MKEP 1.2: Particle Physics WS 2012/13menzemer/PP... · Particle Physics WS 2012/13 (15.1.2013)...
Transcript of MKEP 1.2: Particle Physics WS 2012/13menzemer/PP... · Particle Physics WS 2012/13 (15.1.2013)...
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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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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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
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