Seminar 1b

CP Violation in D mesons

Aljoša Polšak Adviser: prof. dr. Peter Križan Co-adviser: dr. Anže Zupanc

Ljubljana, November 2013

Abstract

In this seminar we take a look at CP violation in neutral D mesons. We firstly examine the theoretical basics for CP violation. We start with the CKM matrix and than develop the formalism for CP violation in neutral D mesons. In the second part we present the results of the measurement of the difference between CP asymmetries in D0 → K −K + and D0 →π−π + decays by the LHCb collaboration.

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Content 1 Introduction ............................................................................................................ 3

2 CP violation in Standard Model ........................................................................... 3 2.1 Cabbibo – Kobayashi – Maskawa (CKM) matrix ................................................... 3

3 CP violation in D mesons ....................................................................................... 4 3.1 D mesons ...................................................................................................................... 4 3.2 Formalism .................................................................................................................... 5 3.3 Decay to CP eingenstates ............................................................................................ 6 3.4 Time integrated CP asymmetry ................................................................................ 6

4 LHCb experiment .................................................................................................. 8 4.1 LHCb detector ............................................................................................................ 8 4.2 Analysis ........................................................................................................................ 9 4.3 Selection process ....................................................................................................... 10 4.4 Gathered data and results ........................................................................................ 11

5 Conclusion ............................................................................................................ 12

6 Bibliography ......................................................................................................... 12

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1 Introduction CP symmetry is basically the symmetry between matter and antimatter. If nature treated matter and antimatter in the same way we would have CP-symmetric nature. In reality there is much more matter than antimatter, which clearly implies that laws of physics are not invariant under the CP transformation. Firstly we need to understand what CP symmetry means in more physical sense. CP symmetry combines two symmetries: C as charge conjugation and P as parity. Charge conjugation is the symmetry between positive and negative charge, and parity is symmetry of spatial coordinates. This symmetry is reported in electromagnetic interactions while it is violated in certain types of weak decays. CP symmetry (as a product of C and P symmetry) was proposed as a way to restore order after Chien Shiung Wu experiment with Co-60 which demonstrated P symmetry violation in weak decays [1]. In 1964 James Cronin and Val Fitch showed that even the CP symmetry is violated in kaon oscillations. For their work they were awarded the Nobel Prize in 1980. In 1973 Kobayashi and Masakawa proposed third quark family that could explain CP violation within the Standard Model. The missing three quarks were observed in 1974 (charm), 1977 (bottom), 1994 (top) and CP violation in B meson decays was observed by B factory experiments BaBar and Belle in 2001, in very good agreement with Kobayashi – Maskawa scheme. Kobayashi and Maskawa were awarded Noble Prize in 2008 [1]. While CP violation in B mesons is already well established, Belle and BaBar Collaboration published first reports of measured CP violation in D mesons decays in 2007; results seem to agree with Standard Model predictions. In 2012 LHCb reported CP violence in charmed meson decays and results were showing quite big asymmetry, possibly beyond Standard Model. Results were updated in 2013 and findings are presented at the end of seminar.

2 CP violation in Standard Model Basics for theoretical explanation is given with the so called CKM matrix and we will start with a brief introduction of the CKM matrix and how it is possible to have CP violation within the Standard Model.

2.1 Cabbibo – Kobayashi – Maskawa (CKM) matrix CKM matrix describes quark mixing. It gives as way to track weak decays of quarks. The matrix elements are the amplitudes for quark mixing:

VCKM =Vud Vus VubVcd Vcs VcbVtd Vts Vtb

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

. (1)

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The matrix can be parameterized in different ways. The standard one, used by the Particle Data Group is [2]:

VCKM =

c12c13 s12c13 s13e− iδ

−s12c23 − c12s23s13eiδ c12c23 − s12s23s13e

iδ s23c13s12s23 − c12c23s13e

iδ −c12s23 − c12c23s13eiδ c23c13

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

, (2)

where sij = sinθij , cij = cosθij and delta represents phase. CP violation is allowed in the Standard Model in case we have complex phases in the CKM matrix, i.e. if δ ≠ 0 . Detailed explanation why is given in [2].

3 CP violation in D mesons Before we start with CP violation in D mesons we need to take a look on what D mesons are and what are their main characteristics. We continue this chapter with the formalism and in the end define the time integrated CP asymmetry, which can be experimentally measured.

