# The LHCb experiment

Post-publication activity

Curator: PierLuigi Campana

## Introduction

The dominance of matter in our Universe is one of the deepest mysteries in Nature. According to theoretical models, matter and anti-matter were produced in equal amounts during the Big Bang, but—through a mechanism whose details remain unknown—they had different fates while the Universe was cooling, so that now only matter can be observed around us. In the current Universe there is no evidence of primordial anti-matter, which was abundant in the first fraction of a second (Sather, 1996).

The Standard Model (SM) of particle physics is a well-tested reference model which encapsulates our experimental understanding of fundamental particles and their interactions. Certain discrete symmetries are fundamental to the SM, among them charge conjugation ($C$) and parity ($P$). Their combined symmetry is known as $CP$. The experimental observation (CERN Courier, 2014) of $CP$ violation in 1964 showed for the first time that particles and anti-particles may behave differently in their decays. The matter-antimatter asymmetry of the Universe is expected to be related to $CP$ violation. However, so far theory and experiments have not been able to find a suitable answer to the problem, as the experimentally observed $CP$ violation is too small to account for the disappearance of anti-matter during the evolution of the Universe. Further new phenomena, not yet discovered, must be present to explain the mystery. In addition to this open question, the SM also fails to explain other experimental observations, notably the existence of dark matter and dark energy, the masses of the neutrinos, and the ordering in mass scale of the known elementary particles.

LHCb is a particle physics experiment at the Large Hadron Collider (LHC) at CERN (LHCb Collaboration, 2008) that has been designed and built to make precise measurements of $CP$ violation and, more broadly, to search for and understand new physics phenomena beyond the Standard Model. LHCb studies principally the properties and decays of heavy particles that contain beauty ($b$) and/or charm ($c$) quarks created in proton-proton collisions at the LHC, a field known as heavy flavour physics. Particles containing $b$ quarks ($b$ hadrons) are of particular interest, since large $CP$ violation is expected in certain of their decays. Collisions at the LHC produce a large quantity of particles, including a high rate of $b$-hadron production, and are therefore an ideal laboratory for these searches. Moreover, LHCb complements studies ongoing in ATLAS and CMS, the two general purpose experiments at LHC, which aim to discover new fundamental particles that may be directly produced in proton-proton collisions.

The LHCb detector is optimized to operate in the forward direction, close to the beam axis, where a higher flux of $b$ and $c$ hadrons is expected. The main strengths of the experiment lie in its ability to measure particle production vertices and trajectories precisely, to identify charged particles efficiently, and to make swift and robust decisions about which events to retain and which to discard, all the while sustaining high rates and high radiation doses in the hostile environment of LHC collisions.

In the LHC data-taking period known as Run 1 (2010-2013), LHCb has collected a total of $$\sim 2 \times 10^{14}$$ collisions at centre-of-mass energies of 7 and 8 TeV, allowing the experiment to produce important results in $b$ and $c$ quark physics, carry out numerous studies of $CP$ violation, and set stringent limits on the existence of new phenomena. After a shutdown of two years, needed to raise the LHC collision energy to 13 TeV, Run 2 started in 2015, and is planned to continue into 2018.

With the current results, no unambiguous evidence of deviation from the SM has been uncovered (Isidori, Teubert, 2014). However, there are some hints of discrepancies with limited statistical significance, discussed further in section 4.

## Project history

Early in the '90s results from the CDF and D0 experiments at the Tevatron proton-antiproton collider at Fermilab had shown that decays of $$B$$ hadrons could be detected and their properties studied at hadron colliders, opening up new possibilities beyond the well-established use of $e^+~e^-$ storage rings and fixed-target detectors.

To complement the $$B$$ physics capabilities of LHC's big detectors (ATLAS and CMS), one dedicated $$B$$ physics experiment was planned for the initial phase of the LHC experimental program. In 1993, three groups submitted Letters of lntent based on different experimental approaches: colliding beams at the full LHC 14 TeV energy (the COBEX project); an internal gas jet target intercepting a circulating beam (the GAJET project); and a beam extracted for a fixed target experiment (the LHB project). Considering these ideas, the LHC Experiments Committee pointed out that the collider approach appeared the most attractive one, being able to exploit the full power of LHC, and encouraged the three groups to submit a fresh design for a collider mode $B$ physics experiment (LHCb: Letter of Intent, 1995; Technical Proposal, 1998). In September 1998, the LHCb experiment was approved by the CERN Research Board.

