z unless the coupling to the extra additional gauge boson is unusually large.

The transverse mass distribution for the events with one charged lepton and a large E̸_{T} is shown in Fig. 6, along with the predicted contribution from the standard model W. There is no excess of high mass events in the data; the events above the

Fig. 6. The transverse mass distribution for the data requiring a charged lepton with P_{T} > 30 GeV/c and E̸_{T} > 30 GeV (points). The histogram shows the prediction from standard model W production and decay.

W signal are consistent with the tail of the W resulting from the E̸_{T} resolution of the CDF detector. A lack of high mass events is also apparent in the dilepton data (see, for example, Fig. 3); the events above the Z resonance are consistent with the expected background from Drell-Yan production. An upper limit on the number of such events in the data is determined by fitting the shape of each mass distributions to a standard model contribution and a contribution from a heavier gauge boson.

The searches place an upper limit on the product of the production cross section for a heavy gauge boson, its coupling to the initial state quarks and its coupling to the final state lepton pair as a function of the mass of the gauge boson. The 95% C.L. upper limits for W′ and Z′ production are shown in Fig. 7(a) and (b). These figures also illustrate the expected rate for new gauge bosons that have the same couplings to quarks and leptons as the standard model W and Z, allowing for a M^{3} scaling as predicted in the standard model. These data require that

M_{W′} > 520 GeV/c^{2} at 95% C.L.  (10)
M_{Z′} > 412 GeV/c^{2} at 95% C.L.  (11)

assuming that the new gauge bosons have such standard model couplings.

Fig. 7. The 95% C.L. upper limit on the W′ production cross section as a function of the W′ mass is shown in (a). The dot-dashed line represents the prediction assuming standard model couplings. The corresponding limit for Z′ production cross section is shown in (b). The dashed line represents the standard model prediction.

6. Massive Stable Particle Search

Several theories predict extended multiplets of fermions containing massive particles that can be pair-produced in \overline{p} p collisions.^{19} These particles are typically produced with velocities much less than the speed of light, and therefore do not interact hadronically because the available kinetic energy in the particle-nucleon center-of-mass frame falls below the threshold for π production. The particles are therefore muon-like with the exception that they have velocities β much less than the speed of light. A recent CDF analysis places the most stringent limits on the pair-production cross section of such particles.^{20}

The collaboration searches for events with at least one charged particle with observed transverse momentum P_{T} > 25 GeV/c. The CDF detector can measure the transit time of particles that penetrate through the central hadron calorimeter (|η| < 1.1), as this subdetector is instrumented with a time-to-digital readout system on each calorimeter tower. The candidate particle’s energy deposition in the calorimeter is required to be that expected of a minimum-ionizing track and its measured velocity is required to be inconsistent with a particle with β = 1. The requirement that the particle not decay during its passage through the detector implicitly requires its lifetime to be > ∼ 10^{−8} s. Only two events pass all these requirements, while the background is estimated to be of order one to two events and come primarily from QCD jet production. Assuming that all of the candidate events come from the production of a heavy, stable

Fig. 8. The 95% C.L. upper limits on the pair-production cross section of a heavy, stable particle as a function of the particle’s mass. The dashed curve is the prediction from a specific model.

particle, the collaboration sets the limits on the pair-production cross section as a function of the particle’s mass shown in Fig. 8.

These data can be used to constrain specific models. For example, a unit-charged fermionic colour triplet^{21} with mass between 50 and 139 GeV/c^{2} is ruled out at the 95% C.L., while charge 2/3 and 4/3 objects are ruled out between the masses of 50 GeV/c^{2} and 116 and 140 GeV/c^{2}, respectively. Similar mass constraints can be applied to other exotic colour multiplets.

7. Search for a First Generation Leptoquark

Leptoquarks are particles that couple to both the leptons and quarks of a given flavour generation. Because of its quark couplings, a leptoquark should be pair-produced in \overline{p} p collisions with a rate that falls as a function of its mass, and it should decay preferentially into the quarks and leptons of the given generation. Leptoquarks with masses greater than ∼ 30 GeV/c^{2} would therefore give rise to events with several energetic leptons and quark jets. The CDF Collaboration has searched for the events that would arise from a first generation scalar leptoquark. Previous searches at e^{+}e^{−} colliders have set limits of M_{LQ} > 44.6 at 95% C.L.,^{22} while the most stringent limit from a \overline{p} p collider^{23} requires M_{LQ} > 74 GeV/c^{2} at 95% C.L.

The analysis searches for events with at least one electron and one positron candidate with P_{T} > 20 GeV/c in the pseudorapidity interval |η| < 1.0 and two jet clusters with E_{T} > 20 GeV. The primary background to a leptoquark signal arises from Drell-Yan production of an electron pair in association with two or more jets, and is dominated by Z+ multijet final states. The Z decays were removed by rejecting all events with invariant electron pair mass between 75 and 105 GeV/c^{2}. No candidate events are observed.

