Particle Physics II CP violation (also known as Physics of - - PowerPoint PPT Presentation

Niels Tuning (1)

Particle Physics II – CP violation

(also known as “Physics of Anti-matter”)

Lecture 6

• N. Tuning

Plan

1) Wed 12 Feb: Anti-matter + SM 2) Mon 17 Feb: CKM matrix + Unitarity Triangle 3) Wed 19 Feb: Mixing + Master eqs. + B0→J/ψKs 4) Mon 9 Mar: CP violation in B(s) decays (I) 5) Wed 11 Mar: CP violation in B(s) and K decays (II) 6) Mon 16 Mar: Rare decays + Flavour Anomalies 7) Wed 18 Mar: Exam postponed...

Niels Tuning (2)

Ø Final Mark:

§ if (mark > 5.5) mark = max(exam, 0.85*exam + 0.15*homework) § else mark = exam

Ø In parallel: Lectures on Flavour Physics by prof.dr. R. Fleischer

Diagonalize Yukawa matrix Yij

– Mass terms – Quarks rotate – Off diagonal terms in charged current couplings

Niels Tuning (4)

Recap

SM Kinetic Higgs Yukawa

= + + L L L L

( , ) ...

I I Yuk L i L Rj d I j

i

d d Y u ϕ ϕ

+

⎛ ⎞ − = + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ L

... 2 2

Kinetic Li Li I I I Li L I i

g g u W d d W u

µ µ µ µ

γ γ

− +

= + + L

( ) ( )

5 5 *

1 1 ... 2 2

ij i CKM i j j j i

g g u W d d u V V W

µ µ µ µ

γ γ γ γ

− +

= − + − + L ( ) ( )

, , , , ...

d u s c L L b t R R

Mass m d m u d s b m s u c t m c m b m t ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ − = + + ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ g g g g

L

I I CKM I

d d s V s b b ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ → ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠

SM CKM Higgs Mass

= + + L L L L

uI dI W u d,s,b W

Niels Tuning (5)

Why bother with all this?

• CKM matrix has origin in LYukawa

Ø Intricately related to quark massed…

• Both quark masses and CKM elements show intriguing

hierarchy

• There is a whole industry of theorist trying to postdict

the CKM matrix based on arguments on the mass matrix in LYukawa…

Niels Tuning (6)

CKM-matrix: where are the phases? u d,s,b W

• Possibility 1: simply 3 ‘rotations’, and put phase on smallest:
• Possibility 2: parameterize according to magnitude, in O(λ):

This was theory, now comes experiment

• We already saw how the moduli |Vij| are determined
• Now we will work towards the measurement of the

imaginary part

– Parameter: η – Equivalent: angles α, β, γ .

• To measure this, we need the formalism of neutral

meson oscillations…

Niels Tuning (7)

Meson Decays

• Formalism of meson oscillations:
• Subsequent: decay

0( )

P t

Interference

P0 àf P0àP0 àf

Interference (‘direct’) Decay

Classification of CP Violating effects

• 1. CP violation in decay
• 2. CP violation in mixing
• 3. CP violation in interference

Niels Tuning (9)

Classification of CP Violating effects

• 1. CP violation in decay

Example:

• 2. CP violation in mixing

Example:

• 3. CP violation in interference

Example:

Niels Tuning (10)

π π

− + + −

→ → B K B K

) sin( ) 2 sin( ) ( mt N N N N t A

f B f B f B f B CP

Δ = + − =

→ → → →

β

B0→J/ψKs

Remember! Necessary ingredients for CP violation:

1) Two (interfering) amplitudes 2) Phase difference between amplitudes

– one CP conserving phase (‘strong’ phase) – one CP violating phase (‘weak’ phase)

Niels Tuning (11)

Remember!

Niels Tuning (12)

Niels Tuning (13)

CKM Angle measurements from Bd,u decays

• Sources of phases in Bd,u amplitudes*
• The standard techniques for the angles:

*In Wolfenstein phase convention.

Amplitude

• Rel. Magnitude

Weak phase bàc Dominant bàu Suppressed

γ

tàd (x2, mixing) Time dependent 2β B0 mixing + single bc decay B0 mixing + single bu decay Interfere bc and bu in B± decay.