The construction of the various elements of the experiment started soon after, and all the project elements were ready and installed in the cavern by the initial LHC startup, in September 2008. The cost of the LHCb experiment amounted to 75 million CHF, and was shared among participating funding agencies. Detector components were built all over the world under the responsibility of the collaborating institutes and with participation of private-sector companies in the member nations, and then delivered to CERN as contributions to the LHCb experiment.

LHCb is an international collaboration. At the time of writing in 2015, it is composed of about 1100 scientists, engineers and technicians from 68 universities and laboratories of Brazil, China, Colombia, France, Germany, Ireland, Italy, Poland, Romania, Russia, Spain, Switzerland, The Netherlands, United Kingdom, United States, Ukraine and CERN. PhD students represent one third of the authors of LHCb physics papers.

## The LHCb detector

### Overall layout

The experiment consists of a spectrometer (Figure 1) with a forward angular acceptance from 10 mrad (due to the beam pipe) up to 300 mrad, and a total length of $$\sim$$ 20 m.

Figure 1: Cross-section view of the LHCb apparatus, showing the different detector layers around the LHC beam axis ($$y=0$$). The collisions occur in the leftmost part of the detector (around $$x=y=0$$). The labels show the main components of the apparatus (see text for more detailed descriptions).

The choice of detector geometry is motivated by the fact that particles with $b$ quarks originating from the colliding beams are emitted mainly at small angles to the beams in the forward or backward directions. LHCb is installed at cavern P8 of the LHC ring and, due to space constraints, is built to detect particles only in the forward cone. The main detector components of LHCb, described in more detail in the following sections, are:

• A vertex locator, to measure with great precision the points at which the proton-proton collisions have occurred (known as primary vertices), and the points at which short-lived particles have decayed in flight (known as secondary vertices). These are relevant to almost all physics studies at LHCb.
• A spectrometer, consisting of a dipole magnet that bends particles in the horizontal plane, plus tracking devices to measure the trajectories of charged particle, and thereby calculate their momenta. Low-momentum charged particles (below approximately 2 GeV/$c$) are swept out by the magnetic field and do not reach the downstream detector components (thus lowering their occupancy).
• A calorimeter system, to absorb and identify photons, hadrons and electrons, and to provide a fast trigger for these particles.
• Charged particle identification systems, to identify pions, kaons, protons, and muons originating from primary and secondary vertices.
• An online readout architecture, capable of real-time filtering to select interesting events and send them to an offline computing grid for further processing.

The density of particles produced in the forward region is high. In order to keep the event complexity at a manageable level, LHCb has operated at a luminosity (a quantity proportional to the number of collisions per second) of $$\sim 4 \times 10^{32}$$ cm $$^{-2}$$ s $$^{-1}$$ during Run 1 (2010-2013). This is a factor of approximately 20 less than the maximum luminosity provided to the ATLAS and CMS experiments.

LHCb will operate in a similar configuration during Run 2 (2015-2018). There will be a number of modifications, notably including the addition of a new, very forward subdetector known as HERSCHEL that will detect proton interactions at very small angles with respect to the beam. A summary of the performance of the LHCb detector and its subsystems during Run 1 can be found in LHCb Collaboration, 2015.

### The vertex locator and the tracking systems

Weakly decaying particles produced at LHCb that contain a $b$ or $c$ quark have lifetimes $$\sim 10^{-12}$$s and travel at most a few cm. By the standards of collider physics experiments, this is a substantial distance. LHCb's vertex locator (VELO) and its tracking systems are used to reconstruct the trajectories of these long-lived particles, determining the points from which they originate and at which they decay. Their decay products often include charged particles; precise measurements of the momenta of these charged decay products is also vital for heavy flavour physics studies. This is achieved by a combination of advanced silicon detectors, covering several regions of the detector: the VELO, which instruments the interaction region and the surrounding region; the Trigger Tracker (TT) stations, which sit upstream of the magnet; and the Inner Tracker (IT) component of the three downstream tracking stations. The IT modules use a silicon strip technology, as do the TT stations, and instrument the innermost region near the beam pipe where the density of particles is very high. They are complemented by Outer Tracker (OT) component of the downstream tracking stations, which consists of straw tubes filled with gas, a technology well suited for large surface area applications.

