University of Ljubljana Faculty of Mathematics and Physics Department of Physics Seminar I Search for New Physics with leptonic decays of B s and B mesons Author: Veronika Vodeb Advisor: dr. Anže Zupanc Ljubljana, Maj 217 Abstract In this seminar the motivation for exploring leptonic decays B s µ + µ and B µ + µ, the main properties of these decays and why they are interesting for todays physicists will be examined. The experiments that measure branching ratios of these decays will also be described, as well as how the data obtained in the experiment is statistically analysed to give as precise results as possible.
Contents 1 Introduction 2 2 B (s) meson decays in the Standard Model 2 3 The search for New Physics 5 4 The experiment 7 4.1 The LHCb experiment................................... 7 5 Kinematics of B (s) decay into two muons 8 6 Data analysis 9 7 Latest experimental results 8 Conclusion 12 1 Introduction The Standard Model of particle physics describes the fundamental particles and their interactions via the strong, electromagnetic, and weak forces. It provides precise predictions for measurable quantities that can be tested experimentally [1]. The rare leptonic decays B s µ + µ and B µ + µ are highly suppressed and their branching fractions are precisely predicted in the Standard Model, which makes them sensitive probes of processes and particles beyond the Standard Model so called New Physics. Difference in observed branching fractions with respect to the predictions of the Standard Model would provide a direction in which the Standard Model should be extended [1]. Any observed deviation would therefore be a clear sign of physics beyond it [2]. 2 B (s) meson decays in the Standard Model Mesons are part of the hadron particle family, and are defined simply as particles composed of two quarks - one quark and one antiquark. Quarks, which make up all composite particles, come in six flavours up, down, strange, charm, top and bottom which give those composite particles their properties. Because mesons are composed of quarks, they participate in both the weak and strong interactions. Mesons with net electric charge also participate in the electromagnetic interaction. The weak interaction is unique in that it allows for quarks to swap their flavour for another [3]. In the Standard Model of particle physics, the Cabibbo Kobayashi Maskawa matrix or CKM matrix, is a unitary matrix which contains information on the strength of flavour-changing weak decays. The CKM matrix describes the probability of a transition from one quark i to another quark j. These transitions are proportional to V ij the magnitude of the corresponding CKM matrix element. These are: Vud Vus Vub.97425 ±.22.2252 ±.9 (4.15 ±.49) 3 Vcd Vcs Vcb =.23 ±.11 1.6 ±.23 (4.9 ± 1.1) 3. (1) V td V ts V tb (8.4 ±.6) 3 (42.9 ± 2.6) 3.89 ±.7 2
The Wolfenstein parameterization of the CKM matrix is an approximation of the standard parameterization. To order λ 3, it reads: V ud V us V ub 1 λ 2 /2 λ Aλ 3 (ρ iη) V cd V cs V cb = λ 1 λ 2 /2 Aλ 2 + O(λ 4 ), (2) V td V ts V tb Aλ 3 (1 ρ iη) Aλ 2 1 where the values of used constants are: λ =.2252 ±.9, A =.814 +.21.22, ρ =.135 +.31.16 and η =.349 +.15.17 [4]. There are two types of weak interaction. The first type is called the charged-current interaction because it is mediated by particles that carry an electric charge (the W + or W bosons). The second type is called the neutral-current interaction because it is mediated by a neutral particle, the Z boson [3]. Whether the process happens via charged W + or W boson or neutral Z boson is determined according to the change of the charge of the transforming quarks. Each quark has a charge of + 2e or 1 e according to the flavour of quarks as shown in the table 1 or an opposite 3 3 of that charge in the case of an antiquark, for example: the charge of an up antiquark (ū) is 2e, 3 whereas the charge of down antiquark ( d) is + 1 e and e is the elementary charge. 3 Figure 1: The table of quarks and the corresponding charges We determine via which current interaction the process happened based on the change of the initial quark s charge to final quark s charge as shown in Fig. 2. (a) (b) Figure 2: Feynman diagrams of propagation of W + and W charged currents: (a) if a + 2e quark 3 transforms into 1e quark, possitively charged boson is emitted and (b) if a 1 e quark changes into 3 3 e quark negatively charged boson is emitted. + 2 3 If a quark interacts with an antiquark (which happens in case of mesons), the transformations are possible between quarks with different absolute value of charge in which case charged bosons are 3
