About the Scientific Life of Harald Fritzsch

About the scientiﬁc life of Harald Fritzsch

Peter Minkowski University of Bern

”Harald Fritzsch Symposium” 6. June , 2008 at the Ludwig-Maximilian University in Munich 1

List of contents

1 ’Strong interactions are mediated by a gauge theory’ 3

... a few remarks on the pre-history of this idea

2 From our collaboration 19

3 From Caltech becoming a Professor ﬁrst in Wuppertal 1977 theninBern1978 26

4 From Bern to the LMU in Munich 1980 – 27

5 Outlook 31

References 32 2

1 ’Strong interactions are mediated by a gauge theory’

... a few remarks on the pre-history of this idea and about QCD

As far as I know from you , Harald , this idea which gave birth to QCD , was strongly impressed in your mind , when you succeeded after obtaining the diploma in physics from the University of Leipzig, to escape through the black sea to Turkey in 1968 . But how these thoughts developed may be the topic of Murray Gell-Mann’s contribution and thus I shall only report here about times long past, starting 1953 with Wolfgang Pauli, and going backwards to about 1937 to more general ideas of Elie´ Cartan on ’connections’ . → 3

Figure 1: ’Many letters, some answers’ ( → ) . 4

P aulis Letters

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des k on tin uierlic hen ektrums Sp der Strahlen sein m ussen und da Bohr mit seinen dies

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n e nrist uretten zu Statistik der Energiesatz den und N M amlic die h oglic k es hk eit elektrisc onn ten h

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n lkrnk Elektron und onstan ist t

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nic h t gr oer sein k ann als die eines Strahls und dann darf w ohl nic h t gr oer sein als

13 Tegernsee 20.-24. Oct. 1997 , ed. by

e mic cm traue Ic h nic er v h ab orl aug publizieren zu Idee et h t diese w as er ub und

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a gr et mal w a Durc oeres hdringungsv esitzen b erm ogen ein wie w urde Strahl

lo ibeRadioaktiv e lieb Also ric pr und e ufet k h tetLeider ic ann nic h ers p h t onlic T in h ubingen G. Raffelt, TU M¨unchen 1998 [1a] . ( → )

ersc heinen da ic h infolge eines in der Nac h t v om zum Dez in Z uric h stattndenden

Balles unabk hier ommlic h bin un Euer Diener tert anigster P W auli

et P Heute aulisc ip Aussc nz hes hlieungspri

et Neutrinos Heute 5

But the strong interactions gauging a nonabelian local SU2 group are subject of another letter , and concerning the association of the gauge group with isospin ( G = SU2) we have to say with Pauli : ’ganz falsch’ , yet ... . The following letter from Wolfgang Pauli to Abraham Pais, 25. July 1953, is from K. Meyenn, ’Wolfgang Pauli, Wissenschaftlicher Briefwechsel’, Band IV, Teil II, Springer Verlag 1999 [2a] . 6

From the ﬁve derivation pages only two shall be shown → 7

M 6 = M 1+3 × S 2 → 8

The equation number is eight → 9

This ﬁrst in time excursion , shall put into perspective your own ideas, Harald , and leave open the eventual existence of other similar ones . In fact it would be incomplete, not to mention here Elie´ Cartan. The interest of the latter in general relativity is documented by a book : Elie´ Cartan - Albert Einstein: Letters on Absolute Parallelism, 1929-1932, Robert Debever Editor, Princeton Univ. Press. 1979 [3a] .

