Especially, I would like to declare as a great honour for nil of us that wc arc expecting Prof.Schopper - the Director-General of CliRN to come. The question which naturally arises in cases like this one is what is our aim , when shall we say that the work has been successful? Wc shall attend lectures and discussions and shall learn a lot of new things, but I think that wc are pursueing also other more general and higher goals. Here I shall remind a sentence of Prof. Gustav Hertz - I remember at the foundation Assembly of JlNR.IIe said that earlier there were physicists - general physicists to explore the properties and the laws of the matter. The job grew more and more complicated and the physicists grew divided into experimentalists and theorists. But this division, from other point of view, is not favourable for the work because it separates the people. Wc need now experimentalists who understand the theory and theorists who know the experiment. Looking over the list of lectures I think that our school will contribute to this very desirable connection between the theorists and the experimentalists. Further I shall allow myself to point out that now our science has grown up as concrete and abstract at the same time. It is concrete because we want not only to describe qualitatively the features of the microworld - that there are particles, interactions, transmutations and so on, but we contrive to know exactly which are the values of the quantities and the shapes of the functions which characterize the investigated phenomena and processes. And our science became abstract because it investigates phenomena and processes that are very deep at the bottom of the matter (although bottom here does not exist). This situation requires precise logics, exact thinking and well posed decisive experiments. We need to know the origin of every statement and its logical connection with the other statements. It will be good our school to contribute something to such style of thinking and working. Then, having brought together here people from different countries with different social conceptions and ways of living, it seems to me that we shall have a good opportunity to exchange our ideas and ideals, and this will contribute to a better understanding between each other, to the friendship especially between young people (to whom, it is a pity, I do not belong any more) and for the preservation and strengthening of the peace on the planet what presents the most important problem before the mankind now. Let me add at the end that this corner of our Bulgaria is remarkable with its natural beauty, with its ancient historical and archeo-

Pig If we consider a polygon (n-angular) it is invariant under rotations through 2Z\z. When ft. tends to infinity, we get the invariance under an arbitrary rotation, i.e. we come to a/continuous symmetry called the U(1) invariance. Global Symmetries Global U(1) Symmetry U(1) is the group of unitary 1x1 matrices with a unit determinant, i.e. just the phase factors of the form e l A Clearly,
ao the group is Abelian. The transformation looks as follows
where is a real parameter independent of X and Q charge of cp , the generator of the transformation* The Lagrangian f - ' ' c = x<f V*cp - mlcf(p - ><?)2

is the

ie dearly invariant under U(1). It can only involve pairs f ^ The Koether current (1.2) is ( u> = l*ol >")
The complex fields components
ir>*, can be written in terms of their real

^ "

The Lagrangian (2.2) becomes
(2.3) It is invariant under the rotation

%->

For oli * ,
<'<* ( 4. C^dl >. O^'r 4>2 + =ttf, ,

4>J_- ^ - 1 ^ ,

The Hoether current then is
Hote that % and ^> are degenerate : 1= / = . Thie is a typical consequence of a symmetry, but not necessary, aa will be seen later.
Another example of invariant Lagrangiana ia
where the ourrent takes the form
Qlobal SU(2) Symmetry SU(2) is the group of unitary 2x2 matrioa minant. with a unit deter

-()= e

where the generators the Pauli matrices (&*/, 2,3)

are T = /2.

T being
Due to the nonzero commutators

[ ^ , 7 ] =

where is a totally antisymmetric tensor, = 1 , SU(2) is a non-Abelian group. , / Wt \ Consider a doublet Z of scalers ^ s | M , where </\, ere complex fields* The conjugated field is <ff= (cf+, <p*) Then the transformation of fields under (2.6) is

-i'ol*

Note that V U- i , i.e. = . The Lagrangian invariant under SU(2) looks like (2.2)
<^ = %4*n>hy - > \ ? - wq>M .

