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Flavour physics : Lecture 1History, CP violation, Neutral meson mixing
Amol DigheDepartment of Theoretical Physics, TIFR
SUSY 2017 pre-school,TIFR Mumbai, Dec 4-8, 2017
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Why Flavour physics
Role of flavour physics in building up the Standard Modelτ − θ puzzle⇒ Parity violationCabibbo angle⇒
weak coupling universality ⊕ quark mixingGIM mechanism⇒ no FCNC at tree level, charmCKM paradigm⇒ (at least) three quark familiesLarge B–B mixing⇒ heavy top quarkRate of radiative B decay⇒ top quark mass
The standard model looks complete now,with no confirmed signals of BSM physics at the LHC yet !Flavour physics may give some indirect hints....
![Page 3: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/3.jpg)
Why Flavour physics
Role of flavour physics in building up the Standard Modelτ − θ puzzle⇒ Parity violationCabibbo angle⇒
weak coupling universality ⊕ quark mixingGIM mechanism⇒ no FCNC at tree level, charmCKM paradigm⇒ (at least) three quark familiesLarge B–B mixing⇒ heavy top quarkRate of radiative B decay⇒ top quark mass
The standard model looks complete now,with no confirmed signals of BSM physics at the LHC yet !Flavour physics may give some indirect hints....
![Page 4: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/4.jpg)
Why Flavour physics
Role of flavour physics in building up the Standard Modelτ − θ puzzle⇒ Parity violationCabibbo angle⇒
weak coupling universality ⊕ quark mixingGIM mechanism⇒ no FCNC at tree level, charmCKM paradigm⇒ (at least) three quark familiesLarge B–B mixing⇒ heavy top quarkRate of radiative B decay⇒ top quark mass
The standard model looks complete now,with no confirmed signals of BSM physics at the LHC yet !Flavour physics may give some indirect hints....
![Page 5: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/5.jpg)
Why Flavour physics
Role of flavour physics in building up the Standard Modelτ − θ puzzle⇒ Parity violationCabibbo angle⇒
weak coupling universality ⊕ quark mixingGIM mechanism⇒ no FCNC at tree level, charmCKM paradigm⇒ (at least) three quark familiesLarge B–B mixing⇒ heavy top quarkRate of radiative B decay⇒ top quark mass
The standard model looks complete now,with no confirmed signals of BSM physics at the LHC yet !Flavour physics may give some indirect hints....
![Page 6: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/6.jpg)
Why Flavour physics
Role of flavour physics in building up the Standard Modelτ − θ puzzle⇒ Parity violationCabibbo angle⇒
weak coupling universality ⊕ quark mixingGIM mechanism⇒ no FCNC at tree level, charmCKM paradigm⇒ (at least) three quark familiesLarge B–B mixing⇒ heavy top quarkRate of radiative B decay⇒ top quark mass
The standard model looks complete now,with no confirmed signals of BSM physics at the LHC yet !Flavour physics may give some indirect hints....
![Page 7: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/7.jpg)
Why Flavour physics
Role of flavour physics in building up the Standard Modelτ − θ puzzle⇒ Parity violationCabibbo angle⇒
weak coupling universality ⊕ quark mixingGIM mechanism⇒ no FCNC at tree level, charmCKM paradigm⇒ (at least) three quark familiesLarge B–B mixing⇒ heavy top quarkRate of radiative B decay⇒ top quark mass
The standard model looks complete now,with no confirmed signals of BSM physics at the LHC yet !Flavour physics may give some indirect hints....
![Page 8: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/8.jpg)
Why Flavour physics
Role of flavour physics in building up the Standard Modelτ − θ puzzle⇒ Parity violationCabibbo angle⇒
weak coupling universality ⊕ quark mixingGIM mechanism⇒ no FCNC at tree level, charmCKM paradigm⇒ (at least) three quark familiesLarge B–B mixing⇒ heavy top quarkRate of radiative B decay⇒ top quark mass
The standard model looks complete now,with no confirmed signals of BSM physics at the LHC yet !Flavour physics may give some indirect hints....