The next picture shows Elie´ Cartan returning from a turbulent ship excursion during an International Mathematics Conference in Oslo , 1936 – from the photo album of George Polya´ [4a] . → 10

He tried to understand general relativity but found general group-valued connections, which include the speciﬁc SU2-valued one derived by Wolfgang Pauli, around 1937 . → 11

The ’Uberbau’¨ structure of fibre bundles, mathematically elaborated later, is fine , but so enormously generalised, that the jewels relevant for quantized gauge field theories are difficult to recognize. a

The next ﬁgure shall serve to put Wolfgang Pauli and Arnold Sommerfeld in perspective with your University, the LMU in Munich. It is taken from the exposition at the ETH library at the occasion of the centenary of W. P., URL http://www.ethbib.ethz.ch/exhibit/pauli/index.html/ [5a] .

a I am grateful to Raymond Stora for pointing out to me two later indirect accounts of this work , by a) Charles Ehresmann, ’Les connexions differentiables´ dans un ﬁbre´ differentiable’,´ Colloque de Topolo- gie (Espaces ﬁbres),´ Centre Belge de Recherches Mathematiques,´ Bruxelles, 5.-8. Juin 1950 [6a] , and b) mimeographed notes of lectures by Shiing-Shen Chern, Institute for Advanced Study, Princeton ∼ 1951 [7a] . 12

Wolfgang Pauli as high school student in Vienna , his student card at the LMU and Arnold Sommerfeld and Wolfgang Pauli during a conference on metals in Geneva 1934 → 13

Varna, Bulgaria the starting point of your escape with Stefan, 1968 . → 14

Igneada, Turkey – the ’road to freedom’, 1968 [8a] . → 15

”Forces between quarks ( and antiquarks ) are mediated by gauge bosons ...” this was your conviction maybe related to your studies of general relativity . This brings you into the group of physicists and mathematicians, which I mentioned in the introduction to your scientiﬁc life .

It brought you – a well conceived plan – to Aspen and later in 1970 to the Stanford Linear Accelerator Center in order to discuss with Murray Gell-Mann and try to initiate your collaboration Three accounts shall be cited here : [1] William A. Bardeen, H. Fritzsch, Murray Gell-Mann , CERN-TH-1538, May 1972, ’Light cone current algebra, π 0 decay, and e + e− annihilation’ , William A. Bardeen, H. Fritzsch and Murray Gell-Mann . CERN-TH-1538, May 1972, presented at Topical Meeting on the Outlook for Broken Conformal Symmetry in Elementary Particle Physics, 4-5 May 1972, Frascati, Italy, hep-ph/0211388.

[3] H. Fritzsch, Murray Gell-Mann and H. Leutwyler (Caltech) , ’Advantages of the Color Octet Gluon Picture’, CALT-68-409, 1973, Phys.Lett.B47 (1973) 365-368.

This shall acknowledge your original and seminal contribution to the conception of QCD . 16

Let me also show ’ The road to freedom (at short distances) ’ quoting four references [4] I. B. Khriplovich, ’Greens functions in theories with a non-abelian gauge group’ , Yad. Fiz. 10 (1969) 409 , engl. transl. Sov. J. Nucl. Phys. 10 (1970) 235 .

[5] G. ’t Hooft, Remarks at the Colloquium on renormalization of Yang-Mills ﬁelds and applications to particle physics, Marseille 1972 .

[6] D. J. Gross and F. Wilczek, ’Ultraviolet behaviour of nonabelian gauge theories’ , Phys. Rev. Lett. 30 (1973) 1343 .

[7] D. Politzer, ’Reliable results for strong interactions ?’ , Phys. Rev. Lett. 30 (1973) 1346 . g 2 3/2 4 µd/dµ log Z / Z 1 = − b 1 + O g “ 3 ” ` ´ 16 π 2 (1) 12 − 1 4 b 1 = C 2 ( G ) − 3 T 2 ( D G ) 3

a b ab C 2 ( SUN ) = N ; tr T ( D ) T ( D ) = T 2 ( D ) δ → 17

... this shows the delight in your collaboration → 18

2 From our collaboration

In fall 1971 you and Murray Gell-Mann arrived for a stay of one year at CERN . Soon later we met and started to collaborate , ﬁrst on problems related to deep inelastic scattering and the short distance expansion of products of local currents . But let me move to fall 1973 , whence I had followed an offer to become a research fellow at Caltech and we resumed there a wider collaboration . First lets turn to a paper on uniﬁed gauge-interactions, which took more than a year to be completed :

[8] Harald Fritzsch and Peter Minkowski (Caltech), ’Uniﬁed Interactions of Leptons and Hadrons’, CALT-68-467, (Received Dec 1974), Annals Phys.93 (1975) 193-266 .

