The standard model of elementary particle physics -- as seen on television

grand unification – a simple dream



32.



grand unification – a simple dream



“



Materie ist geronnenes Licht.*

Albertus Magnus



”



Is there a common origin of the three particle interactions? We have seen in the preceding sections that the Lagrangians of the electromagnetic, the weak and the strong nuclear

interactions are determined almost uniquely by two types of requirements: to possess a

certain symmetry and to possess mathematical consistency. The search for unification of

the interactions thus requires the identification of th unified symmetry of nature. In recent decades, several candidate symmetries have fuelled the hope to achieve this program:

grand unification, supersymmetry, conformal invariance and coupling constant duality.

The first of them is conceptually the simplest.

At energies below 1000 GeV there are no contradictions between the Lagrangian of

the standard model and observation. The Lagrangian looks like a low energy approximation. It should thus be possible (attention, this a belief) to find a unifying symmetry that

contains the symmetries of the electroweak and strong interactions as subgroups and

thus as different aspects of a single, unified interaction; we can then examine the physical

properties that follow and compare them with observation. This approach, called grand

unification, attempts the unified description of all types of matter. All known elementary

particles are seen as fields which appear in a Lagrangian determined by a single symmetry

group.

Like for each gauge theory described so far, also the grand unified Lagrangian is mainly

determined by the symmetry group, the representation assignments for each particle, and

the corresponding coupling constant. A general search for the symmetry group starts

with all those (semisimple) Lie groups which contain U(1) SU(2) SU(3). The smallest

groups with these properties are SU(5), SO(10) and E(8); they are defined in Appendix D.

For each of these candidate groups, the experimental consequences of the model must be

studied and compared with experiment.

Experimental consequences



is close to the measured value of



sin2 θ W,th = 0.2

sin2 θ W,ex = 0.231(1) .



(634)



(635)



* ‘Matter is coagulated light.’ Albertus Magnus (b. c. 1192 Lauingen, d. 1280 Cologne), the most important

thinker of his time.



Copyright © Christoph Schiller November 1997–May 2006



Grand unification makes several clear experimental predictions.

Any grand unified model predicts relations between the quantum numbers of all elementary particles – quarks and leptons. As a result, grand unification explains why the

electron charge is exactly the opposite of the proton charge.

Grand unification predicts a value for the weak mixing angle θ W that is not determined

by the standard model. The predicted value,



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Ref. 956



941



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942



Ref. 959



viii inside the nucleus • 32. grand unification – a simple dream



4

MX

1

2

5

αG (M X ) M p



τp



Ref. 960



1031 1 a



(636)



where the uncertainty is due to the uncertainty of the mass M X of the gauge bosons involved and to the exact decay mechanism. Several large experiments aim to measure this

lifetime. So far, the result is simple but clear. Not a single proton decay has ever been

observed. The experiments can be summed up by

τ(p

τ(p

τ(n

τ(n



e + π0 )



¯

K + ν)



e + π− )



¯

K 0 ν)



5 ë 1033 a

1.6 ë 1033 a

5 ë 1033 a

1.7 ë 1032 a



(637)



The state of grand unification



Ref. 961



The estimates of the grand unification energy are near the Planck energy, the energy at

which gravitation starts to play a role even between elementary particles. As grand unification does not take gravity into account, for a long time there was a doubt whether something was lacking in the approach. This doubt changed into certainty when the precision

measurements of the coupling constants became available. This happened in 1991, when

* As is well known, diamond is not stable, but metastable; thus diamonds are not for ever, but coal might be,

if protons do not decay.



Copyright © Christoph Schiller November 1997–May 2006



These values are higher than the prediction by SU(5). To settle the issue definitively, one

last prediction of grand unification remains to be checked: the unification of the coupling

constants.