emitted or between a quark and its antiquark, where a neutral boson is emitted. Examples of such transformations are shown in Fig. 3. (a) (b) Figure 3: Feynman diagrams of propagation of W + charged current and Z neutral current: (a) if a + 2 3 e quark transforms into + 1 3 e antiquark, possitively charged W + boson is emitted (in case where up and down flavours are switched negatively charged boson W is emitted) and (b) interaction between quark and it s antiquark, where neutrally charged Z boson is emitted. In order to understand the decay mechanism of the Bs and B mesons via the weak interaction, we must therefore first know their quark structure. The B meson consists of a bottom (b) antiquark and a down (d) quark. The Bs meson consists again of a bottom (b) antiquark and as the name suggests a strange (s) quark. Bottom antiquark has Q b = + 1 e, whereas down and strange quarks 3 have Q d = Q s = 1 e. This leads us into thinking, that those interactions could happen via neutralcurrent weak interaction, where a neutral Z boson is emitted. Such diagrams for both Bs and B 3 mesons are shown in Fig. 4. (a) (b) Figure 4: The Feynman diagrams of Standard Model forbidden decays B s µ + µ and B µ + µ. Such transformations are forbidden in the Standard Model at the elementary level because the Z bosons cannot couple directly to quarks of different flavours, that is, there are no flavour changing neutral currents at the tree level known in the Standard Model [1]. Such transitions are possible only in higher orders which makes them then also highly suppressed, since every additional interaction vertex in the Feynman diagram reduces their probability significantly. Examples of Feynman diagrams of such decays are shown in Fig. 5. 4
(a) (b) (c) (d) Figure 5: Standard Model allowed Feynman diagrams of higher order flavour changing neutral current processes for the B s µ + µ and B µ + µ decays. The measurable quantity connected to these decays, which can also be observed in the experiment is the branching fraction. The branching fraction of a decay A B + C is defined as: B(A B + C) = Γ(A B + C), (3) Γ tot A where Γ(A B + C) is the decay width of the A B + C decay and Γ tot A is the total decay width of particle A. The branching fractions of B (s) µ+ µ decays, accounting for higher-order electromagnetic and strong interaction effects, and using lattice quantum chromodynamics to compute the B s and B meson decay constants, are reliably calculated in the Standard Model. Their values are B(B s µ + µ ) SM = (3.65±.23) 9 and B(B µ + µ ) SM = (1.6±.9) [5]. Concrete theoretical calculations and discussion about how these numbers are obtained are not the topic of this seminar. 3 The search for New Physics Many theories that seek to go beyond the Standard Model include new phenomena and particles, such as diagrams shown in Fig. 6, that can significantly modify the Standard Model branching fractions [1]. 5
(a) (b) Figure 6: Examples of processes for the same decay in theories extending the Standard Model, where new particles, denoted as X and X +, can alter the decay rate. Branching fractions B are proportional to the square of the absolute value of an amplitude for a certain process, so for example, the branching fraction for a certain decay in the Standard Model would be: B SM ASM 2, (4) where A SM can in general be a complex number. In case that there are other phenomena and particles involved that go beyond the Standard Model, then we have to write the amplitude for our process as the sum of two amplitudes, one of the Standard Model and the other of New Physics phenomena: A SM+NP = A SM + A NP, as shown in the Fig. 7. Branching fraction would then be: B ASM + A NP 2 = ASM 2 + ANP 2 + A SM A NP + A NP A SM. (5) Deviations from the Standard Model predictions for the branching ratios of certain decays would therefore imply that some unknown phenomena have altered the amplitude of the process and according to whether the amplitude is larger or smaller than expected, new constraints can be applied to the theories that extend the Standard Model. In case of decays that aren t highly suppressed in the Standard Model, such small deviations from the Standard Model predictions cannot be noticed in the experiment, since they are smaller then the error of the measurement. Decays such as B s and B to two oppositely charged muons are perfect for such observations, because Standard Model preditions of their branching ratios are extremelly small and therefore sensitive to such small deviations. Im Im NP SM+NP NP SM+NP SM Re SM Re (a) (b) Figure 7: New Physics phenomena can alter the amplitude for a certain process in such a way that (a) the absolute value or length of the new, combined amplitude is larger than the Standard Model amplitude or (b) the length of the combined amplitude is smaller than the Standard Model amplitude. 6