It is not that you, Harald, were working slowly that this took so long, to the contrary, but many things developed alongside. First on the experimental side a) in September 1973 the neutral current interaction was found in the reactions

(2) ν µ ( ν µ ) N → ν µ ( ν µ ) + hadrons

in the Gargamelle bubble chamber [9] ﬁlled with freon , reﬁning inconclusive earlier searches. → 19

[9] F.J. Hasert et al., Gargamelle Neutrino Collaboration, ’Observation of Neutrino Like Interactions Without Muon Or Electron in the Gargamelle Neutrino Experiment’, Phys.Lett.B46 (1973) 138-140 . b) in November 1974 the joint efforts of Samuel Ting et al. at Brookhaven ,

[10] J.J. Aubert et al., E598 Collaboration, ’Experimental Observation of a Heavy Particle J’, COO-3069-271, 1974, Phys.Rev.Lett.33 (1974) 1404-1406 ,

and Burton Richter et al. at SLAC ,

[11] J.E. Augustin et al., SLAC-SP-017 Collaboration, ’Discovery of a Narrow Resonance in e+ e- Annihilation’, SLAC-PUB-1504, Nov 1974, Phys.Rev.Lett.33 (1974) 1406-1408 ,

led to the discovery of (closed) charm in the form of the vector meson resonance J/ψ in the reactions − p + Be → J/ψ + X → e + e + X [10]

(3) hadrons + − 8 e e → J/ψ → < [11] µ + µ − : Furthermore the resonance was almost immediately after ﬁrst announcements conﬁrmed jointly by three experimental groups extending the energy range at the Adone facility at Frascati . → 20

On the theoretical side – without detailed quotations nor attempt of completeness here – (some) seminal insights and results, beyond what I have already mentioned, were

1967 [12] L.D. Faddeev, V.N. Popov (Steklov Math. Inst., St. Petersburg) , 1967, ’Feynman Diagrams for the Yang-Mills Field’ , Phys.Lett.B25 (1967) 29-30 , with references therein to Chen-Ning Yang and Robert Mills, Ryoyu Utiyama, Sheldon Glashow and Murray Gell-Mann, Bryce de Witt and Richard Feynman .

1971 a spontaneously broken SU2 w gauge theory with one doublet of (pseudo-) scalars was proven to be renormalizable (to 2 loops) by Gerardus ’t Hooft after a long preparation-phase in collaboration with Martinus Veltman .

1973 Abdus Salam and Jogesh Pati formulated a ’Uniﬁed Lepton-Hadron Symmetry and a Gauge Theory of the Basic Interactions’, noting the implication of baryon-number instability in such a framework .

1974 Howard Georgi and Sheldon Glashow presented a uniﬁed gauge theory based on the group SU5, ’Unity of All Elementary Particle Forces’ . a → a I thank Nevena Ilieva for her thoughtful insisting on considering all contributions in particular those due to Ludwig Faddeev . 20a

with Abdus Salam → 21

1974 Claudio Becchi, Alain Rouet and Raymond Stora formulated the algebraic anticommuting structure at ’first ghost level’ of what became known as the BRST formalism , T for Igor Tyutin ( and Efim Fradkin & ) . back to our paper : [8] ’Unified Interactions of Leptons and Hadrons’ .

