Lead I Ii Iii Ecg

The Cms And Lhcb Collaborations†

†Lists of the participants and their affiliations appear at the end of the Letter.

Arxiv:1411.4413V2 [Hep-Ex] 17 Aug 2015

The standard model of particle physics describes the fundamental particles and their interactions via the strong, electromagnetic, and weak forces. It pro- vides precise predictions for measurable quantities that can be tested exper- imentally. The probabilities, or branching fractions, of the strange B meson

(B0

s) and the B0 meson decaying into two oppositely charged muons (µ+ and µ−) are especially interesting because of their sensitivity to theories that ex- tend the standard model. The standard model predicts that the B0

S →Μ+Μ−

and B0 →µ+µ−decays are very rare, with about four of the former occurring

For Every Billion B0

s mesons produced and one of the latter occurring for every 10 billion B0 mesons1. A difference in the observed branching fractions with respect to the predictions of the standard model would provide a direction in which the standard model should be extended. Before the Large Hadron Col- lider (LHC) at CERN2 started operating, no evidence for either decay mode had been found.

Upper limits on the branching fractions were an order of magnitude above the standard model predictions. The CMS (Compact Muon Solenoid) and LHCb (Large Hadron Collider beauty) collaborations have per- formed a joint analysis of the data from proton-proton collisions that they collected in 2011 at a centre-of-mass energy of seven teraelectronvolts and in 2012 at eight teraelectronvolts. Here we report the first observation of the

B0

s →µ+µ−decay, with a statistical significance exceeding six standard devia- tions, and the best measurement so far of its branching fraction. Furthermore, we obtained evidence for the B0 →µ+µ−decay with a statistical significance of three standard deviations. Both measurements are statistically compatible with standard model predictions and allow stringent constraints to be placed on theories beyond the standard model. The LHC experiments will resume data taking in 2015, recording proton-proton collisions at a centre-of-mass en- ergy of 13 teraelectronvolts, which will approximately double the production

Rates For B0

s and B0 mesons and lead to further improvements in the precision of these crucial tests of the standard model. Experimental particle physicists have been testing the predictions of the standard model of particle physics (SM) with increasing precision since the 1970s.

Theoretical

developments have kept pace by improving the accuracy of the SM predictions as the experimental results gained in precision. In the course of the past few decades, the SM has passed critical tests from experiment, but it does not address some profound questions about the nature of the Universe. For example, the existence of dark matter, which has been confirmed by cosmological data3, is not accommodated by the SM. It also fails to explain the origin of the asymmetry between matter and antimatter, which after the Big Bang led to the survival of the tiny amount of matter currently present in the Universe3,4.

Many theories have been proposed to modify the SM to provide solutions to these open questions.

The B0

s and B0 mesons are unstable particles that decay via the weak interaction. The measurement of the branching fractions of the very rare decays of these mesons into a dimuon (µ+µ−) final state is especially interesting.

At the elementary level, the weak force is composed of a ‘charged current’ and a ‘neutral current’ mediated by the W ± and Z0 bosons, respectively. An example of the

1

charged current is the decay of the π+ meson, which consists of an up (u) quark of electrical charge +2/3 of the charge of the proton and a down (d) antiquark of charge +1/3. A pictorial representation of this process, known as a Feynman diagram, is shown in Fig. 1a. The u and d quarks are ‘first generation’ or lowest mass quarks. Whenever a decay mode is specified in this Letter, the charge conjugate mode is implied.

The B+ meson is similar to the π+, except that the light d antiquark is replaced by the heavy ‘third generation’ (highest mass quarks) beauty (b) antiquark, which has a charge of +1/3 and a mass of ∼5 GeV/c2 (about five times the mass of a proton). The decay B+ →µ+ν, represented in Fig. 1b, is allowed but highly suppressed because of angular momentum considerations (helicity suppression) and because it involves transitions be- tween quarks of different generations (CKM suppression), specifically the third and first generations of quarks. All b hadrons, including the B+, B0

S And B0 Mesons, Decay Predom-

inantly via the transition of the b antiquark to a ‘second generation’ (intermediate mass quarks) charm (c) antiquark, which is less CKM suppressed, in final states with charmed hadrons. Many allowed decay modes, which typically involve charmed hadrons and other particles, have angular momentum configurations that are not helicity suppressed.

