University of LjubljanaFaculty of Mathematics and Physics

Department of Physics

Seminar I

Search for New Physics with leptonic decays of B0s

and B0 mesons

Author: Veronika Vodeb

Advisor: dr. Anze Zupanc

Ljubljana, Maj 2017

Abstract

In this seminar the motivation for exploring leptonic decays B0s → µ+µ− and B0 → µ+µ−,

the main properties of these decays and why they are interesting for todays physicists will beexamined. 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 preciseresults as possible.

Contents

1 Introduction 2

2 B0(s) meson decays in the Standard Model 2

3 The search for New Physics 5

4 The experiment 74.1 The LHCb experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 Kinematics of B0(s) decay into two muons 8

6 Data analysis 9

7 Latest experimental results 10

8 Conclusion 12

1 Introduction

The Standard Model of particle physics describes the fundamental particles and their interactions viathe strong, electromagnetic, and weak forces. It provides precise predictions for measurable quantitiesthat can be tested experimentally [1]. The rare leptonic decays B0

s → µ+µ− and B0 → µ+µ− arehighly suppressed and their branching fractions are precisely predicted in the Standard Model, whichmakes them sensitive probes of processes and particles beyond the Standard Model – so called NewPhysics. Difference in observed branching fractions with respect to the predictions of the StandardModel would provide a direction in which the Standard Model should be extended [1]. Any observeddeviation would therefore be a clear sign of physics beyond it [2].

2 B0(s) meson decays in the Standard Model

Mesons are part of the hadron particle family, and are defined simply as particles composed of twoquarks - one quark and one antiquark. Quarks, which make up all composite particles, come in sixflavours – up, down, strange, charm, top and bottom – which give those composite particles theirproperties. Because mesons are composed of quarks, they participate in both the weak and stronginteractions. Mesons with net electric charge also participate in the electromagnetic interaction. Theweak interaction is unique in that it allows for quarks to swap their flavour for another [3]. In theStandard Model of particle physics, the Cabibbo–Kobayashi–Maskawa matrix or CKM matrix, is aunitary matrix which contains information on the strength of flavour-changing weak decays. TheCKM matrix describes the probability of a transition from one quark i to another quark j. Thesetransitions are proportional to

∣∣Vij∣∣ – the magnitude of the corresponding CKM matrix element.These are:∣∣Vud∣∣ ∣∣Vus∣∣ ∣∣Vub∣∣∣∣Vcd∣∣ ∣∣Vcs∣∣ ∣∣Vcb∣∣∣∣Vtd∣∣ ∣∣Vts∣∣ ∣∣Vtb∣∣

=

0.97425± 0.00022 0.2252± 0.0009 (4.15± 0.49)× 10−3

0.230± 0.011 1.006± 0.023 (40.9± 1.1)× 10−3

(8.4± 0.6)× 10−3 (42.9± 2.6)× 10−3 0.89± 0.07

. (1)

2

The Wolfenstein parameterization of the CKM matrix is an approximation of the standard parame-terization. To order λ3, it reads:Vud Vus Vub

Vcd Vcs VcbVtd Vts Vtb

=

1− λ2/2 λ Aλ3(ρ− iη)−λ 1− λ2/2 Aλ2

Aλ3(1− ρ− iη) −Aλ2 1

+O(λ4), (2)

where the values of used constants are: λ = 0.2252 ± 0.0009, A = 0.814+0.021−0.022, ρ = 0.135+0.031

−0.016 andη = 0.349+0.015

−0.017 [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). Thesecond type is called the neutral-current interaction because it is mediated by a neutral particle,the Z0 boson [3]. Whether the process happens via charged W+ or W− boson or neutral Z0 bosonis determined according to the change of the charge of the transforming quarks. Each quark hasa charge of +2

3e or −1

3e according to the flavour of quarks as shown in the table 1 or an opposite

of that charge in the case of an antiquark, for example: the charge of an up antiquark (u) is −23e,

whereas the charge of down antiquark (d) is +13e and e is the elementary charge.

Figure 1: The table of quarks and the corresponding charges

We determine via which current interaction the process happened based on the change of theinitial 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 +23e quark

transforms into −13e quark, possitively charged boson is emitted and (b) if a −1

3e quark changes into

+23e quark negatively charged boson is emitted.

If a quark interacts with an antiquark (which happens in case of mesons), the transformationsare 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 suchtransformations are shown in Fig. 3.