One aspect , which shall be singled out here, concerned the (eventual) role of the a gauge group SO10 ( its covering group D 5 or spin10 ) . SO10 did not fall into a seemingly inﬁnite chain of possible gauge groups SOn ; n ≥ 10 , in order to avoid mirror fermion families , but revealed itself as the largest possible group within such orthogonal chains . This leaves unanswered – to this day – the question why ( not to speak of if) there exist 3 families of 16-ﬂavor spin 1/2 families b .

a [13] H. Georgi (Harvard U.), 1975, ’Uniﬁed Gauge Theories’ , in *Coral Gables 1975, Proceedings, Theories and Experiments In High Energy Physics*, New York 1975, 329-339. b Maybe here is a good place to remember : [14] F. G ¨ursey, Pierre Ramond (Yale U.), P. Sikivie (Maryland U.), ’A Universal Gauge Theory Model Based on E6’, YALE-3075-118, Sep 1975, Phys.Lett.B60 (1976) 177. 22

Let me mention 2 more papers from the time at Caltech :

[15] Harald Fritzsch, Peter Minkowski (Caltech) , ’Psi Resonances, Gluons and the Zweig Rule’, CALT-68-492, Mar 1975, Nuovo Cim.A30 (1975) 393.

[16] ’Vector-Like Weak Currents, Massive Neutrinos, and Neutrino Beam Oscillations’, CALT-68-525, (Received Nov 1975), Phys.Lett.B62 (1976) 72. In [15] a hypothesis is layed out, that the gauge-boson degrees of freedom in QCD also materialize in resonances , with clear simplifying dynamics , to be revealed, allowing a classification and phenomenological identification . This expectations have – as yet – not been met , excepting very definite results obtained in lattice simulations without (anti-)quarks , or with the latter all beeing very heavy, with masses comparable to the one pertaining to the bottom quark .

In [16] the theme of neutrino ﬂavors – light and heavy – and (anti-)neutrino oscillations is taken up and embedded within a vectorlike form of chiral gauge interactions . You, Harald, were also very active in communicating these results to Bruno Pontecorvo and beyond to convince ﬁrst Felix Bohm,¨ Peter Vogel and collaborators at Caltech and then Robert Mossbauer,¨ then director of the Institut Laue Langevin in Grenoble, to perform a search for the oscillations, entailing a demanding precision of a possible detector not too near to a reactor source.

The letter never arrived (according to Samoil Bilenky) and the ﬁrst oscillation experiments yielded null-results but → 23

’Geduld bringt Rosen’ ( ’Patience brings roses’ ) from [17] S. Abe et al., KamLAND Collaboration, ’Precision Measurement of Neutrino Oscillation Parameters with KamLAND’, Feb 2008, arXiv:0801.4589 [hep-ex] 24

3 From Caltech becoming a Professor ﬁrst in Wuppertal 1977 then in Bern 1978 Time is (probably) getting short . Thus I select several papers from the above time with only short comments possible .

[18] H. Fritzsch (Wuppertal U. & CERN) , 1978, ’Chromodynamics’, Talk in *Singapore 1978, Proceedings, 1978 International Meeting On Frontier Of Physics, Vol.2*, Singapore 1978, 1005-1042.

[19] H. Fritzsch (CERN & Wuppertal U.) , ’Weak Interaction Mixing in the Six - Quark Theory’, CERN-TH-2433, Dec 1977, Phys.Lett.B73 (1978) 317-322.

[20] Harald Fritzsch (Bern U.) , ’How to discover the b ﬂavored baryons’, Print-79-0922 (BERN), (Received Nov 1979), Phys.Lett.B90 (1980) 167. In this paper you discuss the transition on the quark level b → c cs inside

Λ b = ( bud ) → J/ψ ( c c ) K p X , an ingenious inclusive decay channel . 25

4 From Bern to the LMU in Munich 1980 – In 1980 you accepted an offer to the prestigious ’chair’ in theoretical physics at the Ludwig-Maximilian University , a chair which had been occupied (shortly) by Ludwig Boltzmann and during the decisive years of the discovery and development of quantum mechanics by Arnold Sommerfeld . This position was accompanied by a participation within the Max Planck Institute for Physics ( Werner Heisenberg Institute ) . In assuming all these functions , you did not only publish 167 papers, as given in the e-archives, but launched as promotor and key organizer several conferences and series :

a) International Conferences on Quantum Chromo Dynamics, in Montpellier, France, beginning 1985, chaired by Stephan Narison.