4 The experiment First experiment that searched for Bs µ + µ and B µ + µ decays was the CLEO detector at the Cornell Electron Storage Ring in 1984 [7], which means that the search for the Bs and B meson decays into two muons has been going on for more than 3 years and the experiments that are involved in this research are shown in the Fig. 8. The first evidence for the Bs µ + µ decay with a signal significance of 3.5 standard deviations was reported by LHCb in 212 [6], with measurement of its branching ratio B(Bs µ + µ ) = (3.2 +1.5 1.2) 9, together with the lowest upper limit on the B decay, B(B µ + µ ) < 9.4 at 95% confidence level. These results are in agreement with the Standard Model, which predicts about four Bs µ + µ decays occurring for every billion Bs mesons and about one B µ + µ decay occurring for every billion B mesons [5]. Let s see how these results are obtained and take a look at the experiemental setting needed to measure such decays. Limit (9% CL) or BF measurement 4 5 6 7 8 9 CLEO ARGUS UA1 CDF L3 D Belle BaBar LHCb CMS ATLAS CMS+LHCb SM: B s SM: B 212 213 214 µ + µ µ + µ 1985 199 1995 2 25 2 215 Year Figure 8: Search for the B s µ + µ and B µ + µ decays, reported by 11 experiments spanning more than three decades, and by the present results. Markers without error bars denote upper limits on the branching fractions at 9% confidence level, while measurements are denoted with errors bars delimiting 68% confidence intervals. The horizontal lines represent the SM predictions for the B s µ + µ and B µ + µ branching fractions1; the blue (red) lines and markers relate to the B s µ + µ (B µ + µ ) decay [1]. 8 9 4.1 The LHCb experiment The LHCb detector is designed to look for phenomena beyond the Standard Model. At the LHC, two counter-rotating beams of protons, contained and guided by superconducting magnets are brought into collision at four interaction points (IPs) [1]. The average number of produced B mesons in the LHCb experiment is of the order of 11. Assuming the branching fractions given by the Standard Model and accounting for the detection efficiencies, the predicted numbers of decays to be observed is 7
less then one hundred for Bs µ + µ and less then ten for B µ + µ. In order to observe a reliable deviation from the Standard Model prediction, branching ratios have to be precisely measured. This means that relevant decays that happened in the collider have to be efficiently reconstructed. Reconstruction of the B(s) mesons decaying into two oppositely charged muons is possible via detection of these two muons and measurement of their energy and momentum. Muons do not interact strongly and are too massive to emit a significant fraction of their energy by electromagnetic radiation. This gives them the ability to penetrate dense materials. The experiments use this characteristic to identify muons. They detect muons with special muon detectors called muon chambers, built on the outer side of the detector. In general, the only charged particles that can penetrate this far are muons, since all other charged particles are likely to have been absorbed within the calorimeters. The tracks of particles that can also be observed in the muon chamber are therefore mainly identified as muon tracks. To track the particles, the detector includes a high-precision tracking system consisting of a silicon strip vertex detector, a large-area silicon strip detector located upstream of a dipole magnet characterised by a field integral of 4 T m, and three stations of silicon strip detectors and straw drift tubes downstream of the magnet. The vertex detector has sufficient spatial resolution to distinguish the slight displacement of the weakly decaying b hadron from the primary production vertex where the two protons collided and produced it. The tracking detectors upstream and downstream of the dipole magnet measure the momenta of charged particles. The combined tracking system provides a momentum measurement with an uncertainty that varies from.4% at 5 Gev/c to.6% at GeV/c [1]. Figure 9: A scheme of the B (s) µ+ µ decay and its detection in the experiment 5 Kinematics of B (s) decay into two muons Decays compatible with B(s) µ+ µ (candidate decays) are found by combining the reconstructed trajectories of oppositely charged particles identified as muons. The separation between genuine B(s) µ+ µ decays and random combinations of two muons (combinatorial background) is achieved using the dimuon invariant mass m µ + µ and the established characteristics of B (s) meson decays. The dimuon invariant mass calculated from the energy and momenta of the reconstructed muons in natural units where c = 1 is: m 2 µ + µ = (E µ + + E µ )2 ( p µ + + p µ ) 2, (6) 8