3.1 D mesons The D mesons are the lightest particles with charm (c) quarks. They were discovered in 1976 by the Mark 1 collaboration [3]. In D mesons decays charm or anticharm quark change into another type of quark or antiquark. In this case these interactions will violate the charm quantum number. Such decays can take place only via the weak interaction. More characteristic of D mesons are listed in Table 1:

Table 1: basic characteristics of D mesons. [3]

Particle symbol

Anti-particle symbol

Quark content

Rest mass (MeV/c2)

IG JP S C Mean lifetime (s)

D+ D− cd 1,869.62 ± 0.20 1⁄2 0− 0 +1 1.040 ± 0.007 × 10−12

D0 D0 cu 1,864.84 ± 0.17 1⁄2 0− 0 +1 4.101 ± 0.015 × 10−13

DS+ DS

− cs 1,968.47±0.33 0 0− +1 +1 5.00±0.07×10−13

D∗+ (2010) D∗− (2010) cd 2,010.27.62 ± 0.17 1⁄2 1− 0 +1 6.9 ± 1.9 × 10−21

D∗0 (2007) D∗0(2007) cu 2,006.97 ± 0.19 1⁄2 1− 0 +1 >3.1 × 10−22

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3.2 Formalism In this section we write down the decay rates of neutral D mesons since they are crucial for understanding how we can measure CP violation. Formalism here is similar to one find in the CP violation of B and K mesons. We start by defining what happens if we make CP transformation on a neutral D meson: CP D0 = − D0 . (3)

D0 can mix into D0 , D0 and D0 are not the eingenstates of the Hamiltonian. The mass eigenestates D1 and D2 can be written as linear superposition of the flavor eigenstates D0 andD0 . D1 = p D0 + q D0 , (4)

D2 = p D0 − q D0 . (5)

where p and q are complex mixing parameters and satisfy: p 2 + q 2 = 1 . (6) We can define average mass (m) and mass difference (Δm ) as:

m ≡ m1 +m2

2, Δm ≡ m1 −m2 (7)

where m1 and m2 represent masses of the mass eigenstates D1 and D2 . We also define the average decay rate and the decay rate difference:

Γ ≡ Γ1 + Γ2

2, ΔΓ=Γ1 − Γ2 , (8)

where Γ1 andΓ2 represent decay rates of the mass eigenstates D1 and D2 . We can obtain the time evolution of initially produced (t=0) neutral D meson from equations (4) and (5) and from the known time evolution of mass eigenstates:

Dphys0 (t) = g+ (t) D

0 + qpg− (t) D

0 , (9)

Dphys0 (t) = g+ (t) D

0 + pqg− (t) D

0 , (10)

where g+ and g- are defined as:

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g+ (t) = e− im+Γ

2⎛⎝⎜

⎞⎠⎟t cosh iΔm − ΔΓ

2⎛⎝⎜

⎞⎠⎟t2

⎛⎝⎜

⎞⎠⎟

, (11)

g− (t) = e− im+Γ

2⎛⎝⎜

⎞⎠⎟t sinh iΔm − ΔΓ

2⎛⎝⎜

⎞⎠⎟t2

⎛⎝⎜

⎞⎠⎟

. (12)

Before we can write decay rates we need to define different decay amplitudes. In general we can have four decay amplitudes [4]:

Af = A(D0 → f ) = f H D0 , A f = A(D

0→ f ) = f H D

0

A f = A(D0→ f ) = f H D

0, A f = A(D0 → f ) = f H D0

. (13)

3.3 Decay to CP eigenstates When we analyze a decay to a CP eigenstate we don’t have different final states for D0 and D0 , so we can write formulas with the following simplification: f = f . (14) Time dependent decay rates into CP eingenstate can be written as [5]:

Γ(D0 (t)→ f ) = e−τ Af

2 1+ λ f

2( )cosh(yτ )+ 1− λ f

2( )cos(xτ )+2Re(λ f )sinh(yτ )− 2Im(λ f )sin(xτ )

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪ , (15)

Γ D0(t)→ f( ) = e−τ A f

2 1+ λ f−1 2( )cosh(yτ )+ 1− λ f

−1 2( )cos(xτ )+2Re(λ f

−1)sinh(yτ )− 2Im(λ f−1)sin(xτ )

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪ , (16)

where λ f =qpA f

Af

.

We get the time-integrated rate from:

Γ(D0 → f ) = Γ(D0 (t)→ f )dt0

∞

∫ . (17)

3.4 Time integrated CP asymmetry Time integrated CP asymmetry for a decay to a final CP eigenstate is defined as:

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af =Γ(D0 → f )− Γ(D

0→ f )

Γ(D0 → f )+ Γ(D0→ f )

. (18)

If we put equations (15) and (16) into equation (18) we can see that af can be different from zero in three cases [4]:

1. If A f

Af

≠ 1 , we say that this is CP violation in decays.

