CP violationin K ﬁnalstatesatLHCb 0 Searchingforconﬁrmationofcharm UniversitàdiPisaGraduatecourseinPhysics

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Graduate course in Physics

XXXIII entrance (2017-2020)

Searching for confirmation of charm

CP violation in K

_S

0

final states at

LHCb

PhD thesis

Author:

Giulia Tuci

Advisor:

Prof. Giovanni Punzi

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To my grandparents Ai miei nonni

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Abstract

This thesis reports a measurement of the CP asymmetry in D0 _{→ K}0

SK

0

S decays, based

on pp data collected by LHCb at a centre-of-mass energy of 13 TeV, corresponding to an

integrated luminosity of 5.7 fb−1. The D∗+ →D0_π+ _{decay is used to infer the flavour of}

the D0 _{meson at production. The D}0 _{→ K}+_K− _{decay, which has a well measured CP}

asymmetry, is used as a calibration channel. The time-integrated CP asymmetry for the

D0 _{→ K}0

SK

0

S decay is measured to be:

ACP_(D0 _{→ K}0

SK

0

S) = (−3.1 ± 1.2 ± 0.4 ± 0.2)%,

where the first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty on the asymmetry of the calibration channel. This is the most precise determination of this quantity to date and it is still compatible, albeit marginally, with zero asymmetry. In view of further measurements in future runs of LHCb, a study of the performance of an innovative real-time tracking system based on FPGAs is presented. This system is designed to process events at the full LHC collision rate of 30 MHz, with

the aim of significantly increasing the trigger efficiency for the D0 _{→ K}0

SK

0

S decay channel

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Preface

The Standard Model of particle physics is the theory describing electroweak and strong interactions. Although it has demonstrated huge success providing a very large number of precise predictions, it leaves some phenomena unexplained and falls short of being a complete theory of fundamental interactions. For example it does not fully explain the baryon asymmetry, it does not account for gravitation and it does not explain the nature of dark matter. It is reasonable to believe that the Standard Model is only a low-energy approximation of a more general theory.

Typical ways of putting the Standard Model under test are the production of particles at higher energies in the search of unexpected phenomena, or high-precision measurements of known quantities to compare experimental results with predictions. In the second approach, processes suppressed within the Standard Model are particularly interesting: enhancements of such processes are evidence of contributions from New Physics. The search for CP violation, i.e. the non-invariance of fundamental interactions under the combined symmetry transformations of charge conjugation (C) and parity inversion (P), in the charm sector plays a key role in this kind of research, and has therefore a relevant place in the LHCb physics program.

In the Standard Model, CP violation is described by the presence of a single complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Until now experimental results support the CKM phase, but to explain the cosmological observations on the abundance

of matter and anti-matter in the Universe additional terms of CP violation are needed. D0

and D0 _{mesons are very interesting particles to study because they are the only mesons}

with an up-type quark as the heavy quark that can oscillate. In fact top quarks decay

before hadronizing and π0 and η mesons, composed of u and ¯u, are their own

antipar-ticle and therefore cannot oscillate. Since, in principle, there might exists some New Physics coupling only to up-type quarks, charm transitions provide a unique opportunity to eventually observe some effects that cannot be explained within the Standard Model.

The experimental study of CP violation in the charm sector is extremely challenging;

CP violation is in fact expected to be equal or less than 10−3 and therefore huge samples of charm-hadrons decays are needed. For this reason CP violation in charm decays was unobserved until 2019, when LHCb made the first observation using about 100 million

of D0 _{→ K}+_K− _{and D}0 _{→ π}+_π− _{decays. The interpretation of the observed effect is}

however nontrivial, because of the large theoretical uncertainties on the predicted value. The theoretical description is not straightforward, since the masses of charmed hadrons, O(2 GeV), are in a range where non-perturbative hadronic physics is operative. Current theoretical approaches to charm dynamics are based on establishing relations among de-cay rates in different modes through amplitudes and phases, allowing the extraction of the theoretical parameters by fitting the measured branching-fractions in several decay channels.

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hadrons decay channels, to improve the existing measurement and eventually get for

con-firmation of CP violation. Because of the size of the expected effect, the D0 _→K0

SK

0

S

decay channel is very interesting. A theoretical argument based on the Standard Model predicts in fact an upper limit on CP violation in this channel of 1.1%, but this value could

result enhanced because of the interference of New Physics. In addition, D0 _→K0

SK

0

S

de-cays provide independent information with respect to the D0 _→π+_π− _{and D}0 _→K+_K−

ones, since they are sensitive to a different set of decay amplitudes. However, selecting K0

S

at trigger level in an experiment like LHCb is challenging. K0

S particles have a relatively

high lifetime τ ∼ 0.9 × 10−10 s and are produced with a high boost in the beam

direc-tion (aligned with the detector). Therefore they often decay outside the vertex detector acceptance, whose information is used to select tracks at the first level of the software

trigger. For this reason the amount of D0 _{→ K}0

SK

0

S decays collected by LHCb is limited

(about 10 thousand using data collected from 2015 to 2018) with respect to other D0

decay channels, and the previously published LHCb measurements were not competitive with the world’s best measurement performed by Belle.

In this thesis I present a new measurement of the CP asymmetry in the D0 _{→ K}0

SK

0

S

decay channel, using data collected by LHCb from 2015 to 2018. To take full advantage of the available statistics, offline selections have been carefully studied and some enhance-ments of the methodology - with the respect to what is usually done in similar analysis at LHCb - have been introduced. Thanks to these improvements, I was able to reduce the uncertainty on the 2015 and 2016 data, already used by the LHCb collaboration in the last publication regarding this measurement, by ∼ 30%, and to perform the world’s best measurement using the full 2015-2018 dataset.

Looking ahead, in 2022 LHCb will start to acquire data with an almost completely new detector and trigger system. The instantaneous luminosity will increase by a factor of 5

and the amount of data collected by LHCb will jump from ∼ 9 fb−1 (collected up to now)

to ∼ 50 fb−1 in 2030. Since the measurement of CP asymmetry in D0 _{→ K}0

SK

0

S decays is

limited by the available statistics, there is a large room for improvement. In addition to the increase of luminosity, there is an ongoing effort to increase the trigger efficiency for this channel, both introducing specific trigger lines at the first level of the software trigger,

optimised to select K0

S decaying inside the vertex detector, and developing a specialised

tracking device to reconstruct and trigger at the earliest possible stage on K0

S decaying

outside the vertex detector acceptance.