![Page 9: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/9.jpg)
Flavour structure of the Standard Model
Three families ofquarks and leptonsQuark masses (GeV):
up charmed top0.005 1.5 175
down strange bottom0.01 0.1 5
Mixing between families:Strong within the same family,Weak across families
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The meson nomenclature
Pions:π+ ≡ ud , π− ≡ du , π0 ≡ (uu − dd)/
√2 (∼ 0.15 GeV)
Strange mesons (Kaons):K + ≡ us ,K− ≡ su ,K 0 ≡ ds ,K 0 ≡ sd (∼ 0.5 GeV)Charmed mesons:D+ ≡ cd ,D+
s ≡ cs ,D0 ≡ cu(And antiparticles: ∼ 1.5− 1.8 GeV)B mesons:B+ ≡ ub ,B0 ≡ db ,Bs ≡ sb ,Bc ≡ cb(And antiparticles: ∼ 5− 6.5 GeV)Quarkonia:φ ≡ ss (∼ 0.7 GeV)J/ψ ≡ cc (∼ 3.1 GeV)Υ ≡ bb (∼ 10 GeV)
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The meson nomenclature
Pions:π+ ≡ ud , π− ≡ du , π0 ≡ (uu − dd)/
√2 (∼ 0.15 GeV)
Strange mesons (Kaons):K + ≡ us ,K− ≡ su ,K 0 ≡ ds ,K 0 ≡ sd (∼ 0.5 GeV)Charmed mesons:D+ ≡ cd ,D+
s ≡ cs ,D0 ≡ cu(And antiparticles: ∼ 1.5− 1.8 GeV)B mesons:B+ ≡ ub ,B0 ≡ db ,Bs ≡ sb ,Bc ≡ cb(And antiparticles: ∼ 5− 6.5 GeV)Quarkonia:φ ≡ ss (∼ 0.7 GeV)J/ψ ≡ cc (∼ 3.1 GeV)Υ ≡ bb (∼ 10 GeV)
![Page 12: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/12.jpg)
The meson nomenclature
Pions:π+ ≡ ud , π− ≡ du , π0 ≡ (uu − dd)/
√2 (∼ 0.15 GeV)
Strange mesons (Kaons):K + ≡ us ,K− ≡ su ,K 0 ≡ ds ,K 0 ≡ sd (∼ 0.5 GeV)Charmed mesons:D+ ≡ cd ,D+
s ≡ cs ,D0 ≡ cu(And antiparticles: ∼ 1.5− 1.8 GeV)B mesons:B+ ≡ ub ,B0 ≡ db ,Bs ≡ sb ,Bc ≡ cb(And antiparticles: ∼ 5− 6.5 GeV)Quarkonia:φ ≡ ss (∼ 0.7 GeV)J/ψ ≡ cc (∼ 3.1 GeV)Υ ≡ bb (∼ 10 GeV)
![Page 13: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/13.jpg)
The meson nomenclature
Pions:π+ ≡ ud , π− ≡ du , π0 ≡ (uu − dd)/
√2 (∼ 0.15 GeV)
Strange mesons (Kaons):K + ≡ us ,K− ≡ su ,K 0 ≡ ds ,K 0 ≡ sd (∼ 0.5 GeV)Charmed mesons:D+ ≡ cd ,D+
s ≡ cs ,D0 ≡ cu(And antiparticles: ∼ 1.5− 1.8 GeV)B mesons:B+ ≡ ub ,B0 ≡ db ,Bs ≡ sb ,Bc ≡ cb(And antiparticles: ∼ 5− 6.5 GeV)Quarkonia:φ ≡ ss (∼ 0.7 GeV)J/ψ ≡ cc (∼ 3.1 GeV)Υ ≡ bb (∼ 10 GeV)
![Page 14: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/14.jpg)
The meson nomenclature
Pions:π+ ≡ ud , π− ≡ du , π0 ≡ (uu − dd)/
√2 (∼ 0.15 GeV)
Strange mesons (Kaons):K + ≡ us ,K− ≡ su ,K 0 ≡ ds ,K 0 ≡ sd (∼ 0.5 GeV)Charmed mesons:D+ ≡ cd ,D+
s ≡ cs ,D0 ≡ cu(And antiparticles: ∼ 1.5− 1.8 GeV)B mesons:B+ ≡ ub ,B0 ≡ db ,Bs ≡ sb ,Bc ≡ cb(And antiparticles: ∼ 5− 6.5 GeV)Quarkonia:φ ≡ ss (∼ 0.7 GeV)J/ψ ≡ cc (∼ 3.1 GeV)Υ ≡ bb (∼ 10 GeV)
![Page 15: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/15.jpg)
Contents
1 Some historical perspective
2 CP violation: discovery and interpretation
3 The Kobayashi-Maskawa mechanism
4 Neutral meson mixing and oscillations
5 Flavour tests of the CKM paradigm
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Outline
1 Some historical perspective
2 CP violation: discovery and interpretation
3 The Kobayashi-Maskawa mechanism
4 Neutral meson mixing and oscillations
5 Flavour tests of the CKM paradigm
![Page 17: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/17.jpg)
Discovery of parity violation: 1956-57