like are to

the one shown in F i g. emitted system allow
19: in the c e n t r e - o f - m a s s , t h e d e b r i s of the nucleon continue while hadronic j e t s in a real experiment i s that the d i s c u s s high q laboratory
in the d i r e c t i o n is a l l boosted
at large a n g l e. The d i f f i c u l t y the t w o - j e t to emerge. W w i l l e
in the photon d i r e c t i o n
and that Q must be l a r g e enough
p r o c e s s e s for Drell-Yan and
t w o - j e t physics o n l y.
7. DRELL-YAN PROCESSES - SUDAKOV FORM FACTORS - W-Z* PRODUCTION AT THE COLLIDER Drell-Yan processes are processes in which lepton pairs are produced (7.1) The interpretation in the framework of the parton model is that lepton pairs in
hadron-hadron c o l l i s i o n s :
originate from quark-antiquark annihilation into a virtual photon of mass Q2 (the invariant mass of the lepton pair) as illustrated in Fig. 20. These processes are very important because they probe the parton content of the hadrons and, since they are electromagnetic processes, they can realistically be predicted in perturbation theory, once the parton densities have been measured in deep inelastic scattering. Moreover, the cross-section depends on the number of colours:
&- ? *I t t iSMN* VWM
In the QCD improved parton model,

formula

in Eq. ( 7. 2 )

i s modified

by s t r o n g
i n t e r a c t i o n s , Leading logarithmic c o r r e c t i o n s change, according to the.define 0(a) the d e n s i t i e s in terms of F2 as d i s c u s s e d to the in Section

factorization order

theorem, the s c a l i n g d e n s i t i e s q(x) i n t o q ( x , Q ). N e x t - t o - l e a d i n g c o r r e c t i o n s , i f we 5, add terms of s i m p l e formula ( 7. 2 ) , analogously to what happens t o Fi ,3 i n DIS. The
r e l e v a n t 0(ot ) diagrams are shown in F i g s. a , b , c. Equation ( 7. 2 ) becomes 2 1.

s f i H s-

1 <->2
turn out to be very important cancel

2 = x.x^-S

(7.3) and a f_)
Unlike for deep i n e l a s t i c s c a t t e r i n g the n e x t - t o - l e a d i n g c o r r e c t i o n s (a f (~100X) at fixed t a r g e t and ISR e n e r g i e s , The c o r r e c t i o n s the c r o s s - s e c t i o n [ c f. Eq. ( 7. 2 ) 1.

V~ W5 GeV.

(1e26)
It is important to note that the Yukawa coupling of * and/or _ fermions with the Higgo 24~plet cannot be written down (without explicit violation of SU(5)), so that fermions cannot acquire masses of order of V To break S U ( 3 ) C X S U ( 2 ) X U ( 1 ) down to SU(3) c xU(1) EM , one has to introduce another Higgs field, some part of which is the standard Higgs doublet. The simplest choice is -plet, whose two lower components form the standard Higgs. The vacuum expectation value of the 5,-plet must be equal to

(1#27)

<i/- 150
Eqs. (1.26) and (1.28) immediately imply that there is a very serious problem with GUTs. Namely, it is very strange that the vacuum expectation values of different Higgs fields are different by many orders of magnitude. Nothing prevents Q?,- to interact with even if this interaction is absent at the tree level, it
appears due to radiative corrections. If 5 would interact with x^/, , the vacuum expectation value of 5 would be either zero or of order which would be a disaster. Therefore, extre mely careful fine tuning i s required to get <C ^ iOO GeV inatead of 10 ^ Q%\J ; this unnatural feature exists in most G T Us and raakes the whole G T idea problematic. To my opininon, no comple U te floiution to this hierarchy problem i s found yet. The fermion masses appear due to their Yukawa interactions with c. The 3U(5)-symmetry impose certain relations between the naaaes of different fermions. However, these relations are modeldepeadent, so w shall not discuss them here. e Thus, the simplest version of a GUI predicts the grand deeert: nothing new happens in between 10 and 10 ^ UeV. W shall see i n e the next section that the minimal SU(5) G T i s ruled out experimen U t a l l y , which presumably means that there i s something in the grand desert. 1.4-. Proton decay, or there must be something in the grand desert The heavy vector fields , and Y, interact with quarks, antiquaries and leptons. So, they can mediate bai'yon number non-con servation. Their interaction with fermionic *-plet has the form ^ V C A
So that the corresponding vertex has the form shown in fig.2
fig. 2 This vertex alone does not lead to the baryon number non-conservat ion. However, the interaction of X^ with 10-plet contains another piece,

/Tax; r

E < fc

(1.30)

which means that there is also a vertex of the type shown in f i g. 3 t where U. denotes antiquark. A combination of these two vertices
fig.3 leads to the proton decay as ahown in f i t :. 4. As suggested by f i . 4 ,

the dominant mode ia

p-> ^ JT.