Find tracks outside the vertex detector at the earliest trigger level is in fact not part of the baseline trigger scheme, on account of the significant CPU time required to execute the search. Not having access to this information limits efficiency for decay modes that

cannot easily be triggered through another signature, as the D0 _{→ K}0

SK

0

S one. The

same is true for decays involving Λ baryons and long-lived exotic particles. A system of specialised processors may be used to find rapidly the downstream tracks through look-up tables, and present these tracks to the software trigger in parallel with all the raw detector information in the event. Such a system is a large and ambitious project, which targets future upgrades of LHCb. However, the feasibility of the system can be demonstrated realising a smaller and cost-effective demonstrator, which performs the tracking of the vertex detector. In this thesis I therefore also describe the work that I have done in developing a software emulator for such a system, fine-tuning the algorithm and studying its performance on simulated data. The system has been approved to run parasitically during the next data-acquisition run of LHCb.

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The thesis is structured as follows. After an introduction on CP violation in charm decays and on the motivations of my work (Chapter 1), I briefly describe the experimental apparatus in Chapter 2. Then in Chapter 3 and Chapter 4 I describe my work on the development of a device able to perform a fast track reconstruction on FPGAs, with the aim of collecting larger charm-dataset in the future, while from Chapter 5 I describe the

measurement of CP asymmetry in D0 _{→ K}0

SK

0

S decays performed using the data available

up to now. In particular, in Chapter 5 I give an overview on the analysis strategy, in Chapter 6 I describe the selections applied on the sample and in Chapter 7 I describe the extraction of the asymmetry. In Chapter 8 I describe the systematic uncertainties, while I discuss the final results in Chapter 9.

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Part I

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Chapter 1

CP violation in charm decays

The study of CP violation plays an important role in the understanding of particle physics and of the entire Universe. In this Chapter I introduce briefly the Standard Model of particle physics, describing how CP violation fits within this model. Than I introduce charm physics and I briefly explain the motivations of my work.

1.1 The Standard Model

The Standard Model (SM) of particle physics [1, 2, 3] is a quantum field theory that describes the fundamental constituents of matter and the interactions among them. The model is defined by the symmetries of the Lagrangian and by the representations of the particles under these symmetries. The gauge group of symmetry of the SM is

GSM = SU (3)C ⊗ SU (2)L⊗ U (1)Y (1.1)

The SU (3)C term describes the symmetry of the strong force theory (Quantum

Chro-modynamics or QCD), where C refers to the color charge of the fields under

transforma-tions of this group; instead the SU (2)L⊗ U (1)Y term describes the symmetry of

elec-troweak interactions as introduced by the theory of Glashow-Weinberg-Salam [4, 3],

where L indicates the chirality of the weak interactions and Y refers to the hypercharge. The fundamental building blocks of matter are the half-odd-integer spin particles that

are representations of the GSM group:

QI_Li(3, 2)+1/6, uIRi(3, 1)+2/3, dIRi(3, 1)−1/3, LILi(1, 2)−1/2, lIRi(1, 1)−1. (1.2)

where i=1,2,3 is the flavour (or generation) index, the index L(R) indicates the left (right) chirality and the index I denotes the interaction eigenstates. This notation makes the representations and the quantum numbers of the fields manifest. Left-handed quarks,

QI

L , are triplets of SU (3)C , doublets of SU (2)L , and carry hypercharge Y = +1/6;

right-handed up-type quarks, uI

R , are triplets of SU (3)C, singlets of SU (2)L , and carry

hypercharge Y = +2/3; right-handed down-type quarks, dI

R , are triplets of SU (3)C ,

singlets of SU (2)L , and carry hypercharge Y = −1/3. Leptons are singlets of SU (3)C

and are classified according to the transformation properties of their fields with respect

to SU (2)L. Left-handed leptons, LIL , are doublets of SU (2)L ; right-handed leptons, lIR,

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representation (1/2, 1/2) Φ = Φ + Φ0 ! (1.3) which assumes a vacuum expectation value of

hΦi = √1 2 0 v ! (1.4) It is often parameterized as:

Φ = exp iσi 2θi 1 √ 2 0 v + H ! , (1.5)

where σi are the Pauli matrices,θi are three real fields and H is the Higgs boson field.

The non-zero vacuum expectation generates a spontaneous breaking of the gauge group

GSM → SU (3)C ⊗ U (1)EM, where U (1)EM is the symmetry group of electromagnetism.

This classification of leptons, quarks and bosons is schematically summarised in Fig. 1.1.

Figure 1.1: Elementary particles forming the Standard Model. The six quarks are highlighted in grey, the six leptons in green, the four gauge

bosons in red and the Higgs boson in blue.

Once the gauge symmetry, the particle content, and the pattern of spontaneous sym-metry breaking are defined, the Lagrangian of the Standard Model is derived as the most general renormalizable Lagrangian satisfying these requirements.

It can be divided in four contributions:

LSM = Lkinetic+ Lgauge+ LHiggs+ LY ukawa (1.6)

The kinetic term describes interaction between quarks and gauge bosons, the boson

kinetic term is described by Lgauge, Higgs self interaction are described by LHiggs and

finally the Yukawa interaction between fermions is described by the last term LY ukawa.

The first term Lkinetic can be written as

Lkinetic = ¯ψγµiDµψ, (1.7)

where γµ _{are the Dirac matrices, ψ is a Dirac spinor, ¯}_{ψ = ψ}†_γ0 _{is the adjoint spinor and}

Dµ is the covariant derivative, defined as

Dµ= ∂µ+ ig 2W d µσd+ ig0 2 BµY + igs 2 G a µλa. (1.8)

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In this equation Y, σd and λaare respectively the U (1)Y , SU (2)W and SU (3)C symmetry

groups generators, while g0 is the electromagnetic coupling constant.

The second term Lgauge can be written as

Lgauge= − 1 4G a µν(G a₎µν₋ 1 4W d µν(W d₎µν ₋1 4BµνB µν_, _(1.9)

where (Ga₎µν _{is the Yang-Mills tensor which represents the eight (a=1,...,8) gluon fields,}

(Wd₎µν _{is the weak field tensor that represent three (d = 1, 2, 3) gauge fields and B}

µν is

the electromagnetic tensor that represents U (1)Y gauge field Bµ.

The third part describes the spontaneous electroweak symmetry breaking which allows all SM particle to acquire mass. The Langrangian is written as

LHigss= (∇µΦ)†(∇µΦ) + µ2Φ†Φ + λ(Φ†Φ)2, (1.10)

where the first term represents the kinetic energy of the Higgs field together with its gauge interactions and the other two represent, respectively, the mass term and the self-interaction term. Those two terms form the Higgs potential, in which µ and λ are param-eters not predicted by the theory.