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All grand unified models predict the existence of magnetic monopoles, as was shown

by Gerard ’t Hooft. However, despite extensive searches, no such particles have been

found yet. Monopoles are important even if there is only one of them in the whole universe: the existence of a single monopole implies that electric charge is quantized. Grand

unification thus explains why electric charge appears in multiples of a smallest unit.

Grand unification predicts the existence of heavy intermediate vector bosons, called

X bosons. Interactions involving these bosons do not conserve baryon or lepton number,

but only the difference B − L between baryon and lepton number. To be consistent with

experiment, the X bosons must have a mass of the order of 1016 GeV.

Most spectacularly, the X bosons grand unification implies that the proton decays.

This prediction was first made by Pati and Salam in 1974. If protons decay, means that

neither coal nor diamond* – nor any other material – is for ever. Depending on the precise symmetry group, grand unification predicts that protons decay into pions, electrons,

kaons or other particles. Obviously, we know ‘in our bones’ that the proton lifetime is

rather high, otherwise we would die of leukaemia; in other words, the low level of cancer

already implies that the lifetime of the proton is larger than 1016 a.

Detailed calculations for the proton lifetime τ p using SU(5) yield the expression



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grand unification – a simple dream



943



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F I G U R E 358 The behaviour of the three coupling constants with

energy for the standard model (left) and for the minimal

supersymmetric model (right) (© Dmitri Kazakov)

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Copyright © Christoph Schiller November 1997–May 2006



these measurements were shown as Figure 358. It turned out that the SU(5) prediction of

the way the constants evolve with energy imply that the three constants do not meet at

the grand unification energy. Simple grand unification by SU(5) is thus definitively ruled

out.

This state of affairs is changed if supersymmetry is taken into account. Supersymmetry

is the low-energy effect of gravitation in the particle world. Supersymmetry predicts new

particles that change the curves at intermediate energies, so that they all meet at a grand

unification energy of about 1016 GeV. The inclusion of supersymmetry also puts the proton lifetime prediction back to a value higher (but not by much) than the present experimental bound and predicts the correct value of the mixing angle. With supersymmetry,

we can thus retain all advantages of grand unification (charge quantization, fewer parameters) without being in contradiction with experiments. The predicted particles, not

yet found, are in a region accessible to the LHC collider presently being built at CERN in

Geneva. We will explore supersymmetry later on.

Eventually, some decay and particle data will become available. Even though these

experimental results will require time and effort, a little bit of thinking shows that they

probably will be only partially useful. Grand unification started out with the idea to unify

the description of matter. But this ambitious goal cannot been achieved in this way. Grand

unification does eliminate a certain number of parameters from the Lagrangians of QCD

and QFD; on the other hand, some parameters remain, even if supersymmetry is added.

Most of all, the symmetry group must be put in from the beginning, as grand unification

cannot deduce it from a general principle.

If we look at the open points of the standard model, grand unification reduces their

number. However, grand unification only shifts the open questions of high energy physics

to the next level, while keeping them unanswered. Grand unification remains a low energy effective theory. Grand unification does not tell us what elementary particles are; the

name ‘grand unification’ is ridiculous. In fact, the story of grand unification is a first hint

that looking at higher energies using only low-energy concepts is not the way to solve the

mystery of motion. We definitively need to continue our adventure.



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944



viii inside the nucleus • 32. grand unification – a simple dream



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Copyright © Christoph Schiller November 1997–May 2006



bibliography



945



Biblio graphy

923 A excellent technical introduction to nuclear physics is B ogdan Povh, Kl aus R ith,



Christoph Scholz & Frank Zetsche, Teilchen und Kerne, Springer, 5th edition,

1999. It is also available in English translation.

One of the best introductions into particle physics is Kurt Gottfried & Victor F.

Weisskopf, Concepts of Particle Physics, Clarendon Press, Oxford, 1984. Victor Weisskopf

was one of the heroes of the field, both in theoretical research and in the management of

CERN, the particle research institution. Cited on page 897.