The Neutral B0

s meson is similar to the B+ except that the u quark is replaced by a second generation strange (s) quark of charge −1/3. The decay of the B0

S Meson To

two muons, shown in Fig. 1c, is forbidden at the elementary level because the Z0 cannot couple directly to quarks of different flavours, that is, there are no direct ‘flavour changing neutral currents’. However, it is possible to respect this rule and still have this decay occur through the ‘higher order’ transitions such as those shown in Fig. 1d and e. These are highly suppressed because each additional interaction vertex reduces their probability of occurring significantly. They are also helicity and CKM suppressed. Consequently, the

Branching Fraction For The B0

s →µ+µ−decay is expected to be very small compared to the dominant b antiquark to c antiquark transitions. The corresponding decay of the B0

S →Μ+Μ−Decay: A, Π+ Meson Decay

through charged-current process; b, B+ meson decay through the charged-current process; c, a

B0

s decay through the direct flavour changing neutral current process, which is forbidden in the SM, as indicated by the large red “X; d and e, higher-order flavour changing neutral current

Processes For The B0

s →µ+µ−decay allowed in the SM; and f and g, examples of processes for the same decay in theories extending the SM, where new particles, denoted as X0 and X+, can alter the decay rate.

2

meson, where a d quark replaces the s quark, is even more CKM suppressed because it requires a jump across two quark generations rather than just one.

Accounting For Higher-Order

electromagnetic and strong interaction effects, and using lattice quantum chromo-

Dynamics To Compute The B0

s and B0 meson decay constants5–7, are reliably cal-

S →Μ+Μ−)Sm = (3.66 ± 0.23) × 10−9 And

B(B0 →µ+µ−)SM = (1.06 ± 0.09) × 10−10. Many theories that seek to go beyond the standard model (BSM) include new phe- nomena and particles8,9, such as in the diagrams shown in Fig. 1f and g, that can signif- icantly modify the SM branching fractions. In particular, theories with additional Higgs bosons10,11 predict possible enhancements to the branching fractions. A significant devia- tion of either of the two branching fraction measurements from the SM predictions would give insight on how the SM should be extended. Alternatively, a measurement compatible with the SM could provide strong constraints on BSM theories.

The ratio of the branching fractions of the two decay modes provides powerful dis- crimination among BSM theories12. It is predicted in the SM1,13–15 to be R ≡B(B0 →

S →Μ+Μ−)Sm = 0.0295+0.0028

−0.0025. Notably, BSM theories with the property of minimal flavour violation16 predict the same value as the SM for this ratio.

S →Μ+Μ−Was Presented By The Lhcb Collabora-

tion in 201217. Both CMS and LHCb later published results from all data collected in proton-proton collisions at centre-of-mass energies of 7 TeV in 2011 and 8 TeV in 2012. The measurements had comparable precision and were in good agreement18,19, although neither of the individual results had sufficient precision to constitute the first definitive

Observation Of The B0

s decay to two muons. In this Letter, the two sets of data are combined and analysed simultaneously to exploit fully the statistical power of the data and to account for the main correlations between them. The data correspond to total integrated luminosities of 25 fb−1 and 3 fb−1 for the CMS and LHCb experiments, respectively, equivalent to a total of approximately 1012

B0

s and B0 mesons produced in the two experiments together. Assuming the branching fractions given by the SM and accounting for the detection efficiencies, the predicted numbers of decays to be observed in the two experiments together are about 100 for

