Measurement of time integrated CP asymmetries in D0->KS0 KS0 decays

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Università degli studi di Pisa

Corso di Laurea Magistrale in Fisica

Anno accademico 2016-2017

Measurement of time integrated CP

asymmetries in D

0

→ K

_S

0

K

_S

0

decays

Tesi di Laurea Magistrale Master thesis

Author:

Giulia Tuci

Supervisors:

Prof. Giovanni Punzi

Dott. Simone Stracka

Dott. John Walsh

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iii

Introduction

The Standard Model (SM) of particle physics is the theory describing electroweak and strong interactions. Although the SM 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 SM is only a low-energy approximation of a more general theory.

To understand where the SM fails and to search for hints of New Physics (NP), sci-entists could directly produce particles at higher energy and see if something unexpected happens. This is, for example, the main goal of ATLAS and CMS experiments at LHC. Another way to test the SM is to perform more precise measurements of known quantities and compare experimental results with predictions. Of particular interest are processes suppressed within the SM: enhancements of such processes are evidence of contributions from NP. The search for CP violation, i.e. the non-invariance of fundamental interactions under the combined symmetry transformations of charge conjugation (C) and parity in-version (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 SM 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. In particular in the charm sector CP violation has not yet been discovered, although time-integrated CP asymmetries in Singly-Cabibbo-Suppressed D0 → h+_h−_{decays have reached a remarkable} precision, O(0.1%). CP violation in the charm sector is predicted to be vary small (direct

CP violation smaller than O(10−3) and indirect CP violation smaller than O(10−4)) and so it is possible to see enhancements caused by interference with NP.

D0 _{and D}0 _{mesons are very interesting particles to study because they are the only} mesons with an up-type quark that can oscillate. In fact top quarks decay before hadroniz-ing and π0 and η mesons, composed of u and ¯u, are their own antiparticle and therefore

cannot oscillate. Mixing is now well established at a level which is consistent with SM expectations, and has recently been measured with a high level of significance by LHCb. Hadronic uncertainties may greatly limit the sensitivity of charm decays in prob-ing new effects. 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 decay 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. An extensive study of the charm decays is therefore fundamental to over-constrain the theory parameters, reduce theoretical uncertainties and advancing our limited understanding of the physics of the charm sector.

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The decay channel D0 _{→ K}0

SK

0

S is very promising for the discovery of CP violation in

this sector. In particular, because of the presence of two different amplitudes involved in this decay and because of the negligible indirect CP violation contribution with respect to the expected sensitivity, this channel gives the possibility to discover direct CP violation. A theoretical argument based on the SM predicts an un upper limit on direct CP violation in this channel of 1.1%, but this value could result enhanced because of the interference of NP.

The realization of this analysis in an experiment like LHCb is challenging. K0

S particles

have a relatively high mean life τ ' 0.9 × 10−10 s and are produced with a high boost in the z direction (the one aligned with the detector). In addition, they are neutral particles and we can detect them only looking at the decay products (in our case, two pions). LHCb is a forward spectrometer and it is possible that these pions go in regions where the detector cannot track them. Therefore, also if in a hadronic machine the number of

D0 produced is higher with respect to an e+_e− _{collider, the final number of D}0 _{→ K}0

SK

0

S

reconstructed is still about 5 times smaller. In addition, also when the tracks are detected, a lot of computer resources are needed to match these tracks with the primary vertex and reconstruct the decay chain. This could be a big problem in particular for the High Luminosity Upgrade of 2021. An accurate study of this channel is therefore essential to find a more efficient way to reconstruct this kind of long living particles, that are so important for the study of CP violation.

In this thesis I present a new measurement of the time integrated CP asymmetry in the

D0 _{→ K}0

SK

0

S decay using Run 2 data collected by LHCb in 2015 and 2016, corresponding

to an integrated luminosity of ' 2 fb−1 at a centre of mass energy of 13 TeV. The central value of this measurements is currently being kept “blind” to avoid any experimenter bias until the final approval of all details of the measurement by the collaboration, but its statistical-power is already determined. The result represents an improvement of ∼ 30% in sensitivity with respect to Run 1 result.

The thesis is structured as follows. In Chapter 1 I introduce CP violation within the Standard Model and I describe the motivations of this analysis. In Chapter 2 I briefly describe the experimental apparatus. In Chapter 3 I give an overview on the analysis strategy, describing also the data samples and the trigger selections. I describe the various sources of background in Chapter 4 and the optimization of rectangular cuts to reduce them in Chapter 5. The use of a multivariate classifier to optimize the selection is discussed in Chapter 6. The extraction procedure of ACP _{is described in Chapter 7,}

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3

Chapter 1

Charm Physics and CP violation

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 could be explained within this model. Than I introduce charm physics and I briefly explain the motivation of this work.

1.1 The Standard Model

The SM of particle physics [66, 60, 33] is a quantum field theory that describes the fun-damental 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 transfor-mations of this group; the SU (2)L⊗ U (1)Y term describes the symmetry of electroweak

interactions as introduced by the theory of Glashow-Weinberg-Salam, 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.