β

• i
• i

γ

1 1 1 1 1 1 1

e e

⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

bu td

Classification of CP Violating effects

• 1. CP violation in decay
• 2. CP violation in mixing
• 3. CP violation in interference

Niels Tuning (14)

Next… Something completely different? No, just K

• 1. CP violation in decay
• 2. CP violation in mixing
• 3. CP violation in interference

Kaons…

Niels Tuning (16)

• Different notation: confusing!

K1, K2, KL, KS, K+, K-, K0

• Smaller CP violating effects

Ø But historically important!

§ Concepts same as in B-system, so you have a chance to understand…

Kaons…

Niels Tuning (17)

• Different notation: confusing!

K1, K2, KL, KS, K+, K-, K0

• Smaller CP violating effects

Ø But historically important!

§ Concepts same as in B-system, so you have a chance to understand…

CP eigenstates =

Kaons…

Niels Tuning (18)

• Different notation: confusing!

K1, K2, KL, KS, K+, K-, K0

• Smaller CP violating effects

Ø But historically important!

§ Concepts same as in B-system, so you have a chance to understand…

Mass/lifetime eigenstates

Kaons…

Niels Tuning (19)

• Different notation: confusing!

K1, K2, KL, KS, K+, K-, K0

• Smaller CP violating effects

Ø But historically important!

§ Concepts same as in B-system, so you have a chance to understand…

Flavour eigenstates

Neutral kaons – 60 years of history

… the θ0 must be considered as a "particle mixture" exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes, and that no more than half of all θ0's undergo the familiar decay into two pions. 1947 : First K0 observation in cloud chamber (“V particle”) 1955 : Introduction of Strangeness (Gell-Mann & Nishijima) K0, K0 are two distinct particles (Gell-Mann & Pais) 1956 : Parity violation observation of long lived KL (BNL Cosmotron) 1960 : Δm = mL-mS measured from regeneration 1964 : Discovery of CP violation (Cronin & Fitch) 1970 : Suppression of FCNC, KL൵ - GIM mechanism/charm hypothesis 1972 : 6-quark model; CP violation explained in SM (Kobayashi & Maskawa) 1992-2000 : K0, K0 time evolution, decays, asymmetries (CPLear) 1999-2003 : Direct CP violation measured: ε’/ε ≠ 0 (KTeV and NA48)

From G.Capon

Niels Tuning (20)

Intermezzo: CP eigenvalue

Niels Tuning (21)

• Remember:

– P2 = 1 (x à -x à x) – C2 = 1 (ψ ψ ψ ) – è CP2 =1

• CP | f > = ± | f >
• Knowing this we can evaluate the effect of CP on the K0

CP|K0> = -1| K0> CP| K0> = -1|K0 >

• Mass/Lifetime eigenstates: almost CP eigenstates!

|KS> = p| K0> +q|K0> |KL> = p| K0> - q|K0> |Ks> (CP=+1) → π π (CP= (-1)(-1)(-1)l=0 =+1) |KL> (CP=-1) → π π π (CP = (-1)(-1)(-1)(-1)l=0 = -1)

( S(K)=0 L(ππ)=0 )

Niels Tuning (22)

Decays of neutral kaons

• Neutral kaons is the lightest strange particle à it must

decay through the weak interaction

• If weak force conserves CP then

– decay products of K1 can only be a CP=+1 state, i.e. |K1> (CP=+1) → π π (CP= (-1)(-1)(-1)l=0 =+1) – decay products of K2 can only be a CP=-1 state, i.e. |K2> (CP=-1) → π π π (CP = (-1)(-1)(-1)(-1)l=0 = -1)

• You can use neutral kaons to precisely test that the

weak force preserves CP (or not)

– If you (somehow) have a pure CP=-1 K2 state and you observe it decaying into 2 pions (with CP=+1) then you know that the weak decay violates CP…

( S(K)=0 L(ππ)=0 )

Niels Tuning (23)

Designing a CP violation experiment

• How do you obtain a pure ‘beam’ of K2 particles?

– It turns out that you can do that through clever use of kinematics

• Exploit that decay of K into two pions is much faster

than decay of K into three pions

– Related to fact that energy of pions are large in 2-body decay – τ1 = 0.89 x 10-10 sec – τ2 = 5.2 x 10-8 sec (~600 times larger!)

