Cooking Up Flavor - National Chiao Tung University · carb on-12 isotop e, de ned to b e exactly 12...

Cooking Up Flavor

We-Fu Chang

NTHU

Oct. 25, 2007

We-Fu Chang, NTHU – p. 1/43

Outline

• The Discovery of Flavor

• Flavor Problem• How does Nature Cook up the Flavor?

• Final Remark


• A thousand years old question: What is our world made of?

• In ancient Greek, philosopher believed the building blocks are the "4 elements":

season element humour body fluid location

Spring air sanguine blood heartSummer fire choleric "yellow bile" liverAutumn earth melancholic "black bile" spleenWinter water phlegmatic phlegm (various)


Mendeleev first trained as a teacher in thePedagogic Institute of St. Petersbug beforeearing his MS in 1856.

Textbook written between 1868-1870


• At that time, the experimentally determined atomic masses were not alwaysaccurate. Mendeleev reordered elements despite their accepted masses.For example, he changed the weight of Beryllium from 14 to 9.In all, he found 17 elements had to be moved to new positions.

• Even so, there are many elements missing at some positions.From the gap, he predicted the existence and properties of unknown elements.

• Gallium (by a French, Gallia is Latin for France), Scandium (by a Scandinavian ),and Germanium (by a German) were found later to fit his prediction quite well.

• In all Medeleev predicted the existence of 10 new elements, of which seven wereeventually discovered.

• After electron, proton, neutron and Quantum Mechanics were known, the periodictable can be easily understood.