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.

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 violation, that is the violation of the symmetry that represents the invariance of physical processes under the inversion of spatial coordinates (parity transformation) and of all intrinsic quantum numbers of involved particles (charge-conjugation transformation). 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 possible coupling of non-SM particles with an up-type quark.

1.2 CP violation in the Standard Model

The Lagrangian of the SM is such that C and P symmetries are preserved in strong and electromagnetic interactions, as supported by all experimental results thus far [16, 62], but violated in weak interactions. Within the SM, CP symmetry is broken by an irreducible complex physical phase in the Yukawa quark-term of the SM Lagrangian. In the basis of mass eigenstates, the charged current weak interactions for quarks have the following form:

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1.2. CP violation in the Standard Model 5 LCC int = − g2 √ 2(¯uL, ¯cL, ¯tL)γ µ_V CKM    dL sL bL   W † µ+ h.c. (1.6)

VCKM is the unitary 3 × 3 Cabibbo-Kobayashi-Maskawa matrix [23] [46], 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    (1.7)

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 [55]:

VCKM =    0.97427 ± 0.00014 0.22536 ± 0.00061 0.00355 ± 0.00015 0.22522 ± 0.00061 0.97343 ± 0.00015 0.0414 ± 0.0012 0.00886+0.00033−0.00032 0.0405+0.0011−0.0012 0.99914 ± 0.00005    (1.8) 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 [67] 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₎ _(1.9)

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

0.232 ± 0.002). 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 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∗.

Fig. 1.1 shows the unitarity triangle in the complex ( ¯ρ − ¯η) plane. 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 [42], which is defined by: Im[VijVklVil∗V ∗ kj] = J X n,n∈(d,s,b) ikmjln (1.10)

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Figure 1.1: 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

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 = (2.96+0.20_−0.16) × 10−5 _{[25]. The geometrical meaning of CP violation is that the unitarity} triangles do not degenerate into lines.

Fig. 1.2 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 measure-ments 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 Stan-dard Model. 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.

1.3 Charm

The existence of a fourth quark was first theoretically discussed in 1964 by Bjorken and Glashow [19], who called it the charm quark. The first c¯c bound state, called J/Ψ, was

discovered in 1974 by two independent research groups at SLAC [15] and Brookhaven Laboratory [14]. After a few years also D0 _{and D}+ _{states were also discovered. The mass} of charmed mesons is approximately 2 GeV/c2_{. D}0 _{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 is still unobserved in the charm sector because all relevant amplitudes within the SM are

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1.3. Charm 7

Figure 1.2: Current experimental status of the global fit to all

available experimental measurements related to the unitarity triangle phenomenology.

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. 1.3) for charm mesons is then V∗

cdVud+ Vcs∗Vus+

V_cb∗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

Figure 1.3: Schematic representation of the charm unitarity triangle

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 hadronic physics is operative and the phenomenological approximations commonly used

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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 first evidence for the D0 _{− D}0 _{mixing provided by} BaBar [13] and Belle [63]. The non-mixing hypothesis in the charm sector is now excluded with a probability corresponding to 9.1 standard deviations, due to the first observation from a single measurement provided by the LHCb collaboration [7]. Until a few years ago experimental sensitivities 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. The most important challenge for the experimental analysis in the charm-sector is to reach the necessary sensitivities of 10−3 or less in order to investigate possible CP -violation effects.

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 recon-structed charm decays were produced by photo-production [12]. 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. The cross section for c¯c pair production is σ ∼ 1.3 nb [21] at the Y(4S) resonance. At

hadron machines the production cross section to produce charm hadrons is significantly higher: σ ∼ 10 mb in the range 0 < pT < 8 GeV/c, 2 < η < 4.5, in pp collisions at LHC

with a center-of-mass energy of 13 TeV. On the other hand, events in hadron colliders are more complex than in Bfactories, resulting in more difficult reconstruction of b and c -hadron decays and requiring higher granularity detectors.

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

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1.4. Types of CP violation 9

if the Lagrangian is real and are called rescatting 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 (also called direct) • CP violation in the mixing

• CP violation in the interference between decay and mixing

The second and third cases are also called indirect CP violation. In 1964 the experiment of J. Cronin and V. Fitch [27] on neutral kaons had shown that CP symmetry is broken in weak interactions. This was the first evidence of indirect CP violation, caused by the fact that the neutral kaon mass eigenstates, K0

L and K

0

S,are not eigenstates of CP . The first

evidence of direct CP violation, still in neutral kaons, was established about 30 years later, in 1999, by both NA48 [32] and KTeV [10] collaborations. In the following description I will focus the attention on charm phenomenology [18].

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 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) (1.11)

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). (1.12)

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 ) (1.13)

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}dir ₌ |Af|2− | ¯Af|2 |Af|2 + | ¯Af|2 = 1 − R 2 f 1 + R2 f (1.14)

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Therefore, CP violation in the decay occurs if Rf = ¯ Af Af 6= 1 (1.15)

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 Bs 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) ! (1.16)

where M and Γ are 2 × 2 Hermitian matrices,

M = M11 M12 M₁₂∗ M22 ! Γ = Γ11 Γ12 Γ∗ 12 Γ22 ! (1.17)

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, (1.18)

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 (1.19)

The eigenvalues of Hef f are

λL,H = (M11− i/2Γ11) ±

q

p(M12− i/2Γ12) ≡ mL,H− i/2ΓL,H (1.20)

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.

