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UWThPh-1984-39

GRAND UNIFIED THEORIES AND DECAY

H. W. Rupertsberger (ic^lOOOSf ) Institut für Theoretische Physik Universität Wien

Summary of a talk presented at the Conference on "Teaching Modern ", CERN, Geneva, 24 - 28 September 1984. 1

1. Main Motives for GUTs

I . Replacement of the present: standard theories of strong and electro- weak interactions corresponding to 1+(1+1) gauge theories with 3 coupling constants by one with only one . 2. Abolishment of the apparent differentiation between quarks and leptons, since looking at the present 3 generations of fundamental spin 1/2 particles they seem to come together. 3. Explanation of charge quantization, especially the relation between quark and lepton charges.

II. Facts of the Standard Models of Strong and Electroweak Interactions

The symmetries of gauge theories are in one to one correspondence to their spin 1 gauge bosons, which create the different particle transitions, representing their transformations under the assumed symmetry. The fundamental spin 1/2 particles come in 3 generations. To obtain the essential features it suffices to look at the first one only. Corresponding to their behaviour with respect to the 3 basic interactions, the 'particles' are described by their color ( for strong interactions), (electromagnetic interactions) and weak charge plus left- and right-handedness (weak interactions).

Leptons Quarks weak Kl. red green blue-» u + 1/2 .red .blue .green - 1/2

red green blue .red .green .blue UR UI UR dR dR dR and their la^t-handed 'antiparticles'. QCD: Gauge bosons are 8 massless , G, carrying color and perform­ ing transitions between the different color states of one quark. 2

Electromagnet ism: is the , y> allowing transitions between the states of one electrically charged particle. Weak Interactions: Gauge bosons are W~, transforming left-handed into and left-handed u-quarks into left-handed d-quarks of the same color and the Z , which transforms a particle state into a state of the same parti'.le, but acting with different strength on right- and left-h. nded 'particles'. Noie: At low energies left-handed neutrinos are quite different from left- handed electrons, as are u- and d-quarks, therefore the corresponding ± gauge symmetry of the standard model is broken, leading to massive W and Z gauge bosons. Their masses determine the scale of symmetry break­ ing.

III. SU(5) as a Special GUT

The dependence of the 3 effective coupling constants of the standard model on energy predicts the possibility . f only one coupling constant at an energy of about My = 1015 GeV/c2. In a unified theory of strong and elnctroweak interactions all 12 gauge bosons have to be considered simultaneously at the same level. They must interact with fundamental spin 1/2 particles such that all interactions are present. The necessary minimal set of particles fulfilling this and having total electric charge zero, for charge quantization, is given by

, .red .green .blue +-. , .., . , , , ^ . j _. (d d° d ,e v ) and a similar quintuplet for left-hande c d e K 'antiparticles'.

To unify one has to treat all these 5 'particles' at the same level, which means one can perform rotations in this 5-dimensional comp)ex space. The corresponding symmetry is SU(5), the complex generalization of proper rotations in a 5-dimensional real space. Since the resulting theory should be a gauge theory, in complete agreement with this symmetry one obtains now 24 gauge bosons, representing the different interactions and allow­ ing transitions between all 5 'particles' (one would expect 25 gauge T

bosons for the 5x5 • 25 possible transitions, but one such boson inter­ acts with all particles in the same way and is therefore excluded, lead­ ing to SU(5) instead of a U(5) symmetry). 12 of the gauge bosons are just the old ones, 12 new, 'exotic' ones, X, create transitions between leptons and quarks, thus their fundamental difference is abolished. The X-bosons carry color, electric and weak charge according to the created transitions, that is

/<

+colo r Tred >'-

* Yred \X-4/3,-l/2

„,, c ,_ „red „green „blue „red „green „blue , _, . Therefore one has X ,,. X_,.- X_A/3X _I/3 X-I/3 X-I/3 and their anti- particles as new gauge bosons. Concerning color, electric and weak charge numbers, each of the remaining 'particles' can be uniquely represented by two 'particles' of one quintuplet, for example

.red .red V d e,R L

7 n > .red VR dR

Taking an antisymmetric combination the action of the 24 gauge bosons on the remaining 20 'particles' is now uniquely defined by their "2-particle" representatives. They are thus divided into two decuplets, 4

. red green blue .red .green .blue + red green blue, (u u* u d d" d ,e ,u u° u )

. red green blue .red .green .blue - red green blue, (u u* u d d d ,e ,u u° u ) , K with the gauge bosons; allowing transitions within a multiplet. Again, since at present energies quarks and leptons are quite diffe­ rent, this additional symmetry must be broken, resulting in massive X- bosons. Their mass is expected to be M„ = 1015 GeV/c2, due to the energy dependence of the effective coupling constants. The different GUTs arc: obtained by choosing different multiplets for the fundamental spin 1/2 particles, even introducing new ones, thus using different symmetries.

IV. Proton Decay in SU(5)

Proton stability is guaranteed by the concept of baryon number con­ servation. X-bosons violate this concept and lead to proton decay. A typical decay induced by the exchange of such a boson is given by

+ eR .red dR

I xred green ^ -4/3 blue y 1 y blue v d

which contributes to the decay p •+ e + ir . Of course, bound may now decay similarly, for example, n •*• V + TT , e The lifetime of the proton depends critically on the mass of the exchanged particle, the higher the mass the less probable is the decay. The calculation gives 5

T -v MJ/M4 = 1031 ys for H^ » I015 GeV/c2 .

(This is an upper limit for the most simple SU(5) model and is a too low value for already existing experimental data.)

V. A Typical Proton Decay Experiment

To observe a decay with this large lifetime one has to look at a large number of nuckons at the „ame time, k typical experiment is the I_rvine-Michigan-Brookhaven (IBM) experiment at the Morton Salt Mine in Ohio. 3300 tons of water are observed and one looks for the Cerenkov radiation of the proton decay products with 2048 phototubes at the 'walls' of the water. Expected are about 200 nucleon decays/year with the above proton lifetime. One has looked through 204 days for nucleon decays in this experiment up to July 1984. The result was among others

i(p -+ e IT ) >_ 2-1032 ys and 3 possible candidates for proton decay. 6 4

References

G. 't Hooft, Gauge Theories of the Forces between Elementary Particles, Scient. Am. 242/6 (1980) 90. H. Georgi, A Unified Theory of Elementary Particles and Forces, Scient. Am. 244/4 (1981) 40. H. Georgi and S.L. Glashov, Unified Theory of Forces, Phys. Today, Sept. 1980, 30. S. Weinberg, The Decay of the Proton, Scient. Am. 244/6 (1981) 52. E. Fiorini, Nucleon Decay Experiments, in "1983 Int. Symp. on Lepton and Photon Interactions at High Energies", edited by D.G. Cassel and D.L. Kreinick, F.R. Newman Lab. of Nucl. Stud., Cornell University, Ithaca, N.Y., 1983, p. 405. H. Fritzsch, Quarks, Piper, München, 6. Aufl., 1984. P. Langacker, Grand Unified Theories and Proton Decay, Phys. Rep. 72/4 (1981) 187.