b) Symposia in Oberwolz,¨ Styria, Austria, jointly with W. Plessas and W. Schweiger, University of Graz , 1998, 2003, 2006 .

c) International Conferences on Flavor Physics beginning 2001 every two years, 2007 at the Kavli Institute for Theoretical Physics China, the Institute of Theoretical Physics (ITP), Chinese Academy of Sciences, in Beijing, China .

d) Workshops on Flavor, 2005 in Chamonix, France and 2007 in Albufeira, Portugal – in the Hapimag resorts . 26

So I shall select two areas of research , which mark – but in no way exhaust – your important contributions until the present

i) maximal CP violating phase in quark ﬂavor mixing ( the CKM matrix ) , with implications also for the lepton sector . This idea you exposed in an original paper in 1979 .

[21] Harald Fritzsch (Munich U.) , Zhi-zhong Xing (Beijing, Inst. High Energy Phys.), ’Lepton mass hierarchy and neutrino mixing’, Jan 2006, Phys.Lett.B634 (2006) 514-519, hep-ph/0601104 .

[22] Harald Fritzsch, Zhi-zhong Xing (Munich U.), ’Mass and ﬂavor mixing schemes of quarks and leptons’, LMU-99-16, Dec 1999, Prog.Part.Nucl.Phys.45 (2000) 1-81, hep-ph/9912358 . →

ii) are natural constants really constant ?

[23] Harald Fritzsch (Munich U.), ’The Fundamental Constants in Physics and their Time Dependence’, LMU-ASC-03-08, Feb 2008, arXiv:0802.0099 [hep-ph] . ( Only the most recent of a sries of papers is cited here. ) For this work, for your ’oeuvre integral’ – as well as for your contributions to the construction of QCD – you were awarded the ’Dirac Silver Medal for the Advancement of Theoretical Physics’ by the University of New South Wales, Sydney, Australia, 15. April 2008 . 27

A comment to i) above : You point out a particular way to parametrize the CKM (also neutrino-) mass matrix, restricting the electroweak symmetry breaking to one (or two) doublet(s) of Higgs-scalar(s)

c −s 0 e −iϕ 0 0 c −s 0 0 u u 1 0 1 0 d d 1 V CKM = B s u c u 0 C B 0 c −s C B s d c d 0 C B C B C B C B C B C B C (4) @ 0 0 1 A @ 0 s c A @ 0 0 1 A

= R z ( ϑ u ) R J ( − i ϕ ) R x ( ϑ ) R z ( ϑ d )

s u,d = sin ϑ u,d , s = sin ϑ ∗ and to compare with the ((u α) d ) × ((u α) b ) unitary triangle or any other pair-triangle

∗ −1 ∗ ∗ ∗ (5) V cdV V udV + V cdV + V tdV = 0 ` cb ´ ` ub cb tb ´ which is congruent with → 28

from [24] E. Barberio et al., Heavy Flavor Averaging Group, ’Averages of b-hadron properties at the end of 2006’, arXiv:0704.3575v1 [hep-ex]

◦ + 13 ◦ (6) PDG : ≡ ↔ ∼ α φ 2 = “ 99 − 8 ” α ϕ = 90

Your derivation based on a particular texture with respect to the mass hierarchies and maximal CP violation is not only remarkably correct but also shows an element of choice or even trial and errror definitely outside the realm of a renormalizable field theory in flat 4-d space-time. c1

5 Outlook We hope that your creative mind, in scientiﬁc life and beyond will continue to bloom – in good health and untouched by the professional change imposed by your retirement .

