Combined fits to the supersymmetric explanation of anomalous lepton-photon-missing E_T events

The CDF experiment reported a lepton photon missing transverse energy (E_T) signal 3 sigma in excess of the Standard Model prediction in Tevatron Run I data. The excess can be explained by the resonant production of a smuon, which subsequently decays to a muon, a photon and a gravitino. Here, we perform combined fits of this model to the CDF gamma lepton missing E_T excess, the D0 measurement of the same channel and the CDF photon missing E_T channel. Although the rates of the latter two analyses are in agreement with the Standard Model prediction, our model is in good agreement with these data because their signal to background efficiency is low at the best-fit point. However, they help to constrain the model away from the best fit point.


Introduction
The CDF experiment has recently discovered an anomaly in the production rate of lepton-photon-E T in pp collisions at √ s = 1.8 TeV, using 86.34 pb −1 of Tevatron 1994-95 data [1]. While the number of events expected from the Standard Model (SM) were 7.6 ± 0.7, the experimentally measured number corresponded to 16. Moreover, 11 of these events involved muons (with 4.2 ± 0.5 expected) and 5 electrons (with 3.4 ± 0.3 expected).
In earlier papers [2] we suggested that the excess can be simply understood in terms of the minimal supersymmetric standard model (MSSM) which has the following ingredients: (1) the model is R-parity violating with an L-violating q q ′ µ χ 0 µG γ Fig. 1. Feynman diagram of resonant smuon production followed by neutralino decay.
λ ′ 211 coupling, and (2) the supersymmetric spectrum includes an ultra-light gravitino of mass ∼ 10 −3 eV. We have demonstrated in our earlier papers [2] that such a model provides a natural explanation of the CDF anomaly and explains not only the excess in the number of µγ E T events but also explains the main features of the kinematic distributions of the excess events. The excess can be explained using a small value of the L-violating coupling λ ′ 211 ∼ 0.01 because of the resonant production of smuons in the annihilation of an initial-state qq pair. The smuon thus produced decays predominantly into a bino-dominated neutralino and a muon, with the neutralino further decaying into a photon and a gravitino. The production and decay has been shown in the Feynman diagram in Fig. 1. The fact that the excess is seen in final states involving photons emerges very neatly in our model because the decay χ 0 1 → γG dominates overwhelmingly over other decay modes.
In the current article, we extend the previous studies by including two additional pieces of independent empirical information. We include the D0 Run I measurement [3] of the µγ missing E T process, as well as γ missing E T data coming from CDF in Run I [4]. The empirical background event-rate in the µγ E T channel is quite different in the CDF and D0 cases due to the different cuts employed. Our scenario predicts excesses in each of these channels, and we determine to what extent it is in accord with their measured rates. By performing a combined fit to all three event rates, we constrain the masses of the relevant sparticles in the event, as well as λ ′ 211 .

The model
In order that the cross-section for the production of the smuon resonance is substantial enough to account for the anomalous events, we need the left- handed smuon to be light i.e. mμ L ∼ 150 GeV. Further, one needs to couple the smuon to valence quarks in the initial state implying that the L-violating operator that we need is L 2 Q 1D1 corresponding to the coupling λ ′ 211 , which generates the interactionsμud andν µ dd (and charge conjugates), along with other supersymmetrised copies involving squarks. Therefore, the operator we invoke in our model predicts supersymmetric signals in other channels which manifest themselves through the production of either sneutrinos or squarks. In our model, we take the squarks to be heavy and so their effects on experimental observables will be negligible. On the other hand, the spontaneously broken SU(2) L symmetry in the MSSM implies that muon sneutrinos have a tree-level mass squared [5] where m µ is the mass of the muon, θ w the Weinberg angle, and tan β the ratio of the MSSM Higgs vacuum expectation values (cos 2β < 0). Since mν < mμ L if we assumed that smuons were produced at the Tevatron Run I energy, we should expect that muon sneutrinos could also be produced. The dominant production mechanism is resonant sneutrino production and subsequent decay, as shown in Fig. 2. It results in a γ E T experimental signature.
The pattern of masses of the super-particles suggested by the CDF µγ E T anomaly is the following: the smuon is around 150 GeV, and the only other light sparticles are the neutralino (which is typically about 45 GeV lighter than the smuon) and the ultra-light gravitino (which is as light as 10 −3 eV). We enforce degeneracy between the first two generations in order to avoid flavour changing neutral currents. Other sparticles do not play a role in this analysis, and are set to be arbitrarily heavy. Such a light gravitino materialises naturally in models of gauge-mediated supersymmetry breaking (GMSB) [6]. However, in the minimal version of GMSB models the chargino and the second-lightest neutralino are not much heavier than the neutralino and this feature of the minimal model is certainly not desirable for our considerations because it leads to large jets+γ + E T rates which are not seen by experiments 1 . If the minimal versions of GMSB models do not yield the pattern of super-particle masses that we need, then the obvious question to ask is what is the high-energy model that yields this mass spectrum at low energies. It is interesting to note that such a mass spectrum can arise in an alternate model of GMSB which is obtained from compactifying 11-dimensional M-theory on a 7-manifold of G2 holonomy [10]. For the purposes of this paper, however, we simply work with the low-energy model with the mass spectrum described above and do not worry about the high energy completion of this model.