τ − θ puzzle: Particles with thesame mass and lifetime decayto ππ and πππTheoretical possibility thatmirror world does not behavethe same as the real worldT.D.Lee and C.N.Yang,Phys. Rev. 104, 254 (1956)Experiments: 1957
Wu (60Co)Friedman-Telegdi(π+ → µ+ → e+)
Nobel prize 1957: Lee–Yang
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Discovery of parity violation: 1956-57
τ − θ puzzle: Particles with thesame mass and lifetime decayto ππ and πππTheoretical possibility thatmirror world does not behavethe same as the real worldT.D.Lee and C.N.Yang,Phys. Rev. 104, 254 (1956)Experiments: 1957
Wu (60Co)Friedman-Telegdi(π+ → µ+ → e+)
Nobel prize 1957: Lee–Yang
![Page 19: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/19.jpg)
Discovery of parity violation: 1956-57
τ − θ puzzle: Particles with thesame mass and lifetime decayto ππ and πππTheoretical possibility thatmirror world does not behavethe same as the real worldT.D.Lee and C.N.Yang,Phys. Rev. 104, 254 (1956)Experiments: 1957
Wu (60Co)Friedman-Telegdi(π+ → µ+ → e+)
Nobel prize 1957: Lee–Yang
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The particle zoo (1960’s)
p ≡ uud
n ≡ udd
π+ ≡ ud
π− ≡ du
π0 ≡ (uu − dd)/√
2
K + ≡ us
K− ≡ su
K 0 ≡ ds
K 0 ≡ sd
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Universality of weak interactions: Cabibbo angleInterrelated coupling constants:
(i) muon decay: geµµ− → νµe−νe
(ii) neutron decay : gudn→ pe−νe (d → ue−νe)(ii) kaon decay: gusK− → π0e−νe (s → ue−νe)
|geµ|2 = |gud |2 + |gus|2
Universality:
There is only one coupling constant, g = geµ
u quark couples to only one combination of d and s:d ′ ≡ cos θc · d + sin θc · s
Cabibbo angle θc : the first quark mixing angle
N. Cabibbo, “Unitary Symmetry and Leptonic Decays,”Phys. Rev. Lett. 10, 531 (1963)
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Universality of weak interactions: Cabibbo angleInterrelated coupling constants:
(i) muon decay: geµµ− → νµe−νe
(ii) neutron decay : gudn→ pe−νe (d → ue−νe)(ii) kaon decay: gusK− → π0e−νe (s → ue−νe)
|geµ|2 = |gud |2 + |gus|2
Universality:
There is only one coupling constant, g = geµ
u quark couples to only one combination of d and s:d ′ ≡ cos θc · d + sin θc · s
Cabibbo angle θc : the first quark mixing angle
N. Cabibbo, “Unitary Symmetry and Leptonic Decays,”Phys. Rev. Lett. 10, 531 (1963)
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Suppression of flavor-changing neutral currents
Cabibbo angle unable to explain whyΓ(KL → µ+µ−) << Γ(K + → µ+νµ)
Possible explanation via another “c” quark:charge +2/3, couples to
s′ ≡ − sin θc · d + cos θc · sThe s → u → d and s → c → d contribution cancel,leading to the suppression of FCNC s → dGIM mechanism: existence of the “charmed” quark.
S. L. Glashow, J. Iliopoulos and L. Maiani,“Weak Interactions with Lepton-Hadron Symmetry,”Phys. Rev. D 2, 1285 (1970)
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Suppression of flavor-changing neutral currents
Cabibbo angle unable to explain whyΓ(KL → µ+µ−) << Γ(K + → µ+νµ)
Possible explanation via another “c” quark:charge +2/3, couples to
s′ ≡ − sin θc · d + cos θc · sThe s → u → d and s → c → d contribution cancel,leading to the suppression of FCNC s → dGIM mechanism: existence of the “charmed” quark.