Thank you r1

References

[1a] Rudolf Mossbauer,¨ Proc. of ’Neutrino Astrophysics’ , Ringberg Castle, Tegernsee 20.-24. Oct. 1997 , ed. by M.Altmann, W. Hillebrandt, H.-T. Janka and G. Raffelt, TU M ¨unchen 1998 . [2a] K. Meyenn, ’Wolfgang Pauli, Wissenschaftlicher Briefwechsel’, Band IV, Brief [1614] und Anlage zum Brief, Teil II, Springer Verlag 1999 . [3a] Elie´ Cartan - Albert Einstein: Letters on Absolute Parallelism, 1929-1932, Robert Debever Editor, Princeton Univ. Press 1979. [4a] George Polya,´ ’The Polya´ picture album : encounters of a mathematician’ , G. L. Alexanderson ed., Birkhauser¨ Verlag. Boston - Basel, 1987 . r2

References

[5a] ’Wolfgang Pauli and Modern Physics’, Exhibition of the ETH-Bibliothek at the occasion of the 100th birthday of Wolfgang Pauli, April 6 to May 6, 2000 in the entrance hall of the ETH Zurich, August 17 to September 26, 2000 at the CERN in Geneva, May 25 to July 27, 2001 at the University Linz, Virtual Exhibition, Rudolf Mumenthaler, Miriam Helvig , http://www.ethbib.ethz.ch/exhibit/pauli/index.html/ . [6a] Charles Ehresmann, ’Les connexions differentiables´ dans un ﬁbre´ differentiable’,´ Colloque de Topologie (Espaces ﬁbres),´ Centre Belge de Recherches Mathematiques,´ Bruxelles, 5.-8. Juin 1950 . r3

References

[7a] Shiing-Shen Chern, mimeographed lecture notes , Institute for Advanced Study, Princeton ∼ 1951 ( unpublished ) . [8a] H. Fritzsch, ’Flucht aus Leipzig’, Piper Verlag M ¨unchen - Z ¨urich 1990 . [1] William A. Bardeen, H. Fritzsch and Murray Gell-Mann, ’Light 0 cone current algebra, π decay, and e + e− annihilation’ , CERN-TH-1538, May 1972, presented at Topical Meeting on the Outlook for Broken Conformal Symmetry in Elementary Particle Physics, 4-5 May 1972, Frascati, Italy, hep-ph/0211388 . r4

References

[2] Harald Fritzsch and Murray Gell-Mann (CERN) ’Current algebra: Quarks and what else?’, Proceedings of 16th International Conference on High-Energy Physics, Batavia, Illinois, 6-13 Sep 1972, published in eConf C720906V2 (1972) 135-165, also in Physics, Proceedings of the XVI International Conference on High Chicago 1972 p.135 (J. D. Jackson, A. Roberts, eds.), hep-ph/0208010 . [3] H. Fritzsch, Murray Gell-Mann and H. Leutwyler (Caltech), ’Advantages of the Color Octet Gluon Picture’, CALT-68-409, 1973, Phys.Lett.B47 (1973) 365-368 . r5

References

[4] I. B. Khriplovich, ’Greens functions in theories with a non-abelian gauge group’ , Yad. Fiz. 10 (1969) 409 , engl. transl. Sov. J. Nucl. Phys. 10 (1970) 235 . [5] G. ’t Hooft, Remarks at the Colloquium on renormalization of Yang-Mills ﬁelds and applications to particle physics, Marseille 1972 . [6] D. J. Gross and F. Wilczek, ’Ultraviolet behaviour of nonabelian gauge theories’ , Phys. Rev. Lett. 30 (1973) 1343 . [7] D. Politzer, ’Reliable results for strong interactions ?’ , Phys. Rev. Lett. 30 (1973) 1346 . r6