B0

s →µ+µ−and 10 for B0 →µ+µ−. The CMS20 and LHCb21 detectors are designed to measure SM phenomena with high precision and search for possible deviations. The two collaborations use different and complementary strategies. In addition to performing a broad range of precision tests of the SM and studying the newly-discovered Higgs boson22,23, CMS is designed to search for and study new particles with masses from about 100 GeV/c2 to a few TeV/c2. Since many of these new particles would be able to decay into b quarks and many of the SM measurements also involve b quarks, the detection of b-hadron decays was a key element in the design of CMS. The LHCb collaboration has optimised its detector to study matter-antimatter asymmetries and rare decays of particles containing b quarks, aiming to detect deviations from precise SM predictions that would indicate BSM effects. These different approaches, reflected in the design of the detectors, lead to instrumentation of complementary angular regions with respect to the LHC beams, to operation at different proton-proton collision rates, and to selection of b quark events with different efficiency (for experimental details,

3

see Methods). In general, CMS operates at a higher instantaneous luminosity than LHCb but has a lower efficiency for reconstructing low-mass particles, resulting in a similar

(S)) Mesons Decaying Into Two

muons. Muons do not have strong nuclear interactions and are too massive to emit a significant fraction of their energy by electromagnetic radiation. This gives them the unique ability to penetrate dense materials, such as steel, and register signals in detectors embedded deep within them. Both experiments use this characteristic to identify muons.

The experiments follow similar data analysis strategies.

B0

(s) →µ+µ−(candidate decays) are found by combining the reconstructed trajecto- ries (tracks) of oppositely charged particles identified as muons. The separation between

Genuine B0

(s) →µ+µ−decays and random combinations of two muons (combinatorial background), most often from semi-leptonic decays of two different b hadrons, is achieved using the dimuon invariant mass, mµ+µ−, and the established characteristics of B0

(S)-Meson

decays. For example, because of their lifetimes of about 1.5 ps and their production at the LHC with momenta between a few GeV/c and ∼100 GeV/c, B0

(S) Mesons Travel Up

to a few centimetres before they decay. Therefore, the B0

(S) →Μ+Μ−‘Decay Vertex’, From

which the muons originate, is required to be displaced with respect to the ‘production vertex’, the point where the two protons collide. Furthermore, the negative of the B0

(S)

candidate’s momentum vector is required to point back to the production vertex. These criteria, amongst others that have some ability to distinguish known signal events from background events, are combined into boosted decision trees (BDT)24–26.

A BDT is an ensemble of decision trees each placing different selection requirements on the individual variables to achieve the best discrimination between ‘signal-like’ and ‘background-like’ events. Both experiments evaluated many variables for their discrimi- nating power and each chose the best set of about ten to be used in its respective BDT.

These include variables related to the quality of the reconstructed tracks of the muons; kinematic variables such as transverse momentum (with respect to the beam axis) of the

Individual Muons And Of The B0

(s) candidate; variables related to the decay vertex topology and fit quality, such as candidate decay length; and isolation variables, which measure the activity in terms of other particles in the vicinity of the two muons or their displaced vertex. A BDT must be ‘trained’ on collections of known background and signal events to generate the selection requirements on the variables and the weights for each tree. In the case of CMS, the background events used in the training are taken from intervals of dimuon mass above and below the signal region in data, while simulated events are used for the signal. The data are divided into disjoint sub-samples and the BDT trained on one sub-sample is applied to a different sub-sample to avoid any bias. LHCb uses simulated events for background and signal in the training of its BDT. After training, the relevant BDT is applied to each event in the data, returning a single value for the event, with high values being more signal-like. To avoid possible biases, both experiments kept the small

Mass Interval That Includes Both The B0

s and B0 signals blind until all selection criteria were established. In addition to the combinatorial background, specific b-hadron decays, such as B0 →π−µ+ν where the neutrino cannot be detected and the charged pion is misidentified as a muon, or B0 →π0µ+µ−, where the neutral pion in the decay is not reconstructed,

Can Mimic The Dimuon Decay Of The B0

(s) mesons. The invariant mass of the reconstructed dimuon candidate for these processes (semi-leptonic background) is usually smaller than

The Mass Of The B0

s or B0 meson because the neutrino or another particle is not detected. There is also a background component from hadronic two-body B0