• Beam of neutral Kaons automatically becomes beam of

|K2> as all |K1> decay very early on…

Initial K0 beam K1 decay early (into ππ ππ) Pure K2 beam after a while! (all decaying into πππ) !

Niels Tuning (24)

The Cronin & Fitch experiment

Incoming K2 beam Decay of K2 into 3 pions If you detect two of the three pions

• f a K2 πππ

πππ decay they will generally not point along the beam line

Essential idea: Look for (CP violating) K2 à ππ decays 20 meters away from K0 production point

Niels Tuning (25)

The Cronin & Fitch experiment

Incoming K2 beam Decay pions If K2 decays into two pions instead of three both the reconstructed direction should be exactly along the beamline (conservation of momentum in K2 ππ ππ decay)

Essential idea: Look for K2 à ππ decays 20 meters away from K0 production point

Niels Tuning (26)

The Cronin & Fitch experiment

Incoming K2 beam Decay pions Result: an excess of events at Θ=0 degrees! K2 ππ ππ decays (CP Violation!)

Essential idea: Look for K2 à ππ decays 20 meters away from K0 production point

K2 πππ πππ decays Note scale: 99.99% of K πππ decays are left of plot boundary

• CP violation, because K2 (CP=-1)

changed into K1 (CP=+1)

"for the discovery of violations of fundamental symmetry principles in the decay of neutral K mesons"

Val Logsdon Fitch 1/2 of the prize Princeton University Princeton, NJ, USA

• b. 1923

James Watson Cronin 1/2 of the prize University of Chicago Chicago, IL, USA

• b. 1931

The discovery emphasizes, once again, that even almost self evident principles in science cannot be regarded fully valid until they have been critically examined in precise experiments.

Nobel Prize 1980

Niels Tuning (27)

Cronin & Fitch – Discovery of CP violation

• Conclusion: weak decay violates CP (as well as C and P)

– But effect is tiny! (~0.05%) – Maximal (100%) violation of P symmetry easily follows from absence

• f right-handed neutrino, but how would you construct a physics law

that violates a symmetry just a tiny little bit?

• Results also provides us with

convention-free definition of matter vs anti-matter.

– If there is no CP violation, the K2 decays in equal amounts to π+ e- νe (a) π- e+ νe (b) – Just like CPV introduces K2 à ππ decays, it also introduces a slight asymmetry in the above decays (b) happens more often than (a) – “Positive charge is the charged carried by the lepton preferentially produced in the decay of the long-lived neutral K meson”

Niels Tuning (28)

Intermezzo: Regeneration

• Different cross section for σ(p K0) than σ(p K0)
• Elastic scattering: same
• Charge exchange : same
• Hyperon production: more for K0 !
• What happens when KL-beam hits a wall ??
• Then admixture changes…: |KL> = p| K0> - q|K0>

à Regeneration of KS !

• Could fake CP violation due to KS→π+π-…

( )

2 1 2

K K K + =

+

+ Λ → + π p K

+

+ + Λ → + K K p K strong interactions: must conserve strangeness leave little free energy – unlikely!

p K n K n K p K + → + + → +

− + Niels Tuning (29)

KS and KL

2 2

, 1 . 1

S L

K K K K K K ε ε ε ε

+ − − +

+ = + + = +

KL and KS are not orthogonal:

, .

S L

K p K q K K p K q K = + = −

( ) (

)

( ) (

)

2 2

2 1 2 1

1 , 1 . p q

ε ε

ε ε

+ +

= + = −

2 2 2

2 1 1 1

S L

p K K q ε ε ε ε ε

∗

+ ℜ = = = − + +

( )

,

S

i t S S

K t e K

ω −

=

( )

.

L

i t L L

K t e K

ω −

=

Usual (historical) notation in kaon physics: Modern notation used in B physics: Regardless of notation:

Niels Tuning (30)

Three ways to break CP; e.g. in K0→ π+π-

1 CP violation in decay:

f f

A A ≠

1 CP violation in mixing: q p ≠

A q p A

π π π π π π

λ

+ − + − + −

=

( )

( ) ( ) ( ) ( )

( )

( )

( ) ( ) ( ) ( )

( )