A large dipole magnet is located between the interaction point and the downstream tracking stations (Figure 2). The integrated magnetic field is approximately 4 Tm, and bends charged particles in the horizontal plane.

Figure 2: The dipole magnet of the LHCb spectrometer during the installation of the experiment, with image of physicist for scale.

#### The VELO detector

The VELO is made of 23 pairs of silicon micro-strip half-modules, segmented in fine strips to provide the best possible vertex resolution (Figure 3). The silicon planes are installed perpendicular to the beam direction. During data-taking, the VELO sensors are moved close to the beam line (approximately 8 mm from beam to active silicon), and are retracted to a distance of several cm when the machine is preparing for collisions.

Figure 3: One of the silicon sensors of the LHCb vertex locator. Charged particles produced in LHC collisions hit the active area (in gray), giving rise to a electronic signals in nearby strips. Combining the information from several sensors, the trajectory of the particle can be reconstructed. This allows for a very precise determination of their vertex decay. The hole at the centre of the semi-circle is for the LHC beams.

To minimize the distance and material between the collision point and the active area, the sensors are immersed in the vacuum of the LHC machine. A very thin aluminium foil is used to shield them electrically from the radio frequency effects of the beam currents. The thickness of the sensors is chosen to reduce the amount of multiple scattering of charged particles crossing the detector, and to allow for efficient operation even after irradiation. Being so close to the beams, the LHCb VELO is subject to a very intense radiation environment. However, the integrated dose has not produced appreciable degradation of its performance to date, and from simulations it is expected that it will be able to take data until the end of Run 2 of LHC.

The VELO has operated and performed as expected during Run 1. The accuracy in the determination of the position of a primary collision vertex is $$\sigma_x \sim \sigma_y \sim 15~\mu$$m and $$\sigma_z \sim 75\,\mu$$m, corresponding to a resolution on the proper decay time of a particle of typically 40-50 fs (1 fs = $$10^{-15}$$ s). Note that this is much smaller than the typical lifetime of $\mathcal{O}$(1 ps). This is key for studies of the behavior of $$B_s$$ mesons (particles made of $$\bar{b}$$ and $s$ quarks), including measurements of important $CP$ violation effects. A quantum mechanical phenomenon causes $$B_s$$ mesons to oscillate between their particle ($$B_s$$) and antiparticle ($$\bar{B_s}$$) states. The $B_s$ oscillations are very rapid, with a characteristic time of order tens of fs, and require excellent time resolution to resolve. This has been achieved at LHCb, and the oscillations are clearly visible from the decay products. (For more details, see the discussion in section 4.)

#### The tracking detectors

Measurement of the trajectories and momenta of charged particles in LHCb is performed by the tracking systems, made of two silicon devices (TT and IT) at low angle, and by straw tubes gaseous detectors (OT) at larger angle in the outermost LHCb acceptance. The silicon detectors use micro-strip sensors (a radiation-hard technology) with a distance between the strips (pitch) of $$\sim 200 ~\mu$$m, a spatial resolution of approximately $$\sim 50 ~\mu$$m, and a granularity fine enough to deal with the occupancy due to density of particles near the beam pipe. The thickness of the layers is chosen to minimize multiple scattering and maintain the desired momentum resolution even for charged particles at low momentum. Straw tubes provide a spatial resolution of approximately $$\sim 200 ~\mu$$m over a very large detector area. The combined use of tracking information from VELO, TT and IT/OT stations, provides a fractional momentum resolution $${\sigma_p \over p} \sim$$ 0.8 % in a very wide range of momentum (5-100 GeV/c), which is the best relative momentum resolution among the four LHC experiments.

#### The particle identification

A further important asset of LHCb experiment lies in the capability to identify correctly the large number of particles produced in the experiment during collisions ($\sim$ 100 in each interaction). In LHCb this is performed using several systems: for charged particles, a Ring Imaging Cherenkov detector (RICH) and a muon filter, while for neutral particles, a calorimetric complex (CALO).

