Sn

1
Od osmeré cesty ke kvarkovému modelu a kvantové
chromodynamice
http//www-hep2.fzu.cz/chyla/lectures/kvarky_hist
orie.ppt

• Shrnutí dnešního stavu
• Nenápadný zacátek Yang a Mills
• Osmerá cesta Neeman a Gell-Mann
• Kvarkový model Zweig a Gell-Mann
• Barevné kvarky Greenberg a Nambu
• Kvantová chromodynamika Gross, Wilczek, Politzer

Tri nejvlivnejší práce nebyly casopisecky
publikovány!
M. Gell-Mann The eightfold way a theory of
strong interaction symmetry G. Zweig An SU(3)
model for strong interaction symmetry and its
breaking Y. Nambu A systematics of hadrons in
subnuclear physics
http//www-hep2.fzu.cz/chyla/sec7
Jsou na
2
Základní dnešní znalosti zákonu mikrosveta jsou
shrnuty ve standardním
modelu Podle nej jsou základními stavebními
kameny hmoty tri generace základních
fermionu tj. cástic se spinem 1/2, jež se dále
delí na kvarky a leptony
3
Vše nasvedcuje tomu, že na rozdíl od leptonu
kvarky v prírode neexistují jako volné cástice
ale vždy jen uvnitr cástic, jako jsou protony a
neutrony.
Experimentální data lze pochopit jen za
predpokládu, že
hadrony jsou bezbarvé kombinace kvarku.
4
Síly mezi kvarky a leptony
gravitacní elektromagnetické slabé silné.
Mají spolecnou charakteristiku lze je popsat
pomocí výmeny zprostredkujících cástic se spinem
1, tzv.
intermediální vektorové bosony (IVB)
5
Silné síly

• základní vlastnosti
• pusobí jen na barevné cástice tj. kvarky i
  gluony
• gluony interagují sami se sebou
• jsou invariantní vuci zámenám
• vpravo ? vlevo a
• cástice ? anticástice
• mají velmi neobvyklé chování na velkých
  vzdálenostech
• jsou popsány kvantovou chromodynamikou (QCD)

6
Síly jako celek tedy

• nejsou invariantní vuci prostorové inversi (P)
• nejsou invariantní vuci nábojové inverzi (C)
• ani vuci kombinované inverzi CP
• ale nemení kvarky na leptony