2 2 2 2 2 2 2 2 2

2 2 1 K g t g t g t g t K g t g A t t g t A g λ λ λ λ λ π π π π

+ − ∗ + − + − + +− +− + +− + − − ∗ + − +− ∗ +− − + −

⎡ ⎤ Γ → ∝ + + ℜ ⎣ ⎦ ⎡ ⎤ Γ → ∝ + + ℜ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦

CP violation in interference mixing/decay:

f f f

A q p A λ ⎛ ⎞ ℑ = ℑ ≠ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

( )

( )

( )

2 2

( ) ( ) 1 ( ) ( ) K A g t g t K A g t g t

π π π π

π π λ π π λ

+ − + −

+ − + − + − + −

Γ → = + ⎛ ⎞ Γ → = + ⎜ ⎟ ⎝ ⎠

Niels Tuning (31)

Classification of CP Violating effects

• 1. CP violation in decay
• 2. CP violation in mixing
• 3. CP violation in interference

Niels Tuning (32)

Time evolution

( )

( )

( )

( )

2 2

2 cos 2 cos

S L S L

t t t t t t

K N e e e m t K N e e e m t π π η η φ π π η η φ

−Γ −Γ + − −Γ +− +− +− −Γ −Γ + − −Γ +− +− +−

⎡ ⎤ Γ → = + Δ ⋅ − ⎣ ⎦ ⎡ ⎤ Γ → = − − + Δ ⋅ ⎣ + ⎦ 1 1 λ η λ

+−

− = +

L S

K pA qA pA qA K π π π π

+ − + −

− = = +

i

e φ η η

+−

+− +−

=

( )

( ) ( )

( )

( ) ( )

2 2

1 1 1 1 2 cos sin 1 1 1 1 1 1 2 cos sin 1 1

S L S L

t t t t t t

e e K e m t m t e e K e m t m t λ λ π π λ λ λ λ λ λ π π λ λ λ λ

−Γ −Γ + − −Γ −Γ −Γ + − −Γ

⎡ ⎤ − + ⎢ ⎥ + ⎢ ⎥ Γ → ∝ ⎢ ⎥ ⎡ − − ⎤ ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ ℜ Δ ⋅ − ℑ Δ ⋅ ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ + + ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎣ ⎦ ⎡ ⎤ − + ⎢ ⎥ + ⎢ ⎥ Γ → ∝ ⎢ ⎥ ⎡ − − ⎤ ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ ℜ Δ ⋅ − ℑ Δ ⋅ ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ + + ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ + ⎣ − ⎦

Niels Tuning (33)

B-system 2. CP violation in mixing K-system

CPLear (2003) ( ) ( ) ( ) ( ) ( )

4 4

1 1

T

q p N t N t A t N t N t q p

++ −− ++ −−

− Δ − Δ Δ = = Δ + Δ +

BaBar, (2002)

X

− +

→ l l

B B

CPLEAR, Phys.Rep. 374(2003) 165-270

( ) ( )

3

6.6 1.6 10 0.9967 0.0008 1

T

A t q p

−

= ± ⇒ = ± ≠

( ) ( ) ( ) ( ) ( )

4 4

1 4 1

e e e T e

I t q p A I t I t I t q t p

νπ ν νπ π νπ

ε

+ − + − − + − +

− − = = = ℜ + +

B-system 2. CP violation in mixing K-system

NA48, (2001)

δL(e) = (3.317 ± 0.070 ± 0.072) × 10-3

( ) ( ) ( ) ( ) ( )

4 4

1 1

T

q p N t N t A t N t N t q p

++ −− ++ −−

− Δ − Δ Δ = = Δ + Δ +

BaBar, (2002)

X

− +

→ l l

B B

L

( ) ( ) ( ) ( ) ( )

L L L L

K e K e e K e K e π ν π ν δ π ν π ν

+ − − + + − − +

Γ → − Γ → = Γ → + Γ →

Niels Tuning (35)

B-system 3.Time-dependent CP asymmetry

) sin( ) 2 sin( ) ( mt N N N N t A

f B f B f B f B CP

Δ = + − =

→ → → →

β

B0→J/ψKs

BaBar (2002)

Niels Tuning (36)

B-system 3.Time-dependent CP asymmetry K-system

π+π- rate asymmetry

CPLear (PLB 1999)

) sin( ) 2 sin( ) ( mt N N N N t A

f B f B f B f B CP

Δ = + − =

→ → → →

β

K0→π-π+ B0→J/ψKs

) , ( ) , ( ) , ( ) , ( ) ( t f k R t f k R t f k R t f k R t Af → + → → − → =

~50/50 decay as Ks and KL + interference!

