ckm physics and flavor anomaliessimi/didattica/1-ckm-and...ckm is a unitary 3x3 matrix it can be...

CKM Physics and Flavor anomaliesLecture1: Motivation and CKM Physics intro

Gabriele SimiUniversitá di Padova and INFN

2018 Lectures for the PhD program in Physics at University of Padova

April 2018 G. Simi - Flavour Phys. and Anomalies 2

Motivation for studying flavour physics


Outline

● Motivation for studying flavor physics

● CP violation and CKM physics

● How to observe CP violation: general considerations

● Bfactories

● Unitarity triangle determination

● Rare Decays

● Universality

● Dark Matter at colliders


Motivation for studying flavor physics

● The study of flavor physics has contributed to many advances in particle physics

– Discovery of CP violation (Christenson, Cronin, Fitch and Turlay - 1964)

– The smallness of KL → μ+ μ– predicts charm quark

– GIM mechanism forbids FCNC at tree level

– KM theory describing CP violation predicts third quark generation

● CP violation cannot be obtained with only two generations

– ΔmK = m(KL) – m(KS ) predicts charm quark mass range

– Frequency of B0 B0 mixing predicts a heavy top quark

– Measurements overconstraining the Cabibbo-Kobayashi-Maskawa matrix confirm the CKM theory

– Search of new sources of flavor and CP violating terms is used as tool to search for new physics with sensitivity extending to high very energy scales



● In the Standard model the Yukawa couplings of the Higgs boson to the fermions determine the quark mixing matrix

● 10 out of 19 of the free parameters of the model are the masses and the mixing parameters of the quarks. Their study gives us fundamental informations. But there are also some fundamental open questions

● Why are there 3 generations?




● 10 out of 19 of the free parameters of the model are the masses and the mixing parameters of the quarks. Their study gives us fundamental informations. But there are also some open fundamental questions

● Why there is a striking hierarchy in the quark masses? Why the Higgs mass is at the EW scale?





● Why is there a striking hierarchy in the quark mixing parameters





● Why is there a large matter anti matter asymmetry in the universe?


CP violation and CKM Physics


Matter dominance and CP violation

● CP is the combination of C=charge conjugation and P=parity (spatial inversion)

● Why is matter dominance related to CP symmetry?

– Anti-matter is composed of anti-particles

– Anti-particles have opposite charge (and opposite baryon and lepton quantum numbers) with respect to matter

● It is not sufficient to change the charge of a particle to transform it into its own antiparticle because the spin is a pseudovector and does not change sign under parity

● Es. take the pion decay: RH neutrino does not exist

π+

νμ

μ+

spin

π−

νμ

μ−

CP

P

π−

νμ

μ−

C


Matter dominance: Sakharov conditions

● Conditions propose by A. Sakharov in 1967 to explain the formation of a baryon asymmetry from the evolution of an initial symmetric state

– (1) baryon number violation

– (2) C & CP violation

– (3) thermal inequilibrium

● An example [from T. Gershon, Univ. Warwick]:

– Suppose initial equal amounts of matter (X) and anti matter (X)

– X decays to:

● A (baryon number NA ) with probability p

● B (baryon number NB ) with probability (1-p)

– X

● A (baryon number -NA) with probability p

● B (baryon number -NB ) with probability (1-p)

– Generated baryon asymmetry:

● ΔNTOT=NAp+NB(1-p)-NAp-NB(1-p)=(p-p)(NA-NB)

● ΔNTOT≠0 requires p≠p (CP violation) and NA ≠ NB (baryon number violation)


CP Violation: a bit of history

● First measured in K decays in 1964


● Christenson, Cronin, Fitch and Turlay - 1964


CP Violation: a bit of history

● First measured in K decays in 1964

● Kobayashi and Maskawa, based on the Cabibbo theory, propose in 1973 a mechanism to include it in the Standard Model, however it needed at least a third generation

● ARGUS measured B anti-B mixing in 1973 => the CP violation effect could be large in B decays (Bigi, Sanda)

● Measured in 2001 by the two dedicated experiments BaBar and BELLE


CKM● In the Standard model Lagrangian the Yukawa couplings of the Higgs boson to the fermions

determine the quark mixing matrix

– H is the Higgs Field <H>=(0,v/√2), YU,D are 3x3 complex matrices, i,j are generation labels

– Physical states obtained by redefinition of the quark states

–

– After diagonalization the interaction term becomes

U L, R→U L , RUL , R , DL, R→ DL , R DL , R


How many parameters does CKM have

● VCKM is a unitary 3x3 matrix

● It can be parameterized by 3 mixing angles (corresponding to real rotation matrices) and 6 complex phases [blackboard]

● However some phases (6) can be re-absorbed by phase rotations of the up and down quarks. An overall phase rotation of all quark phases does not affect the CKM matrix => only 5 phases can be re-absorbed

● => CKM matrix can be parameterizes by 3 mixing angles and one complex phase


CKM Parameterizations


The Unitarity triangle

● The unitarity of the matrix can be represented as a triangle relation between its elements

● Measuring angles and sides of the triangle and over-constrains the model => consistency checks


CP Violation

● In the standard model CP violation is described in by a single weak phase in the quark mixing (CKM) matrix

● The relative magnitude of the CKM elements has a very intriguing pattern, with no a-priori reason and very different from the neutrino sector

● Since the CP symmetry corresponds to the complex conjugate operation the phase in the CKM matrix gives rise to CP symmetry violation.

ie

ie



● The CKM mechanism is extremely successful in describing the observed pattern of decays, mixing and CP violation

● In the SM the phase in the CKM matrix is the sole origin of CP violation therefore all measurements must agree on the apex of the unitarity triangle



● The CKM mechanism is extremely successful in describing the observed pattern of decays, mixing and CP violation

CP conserving CP violating

looptree


However...

● Baryon asymmetry requires large CP violation: why is that?

● We can estimate the baryon asymmetry of the Universe cause the CKM mechanism [PRL 55 (1985) 1039]

ΔnBobserved

n

= 10−9

ΔnBCKM

n

=10−17


How to observe CP violation?


CP violation observable


B Mesons

● B Mesons have a long lifetime ~1.5ps


B Mesons


● Can be produced in pairs in the decay of bb in a coherent L=1 state

OffOn

)MeV(ME )S4(CM

PEP-II BABAR


B Mesons


● Can be produced in pairs in the decay of bb in a coherent L=1 state

● B Mesons Mix

– Y(4S)→BB→B1B2

● B1→D1*-μ1ν1

● B2 D→ 2*-μ2ν2

ARGUS, PL B 192, 245 (1987)


How can CP violation be observed

● Three types of CP violation

– trough the interference of decay amplitudes


How can CP violation be observed

– Trough the interference of mixing diagrams

– Trough the interference between mixing and decay amplitudes

● Directly related to CKM angles for single amplitude

● Golden channel B0→J/psi KS,L

● Tree level diagram

● Higher order contributions have

the same weak phase

– => theoretically clean

measurement of CKM phase

beta

● Clear experimental signature

– A pair of high momentum leptons and a pair of low momentum pions

● Relatively large branching fractions

0Bfi

CPA eCPf

0B

12

2 Mi

M

ie fi

CPA e


Time evolution of the B system

[from P. Krizan, Univ. Lubljana]

ckm physics and flavor anomaliessimi/didattica/1-ckm-and...ckm is a unitary 3x3 matrix it can be...

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