S. L. Glashow, J. Iliopoulos and L. Maiani,“Weak Interactions with Lepton-Hadron Symmetry,”Phys. Rev. D 2, 1285 (1970)
![Page 25: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/25.jpg)
Suppression of flavor-changing neutral currents
Cabibbo angle unable to explain whyΓ(KL → µ+µ−) << Γ(K + → µ+νµ)
Possible explanation via another “c” quark:charge +2/3, couples to
s′ ≡ − sin θc · d + cos θc · sThe s → u → d and s → c → d contribution cancel,leading to the suppression of FCNC s → dGIM mechanism: existence of the “charmed” quark.
S. L. Glashow, J. Iliopoulos and L. Maiani,“Weak Interactions with Lepton-Hadron Symmetry,”Phys. Rev. D 2, 1285 (1970)
![Page 26: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/26.jpg)
Outline
1 Some historical perspective
2 CP violation: discovery and interpretation
3 The Kobayashi-Maskawa mechanism
4 Neutral meson mixing and oscillations
5 Flavour tests of the CKM paradigm
![Page 27: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/27.jpg)
Can Charge ⊕ Parity may be conserved ?
Parity: left landed↔ right handed
Neutrinos violate parity: they are only left-handedBut antineutrinos are right-handed !Does that mean C and P violations cancel each other togive CP conservation ?
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Prediction of CP violation in K decay
K 0 ≡ ds K 0 ≡ sd
CP eigenstates:K1 ≡ (K 0 + K )/
√2 (CP even)
K2 ≡ (K 0 − K )/√
2 (CP odd)
CP even decay channel: ππCP odd decay channel: πππCP conservation⇒
K1 → ππ short-lived, KShortK2 → πππ long-lived, KLong
Original K 0 = (KShort + KLong)/√
2
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Prediction of CP violation in K decay
K 0 ≡ ds K 0 ≡ sd
CP eigenstates:K1 ≡ (K 0 + K )/
√2 (CP even)
K2 ≡ (K 0 − K )/√
2 (CP odd)
CP even decay channel: ππCP odd decay channel: πππCP conservation⇒
K1 → ππ short-lived, KShortK2 → πππ long-lived, KLong
Original K 0 = (KShort + KLong)/√
2
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Prediction of CP violation in K decay
K 0 ≡ ds K 0 ≡ sd
CP eigenstates:K1 ≡ (K 0 + K )/
√2 (CP even)
K2 ≡ (K 0 − K )/√
2 (CP odd)
CP even decay channel: ππCP odd decay channel: πππCP conservation⇒
K1 → ππ short-lived, KShortK2 → πππ long-lived, KLong
Original K 0 = (KShort + KLong)/√
2
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Discovery of CP violation: 1964
Cronin-Fitch experiment
Nobel prize 1980
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Charge-parity violated slightly
“Day and Night”, M.C.Escher
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Questions raised by the discovery of CP violation
Is it small or large ? Is CP an approximate symmetry ?
Is the symmetry breaking spontaneous ?
Where does it come from ? Are there extra interactions ?
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CP violation and complex coupling
CP violation: A(X → Y ) 6= A(X → Y )
If all amplitudes are real, |A(X → Y )|2 = |A(X → Y )|2
CP violation possible if complex numbers involved in
|A(X → Y )|2 = |A(X → w → Y ) + A(X → z → Y )|2
|A(X → Y )|2 = |A(X → w → Y ) + A(X → z → Y )|2
CP violation⇒ Amplitudes complex⇒ Couplings complex
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Outline
1 Some historical perspective
2 CP violation: discovery and interpretation
3 The Kobayashi-Maskawa mechanism
4 Neutral meson mixing and oscillations
5 Flavour tests of the CKM paradigm
![Page 36: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/36.jpg)
The paper and the authors
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Two generations of quarks are not enough
The mixing matrix between up-type and down-type quarkshas to be a 2× 2 unitary matrix
L ∝ (uL, cL)
(cos θeiφ1 sin θeiφ2
− sin θeiφ3 cos θei(φ2+φ3−φ1)
)(dLsL
)Can change three relative phases of quarks to get rid of allthree complex phases φ1, φ2, φ3
L ∝ (uL, cLei(φ3−φ1))
(cos θ sin θ− sin θ cos θ
)(dLeiφ1
sLeiφ2
)Mixing matrix real⇒ no CP violation
![Page 38: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/38.jpg)
Two generations of quarks are not enough