#### The RICH detectors

Charged particles of a given mass, which travel in a material at velocity above a defined threshold (equivalent to c/n, where c and n are the velocity of light in vacuum and the material refractive index respectively), undergo the emission of a specific type of radiation: the Cherenkov light. The angle of emission of the Cherenkov light with respect to the trajectory of the particle is related to its speed. This phenomenon is used by the LHCb RICH to measure the speed of the particles, which is associated to the knowledge of their momentum. This determines their mass and therefore their identity (pions, kaons or protons in this case). The RICH operation is based on the challenging detection of a minimal amount of low energy photons. Two different RICH detectors are located upstream and downstream the magnet to cover a broad momentum spectrum (10-100 GeV/c).

The extensive use of this technique of particle identification is a special feature of LHCb operation. As kaon particles are the relevant products of most $b$ and $c$ flavoured hadron decays, the use of RICH detectors has allowed the extraction of very important physics results, as reported in section 4.

#### The calorimeters

A massive detector, made of a heavy materials (such as lead and iron) interleaved with plastic scintillator, represents the bulk of the structure of the LHCb calorimeters, the electromagnetic (ECAL) and the hadronic one (HCAL). These devices have the task of detecting electrically neutral particles, such as photons or neutral hadrons, that are invisible to the upstream tracking system. Isolated and high energy photons are particularly important as they are a clean signature of b or c quarks. Calorimeters are also used to identify electrons, and in helping muon identification. Moreover, the LHCb calorimeters have the important role of providing a real-time trigger for electromagnetic or hadronic energy deposits in the detector, allowing the selection of interesting event topologies at a very early stage.

#### The muon system

Muons originate mostly from decays of particles consisting of heavy quarks, the b or the c. Compared to hadrons, they have a much lower probability of interaction when passing through material. Moreover, upon interaction, they deposit a relatively small amount of energy. It is expected that if a particle reaches the very end of the detector, the probability of it being a muon is very high. This property is exploited for their detection which is performed by a shielding complex composed of three walls of iron located at the end of experiment. Each of the walls is alternated with a layer of wire chamber detectors, to provide the coordinate of the passage of the particle. Similar to the calorimeter system, the muon system supplies a prompt trigger to select with high efficiency, interesting events to be stored on disk.

#### Trigger and data processing

Proton-proton collisions at the LHC provide a huge amount of data, where approximately in 1 out of every 200 events a pair of b flavoured hadrons is produced. The data are therefore filtered at several different levels, to store on disk only the events in which signal decays are likely to have occurred, discarding the overwhelming background. The LHCb trigger architecture is based on the requirement of making a hardware-based real-time selection with short latency and high efficiency for events which contain b or c quarks.

The calorimeter and muon front end electronics systems record signals at a rate of 40 MHz, sending the information to arrays of FPGAs (field programmable gate arrays) to select hadrons or leptons with large transverse momentum $$p_{T}$$, greater than 4 GeV/c and 1.5 GeV/c (typical values), respectively. The presence of high $$p_{T}$$ particles in an event is a clean signature of the production of hadrons with b quarks. This first selection, processed in real time, already reduces the rate from 40 MHz to 1 MHz.

If an event passes this hardware trigger decision, the data stored on the front end electronics buffers are transferred via a large network and an array of data switches, to an Event Filter Farm (EFF). In the EFF, a software based High Level Trigger (HLT) applies further selection criteria which are a simplified and faster version of the full offline reconstruction program. The EFF for Run 1 was based on 29,000 core processors and processed a single event in $\sim$ 40 ms. In 2015, the system has been doubled in its computing capabilities. In Run 1, the HLT reduced the data rate from ~1 MHz to ~5 kHz, retaining signal events from b and c quark decays with muons in the final state (~90% efficiency) or with hadrons (~50% efficiency). The output of the HLT is sent to the CERN central computing infrastructure for the final processing.

Reconstructed events are then stored on disk and tapes and distributed over the GRID computer network, throughout the world and functionally interconnected, for user analyses. One full year of LHCb data taking generates an amount of stored data corresponding to $$\sim$$1.5 PB, 20% of which is selected and made available permanently on disk for physics analyses.

### Operation of LHCb

A non-trivial operation of the LHCb experiment with respect to the LHC accelerator was foreseen from early on due to the challenging position of its vertex detector only few mm far from the beam pipe as well as need of operating at a reduced LHC luminosity to avoid an excessive particle flux in the inner part of the detector. In the LHC Run 1, while the ATLAS and CMS interaction points reached a maximum instantaneous luminosity of $\sim 8 \times 10^{33}~$cm$^{-2}$s$^{-1}$, LHCb working point was set at $\sim 4 \times 10^{32}~$cm$^{-2}$s$^{-1}$, considered as the maximum possible bearable for the detector.

