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Physics of Flavour

Physics of Flavour

of flavour

PPSS 2019 Olga Werbycka

1 18/07/2019 Institute of PAS Outline

★ ★ Flavor ★ ★ ★ FCNC ★ B-physics ★ Belle/Belle II experiments

2 Symmetry

3 in Physics

★ A symmetry of a system is a property or feature of the system that remains the same under a transformation (or change). ★ For us the most important aspect of symmetry is the invariance of Physical Laws under an arbitrary differentiable transformation

★ Noether’s Theorem (1918) - symmetry properties of a physical system are closely related to Conservation Laws for the system

Noether E (1918). “Invariante Variationsprobleme” Nachr. D. Kónig. Gesellsch. D. Wiss. Zu Gottingen, Math-Phys. Klasse 1918: 235-257. http://arxiv.org/abs/physics/0503066v1. 4 Continuous Symmetries and Conservation Laws Standard Model is written as symmetry group U(1) SU(2) x SU(3)

The simplest internal symmetry group is U(1). SU(2) is the rotatio- Similarly, SU(3) Geometrically, it is the nal symmetry of a rotational symmetry of a sphere - a set of 2 x is for strong circle - Circle rotated 2 matrices with unit nuclear forces - by an angle in 3D space. determinant. They between 8 bosons So, SU(1) is set of 1 x model the weak nuclear 1 matrices - a symmetry () and a group for electromagne- interactions - between tic interactions pair of set of three (fermions acting as (e.g. and fermions (e.g. singles). For instance, ) and a set red, green and interaction of of three bosons: Z (a massless ) and W (+,-) blue ). and electron.

5 CP symmetry

★ CP symmetry is the combined operation of C and P ★ C ( Conjugation): Charge Conjugation changes a to its . In particular, it reverses the sign of the and magnetic moment of the particle. ○ Strong and e/m interactions are found to be invariant under the C operation ○ BUT in Weak interaction C invariance is broken ★ P (): Parity operation reverses the direction of any spatial vector (Mirror reflection). ○ Under parity a left-handed particle transforms to a left-handed. ○ Parity is conserved in strong and e/m interactions ○ But not in weak 6 Symmetry Summary:

Transformation Symmetry Type Conserved Quantity

translation global, continuous linear momentum

rotation global, continuous angular momentum

time global, continuous energy additive

rotation in global, continuous “isospin-space” (“internal”)

electromagnetic local, continuous, gauge charge /vector potential

--- global, continuous, gauge barion number

--- global, continuous, gauge number 7 Symmetry Summary (2):

Transformation Symmetry Type Conserved Quantity multiplicative parity global, discreet “P-value”

charge conjugation global, discreet “C-value”

time reversal global, discreet none!

In addition: Local, Lorentz-Invariant, Quantum Theories ⇒ CPT

8 What is flavour?

Flavour refers to the species of an .

The Standard Model counts 6 flavours of quarks and 6 flavours of .

They are conventionally parameterized with flavour quantum numbers that are assigned to all subatomic .

Within the Standard Model (SM), flavour physics refers to the weak and Yukawa interactions.

9 What is flavour?

Flavour refers to the species of an elementary particle.

The Standard Model counts 6 flavours of quarks and 6 flavours of leptons.

They are conventionally parameterized with flavour quantum numbers that are assigned to all subatomic particles.

Bottomness Isospin

Charm

10 Isospin (original motivation)

Isospin was introduced as a concept in 1932, well before the 1960s development of the model by in order to explain symmetries of the :

➔ The of the neutron and the (symbol p) are almost identical: they are nearly degenerate, and both are thus often called . Although the proton has a positive electric charge, and the neutron is neutral ➔ The strength of the between any pair of nucleons is the same, independent of whether they are interacting as or as .

The neutron and the proton are assigned to the doublet (the -½ ,2) of SU(2). The are assigned to the triplet (the spin-1, 3) of SU(2). Though there is a difference from the theory of spin: the group action does not preserve flavor.

Similar to a spin ½ particle, which has two states, protons and neutrons were said to be of isospin ½. The proton and neutron were then associated with different isospin projections I3 = ½ and -½ respectively.

11 Why do we care about flavour?

Flavour physics can predict new physics (NP) before it’s directly observed. Some examples are:

★ + − + + The smallness of Γ(KL → μ μ )/Γ(K → μ ν) allowed for the prediction of the quark ★ The size of ΔmK allowed for the charm mass prediction ★ The measurement of K allowed for the prediction of the third generation ★ ∼ The size of ΔmB allowed for a quite accurate top mass prediction ( 150 GeV) ★ The measurement of neutrino flavour transitions led to the discovery of neutrino

12 13 Weak interaction

Properties:

★ It is the only interaction capable of changing the flavor of quarks (i.e., of changing one type of quark into another) ★ It is the only interaction that violates P symmetry. It is also the only one that violates charge-parity (CP) symmetry. ★ It is propagated by intermediate bosons that have significant masses, an unusual feature which is explained in the Standard Model by the Higgs mechanism.

Weak isospin is a relating to the weak interaction (an equivalent of the isospin for strong interactions).

The relates the conservation of I3 ; all weak interactions must preserve I3. It is also conserved by the electromagnetic and strong interactions. Weak charge: vector coupling of nucleons to the Z boson, namely 2I3 - 4Qsin2ΘW, where Θ is the weak mixing angle. 14 Universality of weak interactions?