The mixing matrix between up-type and down-type quarkshas to be a 2× 2 unitary matrix
L ∝ (uL, cL)
(cos θeiφ1 sin θeiφ2
− sin θeiφ3 cos θei(φ2+φ3−φ1)
)(dLsL
)Can change three relative phases of quarks to get rid of allthree complex phases φ1, φ2, φ3
L ∝ (uL, cLei(φ3−φ1))
(cos θ sin θ− sin θ cos θ
)(dLeiφ1
sLeiφ2
)Mixing matrix real⇒ no CP violation
![Page 39: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/39.jpg)
Paremeter counting for two generations
2× 2 complex matrix⇒ 4 real + 4 imaginary quantities
Unitarity U†U = I: 3 real and 1 imaginary conditions1 real and 3 imaginary parameters left
Can choose the 3 relative phases between quarks to getrid of the 3 imaginary parametersThe mixing matrix is completely real
![Page 40: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/40.jpg)
Paremeter counting for two generations
2× 2 complex matrix⇒ 4 real + 4 imaginary quantities
Unitarity U†U = I: 3 real and 1 imaginary conditions1 real and 3 imaginary parameters left
Can choose the 3 relative phases between quarks to getrid of the 3 imaginary parametersThe mixing matrix is completely real
![Page 41: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/41.jpg)
Paremeter counting for two generations
2× 2 complex matrix⇒ 4 real + 4 imaginary quantities
Unitarity U†U = I: 3 real and 1 imaginary conditions1 real and 3 imaginary parameters left
Can choose the 3 relative phases between quarks to getrid of the 3 imaginary parametersThe mixing matrix is completely real
![Page 42: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/42.jpg)
Three generations work !
3× 3 matrix⇒ 9 real + 9 imaginary quantitiesUnitarity U†U = I: 6 real and 3 imaginary conditions3 real and 6 imaginary parameters leftCan choose the 5 relative phases between quarks to getrid of 5 imaginary parametersIn addition to 3 real parameters (Euler angles of rotation),one imaginary quantity is unavoidableMixing matrix complex⇒ CP violation may be present c1 −s1c3 −s1s3
s1c2 c1c2c3 − s2s3eiδ c1c2s3 + s2c3eiδ
s1s2 c1s2c3 + c2s3eiδ c1s2s3 − c2c3eiδ
Three families needed for the complex nature
![Page 43: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/43.jpg)
Three generations work !
3× 3 matrix⇒ 9 real + 9 imaginary quantitiesUnitarity U†U = I: 6 real and 3 imaginary conditions3 real and 6 imaginary parameters leftCan choose the 5 relative phases between quarks to getrid of 5 imaginary parametersIn addition to 3 real parameters (Euler angles of rotation),one imaginary quantity is unavoidableMixing matrix complex⇒ CP violation may be present c1 −s1c3 −s1s3
s1c2 c1c2c3 − s2s3eiδ c1c2s3 + s2c3eiδ
s1s2 c1s2c3 + c2s3eiδ c1s2s3 − c2c3eiδ
Three families needed for the complex nature
![Page 44: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/44.jpg)
Three generations work !
3× 3 matrix⇒ 9 real + 9 imaginary quantitiesUnitarity U†U = I: 6 real and 3 imaginary conditions3 real and 6 imaginary parameters leftCan choose the 5 relative phases between quarks to getrid of 5 imaginary parametersIn addition to 3 real parameters (Euler angles of rotation),one imaginary quantity is unavoidableMixing matrix complex⇒ CP violation may be present c1 −s1c3 −s1s3
s1c2 c1c2c3 − s2s3eiδ c1c2s3 + s2c3eiδ
s1s2 c1s2c3 + c2s3eiδ c1s2s3 − c2c3eiδ
Three families needed for the complex nature
![Page 45: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/45.jpg)
Three generations work !
3× 3 matrix⇒ 9 real + 9 imaginary quantitiesUnitarity U†U = I: 6 real and 3 imaginary conditions3 real and 6 imaginary parameters leftCan choose the 5 relative phases between quarks to getrid of 5 imaginary parametersIn addition to 3 real parameters (Euler angles of rotation),one imaginary quantity is unavoidableMixing matrix complex⇒ CP violation may be present c1 −s1c3 −s1s3
s1c2 c1c2c3 − s2s3eiδ c1c2s3 + s2c3eiδ
s1s2 c1s2c3 + c2s3eiδ c1s2s3 − c2c3eiδ
Three families needed for the complex nature
![Page 46: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/46.jpg)
Experimental discovery of the third generation
Discovery of τ : 1976Υ,B,Bs, λb contain b quarkTop quark: 1995The last element, ντ , discovered in 2000.