(1.31)

An estimate for the proton lifetime i s as follows. The propagator of X boson contributes a f a c t o r Mx = $ to the amplitude, while two v e r t i c e s ,ive Q 0. The l i f e t i m e i s inverse proportional t o the amplitude squared, so i t behaves l i k e

i$> =

c~lnQ/

+- >

where Q i s a r b i t r a r y parameter running from 0 t o 3.3\. These e i g e n s t a t e s are called 9 -vacua, they are e i g e n s t a t e s of the hamiltonian and obey U /9>= e

'/0>-

<*-22>
The -parameter i s a new parameter 6f the gauge theory; since \J commutes with the hamiltonian, Q does not change during the evolution. The parameter & should be considered on the same footing as the parameters of the l a g r a n g i a n , l i k e gauge coup l i n g c o n s t a n t , lligga vacuum expectation v a l u e , e t c. 4. 2. CP-violation At a g e n e r i c value of (7 , the gauge theory does not conserve CP. To see t h i s , one notes t h a t under CP CP: so that 1) ~> A(-xl) (4.23)

and thus CP :

/1 - -/

1 I - *L>-

The l a t t e r property implies that te of C at P 60,
-vacuum i s not an eigenata-

C?: / 0 > - / - 9>

Therefore, the theory constructed above the -vacuum with QJ-Oj'Ol is not CP-invariant. It is worth pointing out again that the effects related to the 0 -vacuum structure are non-perturbative effects occuring due to the tunneling between different & -vacua. Therefore, the magnitu de of the CP-violation i s proportional to the tunneling probability. In weakly coupled theories this probability i s exponentially suppre ssed, so the CP-violation is extremely small. However, in Q D the C coupling constant is not small at large distances, so the GP-viola tion in strong interactions might be expected to be large. This i s the essence of the strong CP-problem. 4.3. Translation into (3+1) dimensions Non-Abelian theories in (3+1) dimensions share most of the r e levant properties of the model discussed above. The analogue of eq. (4.11) in four-dimensional Q D i s C
ra4c where -j are the structure constants of the gauge group Sf () * bj a 123. NQ^l i s integer for pure gauge con figurations of the gauge field (classical vacua). Configurations of the gauge field describing tunneling transitions between vacua with / = 0 and N[b~\-tl obey (cf. (4.12))
The reason is exactly the same as in sect. 4.1: the integrand of eq. (4.27) is a total derivative, (4.28)
si1-- "* * - i rfe'A A'Af'J
The reet of sects. 4.1, 4.2 is straightforwardly translated; in particular, CP is expected to be violated by strong interactions. This, of course, makes a serious problem. CP-violation is very tiny in nature. This places a strong limit on the Q -parameter

of QCD:

Q$ 10~*.

(4.29)

Therefore, an unnatural fine tuning i s required in the standard mo d e l. Furthermore, i f the bare value of 9 was aet by hand equal to zero, weak i n t e r a c t i o n s would renormaliae & to an unacceptably large value. Therefore, one should invent some mechanism, which n a t u r a l l y makes Q to be zero (or extremely small) in QCD. 4.4. A s o l u t i o n to the strong CP-problem and axion The i d e a behind a s o l u t i o n to the strong -problem i s to i n t r o duce an e x t r a c l a s s i c a l symmetry which makes quantum t h e o r i e s with d i f f e r e n t values of equivalent to each o t h e r. The simplest ver sion of t h i s idea i s r e a l i z e d i n QCD with maosless fermions. Consider a toy model, which i s Q D with a massless quark. At C the c l a s s i c a l l e v e l , the lagrangian i s i n v a r i a n t under the global a x i a l symmetry