The last term, the Yukawa Lagrangian, accomodates fermions masses through their interaction with the Higgs field:

LY ukawa = −YijdQ¯ I LiΦD I Rj− Y u ijQ¯ I LiΦU˜ I Rj− Y l ijL¯ I LiΦl˜ I Rj+ h.c. (1.11)

Although the SM currently provides the best description of the subatomic world, it does not explain the complete experimental picture. It incorporates only three out of the four fundamental forces, omitting gravity, and it does not describe the nature of dark matter. Moreover the SM does not explain why there are three generations of quarks and leptons and their mass scale hierarchy, nor the matter-antimatter asymmetry of the Universe. The presence of these and other open questions suggest that the SM could be an effective theory corresponding to a low-energy approximation of a more complete theory of fundamental interactions.

A very important role in the search of physics beyond the SM is played by CP vio-lation, that is the violation of the symmetry that represents the invariance of physical processes under the inversion of spatial coordinates (parity transformation, denoted ad

P ) and of all intrinsic quantum numbers of involved particles (charge-conjugation

trans-formation, denoted as C). Currently, an important field of CP violation investigation is represented by heavy flavor physics, involving charmed and bottom hadrons. The charm quark is particularly relevant, since it represents a unique opportunity to study the possi-ble coupling of non-SM particles with an up-type quark. In fact top quarks decay before

hadronizing and π0 _{and η mesons, composed of u and ¯}_{u, are their own antiparticle and}

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1.2 CP violation in the Standard Model

Within the SM, CP symmetry is broken by an irreducible complex physical phase in the

Yukawa quark-term of the SM Lagrangian. CP symmetry is therefore preserved in strong1

and electromagnetic interactions, as supported by all experimental results thus far [6, 7], but violated in weak interactions.

In the basis of mass eigenstates, the charged current weak interactions for quarks have the following form:

LCC int = − g2 √ 2(¯uL, ¯cL, ¯tL)γ µ_V CKM    dL sL bL   W † µ+ h.c. (1.12)

VCKMis the unitary 3×3 Cabibbo-Kobayashi-Maskawa matrix [8] [9], which parametrizes

complex couplings between the quark-mass eigenstates and the charged weak gauge bosons

(W±): VCKM =    Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb    (1.13)

The CKM matrix for three generations of quarks can be parameterized by three mixing-angles and one complex phase. The latter is the CP -violating phase, also known as the

Kobayashi-Maskawa phase δKM , which makes the wave function asymmetric under the

T-transformation. Magnitudes of CKM matrix elements can be determined using a global

fit to all available measurements with the VCKM unitarity constraint. The current

knowl-edge of the magnitudes of all nine CKM elements is as follows [10]:

VCKM =    0.97410 ± 0.00011 0.22650 ± 0.00048 0.00361+0.00011_−0.00009 0.22636 ± 0.00048 0.97320 ± 0.000011 0.04053+0.00083−0.00061 0.00854+0.00023_−0.00016 0.03978+0.00082_−0.00060 0.999172+0.000024_−0.000035    (1.14)

As seen by the values of |Vij|, transitions between the same generation are favoured

com-pared to those between two different generations. For example, transitions between the

first and the second generation are suppressed by factors of O(10−1), and those between

the first and the third one are suppressed by O(10−3). Transitions between the same

generation are represented by diagonal elements and are of the order of 1. The VCKM

Wolfenstein parameterization [11] brings out this hierarchical pattern by introducing four quantities λ, A, ρ, η: VCKM =    1 − λ2_/2 _λ _Aλ3_{(ρ − iη)} −λ 1 − λ2/2 Aλ2

Aλ3_{(1 − ρ − iη)} _{− Aλ}2 ₁





+ O(λ

4₎ _(1.15)

where λ is the expansion parameter, which is related to the Cabibbo angle (sin θc =

0.232 ± 0.002 [10]). The δKM phase is related to the ρ − iη term in this parametrization.

The unitarity condition of the VCKM matrix is V

†

CKMVCKM = I. This relationship results

in 6 normalization and 6 orthogonality equations. The six vanishing equations can be

1_{CP symmetry in the strong interaction is not guaranteed by the SM. However, no evidence of CP V}

has been detected so far in QCD and the coefficient of the CP -violating term of the Lagrangian of the QCD is measured to be θQCD < 1010 [5]

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represented as triangles in a complex plane, all having the same area. These are all known as unitarity triangles, although the most commonly used among them is the triangle

arising from VudVub∗+VcdVcb∗+VtdVtb∗. Figure 1.2 shows the unitarity triangle in the complex

(¯ρ − ¯η) plane.

Figure 1.2: Unitarity triangle in the ( ¯ρ, ¯η) plane. The parameters ¯ρ and

¯

η are related to the CKM matrix elements by te equation ¯ρ + i¯η = −V

∗

udVub

V_cd∗Vcb

The vertices are fixed at (0,0) and (1,0), while the third has ¯ρ and ¯η parameters as

coordinates. The area of the unitarity triangles is equal to |J |/2, where J is the Jarlskog invariant [12], which is defined by:

Im[VijVklVil∗V ∗ kj] = J X n,n∈(d,s,b) ikmjln (1.16)

and approximated by J ≈ λ6_A2_{η in the Wolfenstein parametrization. The Jarlskog}

in-variant appears in any CP -violating quantity in the SM as a constant of

proportion-ality, thus CP violation occurs only if J 6= 0. Current measurements indicate J =

(3.00+0.15_−0.09) × 10−5 _{[10]. The geometrical meaning of CP violation is that the unitarity}

triangles do not degenerate into lines.

Fig. 1.3 illustrates the global fit result of CKM parameters in (¯ρ − ¯η) plane, obtained

by combining various measurements. The peak vertex of the triangle is lying in a red-outlined region, which represents the constraint obtained by combining all measurements. By improving the current measurements on CKM matrix parameters it is possible to reduce the size of this allowed region, measuring the position of the vertex more precisely. An experimental result inconsistent with this vertex could represents a glimpse of New Physics, i.e. physics beyond the SM. In this scenario, CP violation could provide a probe of non-SM physics. The amount of CP violation in the SM does not provide an explanation for the cosmological baryon asymmetry in the Universe. Indeed, many extensions of the SM include additional sources of CP violation in non-SM processes. For this and other reasons there are several experiments, like LHCb at CERN, whose aim is to study physics processes sensitive to CP violation and improve our knowledge of Nature.

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Figure 1.3: Current experimental status of the global fit to all available experimental measurements related to the unitarity triangle

phenomenology. From Ref. [13].