![Page 47: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/47.jpg)
CKM paradigm in modern language
Flavor basis vs. mass basis:
U ′ ≡
uct
, D′ ≡
dsb
Charged current in the basis of flavor eigenstates:
LCC = g√2U ′Lγ
µD′LW +µ + h.c.
Charged current in the basis of mass eigenstates:
LCC = g√2ULγ
µ(V †ULVDL)DLW +µ + H.c.
VUL,VDL: unitary matrices that change the basis
Cabibbo-Kobayashi-Maskawa (CKM) matrix
Coupling between UL and DL: (g/√
2)VCKM
VCKM ≡ V †ULVDL
![Page 48: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/48.jpg)
CKM paradigm in modern language
Flavor basis vs. mass basis:
U ′ ≡
uct
, D′ ≡
dsb
Charged current in the basis of flavor eigenstates:
LCC = g√2U ′Lγ
µD′LW +µ + h.c.
Charged current in the basis of mass eigenstates:
LCC = g√2ULγ
µ(V †ULVDL)DLW +µ + H.c.
VUL,VDL: unitary matrices that change the basis
Cabibbo-Kobayashi-Maskawa (CKM) matrix
Coupling between UL and DL: (g/√
2)VCKM
VCKM ≡ V †ULVDL
![Page 49: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/49.jpg)
CKM paradigm in modern language
Flavor basis vs. mass basis:
U ′ ≡
uct
, D′ ≡
dsb
Charged current in the basis of flavor eigenstates:
LCC = g√2U ′Lγ
µD′LW +µ + h.c.
Charged current in the basis of mass eigenstates:
LCC = g√2ULγ
µ(V †ULVDL)DLW +µ + H.c.
VUL,VDL: unitary matrices that change the basis
Cabibbo-Kobayashi-Maskawa (CKM) matrix
Coupling between UL and DL: (g/√
2)VCKM
VCKM ≡ V †ULVDL
![Page 50: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/50.jpg)
Wolfenstein parametrization of the CKM matrix
VCKM =
Vud Vus VubVcd Vcs VcbVtd Vts Vtb
=
1− λ2/2 λ Aλ3(ρ− iη)−λ 1− λ2/2 Aλ2
Aλ3(1− ρ− iη) −Aλ2 1
+O(λ4)
λ ≈ 0.2: Cabibbo angleη: the imaginary component of VCKM
η/ρ large⇒ CP violation is large, not approximateAll CP violation in terms of a single number:Jarlskog invariant J ≡ s1s2s3c2
1c2c3sδ = A2λ6η
![Page 51: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/51.jpg)
Wolfenstein parametrization of the CKM matrix
VCKM =
Vud Vus VubVcd Vcs VcbVtd Vts Vtb
=
1− λ2/2 λ Aλ3(ρ− iη)−λ 1− λ2/2 Aλ2
Aλ3(1− ρ− iη) −Aλ2 1
+O(λ4)
λ ≈ 0.2: Cabibbo angleη: the imaginary component of VCKM
η/ρ large⇒ CP violation is large, not approximateAll CP violation in terms of a single number:Jarlskog invariant J ≡ s1s2s3c2
1c2c3sδ = A2λ6η
![Page 52: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/52.jpg)
Wolfenstein parametrization of the CKM matrix
VCKM =
Vud Vus VubVcd Vcs VcbVtd Vts Vtb
=
1− λ2/2 λ Aλ3(ρ− iη)−λ 1− λ2/2 Aλ2
Aλ3(1− ρ− iη) −Aλ2 1
+O(λ4)
λ ≈ 0.2: Cabibbo angleη: the imaginary component of VCKM
η/ρ large⇒ CP violation is large, not approximateAll CP violation in terms of a single number:Jarlskog invariant J ≡ s1s2s3c2
1c2c3sδ = A2λ6η
![Page 53: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/53.jpg)
Wolfenstein parametrization of the CKM matrix
VCKM =
Vud Vus VubVcd Vcs VcbVtd Vts Vtb
=
1− λ2/2 λ Aλ3(ρ− iη)−λ 1− λ2/2 Aλ2