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FiT TOP C O N T E N T IN 6 +" AK>X> 1+ EVENTS SIMULTANEOUSLY
COMBINED ELECTRON AND MUON CHANNELS raz*UAV UPPER LIMITS (W-*MJ ) Ipp-^IF X) (W-tb ) -

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DISCVJSSJQM OP RESULTS-

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fct T>RO^. Ow^OGeV)

variability

Cygnus

hinder*

of from
unserv/it lone. 11i*ri' liuve been more than a do/,eit reported observations of y-
Cygiiu* X - ' ) , a t energies raiiin# from 30 MeV to 5 OeV (iron) balloon and s a t e l l i t e s ) , 100 r>V t o 100 feV ( a i r (IMP: reported arc not C'erenkov) and J00 TeV fo 10 J'eV (extended a i r - s h o w e r s ) , Hit always consistent, and d i f f e r e n t * rials at different

phases of

t h e 4,1) hour period reported mimns

, in f i g. tng feature

3, One of the extended air-shower tliat the induced showers contained SllGUPr, WhorPflS V^ndUEed

experiment* lmr,nt

t h e putti\

conventional frwer ,

badfftfi-i/Vjuepd Hie convpntional

showers ahould cvntnin

model for Cygnu* X-3 i e a Material emitting Infra-red
neutron star and a main-sequence s t a r in a binary system as seen In P i g. 4 , from the conventional star accretes in a disc around the neutron star,
r a d i o wave, and then f a l l s on to the poles of the neutron s t a r , and / , - r a y s. the 4. hour period aysMtti, and f'e variability of is believed the to -e the o r b i t a l Is i-seiibed to

emitting

period of the M n * r y fluctuation* in the

emtslone

accretion r a t e ,
was a b i g s u r p r i s e

when two underground

proton decay experiments
evidence for a periodic ttiuon f l u x from the approximate d i r e c t i o n of Cygnus X - 3. One was the Soudan 1 experiment from w i t h i n 3* at , which reported ( F i g. 5a) an excess o f 84 i 4 3. 5 * , a 306.7* I n the ( 0. , 0. ) em"2~K "hey a l a o 20 tuofl* range of reported
the d i r e c t i o n 6 -
Cygfius X^J phases corresponding

to a flur. ~ 7*10"^

eomv evidence for an excess of p a i r s of mucins a r r i v i n g w i t h i n i hour of each o t h e r. Worrying f e a t u r e s were the f a c t a t h a t the s i n g l e signal waa v a r i a b l e i n t i m e , and did not come e x a c t l y from the d i r e c t i o n of Cygnu* X-3 (, experiment 11.39 i was N'JSEX , which r e p o r t e d a 8 * ). The other
( f i g. 5b) 30 muons above a background of ( 6 - * , a - 8 * ) i n the
0. from w i t h i n 4. J* of the c o r r e c t d i r e c t i o n
rn s e ( 0 , 7 , 0. 8 ) at

Cygmii X3 phases corresponding so f t. * f ~ $ * " * " '.
worrying f e a t u r e I n t h i s case we the f a c t t h a t the angular spread g r e a t l y exceeded those expected from angular r e s o l u t i o n ( 1 * ) and from m u l t i p l e s c a t t e r i n g ( 0. 6 * ). the d i f f e r e n c e between the Soudan 1 and NUSEX f l u x e s could perhaps be explained by t h e i r difference penetration correspond is the in of depth underground of (measured the parent in m.w.e), corresponding to differing

the onions (or

particles
producing them) which could however, atringent

to d i f f e r e n t

energy ranges. Worrying f o r both the experiments, seven n u l l reaulta, i n c l u d i n g a very experiment42' 6.

subsequent limit fro*

p r o l i f e r a t i o n of the Prejua

at a similar

d e p t h t o t h e NUSEX
experiment. For a c o m p i l a t i o n , see r i g.