The collaboration sets a 95% confidence level upper limit on the leptoquark pair production cross section by convoluting a Poisson distribution for the number of observed events with a Gaussian probability distribution to take into account the systematic uncertainties in the estimate of the integrated luminosity and the lepton and jet selection efficiencies. This upper limit, shown in Fig. 9, falls with increasing leptoquark mass due to the variation in kinematic acceptance for leptoquark pair production with M_{LQ}. This upper limit can be used to set a lower limit on M_{LQ} for a specific model of leptoquark pair production. The curve in Fig. 9 results from the lowest order ISAJET prediction for this process, and sets a limit of

M_{LQ} > 113 GeV/c^{2} at 95% C.L.  (12)

This mass limit is sufficiently high that only experiments at the HERA ep collider will have the sensitivity to extend this search in the near future.

8. The Rare Decay W^{±} → π^{±}γ

The radiative decay W^{±} → π^{±}γ is predicted to be strongly suppressed. A standard model calculation^{24} predicts a partial width of

Γ(W → πγ)/Γ(W → eν_{e}) ∼ 3 × 10^{−8}.  (13)

However, this partial width is sensitive to both the W − γ coupling and to the QCD effects involved in the hadronization of the final state partons. There has also been speculation that it is a sensitive probe of physics outside the standard model.

Hadron collider experiments have now collected enough data on W decays that constraints on this partial width can be placed. Experiments at the CERN \overline{p} p Collider established an upper limit^{25} of

Γ(W → πγ)/Γ(W → eν_{e}) < 5.4 × 10^{−4} at 90% C.L.  (14)

The CDF collaboration has recorded a data set in which ∼ 24, 000 W + X events were produced, and has searched for events consistent with the radiative decay W → πγ. Events collected using the inclusive photon trigger were required to have a wellidentified photon candidate in the central detector. In addition, the events were required to have a jet with E_{T} > 25 GeV associated with a single charged particle. This selection results in 11 candidate events.

Fig. 9. The CDF 95% C.L. upper limit on the first generation leptoquark production cross section. The curve is the ISAJET prediction for leptoquark production, asuming a K-factor of 1.0.

Events from W decay are expected to have large πγ invariant mass. The signal region defined by 71 < M(πγ) < 89 GeV/c^{2} contains three events. However, background from QCD production of high P_{T} jets is estimated to contribute at least 1.4 events to this signal region. A 95% C.L. upper limit on the W → πγ branching ratio is determined by assuming that the three observed events come from a combination of this background and the W → πγ signal. This limit is

\frac{Γ(W^{±} → π^{±}γ)}{Γ(W^{±} → e^{±}ν_{e})} < 7.5 × 10^{−3} at 95% C.L.

If the standard model value of BR(W^{±} → e^{±}ν_{e}) = 0.109 is assumed (this implies that M_{top} > M_{W}), then we infer

BR(W^{±} → π^{±}γ) < 8.2 × 10^{−4} at 95% C.L.  (15)

is inferred.

This is still many orders of magnitude greater than the expected standard model rate, but does rule out a large partial width for this decay mode.

9. High E_{T} Events

The CDF collaboration has studied the events with the largest ∑ E_{T} depositions in the detector in order to search for the production of massive particles that may be produced in \overline{p} p collisions.^{26} Such events are characterized by unusually large energy depositions, high-P_{T} charged or neutral leptons or an unusual number of high-E_{T} jets. The standard model predicts that QCD production of two and three-jet final states should be the predominate source of such large E_{T} events.

The analysis selects those events with at least 400 GeV of observed transverse energy in the detector. There are 1189 events that satisfy this requirement. After removal of events coming from beam halo and cosmic ray interactions, 279 events remain in the event sample. The ∑ E_{T} distribution for these events is shown in Fig. 10. The QCD prediction, as calculated using the HERWIG Monte Carlo programme,^{27} is also shown for comparison.

The QCD prediction is in good agreement with the data distribution and rules out any obvious discrepancy with the standard model. The collaboration has also searched for unusual events with high-P_{T} electrons, muons or neutrinos, and has concluded that there is no evidence for anomolous production of such events. The characteristics of these large Q^{2} interactions are in good agreement with the standard model predictions for these final states.

10. Summary

The search for new phenomena using CDF has yielded no evidence for physics beyond the standard model. The collaboration has searched for: supersymmetric particles (q̃ or g̃); W′ and Z′ gauge bosons; quark or lepton compositeness; leptoquarks; anomolously large BR(W^{±} → π^{±}γ); and unusual (e.g. high ∑ E_{T}) events. The data is in good agreement with the standard model.

The CDF collaboration expects to increase its data set by a factor of ∼ 25 over the next year. This will increase the sensitivity of all of these searches, and will allow the collaboration to study even rarer processes (such as W^{±}W^{∓} production). Perhaps the most important goals of this coming run are the discovery of the long sought-after top quark and a measurement of the W boson mass to an accuracy of < ∼ 0.2%. However, an even more exciting prospect would be the discovery of new physics that would show us the way to a theory of elementary particles more fundamental than the standard model.

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Fig. 10. The ∑ E_{T} distribution for the the highest transverse energy events recorded by CDF. The histogram represents the prediction from QCD production, while the dashed lines represent the systematic uncertainty in this prediction resulting from the uncertainty on the calorimeter energy scale.

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