(a) (b)

Figure 3: Feynman diagrams of propagation of W+ charged current and Z0 neutral current: (a) if a+2

3e quark transforms into +1

3e antiquark, possitively charged W+ boson is emitted (in case where

up and down flavours are switched negatively charged boson W− is emitted) and (b) interactionbetween quark and it’s antiquark, where neutrally charged Z0 boson is emitted.

In order to understand the decay mechanism of the B0s and B0 mesons via the weak interaction,

we must therefore first know their quark structure. The B0 meson consists of a bottom (b) antiquarkand a down (d) quark. The B0

s meson consists again of a bottom (b) antiquark and as the namesuggests a strange (s) quark. Bottom antiquark has Qb = +1

3e, whereas down and strange quarks

have Qd = Qs = −13e. This leads us into thinking, that those interactions could happen via neutral-

current weak interaction, where a neutral Z0 boson is emitted. Such diagrams for both B0s and B0

mesons are shown in Fig. 4.

(a) (b)

Figure 4: The Feynman diagrams of Standard Model forbidden decays B0s → µ+µ− and B0 → µ+µ−.

Such transformations are forbidden in the Standard Model at the elementary level because theZ0 bosons cannot couple directly to quarks of different flavours, that is, there are no flavour changingneutral currents at the tree level known in the Standard Model [1]. Such transitions are possibleonly in higher orders which makes them then also highly suppressed, since every additional interac-tion vertex in the Feynman diagram reduces their probability significantly. Examples of Feynmandiagrams of such decays are shown in Fig. 5.

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(a) (b)

(c) (d)

Figure 5: Standard Model allowed Feynman diagrams of higher order flavour changing neutral currentprocesses for the B0

s → µ+µ− and B0 → µ+µ− decays.

The measurable quantity connected to these decays, which can also be observed in the experimentis the branching fraction. The branching fraction of a decay A→ B + C is defined as:

B(A→ B + C) =Γ(A→ B + C)

ΓtotA

, (3)

where Γ(A→ B + C) is the decay width of the A→ B + C decay and ΓtotA is the total decay width

of particle A. The branching fractions of B0(s) → µ+µ− decays, accounting for higher-order electro-

magnetic and strong interaction effects, and using lattice quantum chromodynamics to compute theB0s and B0 meson decay constants, are reliably calculated in the Standard Model. Their values areB(B0

s → µ+µ−)SM = (3.65±0.23)×10−9 and B(B0 → µ+µ−)SM = (1.06±0.09)×10−10 [5]. Concretetheoretical calculations and discussion about how these numbers are obtained are not the topic ofthis 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 branchingfractions [1].

5

(a) (b)

Figure 6: Examples of processes for the same decay in theories extending the Standard Model, wherenew particles, denoted as X0 and X+, can alter the decay rate.

Branching fractions B are proportional to the square of the absolute value of an amplitude fora certain process, so for example, the branching fraction for a certain decay in the Standard Modelwould be:

BSM ∝∣∣ASM∣∣2, (4)

where ASM can in general be a complex number. In case that there are other phenomena andparticles involved that go beyond the Standard Model, then we have to write the amplitude for ourprocess as the sum of two amplitudes, one of the Standard Model and the other of New Physicsphenomena:

ASM+NP = ASM +ANP ,

as shown in the Fig. 7. Branching fraction would then be:

B ∝∣∣ASM +ANP

∣∣2 =∣∣ASM ∣∣2 +

∣∣ANP ∣∣2 +A∗SMANP +A∗NPASM . (5)

Deviations from the Standard Model predictions for the branching ratios of certain decays wouldtherefore imply that some unknown phenomena have altered the amplitude of the process and ac-cording to whether the amplitude is larger or smaller than expected, new constraints can be appliedto the theories that extend the Standard Model. In case of decays that aren’t highly suppressed in theStandard Model, such small deviations from the Standard Model predictions cannot be noticed in theexperiment, since they are smaller then the error of the measurement. Decays such as B0

s and B0 totwo oppositely charged muons are perfect for such observations, because Standard Model preditionsof their branching ratios are extremelly small and therefore sensitive to such small deviations.

NP

SM

SM+NP

Re

Im

(a)

NP

SM

SM+NP

Re

Im

(b)

Figure 7: New Physics phenomena can alter the amplitude for a certain process in such a waythat (a) the absolute value or length of the new, combined amplitude is larger than the StandardModel amplitude or (b) the length of the combined amplitude is smaller than the Standard Modelamplitude.