1.3 The charm sector

The mass of charmed mesons is approximately 2 GeV/c2_. _D0 _{neutral mesons, which}

are formed by a charm quark and an up antiquark, have a lifetime of about 410 fs,

corresponding to a cτ of almost 130 µm. While the phenomenology of strange and

beauty hadrons decays has been already broadly studied in the past few years, the charm-dynamic is still partially unexplored, due to both experimental and theoretical limitations.

CP violation in the charm sector is expected to be very small (O(10−3)), as all relevant amplitudes within the SM are described, to an excellent approximation, by the physics of the first two generation only. In fact charmed meson decays involve quark transitions from the c quark to lighter quarks, and therefore the elements of the CKM matrix involved are those of the first two rows. The relevant unitary relationship (Fig. 1.4) for charm mesons

is then V_cd∗Vud + Vcs∗Vus + Vcb∗Vub = 0 that can be rewritten into a more compact form,

introducing the coefficient Λq= Vcq∗Vuq(q ∈ d, s, b) obtaining Λd+ Λs+ Λb = 0. Therefore

a roughly estimate from the CKM scheme gives CP -violation ≤ O(VubVcb∗/VusVcs∗) ∼ 10

−3_.

From a theoretical point of view, the predictions in this field are not straightforward since the masses of charmed hadrons, O(2 GeV), belong to a range where non-perturbative

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Figure 1.4: Schematic representation of the charm unitarity triangle

hadronic physics is operative and the phenomenological approximations commonly used in the strange and bottom sectors are of little help. This leads to large uncertainties in the theoretical picture of charm-dynamics. In particular the computational power available today is not enough for the determination of relevant charm properties using lattice-QCD. Exclusive approaches rely on explicitly accounting for all possible intermediate states, which may be modelled or fitted directly to experimental data. The problem is that D-mesons have many final states, therefore precise measurements of amplitudes and strong phases are needed to avoid assumption that can limit predictions.

On the experimental side, the interest in the charm flavor sector has increased during

the past few years because of the observation of D0− D0 _{mixing [14] provided by LHCb}

(evidence also from BaBar [15] and Belle [16]). Until a few years ago experimental sen-sitivities to parameters related to mixing and CP -violation in the charm sector were still orders of magnitude larger than most SM and non-SM expectations. Finally, in 2019 CP

violation has been observed for the first time also in D0 _{mesons [17]. However, given the}

uncertainties in the theoretical predictions based on the SM, it is not currently possible to evaluate their agreement with observations [18, 19, 20]. Further measurements in the charm sector are crucial to shed light on CP V phenomenology in the up-quark sector, that might possibly involve new dynamics beyond the SM, not necessarily constrained to be the same as in down-type quarks. The value of CP violation in charm can be in fact a significant probe for the presence of particles not included in the SM. These can enter in the decay amplitudes, affecting results in a detectable way. In particular, non-SM

particles, such as the hypothetical massive and neutral gauge boson Z0, could give rise

to CP violation in charm decays via tree-level decay amplitudes [21, 22, 23]. Moreover, enhancements of CP V could arise also from loop-induced effects, as in the presence of supersymmetric particles [24]. However, it has to be noted that various supersymmetric models have been already excluded by other measurements [25, 10].

1.3.1 Experiments

Several types of experiments, operating in different conditions, have contributed and are still contributing to the study of charm physics. The pioneers in this field were the fixed target experiments, among which those operating at Fermilab, such as E691 and Focus, were the most significant ones. In the E691-experiment samples of nearly 10000 reconstructed charm decays were produced by photo-production [26]. Nearly ten years

later the FOCUS experiment was able to produce over 106 _{charm decays. Over the last}

few decades the most important contributions to flavor physics came from e+e− machines

and hadron colliders.

About e+_e− _{machines, the majority of the results have come from the CLEO, BaBar}

and Belle experiments, which operated at the Y(4S) resonance (corresponding to

center-of-mass energies of approximately 10.6 GeV/c2 _{) producing B}0_B0 _{and B}+_B− _{pairs. From}

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mass energy between 3.8 − 4.6 GeV. Even if BESIII is not able to compete both BaBar and Belle in statistics on charm physics, data taken at charm threshold still have pow-erful advantages over the data at Y(4S). In fact charm events produced at threshold are extremely clean and the signal/background ratio is optimum.

While experiments performed at e+_e− _{colliders have the advantage of operating in a}

clean environment, where the level of background is low and where its easier to control

systematic uncertainties, the production cross section for c¯c is much higher at hadron

colliders. The cross section for c¯c pair production is in fact σ ∼ 1.3 nb [27] at the

Y(4S) resonance, while at LHC in pp collisions at a centerofmass energy of 13 TeV

-σ(pp → c¯cX) = (2940±3±180±160) µb in the range 0 < pT < 8 GeV/c, 2 < η < 4.5 [28].

This is why LHCb, located at LHC, is now playing a major role in charm physics. LHCb

has collected about a billion of D0 _{decays up to now, and it is currently being upgraded}

to collect about five times more event in the next 10 years.

The begin of data-taking of the new Belle II experiment in 2018 and the currently ongoing upgrade of LHCb are starting a even more exciting era in this field.

1.4 Types of CP violation

The CP transformation law for a final CP -eigenstate f is CP |f i = ωf|f i and CP |f i =

ω_f∗|f i, where ωf is a complex phase (|ωf| = 1). It is important to discuss the phases

that can arise in those amplitudes since they are responsible for the phenomenon of CP violation. Usually, two types of phases are present and are called weak and strong phases. Weak phases come from any complex term in the Lagrangian appearing as complex con-jugated in the CP conjugate amplitude. They are called weak phases because in the SM Lagrangian they occur only in the CKM matrix, which is part of the electroweak sector. Strong phases come from final state interactions and they contribute to the amplitudes through the intermediate on-shell states in the decay process. These phases arise even if the Lagrangian is real and are called rescattering phases. If there are hadrons in the final state, they are generated by strong interactions and therefore are also called strong phases. Strong phases do not change sign under CP transformation. Experimentally, there are three manifestations of CP violation:

• CP violation in the decay • CP violation in the mixing

• CP violation in the interference between decay and mixing

In 1964 the experiment of J. Cronin and V. Fitch [29] on neutral kaons had shown that CP symmetry is broken in weak interactions. This was the first evidence of

mixing-induced CP violation, caused by the fact that the neutral kaon mass eigenstates, K0

L

and K0

S,are not eigenstates of CP . The first evidence of CP violation in the decay, still in

neutral kaons, was established about 30 years later, in 1999, by both NA48 [30] and KTeV [31] collaborations. In the following description I will focus on charm phenomenology [32].