The mass difference ∆m ≡ mL− mH is conventionally assumed positive, while the sign

of the decay width difference ∆Γ ≡ ΓL− ΓH is determined experimentally. 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.}

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1.5. Charm decay amplitudes and the D0 → K0

SK

0

S decay 11

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 (1.21)

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, D}0 _{→ D}0 _{→ f .}

The phenomenology of flavor oscillations is described using two dimensionless mixing parameters x ≡ ∆m/Γ and y ≡ ∆Γ/2Γ, where 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 = Afg+(t) + ¯Af q pg−(t), (1.22) where |g±(t)|2 = 1 2e −t/τ cos _xt τ ± cosh _yt τ (1.23) 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.

CP violation in interference occurs when

Im(λf) 6= 0 (1.24)

1.5 Charm decay amplitudes and the D

0

→ K

_S0

K

_S0

de-cay

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∗

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

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The relative hierarchy of these amplitudes is 1 : λ : λ : λ2_{. A way to describe these} transitions is the so-called topological diagram approach, whose basic idea is to establish relations among different decay modes [26]. 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-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. 1.4 the corresponding

topological-diagrams are shown.

Figure 1.4: Topological diagrams. From Ref. [26]

Regarding SCS decays, a common choice [54] for the decomposition of a decay ampli-tude in terms of CKM elements is :

A = 1

2[(λs− λd)Asd+ λbAb] , (1.25) where λq ≡ Vcq∗Vuq is the CKM amplitude. Within the SM a non-vanishing direct CP

asymmetry involves the interference of λbAb with (λs− λd)Asd. Neglecting quadratic (and

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

Adir_{= Im} λb

(λs− λd)

ImAb Asd

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1.5. Charm decay amplitudes and the D0 → K0

SK

0

S decay 13

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 [54, 53], Asd = E1+ E2− E3 √ 2 (1.27) and Ab = 2E + E1+ E_√2+ E3+ P A 2 , (1.28)

where E1, E2 and E3 amplitudes are shown in Fig. 1.5, while E and PA are shown in Fig. 1.4. Since only the SU(3) breaking breaking amplitudes E1, E2, E3 contribute to Eq. 1.27, Asd vanishes in the SU(3) limit [39]. 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_,

ImAb Asd

can be large and enhance the direct CP asymmetry (Eq. 1.26) to an observable level [22] , i.e., as large as 1.1% (95% C.L.) [54].

Figure 1.5: SU(3)-breaking topological amplitudes. From Ref. [50].

In performing a time-integrated measurement, because of the slow mixing rate of charm mesons (x,y∼ O(10−3)), the CP asymmetry can be expanded as

ACP ' Adir− AΓ hti

τ . (1.29)

where AΓ is the asymmetry between the D0 and ¯D0 effective decay widths [4], while Adir is the direct CP asymmetry

Adir ₌ |Af| 2_{− | ¯}_A ¯ f|2 |Af|2 + | ¯A_f¯|2 . (1.30)

Here, Af is the amplitude of the decay D0 → f and ¯A_f¯ is the amplitude of the decay ¯

D0 _{→ ¯}_{f . The parameter A}

Γhas been measured to be (−0.29±0.28)×10−3[4] and is largely independent of the final state [34], while hti/τ is of order 1. The second term of Eq.1.29 can be therefore neglected, being much smaller than the expected sensitivity on ACP_{, and}

we have ACP _{' A}dir_{. Therefore the study of CP asymmetry in D}0 _{→ K}0

SK

0

S channel

could lead to the first measurement of direct CP violation in the charm sector. Any improvement in precision of the measurements of Adir_(D0 _{→ K}0

SKS0) would considerably

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15

Chapter 2

The LHCb experiment

The LHCb experiment, the only one specifically designed to perform bottom and charm flavor physics at the Large Hadron Collider, provides very interesting opportunities to measure precisely CP asymmetries in a hadronic environment. In this Chapter I describe briefly the LHC accelerator and LHCb detector.