This value is kept stable during the whole duration of the colliding proton-proton beams (on average $\sim$ 10 hours at a time), allowing a constant trigger rate and very stable conditions. The reduction of luminosity is obtained through a sophisticated local modification of the beams at the interaction point ("luminosity leveling"), to lower the number of collisions. A feed-back is continuously sent to the LHC control system to adjust leveling during beam coasting in order to keep the luminosity constant while the global LHC beam intensity is decreasing. This scheme has been very successful, and it is planned to be used at the High Luminosity LHC upgrade to level the peak luminosities in ATLAS and CMS, improving the overall efficiency of data taking.

Globally, LHCb recorded 1 $${fb}^{-1}$$ and 2 $${fb}^{-1}$$ at the collision energies of 7 and 8 TeV respectively, during Run 1, with an overall data taking efficiency of 93 %. A sample of p-Pb collisions data was recorded too, corresponding to a total integrated luminosity of 2 $${nb}^{-1}$$. During Run 2, LHCb expects to collect $\sim$ 5 $${fb}^{-1}$$ at 13 and 14 TeV centre-of-mass energies, and at a LHC beam bunch spacing of 25~ns.

## Physics highlights

The SM is the current and the most well tested model of the fundamental particles and their interactions. However, as mentioned in the introduction, many experimental observations such as the presence of Dark Matter, the mass of neutrinos and the ordering in mass scale of the known elementary particles, do not fit the SM. The mechanism of generating matter anti-matter asymmetry, such as the one observed in the universe today, also remains obscure. Due to these and other unanswered questions, the SM is considered to be a very good approximation of a more detailed theory, much like Newtonian mechanics is a very good low energy approximation of relativity. The bulk of the effort in particle physics at present is therefore aimed at discovering which physics lies beyond the SM (BSM).

LHCb aims to uncover signs of BSM by analysing particle reactions and comparing their properties to the ones predicted by the SM. The simplest of these properties is perhaps the "branching ratio" (BR), which is the probability for a particle to disintegrate into certain decay products. Other properties include CP asymmetries and angular distributions of the decay products. The physics program and reach of the LHCb experiment is very different from and complementary to the general purpose detectors ATLAS and CMS. In the following, a few recent LHCb measurements are discussed.

### Rare $$B$$ meson decays

Rare decays refer to transitions of b flavoured particles that occur with a very low probability: typically one in 10 or 100 million. Such decays usually occur via loop diagrams (described below) and are excellent probes of BSM. Two of the many topics studied at LHCb are presented here, choosing as examples B decays with two muons in the final state.

#### $$B_s \to \mu^+ \mu^-$$ and $$B_d \to \mu^+ \mu^-$$

The decay of $$B_s$$ (and $$B_d$$) mesons into a muon-antimuon pair ($$\mu^+\mu^-$$) is of great interest in the search for BSM physics. Mesons are particles composed of two quarks (as opposed to three quarks for baryons e.g. proton and neutron) and the $$B_s$$($$B_d$$) consists of a $\bar{b}$ and a $${s}~$$($$d$$) quark.

Both the $$B_s \to \mu^+ \mu^-$$ and $$B_d \to \mu^+ \mu^-$$ decays can only take place via a very rare transition like the one shown in Figure 4. The diagram shows this reaction with the use of lines and arrows where the initial state is to the left and the final state is to the right (Feynman diagram). Therefore what started as a $$B_s$$ ($$B_d$$) meson on the left ends up as two muons on the right, and such diagrams are called "loops" due to the structure formed by the virtual particles mediating the process (in this case a $$t$$ quark and the $$Z^0$$ and $$W^{\pm}$$ bosons). Charged BSM particles can also contribute to the virtual loop and as a result, enhance or suppress the rate of this reaction, which can be precisely calculated in the SM by taking into account all the known particles, including the virtual ones. This is why this decay mode is very sensitive to the presence of BSM physics.

Figure 4: One of the dominant Feynman diagrams for the $$B_s (B_d) \to \mu^+ \mu^-$$ decay.