BaBar (2002)

K0 K0 _

The Quest for Direct CP Violation

Indirect CP violation in the mixing: ε

Direct CP violation in the decay: ε’ A fascinating 30-year long enterprise: “Is CP violation a peculiarity of kaons? Is it induced by a new superweak interaction?”

Niels Tuning (38)

B system 1. Direct CP violation K system

) ( ) ( ) ( ) (

• s
• L
• s

L

k Amp k Amp k Amp k Amp π π π π η π π π π η → → ≡ → → ≡

− + − + − +

Different CP violation for the two decays Some CP violation in the decay!

B0→K+π-

BR(KL → π+π−) BR(Ks → π+π−) BR(KL → πoπo) BR(Ks → πoπo) = η+− ηoo

2

= ε + ʹ ε 2 ε − 2 ʹ ε 2 ≈1 + 6Re ʹ ε ε ⎛ ⎝ ⎞ ⎠

ε’≠ 0

B0→K-π+ K0→π-π+ K0→π0π0 K0→π-π+ K0→π0π0

Niels Tuning (39)

Niels Tuning (40)

Niels Tuning (41)

Hints for new physics? φ Ks B

s b d d s t s

g,b,…? ~~

1) sin2β≠sin2β ? 4th generation, t’ ? 3) βs≠0.04 ? 2) ACP (B0K+π-)≠ACP (B+K+π0) ? 4) P(B0

s→B0 s) ≠ P(B0 s←B0 s)

Present knowledge of unitarity triangle

Niels Tuning (42)

“The” Unitarity triangle

• We can visualize the CKM-constraints in (ρ,η) plane

Present knowledge of unitarity triangle

I) sin 2β

) sin( ) 2 sin( ) ( mt N N N N t A

f B f B f B f B CP

Δ = + − =

→ → → →

β

I) sin 2β

) sin( ) 2 sin( ) ( mt N N N N t A

f B f B f B f B CP

Δ = + − =

→ → → →

β

II) ε and the unitarity triangle: box diagram

2 2

, 1 . 1

S L

K K K K K K ε ε ε ε

+ − − +

+ = + + = +

, .

S L

K p K q K K p K q K = + = −

( ) (

)

( ) (

)

2 2

2 1 2 1

1 , 1 . p q

ε ε

ε ε

+ +

= + = −

CP violation in mixing

II) ε and the unitarity triangle: box diagram

II) ε and the unitarity triangle: box diagram

Im(z2)=Im( (Rez+iImz)2)=2RezImz

II) ε and the unitarity triangle

ρ

Niels Tuning (50)

III.) |Vub| / |Vcb|

• Measurement of Vub

– Compare decay rates of B0 à D*-l+ν and B0 à π-l+ν – Ratio proportional to (Vub/Vcb)

2

– |Vub/Vcb| = 0.090 ± 0.025 – Vub is of order sin(θc)3 [= 0.01] 2 2 2 2 2 2

( ) ( / ) ( / ) ( )

ub cb l u b c b l

b ul f m m f m m b c V V l ν ν

− −

⎛ ⎞ Γ → = ⎜ ⎟ Γ → ⎝ ⎠

IV.) Δmd and Δms

2 2 2 2 2 2 2 td ts Bd Bs td ts Bd Bd Bs Bs Bd Bs d s

V V m m V V B f B f m m m m ξ = = Δ Δ

• Δm depends on Vtd
• Vts constraints hadronic uncertainties

Present knowledge of unitarity triangle

Niels Tuning (53)

Niels Tuning (54)

Hints for new physics? φ Ks B

s b d d s t s

g,b,…? ~~

1) sin2β≠sin2β ? 4th generation, t’ ? 3) βs≠0.04 ? 2) ACP (B0K+π-)≠ACP (B+K+π0) ? 4) P(B0

s→B0 s) ≠ P(B0 s←B0 s)

Niels Tuning (55)

More hints for new physics?

5) εK ?

§ Treatment of errors… § Input from Lattice QCD BK § Strong dependence on Vcb

Niels Tuning (56)

More hints for new physics?

