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About the scientific life of Harald Fritzsch
Peter MinkowskiUniversity 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’
... a few remarks on the pre-history of this idea
3
2 From our collaboration 19
3 From Caltech becoming a Professor first in Wuppertal 1977 th en in Bern 1978 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 toQCD , was strongly impressed in your mind , when you succeededafter obtaining the diploma in physics from the University o fLeipzig, to escape through the black sea to Turkey in 1968 .
But how these thoughts developed may be the topic of MurrayGell-Mann’s contribution and thus I shall only report here a bouttimes long past, starting 1953 with Wolfgang Pauli, and goin gbackwards to about 1937 to more general ideas of Elie Cartan on’connections’ . →
3
Figure 1: ’Many letters, some answers’ ( → ) .
44Pauli's LettersBrief an Oskar Klein, Stockholm, vom 18. 2. 1929Aber ich verstehe zu wenig von Experimentalphysik um diese Ansicht beweisen zu k�onnenund so ist Bohr in der f�ur ihn angenehmen Lage, unter Ausnutzung meiner allgemeinenHil osigkeit bei der Diskussion von Experimenten sich selber und mir unter Berufung aufCambridger Autorit�aten (�ubrigens ohne Literaturangabe) da etwas beliebiges vormachen zuk�onnen.Brief an Oskar Klein, Stockholm, 1929Ich selbst bin ziemlich sicher (Heisenberg nicht so unbedingt), da� -Strahlen die Ursachedes kontinuierlichen Spektrums der �-Strahlen sein m�ussen und da� Bohr mit seinen dies-bez�uglichen Betrachtungen �uber eine Verletzung des Energiesatzes auf vollkommen falscherF�ahrte ist. Auch glaube ich, da� die w�armemessenden Experimentatoren irgendwie dabeimogeln und die -Strahlen ihnen nur infolge ihrer Ungeschicklichkeit bisher entgangen sind.Brief an die Gruppe der \Radioaktiven" 1930Physikalisches Institutder Eidg. Technischen HochschuleZ�urich Z�urich, 4. Dez. 1930Liebe Radioaktive Damen und Herren!Wie der �Uberbringer dieser Zeilen, den ich huldvollst anzuh�oren bitte, Ihnen des n�aheren aus-einandersetzen wird, bin ich angesichts der falschen Statistik der N- und Li 6-Kerne, sowie deskontinuierlichen �-Spektrums auf einen verzweifelten Ausweg verfallen, um den Wechselsatzder Statistik1 und den Energiesatz zu retten. N�amlich die M�oglichkeit, es k�onnten elektrischneutrale Teilchen, die ich Neutronen2 nennen will, in den Kernen existieren, welche den Spin1/2 haben und das Ausschlie�ungsprinzip befolgen und sich von Lichtquanten au�erdem nochdadurch unterscheiden, da� sie nicht mit Lichtgeschwindigkeit laufen. | Das kontinuierliche�-Spektrum w�are dann verst�andlich unter der Annahme, da� beim �-Zerfall mit dem Elektronjeweils noch ein Neutron emittiert wird, derart, da� die Summe der Energien von Neutronund Elektron konstant ist.Nun handelt es sich weiter darum, welche Kr�afte auf die Neutronen wirken. Das wahr-scheinlichste Modell f�ur das Neutron scheint mir aus wellenmechanischen Gr�unden dieseszu sein, da� das ruhende Neutron ein magnetischer Dipol von einem gewissen Moment �ist. Die Experimente verlangen wohl, da� die ionisierende Wirkung eines solchen Neutronsnicht gr�o�er sein kann als die eines -Strahls, und dann darf � wohl nicht gr�o�er sein alse � (10�13 cm). Ich traue mich vorl�au�g aber nicht, etwas �uber diese Idee zu publizieren, undwende mich erst vertrauensvoll an Euch, liebe Radioaktive, mit der Frage, wie es um denexperimentellen Nachweis eines solchen Neutrons st�ande, wenn dieses ein ebensolches oderetwa 10mal gr�o�eres Durchdringungsverm�ogen besitzen w�urde wie ein -Strahl. : : :Also, liebe Radioaktive, pr�ufet, und richtet.|Leider kann ich nicht pers�onlich in T�ubingenerscheinen, da ich infolge eines in der Nacht vom 6. zum 7. Dez. in Z�urich statt�ndendenBalles hier unabk�ommlich bin. : : : Euer untert�anigster Diener W. Pauli1Heute Pauli'sches Ausschlie�ungsprinzip2Heute Neutrinos