Aλ3(1− ρ− iη) −Aλ2 1
+O(λ4)
λ ≈ 0.2: Cabibbo angleη: the imaginary component of VCKM
η/ρ large⇒ CP violation is large, not approximateAll CP violation in terms of a single number:Jarlskog invariant J ≡ s1s2s3c2
1c2c3sδ = A2λ6η
![Page 54: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/54.jpg)
Wolfenstein parametrization of the CKM matrix
VCKM =
Vud Vus VubVcd Vcs VcbVtd Vts Vtb
=
1− λ2/2 λ Aλ3(ρ− iη)−λ 1− λ2/2 Aλ2
Aλ3(1− ρ− iη) −Aλ2 1
+O(λ4)
λ ≈ 0.2: Cabibbo angleη: the imaginary component of VCKM
η/ρ large⇒ CP violation is large, not approximateAll CP violation in terms of a single number:Jarlskog invariant J ≡ s1s2s3c2
1c2c3sδ = A2λ6η
![Page 55: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/55.jpg)
Unitarity relations and triangles
Unitarity relation VudV ∗ub + VcdV ∗cb + VtdV ∗tb = 0
α ≡ Arg(−
VtdV ∗tb
VudV ∗ub
), β ≡ Arg
(−
VcdV ∗cb
VtdV ∗tb
), γ ≡ Arg
(−
VudV ∗ub
VcdV ∗cb
),
![Page 56: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/56.jpg)
More unitarity triangles
All triangles have the same area, J/2
χ ≡ βs ≡ φs ≡ Arg(−VcsV∗
cbVtsV∗
tb
)∼ λ2 ,
χ′ ≡ βK ≡ Arg(−Vcd V∗
csVcd V∗
cs
)∼ λ4 ,
![Page 57: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/57.jpg)
Outline
1 Some historical perspective
2 CP violation: discovery and interpretation
3 The Kobayashi-Maskawa mechanism
4 Neutral meson mixing and oscillations
5 Flavour tests of the CKM paradigm
![Page 58: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/58.jpg)
Bq–Bq mixing: parametrization
Oscillation and decay of a|Bq〉+ b|Bq〉 :
iddt
(ab
)=
(M− i
2Γ
) (ab
)
M ≡(
M11 M12M21 M22
), Γ ≡
(Γ11 Γ12Γ21 Γ22
)CP|Bq〉 = eiϕ|Bq〉, CP|Bq〉 = e−iϕ|Bq〉
CPT invariance : M11 = M22, Γ11 = Γ22
Hermiticity : M21 = M∗12, Γ21 = Γ∗12
![Page 59: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/59.jpg)
Mass difference and lifetime difference
Mass eigenstates:|BL,H〉 = p|Bq〉 ± q|Bq〉 (|q|2 + |p|2 = 1)
Mass difference Lifetime difference∆m = MH −ML ∆Γ = ΓL − ΓH
(→ ∆m > 0,∆Γ > 0 in SM)Eigenvalue equations:
(∆m)2 − 14
(∆Γ)2 = (4|M12|2 − |Γ12|2)
∆m∆Γ = −4Re(M∗12Γ12).
∆m = 2|M12|+ O(m4b/m
4t )
∆Γ = −2Re(M∗12Γ12)
|M12|+ O(m4
b/m4t ).
![Page 60: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/60.jpg)
Mass difference and lifetime difference
Mass eigenstates:|BL,H〉 = p|Bq〉 ± q|Bq〉 (|q|2 + |p|2 = 1)
Mass difference Lifetime difference∆m = MH −ML ∆Γ = ΓL − ΓH
(→ ∆m > 0,∆Γ > 0 in SM)Eigenvalue equations:
(∆m)2 − 14
(∆Γ)2 = (4|M12|2 − |Γ12|2)
∆m∆Γ = −4Re(M∗12Γ12).
∆m = 2|M12|+ O(m4b/m
4t )
∆Γ = −2Re(M∗12Γ12)
|M12|+ O(m4
b/m4t ).
![Page 61: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/61.jpg)
Mass difference and lifetime difference
Mass eigenstates:|BL,H〉 = p|Bq〉 ± q|Bq〉 (|q|2 + |p|2 = 1)
Mass difference Lifetime difference∆m = MH −ML ∆Γ = ΓL − ΓH
(→ ∆m > 0,∆Γ > 0 in SM)Eigenvalue equations:
(∆m)2 − 14
(∆Γ)2 = (4|M12|2 − |Γ12|2)
∆m∆Γ = −4Re(M∗12Γ12).