6) Vub: 2.9σ ?? BR(B+→τυ)=1.68 ± 0.31 10-4 Predicted: 0.764± 0.087 10-4

(If fBd off, then BBd needs to be off too, to make Δmd agree)

|Vub| from B→τν

From: H.Lacker, and A.Buras, Beauty2011, Amsterdam

|Vub| from fit

|Vub| avg from semi-lep

?

A.Buras, Beauty2011:

Niels Tuning (57)

A.Buras, Beauty2011:

Niels Tuning (58)

Standard Model: 25 free parameters Strong interaction: αs(mZ)≈ 0.117 νe νµ ντ = ν1 ν2 ν3

neutrino mixing (4)

Electro-weak interaction: αe(0) ≈ 1/137.036 mW

≈ 80.42 GeV

mZ

≈ 91.188 GeV

mH >114.3 GeV Elementary particle masses (MeV):

me ≈ 0.51099890 mµ ≈ 105.658357 mτ ≈ 1777.0 mu ≈ 3 mc ≈ 1200 mt ≈ 174000 md ≈ 7 ms ≈ 120 mb ≈ 4300 mν < 0.000003 mν < 0.19 mν < 18.2

e µ τ

u’ d’ s’ = u d s

quark mixing (4)

Vij

q

Vij

l

mH >114.3 GeV CMS CMS LHC LHCb

Niels Tuning (59)

The CKM matrix

' ' '

ud us ub cd cs cb td ts tb

d V V V d s V V V s b V V V b ⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎜ ⎟ ⎜ ⎟⎜ ⎟ = ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠

( ) ( )

2 3 2 2 3 2

1 2 1 2 1 1

L L

A i d d s A s b b A i A λ λ λ ρ η λ λ λ λ ρ η λ ⎛ ⎞ − − ⎜ ⎟ ⎜ ⎟ ʹ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ʹ = − − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ʹ ⎝ ⎠ ⎝ ⎠ − − − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

0.9738 0.0002 0.227 0.001 0.00396 0.00009 0.227 0.001 0.9730 0.0002 0.0422 0.0005 0.0081 0.0005 0.0416 0.0005 0.99910 0.00004

ud us ub cd cs cb td ts tb

V V V V V V V V V ⎛ ⎞ ± ± ± ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ = ± ± ± ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ± ± ± ⎝ ⎠ ⎝ ⎠

β

• i
• i

γ

1 1 1 1 1 1 1

e e

⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

• Couplings of the

charged current:

• Wolfenstein

parametrization:

• Magnitude:
• Complex phases:

b W- u gVub

Niels Tuning (60)

The CKM matrix

0.9738 0.0002 0.227 0.001 0.00396 0.00009 0.227 0.001 0.9730 0.0002 0.0422 0.0005 0.0081 0.0005 0.0416 0.0005 0.99910 0.00004

ud us ub cd cs cb td ts tb

V V V V V V V V V ⎛ ⎞ ± ± ± ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ = ± ± ± ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ± ± ± ⎝ ⎠ ⎝ ⎠

β

• i
• i

γ

1 1 1 1 1 1 1

e e

⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

• Couplings of the

charged current:

• Wolfenstein

parametrization

• Magnitude:
• Complex phases:

( ) ( )

( , ) ... ...

I I I Yuk d u l ij ij j L Rj i L

i

u Y d Y d Y ϕ ϕ

+

⎛ ⎞ − = + + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ L

( ) ( )

, , 2

CKM L W L

d u c t V s b g W

µ µ

γ

+

+

⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ = ⎟ ⎝ ⎠ −L

2

I I Li L W i

g W u d

µ µ

γ

+

+

− = L

1) 2) 3)

Niels Tuning (61)

• Complex phases:

The CKM matrix

0.9738 0.0002 0.227 0.001 0.00396 0.00009 0.227 0.001 0.9730 0.0002 0.0422 0.0005 0.0081 0.0005 0.0416 0.0005 0.99910 0.00004

ud us ub cd cs cb td ts tb

V V V V V V V V V ⎛ ⎞ ± ± ± ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ = ± ± ± ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ± ± ± ⎝ ⎠ ⎝ ⎠

β

• i
• i

γ

1 1 1 1 1 1 1

e e

⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

• Couplings of the

charged current:

• Wolfenstein

parametrization:

• Magnitude:

Remember the following:

• CP violation is discovered in the K-system
• CP violation is naturally included if there are 3 generations or more

– 3x3 unitary matrix has 1 free complex parameter

• CP violation manifests itself as a complex phase in the CKM matrix
• The CKM matrix gives the strengths and phases of the weak couplings
• CP violation is apparent in experiments/processes with 2 interfering

amplitudes with different strong and weak phase

– Often using “mixing” to get the 2nd decay process

• Flavour physics is powerful for finding new physics in loops!