Here three letters in conjunction
with the neutrino hypothesis
are shown , from
Rudolf M ossbauer, Proc. of
’Neutrino Astrophysics’ Ringberg Castle
Tegernsee 20.-24. Oct. 1997 , ed. by
M.Altmann, W. Hillebrandt, H.-T. Janka and
G. Raffelt, TU Munchen 1998 [1a] . ( → )
5
But the strong interactions gauging a nonabelian local SU2 g roupare subject of another letter , and concerning the associati on of thegauge group with isospin ( G = SU2 ) we have to say with Pauli :’ganz falsch’ , yet ... . The following letter from Wolfgang P auli toAbraham Pais, 25. July 1953, is fromK. Meyenn, ’Wolfgang Pauli, Wissenschaftlicher Briefwech sel’,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 ownideas, Harald , and leave open the eventual existence of othe rsimilar ones .
In fact it would be incomplete, not to mention here Elie Cartan. Theinterest of the latter in general relativity is documented b y a book :Elie Cartan - Albert Einstein: Letters on Absolute Parallel ism,1929-1932, Robert Debever Editor, Princeton Univ. Press. 1 979 [3a] .
The next picture shows Elie Cartan returning from a turbulent ship excursion durin g an InternationalMathematics Conference in Oslo , 1936 – from the photo album o f George P olya [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 elabor atedlater, is fine , but so enormously generalised, that the jewel srelevant for quantized gauge field theories are difficult to r ecognize.a
The next figure shall serve to put Wolfgang Pauli and Arnold So mmerfeld in perspective with your
University, the LMU in Munich. It is taken from the expositio n at the ETH library at the occasion of the
centenary of W. P., URL http://www.ethbib.ethz.ch/exhibi t/pauli/index.html/ [5a] .
aI am grateful to Raymond Stora for pointing out to me two later indirect accounts of this work , by
a) Charles Ehresmann, ’Les connexions diff erentiables dans un fibr e diff erentiable’, Colloque de Topolo-
gie (Espaces fibr es), Centre Belge de Recherches Math ematiques, Bruxelles, 5.-8. Juin 1950 [6a] , and
b) mimeographed notes of lectures by Shiing-Shen Chern, Ins titute 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 Stefa n, 1968 . →
14
Igneada, Turkey – the ’road to freedom’, 1968 [8a] . →
15
”Forces between quarks ( and antiquarks ) are mediated by gau ge bosons ...” this was your conviction
maybe related to your studies of general relativity . This br ings you into the group of physicists and
mathematicians, which I mentioned in the introduction to yo ur scientific life .
It brought you – a well conceived plan – to Aspen and later in 19 70 to the Stanford Linear Accelerator
Center in order to discuss with Murray Gell-Mann and try to in itiate 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 Me eting on the Outlook for Broken
Conformal Symmetry in Elementary Particle Physics, 4-5 May 1972, Frascati, Italy, hep-ph/0211388.
[2] Harald Fritzsch and Murray Gell-Mann (CERN) ’Current algeb ra: Quarks and what else?’,
Proceedings of 16th International Conference on High-Ener gy Physics, Batavia, Illinois, 6-13 Sep
1972, published in eConf C720906V2 (1972) 135-165, also in P hysics, Proceedings of the XVI
International Conference on High Chicago 1972 p.135 (J. D. J ackson, 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) 365-36 8.
This shall acknowledge your original and seminal contribut ion 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 nonabe lian gauge theories’ , Phys. Rev. Lett. 30
(1973) 1343 .