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924 W.C.M. Weijmar Schultz & al., Magnetic resonance imaging of male and female



genitals during coitus and female sexual arousal, British Medical Journal 319, pp. 1596–1600,

December 18, 1999, available online as http://www.bmj.com/cgi/content/full/319/7225/1596.

Cited on page 898.

925 A good overview is given by A.N. Halliday, Radioactivity, the discovery of time and the

926 An excellent summary on radiometric dating is by R. Wiens, Radiometric dating – a chris-



tian perpective, http://www.asa3.org/ASA/resources/Wiens.html. The absurd title is due to

the habit in many religious circles to put into question radiometric dating results. Apart

from the extremely few religious statements in the review, the content is well explained.

Cited on pages 910 and 919.

927 The slowness of the speed of light inside stars is due to the frequent scattering of photons



by the star matter. The most common estimate for the Sun is an escape time of 40 000 to 1

million years, but estimates between 17 000 years and 50 million years can be found in the

literature. Cited on page 921.

928 See the freely downloadable book by John Wesson, The Science of JET - The Achievements



of the Scientists and Engineers Who Worked on the Joint European Torus 1973-1999, JET

Joint Undertaking, 2000, available at http://www.jet.edfa.org/documents/wesson/wesson.

html. Cited on page 924.

929 J.D. L awson, Some criteria for a power producing thermonuclear reactor, Proceedings of



the Physical Society, London B 70, pp. 6–10, 1957. The paper had been kept secret for two

years. Cited on page 925.

930 Kendall, Friedman and Taylor received the 1990 Nobel Prize for Physics for a series of ex-



931 G. Zweig, An SU3 model for strong interaction symmetry and its breaking II, CERN Re-



port No. 8419TH. 412, February 21, 1964. Cited on page 927.

932 F. Wilczek, Getting its from bits, Nature 397, pp. 303–306, 1999. Cited on page 928.

933 For an overview of lattice QCD calculations, see ... Cited on page 928.



934 S. Strauch & al., Polarization transfer in the 4 He (e,e’p) 3 H reaction up to Q 2 = 2.6(GeV/



c)2 , Physical Review Letters 91, p. 052301, 2003. Cited on page 929.



935 The excited states of the proton and the neutron can be found in on the particle data group



website at http://pdg.web.cern.ch. Cited on page 929.



Copyright © Christoph Schiller November 1997–May 2006



periments they conducted in the years 1967 to 1973. The story is told in the three Nobel

lectures R.E. Taylor, Deep inelastic scattering: the early years, Review of Modern Physics 63, pp. 573–596, 1991, H.W. Kendall, Deep inelastic scattering: Experiments on the

proton and the observation of scaling, Review of Modern Physics 63, pp. 597–614, 1991, and

J.I. Friedman, Deep inelastic scattering: Comparisons with the quark model, Review of

Modern Physics 63, pp. 615–620, 1991. Cited on page 926.



Motion Mountain – The Adventure of Physics available free of charge at www.motionmountain.net



earliest history of the Earth, Contemporary Physics 38, pp. 103–114, 1997. Cited on page 910.



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946



viii inside the nucleus



936 An older but fascinating summary of solar physics is R. Kippenhahn, Hundert Milliarden

937



938

939



940

941



943

944



945

946

947

948

949



951



952



Copyright © Christoph Schiller November 1997–May 2006



950



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942



Sonnen, Piper, 1980. which is available also in English translation. No citations.

M. Brunetti, S. Cecchini, M. Galli, G. Giovannini & A. Pagliarin, Gammaray bursts of atmospheric origin in the MeV energy range, Geophysical Research Letters 27,

p. 1599, 1 June 2000. Cited on page 917.

A book with nuclear explosion photographs is Michael Light, 100 Suns, Jonathan Cape,

2003. Cited on page 919.

J. Dudek, A. God, N. Schunck & M. Mikiewicz, Nuclear tetrahedral symmetry:

possibly present throughout the periodic table, Physical Review Letters 88, p. 252502, 24

June 2002. Cited on page 912.