Modern Periodic Table4.Periodictableoftheelements1

4.PERIODICTABLEOFTHEELEMENTS

Table 4.1. Revised 2004 by C.G. Wohl (LBNL). Adapted from the Commission of Atomic Weights and Isotopic Abundances, \Atomic Weights of the Elements 1995,"Pure and Applied Chemistry 68, 2339 (1996), and G. Audi and A.H. Wapstra, \The 1993 Mass Evaluation," Nucl. Phys. A565, 1 (1993). The atomic number (topleft) is the number of protons in the nucleus. The atomic mass (bottom) is weighted by isotopic abundances in the Earth's surface. For a new determination of atomicmasses, not weighted by abundances, see G. Audi, A.H. Wapstra, and C. Thibault, Nucl. Phys. A729, 337 (2003). Atomic masses are relative to the mass of thecarbon-12 isotope, dened to be exactly 12 unied atomic mass units (u). Errors range from 1 to 9 in the last digit quoted. Relative isotopic abundances often varyconsiderably, both in natural and commercial samples. A number in parentheses is the mass of the longest-lived isotope of that element|no stable isotope exists.However, although Th, Pa, and U have no stable isotopes, they do have characteristic terrestrial compositions, and meaningful weighted masses can be given. Forelements 110 and 111, the numbers of nucleons A of conrmed isotopes are given.1IA 18VIIIA1 HHydrogen1.00794 2IIA 13IIIA 14IVA 15VA 16VIA 17VIIA 2 HeHelium4.0026023 LiLithium6.941 4 BeBeryllium9.012182 PERIODICTABLEOFTHE ELEMENTS 5 BBoron10.811 6 CCarbon12.0107 7 NNitrogen14.00674 8 OOxygen15.9994 9 FFluorine18.9984032 10 NeNeon20.179711 NaSodium22.989770 12 MgMagnesium24.3050 3IIIB 4IVB 5VB 6VIB 7VIIB 8 9VIII 10 11IB 12IIB 13 AlAluminum26.981538 14 SiSilicon28.0855 15 PPhosph.30.973761 16 SSulfur32.066 17 ClChlorine35.4527 18 ArArgon39.94819 KPotassium39.0983 20 CaCalcium40.078 21 ScScandium44.955910 22 TiTitanium47.867 23 VVanadium50.9415 24 CrChromium51.9961 25 MnManganese54.938049 26 FeIron55.845 27 CoCobalt58.933200 28 NiNickel58.6934 29 CuCopper63.546 30 ZnZinc65.39 31 GaGallium69.723 32 GeGerman.72.61 33 AsArsenic74.92160 34 SeSelenium78.96 35 BrBromine79.904 36 KrKrypton83.8037 RbRubidium85.4678 38 SrStrontium87.62 39 YYttrium88.90585 40 ZrZirconium91.224 41 NbNiobium92.90638 42 MoMolybd.95.94 43 TcTechnet.(97.907215) 44 RuRuthen.101.07 45 RhRhodium102.90550 46 PdPalladium106.42 47 AgSilver107.8682 48 CdCadmium112.411 49 InIndium114.818 50 SnTin118.710 51 SbAntimony121.760 52 TeTellurium127.60 53 IIodine126.90447 54 XeXenon131.2955 CsCesium132.90545 56 BaBarium137.327 5771Lantha-nides 72 HfHafnium178.49 73 TaTantalum180.9479 74 WTungsten183.84 75 ReRhenium186.207 76 OsOsmium190.23 77 IrIridium192.217 78 PtPlatinum195.078 79 AuGold196.96655 80 HgMercury200.59 81 TlThallium204.3833 82 PbLead207.2 83 BiBismuth208.98038 84 PoPolonium(208.982415) 85 AtAstatine(209.987131) 86 RnRadon(222.017570)87 FrFrancium(223.019731) 88 RaRadium(226.025402) 89103Actinides 104 RfRutherford.(261.1089) 105 DbDubnium(262.1144) 106 SgSeaborg.(263.1186) 107 BhBohrium(262.1231) 108 HsHassium(265.1306) 109 MtMeitner.(266.1378) 110 DsDarmstadt.[269,271] 111[272]Lanthanideseries 57 LaLanthan.138.9055 58 CeCerium140.116 59 PrPraseodym.140.90765 60 NdNeodym.144.24 61 PmPrometh.(144.912745) 62 SmSamarium150.36 63 EuEuropium151.964 64 GdGadolin.157.25 65 TbTerbium158.92534 66 DyDyspros.162.50 67 HoHolmium164.93032 68 ErErbium167.26 69 TmThulium168.93421 70 YbYtterbium173.04 71 LuLutetium174.967Actinideseries 89 AcActinium(227.027747) 90 ThThorium232.0381 91 PaProtactin.231.03588 92 UUranium238.0289 93 NpNeptunium(237.048166) 94 PuPlutonium(244.064197) 95 AmAmeric.(243.061372) 96 CmCurium(247.070346) 97 BkBerkelium(247.070298) 98 CfCaliforn.(251.079579) 99 EsEinstein.(252.08297) 100 FmFermium(257.095096) 101 MdMendelev.(258.098427) 102 NoNobelium(259.1011) 103 LrLawrenc.(262.1098)


Cavendish Laboratory

The marked ones in the seated row are: Chadwick, Thomson, Rutherford, Wilson,andKapitza. You my also notice the crocodile and a Chinese gentleman, P.C. Ho.


dσ

dΩ=

(

q1q2

4E sin2 θ2

)2


J Thomsonelectron, 1906

Rutherfordproton, 1908 (chem)

J. Chadwickneutron, 1935

C Andersonpositron, 1936

Yukawapion theory, 1949

C. Powellpion, 1950


E2c2 = m2c4 + p2c2,√s ∼

√EM,

√s ∼ E


Baryon Octet Baryon decuplet

Pseudoscalar meson nonet Vector meson nonet


In 1964, Murray Gell-Mann and George Zweig tentatively put forth the idea of quarks.They suggested that mesons and baryons are composites of three quarks or antiquarks,called up, down, or strange (u, d, s) with spin 1/2 and electric charges 2/3, -1/3, -1/3,respectively (it turns out that this theory is not completely accurate). Since the chargeshad never been observed, the introduction of quarks was treated more as amathematical explanation of flavor patterns of particle masses than as a postulate ofactual physical object. Later theoretical and experimental developments allow us to nowregard the quarks as real physical objects, even though they cannot be isolated.