[7] D. Politzer, ’Reliable results for strong interactions ?’ , Phys. Rev. Lett. 30 (1973) 1346 .
µ d / d µ log“
Z3/2
3/ Z 1
”
= − b 1
g 2
16 π 2
+ O`
g 4´
b 1 =
12 − 1
3
C 2 (G ) − 4
3T 2 ( D G )
C 2 ( SUN ) = N ; tr T a ( D ) T b ( D ) = T 2 ( D ) δ ab
(1)
→
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 ine lastic 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 b ecome a research fellow at Caltech and
we resumed there a wider collaboration . First lets turn to a p aper on unified gauge-interactions, which
took more than a year to be completed :
[8] Harald Fritzsch and Peter Minkowski (Caltech), ’Unified Int eractions of Leptons and Hadrons’,
CALT-68-467, (Received Dec 1974), Annals Phys.93 (1975) 19 3-266 .
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 fou nd in the reactions
ν µ ( ν µ ) N → ν µ ( ν µ ) + hadrons(2)
in the Gargamelle bubble chamber [9] filled with freon , refini ng 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 Experim ent’, Phys.Lett.B46 (1973) 138-140 .
b) in November 1974 the joint efforts of Samuel Ting et al. at B rookhaven ,
[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, ’Dis covery of a Narrow Resonance in e+ e-
Annihilation’, SLAC-PUB-1504, Nov 1974, Phys.Rev.Lett.3 3 (1974) 1406-1408 ,
led to the discovery of (closed) charm in the form of the vecto r meson resonance J/ψ in the
reactions
p + Be → J/ψ + X → e + e − + X [10]
e + e − → J/ψ →
8
<
:
hadrons
µ + µ −
[11](3)
Furthermore the resonance was almost immediately after firs t announcements confirmed jointly
by three experimental groups extending the energy range at t he Adone facility at Frascati .→
20
On the theoretical side – without detailed quotations nor at tempt 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 re ferences therein to Chen-Ning Yang and
Robert Mills, Ryoyu Utiyama, Sheldon Glashow and Murray Gel l-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 o f baryon-number instability in such a
framework .
1974 Howard Georgi and Sheldon Glashow presented a unified ga uge theory based on the group SU5,
’Unity of All Elementary Particle Forces’ .a →
aI thank Nevena Ilieva for her thoughtful insisting on consid ering all contributions in particular
those due to Ludwig Faddeev .
20a
with Abdus Salam →
21
1974 Claudio Becchi, Alain Rouet and Raymond Stora formulat ed the algebraic anticommuting
structure at ’first ghost level’ of what became known as the BR ST formalism , T for
Igor Tyutin ( and Efim Fradkin & ) .
back to our paper : [8] ’Unified Interactions of Leptons and Ha drons’ .
One aspect , which shall be singled out here, concerned the (e ventual) role of the
gauge group SO10 ( its covering group D 5 or spin10 ) a .
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 la rgest possible group within such orthogonal
chains . This leaves unanswered – to this day – the question wh y ( 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 1 975, 329-339.b
Maybe here is a good place to remember : [14] F. Gursey, Pierr e Ramond (Yale U.),
P. Sikivie (Maryland U.), ’A Universal Gauge Theory Model Ba sed 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 Reso nances, Gluons and the Zweig Rule’,
CALT-68-492, Mar 1975, Nuovo Cim.A30 (1975) 393.
[16] ’Vector-Like Weak Currents, Massive Neutrinos, and Ne utrino Beam Oscillations’, CALT-68-525,
(Received Nov 1975), Phys.Lett.B62 (1976) 72.
In [15] a hypothesis is layed out, that the gauge-boson degre es of freedom in QCD also materialize in
resonances , with clear simplifying dynamics , to be reveale d, 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 bo ttom quark .
In [16] the theme of neutrino flavors – light and heavy – and (an ti-)neutrino oscillations is taken up and
embedded within a vectorlike form of chiral gauge interacti ons . You, Harald, were also very active in
communicating these results to Bruno Pontecorvo and beyond to convince first Felix B ohm, Peter Vogel
and collaborators at Caltech and then Robert M ossbauer, then director of the Institut Laue Langevin in
Grenoble, to perform a search for the oscillations, entaili ng a demanding precision of a possible detector
not too near to a reactor source.