2.1 The Large Hadron Collider

The Large Hadron Collider (LHC) is a proton–proton (pp) and heavy ion collider located at the European Organization for Nuclear Research (CERN) laboratory, on the French-Swiss border. The LHC is located in a 27 km long, nearly circular tunnel about 100 m underground. Before circulating into the LHC, protons are extracted from hydrogen gas and accelerated by a succession of machines, as shown in Fig. 2.1. Protons are first linearly

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accelerated in the Linac 2 up to energy of 50 MeV, than in the Booster up tp 1.4 GeV and subsequently they reach the energy of 25 GeV in the Proton Synchrotron. Protons are then injected into the Super Proton Synchrotron (SPS), and finally transferred into the LHC at an average energy of 450 GeV. In the LHC, two proton or ion beams are ac-celerated in opposite direction. Two separate dipole cavities, sharing the same iron yoke, are required to accelerate the two beams. They are bent around the circumference of the LHC using NbTi superconducting dipole magnets which, maintained at a temperature of 1.9 K by a liquid helium cooling system, produce a field of 8.3 T. Proton beams are not continuous, but spaced in bunches of about 1011 _{protons each and are time-spaced for a} multiple of 25 ns, corresponding to a bunch-crossing rate of 40 MHz. Beams collide in four point placed along the LHC ring, where the detectors of the four major LHC experiments are installed. The LHC machine is designed to collide protons up to a centre-of-mass energy (Ecm) of 14 TeV, at an instantaneous luminosity of 1034 cm−2s−1. However during

Run1 in 2010 and 2011 Ecm was equal to 7 TeV, in 2012 Ecm= 8 TeV. During Run2, in

2015, 2016 and 2017, Ecm has reached the value of 13 TeV.

2.2 The LHCb detector

The Large Hadron Collider beauty (LHCb) experiment is the only LHC experiment en-tirely dedicated to heavy flavor physics. Its primary goal is to search for indirect evi-dences of non-SM physics in heavy quark transitions, mainly by studying CP violation and rare decays of charmed and bottom hadrons. The LHCb detector [11] is a single-arm spectrometer with a forward angular coverage from 10 mrad to 300 (250) mrad in the bending (non bending) plane, corresponding to a pseudorapidity interval of 1.8 < η < 4.9 (η = − log[tan(θ/2)]) and θ is the polar angle with respect to the beam direction).

It consists of a charged particle tracking system and a particle identification system. The tracking system includes a magnet and three different detectors: the vertex locator (VELO) and the tracker turicensis (TT), both upstream of the magnet, and three tracking stations (T1–T3), downstream of the magnet. The particle–identification system includes several detectors, each one exploiting a different technology: two ring imaging Cherenkov (RICH) detectors, the calorimeter detectors and the muon detectors. The layout of the LHCb detector is shown in Fig. 2.2. The right handed coordinate system has the x axis pointing toward the center of the LHC ring, the y axis pointing upwards, and the z axis pointing along the beam direction. The design and forward geometry of the LHCb detector allow exploiting unprecedented heavy flavor production rates.

When the beams intersect, multiple primary pp interactions may occur causing high particle occupancy in the detector. This makes event more difficult to manage, especially for online systems, and high particle density may cause important radiation damage to the detector. In addition the detector can not be readout at a higher rate than 1 MHz. For these reasons the nominal LHC luminosity is reduced in the LHCb intersection point and the average number of primary pp interaction per bunch crossing is reduced to almost 1. The technique of luminosity leveling is used, defocusing the beams by moving them apart transversely. The recorded LHCb luminosity in 2015 and 2016 is shown in Fig. 2.3.

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2.2. The LHCb detector 17

Figure 2.2: Layout of LHCb detector.

Figure 2.3: Integrated LHCb luminosity in 2015 (left) and 2016 (right).

2.2.1 Tracking detectors

The tracking system must provide accurate spatial measurements of charged particle tracks,in order to allow quantities such as charge, momentum, and vertex locations to be determined.

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The dipole magnet

The LHCb warm dipole magnet provides bending for the measurement of the momentum of particles. The magnet is formed by two coils placed with a small angle with respect to the beam axis, to increase the opening window with z in order to follow the acceptance of the LHCb detector. The main component of the magnetic field is along the y-axis as shown in Fig. 2.4, therefore, the (x,z)-plane can be considered with good approximation the bending plane. The maximum magnetic field strength is above 1 T, while its

inte-Figure 2.4: Measured By component of LHCb magnetic field.

gral is about R

B dl = 4 Tm. All the tracking detectors are located outside the magnetic

dipole. The magnetic field is measured before the data-taking periods with Hall probes to obtain a precise map, which is crucial to have a good momentum resolution and conse-quently a good mass resolution that helps to select more efficiently processes of interest. Among the main LHC experiments, the LHCb detector has a unique feature consisting into the possibility to reverse the polarity of the magnetic field (MagUp or MagDown). This allows a precise control of the charge asymmetries introduced by the detector. Par-ticles hit preferentially one side of the detector, depending on their charges, generating large detection asymmetries. If data samples collected with the two different polarities have approximately equal size and the operating conditions are stable enough, effects of detection charge asymmetries are expected to cancel. The magnet polarity is therefore reversed approximatively every two weeks to meet these constraints.