Narušení P, C a hlavne CP invariance bylo
zpocátku nevítané, nebot fyzikové ocekávali, že
prírodní zákony jsou vuci temto prirozeným
symetriím invariantní i v mikrosvete.
Dnes se jasné, že práve narušení CP invariance
sil v mikro- svete vdecíme za naši existenci,
nebot bez nej by se vesmír nemohl vyvinout do
dnešní podoby.
7
efektivní barevný náboj
Potenciál mezi kvarky
8
Duvod, proc nelze proton ionizovat jako atom
vodíku je dusledkem pozoruhodných vlastností
barevných sil pusobících mezi kvarky
výsledkem vyrážení kvarku z protonu je úhlove
kolimovaná sprška cástic (piony, kaony,
nukleony..) nazývaná jet.
9
Proc se nám zdají být ruzné síly tak rozdílne
silné?
Protože je porovnáme na vzdálenostech mnohem
vetších než je polomer protonu,tj. rp10-13 cm.
Na vzdálenostech cca rlt0.001 rp jsou
elektromagnetické, silné a slabé síly skoro
stejne velké.
Této vzdálenosti odpovídají energie MEW 100
GeV
10
Nenápadný zacátek
11
starting point isotopic dublet of nucleons
17. 12. 2009
11
12
tento požadavek je vedl na následující hustotu
Lagrangiánu
dnešní vektorové mesony
Tri elektricky nabití kalibracní bosony a jejich
samointerakce z tohoto tvaru automaticky vyplynuly
Kvanta pole b mají spin jedna a isospin také
jedna. Také známe jejich elektrické náboje,
protože všechny interakce, které navrhujeme,
splnují zákon zachování elektrického náboje, jenž
platí presne.
17. 12. 2009
12
Sto let od narození Václava Votruby
13
ale otázka jejich hmotnosti zustala otevrená
We next come to the question of the mass of the
b-quantum, to which we do not have a satisfactory
answer. One may argue that without a nucleon
field the lagrangian would contain no quantity of
the dimension of a mass and that therefore the
mass of the b-quantum in such a case is zero. The
argument is how- ever subject to the criticism
that, like all field theories, the b-field is
beset with divergences and dimensional arguments
are not sarisfactory.
b
b
hmotnost kalibracního bosonu je urcena úplným
propagátorem
a YM vážne uvažovali možnost, že kalibracní
bosony budou mít nenulovou hmotnost
A conclusion about the mass of the b-quantum is
of course very important in deciding whether the
proposal of the existen- ce of the b-field is
consistent with experimental information.
17. 12. 2009
13
Sto let od narození Václava Votruby
14
Osmerá cesta
15
Osmerá cesta podle Y. Neemana
16
Jasne a jednoznacne napsaná práce, v níž je
kalibracní teorie silných interakcí, v níž je
puvodní teorie Yanga a Millse rozšírena na grupu
vnitrní symetrie SU(3).
Baryony se spinem ½ a pseudoskalární mezony jsou
zarazeny do oktetu grupy SU(3) a je predpovezena
existence oktetu vektorových mezonu, které v té
dobe ješte nebyly známy.
17
Osmerá cesta podle M. Gell-Manna
MGMs preprint
is truly remarkable for clarity with which the
idea is presented.
18
The vector mesons are introduced in a very
natural way, by extension of the the gauge
principle of Yang and Mills. Here we have a
supermultiplet of eight mesons. In the limit of
unitary symmetry we have completely
gauge-invariant and minimal theory like
electromagnetism.
and on another place
Now the vector mesons themselves carry F spin and
there- fore contribute to the current which is
their source. The prob- lem of constructing a
nonlinear theory of this kind has been
completely solved in the case of isotopis spin
by Yang and Mills and by Shaw. We have only to
generalize their result (for three vector
mesons) to the case of F spin and eight vector
mesons.
19
leptons played the role of quarks
gauge transformations on all particles involved
20
full Yang-Mills Lagrangian written out
unique coupling
noting that
There are trilinear and quadrilinear
interactions amongst the vector mesons, as usual
...
But this preprint has never been published!!
21
instead we find in Symmetries of Baryons and
Mesons
In Section VIII we propose, as an alternative to
the symmetrical Sakata model, another scheme with
the same group, which we call eightfold way''.
Here the baryons, as well as mesons, can form
octets and singlets, and the baryons N, ?, ? and
? are supposed to constitute an approximately
degenerate octet. Nowhere does our work conflict
with the program of the Chew et al. of dynamical
calculation of the S-matrix from strong
interactions using dispersion relations. If
there are no fundamental fields . all baryons
and mesons being bound or resonant states of one
another, models like Sakata will fail the
symmetry properties we have abstracted can still
be correct, however.
Remarkably, this paper does not mention the gauge
principle and does not refer to Yang-Mills paper
at all!
22
S-maticová teorie a bootstrap teorie všeho?
From G. Chew S-Matrix Theory, (W.A. Benjamin
Inc, 1963).
I believe the conventional association of fields
with strong interacting particles to be empty. It
seems to me that no aspect of strong interactions
has been clarified by the field concept. Whatever
success theory has achieved in this area is based
on the unitarity of the analytically continued
S-matrix plus symmetry principles.
I do not wish to assert (as does Landau) that
conventional field theory is necessarily wrong,
but only that it is sterile with respect to the
strong interactions and that, like an old
soldier, it is destined not to die but just to
fade away The notion, inherent in conventional
Lagrangian field theory, that certain particles
are fundamental while others are complex, is
becoming less and less palatable
23
1961 rok objevu vektorových mezonu
proceeding as quasi two-body process
followed by ? in May, F in July and ? in August
1961
24
Elementární cástice známé v polovine roku 1962