A good introduction is R. Cl ark & B. Wodsworth, A new spin on nuclei, Physics World

pp. 25–28, July 1998. Cited on page 912.

M. Nauenberg & V.F. Weisskopf, Why does the sun shine?, American Journal of Physics 46, pp. 23–31, 1978. Cited on page 916.

R.A. Alpher, H. Bethe & G. Gamow, The Origin of Chemical Elements, Physical Review 73, p. 803-804, 1948. No citations.

John Horgan, The End of Science – Facing the Limits of Knowledge in the Twilight of the

Scientific Age, Broadway Books, 1997, chapter 3, note 1. Cited on page 915.

M. Chantell, T.C. Weekes, X. Sarazin & M. Urban, Antimatter and the moon,

Nature 367, p. 25, 1994. M. Amenomori & al., Cosmic ray shadow by the moon observed

with the Tibet air shower array, Proceedings of the 23rd International Cosmic Ray Conference, Calgary 4, pp. 351–354, 1993. M. Urban & al., Nuclear Physics, Proceedings Supplement 14B, pp. 223–236, 1990. Cited on page 906.

See also C. Bernard & al., Light hadron spectrum with Kogut–Susskind quarks, Nuclear

Physics, Proceedings Supplement 73, p. 198, 1999, and references therein. Cited on page 930.

F. Abe & al., Measurement of dijet angular distributions by the collider detector at Fermilab, Physical Review Letters 77, pp. 5336–5341, 1996. Cited on page 933.

The approximation of QCD with zero mass quarks is described by F. Wilczek, Getting its

from bits, Nature 397, pp. 303–306, 1999. Cited on page 933.

F. Close, Glueballs and hybrids: new states of matter, Contemporary Physics 38, pp. 1–12,

1997. Cited on page 934.

K. Grotz & H.V. Kl apd or, Die schwache Wechselwirkung in Kern-, Teilchen- und Astrophysik, Teubner Verlag, Stuttgart, 1989. Also available in English and in several other

languages. Cited on page 938.

D. Treille, Particle physics from the Earth and from teh sky: Part II, Europhysics News

35, no. 4, 2004. Cited on page 938.

P.W. Higgs, Broken symmetries, massless particles and gauge fields, Physics Letters 12,

pp. 132–133, 1964. He then expanded the story in P.W. Higgs, Spontaneous symmetry

breakdown without massless bosons, Physical Review 145, p. 1156-1163, 1966. Higgs gives

most credit to Anderson, instead of to himself; he also mentions Brout and Englert, Guralnik, Hagen, Kibble and ‘t Hooft. Cited on page 936.

M.A. B ouchiat & C.C. B ouchiat, Weak neutral currents in atomic physics, Physics

Letters B 48, pp. 111–114, 1974. U. Amaldi, A. B öhm, L.S. Durkin, P. L angacker,

A.K. Mann, W.J. Marciano, A. Sirlin & H.H. Williams, Comprehensive analysis

of data pertaining to the weak neutral current and the intermediate-vector-boson masses,

Physical Review D 36, pp. 1385–1407, 1987. Cited on page 936.



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953 M.C. Noecker, B.P. Masterson & C.E. Wiemann, Precision measurement of parity



954

955



957



958 S.C. Bennet & C.E. Wiemann, Measurement of the 6S – 7S transition polarizability



in atomic cesium and an improved test of the standard model, Physical Review Letters 82,

pp. 2484–2487, 1999. The group has also measured the spatial distribution of the weak

charge, the so-called the anapole moment; see C.S. Wood & al., Measurement of parity

nonconservation and an anapole moment in cesium, Science 275, pp. 1759–1763, 1997. Cited

on page 936.

959 H. Jeon & M. Longo, Search for magnetic monopoles trapped in matter, Physical Review

Letters 75, pp. 1443–1447, 1995. Cited on page 942.