∆m = 2|M12|+ O(m4b/m
4t )
∆Γ = −2Re(M∗12Γ12)
|M12|+ O(m4
b/m4t ).
![Page 62: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/62.jpg)
Time evolution of a tagged Bq or Bq decay
Af ≡ 〈f |Bq〉, Af ≡ 〈f |Bq〉 , λf ≡qp
Af
Af
(λf independent of the unphysical phase ϕ)
Γ(Bq(t)→ f ) = Nf |Af |21 + |λf |2
2e−Γt ×[
cosh∆Γq t
2+Adir
CP cos(∆m t) + A∆Γ sinh∆Γq t
2+Amix
CP sin (∆m t)],
Γ(Bq(t)→ f ) = Nf |Af |21 + |λf |2
2e−Γt ×[
cosh∆Γq t
2−Adir
CP cos(∆m t) + A∆Γ sinh∆Γq t
2−Amix
CP sin(∆m t)].
AdirCP =
1− |λf |2
1 + |λf |2, Amix
CP = − 2 Imλf
1 + |λf |2A∆Γ = − 2 Reλf
1 + |λf |2,
![Page 63: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/63.jpg)
Outline
1 Some historical perspective
2 CP violation: discovery and interpretation
3 The Kobayashi-Maskawa mechanism
4 Neutral meson mixing and oscillations
5 Flavour tests of the CKM paradigm
![Page 64: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/64.jpg)
B factories: B ≡ bu, bd , bs, bc, B ≡ ub, db, sb, cb
Babar (SLAC, USA) BELLE (KEK, Japan)
e+e− → BB → decayproducts
![Page 65: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/65.jpg)
More and more stringent tests of the CKM mechanism
Semileptonic decay B → D`ν
![Page 66: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/66.jpg)
More and more stringent tests of the CKM mechanism
Semileptonic decay B → D`ν“Charmed” decays B → DK
![Page 67: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/67.jpg)
More and more stringent tests of the CKM mechanism
Semileptonic decay B → D`ν“Charmed” decays B → DKCP violation in K mesons
![Page 68: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/68.jpg)
More and more stringent tests of the CKM mechanism
Semileptonic decay B → D`ν“Charmed” decays B → DKCP violation in K mesons∆M in Bd–Bd system
![Page 69: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/69.jpg)
More and more stringent tests of the CKM mechanism
Semileptonic decay B → D`ν“Charmed” decays B → DKCP violation in K mesons∆M in Bd–Bd system∆M in Bs–Bs system
![Page 70: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/70.jpg)
More and more stringent tests of the CKM mechanism
Semileptonic decay B → D`ν“Charmed” decays B → DKCP violation in K mesons∆M in Bd–Bd system∆M in Bs–Bs systemDecays to π and K
![Page 71: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/71.jpg)
More and more stringent tests of the CKM mechanism
Semileptonic decay B → D`ν“Charmed” decays B → DKCP violation in K mesons∆M in Bd–Bd system∆M in Bs–Bs systemDecays to π and KCP asymmetry in B → J/ψKS
![Page 72: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/72.jpg)
Concluding remarks: end of Lecture 1
No deviation from the CKM predictions has been observed⇒ Constrains many new physics models
CP violation required for baryon asymmetry, but the CKMis not enough, so there will be life beyond CKM
Physics beyond the Standard Model must exist !
Where to look for it ?How to identify and quantify it ?⇒ Lecture 2
![Page 73: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/73.jpg)
Concluding remarks: end of Lecture 1
No deviation from the CKM predictions has been observed⇒ Constrains many new physics models
CP violation required for baryon asymmetry, but the CKMis not enough, so there will be life beyond CKM
Physics beyond the Standard Model must exist !
Where to look for it ?How to identify and quantify it ?⇒ Lecture 2
![Page 74: Flavour physics : Lecture 1theory.tifr.res.in/~amol/talks/technical/2017/susy...Flavour physics : Lecture 1 History, CP violation, Neutral meson mixing Amol Dighe Department of Theoretical](https://reader034.vdocuments.net/reader034/viewer/2022042802/5f4026c1b16c311305681ba0/html5/thumbnails/74.jpg)
Concluding remarks: end of Lecture 1
No deviation from the CKM predictions has been observed⇒ Constrains many new physics models
CP violation required for baryon asymmetry, but the CKMis not enough, so there will be life beyond CKM
Physics beyond the Standard Model must exist !
Where to look for it ?How to identify and quantify it ?⇒ Lecture 2