Particle Physics WS 2012/13 (15.1.2013)

Stephanie Hansmann-Menzemer Physikalisches Institut, INF 226, 3.101

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Homework & Exams

- Sheet 11 (20 points) available on the web today (15.1.), to be handed in 22.1.

- Sheet 12 (15 points) optional [for those who still need a few points]

- Requirement to participate in exam ≥ 135 points (out of 225 from sheet 1-11)

- Exam takes place 5.02. 14:15h-16:00h, please show up at 14:00h!

- Please bring your students card

- You can bring one double sided hand written A4 sheet

- You can bring your own „normal“ calculators (no devices internet access, no programable computers, no mini-computers) We have some calculators for those which have no „normal“ one

- In case you have a very good reason to be not available that day, please contact me beforehand. In case you are ill, please hand in a medical certificate.

- Wed. 6.02. 12:00-14:00h, INF 226, SR 3.410: possibility to look at corrected exams (later only possible upon request)

- Depending on the number of people which have to take part in a second exam, the second exam will be oral or written.

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colour hypercharge Y = λ8/3

Lectures

- 15.01. (today) : Neutral Meson Mixing

- 18.01.: CP Violation + Evaluation from „Fachschaft“

- 22.01.: Neutrino Physics

- 25.01.: no lecture

- 29.01.: Neutrino Physics

- 01.02.: if you are interessted – repetition lecture; Concept: you ask questions – best before hand per email

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Quark/Lepton Eigenstates

Strong, electromagnetic and weak NC interaction conserve flavour. gA,gV

They have identical coupling constants for all up-type and down-type quarks, all charge leptons and all neutrinos!

Assuming massless particles, this leaves ambiguity for definiton of quark and lepton eigenstates.

E.g. rotational freedom in u-type quarks. Lagrangian for x = 1

2 (u+c) would look the same .

μ-, e-, τ-

μ+, e+, τ+

u, c, t

u, c, t e 4/9 e 1/9 e

d, s, b

d, s, b

μ-, e-, τ-

μ+, e+, τ+

u, c, t

u, c, t gA,gV gA,gV gA,gV

d, s, b

d, s, b

μ-, e-, τ-

μ+, e+, τ+

u,d,c,s,t,b

u,d,c,s,t,b αs

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Quark/Lepton Eigenstates

Weak charged current interaction couples up-type with down-type quarks.

Due to this amibuity (degeneracy of strong, elm and NC) interaction eigenstates, we can choose to write down the theory in terms of mass eigenstates with no change in the form of the Lagrangian for elm, strong and NC interaction.

νμ, νe, ντ

μ+, e+, τ+

u-type

d -type

W+ W+

We have the freedom to write down the Lagrangian in terms of mass-eigenstates for up type quarks and charged leptons. But then the neutrinos and the down-type quarks are defined via their coupling to the W. As neutrinos are massless, the neutrino mass eigenstates are degenrated, thus Lagrangian stays unchanged.

For quark-sector however we cannot find common mass and flavour eigenstates for up-type and down-type quarks simultaneously.

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Quark Mixing in SM

Jμ

CC ~ (𝑢 , 𝑐 , 𝑡 ) γμ (1-γ5) VCKM

𝑑

𝑠 𝑏

𝑑′𝑠′𝑏′

= 𝑉𝑢𝑑

𝑉𝑐𝑑

𝑉𝑡𝑑

𝑉𝑢𝑠

𝑉𝑐𝑠

𝑉𝑡𝑠

𝑉𝑢𝑏

𝑉𝑐𝑏

𝑉𝑡𝑏

x 𝑑

𝑠 𝑏

For down-type quarks: flavour eigenstates ≠ mass eigenstates! Direct result of coupling of Higgs to quarks, which give rise to masses!

flavour CKM matrix mass

d Vud u

W

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CKM Matrix

𝑑′𝑠′𝑏′

= 𝑉𝑢𝑑

𝑉𝑐𝑑

𝑉𝑡𝑑

𝑉𝑢𝑠

𝑉𝑐𝑠

𝑉𝑡𝑠

𝑉𝑢𝑏

𝑉𝑐𝑏

𝑉𝑡𝑏

x 𝑑

𝑠 𝑏

flavour CKM matrix mass

18 parameters (9 complex elements) - 9 unitarity conditions - 5 relative quark phases (unobservables) -------------------------------------------------------- 4 independent parameter: 3 Euler angels and 1 Phase

4 fundamental SM parameters (out of 18 [28 with neutrino masses ])