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4 The experiment

First experiment that searched for B0s → µ+µ− and B0 → µ+µ− decays was the CLEO detector

at the Cornell Electron Storage Ring in 1984 [7], which means that the search for the B0s and B0

meson decays into two muons has been going on for more than 30 years and the experiments that areinvolved in this research are shown in the Fig. 8. The first evidence for the B0

s → µ+µ− decay witha signal significance of 3.5 standard deviations was reported by LHCb in 2012 [6], with measurementof its branching ratio B(B0

s → µ+µ−) = (3.2+1.5−1.2) × 10−9, together with the lowest upper limit on

the B0 decay, B(B0 → µ+µ−) < 9.4× 10−10 at 95% confidence level. These results are in agreementwith the Standard Model, which predicts about four B0

s → µ+µ− decays occurring for every billionB0s mesons and about one B0 → µ+µ− decay occurring for every 10 billion B0 mesons [5]. Let’s see

how these results are obtained and take a look at the experiemental setting needed to measure suchdecays.

Year1985 1990 1995 2000 2005 2010 2015

Lim

it (9

0% C

L) o

r B

F m

easu

rem

ent

10−10

9−10

8−10

7−10

6−10

5−10

4−10

−µ+µ → 0sSM: B

−µ+µ → 0SM: BD0L3CDFUA1ARGUSCLEO

CMS+LHCbATLASCMSLHCbBaBarBelle

2012 2013 2014

10−10

9−10

8−10

Figure 8: Search for the B0s → µ+µ− and B0 → µ+µ− decays, reported by 11 experiments spanning

more than three decades, and by the present results. Markers without error bars denote upper limitson the branching fractions at 90% confidence level, while measurements are denoted with errorsbars delimiting 68% confidence intervals. The horizontal lines represent the SM predictions for theB0s → µ+µ− and B0 → µ+µ− branching fractions1; the blue (red) lines and markers relate to the

B0s → µ+µ− (B0 → µ+µ−) decay [1].

4.1 The LHCb experiment

The LHCb detector is designed to look for phenomena beyond the Standard Model. At the LHC, twocounter-rotating beams of protons, contained and guided by superconducting magnets are broughtinto collision at four interaction points (IPs) [1]. The average number of produced B mesons in theLHCb experiment is of the order of 1011. Assuming the branching fractions given by the StandardModel and accounting for the detection efficiencies, the predicted numbers of decays to be observed is

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less then one hundred for B0s → µ+µ− and less then ten for B0 → µ+µ−. In order to observe a reliable

deviation from the Standard Model prediction, branching ratios have to be precisely measured. Thismeans that relevant decays that happened in the collider have to be efficiently reconstructed. Recon-struction of the B0

(s) mesons decaying into two oppositely charged muons is possible via detection ofthese two muons and measurement of their energy and momentum. Muons do not interact stronglyand are too massive to emit a significant fraction of their energy by electromagnetic radiation. Thisgives them the ability to penetrate dense materials. The experiments use this characteristic to iden-tify muons. They detect muons with special muon detectors called muon chambers, built on the outerside 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 tracksof particles that can also be observed in the muon chamber are therefore mainly identified as muontracks.

To track the particles, the detector includes a high-precision tracking system consisting of asilicon strip vertex detector, a large-area silicon strip detector located upstream of a dipole magnetcharacterised by a field integral of 4 T · m, and three stations of silicon strip detectors and straw drifttubes downstream of the magnet. The vertex detector has sufficient spatial resolution to distinguishthe slight displacement of the weakly decaying b hadron from the primary production vertex wherethe two protons collided and produced it. The tracking detectors upstream and downstream of thedipole magnet measure the momenta of charged particles. The combined tracking system providesa momentum measurement with an uncertainty that varies from 0.4% at 5 Gev/c to 0.6% at 100GeV/c [1].