A challenge

Following is a famous puzzle which mimics what the high energy physicists’ work are:

Imagining that we are living in a 2-dimensional world. The first row shows some of theobserved 2-dimension “Atoms”. The shapes in white in the second row are those neverbeen seen ever. Try to find out what are the fundamental particles and to decipher thephysics rules for the 2-D world.


The term "Flavour" was first used in the quark model of hadrons in 1968. It is said tohave been found on the way to lunch by Murray Gell-Mann and Harald Fritzsch whenthey passed a Baskin-Robbins advising 31 flavours.


November Revolution in Physics

The world of physics was dazzled in November 1974 when two separate experiments atSLAC and at Brookhaven independently discovered the first of a new set of particlestates, the J/Psi particle.Burton Richter of the SLAC collaboration, and Sam Ting, of the Brookhaven group,received the 1976 Nobel Prize in Physics"for their pioneering work in the discovery of a heavy elementary particle of a new kind."


Standard Model• Standard Model(SM) is the most successful theoretical understanding of the

Mother Nature in human history ( with only 19 free parameters. )

SM = Quantum Mechanics + Special Relativity + Field theory

+Gauge Symmetry [≡ SU(3)c × SU(2)L × U(1)]

+ Matter Content [quarks, leptons] + Higgs Mechanism.

• Predicts that weak interaction is mediated by exchange of W± and Z0 bosons.

S. Glashow Abdus Salam Steven Weinberg


The subtle periodic table in the modern particle physics:


We know much better about the neutrino properties in the past decade:

So far, the only confirmed new physics beyond SM. We-Fu Chang, NTHU – p. 26/43

It’s interesting to recall the neutrino physics back to 90s and before. The widely accepted"theoretical believes" at that time were:

• For solar neutrino problem, it must be solved by small mixing angle with MSW.

• m223

∼ eV2 Cosmologically interesting

• Uµ3 ∼ Vbc because of GUTThe one of few large mixing prediction was given by Ramond et el (1979) based onmt = 25 GeV!(for mt = 175 GeV, Uµ3 ∼ 0.1)

• Atmospherical neutrino problem doesn’t exist, because it would require a largemixing angle solution.

Now we know none of the above is correct!(Someone puts it "almost every neutrino model before 1998 is useless"!)The neutrino exps are important keys to Flavor Physics.


Fermion masses

•• Fermion masses in log scale

e µ τ

u

d

c

s b

t

ν1 ν2 ν3

Te

V

Ge

V

Me

V

ke

V

eV

me

V

µe

V

f e r m i o n m a s s e s

( l a r g e a n g l e M S W )

• Where comes the mass?


Fermion Mixing

• We have learnt that:the mixing among neutrinos are "Bi-LARGE" and only few mass matrix patternscan explain the data.

UMNS =

eiφ1 0 0

0 c23 s23

0 −s23 c23

c13 0 s13

0 e−iδ+iφ2 0

−s13 0 c13

c12 s12 0

−s12 c12 0

0 0 1

θ12 ∼ 33,θ23 ∼ 45, θ13 < 13; δ, φ1, φ2 are still unknown.

• Compared to the SM quark sector:

VCKM =

1 0 0

0 c23 s23

0 −s23 c23

c13 0 s13

0 e−iδ 0

−s13 0 c13

c12 s12 0

−s12 c12 0

0 0 1

θ12 ∼ 13, θ23 ∼ 2, θ13 ∼ 0.2; δ ∼ 65.• Puzzles!!


Flavor problem: How to understandfermion masses and mixing(22/28)?

(Adopted from Fritzsch’s talk)



Equivalence principleEötvös exp, < 10−9

Einstein EqNeed unify concept of mass.

Gravity and mass Quantum Physics

Planck Mass

Mp =

√

~c

G= 1.2 × 1019 GeV

∼ 0.02 mg

Also, tP ∼ 10−44 sec, lP ∼ 10−33 cm.Our ultimate goal (still far ahead): All physical quantities be calculated in terms of Planckunits.


Masses and the Higgs field

• The left-handed and right-handedfermions are coupled by Higgs bosonand get their mass through nonzeroVEV.