1.4.1 CP violation in the decay

Since all observables are related to the squared amplitudes, phases are not experimentally measurable, but only phase differences are accessible. Thus, CP violation in the decay

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appears as a result of the interference among various terms in the decay amplitude, and it does not occur unless at least two terms have different weak phases and different strong

phases. Let’s define Af as the amplitude of D → f decay and ¯Af the amplitude of ¯D → f

decay. The final state f is accessible from D and ¯D, i.e. is a CP eigenstate. We can for

example consider a decay process which can proceed through several amplitudes

Af = X k |Ak|ei(Φk+δk) A¯f = X k |Ak|ei(−Φk+δk) (1.17)

where δk are the strong phases, which do not change sign under CP , and φk are the weak

phases. The difference between the two amplitudes is

|Af|2− | ¯Af|2 = −2

X

l,k

|Al||Ak| sin(φl− φk) sin(θl− θk). (1.18)

To observe CP violation one needs |Af| 6= | ¯Af|, therefore there must be a contribution

from at least two processes with different weak and strong phases in order to have a non vanishing interference term.

A golden observable sensitive to the CP violation in the decay is the CP asymmetry defined as

ACP_{(f ) =} Γ(D → f ) − Γ( ¯D → f )

Γ(D → f ) + Γ( ¯D → f ) (1.19)

where Γ is the time-integrated decay width of the D → f decay process and it is

propor-tional to the squared amplitude (Γ(D → f ) ∝ |Af|2 and Γ( ¯D → f ) ∝ | ¯Af|2), thus

ACP_{(f ) = A}dec ₌ |Af|2− | ¯Af|2 |Af|2+ | ¯Af|2 = 1 − R 2 f 1 + R2 f (1.20) Therefore, CP violation in the decay occurs if

Rf = ¯ Af Af 6= 1 (1.21)

1.4.2 CP violation in the mixing

The phenomenology of CP violation in neutral D meson decays is enriched by the

possi-bility that D0 _{→ D}0 _{flavor oscillations may occur. Particle-antiparticle oscillations, which}

have been observed in K, D, B, and B0

s systems, cause an initial (at time t = 0) pure D0

(D0_{) state to evolve in time to a linear combination of D}0 _{and D}0 _{states. If the typical}

times t of the observation are much larger than the typical strong interaction scale, then the time evolution is described by the approximate Schrödinger equation

id dt D0(t) D0_(t) ! = M − i 2Γ _D0_(t) D0_(t) ! (1.22) where M and Γ are 2 × 2 Hermitian matrices,

M = M11 M12 M₁₂∗ M22 ! Γ = Γ11 Γ12 Γ∗₁₂ Γ22 ! (1.23)

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Diagonal elements of the effective Hamiltonian Hef f = M − iΓ/2 are associated with

the flavor-conserving transitions D0 _{→ D}0 _{and D}0 _{→ D}0 _{, off-diagonal elements are}

associated with the flavor-changing transitions D0 _{↔ D}0 _{. The matrix elements of M}

and Γ satisfy M11 = M22 and Γ11= Γ22 to obey CPT invariance. If Hef f is not diagonal,

flavor eigenstates are not mass eigenstates and thus do not have well defined masses and

decay widths. The eigenstates of Hef f are a superposition of D0 and D0 states,

|DL,Hi = p|D0i ± q|D0i, (1.24)

where p and q are complex coefficients satisfying

|p|2 _{+ |q|}2 _{= 1} _and q p = v u u t M₁₂∗ − i/2Γ∗ 12 M12− i/2Γ12 = q p eiΦ (1.25)

The eigenvalues of Hef f are

λL,H = (M11− i/2Γ11) ±

q

p(M12− i/2Γ12) ≡ mL,H− i/2ΓL,H (1.26)

The |DL,Hi eigenstates have well defined masses and decay widths, whose values are

given by the real and imaginary parts of the λL,H eigenvalues, respectively. The L and H

subscripts stand for light and heavy and refer to the mass of the |DL,Hi eigenstates. Due

to the non correspondence between flavor and mass eigenstates, an initially pure D0 _(D0₎

state can interact as a D0 _{or a D}0 _{at a given time t.}

CP violation in the mixing occurs when the probability for the oscillation process depends

on the initial state, i.e. the probability for the D0 _{→ D}0 _{process is different from the CP}

conjugated one, D0 _{→ D}0 _{. CP violation in mixing is defined by the parameter}

Rm = q p 6= 1 (1.27)

1.4.3 CP violation in the interference between decay and mixing

In the case of a common final state f shared simultaneously by the D0 _{and the D}0 _meson,

the CP symmetry can be violated in the interference between the decay without mixing,

D0 → f , and the decay with mixing, D0 _{→ D}0 _{→ f .}

The phenomenology of flavor oscillations is described using two dimensionless mixing

parameters x ≡ ∆m/Γ and y ≡ ∆Γ/2Γ, where ∆m ≡ mL− mH is the mass difference,

∆Γ ≡ ΓL− ΓH is the decay width difference and Γ ≡ (ΓL+ ΓH)/2 = 1/τ is the average

decay width. The time-dependent decay amplitude of an initially pure D0 _{state decaying}

to a final state f , accessible from both D0 _{and D}0 _{states, is given by}

hf |H|D0_{(t)i = A} fg+(t) + ¯Af q pg−(t), (1.28) where |g±(t)|2 = 1 2e −t/τ cos _xt τ ± cosh _yt τ (1.29)

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represents the time dependent probability to conserve the initial flavor (+) or oscillate into

the opposite flavor (-). The time dependent decay rate, proportional to |hf |H|D0_(t)i|2 _is

dΓ dt(D 0_{(t) → f ) ∝ |A} f|2[(1 − |λf|2) cos _xt τ + (1 + |λf|2) cosh _yt τ −2Im(λf) sin _xt τ + 2Re(λf) sinh _yt τ ] where λf = q ¯Af pAf

. Analogous calculations apply for an initially pure D0 state.