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Tyy
Objevy techto dvou cástic byly oznámeny v léte
1962 na konferenci v Ženeve
28
na základe této zprávy na konferenci v Ženeve
tuto cástici predpovedeli Gell-Mann i Neeman
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Historie kvarkového modelu
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Predchudci kvarkového modelu
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Sakatuv model
Proton, neutron a Lambda jsou základní cástice,
ostatní jsou jejich kombinacemi.
34
Dva zásadne odlišné pohledy na roli
kvarku Gell-Mann pomocné matematické objekty
Zweig a Nambu fyzikální objekty
35
Kvarkový model podle Zweiga
36
Both mesons and baryons are constructed from a
set of three fundamental particles, called aces.
Each ace carries baryon number 1/3 and is
fractionally charged. SU(3) is adopted as a
higher symmetry for the strong inte-
interactions. Extensive space-time and group
theoretic structure is then predicted for both
mesons and baryons An experimental search for
the aces is suggested.
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Grafické znázornení vlnových funkcí baryonového
oktetu
39
Zweigova cesta ke konstituentum hadronu zacala
snahou pochopit rozpady f mezonu
Proc se rozpadá dominantne na a ne na piony?
Zweig protože je složen z páru podivných kvarku
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Zweigovo pravidlo
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Kvarkový model podle Gell-Manna



43
Pentakvarky!
44

poprení kalibracní teorie
45
MGMs view of the role of quarks (Physics 1
(1964), 63)
In order to obtain such relations that we
conjecture to be true, we use the method of
abstraction from a Lagrangian field theory model.
In other words, we construct a mathematical
theory of the strongly interacting particles,
which may or may not have anything to do
with reality, find suitable algebraic relations
that hold in the model, postulate their validity
and then throw away the
model. We may compare this process to a method
some-times employed in French cuisine a piece of
phea-sant meat is cooked between two slices of
veal, which are then
discarded.
46
Gell-Mann on quarks (summer 1967)
The idea that mesons and baryons are made
primarily of quarks is difficult to believe,
since we know that, in the sense of dispersion
theory, they are mostly, if not entirely, made up
out of one another. The probability that a meson
consists of a real quark pair rather than two
mesons or a baryon and antibaryon must be quite
small. Thus it seems to me that whether or not
real quarks exist, the q or q we have been
talking about are mathematical entities ......
If the mesons and baryons are made of
mathematical quarks, then the quark model may
perfectly well be compatible with bootstrap
hypothesis, that hadrons are made up out of one
another.
47
In 1972 quarks were still not taken seriously
In Summer 1972 Gell-Mann and Fritzsch presented
their view at XVI ICHEP in Chicago in a
contribution called
Current Algebra Quarks and What Else?
We assume here that quarks do not have real
counterparts that are detectable in isolation in
the laboratory they are supposed to be
permanently bound inside mesons and baryons
.........It might be a convenience
to abstract quark operators themselves, or other
nonsinglets with respect to color, , but it
is not a necessity. It may not even be much of a
convenience
since we would .... be discussing a fictitious
spectrum for each fictitious sector of Hilbert
space, and
we probably dont want to load ourselves with so
much spurious information.
48
Their hope that
We might eventually abstract from the quark
vectorgluon field theory model enough algebraic
information about the color singlet operators in
the model to describe all the degrees of freedom
that are present.
and thus
We would have a complete theory of the hadrons
and their currents, and we need never mention any
operators other than color singlets.