Simulating the experiments
In our model, we have essentially four free parameters that are relevant to the data we fit: the gravitino mass, mG, the neutralino mass m χ 0 1 , the smuon mass, Mμ and the R-violating coupling λ ′ 211 . However, instead of simultaneously fitting the four parameters using the experimental data, we choose to work with fixed values of two of these parameters close to their best-fit values while performing fits in the two other parameters. For our analysis, we take other parameters like tanβ = 10 to be constant. The coupling, λ ′ 211 , is constrained from R π = Γ(π → eν)/(π → µν) [11] to be < 0.059 × md R 100 GeV [12]. But since the constraint involves a squark mass which is large in our model, it is not very relevant. While the production of the smuon resonance is through the R-violating mode, to produce the lγ E T excess we require that its decay goes through the R-conserving channel to a neutralino and muon final state. The R-violating decay of the slepton is possible but constrained, in principle, by the Tevatron di-jet data [13] which exclude a σ.B > 1.3 × 10 4 pb at 95% C.L. for a resonance mass of 200 GeV. However, in practice this does not provide a restrictive bound upon our scenario as long as the R-violating coupling is sufficiently small, < O(1). We also add that the di-jet bound is not restrictive because it suffers from a huge QCD background. By restricting λ ′ 211 to be small, we also avoid significant rates for the possible R-violating decays of We use the ISASUSY part of the ISAJET7.58 package [14] to generate the spectrum, branching ratios and decays of the sparticles. For an example of parameters, we choose (in the notation used by ref. [14]) tan β = 10 and A t,τ,b = 0. µ together with other flavour diagonal soft supersymmetry breaking parameters efficiency 40% 47% 51% 54% Table 1 Photon efficiency in the CDF γ E T analysis experiment luminosity observed number background Table 2 Observed number of events passing cuts in the text and Standard Model backgrounds for the three pieces of data included in the combined fit. The integrated luminosity for each analysis is also listed.
are set to be very large. We emphasise that this is a representative point in the supersymmetric parameter space and not a special choice.
As stated earlier, we present analyses for three sets of data in this paper: the CDF Run I data on lγ E T [1], the D0 Run I data on µγ E T [3] and the CDF Run I data on γ E T [4]. We now present our fiducial efficiencies and cuts, which mimic those of the relevant experiments. The CDF experiment detects photons with the constraints that the following pseudo-rapidity regions are excluded: |η γ | > 1, |η γ | < 0.05 and the region 0.77 < η γ < 1.0, 75 • < φ < 90 • . For the lγ E T data, photon detection efficiency within these cuts is η γ = 81%. Muons have a 60% detection efficiency if |η µ | < 0.6 or 45% if 0.6 ≤ η µ ≤ 1.1. To improve signal to background ratio efficiency, the following cuts are used: E T (µ) > 25 GeV, E T (γ) > 25 GeV and E T > 25 GeV. For the γ E T analysis, the CDF experiment [4] has chosen the following cuts: |η γ | ≤ 1.0, E γ T > 55 GeV and E T > 45 GeV. The cut on the photon E T is chosen to be as large as 55 GeV so as to beat down the background due to cosmic rays. Photon fiducial efficiencies are shown in table 1, and were obtained from ref. [4] In contrast, in order to simulate the D0 experiment, we specify |η µ | ≤ 1.0, |η γ | ≤ 1.1 or 1.5 ≤ |η γ | ≤ 2.5. We use the same cuts as D0: p µ T > 15 GeV, p γ T > 10 GeV on the muon and photon p T respectively. Also, E T ≥ 15 GeV, ∆R(µγ) ≥ 0.7 and M T (µ E T ) ≥ 30 GeV. Here, ∆R(µγ) is the distance between the photon and muon in pseudo-rapidity (η) and transverse angle (φ) space. M 2 T ≡ E 2 T − p 2 T is the transverse mass. Within these cuts, we have fiducial efficiencies of 71.1%, 50.1% and 51.0% for the trigger, muon and photon respectively. These cuts have been optimised by D0 with a view to studying the effects of anomalous gauge boson couplings on this final state. Unfortunately, the signal to background ratio for our model in the D0 analysis is far from optimal for the signal that we propose to study.