The Veretx locator detector

The vertex detector (VELO) [29] measures charged particle trajectories in the region closest to the interaction point. Its main purpose in to reconstruct primary vertices and displaced secondary vertices, the latter being a signature of heavy flavor decays. Typical b hadrons in LHCb have a decay length cτ ≈ 500 µm and for c hadrons cτ ≈ 100−300 µm (for neutral and charged charmed mesons respectively), so the vertex detector spatial resolution is required to be far better to discriminate between primary vertices and displaced secondary vertices. The vertex detector consists of 21 disk–shaped tracking stations positioned along the beam axis, both upstream and downstream of the nominal

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interaction point. Each tracking station is divided in two retractile halves, referred to as modules, each consisting of two silicon strip sensors, one with radial and one with azimuthal segmentation, as shown in Fig 2.5. Both r and φ sensors are centred around

Figure 2.5: Representation of VELO detector, with a transverse view in the (x,z) plane (top) and a front-view of a single station (bottom).

the nominal beam position and have a sensitive area covering the region from r = 8 mm to r = 44 mm. The r sensor consists of concentric semicircular strips, which are subdivided in four 45◦ sectors each, to reduce occupancy. The pitch increases linearly from 38 µm at the innermost radius to 101.6 µm at the outermost radius. The φ sensor is subdivided in two concentric regions: the inner region at r=8 - 17.25 mm, the outer region at r=17.25 - 42 mm. The pitch increases linearly from the centre, with a discontinuity in passing from the inner to the outer region. A representation of rΦ geometry of VELO sensors is shown in Fig. 2.6.

Each VELO module is encased in a shielding box, to protect it form the radiofrequency electric field. The portion in common between two boxes is called RF-foil and forms a corrugated structure (Fig. 2.7) to allow an overlap between the two module of the same VELO stations in closed configuration. VELO performance have been determined in test beams. Raw hit resolution varies from ≈ 10µm to ≈ 25µm.

Silicon Tracker: Tracker Turicensis and Inner Tracker

The silicon tracker [17] consists of two detectors based on the same technology and sharing a similar design: the tracker turicensis (TT), upstream of the magnet, and the inner

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Figure 2.6: rΦ geometry of VELO sensors.

Figure 2.7: Representation of RF-foils in closed configuration.

tracker (IT), downstream of it.

The TT is a silicon microstrip detector placed just before the dipole magnet. It consists of four layers grouped in two stations separated of about 30 cm along the beam line. The four layers are arranged in a “x-u-v-x” pattern. The first and last layer (“x” configuration) consist of vertical strips, Fig. 2.8, while the “u” and “v” layers are rotated by ±5◦. The slight rotation with respect to the vertical layers avoid the ambiguities that would arise with an horizontal orientation providing a measurement in y-direction as well. The TT has two purposes: to reconstruct trajectory of low-momentum particles that are swept away from the acceptance by the magnet and to reconstruct long lived particles, as K0

S

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Figure 2.8: "x-u-v-x" configuration of TT station.

The TT covers he full acceptance of the experiment, while the IT, placed downstream of the magnet, covers an acceptance of ' 150 − 200 mrad in the bending plane and ' 40 − 60 mrad in the y − z plane. The IT is mounted in three tracking stations, called T-stations, each one with four overlapped detection planes. Planes configuration is the same of TT sub-detectors. The purpose of IT is to reconstruct tracks that passed through the magnetic field region near the beam axis. The IT layout is shown in Fig. 2.9. Single-hit resolution of both TT and IT detectors is ' 50 µm.

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The Outer Tracker

The Outer Tracker (OT) [28] is a gaseous ionisation detector consisting of straw tubes operating as proportional counters. As the IT, the OT is arranged in three stations composed by four detection planes. The planes configuration is equal to the IT and the TT ones (x-u-v-x). The drift tubes are 2.4 m long with an inner diameter of 4.9 mm. The gas mixture filling the tube is Ar/CO2 /O2 to achieve a drift time of 50 ns. Typical occupancies are at the order of 10% and hit efficiency above 99% for tracks passing close to the centre of a tube. The OT Layout is shown in Fig. 2.10.

Figure 2.10: Layout of OT subdetector and representation of one OT module.

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2.2.2 Particle identification detectors

Particle identification plays an important role in decays studied by LHCb. Cherenkov detectors are able to separate between charged kaon and pions, while calorimeter detectors allow identification of electron, photon and hadrons. Finally muons are identified by muon chambers.

The Ring Cherenkov detectors

Two Ring Cherenkov detectors, RICH1 and RICH2 [9], allow the identification of charged particles over a momentum range 1−100 GeV/c. In particular, RICH1 aims to identify low-momentum particles (between 1 and 60 GeV/c), while RICH2 is tuned for particles with higher momenta (between 15 and 100 GeV/c). Covering different momentum ranges is made possible by filling the two detectors with different radiators: RICH1 uses separate aerogel and C4F10 radiators, while RICH2 is filled with CF4 radiators. In Fig. 2.11 is shown the relation between the Cherenkov angle and particle momentum for different particles and radiators.

Figure 2.11: Cherenkov angle in the C4F10 radiator of RICH1.

In Fig. 2.12 RICHs geometry is shown. Each detector is composed of two kinds of mirrors: a spherical mirror for ring-imaging and a set of flat mirrors that guide pho-tons onto the Hybrid Photon Detectors, located outside the detector acceptance. RICHs are magnetically shielded in order to guarantee a proper activity of the hybrid photon detectors. These are used to detect Cherenkov photons with λ between 200 and 600 mm. RICH1 is located upstream the magnet and covers the full detector acceptance, while RICH2 is downstream the magnet (after the last tracking station) and covers angular acceptance from 15 to 120 (100) mrad in the bending (non–bending) plane. The π − K separation is 90% efficient for momenta up to 30 GeV/c.