960 On proton decay rates, see the data of the particle data group, at http://pdg.web.cern.ch.

Cited on page 942.

961 U. Amaldi, W. de B oer & H. Fürstenau, Comparison of grand unified theories with

elektroweak and strong coupling constants measured at LEP, Physics Letters 260, pp. 447–

455, 1991. This widely cited paper is the standard reference for this issue. Cited on page 942.



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956



nonconservation in atomic cesium: a low-energy test of electroweak theory, Physical Review

Letters 61, pp. 310–313, 1988. See also D.M. Meekhof & al., High-precision measurement

of parity nonconserving optical rotation in atomic lead, Physical Review Letters 71, pp. 3442–

3445, 1993. Cited on page 936.

Rumination is studied in P. Jordan & R. de L aer Kronig, in Nature 120, p. 807, 1927.

Cited on page 939.

K.W.D. Ledingham & al., Photonuclear physics when a multiterawatt laser pulse interacts with solid targets, Physical Review Letters 84, pp. 899–902, 2000. K.W.D. Ledingham

& al., Laser-driven photo-transmutation of Iodine-129 – a long lived nuclear waste product,

Journal of Physics D: Applied Physics 36, pp. L79–L82, 2003. R.P. Singhal, K.W.D. Ledingham & P. McKenna, Nuclear physics with ultra-intense lasers – present status and future prospects, Recent Research Developments in Nuclear Physics 1, pp. 147–169, 2004. Cited

on page 940.

For the bibliographic details of the latest print version of the Review of Particle Physics, see

Appendix C. The online version can be found at http://pdg.web.cern.ch/pdg. The present

status on grand unification can also be found in the respective section of the overview. Cited

on page 941.

J. Tran Thanh Van, ed., CP violation in Particle Physics and Astrophysics, Proc. Conf.

Chateau de Bois, France, May 1989, Editions Frontières, 1990. No citations.



Copyright © Christoph Schiller November 1997–May 2006



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C h a p t e r IX



ADVANC ED QUANTUM THEORY (NOT

YET AVAI L ABLE)



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– CS – this chapter will be made available in the future – CS –



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C hap t e r X



QUANTUM PHYSIC S

IN A NUTSHELL



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Quantum theory’s essence – the l ack of the infinitely

small



Achievements in precision

Quantum theory improved the accuracy of predictions from the few – if any – digits

common in classical mechanics to the full number of digits – sometimes fourteen – that

can be measured today. The limited precision is usually not given by the inaccuracy of

theory, it is given by the measurement accuracy. In other words, the agreement is only

limited by the amount of money the experimenter is willing to spend. Table 71 shows this

in more detail.

TA B L E 71 Some comparisons between classical physics, quantum theory and experiment



O b se r va b l e



0

none



∆x∆p ħ 2

λp = 2πħ



(1 10−2 ) ħ 2

(1 10−2 ) ħ



λc = h me c



(1 10−3 ) λ



0

none



τ = ...



(1 10−2 ) τ



C o st

e st i m at e b



10 k€

10 k€

0.5 M€

20 k€



Copyright © Christoph Schiller November 1997–May 2006



Prediction

of q ua n t um

theorya



Simple motion of bodies

Indeterminacy

Wavelength of matter

beams

Tunnelling rate in alpha

decay

Compton wavelength



M e a su r e ment



C l assi c a l

prediction



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C



ompared to classical physics, quantum theory is remarkably more

omplex. The basic idea however, is simple: in nature there is a minimum

hange, or a minimum action, or again, a minimum angular momentum ħ 2.

The minimum action leads to all the strange observations made in the microscopic

domain, such as wave behaviour of matter, tunnelling, indeterminacy relations, randomness in measurements, quantization of angular momentum, pair creation, decay,

indistinguishability and particle reactions. The mathematics is often disturbingly involved. Was this part of the walk worth the effort? It was. The accuracy is excellent and

the results profound. We give an overview of both and then turn to the list of questions

that are still left open.



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