If reaulta called

we abandon our completely at
sceptic!* face v a l u e ,

a moment and led

Soudan

and NUSEX particle

we are

to p o s t u l a t e

a bitarre
the- c y g n e t * 3 '. I n order f o r t h e p a r t i c l e t o have r e t a i n e d the (approximate) of by Cygnus the X-3 it must be e l e c t r i c a l l y field. neutral ao as to it have avoided quite

direction deflection

g a l a c t i c magnetic

have reached

10 -jymp-rinn

i-TTTtrnp-iTtim\

Iffri*

l.,tMiii4I

mlllll

i. u i m. 1.i.i.nnirf

lin. "

Figure 3.

a) CoMullatlon 1 ' of high-energy fluxes from Cygnue x - 3 ; b) Compilation of phases o f bigb-energy o b s e r v a t i o n s.

Neutron Srar

figure A. Sketch of the "Standard Model" for Cygnus x - 3.

long-lived: t

> (1012/y)s,
To have retained the phase coherence of the source,
must have > 10. On the other hand, t o produce the observed d i s p e r s i o n in a n g l e s o f 5 * , t h e primary c y g n e t and secondary suon energies must be small: E < 2. ) TeV and E < 250 CeV. S i n c e such low-energy muons have low penetration, they. Therefore the eygnet-nucleon provides a lower bound on the must have been produced j u s t above t h e d e t e c t o r aiimuthal angle of the NUSEX muon data also

i n t e r a c t i o n c r o s s - s e c t i o n cannot be very l a r g e , on the other hand, the dependence on c r o s s - s e c t i o n ; we conclude

<rw * 4/vlr. 396

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, y T.i. , , ,- - j , y T - - , f -. f i. f -. f

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.I.,.,

F i g u r e 5.

,40) and b) MU8EX 41) for underground muone from Evidence from a) Soudan 1 Cygnue X-3.
EXCESS MfONFL'w'X FROM CYGNL'S X-3

MB r, * I SOCDAN I SOfC

JGOTTHARD
1) Figure 6. Compilation of underground muoft measurement* and upper l i m i t s. "" * * h i.

BAJCSA.V 1MB

"NVSEX *

FRED'S

:o7. i n

fFRETuS

:O.7.OII
-ooe <o o ROCK /ESS [hg/em ] Such a p a r t i c l e i s unknown, and one might worry that i t s e x i s t e n c e i s incompatible with beam-dump not searches much lower for new neutral those particles. for These the have taken there place are at energies than deduced cygnet, many
s i m i l a r i t i e s between the beam-dump experimental s e t - u p s and Cygnue X-3, as seen in Fig. 7, and the beam-dumps aeem to c o n f l i c t with the range ( 2. ) by many order* of magnitude. association This possible conflict with could energy, evaporate but this if is the cygnet particle to pile is whose produced in with, or by the decay o f , rises steeply a more massive production upon

cross-section

speculation

- 6Cygnui -

Surface of txh

AcMlirator

1x10 g/tm 2 Beam dump

Otttcfof

,.43) Figure 7. Beam dump analogy ' for cygnet production by Cygnus X-3.
speculation. The result of this reductio the data should be disregarded. Some or all?

ad absurdun

process of taking all the
C'ygnus X-3 date completely seriously is to convince ourselves thut at least some of
2.A Supernova SN 1987a The observation of this supernova collapse waa a lucky spin-off of the proton A) of supernova collapse is as follows. A
decay experiment*. The standard theory
main-sequence star first burns Hydrogen to Helium, then Helium to Carbon, Nitrogen and Oxygen, then these to Silicon and finally Silicon to Cobalt, Nickel and iron. At each stage, the star contracts and heats up. Finally, the pressure in the central Core of ~ 1.4 Mfl is no longer large enough to resist gravity, and the core collapses within a few milliseconds. When it does, the core neutronizee via the reaction p+e" + T)+v and forms a neutron star, whose radius is a few dozen kilometers, and whose density varies between 1 and lO 14 gem -3. The binding energy of the neutron star is thermalized, giving it a characteristic temperature of a few MeV. The dominant mechanism for energy loss is neutrino emission, and the duration of this thermal the core first falls on to it, it.then bounces and forms an phase is set by the neutrino diffusion time which is a few seconds. After the material outside outgoing shock wave which blows off the outer layers of the star. This produces a gas cloud which emits radio waves, and contains relativistic electrons which emit X-rays. The gas cloud contains radioactive heavy nuclei which lead to most of the optical radiation. The most important transitions are of 5.6d and

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