• has not been born out by further theoretical
  developments and experimental results, in
  particular those on
• heavy quarkonia spectra and
• jet phenomena

tj. kvarky podle Zweiga
which require that we treat quarks and gluons in
the same way as leptons and basically forget
about confinement.
49
Confinement consequence or source of nuclear
democracy?
M. Gell-Mann at 1992 ICHEP
I was reflecting that if those objects (i.e.
quarks) could not emerge to be seen
individually, then all observable hadrons could
still have integral charge and also the principle
of nuclear democracy could be preserved
unchanged for observable hadrons. With this
proviso, the scheme appealed to me.
For MGM nuclear democracy was fundamental
principle of strong interactions and confinement
its consequence
Since I was always convinced that quarks would
not emerge to be observed as single particles
(real quarks), I never paid much attention to
the Hahn-Nambu model in which their emergence was
supposed to be made possible by giving them
integral charges.
50
Slepá ulicka kvarky s celocíselnými náboji
51
Barevné kvarky
Existence dekupletu baryonu se spinem 3/2 a
magnetické momenty baryonu se spinem ½
vyžadovaly, aby vlnové funkce všech techto
baryonu byly plne symetrické vuci permutacím
poradí kvarku, v rozporu s Pauliho
principem. Gell-Mann nevadí, kvarky nejsou
reálné Sacharov prostorová cást vlnové funkce
antisymetrická Greenberg (1964) kvarky jako
parafermiony rádu 3 Nambu (1965) každý kvark
dané vune existuje ve trech
ruzných stavech, Paisem nazvaných barvy
1985 Erice Summer School).
52
While for most of theorists color was introduced
to solve the quark statistics problem
Nambu had used it since early 1965 as a dynamical
variable generating the force between quarks,
assuming furthermore that the force between
colored quarks is due to the exchange of octet
of colored gauge bosons, which induce the
effective four quark coupling of the type
and lead to (potentially infinite) gap between
colorless and colored states.
In this way his model contained all essential
elements of QCD, except that it was not Quantum
Field Theory.
53
Y. Nambu Preludes in theoretical physics, eds.
A. de-Shalit, H. Feschbach, L. van Hove, North
Holland Amsterdam 1966, p.133 Text z ledna 1965
Triplety míní kvarky, navazuje na referenci 3)
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Color as a dynamical variable
Nambus model has been resurrected and cast into
modern langu-age by Lipkin shortly after the
discovery of asymptotic freedom.
The color part of the interaction between pairs
of quarks is assu-med to have form analogous to
isospin-isospin interaction term
implying the following form of interaction energy

where C stands for quadratic Casimir operator
The total mass of a system of n colored quarks,
each of large mass Mq equals
Assuming Mqcv/2, we finally get
i.e. only color singlet states have zero (small)
mass, whereas all color non-singlet ones have
masses of the order of Mq and cannot thus be
observed!
56
Nambu netrval na úplném uvez- není kvarku, jen na
mezere mezi základním stavem (singletem) a
excitacemi. Kvarky tedy mohly existovat jako
volné cástice. Tesne pred objevem J/?
inter- pretoval data o rustu R jako svedectví o
produkci barevných stavu
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Reakce na data o rustu R volné kvarky
produkovány
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1977 volné kvarky objeveny po druhé!!
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A co bylo dále? Nic!
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Vzestup a pád pentakvarku
The Year of
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Pentakvarky o dva roky pozdeji
CLAS at JLAB
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Kvantová chromodynamika
64
D. Gross QFT must be destroyed!
I decided, quite deliberately, to prove that
local field theory could not explain the
experimental fact of scaling and thus was not an
appropriate framework for the description of the
strong interactions. Thus, deep inelastic
scattering would finally settle the issue as to
the validity of quantum field theory. The plan of
the attack was twofold.
First, I would prove that ultraviolet
stability, the vanishing of the efective
coupling at short distances, later called
asymptotic freedom, was necessary to explain
scaling.
65
Second, I would show that there existed no
asymptotically free field theories. The latter
was to be expected. After all the paradigm of
quantum field theory QED- was infrared stable
in other words, the efective charge grew larger
at short distances and no one had ever
constructed a theory in which the opposite
occurred
Together with Frank Wilczek they succeeded in the
first step, but failed in the second because
Nonabelian gauge theories have turned out to be
(under certain circumstances) asymptotically
free!
D. Gross For me the discovery of asymptotic
freedom was totally unexpected. . Field theory
was not wrong, instead scaling must be explained
by an asymptotically free gauge theory of the
strong interactions.
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