With data collected in Run 1, the LHCb experiment (LHCb Collaboration, 2013) was able to isolate the first experimental evidence of $$B_s \to \mu^+ \mu^-$$ decay. This is done by reconstructing the mass of the particle which could have generated the two muons, which relies heavily on the momentum measurement of the two muons performed by the LHCb tracking system. The masses of the $$B_s \to \mu^+ \mu^-$$ and $$B_d \to \mu^+ \mu^-$$ candidates are shown in a region of phase space where the level of background is low (Figure 5). The LHCb measured branching ratio of the $$B_s \to \mu^+ \mu^-$$ decay is $(2.8^{+0.7}_{-0.6}) \times 10^{-9}$ in quite good agreement with the theoretical SM expectation of $(3.65 \pm 0.23) \times 10^{-9}$.

Figure 5: The invariant mass of the muon pairs reconstructed in LHCb. The dashed red curve represents the $$B_s \to \mu^+ \mu^-$$ signal component, while the dashed green represents the $$B_d \to \mu^+ \mu^-$$ signal. The other curves show the different background components. The solid blue curve is the result of a fit, sum of all components.

The LHCb data have been combined with those of CMS, to give a more precise determination of these decay rates (LHCb and CMS Collaborations, 2015). The final results from LHCb and CMS Run 1 data set on the measured branching ratios of the $$B_s$$ and $$B_d$$ decays are compatible with the SM predictions within the estimated uncertainties, therefore excluding large effects from possible new physics. The results from the LHC Run 2 data will reduce the experimental uncertainties, giving better sensitivity to new physics models.

#### $$B \to K \mu^+ \mu^-$$ decays

The decays of $$B$$ mesons to a $$K$$ meson and two muons also involve a loop diagram similar to the $$B_s \to \mu^+ \mu^-$$ decay channel. BSM particles can contribute to the loop and produce measurable departures from the SM expectations. The family of $$B \to K \mu^+ \mu^-$$ decays is a corner stone of the LHCb rare decays program because it offers a rich assortment of variables, in addition to branching ratios. In one of these channels ($$B^0 \to K^{*0} \mu^+ \mu^-$$), the final state consists of four particles (the $$K^{*0}$$ meson is reconstructed in its decay to a charged kaon and a pion), which allows the study of angular variables formed by them. The branching ratio of this decay measured at LHCb is compatible with the SM expectations, while a discrepancy with respect to the SM has been observed in one of the angular variables. The discrepancy persists in a recent analysis of the full Run 1 data set, and has generated a lot of theory interest and different interpretations have been put forward. For example, some theorists ascribe it to the contribution from a new $$Z^\prime$$ particle, while others attribute the discrepancy to an underestimation of theoretical uncertainties.

Another interesting result from LHCb is the measurement of the ratio ($$R_K$$) of the branching ratios of the decays $$B^+ \to K^+ \mu^+ \mu^-$$ and $$B^+ \to K^+ e^+ e^-$$. The SM respects lepton universality, i.e. that all interactions behave in the same way for the three generations of leptons. Any departure of $$R_K$$ from unity will therefore point to BSM physics. The LHCb measurement of $$R_K$$ with Run 1 data is $$0.74^{+0.10}_{-0.08}$$ and is only partially compatible with the SM prediction.

Some theorists believe that the angular $$B^0 \to K^{*0} \mu^+ \mu^-$$ and the $$R_K$$ anomalies originate from the same source of BSM physics. Further experimental and theoretical effort is required to clarify if the claims of a BSM signals are indeed supported by data. See Blake, T; Gershon, T, Hiller, G, 2015 for a detailed discussion of the subject.

### CP violation

CP violation is an essential ingredient for generating a matter and anti-matter imbalance in the universe, as we observe today. In the SM, with three generations of particles, CP violation can be explained assuming that the 6 quarks can interact weakly among each other through a 3$$\times$$3 matrix (the Cabibbo-Kobayashi-Maskawa matrix or the CKM matrix) made of three angles and a single global phase. However, matrix elements are subject to the conditions that the total probability of a quark transitioning to any quark should sum up to one. These constraints can be represented in the form of triangles in the complex plane, and one of such triangles, referred to as the unitarity triangle, is shown in Figure 6. The angles of this particular triangle are denoted with $$\alpha$$, $$\beta$$ and $$\gamma$$, and the constraints on these angles from different measurements are shown by coloured error bands. These angles are variables that enter in the determination of CP violating parameters in $$B$$ meson decays and therefore it is important to measure them precisely. It can be noticed that the angle $$\gamma$$ is one of the least constrained of the three: the LHCb measurement $$\gamma$$ $$=$$ $$\left(72.9 ^{+9.2}_{-9.9} \right)^{\circ}$$ is the most precise measurement of this parameter from a single experiment (LHCb Collaboration, 2014).