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Figure 2.12: RICH1 (left) and RICH2 (right) geometry.

Calorimeter detectors

Calorimeter detectors provide fast information for the low level trigger and offer iden-tification of electrons, photons, and hadrons, together with a raw measurement of their energies and positions.

Calorimetric system is formed by an electromagnetic calorimeter (ECAL) [49] and a hadron calorimeter (HCAL) [35].Both are placed between the first and the second muon station and cover the angular acceptance from 25-300 (250) mrad in the bending (non bending) plane. The ECAL is equipped with two additional sub-detectors, a pre-shower detector (PS) and a scintillator pad detector (SPD), placed in front of it and separated by a thin lead converter. They are used by the low level electron trigger to reject charged and neutral pions, in order to improve electron identification. Charged pions are rejected by looking at the longitudinal development of the electromagnetic shower in the PS. The lead converter is 15 mm thick and corresponds to ' 2.5 radiation lengths for electrons, which start showering and produce significantly larger signals than charged pions. Neutral pions are rejected by looking at the signal from the SPD. The last one is also used to measure the number of tracks per event, in order to veto online too crowded events. Calorimeter detectors are subdivided in four quadrants that surround the beampipe. Each quadrant has a lateral segmentation in cells of different sizes, depending on the distance from the beam axis. The lateral segmentation is finer in the ECAL, PS and SPD than in the HCAL, as shown in Fig. 2.13.

ECAL thickness corresponds to 25 radiation lengths, to guarantee a nearly com-plete electromagnetic shower containment and a good energy resolution. The thick-ness of HCAL corresponds to 5.6 interaction lengths. The readout is common to all

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Figure 2.13: Segmentation of calorimeter detectors for a detector quad-rant of ECAL (left) and HCAL (right).

detectors: scintillation light is transmitted to photomultipliers using wavelength shift-ing fibers. The electromagnetic calorimeter consists of alternate 4 mm thick scintillators tiles and 2 mm thick lead plates. The hadron calorimeter is structured in 4 mm thick scintillator tiles sandwiched between 16 mm iron sheets. The energy resolution of the ECAL is σE/E( GeV) ' 10%/

q

E( GeV) while the energy resolution of the HCAL is σE/E( GeV) ' 70%/

q

E( GeV). Muon detectors

Muon detectors [44] provide identification and transverse momentum measurement of penetrating muons for both low level and high level triggers, as well as for offline recon-struction. They consist of five rectangular stations, referred to as M1-M5, placed along the beam axis and covering the angular acceptance from 20 (16) to 306 (258) mrad in the bending (non bending) plane. M1 station, which is installed between RICH2 and the calorimeter detectors, improves transverse momentum measurements for muons that are detected also in the next stations. M2-M5 stations are placed downstream of the calorimeter detectors. They are interleaved with 80 cm of thick iron absorbers that select penetrating muons and result in a total thickness of '20 interaction lengths. In order to traverse the whole detector, a muon is typically required to have at minimum momentum of 6 GeV/c. The stations are subdivided in four quadrants, arranged around the beampipe. Each quadrant comprises four regions, labelled with R1-R4, installed at increasing radii from the beampipe. A side view of the muon detectors and a station layout are shown in Fig. 2.14. Muon detectors rely on two technologies to detect muons: triple gas electron multiplier and multiwire proportional chamber detectors. The former are used in the innermost region (R1) of the first station (M1), where high particle density requires a radiation tolerant detector; the latter are used in the rest of detectors. The gas mixture consists of Ar , CO2, and CF4 for both detectors, although in different proportions. The first three stations (M1-M3) contribute to transverse momentum measurements, while the last two stations (M4 and M5) detect particles that pass through the absorber mate-rial. An average transverse momentum resolution of 20% is achieved in stand-alone muon reconstruction, which is used in the trigger.

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Figure 2.14: Side view of muon detectors (left) and geometrical repre-sentation of a M1 quadrant (right).

2.3 The LHCb trigger

LHCb trigger [38] is projected to efficiently select heavy flavor decays from the large light quark background, sustaining the LHC bunch-crossing rate of 40 MHz and selecting up to 12.5 KHz of data to be stored. Events that contain a b-hadron decay, with all possible final states, represent a small fraction, approximately 15 KHz. The subset of interesting b hadron decays is even smaller, corresponding to only few Hz. The corresponding values for c hadrons are nearly 20 times larger. Therefore, it is a crucial point for the trigger to reject background as early as possible in the data flow. The trigger is organized in two levels, that represent two consecutive stages in event processing: the Level-0 trigger (L0) and the High-Level trigger (HLT). This two-level structure allows coping with timing and selection requirements, with a fast and partial reconstruction at low level, followed by a more accurate and complex reconstruction at high level. The hardware-based L0 trigger operates synchronously with the bunch crossing. It uses information from calorimeter and muon detectors to reduce the 40 MHz bunch–crossing rate to below 1.1 MHz, which is the maximum value at which the detector can be read out by design. In the next step, the asynchronous software based HLT performs a finer selection based on information from all detectors and reduces rate to 12.5 kHz, that is the maximum frequency at which events can be stored. In Fig. 2.15 the LHCb trigger flow is shown, with typical rates for the accepted events at each stage.