where energy is obtained from the measured momentum and the mass of the particle, which is known once the particle is identified, as: E µ ± = m 2 µ + p 2 ± µ. (7) ± Because of their lifetimes of about 1.5 ps and their production at the LHC with momenta between a few Gev/c and Gev/c, B(s) mesons travel up to a few centimetres before they decay. Therefore, the B(s) µ+ µ decay vertex from which the muons originate (secundary vertex or SV), is required to be displaced with respect to the production vertex (primary vertex or PV) - the point where the two protons collide, as shown in the Fig. 9. Furthermore, the negative of the B(s) candidate s momentum vector is required to point back to the production vertex [1]. The LHCb implement triggers that specifically select events containing two muons. The triggers have a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, consisting of a large computing cluster that uses all the information from the detector, including the tracking, to make the final selection of events to be recorded for subsequent analysis. The large majority of events are triggered by requirements on one or both muons of the signal decay. The LHCb detector triggers on muons with transverse momentum p T > 1.5 GeV/c [8]. 6 Data analysis The signals appear as peaks at the Bs and B masses in the invariant-mass distributions, observed over background events. One of the components of the background is combinatorial in nature, as it is due to the random combinations of genuine muons. These produce a smooth dimuon mass distribution in the vicinity of the Bs and B masses. In addition to the combinatorial background, specific b-hadron decays, such as the semi-leptonic decays B π µ + ν, Bs K µ + ν, Λ b pµ ν, where the neutrinos cannot be detected and the charged hadrons are misidentified as muons, or B π µ + µ, where the neutral pion in the decay is not reconstructed, can mimic the dimuon decay of the B(s) mesons. The invariant mass of the reconstructed dimuon candidate for these processes (semi-leptonic background) is usually smaller than the mass of the Bs or B meson because the neutrino or another particle is not detected, except in the case of the decay Λ b pµ ν, which can also populate, with a smooth mass distribution, higher-mass regions. There is also a background component from hadronic two-body B(s) decays (peaking background) as B 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 B 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 [1]. The distributions for the backgrounds are obtained from simulation with the exception of the combinatorial background. The latter is obtained by interpolating from the data invariant-mass sidebands, after the substraction of the other background components. Excellent mass resolution is mandatory for distinguishing between B and Bs mesons with a mass difference of about 87 MeV/c 2 and for separating them from backgrounds. LHCb achieves a uniform mass resolution of about 25 MeV/c 2 [1]. Kinematic criteria, amongst others that have some ability to distinguish known signal events from background events, are combined into boosted decision trees (BDT). A BDT is a group of decision trees each placing different selection requirements on the individual variables to achieve the best discrimination between signal-like and background-like events. A BDT must be trained on collections of known background and signal events to generate the selection requirements on the 9
variables and the weights for each tree. 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, similar to an example shown in the Fig.. To avoid possible biases, the experiment kept the small mass interval that includes both the B s and B signals blind until all selection criteria were established [1]. Figure : An example of a BDT, where we are trying to distinguish between individuals who have high interest in computer games and those who do not. The branching fractions are determined from the observed number, efficiency-corrected, of B(s) mesons that decay into two muons and the total numbers of B(s) mesons produced. The total number of produced mesons is derived from the number of observed B + J/ψ(µ + µ )K + decays, with branching fraction B ( B + J/ψ(µ + µ )K +) = (6. ±.19) 5 and B K + π decays with B ( B K + π ) = 1.96 ±.5) 5 [1]. Hence, the Bs µ + µ branching fraction is expressed as a function of the number of signal events (N B s µ + µ ) in the data normalised to the numbers of B + J/ψK + and B K + π events: B ( B s µ + µ ) = N B s µ+ µ N norm. f d ɛ norm. B norm. = α norm. N B f s ɛ s µ + µ, (8) B s µ + µ where the norm. subscript refers to either of the normalisation channels. The values of the normalisation parameter α norm. obtained by LHCb from the two normalisation channels are found in good agreement and their weighted average is used. In this formula ɛ indicates the total event detection efficiency including geometrical acceptance, trigger selection, reconstruction, and analysis selection for the corresponding decay. The f d /f s factor is the ratio of the probability for a b quark to hadronise into a B as compared to a Bs meson; the probability to hadronise into a B + (f u ) is assumed to be equal to that into B (f d ) on the basis of theoretical grounds, and this assumption is checked on data. The value of f d /f s = 3.86 ±.22 measured by LHCb is used in this analysis. An analogous formula to that in equation (8) holds for the normalisation of the B µ + µ decay, with the notable difference that the f d /f s factor is replaced by f d /f u = 1 [1]. 7 Latest experimental results The latest experiemental results on the topic were reported by the LHCb collaboration in march 217. They reported measurements of the B s µ + µ and B µ + µ time-integrated branching
fractions and the first measurement of the Bs µ + µ effective lifetime. Results were based on data colected with the LHCb detector, corresponding to an integrated luminosity of 1 fb 1 of pp coliisions at the centre-of-mass energy s = 7 TeV, 2 fb 1 at s = 8 TeV and 1.4 fb 1 recorded at s = 13 TeV [8]. The values of the branching fractions obtained from the fit are B ( Bs µ + µ ) = (3.±.6 +.3.2) 9 and B ( B µ + µ ) = (1.5 +1.2+.2 1..1). The statistical uncertainty is derived by repeating the fit after fixing all the fit parameters, except the B µ + µ and Bs µ + µ branching fractions, the background yields and the slope of the combinatorial background, to their expected values. The mass distribution of the B(s) µ+ µ candidates with BDT >.5 is shown in the Fig. 11, together with the fit result [8]. Likelihood contours in the B(B µ + µ ) versus B(Bs µ + µ ) plane, the best-fit central value and the Standard Model expectation and its uncertainty are shown in Fig. 12. An excess of Bs µ + µ candidates with respect to the expectation from background is observed with a significance of 7.8 standard deviations (7.8σ), while the significance of the B µ + µ signal is 1.6 standard deviations (1.6σ). Since no significant B µ + µ signal is observed, an upper limit on the branching fraction is set, resulting in B ( B µ + µ ) < 3.4 at 95% confidence level [8]. ) 2 Candidates / ( 5 MeV/c 35 Total 3 25 2 15 LHCb BDT >.5 B s B µ + µ µ + µ Combinatorial + B h h' (s) (+) B B b + Λ B c π (K )µ + (+) π µ + µ pµ ν µ + J/ψµ ν µ ν µ 5 5 52 54 56 58 6 m [MeV/c 2 µ + µ ] Figure 11: Mass distribution of the selected B (s) µ+ µ candidates (black dots) with BDT >.5. The result of the fit is overlaid and the different components are detailed [8]. 11
Figure 12: Likelihood contours in the B(B µ + µ ) versus B(Bs 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 [1]. 8 Conclusion We have learned about the physics in the Standard Model that makes Bs µ + µ and B µ + µ decays very rare and the mechanism via which those decays can happen. We have examined the weak interaction and how its charged and neutral currents mediate the quark flavour transitions and in combination with the Cabibbo-Kobayashi-Maskawa matrix make certain decays more frequent than others, some of them even forbidden on the tree level in the Standard Model. In the next part we have looked at the experiemental setting that makes measurements of such decays possible, and the analysis that is required to filter the signal from the received data as efficiently as possible. We have looked at different types of backgrounds and their sources, that can cause false signal to appear as the actual signal. We can conclude that the observations of the Bs and B decays into to oppositely charged muons with the measured branching fraction B ( Bs µ + µ ) = (3. ±.6 +.3.2) 9 and an upper limit on the branching fraction B ( B µ + µ ) < 3.4 at 95% confidence level, do not show evidence for the physics beyond the Standard Model and are in agreement with the Standard Model predictions, with values B(Bs µ + µ ) SM = (3.65 ±.23) 9 and B(B µ + µ ) SM = (1.6 ±.9). 12
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