• Mathematically, the fermion mass term can be expressed as

LY ukawa = fijψLiψRjH +H.c.

• A thought experiment:If a left-handed fermion has mass, we can move fast enough to pass and find aright-handed partner.Since we observe no right-handed neutrino neutrinos are massless in (old)Standard Model. Left ? Right

1


Let’s look back.

• Too many elements=⇒ Periodic Table=⇒ Atoms consist of electrons and nuclei

• Too many isotopes=⇒ nuclei is made of protons and neutrons

• Too many hadrons=⇒ quarks, SU(3)F , and SU(3)c

• Too many redundant generations=⇒ Preon and Hypercolor??


Preon doesn’t work!

In the 1980s, the preon was a very popular research topic. But it doesn’t look promisinganymore:

• No direct experimental evidence or hints of the existence of substructure of quarksor lepton.Contact interaction search at LEP

=⇒ Λp > TeV

• The theory is difficult.

• Must be another Yang-Mills:Which group? Which representation? How to calculate?

• Why are quarks and leptons so light?Natural expectation is mass∼ Λp > TeV.Chiral symmetry is the only known symmetry to protect large mass, no oneknows how to make it work here.

• How to get the SM quantum number?• Some generic bad predictions:

exotic boson, quarks, and leptons..


Other tries.

• Bigger symmetry group?

SU(5) → SU(8) , SO(10) → SO(10 + 4k) , E6 → E8

However, familon problem, predicts K+ → π+ + f

• Being more conservative, people play with the symmetry game (extra quantumnumber ) only in the Yukawa sector.

• In the past 20 something years, people have been playing the game based on only2 ideas:• Structure Zeros• Froggatt-Nielsen• or the hybrid

• Statistics:Anarchy, Landscape..


Structure Zeros in mass matrixFirst proposed by F. Wilczek and A. Zee, and independently by H. Fritzsch in 1977.

• For example, by assigning a special discrete symmetry to a 2 family LR model withSU(2)L × SU(2)R × U(1), leads to

L ⊃ (D, S)L

(

x 0

y x

)(

DR

SR

)

, tan2 θc ∼ md

ms

• more


Froggatt Nielsen Mechanism

• An additional global U(1) symmetry

• plus extra SU(2) singlet scalars

• plus exotic vector like fermions

• Small Yukawa are due to U(1) invariant effective operator,

mij = h0uqa

i uqb

j ǫa+b, ǫ≪ 1


Geometry in extra Dimension?

• 5D fermion localizes at different position, zi, in extra dimension y ∈ [−πR, πR],ψi(x, y) = g(zi, y)ψ(x),

g(zi, y) =1

(πσ2)1/4exp

[

− (y − zi)2

2σ2

]

g(z1, y)g(z2, y) = exp

[

− (z1 − z2)2

4σ2

]

g

(

z1 + z2

2, y

)

• Exponential Yukawa hierarchy becomes linear displacement between left-handedand right-handed fermions in the fifth dimension.

• The following map can reproduce all quarks’ masses and CKM mixingsQ1 Q2Q3U1 U2U3 D1D2 D3

5 0 5 10 15 20 25


Intersecting brane?

It may provide a topological reason why we have 3 generations.

a U(3)

b

U(2)

c

U(1)

d U(1)

Q U D

L E

L R R

RL


LHC is coming soon

length = 26.7 km,√s = 14 TeV.

Maybe LHC will reveal more secretes of flavor physics and how the symmetry is brokento us.


Summary• Human being has been working hard and long to find out the ultimate constituent

around us.• So far, we know that the most fundamental building blocks of our world are quarks,

leptons, and gauge bosons.

• We have tried very hard to decipher Nature’s recipe of cooking up falvor.

• However, we still don’t really understand their pattern: Where come their masses,and what’s behind their mixing?

• The LHC will be able to probe the Higgs sector. It may tell us more about the flavorphysics.


Cooking Up Flavor - National Chiao Tung University · carb on-12 isotop e, de ned to b e exactly 12...

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