If the time-dependent CP asymmetry is calculated substituting the Γ(D0(t) → f )

expression in Eq. 1.19, it can be seen that CP violation in interference occurs when

Im(λf) 6= 0. (1.30)

1.5 State of the art at LHCb and motivations for this

work

Since the start of data-taking in 2011, LHCb has collected ∼ 1 billion of D0 _decays,

events that have been (and still currently are) used to increase the physics knowledge of the charm sector. The actual knowledge of mixing parameters and CP violation in mixing and interference is summarised in Fig. 1.5 [33]. The mixing is now well established and

Figure 1.5: Left: value of x and y mixing parameters, resulting from a global fit to all available measurements, compared with the no-mixing hypothesis (x = y = 0). Right: Value of Arg(q/p) and |q/p|. A value of Arg(q/p) different from 0 indicates CP violation in the interference between mixing and decay, while a value of |q/p| different from 1 is an evidence of

CP violation in mixing. Current measurements show therefore no evidence

of such violations. From Ref. [33]

there is a first 3σ evidence of a non-zero x (which is proportional to ∆m), i.e. an evidence of a positive mass difference between the neutral charm meson eigenstates. In particular

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the obtained value of x is x = (3.9+1.1−1.2× 10−3) [34]. Instead, mixing-induced CP violation remains unobserved.

However, thanks to the huge dataset of D0 _{meson decays collected, in 2019 CP}

viola-tion in the decay was observed for the first time in the charm sector. The measurement,

which has been performed using more than 60 million of D0 _{→ K}+_K− _{and D}0 _{→ π}+_π−

decays, is discussed in the next Section.

1.5.1 First observation of CP violation in charm decays

From the first observation of CP violation in the kaon system (1964), which led to the Nobel Prize to James Cronin and Val Fitch, it took more than 40 years to discover CP violation also in beauty particle decays. The observation was done by the BaBar [35] and Belle [36] collaborations, which results in the award of the 2008 Nobel Prize in physics to Kobayashi and Maskawa. For the first time, at the beginning of 2019, CP violation

has been observed in the charm sector by the LHCb collaboration in D0 → h+_h− _decays

(where h = πK) [17]. These decays have been used to measure ∆ACP _{, i.e. the difference}

ACP_(K+_K−_{) − A}CP_(π+_π−_).

The time-dependent CP asymmetry between states produced as D0 or D0 mesons

decaying to a CP eigenstate f at time t is defined as:

ACP(f, t) = Γ(D

0_{(t) → f ) − Γ(D}0_{(t) → f )}

Γ(D0_{(t) → f ) + Γ(D}0_{(t) → f )}, (1.31)

where Γ denotes the time-dependent rate of the D0decay. For f = K+K−and f = π+π−,

ACP_{(f, t) can be expressed in terms of a component associated to CP violation in the decay}

amplitude and another component associated to CP violation in D0_{− D}0 _{mixing or in the}

interference between mixing and decay. The corresponding time-integrated asymmetry,

ACP_{(f ), can be written (to first order in the mixing parameters) as [37]}

ACP_{(f ) = a}dec

CP(f ) −

ht(f )i

τ (D0₎AΓ(f ), (1.32)

where ht(f )i denotes the mean decay time of D0 _{→ f decays in the reconstructed sample,}

adec

CP(f ) is the CP asymmetry in the decay, τ (D0) is the D0 lifetime and AΓ(f ) is the

asymmetry between D0 → f and D0 _{→ f effective decay widths [38, 39, 40]. Since A}

Γ can be considered independent from the final state [41], the difference between the CP

asymmetries in D0 _{→ K}+_K− _{and D}0 _{→ π}+_π− _{decays is:}

∆ACP ≡ ACP_(K+_K−_{) − A}CP_(π+_π−_{) ≈ ∆a}dec

CP −

∆hti

τ (D0₎AΓ, (1.33)

where ∆adec

CP ≡ adecCP(K+K

−_{) − a}dec

CP(π+π

−_{) and ∆hti ≡ ht(K}+_K−_{)i − ht(π}+_π−_{)i. The}

quantity measured by LHCb is the raw asymmetry

Araw ₌ N (D0 → f ) − N (D0 → f )

N (D0 _{→ f ) + N (D}0 _{→ f )}, (1.34)

where N (D0 _{→ f ) and N (D}0 _{→ f ) is the number of D}0 _{and D}0 _{decays into the final}

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To distinguish between D0 _{and D}0 _{decays is necessary to tag the D}0_{. This has been}

done using both D0 _{produced promptly at the pp collision point (primary vertex, PV) in}

the strong D∗+(2010) → D0_π+ _{decay or D}0 _{produced at a vertex displaced from any PV}

in semileptonic ¯B → D0_µ−_ν_¯

µX decays, where ¯B denotes a hadron containing a b quark

and X stands for additional particles. The flavour at production of D0 _{mesons from D}∗+

decays is obtained from the charge of the accompanying pion, while the one of D0 _mesons

from semileptonic b-hadron decays is determined from the charge of the accompanying muon.

The raw asymmetry is related to the CP asymmetry by the following equation :

Araw

w ACP + Aprod+ Adet, (1.35)

where Aprod _{is the production asymmetry of the D}∗ _{or the b-hadron (respectively for the}

prompt and semileptonic decays), while Adet _{is the detection asymmetry of the tag pion}

or muon, due to different reconstruction efficiencies between positive and negative tagging

particles. The previous equation is valid up to correction of O(10−6).

Production and detection asymmetries depend on the kinematic of the decay, but

they are independent from the D0 final state, because it is charge symmetric in both

cases (π+_π− _{and K}+_K−_{). Therefore, if the kinematics of the two decay channel are}

equalised, they cancel out in the difference

∆Araw ≡ Araw(K+K−) − Araw(π+π−) = ACP(K+K−) − ACP(π+π−) ≡ ∆ACP. (1.36)

This makes the determination of ∆ACP largely insensitive to systematic uncertainties.

Data collected at a centre of mass energy of 13 TeV from 2015 to 2018, which

corre-sponds to an integrated luminosity of 5.9 fb−1, have been used to perform the

measure-ment. The measured values of ∆ACP are

∆ACP π−tagged= [−18.2 ± 3.2(stat.) ± 0.9(syst.)] × 10−4 (1.37)

∆ACP µ−tagged= [−9 ± 8(stat.) ± 5(syst.)] × 10−4 (1.38) both in good agreement with world average [33] and previous LHCb results [42, 43].

The full combination with all LHCb measurements gives the following value

∆ACP = [−15.4 ± 2.9] × 10−4, (1.39)

where the uncertainty includes statistical and systematic contributions. The significance of the deviation from zero corresponds to 5.3 standard deviations. Therefore this is the first observation of CP violation in the decay of charm hadrons.

Given Eq. 1.32, since the LHCb average for AΓis (−2.8±2.8)×10−4, and ∆hti/τ (D0) =

0.115 ± 0.002, the measurement is a clear indication on CP violation in the decay

∆adec_CP = (−15.7 ± 2.9) × 10−4. (1.40)

Since the parameter AΓ is mostly sensitive to effect of CP violation in the mixing and

in the interference between decay and mixing, but is also slightly related to CP violation

in the decay, it is possible to combine the most precise measurements on ∆adec_CP and AΓ

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“direct”, while CP violation in the interference and in the mixing is also called “indirect”.