– Complementary to Atlas/CMS

Niels Tuning (63)

Remember the following:

• CP violation is discovered in the K-system
• CP violation is naturally included if there are 3 generations or more

– 3x3 unitary matrix has 1 free complex parameter

• CP violation manifests itself as a complex phase in the CKM matrix
• The CKM matrix gives the strengths and phases of the weak couplings
• CP violation is apparent in experiments/processes with 2 interfering

amplitudes with different strong and weak phase

– Often using “mixing” to get the 2nd decay process

• Flavour physics is powerful for finding new physics in loops!

– Complementary to Atlas/CMS

Niels Tuning (64)

Personal impression:

• People think it is a complicated part of the Standard Model

(me too:-). Why? 1) Non-intuitive concepts?

§ Imaginary phase in transition amplitude, T ~ eiφ § Different bases to express quark states, d’=0.97 d + 0.22 s + 0.003 b § Oscillations (mixing) of mesons: |K0> ↔ |K0>

2) Complicated calculations? 3) Many decay modes? “Beetopaipaigamma…”

– PDG reports 347 decay modes of the B0-meson:

• Γ1 l+ νl anything

( 10.33 ± 0.28 ) × 10−2

• Γ347 ν ν γ

<4.7 × 10−5 CL=90%

– And for one decay there are often more than one decay amplitudes…

Niels Tuning (65)

( )

( ) ( ) ( ) ( )

( )

( )

( ) ( ) ( ) ( )

( )

2 2 2 2 2 2 2 2 2

2 1 2

f f

B f A g t g t g t g t B f A g t g t g t g t λ λ λ λ λ

∗ + − + − ∗ ∗ + − + −

⎡ ⎤ Γ → ∝ + + ℜ ⎣ ⎦ ⎡ ⎤ Γ → ∝ + + ℜ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦

Backup

Niels Tuning (66)

SLAC: LINAC + PEPII

PEP-II accelerator schematic and tunnel view

( )

4

3.1 0.56, 9 GeV GeV

e S e

E s M E βγ

+ −

= ⎫ = = ϒ ⎬ = ⎭

LER HER Linac

Coherent Time Evolution at the ϒ(4S)

B-Flavor Tagging

Exclusive B Meson Reconstruction PEP-2 (SLAC) Vertexing & Time Difference Determination

Niels Tuning (68)

LHCb: the Detector

pT of B-hadron η of B-hadron

• High cross section
• LHC energy
• Bs produced in large quantities
• Large acceptance
• b’s produced forward
• Small multiple scattering
• Large boost of b’s
• Trigger
• ↓ Low pT
• Leptons + hadrons (MUON, CALO)
• Particle identification (RICH)

The well known triangle: γ α β γ β

ud us ub cd cs cb td ts tb

V V V V V V V V V V ⎛ ⎞ ⎜ ⎟ = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

q W q’ Vq’q

* * * ub ud cb cd tb td

V V V V V V + + =

* *

*

ub ud tb td

cb cd

V V V V

V V

+ + =

*

* *

ub ud

cb cd tb td

V V

V V V V

+ =

+

* * * ub ud cb cd tb td

V V V V V V + + =

β

• i
• i

γ

1 1 1 1 1 1 1

e e

⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

CP phases:

• Measure the CKM triangle to unprecedented precision
• Measure very small Branching Ratios

Measuring the Quark Couplings

Niels Tuning (70)

LHCb

• https://wiki.nikhef.nl/lhcb/Master_student_Projects

Niels Tuning (71)

LHCb

• Λb

0àDsp

– Never observed – Background to others – Sensitivity to Vub? – Measure factorization

• Heavy neutrino’s

– Holy grail

• Scintillator Fiber tracker

– New detector for LHCb – Constructed at Nikhef, to be installed in 2019

• Majorana neutrino in Bc

+ decays

– Hole grail

Niels Tuning (72)