2.3.1 The Level-0 trigger

The Level-0 trigger consists of three independent trigger decisions: the L0 pileup, the L0 muon, and the L0 calorimeter. Each decision is combined with the others through a logic or in the L0 decision unit, reducing the 40 MHz bunch-crossing rate to below 1.1 MHz. The L0 decision unit provides the global L0 trigger decision, which is transferred to the readout supervisor board and, subsequently, to the front-end boards. This is necessary since the full detector information for a given bunch crossing is not read out from the front-end boards until the L0 decision unit has accepted it. Data from all detectors are stored in memory buffers consisting in an analog pipeline that is read out with a

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2.3. The LHCb trigger 27

Figure 2.15: LHCb trigger flow and typical event-accept rate for each stage.

fixed latency of 4 µs; in this time a trigger decision must be available. To accomplish this task, the L0 trigger is entirely based on custom-built electronic boards, relying on parallelism and pipelining to make a decision within the fixed latency. At this stage, trigger requests can only involve simple and immediately available quantities, like those provided by calorimeter and muon detectors.

The L0 pileup trigger contributes to luminosity measurements and is not involved in the selection of interesting events. It uses the information from the veto stations of the VELO to estimate the event pile-up, which is the number of primary vertexes generated by a single bunch crossing, and the backward charged particle multiplicity.

The L0 muon trigger uses the information from the five muon stations in order to identify the most energetic muons. Once the two highest transverse momentum muon candidates per quadrant are identified, the trigger decision is set depending on two thresh-olds: one on the highest transverse momentum (L0 muon) and one on the product of the two highest transverse momenta (L0 dimuon).

The L0 calorimeter trigger uses the information from ECAL, HCAL, PS, and SPD. It calculates the transverse energy deposited in a cluster of 2x2 cells of the same size, for both the electromagnetic and hadron calorimeters. This quantity is combined with information on the number of hits on PS and SPD in order to define three types of trigger candidates: photon,electron and hadron.

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decays. Final state particles from such decays have on average higher transverse momenta than particles originated from light quark processes. This property helps in discriminating between signal and background.

Tab. 2.1 shows de variation of L0 configuration in 2015 and 2016 and the fraction of events triggered by each specific configuration.

Table 2.1: Summary of L0 thresholds for the main Physics lines. The TCK, Trigger Configuration Key, is a unique key that defines the sequence of algorithms, and the cuts applied in a specific trigger configuration. The fraction of collected events per L0 TCK is estimated from the A_Γ sample. *: includes a cut on SumEtPrev, i.e., the total transverse energy measured

in the previous event, for lines other than L0DiMuon.

2015 2016

TCK (hex) 0x00a2 0x00a3 0x00a8 0x1600 0x1603 0x1604 0x1605

168 5632 5635 5636 5638 Fraction of events (%) 50.4 27.2 22.4 0.6 3.1 1.9 5.3 L0Hadron ET ( MeV) 3600 3096 4008 2928 3216 3552 3696 L0Photon ET ( MeV) 2688 2280 2688 2112 2304 2784 2976 L0Electron ET ( MeV) 2688 2280 2688 1872 2112 2256 2592 L0Muon pT ( MeV/c) 2800 2400 2800 700 1100 1300 1500 L0DiMuon√p_T1p_T2( MeV/c) 1300 1300 1300 900 1000 1200 1300 2016 TCK (hex ) 0x1609 0x160E 0x160F 0x1611 0x1612 0x1613 Fraction of events (%) 44.5 3.6 33.2 2.9 5.1 0.0 L0Hadron ET ( MeV) 3696 3696 3744 3888 3888 3744∗ L0Photon ET ( MeV) 2832 2976 2784 2976 2976 3192∗ L0Electron ET ( MeV) 2352 2592 2400 2616 2616 2376∗ L0Muon pT ( MeV/c) 1300 1500 1800 1500 1600 1350∗ L0DiMuon√p_T1p_T2( MeV/c) 1300 1300 1500 1400 1500 1550

Because of the presence of a different cut in TCK 0x1613, which does not trigger any event in the AΓ sample, this configuration has been excluded in the analysis.