Therefore ∆adec

CP ≡ ∆adirCP and AΓ ∝ aindCP [37].

Figure 1.6: Values of ∆adirCP and aindCP resulting from a global fit to the

available measurements of ∆ACP and A_Γ. From Ref. [33].

1.5.2 The D

0

→K

0

S

K

0

S

decay channel

As discussed in Sec. 1.3 theoretical predictions in the charm sector are not very precise. Therefore, even if the measured value of CP violation is consistent with - although in

magnitude at the upper end of - SM expectations (10−4−10−3_{), further measurements are}

needed to better clarify the physics picture. Obviously, there is now a strong motivation to look at other channels - where CP violation is either currently observable, or will be in the next future - to get for confirmation and improved measurements in this new sector that just opened. That is especially true in the LHCb experiment, that has performed the first observation and has much more data still to be analyzed. Among all the possible

decay channels, the D0 _→K0

SK

0

S one is very promising, because of the size of the expected

effect [44, 45].

Charm decay amplitudes

Charmed hadronic decays are classified according to the degree of CKM matrix element suppression:

• Cabibbo-Favored decays (CF), with amplitudes proportional to the product VudVcs∗

• Singly Cabibbo-Suppressed decays (SCS) with amplitudes proportional to the

prod-uct VusVcs∗ or VudVcd∗ (this is the case of the D0 → KS0K

0

S decay)

• Doubly Cabibbo-Suppressed decays (DCS) with amplitudes proportional to the

product VusVcd∗

The relative hierarchy of these amplitudes is 1 : λ : λ : λ2_{. A way to describe these}

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relations among different decay modes [46]. These relations allow to estimate theoretical parameters by fitting the branching ratio (BR) measured in several decay channels. Vice versa, they are useful when some measured decay rates are related to some unknown decay rates, providing us a prediction of the latter ones. In the topological-diagram approach relations can be built on a set of topological amplitudes describing D mesons decays over the strong interaction scale and which are classified according to the topologies of weak interactions. The parametrization of decay amplitudes with the use of topological amplitudes permits an easy and intuitive implementation of SU(3) relations.

These amplitudes could be distinguished in two main groups: tree and penguin am-plitudes, and weak annihilation amplitudes. The first group includes the following ampli-tudes: color-allowed (T) and color-suppressed (C) tree amplitudes, with an external and

internal W-emission respectively, QCD-penguin amplitude (P), color-favored (PEW) and

color-suppressed (PC

EW) electro-weak penguin amplitudes and the singlet QCD-penguin

amplitude (S), which involves SU(3)-singlet mesons like η , ω and φ. The second group in-cludes W-exchange (E) and W-annihilation (A) amplitudes, QCD-penguin exchange (PE)

and QCD-penguin annihilation (PA) amplitudes, electro-weak penguin exchange (P EEW)

and electro-weak penguin annihilation (P AEW) amplitudes. In Fig. 1.7 the corresponding

topological-diagrams are shown.

Figure 1.7: Topological diagrams. From Ref. [46]

The D0 _→K0

SK

0

S case

Regarding SCS decays, a common choice [45] for the decomposition of a decay amplitude in terms of CKM elements is :

A = 1

2[(λs− λd)Asd+ λbAb] , (1.41)

where λq ≡ Vcq∗Vuq is the CKM amplitude. Within the SM a non-vanishing CP asymmetry

in the decay involves the interference of λbAb with (λs − λd)Asd. Neglecting quadratic

(and higher) terms in |λb|/|(λs− λd)| the direct CP asymmetry reads

adec_CP = |A| 2_{− | ¯}_A|2 |A|2_{+ | ¯}_A|2 = Im λb (λs− λd) ImAb Asd (1.42)

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Asd and Ab can be expressed as sum of topological amplitudes multiplied by a proper

co-efficient. These coefficient are called “Wilson coefficients”. For the D0 _{→ K}0

SK 0 S decay [45, 47], Asd = E1+ E2− E3 √ 2 (1.43) and Ab = 2E + E1+ E_√2+ E3 + P A 2 , (1.44)

where E1, E2 and E3 amplitudes are shown in Fig. 1.8, while E and PA are shown in

Fig. 1.9. Since only the SU(3)-breaking2 amplitudes E1, E2, E3 contribute to Eq. 1.43,

Figure 1.8: SU(3)-breaking topological amplitudes. From Ref. [48].

Figure 1.9: Exchange (left) and penguin annihilation (right) diagrams

contributing to the D0 →K0

SK

0

S amplitude. From Ref. [49].

Asd vanishes in the SU(3) limit [50]. Instead, Ab does not vanish in this limit, because of

the contribution from E and PA. As a result, while

Im λb

(λs− λd)

∼ 6 × 10−4_,

Im(Ab/Asd) can be large and enhance the CP asymmetry (Eq. 1.42) to an observable

level [44] , i.e., as large as 1.1% (95% C.L.) [45]. This is an upper limit, and the majority

of predictions places the value of ACP_(K0

SK

0

S) at the level of 10

−3 _{[51, 52, 53], but further}

enhancements could result from contributions from physics beyond the SM [50]. 2_{In the limit of m}

u = ms = md, we can talk about an SU(3) symmetry (usually denoted as SU(3) flavour symmetry) that rotates these quarks into each other. In reality, the light quarks do not have degenerate masses, therefore the SU(3) flavour symmetry is broken by the different quark masses.

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As in the case of the D0 _{→ K}+_K− _{and D}0 _{→ π}+_π− _{decays, because of the slow}

mixing rate of charm mesons (x,y∼ O(10−3)), the CP asymmetry can be expanded as

ACP_(K0 SK 0 S) = a dec CP(KS0K 0 S) − ht(K0 SK 0 S)i τ (D0₎ AΓ, (1.45) where, as a reminder, ht(K0 SK 0

S)i denotes the mean decay time of D

0 _{→ K}0

SK

0

S decays

in the reconstructed sample. Since AΓ has been measured to be compatible with zero at

a level of 10−4, while hti/τ is of order of 1, the second term of Eq.1.45 can be therefore

neglected, being much smaller than the expected sensitivity on ACP_{, and A}CP _{' a}dec

CP.

Therefore the study of CP asymmetry in D0 _{→ K}0

SK

0

S channel is a test of CP violation

in the decay.

The measurement of CP asymmetry in D0 _{→ K}0

SK

0

S decays is sensitive to a different

mix of CP -violating amplitudes w.r.t D0 _{→ K}+_K− _{and D}0 _{→ π}+_π− _{[46]. Therefore it}

provides independent information on CP V and improving the measurement, and possibly detecting the effect, will help in the understanding of the mechanism of CP violation in charm decays.