2. If qp≠ 1 , we say that this is CP violation in mixing.

3. If Im(λ f ) ≠ 0 , we say that this is CP violation in the interference between

decay without and with mixing. Amplitudes for equation (13) are related trough CP transformation acting on initial and final states and we can write them as [5]: , (19)

, (20)

where represents Standard Model three level contribution, represents all higher order diagrams ( is the ratio between subleading contribution

with a weak phase different from and SM three level contribution) , for

CP even (+) of odd (-) states. We need to take a look at phases. Phases are weak phases and change sign under CP conjugation, phase is strong and is invariant to CP conjugation. If we neglect rf in equations (19) and (20), λ f is universal and we can write:

λ f = − qpeiφD , (21)

where φD is the relative weak phase between the mixing amplitude and the decay amplitude. If we put formulas (15) and (16) into (18) and take into consideration experimental constrains (x,y,r << 1) and we expend to first order of these parameters, we can write CP asymmetry as:

Af = AfT eiφt

T

1+ rf ei(δ f +φ f )( )

nfCP A f = Af

T e− iφtT

1+ rf ei(δ f −φ f )( )

AfT e± iφt

T rf ei(δ f ±φ f )

rfφ fT nf

CP = ±1

φT and φ f

δ f

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af = afd + af

m + afi , (22)

whereaf

d signals CP violation in decay, afm signals CP violation in mixing and af

i signals CP violation in interference of both. We can distinguish between direct and indirect CP violation. Direct CP violation will contribute to decay amplitudes while indirect contributes to mixing amplitude, it is also possible that new CP violation contributes in both ways. Indirect CP violation generates af

m and afi , direct CP violation on the other hand generates af

d . Currently there is no precise theoretical prediction of the CP asymmetry in the charm sector.

4 LHCb experiment LHCb experiment measured time integrated CP violation between D→ K −K + and D→π−π + decays. Preliminary results were published in March 2013. On quark level these decays proceed trough c→ udd and c→ uss transformations.

4.1 LHCb detector Detector is designed for studies of particles that contain b or c quarks. It consist of several different parts [6]:

1. VELO (Vertex Locator) 2. Ring Imaging Cherenkov (RICH) detectors 3. Magnet 4. Silicon and outer trackers 5. Calorimeters 6. Muon systems

Dipole magnet can have two configurations: up and down. 40% of data came form polarity pointing up and 60% from pointing down.

Figure1: LHCb detector. On left side is the vertex detector, which is followed by RICH detectors (RICH 1, RICH 2), silicon tracker (TT), magnet, outer trackers (T1 –T3), Calorimeters (ECAL and HCAL) and muon systems (M1 – M5).

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RICH detectors identify charged hadrons. For detection of photons, electrons and neutral hadrons the detector a uses calorimeter system. Muons are identified separately. Momentum resolution of the system is 0,4% at 5 GeV/c up to 0,6% at 100GeV/c. LHCb trigger consist of two stages, a hardware stage and a software stage. The hardware stage is based on information from calorimeters and muon system; the software stage applies full event reconstruction. Data was collected from proton collision in 2011. The center of mass energy was 7TeV and the integrated luminosity 1.0 fb-1 (for which we need around 1014 proton collisions) [7]. After proton - proton reaction initial flavor states D0 or D

0 are flagged by the charge

of soft pions in initial decays: D∗+ → D0π s

+ , D∗− → D0π s+ . (23)

Problem of the study is the fact that in the experiment we measure not only CP asymmetry but also production asymmetry and reconstruction asymmetry (further explained in analysis section). For that purpose we define difference between quantities for both decays: ΔaCP = aCP (K

−K + )− aCP (π−π + ) , (24)

where production and reconstruction asymmetries should be equal. The time-integrated asymmetry as measured by an experiment, depends on the decay time acceptance of experiment. It can be written as [7]:

aCP ( f ) = aCPdir ( f )+ t

TaCPind , (25)

where t is average decay time in reconstructed sample, aCP

dir is direct CP asymmetry, aCP

ind is the indirect asymmetry and T is D0 lifetime. If we put equation (25) into equation (24) we can write:

ΔaCP = aCPdir (K −K + )− aCP

dir (π −π + )⎡⎣ ⎤⎦ +Δ tT

aCPind . (26)

In the limit when Δ t → 0 , the indirect part vanishes. However, if the time-acceptance is different for the two final states, a possible contribution from indirect CP violation remains.

4.2 Analysis LHCb measures the raw asymmetry of the tagged mesons: defined as [7]:

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araw ( f ) =N(D∗+ → D0 ( f )π s

+ )− N(D∗− → D0( f )π s

− )N(D∗+ → D0 ( f )π s

+ )+ N(D∗− → D0( f )π s

− ) , (27)

where N represents the number of reconstructed events after background subtraction. The raw symmetry can be written for the first order as [7]: araw ( f ) = aCP ( f )+ aD ( f )+ aD (π S

+ )+ aP (D∗+ ) . (28)

In this equation aD ( f ) represents the asymmetry in selecting D0 decay, aD (π S

+ ) is the asymmetry in the selection of soft pions from decays from equation (23) and aP (D