2.3.2 The High Level trigger

Event accepted at L0 are transferred to the event filter farm, which consists of an array of computers, for the HLT stage. HLT is implemented through a C++ executable that runs on each processor of the farm, reconstructing and selecting events in a way as sim-ilar as possible to the offline processing. The substantial difference between online and offline selection is the available time to completely reconstruct a single event. The offline reconstruction requires almost 2 s per event, while the maximum available time for the online reconstruction is typically 50 ms. HLT trigger consists of several trigger selections designed to collect specific events. Every trigger selection is specified by reconstruction algorithms and selection criteria that exploit the kinematic features of charged and neu-tral particles, the decay topology and the particle identities. If the accepted-event rate is too high, individual trigger selections can be prescaled by randomly selecting only a subset of events satisfying their requirements. The total HLT processing time is shared

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2.4. Track reconstruction 29

between two different levels: the first stage (HLT1) and the second stage (HLT2). The main differences between HLT1 and HLT2 are the complexity of the information that they are able to process and the available time to do this. Partial event reconstruction is done in the first stage in order to significantly reduce accepted-event rate to 30 kHz, and a more complete event reconstruction follows in the second stage. At the first level, tracks are reconstructed in the VELO and selected based on their probability to come from heavy flavor decays. At the second level a complete forward tracking of all tracks reconstructed in the VELO is performed. Several trigger selections, either inclusive or exclusive, are available at this stage.

A key computing challenge is to store and process this data, which limits the maximum output rate of the LHCb trigger. So far, LHCb has written out a few kHz of events containing the full raw sub-detector data, which are passed through a full offline event reconstruction before being considered for physics analysis. Charm physics in particular is limited by trigger output rate constraints. A new streaming strategy includes the possibility to perform the physics analysis with candidates reconstructed in the trigger, thus bypassing the offline reconstruction. In the Turbo stream the trigger will write out a compact summary of physics objects containing all information necessary for analyses, and this allows an increased output rate and thus higher average efficiencies and smaller selection biases. The analysis described in this thesis is one of the first done using the Turbo stream.

2.4 Track reconstruction

Trajectories of charged particles, here referred as tracks, are reconstructed in the LHCb using the hits of the tracking subdetectors [64] (VELO, TT and T-stations). Tracks reconstruction starts with the pattern recognition where a sequence of hits produced by the charged particle is identified. Different types of tracks are distinguished in LHCb according to the subdetectors crossed, as shown in Fig. 2.16:

• Long tracks require particles traversing the full tracking system. They are recon-structed combining hits from the VELO and the T-stations, and when possible hits from TT are added.

• Downstream tracks are reconstructed only in the TT and in the T-stations. These are mainly long-lived particles as KS0 decaying outside the VELO region.

• VELO tracks are tracks with only VELO hits. They are used in the primary vertex reconstruction and as seeds for reconstructing long and upstream tracks. • Upstream tracks are low momentum tracks with hits only in the VELO and TT

since they are swept out the LHCb acceptance by the magnetic field. • T tracks are formed only using hits into the T-stations.

In the analysis described in this document both Long and Downstream tracks are used.

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31

Chapter 3

Analysis overview and data samples

The goal of this analysis is to provide a new measurement of the time-integrated CP asymmetry ACP _{in the decay D}0 _{→ K}0

SK

0

S using Run 2 data collected in 2015 and 2016.

In this Chapter I describe how I want to perform this measurement and the dataset that I use.

3.1 Analysis overview

3.1.1 D

0

flavor tagging

For an ACP _{measurement an important task is the determination of the flavor of the}

de-caying particles. In particular, in this analysis for each event it is necessary to know if the event under investigation is a D0 _{→ K}0

SK 0 S decay or a D 0 _{→ K}0 SK 0

S decay. For a charged

particle the flavor can be determined from the sum of the charges of the decay products, but this strategy does not work for a neutral particle. Therefore the D0 flavor has to be tagged looking at the production mechanism. In particular the D0 _{is required to come} from the D∗+ → D0_π+ _(D∗− _{→ D}0_π−_{) strong decay. The D}0 _{flavor can be therefore} determined from the charge of the pion coming from the D∗ decay. No CP violation has to be considered in this decay because it is a strong process, in which CP is conserved. From now on I will refer to the pion from the D∗ decay as the “tag pion”(πtag). KS0

candidates are reconstructed in the π+π− decay channel. In Fig. 3.1 the complete decay chain is shown.

Figure 3.1: Schematic representation of the decay chain. Typical decay lengths not to scale.

Measurement of time integrated CP asymmetries in D0->KS0 KS0 decays

Università degli studi di Pisa

Corso di Laurea Magistrale in Fisica

Measurement of time integrated CP

asymmetries in D

0

→ K

S

0

K

S

0

decays

Author:

Giulia Tuci

Supervisors:

Prof. Giovanni Punzi

Dott. Simone Stracka

Dott. John Walsh

Contents

Introduction

Chapter 1

Charm Physics and CP violation

1.1

The Standard Model

1.2

CP violation in the Standard Model

1.3

Charm

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

Charm decay amplitudes and the D

→ K

K

de-cay

Chapter 2

The LHCb experiment

2.1

The Large Hadron Collider

2.2

The LHCb detector

2.2.1

Tracking detectors

2.2.2

Particle identification detectors

2.3

The LHCb trigger

2.3.1

The Level-0 trigger

2.3.2

The High Level trigger

2.4

Track reconstruction

Chapter 3

Analysis overview and data samples

3.1

Analysis overview

3.1.1

D

flavor tagging

_S

_S