Figure 9: A scheme of the B0(s) → µ+µ− decay and its detection in the experiment

5 Kinematics of B0(s) decay into two muons

Decays compatible with B0(s) → µ+µ− (candidate decays) are found by combining the reconstructed

trajectories of oppositely charged particles identified as muons. The separation between genuineB0

(s) → µ+µ− decays and random combinations of two muons (combinatorial background) is achievedusing the dimuon invariant mass mµ+µ− and the established characteristics of B(s) meson decays.The dimuon invariant mass calculated from the energy and momenta of the reconstructed muons innatural units where c = 1 is:

m2µ+µ− = (Eµ+ + Eµ−)2 − (~pµ+ + ~pµ−)2, (6)

8

where energy is obtained from the measured momentum and the mass of the particle, which is knownonce the particle is identified, as:

Eµ± =√m2µ± + ~p2

µ± . (7)

Because of their lifetimes of about 1.5 ps and their production at the LHC with momenta between afew 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 (secundary vertex or SV), is required

to be displaced with respect to the production vertex (primary vertex or PV) - the point wherethe two protons collide, as shown in the Fig. 9. Furthermore, the negative of the B0

(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 asoftware 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 pT > 1.5 GeV/c [8].

6 Data analysis

The signals appear as peaks at the B0s and B0 masses in the invariant-mass distributions, observed

over background events. One of the components of the background is combinatorial in nature, asit is due to the random combinations of genuine muons. These produce a smooth dimuon massdistribution in the vicinity of the B0

s and B0 masses. In addition to the combinatorial background,specific b-hadron decays, such as the semi-leptonic decays B0 → π−µ+ν, B0

s → K−µ+ν, Λ0b → pµ−ν,

where the neutrinos cannot be detected and the charged hadrons are misidentified as muons, orB0 → π0µ+µ−, where the neutral pion in the decay is not reconstructed, can mimic the dimuon decayof 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 B0s or B0 meson because the

neutrino or another particle is not detected, except in the case of the decay Λ0b → pµ−ν, which can

also populate, with a smooth mass distribution, higher-mass regions. There is also a backgroundcomponent from hadronic two-body B0

(s) decays (peaking background) as B0 → K+π−, when bothhadrons from the decay are misidentified as muons. These misidentified decays can produce peaksin 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 kaonsare misidentified as muons, and thus suppress these background sources [1].

The distributions for the backgrounds are obtained from simulation with the exception of thecombinatorial background. The latter is obtained by interpolating from the data invariant-masssidebands, after the substraction of the other background components. Excellent mass resolution ismandatory for distinguishing between B0 and B0

s mesons with a mass difference of about 87 MeV/c2

and for separating them from backgrounds. LHCb achieves a uniform mass resolution of about 25MeV/c2 [1].

Kinematic criteria, amongst others that have some ability to distinguish known signal eventsfrom background events, are combined into boosted decision trees (BDT). A BDT is a group ofdecision trees each placing different selection requirements on the individual variables to achievethe best discrimination between signal-like and background-like events. A BDT must be trainedon collections of known background and signal events to generate the selection requirements on the

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variables and the weights for each tree. LHCb uses simulated events for background and signal in thetraining of its BDT. After training, the relevant BDT is applied to each event in the data, returninga single value for the event, with high values being more signal-like, similar to an example shown inthe Fig. 10. To avoid possible biases, the experiment kept the small mass interval that includes boththe B0

s and B0 signals blind until all selection criteria were established [1].

Figure 10: An example of a BDT, where we are trying to distinguish between individuals who havehigh interest in computer games and those who do not.

The branching fractions are determined from the observed number, efficiency-corrected, of B0(s)

mesons that decay into two muons and the total numbers of B0(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+

)= (6.10 ± 0.19) × 10−5 and B0 → K+π− decays

with B(B0 → K+π−

)= 1.96 ± 0.05) × 10−5 [1]. Hence, the B0

s → µ+µ− branching fraction isexpressed as a function of the number of signal events (NB0

s→µ+µ−) in the data normalised to thenumbers of B+ → J/ψK+ and B0 → K+π− events:

B(B0s → µ+µ−

)=NB0

s→µ+µ−

Nnorm.

× fdfs× εnorm.

εB0s→µ+µ−

× Bnorm. = αnorm. ×NB0s→µ+µ− , (8)

where the ’norm.’ subscript refers to either of the normalisation channels. The values of the normal-isation parameter αnorm. obtained by LHCb from the two normalisation channels are found in goodagreement and their weighted average is used. In this formula ε indicates the total event detectionefficiency including geometrical acceptance, trigger selection, reconstruction, and analysis selectionfor the corresponding decay. The fd/fs factor is the ratio of the probability for a b quark to hadroniseinto a B0 as compared to a B0

s meson; the probability to hadronise into a B+ (fu) is assumed tobe equal to that into B0 (fd) on the basis of theoretical grounds, and this assumption is checked ondata. The value of fd/fs = 3.86 ± 0.22 measured by LHCb is used in this analysis. An analogousformula to that in equation (8) holds for the normalisation of the B0 → µ+µ− decay, with the notabledifference that the fd/fs factor is replaced by fd/fu = 1 [1].