Figure 6: Graphical representation of constraints in the CKM matrix elements drawn as a triangle in the complex plane. The $$\bar{\rho}$$ and $$\bar{\eta}$$ represent two of the four parameters of the CKM matrix. The three angles ($$\alpha$$, $$\beta$$ and $$\gamma$$) are indicated along with the coloured bands (light blue, blue and grey) representing their uncertainties from direct measurements. Other quantities that help to constrain the CKM triangle are shown e.g. $$V_{ub}$$ is measured via the decay rate of $$B$$ mesons to $$\pi l \nu$$ where $$l$$ is a muon or an electron, and constrains the length of the left side of the triangle (green band); $$\Delta m_d$$ and $$\Delta m_s$$ are the oscillation frequencies of the $$B_d$$ and $$B_s$$ mesons respectively (see text), and constrain the length of the right side of the triangle (yellow and orange bands); $$\epsilon_K$$ is the only parameter that cannot be measured in $$B$$ meson decays, as it is accessed via a measurement of CP violation in the decays of $$K^0$$ mesons (courtesy of Charles J et al, 2005).

An interesting and important phenomenon exhibited by neutral mesons is mixing or oscillation. This is a quantum mechanical process where a neutral meson can continuously change its nature into its anti-particle and vice versa. This phenomenon has been experimentally observed in $$K^0$$, $$D^0$$, $$B_d$$ and $$B_s$$ mesons. The time development of the oscillation can be measured experimentally, provided that the time resolution of the detector is good enough. An illustration of this effect is shown in Figure 7.

The use of this phenomenon leads to the measurement of another important CP observable in the $$B_s$$ system, using the decay of these mesons to $$J/\psi \phi$$ final state (being $$J/\psi$$ and $$\phi$$ two mesons). The $$B_s$$ ($$\bar{B_s}$$) can decay to this specific final state either directly or by first oscillating into a $$\bar{B_s}$$ ($$B_s$$) meson and then decaying. The quark level diagram of this process involves loops from virtual particles and a CP observable (called $$\phi_s$$) measured in this analysis is very sensitive to contributions from BSM physics. The LHCb measurement (LHCb Collaboration, 2015) is the world best currently available, $$\phi_s = -0.058 \pm 0.049$$, and is consistent with the SM prediction of $$-0.040 \pm 0.003$$.

Figure 7: Decay time distribution for $$B_s$$ mesons observed in the LHCb experiment. The red coloured points represent the $$B_s$$ mesons that oscillated into their anti-particle while the blue ones (unmixed) represent the ones that did not oscillate. The points are experimental data and the lines are the result of a fit. Abscissa is in units of picoseconds (1 ps $$= 10^{-12}$$ s).

### Charm physics

Charm mesons consist of a c quark and another quark among u, d, s. Their decays provide the only opportunity to study CP violation in up type quarks (up type quarks are the u, c and t). This is because the t quark decays before it can hadronize, i.e. before it can form any mesons or baryons, and the u quark being the lightest quark, cannot decay to lower mass quarks. There is a strong theoretical interest in studying and measuring a possible CP violation in charm decays, also in connection with the search for new physics. Even though LHCb is optimized for b quark studies, the experiment can detect efficiently the huge amount of charm mesons produced at the LHC (charm cross section, i.e. the probability of the production of a charm hadron, is about 20 times the beauty one).

Searches for CP violation in charm decays at LHCb have reached a sensitivity of $$10^{-3}$$ to $$10^{-4}$$, the best currently available, and have so far not yielded any evidence. Mixing of neutral $$D$$ mesons was recently established by LHCb to a significance of 9$$\sigma$$. Prior to this result, $$D$$ mixing was established only by combining measurements from many experiments. Searches for very rare decays of charm mesons are also performed (such as $$D^0 \to \mu^+ \mu^-$$), considering that the branching ratios could be enhanced by new physics BSM. From the analysis of Run 1 data there is no evidence of anomalous measurements. These results demonstrates the capability of the LHCb detector to make precision measurements in the charm sector.