1.5.3 Experimental status

The existing measurements on the D0 _{→ K}0

SK

0

S decay channel are listed in Tab 1.1. All

measurements, and their average, are compatible with no CP asymmetry within uncer-tainties.

Table 1.1: Existing measurements of ACP(D0 → K0

SK 0 S). ACP_(K0 SK 0

S) (%) Yield Year Collaboration

−23. ± 19. 65 ± 14 2008 CLEO [54]

−2.9 ± 5.2 ± 2.2 635 ± 74 2015 LHCb Run 1 [55]

−0.02 ± 1.53 ± 0.17 5399 ± 87 2016 Belle [56]

4.3 ± 3.4 ± 1.0 1067 ± 41 2018 LHCb 2015+2016 [57]

0.4 ± 1.4 World average [10]

e+e− machines The first measurement of ACP(KS0K

0

S) was made by CLEO, who

mea-sured ACP _{with a statistical uncertainty of 19% [54]. The data used correspond to an}

integrated luminosity of 13.7 fb−1 collected at the Υ(4S) resonance. The world’s best

measurement has been instead made by Belle, who measured ACP with a statistical

un-certainty of 1.53% [56]. In this case the data correspond to an integrated luminosity of

921 fb−1, collected at or slightly below the Υ(4S) resonance and at the Υ(5S) resonance.

To note that at the recent ICHEP2020 conference, the Belle II collaboration has shown

that a total of 177 ± 14 D0 _{→ K}0

SK

0

S events have been already collected [58] after 1.5

years of data-taking.

Hadron colliders At hadron colliders, the only experiment who measured ACP _(K0

SK

0

S)

is the LHCb experiment. On Run 1 data, which correspond to an integrated luminosity

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TeV, LHCb as reached a statistical uncertainty of 5.2% [55]. Then, using 2015 and 2016

collected at 13 TeV and corresponding to an integrated luminosity of about 2 fb−1, LHCb

has reached a statistical uncertainty of 3.4% [57]. To be noted that, for the majority of

Run 1 data-taking, no dedicated trigger line was present to select D0 _{→ K}0

SK

0

S decays.

This because of the low reconstruction efficiency in selecting K0

S. These particles are in

fact produced with an high boost in the beam direction, they have a relatively high lifetime

(τ ∼ 0.9 × 10−10s [10]) and the often decay outside the LHCb vertex detector acceptance.

Since the information coming from this detector is used to select track at the first level of

the software trigger (see Sec. 2.2.2), in the D0 _→K0

SK

0

S decay, where only K

0

S are present

in the final state, the trigger does not fire in the majority of the cases. The low trigger efficiency limits the available statistics, and therefore it limits also the sensitivity on the measured CP asymmetry. However, given also the potential in observing an effect, the

D0 _{→ K}0

SK

0

S decays offer a great opportunity to rethink the analysis strategy, eventually

developing novel approaches, to take fully advantage of the data collected and to improve the sensitivity on CP -violating effects.

1.5.4 Prospects for the future

Looking ahead, in 2022 LHCb will start to acquire new data with an almost completely new detector and trigger system. The instantaneous luminosity will increase by a factor

of 5, reaching 2 × 1033cm−2s−1. When the planned 50 fb−1 of data will be collected, it

is estimated that the sensitivity on ∆ACP _{will reach the level 7 × 10}−5 _{[59]. In addition,}

the statistical sensitivity on the asymmetry in the single D0 _{→ K}+_K− _{and D}0 _{→ π}+_π−

channels will reach the level of 1.5 × 10−4, [59], therefore it could be possible to observe

CP violation not only looking at the difference between the two channels, but also in the

single channel. With this improved precision it should be possible to better understand the nature of CP violation in charm decays.

Regarding the study of CP violation in D0 _→K0

SK

0

S decays, there is a large room for

improving the result in the future runs of LHCb. The measurement is in fact limited by

the difficulty of selecting K0

S at trigger level in LHCb. An effort to increase the trigger

efficiency is actually ongoing, both introducing specific trigger lines at the first level of the

software trigger, optimised to select K0

S decaying inside the vertex detector, and developing

a specialised tracking device to reconstruct and trigger at the earliest possible stage on K0

S

decaying outside the vertex detector acceptance. Find tracks downstream of the magnet at the earliest trigger level is in fact not part of the baseline trigger scheme, on account of the significant CPU time required to execute the search. A system of specialised processors may be used to find rapidly these tracks through look-up tables, and present them to the software trigger in parallel with all the raw detector information in the event [60]. This

will be a benefit not only for the D0 _{→ K}0

SK

0

S decay channel, but also for other channels

containing K0

S in the final state, as for example the D

0 _{→ K}0

SK

∗0 _{decay channel (where}

ACP _{is expected to be of O(10}−3_{) [61]), and other decays involving Λ baryons and}

long-lived exotic particles. Such a system is a large and ambitious project, which targets future upgrades of LHCb. However, the feasibility of the system can be demonstrated realising a smaller and cost-effective demonstrator, which performs for example the tracking of the vertex detector.

In this thesis I first describe my contribution to the development of a device capable to perform fast reconstruction of tracks in the vertex detector, and then I present the

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measurement of CP violation in D0 _→K0

SK

0

S decays performed with the available data

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CP violationin K ﬁnalstatesatLHCb 0 Searchingforconﬁrmationofcharm UniversitàdiPisaGraduatecourseinPhysics

Graduate course in Physics

XXXIII entrance (2017-2020)

Searching for confirmation of charm

CP violation in K

S

0

final states at

LHCb

PhD thesis

Author:

Giulia Tuci

Advisor:

Prof. Giovanni Punzi

Abstract

Contents

I

Introduction

5

II

Towards future runs: fast track reconstruction with

FP-GAs

47

III

Measurement of CP asymmetry in D

→ K

K

decays with

Run 2 data

81

IV

Final remarks

197

Preface

Part I

Chapter 1

CP violation in charm decays

1.1

The Standard Model

1.2

CP violation in the Standard Model

1.3

The charm sector

1.3.1

Experiments

1.4

Types of CP violation

1.4.1

CP violation in the decay

1.4.2

CP violation in the mixing

1.4.3

CP violation in the interference between decay and mixing

1.5

State of the art at LHCb and motivations for this

work

1.5.1

First observation of CP violation in charm decays

1.5.2

The D

→K

K

decay channel

1.5.3

Experimental status

1.5.4

Prospects for the future

_S