The observed number of events in the different analyses, and their Standard
Model backgrounds (taken from the experimental papers [1,3,4]) are shown in Table 2.
We now simulate the signal events for the processes in Figs. 1,2. We use HERWIG6.4 [15] including parton showering (but not including jet isolation cuts) to calculate cross-sections for single slepton production.

Combined fits
For each of the three data listed in Table 2, we can define a log likelihood defined by the Poissonian log-likelihood for n o observed events, n s expected signal events (for fixed values of SUSY breaking parameters), convoluted with a Gaussian probability distribution of the number of expected Standard Model background events n SM and its uncertainty σ SM : This is a good approximation provided n SM is several times σ SM above zero, as is the case here. ln(L(n s )/L(0)) is then the (signal+background) to background likelihood ratio for a given analysis. We can form the total fit likelihood ratio ln L tot by adding the likelihood ratio from each of the three analyses in Table 2. We will always consider two relevant parameters to be fixed and fit the model to the other two. The best-fit point in parameter space corresponds to the maximum value of the likelihood ratio and is found by using MINUIT [16]. −2 ln L tot max corresponds to the equivalent number of χ 2 (Standard Model) -χ 2 (best-fit)≡ ∆χ 2 . We have one degree of freedom, and therefore the 90% and 95% confidence level (C.L.) limits on parameters then lead to [16] ln L tot max − ln L tot = 1.35, 1.92 respectively in the fit. We will constrain M χ 0 1 > 100 GeV, as implied by γγ E T LEP2 data [17]. We now discuss the results of combined fits for various hyper planes of parameter space. 1 produces a lower cross-section because of kinematical suppression, but this effect can be compensated by raising λ ′ 211 , thus increasing the production rate. The best-fit point is λ ′ 211 = 0.11, M χ 0 1 = 100 GeV, with ∆χ 2 = 6.90. Fig. 3a shows that we expect between 3-8 signal events in the CDF lγ E T channel. This data dominates the fit because backgrounds (and their uncertainties) are larger in the other analyses. 1.5-6 events are expected at D0, and between 1.5 and 8 signal events were predicted for the CDF γ E T signature, depending on the parameters.   Fig. 5a shows that we expect between 1-12 signal events in the CDF lγ E T channel. 1-8 events are expected at D0, and up to 4 signal events were predicted for the CDF γ E T signature, depending on the parameters. Mμ = 142 GeV, with ∆χ 2 = 6.76. Fig. 6a shows that we expect between 1-6 signal events in the CDF lγ E T channel. 0-4 events are expected at D0, and up to 0.2 signal events were predicted for the CDF γ E T signature, depending on the parameters.

Conclusions
We have provided combined fits for a supersymmetric model that explains the lγ E T CDF Run I excess in events, which was at the 2.7σ level [1]. We have used the Run I γ E T data recently presented by CDF, as well as anomalous trilinear gauge boson coupling data from D0. Constraints upon various hyper planes in the gravitino, smuon, neutralino and R-parity violating coupling space have been displayed. In totality, the signal rates predicted by our model for the three analyses fit the data well, best fit points corresponding to a ∆χ 2 = 6.9 fit compared to the Standard Model, for one degree of freedom.
Unfortunately, background rates in the D0 anomalous trilinear gauge boson coupling data are too high for it to be very sensitive to the predicted signal rate. We note, however, that another analysis on existing D0 Run I data with cuts optimised to test a µγ E T excess would provide a good test of our scenario.
The CDFγ E T channel suffers from a high E T (γ) > 55 cut because of cosmic backgrounds, which unfortunately also cuts most of the signal. It was shown in ref. [2], that if the cut could be reduced to 25 GeV, a signal rate of several times that in the CDF lγ E T channel is possible. This is an important observation for Run II, where cosmic backgrounds could be cut by additional timing information in the detector. We look forward to the analysis of Run II data, which will be the final arbiter on lγ E T excess, as well as on our scenario.