LHCb has also been studying the so called exotic particles which do not fit into the description of being composed of two or three quarks, as are mesons and baryons respectively. The LHCb measurement of the properties of the $$Z(4430)$$ particle, first discovered by the Belle experiment at the KEK beauty factory, supports its interpretation as either a four quark state or a combination of two $$D$$ mesons, and the fact that the particle is a true resonance and is not just an artifact.

The establishment of a first tetra quark state was closely followed by the results on another exotic particle called $$X(3872)$$. This state was also discovered by the Belle collaboration, but only the high statistics sample at LHCb has allowed the measurement of its quantum numbers. More studies of the production and decay properties of these particles are underway, and the results have inspired a lot of theoretical work. The challenge is to describe the composition and nature of these particles making use of a deeper understanding of QCD (Quantum Chromo Dynamics), the theory that describes the strong interactions.

### Other physics topics

The LHCb physics program is very diverse, including but not limited to the areas described above. It also includes electroweak physics, for example the production and decay properties of the Z and W bosons, the searches for charged lepton flavour violating decays, the evaluation of beauty and charm hadron production cross sections, the study of the properties of quarkonium resonances (formed by excited states of the bound $$b~\overline{b}$$ and $$c~\overline{c}$$ systems) and the search for new long-lived particles, produced in the forward direction. In fact, LHCb provides an excellent opportunity to study physics phenomena in its unique pseudorapidity coverage (Figure 8). These measurements serve as important consistency checks of our knowledge from experiments like ATLAS and CMS, whose acceptance is in the lower pseudorapidity region, and are crucial input to theoretical calculations of the quark distribution functions inside the colliding protons, and simulation models describing the proton-proton collisions.

Figure 8: Detector acceptance intervals (red bands) in the pseudorapidity variable for the LHC experiments. Pseudorapidity is a commonly used variable describing the angle of a particle relative to the beam axis: large pseudorapidity values (negative or positive) represent very small angles.

## Future perspectives

The LHCb experiment has already provided a large amount of measurements of the Standard Model parameters using data from Run 1. During Run 2, at a centre-of-mass energy of 13 TeV, the probability of producing b or c quarks will be nearly double due to the increase in their cross sections. The larger data sample will help reduce the statistical errors on several of the above mentioned observables. However, for some of the most interesting ones, the error will be still bigger than the one expected from theory uncertainties, leaving room for some new physics effects. As an example, at the end of Run 2, the experimental error on the CP violating phase $$\phi_s$$ will be still 10 times larger than the theoretical one (0.003). For these reasons, the LHCb collaboration has proposed a substantial upgrade of the detector (CERN Courier, 2011), which will increase the instantaneous luminosity up to $$2 \times 10^{33}$$cm$$^{-2}$$s$$^{-1}$$. The plan has been financed by LHCb funding agencies and approved by CERN Research Board in 2014.

The experiment will have a readout rate of 40 MHz, in which each proton-proton interaction, that happens every 25 ns, will be recorded. Afterwards, the events collected will be routed to a very large farm of processing units, where a full software filter will analyze and process the huge amount of information, selecting and writing on disk only the interesting events at much lower rate. The possibility of reading out all the collisions and performing software trigger selections on data will increase substantially the trigger efficiency in several physics channels, especially those with tracks with low momentum, typically in multibody decays. This translates in an enlargement of the collected statistics by factors from 5 to 10 with respect to the current operation.

The upgrade of the detector is in preparation and the new, improved detector is planned to be ready for data taking at LHC in 2021. By the end of Run 3 (2023), the upgraded LHCb detector should have collected $$\sim 23~fb^{-1}$$, more than 15 times the statistics collected in Run 1, therefore reducing the current error on most of the heavy flavour observables by a factor of 4.

## References

• Isidori, G and Teubert, F (2014). Status of indirect searches for New Physics with heavy favour decays after the initial LHC run. arXiv: http://arxiv.org/abs/1402.2844.
• LHCb Collaboration and CMS Collaboration (2015). Observation of the rare $$B_s \to \mu^+ \mu^-$$ decay from the combined analysis of CMS and LHCb data. Nature 522. doi:10.1038/nature14474.