➔ Do all leptons and quarks carry the same unit of weak charge? ◆ “YES” for leptons ◆ “NO” for quarks

➔ for quarks, the couplings for the weak gauge bosons depend on the quark flavors, due to “quark mixing” -> CKM mechanism

15 Weak decays of quarks

➔ Consider the (semileptonic) weak decay

Assuming universality of weak decays of quarks we expect both decays would happen with similar rate, but….

16 Weak decays of quarks (2)

It was also noticed that the value of Fermi constant GF deduced from nuclear β-decay was slightly less than that obtained from decay

So what are we going to do?

Discard the universality of weak interaction? 17 Cabibbo theory

➔ Try to keep the universality, but modify the quark doublet structure… ➔ Assume that the charged current (W±) couples the “rotated” quark states

➔ Where d’, s’ (weak interaction eigenstates) are linear combinations of mass eigenstates d, s.

Θc: the quark mixing angle “Cabibbo” angle

18 Cabibbo theory (2)

➔ What we have done is to change our mind about the charged current: “Cabibbo-favoured” vs. “Cabibbo-suppressed”

➔ → effective weak coupling for ΔS = 0 (d uW) is cosΘc ➔ → effective weak coupling for ΔS = 1 (s uW) is sinΘc

⇒ Θc ≈ 12º

19 Suppression of flavor changing neutral currents ➔ A very stringent suppression of flavor-changing reactions

20 Flavor-changing neutral currents (FCNC) Neutral current reactions for (u, d’) quarks

In this picture, is FCNC perfectly allowed by theory???

21 GIM mechanism for FCNC suppression

➔ In 1970, Glashow, Iliopoulos and Maiani (GIM) proposed the introduction of a new quark Q = ⅔ , with label c for ‘charm’. ➔ With this new quark a second doublet is also introduced

➔ Then we have additional terms for the neutral current reactions

22 GIM mechanism (2)

FCNC has disappeared!!! 23 GIM mechanism (3)

➔ At the price of new quark ‘charm’ and another quark doublet, the (experimentally) unwanted FCNC has been removed!

➔ Later, in 1974, the bound state of charm-- anti-charm was discovered: J/ψ ➔ Indeed, just before this discovery, it had been possible to estimate the mass of the new quark!

← by considering K0K0 -bar mixing

24 Extension of Cabibbo theory to 3 quark generations

➔ Leptons are not involved in the strong interactions ➔ Quarks & Leptons do not change its flavor when interacting with neutral gauge bosons ◆ quarks do not change flavor under strong interaction ◆ leptons & quarks do not change flavor when interacting with γ or Z0 ◆ leptons & quarks only change flavor when interacting with W±, and only within its family

± ↕ W

25 The strengths of the weak interactions between the six quarks.

26 CKM matrix

Cabibbo–Kobayashi–Maskawa matrix is a unitary matrix which contains information on the strength of the flavour-changing weak interaction.

➔ CKM is 3 × 3 and unitary ◆ only 3 generations in Standard Model ➔ CKM is almost 1, but not exactly

27 CKM matrix in the Wolfenstein parametrization

★ In 1983, it was realized that the decays predominantly to the : ★ Wolfenstein then noticed that and introduced an approximate parametrization of the CKM matrix

|λ| ≈ O(0.1) 3 real parameters (λ, A, ρ) and 1 phase (η)

28

Types of CP Violation

❖ Direct CPV

❖ Indirect CPV

❖ CP interference between mixing and decay

29 Direct CP Violation

★ CP violation arises from the difference between the magnitudes of a decay amplitude and its CP conjugate amplitude. ★ The measurement is to compare the decay rate of B and its CP conjugate. ★ Only possible source of CP in charged meson decays

30 Beauty of the

➔ The beauty of B meson lies in its large mass in the mass hierarchy ➔ → In the heavy quark limit, mQ 1 we have ◆ Flavor symmetry: dynamics unchanged under heavy flavor exchange (b → c), corrections

incorporated in powers of 1/mb - 1/mc ◆ Spin symmetry: dynamics unchanged under heavy quarks spin flips, corrections incorporated

in powers 1/mc ➔ B provide an ideal system for studying heavy-to-heavy transitions ➔ Much progress has been made in understanding heavy-to-light transitions in recent years ◆ Perturbative approach: factorization, QCD-improved factorization, pQCD, SCET ◆ Nonperturbative approach: flavor SU(3) symmetry

31

Decays of b quark

➔ then how does b quark decay at all?

Note: b → W-t but m(t) ≫ m(b)

➔ For Quarks, ◆ mass eigenstates ≠ weak interaction eigenstates ◆ flavor mixing through CKM matrix

32 Intensity frontier vs. Energy frontier

Energy frontier Intensity frontier

limited by beam energy limited by statistics

33 34 SuperKEKB - where?

SuperKEKB - where?

35 Belle II collaboration

> 900 members > 100 institutions

36 Why do we need B-factory?

⇒ nothing but BB-bar in the final state

We exploit the reaction process

➔ full reconstruction of Btag decay chain ➔ constrain the (E, p), charge, flavor, etc. of Bsig

37 Belle II detector

38 Belle II

39 Questions?

40 Standard Model

41 Standard Model

42

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