The letter never arrived (according to Samoil Bilenky) and t he first oscillation experiments yielded
null-results but →
23
’Geduld bringt Rosen’ ( ’Patience brings roses’ )
from [17] S. Abe et al., KamLAND Collaboration, ’Precision M easurement of
Neutrino Oscillation Parameters with KamLAND’, Feb 2008, a rXiv:0801.4589 [hep-ex]
24
3 From Caltech becoming a Professor first in Wuppertal 1977 th en in Bern 1978
Time is (probably) getting short . Thus I select several pape rs from the above time with only short
comments possible .
[18] H. Fritzsch (Wuppertal U. & CERN) , 1978, ’Chromodynami cs’, Talk in *Singapore 1978,
Proceedings, 1978 International Meeting On Frontier Of Phy sics, Vol.2*, Singapore 1978,
1005-1042.
[19] H. Fritzsch (CERN & Wuppertal U.) , ’Weak Interaction Mi xing 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 flavore d 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 c s inside
Λ b = ( bud ) → J/ψ ( c c ) K pX , 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 th eoretical physics at the Ludwig-Maximilian
University , a chair which had been occupied (shortly) by Lud wig 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 Ins titute 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, i n Montpellier, France, beginning 1985,
chaired by Stephan Narison.
b) Symposia in Oberw olz, Styria, Austria, jointly with W. Plessas and W. Schweig er, University of Graz ,
1998, 2003, 2006 .
c) International Conferences on Flavor Physics beginning 2 001 every two years, 2007 at the Kavli
Institute for Theoretical Physics China, the Institute of T heoretical Physics (ITP), Chinese
Academy of Sciences, in Beijing, China .
d) Workshops on Flavor, 2005 in Chamonix, France and 2007 in A lbufeira, Portugal – in the Hapimag
resorts .
26
So I shall select two areas of research , which mark – but in no w ay exhaust – your important
contributions until the present
i) maximal CP violating phase in quark flavor mixing ( the CKM m atrix ) , with implications also for the
lepton sector . This idea you exposed in an original paper in 1 979 .
[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 (2 000) 1-81, hep-ph/9912358 . →
ii) are natural constants really constant ?
[23] Harald Fritzsch (Munich U.), ’The Fundamental Constan ts 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 Advance ment of Theoretical Physics’ by
the University of New South Wales, Sydney, Australia, 15. Ap ril 2008 .
27
A comment to i) above :
You point out a particular way to parametrize the CKM (also ne utrino-) mass matrix, restricting the
electroweak symmetry breaking to one (or two) doublet(s) of Higgs-scalar(s)
V CKM =
0
B
B
B
@
c u −s u 0
s u c u 0
0 0 1
1
C
C
C
A
0
B
B
B
@
e −iϕ 0 0
0 c −s
0 s c
1
C
C
C
A
0
B
B
B
@
c d −s d 0
s d c d 0
0 0 1
1
C
C
C
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
(4)
and to compare with the ( (u α) d ) × ( (u α) b ) ∗ unitary triangle or any other pair-triangle
`
V cdV∗
cb
´
−1 `
V udV∗
ub + V cdV∗
cb + V tdV∗
tb
´
= 0(5)
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]
PDG : α ≡ φ 2 =“
99 + 13
− 8
”
◦
↔ α ∼ ϕ = 90 ◦(6)
Your derivation based on a particular texture with respect t o the mass hierarchies and maximal CP
violation is not only remarkably correct but also shows an el ement 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 retire ment .
Thank you
r1
References
[1a] Rudolf M ossbauer, Proc. of ’Neutrino Astrophysics’ , RingbergCastle, Tegernsee 20.-24. Oct. 1997 , ed. by M.Altmann,W. Hillebrandt, H.-T. Janka and G. Raffelt, TU Munchen 1998 .