(S) Decays (Peaking Back-

ground) as B0 →K+π−, when both hadrons from the decay are misidentified as muons. These misidentified decays can produce peaks in the dimuon invariant-mass spectrum near the expected signal, especially for the B0 →µ+µ−decay. Particle identification algorithms are used to minimise the probability that pions and kaons are misidentified as muons, and thus suppress these background sources. Excellent mass resolution is mandatory for dis-

Tinguishing Between B0 And B0

s mesons with a mass difference of about 87 MeV/c2 and for separating them from backgrounds. The mass resolution for B0

S →Μ+Μ−Decays In

CMS ranges from 32 to 75 MeV/c2, depending on the direction of the muons relative to the beam axis, while LHCb achieves a uniform mass resolution of about 25 MeV/c2. The CMS and LHCb data are combined by fitting a common value for each branching fraction to the data from both experiments. The branching fractions are determined from

And The Total Numbers Of B0

(s) mesons produced.

Both Experiments Derive The Latter

from the number of observed B+ →J/ψK+ decays, whose branching fraction has been precisely measured elsewhere14. Assuming equal rates for B+ and B0 production, this gives the normalisation for B0 →µ+µ−. To derive the number of B0

S Mesons From This

B+ decay mode, the ratio of b quarks that form (hadronise into) B+ mesons to those

That Form B0

s mesons is also needed. Measurements of this ratio27,28, for which there is additional discussion in Methods, and of the branching fraction B(B+ →J/ψK+) are used to normalise both sets of data and are constrained within Gaussian uncertainties in the fit. The use of these two results by both CMS and LHCb is the only significant source of correlation between their individual branching fraction measurements. The combined fit takes advantage of the larger data sample to increase the precision while properly accounting for the correlation.

In the simultaneous fit to both the CMS and LHCb data, the branching fractions of the two signal channels are common parameters of interest and are free to vary. Other parameters in the fit are considered as nuisance parameters. Those for which additional knowledge is available are constrained to be near their estimated values by using Gaussian penalties with their estimated uncertainties while the others are free to float in the fit.

The ratio of the hadronisation probability into B+ and B0

S Mesons And The Branching

fraction of the normalisation channel B+ →J/ψK+ are common, constrained parameters. Candidate decays are categorised according to whether they were detected in CMS or LHCb and to the value of the relevant BDT discriminant. In the case of CMS, they are further categorised according to the data-taking period, and, because of the large variation in mass resolution with angle, whether the muons are both produced at large angles relative to the proton beams (central-region) or at least one muon is emitted at small angle relative to the beams (forward-region).

An Unbinned Extended Maximum

likelihood fit to the dimuon invariant-mass distribution, in a region of about ±500 MeV/c2

Around The B0

s mass, is performed simultaneously in all categories (12 categories from CMS and eight from LHCb). Likelihood contours in the plane of the parameters of

Cms And Lhcb (Lhc Run I)

Figure 2 | Weighted distribution of the dimuon invariant mass, mµ+µ−, for all cate- gories. Superimposed on the data points in black are the combined fit (solid blue line) and its

Components: The B0

s (yellow shaded area) and B0 (light-blue shaded area) signal components; the combinatorial background (dash-dotted green line); the sum of the semi-leptonic backgrounds (dotted salmon line); and the peaking backgrounds (dashed violet line). The horizontal bar on each histogram point denotes the size of the binning, while the vertical bar denotes the 68% confidence interval. See main text for details on the weighting procedure.

S →Μ+Μ−), Are Obtained By Constructing The Test

statistic −2∆lnL from the difference in log-likelihood (lnL) values between fits with fixed values for the parameters of interest and the nominal fit. For each of the two branching fractions, a one-dimensional profile likelihood scan is likewise obtained by fixing only the single parameter of interest and allowing the other to vary during the fits. Additional fits are performed where the parameters under consideration are the ratio of the branching

(S) →Μ+Μ−)Sm,

or the ratio R of the two branching fractions. The combined fit result is shown for all 20 categories in Extended Data Fig. 1. To represent the result of the fit in a single dimuon invariant-mass spectrum, the mass dis- tributions of all categories, weighted according to values of S/(S + B), where S is the

Expected Number Of B0

s signals and B is the number of background events under the B0

S

peak in that category, are added together and shown in Fig. 2. The result of the simulta- neous fit is overlaid. An alternative representation of the fit to the dimuon invariant-mass distribution for the six categories with the highest S/(S + B) value for CMS and LHCb, as well as displays of events with high probability to be genuine signal decays, are shown in the Extended Data Figs. 2–4.