∗+ ) is the production asymmetry. In our case of self-conjugate final states there is no asymmetry in the selection of D decays. The asymmetry in selecting soft pions and the production asymmetry are independent of the final state in any kinematic region. For the first order we can rewrite equation (24) as: ΔaCP = araw (K

−K + )− araw (π−π + ) . (29)

4.3 Selection process In order to remove background process from analysis several selections are applied. Firstly the candidates need to pass trough hardware and software trigger levels. First selection happens in the final stage of the software trigger and than we continue with offline analysis. Trigger and offline selections impose different requirements, so that we can isolate decays that interest us. These requirements include [8] [7]:

• Track fit quality, • D0 and D∗+ vertex fit quality, • Transverse momentum of the D0 candidate – it must be more than 2

GeV/c, • Decay time of D0 candidate – ct >100µm , • Angle between the D0 momentum in lab frame and rest frame, • D0 track points back to primary vertex while D0 daughter tracks do

not. We use RICH systems to distinguish between pions and kaons when reconstructing D0 candidates. At this point we define the mass difference as: δm = m(h+h−π + )−m(h+h− )−m(π + ) , (30) where h=K, π. Now we add requirement that the candidates must lie inside a δm window of 0 – 12 MeV/c2. With that we can plot invariant mass spectra shown in Figure 2. For all following results candidates must be inside mass signal window of

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1844 MeV/c2 < m(h+h-) < 1884 MeV/c2. After this we make a mass difference distributions and fit them.

Figure 2: m(K −K + ) (left) and m(π −π + ) spectra of D∗+ candidates that passed the selection and satisfy the mass difference requirement [7].

4.4 Gathered data and results Data was dived into several groups, dependent on the final state, magnet polarity and hardware trigger category. For every given final state there is a variation due to differences in kinematic distributions and detector conditions. When we combine all results we get the following result [7]: ΔaCP = (−0.34 ± 0.15 ± .10)% , (31) where the first uncertainty is statistical and the second systematic. Systematic uncertainty is sum a of different effects shown in Table 2 [7]:

Table 2: uncertainties of LHCb experiment [7].

Previous LHCb result published in 2012 was: ΔaCP = (−0.82 ± 0.21± 0.11)% [7], [8]. We can see that the new result shows a considerably smaller CP asymmetry as the previous one. The main reasons for difference are: a larger data sample that was analyzed, changes in detector calibration, changes in reconstruction software, and differences in analysis techniques. Approximately 15% of the K −K + events and 14% of π −π + events were no longer selected when data was reprocessed with the new calibration and the new reconstruction software [7]. We need to keep in mind that these are still preliminary results.

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5 Conclusion In this seminar we took a look at basics of violation of CP symmetry in neutral D mesons. We firstly wrote down the formalism and theoretical basics that help us understand the experiment, which was further discussed in the second part of this seminar. Taking a look at theoretical basics we found out that CP violation can happen in three different cases. Firstly it happens if the decay rates of neutral D meson and antimeson are different; the second option is in mixing of meson and antimeson and lastly it can be due to the interference of both phenomena. In the experimental part of this seminar we saw that the experiment measures difference between CP violations in decays to pion and kaon final states. We saw that certain selections must be applied in order to select signal event from the background. Final result shows that there is in fact a difference in time integrated CP violation between both decays, but the result is not yet conclusive.

6 Bibliography [1]  Daan van Eijk. (2012, Oct.) Ageing and the Decay of Beauty. [Online].

http://hdl.handle.net/1871/38392 [2]  Particle Data Group. (2012, Mar.) The CKM Quark-Mixing Matrix. [Online].

http://pdg.lbl.gov/2012/reviews/rpp2012-rev-ckm-matrix.pdf [3]  Wikipedia. (2013, Nov.) D meson. [Online].

http://en.wikipedia.org/wiki/D_meson [4]  Yosef Nir. (2005, Oct.) CP Vioaltion in Meson Decays. [Online].

http://arxiv.org/pdf/hep-ph/0510413v1.pdf [5]  Yuval Grossman, Alexander Kagan, and Yosef Nir. (2006, Sep.) New Physics and

CP Violation in Singly Cabibbo Suppressed D Decays. [Online]. http://arxiv.org/pdf/hep-ph/0609178v1.pdf

[6]  LHCb - Large Hadron Collider beauty experiment. (2013, Nov.) The LHCb Detector. [Online]. http://lhcb-public.web.cern.ch/lhcb-public/en/detector/Detector-en.html

[7]  The LHCb collaboration. (2013, Mar.) A search for time integrated CP violation. [Online]. http://cds.cern.ch/record/1521995/files/LHCb-CONF-2013-003.pdf

[8]  Angelo Carbone. (2012, Nov.) A search for time-integrated CP vioaltion in D ->hh decays. [Online]. http://arxiv.org/pdf/1210.8257.pdf