References

[8] Harald Fritzsch and Peter Minkowski (Caltech), ’Uniﬁed Interactions of Leptons and Hadrons’, CALT-68-467, (Received Dec 1974), Annals Phys.93 (1975) 193-266 . [9] F.J. Hasert et al., Gargamelle Neutrino Collaboration, ’Observation of Neutrino Like Interactions Without Muon Or Electron in the Gargamelle Neutrino Experiment’, Phys.Lett.B46 (1973) 138-140 . [10] J.J. Aubert et al., E598 Collaboration, ’Experimental Observation of a Heavy Particle J’, COO-3069-271, 1974, Phys.Rev.Lett.33 (1974) 1404-1406 . r7

References

[11] J.E. Augustin et al., SLAC-SP-017 Collaboration, ’Discovery of a Narrow Resonance in e+ e- Annihilation’, SLAC-PUB-1504, Nov 1974, Phys.Rev.Lett.33 (1974) 1406-1408 . [12] L.D. Faddeev, V.N. Popov (Steklov Math. Inst., St. Petersburg) , 1967, ’Feynman Diagrams for the Yang-Mills Field’ , Phys.Lett.B25 (1967) 29-30 . [13] H. Georgi (Harvard U.), 1975, ’Uniﬁed Gauge Theories’ , in *Coral Gables 1975, Proceedings, Theories and Experiments In High Energy Physics*, New York 1975, 329-339. [14] F. G ¨ursey, Pierre Ramond (Yale U.) , P. Sikivie (Maryland U.) , ’A Universal Gauge Theory Model Based on E6’, YALE-3075-118, Sep 1975, Phys.Lett.B60 (1976) 177. r8

References

[15] Harald Fritzsch, Peter Minkowski (Caltech) , ’Psi Resonances, Gluons and the Zweig Rule’, CALT-68-492, Mar 1975, Nuovo Cim.A30 (1975) 393. [16] Harald Fritzsch, Peter Minkowski (Caltech) , ’Vector-Like Weak Currents, Massive Neutrinos, and Neutrino Beam Oscillations’, CALT-68-525, (Received Nov 1975), Phys.Lett.B62 (1976) 72. [17] S. Abe et al., KamLAND Collaboration, ’Precision Measurement of Neutrino Oscillation Parameters with KamLAND’, Feb 2008, arXiv:0801.4589 [hep-ex] . r9

References

[18] H. Fritzsch (Wuppertal U. & CERN) , 1978, ’Chromodynamics’, Talk in *Singapore 1978, Proceedings, 1978 International Meeting On Frontier Of Physics, Vol.2*, Singapore 1978, 1005-1042. [19] H. Fritzsch (CERN & Wuppertal U.) , ’Weak Interaction Mixing in the Six - Quark Theory’, CERN-TH-2433, Dec 1977, Phys.Lett.B73 (1978) 317-322. [20] Harald Fritzsch (Bern U.) , ’How to discover the b ﬂavored baryons’, Print-79-0922 (BERN), (Received Nov 1979), Phys.Lett.B90 (1980) 167. r10

References [21] Harald Fritzsch (Munich U.) , Zhi-zhong Xing (Beijing, Inst. High Energy Phys.), ’Lepton mass hierarchy and neutrino mixing’, Jan 2006, Phys.Lett.B634 (2006) 514-519, hep-ph/0601104 . [22] Harald Fritzsch, Zhi-zhong Xing (Munich U.), ’Mass and ﬂavor mixing schemes of quarks and leptons’, LMU-99-16, Dec 1999, Prog.Part.Nucl.Phys.45 (2000) 1-81, hep-ph/9912358 . [23] Harald Fritzsch (Munich U.), ’The Fundamental Constants in Physics and their Time Dependence’, LMU-ASC-03-08, Feb 2008, arXiv:0802.0099 [hep-ph] . [24] E. Barberio et al., Heavy Flavor Averaging Group, ’Averages of b-hadron properties at the end of 2006’, arXiv:0704.3575v1 [hep-ex] .