Search for the decay D0 to \pi+ \pi- \mu+ \mu-

A search for the D0 to \pi+ \pi- \mu+ \mu- decay, where the muon pair does not originate from a resonance, is performed using proton-proton collision data corresponding to an integrated luminosity of 1.0 fb-1 recorded by the LHCb experiment at a centre-of-mass energy of 7 TeV. No signal is observed and an upper limit on the relative branching fraction with respect to the resonant decay mode D0 to \pi+ \pi- \phi(to \mu+ \mu-), under the assumption of a phase-space model, is found to be B(D0 to \pi+ \pi- mu+ mu-)/B(D0 to \pi+ \pi- \phi(to \mu+ \mu-))<0.96 at the 90% confidence level. The upper limit on the absolute branching fraction is evaluated to be B(D0 to \pi+ \pi- \mu+ \mu-)<5.5 x 10-7 at 90% confidence level. This is the most stringent to date.

with potential for physics beyond the SM, such as FCNC decays of D mesons, and the 8 coupling of up-type quarks in electroweak processes illustrated in Fig. 1, to be probed 9 more precisely. 10 The total branching fraction for these decays is expected to be dominated by long- asymmetries that allow for a theoretically robust separation of long-and short-distance 16 effects, the latter being more sensitive to physics beyond the SM [4]. No such decays have 17 been observed to date and the most stringent limit reported is B(D 0 → π + π − µ + µ − ) < 18 3.0 × 10 −5 at 90% confidence level (CL) by the E791 collaboration [5]. The same processes 19 can be probed using D + (s) → π + µ + µ − decays. Upper limits on their branching fractions have 20 been recently set to B(D + → π + µ + µ − ) < 7.3 × 10 −8 and B(D + s → π + µ + µ − ) < 4.1 × 10 −7 21 at 90% CL by the LHCb collaboration [6].
This Letter presents the result of a search for the D 0 → π + π − µ + µ − decay, in which 23 the muons do not originate from a resonance, performed using D * + → D 0 π + decays, with 24 the D * + meson produced directly at the pp collision primary vertex. The reduction in  The trigger [10] consists of a hardware stage, based on information from the calorimeter 52 and muon systems, followed by a software stage, which applies a full event reconstruction.

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The hardware trigger selects muons with transverse momentum, p T , exceeding 1.48 GeV/c, 54 and dimuons whose product of p T values exceeds (1.3 GeV/c) 2 . In the software trigger, 55 at least one of the final state muons is required to have momentum larger than 8 GeV/c, 56 and to have an impact parameter, IP, defined as the minimum distance of the particle 57 trajectory from the associated primary vertex (PV) in three dimensions, greater than 58 100 µm. Alternatively, a dimuon trigger accepts events with oppositely charged muon 59 candidates having good track quality, p T exceeding 0.5 GeV/c, and momentum exceeding 60 6 GeV/c. In a second stage of the software trigger, two algorithms select D 0 → π + π − µ + µ − 61 candidates. The first algorithm, used to increase the efficiency in the highest dimuon mass  Figure 1: Leading Feynman diagrams for the FCNC decay D 0 → π + π − µ + µ − in the SM. Candidate D 0 → π + π − µ + µ − decays are required to originate from D * + → D 0 π + decays.

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The D 0 candidate is formed by combining two pion and two muon candidates where both particles, the maximum distance of closest approach between all pairs of tracks forming the 92 D 0 and D * + candidates, and the p T and χ 2 IP of the bachelor pion from the D * + candidate.

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The BDT discriminant is used to classify each candidate. Assuming a signal branching 94 fraction of 10 −9 , an optimisation study is performed to choose the combined BDT and hypotheses (DLL) [8,18]. The optimisation procedure yields an optimal threshold for the 100 BDT discriminant and a minimum value for DLL µπ (the difference between the muon and 101 pion hypotheses) of 1.5 for both µ candidates. In addition, the pion candidate is required 102 to have DLL Kπ less than 3.0 and DLL pπ less than 2.0, and each muon candidate must not 103 share hits in the muon stations with any other muon candidate. In the 2% of events in 104 which multiple candidates are reconstructed, the candidate with the smallest D 0 vertex χ 2 105 is chosen.

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The bachelor π + of the D * + → D 0 π + decay is constrained to the PV using a Kalman filter [19]. This constraint improves the resolution for the mass difference between the D * + and the D 0 candidates, ∆m ≡ m(π + π − µ + µ − π + )−m(π + π − µ + µ − ), by a factor of two, down Candidates from the kinematically similar decay D 0 → π + π − π + π − form an important 111 peaking background due to the possible misidentification of two oppositely charged pions as 112 muons. A sample of this hadronic background is retained with a selection that is identical to 113 that applied to the signal except that no muon identification is required. These candidates 114 are then reconstructed under the D 0 → π + π − µ + µ − hypothesis and a subsample of the 115 candidates, in which at least one such pion satisfies the muon identification requirements, 116 is used to determine the shape of this peaking background in each region of dimuon mass, Under the correct mass hypotheses the D 0 → π + π − π + π − candidates are also 118 used as a control sample to check differences between data and simulation that may affect 119 the event selection performance. Moreover, they are used to determine the expected signal 120 shape in each m(µ + µ − ) region by subdividing the D 0 → π + π − π + π − sample in the same 121 regions of m(π + π − ).