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CKM Matrix

JμCC ~ (𝑢 , 𝑐 , 𝑡 ) γμ (1-γ5) VCKM

𝑑

𝑠 𝑏

JμCC ~ (𝑢 , 𝑐 , 𝑡 )

𝑒−𝑖φ(𝑢) 0 00 𝑒−𝑖φ(𝑐) 00 0 𝑒−𝑖φ(𝑡)

𝑒𝑖φ(𝑢) 0 00 𝑒𝑖φ(𝑐) 00 0 𝑒𝑖φ(𝑡)

γμ (1-γ5) VCKM 𝑒−𝑖φ(𝑑) 0 00 𝑒−𝑖φ(𝑠) 00 0 𝑒−𝑖φ(𝑏)

𝑒𝑖φ(𝑢) 0 00 𝑒𝑖φ(𝑐) 00 0 𝑒𝑖φ(𝑡)

𝑑

𝑠 𝑏

JμCC ~ (𝑢 , 𝑐 , 𝑡 ) γμ (1-γ5)

𝑒𝑖𝜑(𝑢) 0 00 𝑒𝑖𝜑(𝑐) 00 0 𝑒𝑖𝜑(𝑡)

VCKM 𝑒−𝑖φ(𝑑) 0 00 𝑒−𝑖φ(𝑠) 00 0 𝑒−𝑖φ(𝑏)

𝑑

𝑠 𝑏

uL → uL 𝑒𝑖φ(𝑢)

Strong, elm, weak NC, Higgs term in Lagrangian are insensitive to a phase transformation of the quarks, they simply cancel out due to flavour conservation of these IA. uR → uR 𝑒𝑖φ(𝑑)

dL → dL 𝑒𝑖φ(𝑑) dR → dR 𝑒𝑖φ(𝑑)

…. (for all quark types)

Unobservable redifinition of quark phases gets rid of 5 parameters of SM

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Structure of CKM Matrix

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Definition of CKM Angles

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Unitarity Triangle

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Neutral Meson Mixing

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Phenomenology ofMixing

Schrödinger equation for unstable mesons (at rest):

i𝑑

𝑑𝑡 |Ψ > = 𝐻 Ψ > = 𝑚 −

𝑖

2Γ Ψ >

→ |Ψ 𝑡 > = |Ψ0 > 𝑒−𝑖𝑚𝑡𝑒−1

2Γt

→ ||Ψ 𝑡 > |2 = ||Ψ0 > |2𝑒−Γt exponential decay

For neutral mesons, consider 2 components (formulas eq. for K0, D0, Bs)

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Mass Eigenstates

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Phenomenology of Mixing II

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Time Evolution I

f±

𝑡 = 1

2(𝑒−𝑖𝑚

𝐻𝑡𝑒−

Γ𝐻𝑡

2 ± 𝑒−𝑖𝑚𝐿𝑡𝑒−Γ

𝐿𝑡/2)

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Time Evolution II

(~ cos (Δmt) for ΓH~ ΓL )

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Phenomenology of Mixing III

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How to Measure Mixing?

Identify initial flavour of meson

Identify flavour at decay of meson → identify meson as mixed or unmixed

If mixing is fast … need to measure decay time: t = m L/p (L: decay length, p: momentum, m: mass) If mixing is slow … can deduce information from time integrated asymmetry

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Neutral Kaons

K long K short

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Measurement of Kaon Mixing

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Example for Kaon-Oscillation

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Kaon Oscillation at CP Lear

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B Production

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Argus 1987

Bs Mixing Analysis at the Tevatron

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Time Dependent Asymmetries

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Time Dependent Asymmetries

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Tagging Dilution

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Bs Mixing Analysis at the Tevatron

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colour hypercharge Y = λ8/3

Asymmetrie Measurement

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colour hypercharge Y = λ8/3

Comparison e+e- versus pp

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Way cleaner event in e+e-, which boost performance of flavour tagging algorithms!

colour hypercharge Y = λ8/3

Comparison e+e- versus pp

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Way cleaner event in e+e-, which boost performance of flavour tagging algorithms!

Babar (e+e-)

LHCb (pp)

CDF: p-anti-p

B Mixing at Babar and CDF

34 Decay time modulo 2π/Δm

colour hypercharge Y = λ8/3

Bs Mixing Analysis at the LHC

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colour hypercharge Y = λ8/3

D0 Mixing

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colour hypercharge Y = λ8/3

D0 Mixing

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charge of pion from D* decay used for tagging

CF: Cabbibo favoured DCS: double Cabbibo suppressed