7 Latest experimental results

The latest experiemental results on the topic were reported by the LHCb collaboration in march2017. They reported measurements of the B0

s → µ+µ− and B0 → µ+µ− time-integrated branching

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fractions and the first measurement of the B0s → 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 coliisionsat 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

(B0s → µ+µ−

)= (3.0±0.6+0.3

−0.2)×10−9 and B

(B0 → µ+µ−

)= (1.5+1.2+0.2

−1.0−0.1)× 10−10. The statistical uncertainty is derived by repeatingthe fit after fixing all the fit parameters, except the B0 → µ+µ− and B0

s → µ+µ− branching fractions,the background yields and the slope of the combinatorial background, to their expected values. Themass distribution of the B0

(s) → µ+µ− candidates with BDT > 0.5 is shown in the Fig. 11, together

with the fit result [8]. Likelihood contours in the B(B0 → µ+µ−) versus B(B0s → µ+µ−) plane, the

best-fit central value and the Standard Model expectation and its uncertainty are shown in Fig. 12.An excess of B0

s → µ+µ− candidates with respect to the expectation from background is observedwith a significance of 7.8 standard deviations (7.8σ), while the significance of the B0 → µ+µ− signalis 1.6 standard deviations (1.6σ). Since no significant B0 → µ+µ− signal is observed, an upper limiton the branching fraction is set, resulting in B

(B0 → µ+µ−

)< 3.4×10−10 at 95% confidence level [8].

]2c [MeV/−µ+µm5000 5200 5400 5600 5800 6000

)2C

andi

date

s / (

50

MeV

/c

0

5

10

15

20

25

30

35 Total−µ+µ → s

0B−µ+µ → 0B

Combinatorial−

h'+ h→B

µν+µ)−(K−π → (s)

0B−µ+µ0(+)π → 0(+)

B

µν−µ p→ b0Λ

µν+µψ J/→ +cB

LHCb

BDT > 0.5

Figure 11: Mass distribution of the selected B0(s) → µ+µ− candidates (black dots) with BDT > 0.5.

The result of the fit is overlaid and the different components are detailed [8].

11

Figure 12: Likelihood contours in the B(B0 → µ+µ−) versus B(B0s → 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 confidencelevel [1].

8 Conclusion

We have learned about the physics in the Standard Model that makes B0s → µ+µ− and B0 → µ+µ−

decays very rare and the mechanism via which those decays can happen. We have examined the weakinteraction and how its charged and neutral currents mediate the quark flavour transitions and incombination with the Cabibbo-Kobayashi-Maskawa matrix make certain decays more frequent thanothers, some of them even forbidden on the tree level in the Standard Model. In the next part wehave looked at the experiemental setting that makes measurements of such decays possible, and theanalysis that is required to filter the signal from the received data as efficiently as possible. We havelooked at different types of backgrounds and their sources, that can cause false signal to appear asthe actual signal.

We can conclude that the observations of the B0s and B0 decays into to oppositely charged muons

with the measured branching fraction B(B0s → µ+µ−

)= (3.0±0.6+0.3

−0.2)×10−9 and an upper limit onthe branching fraction B

(B0 → µ+µ−

)< 3.4×10−10 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(B0

s → µ+µ−)SM = (3.65±0.23)×10−9 and B(B0 → µ+µ−)SM = (1.06±0.09)×10−10.

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References

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[3] D. Griffiths, “Introduction to elementary particles,” Weinheim, Germany: Wiley-VCH (2008)454 p. pp. 59–60.

[4] J. Beringer et al. [Particle Data Group], “Review of Particle Physics (RPP),” Phys. Rev. D 86(2012) 010001. doi:10.1103/PhysRevD.86.010001

[5] C. Bobeth, M. Gorbahn, T. Hermann, M. Misiak, E. Stamou and M. Steinhauser, Phys. Rev.Lett. 112 (2014) 101801 doi:10.1103/PhysRevLett.112.101801 [arXiv:1311.0903 [hep-ph]].

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[8] R. Aaij et al. [LHCb Collaboration], Phys. Rev. Lett. 118 (2017) no.19, 191801doi:10.1103/PhysRevLett.118.191801 [arXiv:1703.05747 [hep-ex]].

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