[2a] K. Meyenn, ’Wolfgang Pauli, Wissenschaftlicher Brief wechsel’,Band IV, Brief [1614] und Anlage zum Brief, Teil II, SpringerVerlag 1999 .
[3a] Elie Cartan - Albert Einstein: Letters on Absolute Parallel ism,1929-1932, Robert Debever Editor, Princeton Univ. Press 19 79.
[4a] George P olya, ’The P olya picture album : encounters of amathematician’ , G. L. Alexanderson ed., Birkh auser Verlag.Boston - Basel, 1987 .
r2
References
[5a] ’Wolfgang Pauli and Modern Physics’, Exhibition of theETH-Bibliothek at the occasion of the 100th birthday ofWolfgang Pauli, April 6 to May 6, 2000 in the entrance hall ofthe ETH Zurich, August 17 to September 26, 2000 at the CERNin 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 diff erentiables dans unfibr e diff erentiable’, Colloque de Topologie (Espaces fibr es),Centre Belge de Recherches Math ematiques, Bruxelles, 5.-8.Juin 1950 .
r3
References
[7a] Shiing-Shen Chern, mimeographed lecture notes , Insti tute forAdvanced Study, Princeton ∼ 1951 ( unpublished ) .
[8a] H. Fritzsch, ’Flucht aus Leipzig’, Piper Verlag Munch en - Zurich1990 .
[1] William A. Bardeen, H. Fritzsch and Murray Gell-Mann, ’L ightcone current algebra, π
0 decay, and e + e− annihilation’ ,CERN-TH-1538, May 1972, presented at Topical Meeting on theOutlook for Broken Conformal Symmetry in ElementaryParticle Physics, 4-5 May 1972, Frascati, Italy, hep-ph/02 11388 .
r4
References
[2] Harald Fritzsch and Murray Gell-Mann (CERN) ’Currentalgebra: Quarks and what else?’, Proceedings of 16thInternational 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 Internatio nalConference 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 anon-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 renormalizatio n ofYang-Mills fields and applications to particle physics, Mar seille1972 .
[6] D. J. Gross and F. Wilczek, ’Ultraviolet behaviour of non abeliangauge 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), ’UnifiedInteractions of Leptons and Hadrons’, CALT-68-467, (Recei vedDec 1974), Annals Phys.93 (1975) 193-266 .
[9] F.J. Hasert et al., Gargamelle Neutrino Collaboration,’Observation of Neutrino Like Interactions Without Muon OrElectron in the Gargamelle Neutrino Experiment’,Phys.Lett.B46 (1973) 138-140 .
[10] J.J. Aubert et al., E598 Collaboration, ’ExperimentalObservation 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, ’Dis covery ofa 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. Pete rsburg) ,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 InHigh Energy Physics*, New York 1975, 329-339.
[14] F. Gursey, Pierre Ramond (Yale U.) , P. Sikivie (Maryla nd 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 Reso nances,Gluons and the Zweig Rule’, CALT-68-492, Mar 1975, NuovoCim.A30 (1975) 393.
[16] Harald Fritzsch, Peter Minkowski (Caltech) , ’Vector- Like WeakCurrents, Massive Neutrinos, and Neutrino Beam Oscillatio ns’,CALT-68-525, (Received Nov 1975), Phys.Lett.B62 (1976) 72 .
[17] S. Abe et al., KamLAND Collaboration, ’PrecisionMeasurement of Neutrino Oscillation Parameters withKamLAND’, Feb 2008, arXiv:0801.4589 [hep-ex] .
r9
References
[18] H. Fritzsch (Wuppertal U. & CERN) , 1978, ’Chromodynami cs’,Talk in *Singapore 1978, Proceedings, 1978 InternationalMeeting On Frontier Of Physics, Vol.2*, Singapore 1978,1005-1042.
[19] H. Fritzsch (CERN & Wuppertal U.) , ’Weak Interaction Mi xingin 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 flavore dbaryons’, Print-79-0922 (BERN), (Received Nov 1979),Phys.Lett.B90 (1980) 167.
r10
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