Quark mass hierarchy, flavor mixing and CP violation in weak/strong interactions

＠ QCD: History and Prospects, Oberwoelz, Austria, 3 — 8/9/2012

Xing Zhi-zhong

邢 志 忠[IHEP, Beijing]

OUTLINE

Flavor puzzles

Quark mass limits

Flavor mixing pattern

Weak/strong CP violation

QUARK MASSESQ F D

QCD

2Origin of “Flavor”

The term Flavor was coined by Harald Fritzsch and Murray Gell-Mann at a Baskin-Robbins ice-cream store in Pasadena in 1971.

Color & Flavor

QCD & QFD

Part A

3

1932: Discovery of neutron (J. Chadwick) up and down

1960: The quark model (M. Gell-Mann; G. Zweig)

1964: Discovery of CP violation (J.W. Cronin, V.L. Fitch)

1970: The GIM mechanism (S. Glashow et al)

1973: The origin of CP violation (M. Kobayshi, T. Maskawa)

1974: Discovery of charm (C.C. Ting; B. Richter)

1977: Discovery of bottom (L. Lederman et al)

1995: Discovery of top (F. Abe et al)

1947: Discovery of Kaon (G. Rochester, C. Butler) strange

1963: The Cabibbo angle of quark mixing (N. Cabibbo)

Quarks Part A

1964: The Higgs mechanism (P. Higgs; F. Englert, R. Brout; …)

1967: The standard model (S. Weinberg)

1972: Quantum Chromodynamics (H. Fritzsch, M. Gell-Mann, …)

4Flavor Puzzles (I) Part A

Gauge Hierarchy & Desert Puzzles / Flavor Hierarchy & Desert Puzzles

Fertile Soil Sterile Land

FLAVOR DESERT

Really nothing in?

5

Who ordered that?

What distinguishes different generations of leptons

or quarks?

----- they have the same gauge quantum numbers,

yet they are quite different from one another.

Hidden flavor quantum numbers or flavor symmetries?

Who ordered that? Part A

6Flavor Puzzles (II) Part A

uct

d s b

CP violation:

(weak/strong)

---- Why is J so small? And why is much smaller?

---- Why are there two right unitarity triangles?

Why A: Why B:

Why C: Why D:

These questions can essentially be answered in the quark mass limits.

7Quark Masses Part B

Quark masses (Higgs mass = 125 GeV. Xing, Zhang, Zhou, arXiv:1112.3112)

Two useful working symmetries based on QCD:

The chiral symmetry: ;

The heavy quark symmetry: .

0u d s, ,m m m

c b t, ,m m m

8Two Mass Limits Part B

Going from the quark mass matrices to the CKM flavor mixing matrix:

We are trying an almost model-independent way to understand some salient features of quark flavor mixing (Fritzsch 87; Xing 97; F+X 99; ….)

Chiral limits

HQ limits

9Trivial Flavor Mixing Part B

The rotation angles of two unitary matrices in two sets of mass limits:

Chiral limits

HQ limits

In either set of quark mass limits, one may easily understand why the CKM matrix is essentially symmetric about its (ud-cs-tb) axis.

10Off-diagonal AsymmetriesPart B

CKM Matrix

(Xing 1995)

11Nontrivial Flavor Mixing Part B

Question: Why the smallest CKM element is at the upper-right corner? Answer: Because of the reasonable mass limits . 0u bm m &

if

The heavy quark mass limits are useful to understand the CKM ratios:

Model-independent result Phenomenological guess Model results

(Fritzsch 78)

(Fritzsch, xing 03)

12Texture Zeros Part B

The hierarchical mass spectrum of the up- and down-type quarks and their hierarchical flavor mixing pattern imply that their mass matrices must have the hierarchical structures.

The structure of mass matrices determines the flavor mixing property.

A simple extension of the Fritzsch ansatz works well(Du, Xing, 93; Fritzsch, Xing, 95)

Texture zeros

Strong hierarchy

Weak hierarchy

Texture zeros of a fermion mass matrix dynamically mean that some matrix elements are strongly suppressed (in comparison with those weakly suppressed or unsuppressed neighboring elements) and may stem from a new kind of flavor symmetry.

(For example, the Froggatt-Nielsen mechanism 1979; or a discrete symmetry)

13Weak CP Violation Part C

Flavor-changing charged current

3cos

14Unitarity Triangles Part C

The Jarlskog rephasing invariant of the CKM quark mixing matrix:

Among the six CKM unitarity triangles in the complex plane, 2 of them are particularly interesting for B-meson physics and CP violation.

Current data:

FX ansatz 1995:(4-zero textures)

But somebody frowns at it …

15Part C

Current Data

PDG 2012

16Part C

Bjorken’s Talk in Hawaii

17Minimal CP Violation? Part C

Note A: is the unique inner angle of the six unitarity triangles which is most insensitive to the RGE running effects (no running at the one-loop level, Xing 09; Luo, Xing 10).

Note B:

Flavor mixing democracy and minimal CP violation in a unique parametrization (Gerard, Xing 2012):

CP violation is a corner effect in the quark sector:

18Strong CP Violation Part D

A P- and T-violating -term in QCD, coming from the instanton solution to the U(1)A problem:

The change of the -term due to the anomaly:

The chiral transformation of the quark fields

leads to the changes:

The mass term of quarks:

19Why a Problem? Part D

Then the effective CP-violating -term in QCD turns out to be:

It is a sum of the QCD contribution (the vacuum angle ) and the electroweak one (related to the phase structure of the quark mass matrix).

QCD

QFD

Best bound on the effective CP-violating term is given by the experimental upper limit on the neutron electric dipole moment

CP-violating

CP-conserving

why so tiny?

20Possible Solutions Part D

Additional chiral symmetry: 1) (Kaplan, Manohar, 86);

2) Peccei-Quinn U(1) symmetry (77).

There are 3 distinct approaches to the strong CP problem (Peccei 98):

----The QCD vacuum dynamics itself selects to be vanishing.

----Impose an additional chiral symmetry to dynamically drive .

----CP symmetry is spontaneously broken, with a natural small .

0

0u

m

A phenomenological measure of weak or strong CP-violating effects?

In any case, the CP-violating effects in the quark sector are not large enough to interpret the cosmological matter-antimatter asymmetry.

21Cosmic CP Violation

CP violation in the SM’s quark sector is highly suppressed; The electroweak phase transition is not strongly first order.

Part E

A Fritzsch-like Plot (29 fundamental parameters in Nature)

um

s

dm

tmbm

em

m

cm12sm

m

q

WM

HM

2m

1m

NG

w

13

23

12

13

23

l

3m