Range description
mass regions and is fitted with a double Crystal Ball function. This provides a well-defined 148 shape for this prominent background, which is included in the fit to the signal sample. two-dimensional shape used in the fit implicitly assumes that m(π + π − µ + µ − π + ) and ∆m 154 are not correlated.

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All the floating coefficients are allowed to vary independently in each of the m(µ + µ − ) 156 regions. Migration between the regions is found to be negligible from simulation studies.

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The yield observed in the φ region is used to normalise the yields in the signal regions.  MeV/c 2 . The data are shown as points (black) and the fit result (dark blue line) is overlaid. The components of the fit are also shown: the signal (filled area), the D 0 → π + π − π + π − background (green dashed line) and the non-peaking background (red dashed-dotted line).

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The values for the efficiency ratio and high-m(µ + µ − ) regions, as estimated from simulations, are 0.24 ± 0.03 and 0.69 ± 0.11, 183 respectively, where the uncertainty reflects the limited statistics of the simulated samples.

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The efficiencies for reconstructing the signal decay mode and the reference mode include 185 the geometric acceptance of the detector, the efficiencies for track reconstruction, particle MeV/c 2 . The data are shown as points (black) and the fit result (dark blue line) is overlaid. The components of the fit are also shown: the signal (filled area), the D 0 → π + π − π + π − background (green dashed line) and the non-peaking background (red dashed-dotted line).
Moreover, tighter particle identification requirements are responsible for a lower efficiency 189 ratio in the low-m(µ + µ − ) region. The accuracy with which the simulation reproduces the 190 track reconstruction and particle identification is limited. Therefore, the corresponding 191 efficiencies are also studied in data and systematic uncertainties are assigned.

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A possible alternative normalisation, with respect to the ρ/ω dimuon mass region, would 213 be heavily limited by the low statistics available and the relatively high contamination 214 from D 0 → π + π − π + π − , as can be seen in Figure 2b. between simulation and data is found to a level of 1%, which is assigned as a systematic 221 uncertainty.

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The particle identification performance for hadrons is investigated by comparing the 223 efficiency in D 0 → π + π − π + π − candidates in data and simulation as a function of the 224 DLL Kπ requirement. The largest discrepancy between data and simulation on the efficiency 225 ratio is found to be 4% and is taken as a systematic uncertainty.

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Several quantities, particularly the impact parameter, are known to be imperfectly 227 reproduced in the simulation. Since this may affect the reconstruction and selection 228 efficiency, a systematic uncertainty is estimated by smearing track properties to reproduce 229 the distributions observed in data. The corresponding variation in the efficiency ratio yields 230 an uncertainty of 5%. The BDT description in simulation is checked using background-231 subtracted D 0 → π + π − π + π − candidates where no significant difference is seen. Therefore, 232 no extra systematic uncertainty is assigned.  The uncertainties on the efficiency ratio due to the finite size of the simulated samples 241 in the low-and high-m(µ + µ − ) regions are 12% and 16% respectively. The production of 242 significantly larger sample of simulated events is impractical due to the low reconstruction 243 and selection efficiencies, particularly in the signal regions. In addition, the statistical 244 uncertainties of the fitted yields in data, listed in Table 1, dominate the total uncertainty.

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The systematic uncertainties affecting the yield ratio are taken into account when 252 the branching fraction limits are calculated. The shapes of the signal peaks are taken 253 from the D 0 → π + π − π + π − samples separately for each m(µ + µ − ) region to account for 254 variations of the shape as a function of m(µ + µ − ). The impact of alternative shapes for the 255 signal and misidentified D 0 → π + π − π + π − decays on the fitted yields and the final limit 256 are investigated. The signal and misidentification background shapes in the signal regions 257 are fitted using the shapes obtained in the φ region, and from D 0 → π + π − π + π − events 258 reconstructed as D 0 → π + π − µ + µ − , but without any muon identification requirements.

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The change in the result is negligible. π + π − µ + µ − to D 0 → π + π − φ(→ µ + µ − ) branching fraction ratio and on the absolute 267 D 0 → π + π − µ + µ − branching fraction are determined using the observed distribution 268 of CL s as a function of the branching fraction in each m(µ + µ − ) search region. The 269 extrapolation to the full m(µ + µ − ) phase space is performed assuming a four-body phase 270 space model for D 0 → π + π − µ + µ − for which fractions in each m(µ + µ − ) region are quoted 271 in Table 1. The observed distribution of CL s as a function of the total branching fraction 272 ratio for D 0 → π + π − µ + µ − is shown in Fig. 4. A similar distribution for the absolute 273 the background-only hypothesis are given in Table 3 and in Table 4. The p-values are 276 computed for the branching fraction value at which CL s+b equals 0.5. Despite the smaller 277 event yield for D 0 → π + π − µ + µ − relative to D 0 → π + π − φ(→ µ + µ − ), the upper limit on

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A search for the D 0 → π + π − µ + µ − decay is conducted using pp collision data, corresponding 295 to an integrated luminosity of 1.0 fb −1 at √ s = 7 TeV recorded by the LHCb experiment.