× 10−10, where the uncertainties include both statistical and systematic sources, the latter contributing 35% and 18% of the total uncertainty for the

B0

s and B0 signals, respectively. Using Wilks’ theorem29, the statistical significance in unit of standard deviations, σ, is computed to be 6.2 for the B0

C

Figure 3 | Likelihood contours in the B(B0 →µ+µ−) versus B(B0 s →µ+µ−) plane. The (black) cross in a marks the best-fit central value. The SM expectation and its uncertainty is shown as the (red) marker. Each contour encloses a region approximately corresponding to the reported confidence level. b, c, Variations of the test statistic −2∆lnL for B(B0

S →Μ+Μ−)

(b) and B(B0 →µ+µ−) (c). The dark and light (cyan) areas define the ±1σ and ±2σ confidence intervals for the branching fraction, respectively. The SM prediction and its uncertainty for each branching fraction is denoted with the vertical (red) band.

and 3.2 for the B0 →µ+µ−mode. For each signal the null hypothesis that is used to compute the significance includes all background components predicted by the SM as well as the other signal, whose branching fraction is allowed to vary freely. The median expected significances assuming the SM branching fractions are 7.4 σ and 0.8 σ for the

B0

s and B0 modes, respectively. Likelihood contours for B(B0 →µ+µ−) versus B(B0

S →

µ+µ−) are shown in Fig. 3. One-dimensional likelihood scans for both decay modes are displayed in the same figure. In addition to the likelihood scan, the statistical significance and confidence intervals for the B0 branching fractions are determined using simulated experiments. This determination yields a significance of 3.0 σ for a B0 signal with respect to the same null hypothesis described above. Following the Feldman–Cousins30 procedure, ±1 σ and ±2 σ confidence intervals for B(B0 →µ+µ−) of [2.5, 5.6] × 10−10 and [1.4, 7.4] × 10−10 are obtained, respectively (see Extended Data Fig. 5).

The fit for the ratios of the branching fractions relative to their SM predictions yields

Sm = 3.7 +1.6

−1.4. Associated likelihood contours and one-dimensional likelihood scans are shown in the Extended Data Fig. 6. The measurements are compatible

S →Μ+Μ−And B0 →Μ+Μ−Decays At The

1.2 σ and 2.2 σ level, respectively, when computed from the one-dimensional hypothesis tests. Finally, the fit for the ratio of branching fractions yields R = 0.14 +0.08

−0.06, Which Is

compatible with the SM at the 2.3 σ level. The one-dimensional likelihood scan for this parameter is shown in Fig. 4. The combined analysis of data from CMS and LHCb, taking advantage of their full statistical power, establishes conclusively the existence of the B0

S →Μ+Μ−Decay And

provides an improved measurement of its branching fraction. This concludes a search that started more than three decades ago (see Extended Data Fig. 7), and initiates a phase of precision measurements of the properties of this decay. It also produces a three

Cms And Lhcb (Lhc Run I)

Figure 4 | Variation of the test statistic −2∆lnL as a function of the ratio of branch-

S →Μ+Μ−). The Dark And Light (Cyan) Areas

define the ±1σ and ±2σ confidence intervals for R, respectively. The value and uncertainty for R predicted in the SM, which is the same in BSM theories with the minimal flavour violation (MFV) property, is denoted with the vertical (red) band.

standard deviation evidence for the B0 →µ+µ−decay. The measured branching fractions of both decays are compatible with SM predictions. This is the first time that the CMS and LHCb collaborations have performed a combined analysis of sets of their data in order to obtain a statistically significant observation.

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