THE AND BEYOND: A descriptive account of fundamental and the quest for the unification of their interactions.

Mesgun Sebhatu ([email protected]) ∗ Department of Chemistry, Physics and Geology Winthrop University, Rock Hill SC 29733

Abstract fundamental interactions|gravity, electroweak, and the strong nuclear|into one. This will be In the last three decades, signiflcant progress has equivalent to having a complete theory of every- been made in the identiflcation of fundamental thing (TOE). Currently, a contender for a TOE particles and the uniflcation of their interactions. is the so called superstring theory. The theoret- This remarkable result is summarized by what ical extensions of the Standard Model and the is confldently called the Standard Model (SM). experimental tests of their predictions is likely This paper presents a descriptive account of the to engage high energy physicists of the 21st cen- Standard Model and its possible extensions. Ac- tury. cording to SM, all in the universe is made up of a dozen |six and six lep- tons. The quarks and interact by ex- 1 HISTORICAL INTRO- changing a dozen gauge (|one) | DUCTION eight and four electroweak bosons. The Standard Model provides a framework for the Our job in physics is to see things sim- uniflcation of the electroweak and strong nu- ply, to understand a great many com- clear forces. A major deflciency of the Standard plicated phenomena in a unifled way, in Model is its exclusion of gravity. The ultimate terms of a few simple principles. Steven goal of high energy physics is to unify all the Weinberg 1

∗This article is based on a module (M305) written for the PHYSNET/CUPLE project. The author is grateful The development of the Standard Model of par- to Michigan State University for awarding him a King— ticle physics may be the best example for the Chavez—Parks Visiting Professorship and to Winthrop major goal of physics|simpliflcation and uni- University for granting him a sabbatical leave during the 1991-92 academic year. He would also like to thank Pro- 1S. Weinberg, Rev. of Mod. Phys.,“Conceptual Foun- fessor Peter Signell for his hospitality at MSU and for en- dations of the Unified Theory of Weak and Electromag- couraging him to participate in the PHYSNET/CUPLE netic Interactions”, 52, 515 (1980). This is the first sen- project. tence of his Nobel lecture.

1 flcation of seemingly diverse and complicated spin = 2. Figure 1a shows a 2nd order Feynman natural phenomena. The Standard Model can diagram of two masses m1 and m2 interacting account for all atomic, nuclear, and subnuclear via a (¡) exchange. phenomena in terms of a dozen fermions and a dozen bosons. Once the model is extended to in- 1.2 Electromagnetism clude gravity, it will be possible, at least in prin- ciple, to explain all phenomena in the universe Prior to the 18th century, magnetic and electrical as a consequence of a single fundamental inter- forces were regarded as unrelated entities. Af- action. i.e., One will have a theory of everything ter Oersted (1819) discovered by accident that a (TOE). To appreciate the Standard Model, we current carrying wire deected a magnetic com- need to start with a brief historical background pass needle, a series of experiments in the 1820s, of the four (three after 1967) fundamental forces by Faraday and independently by Henry showed - Gravity, Electromagnetism, the Weak Nuclear a change in a magnetic fleld creates an elec- force and the Strong Nuclear force. tric fleld. In addition, Ampere was able to con- clude that an electric current loop of molecular 1.1 Gravity (atomic) size was the basis for all magnetism. The intimate relationship between electric and The flrst fundamental force (interaction) to be magnetic forces culminated in the development deflned accurately was gravity. This was ac- of electromagnetic theory by Clerk Maxwell in complished by Isaac Newton in the 17th century 1879. Maxwell’s electromagnetic theory pro- when he stated his universal gravitational law in vides a complete uniflcation of electricity and his Principa. Using his law, Newton was able magnetism{electromagnetism. This is the flrst to show that the force of gravity was responsi- example of a uniflcation of forces. At any point ble for motions of planets around the sun as well in space a change in electric fleld (force per unit as for projectile motion on the earth’s surface. charge) is compensated force by a corresponding This was a revolutionary achievement since ce- change in magnetic fleld. This is characteristic of lestial and terrestrial motions were believed to vector flelds called gauge flelds were local sym- be caused by two difierent forces2 His gravita- metry is preserved via a compensating change tional law was reflned by Albert Einstein in 1916 in the fleld components. A relativistic quantum (almost three centuries later). According to Ein- theory (quantum fleld theory) version of electro- stein’s general theory of relativity, gravity results magnetic theory was developed mainly by Feyn- form the curvature of space-time due to the pres- man, Schwinger, and Tomonaga in the 1940s. It ence of mass (or energy). There is now a con- is called quantum electrodynamics (QED). It is certed efiort to develop the quantum theory of a theory unprecedented for its precise determi- gravity. In the quantum theory formalism, the nation of observable quantities. Besides being gravitational interaction is a consequence of the the flrst example of uniflcation of forces and a exchange of -a massless with prototype gauge theory, electromagnetism is the

2 interaction responsible for all atomic, molecular, Before Newton. it was believed that heavenly bodies were governed by celestial gravity and free fall and pro- and hence biochemical phenomena. In the lan- jectile motion on earth were caused by terrestrial gravity. guage of quantum fleld theory, the electromag-

2 netic interaction is mediated by a massless gauge interactions. (spin{one) |the (γ) and can be represented by the second order (two vertices) 1.4 The Strong Nuclear Force Feynman diagram. Figure 1b represents 2nd or- der Feynman diagram for { (ep) The was discovered in 1932. This meant scattering. Despite the similarity between Fig- that the nucleus is made up of and neu- ures 1a and 1b, and the similarity between the trons (). Using the then known forces, formulas for the Newton’s gravitational law and primarily the electromagnetic force, it was im- Coulomb’s law, uniflcation of these two forces is possible to account for the stability of nuclei. still a di–cult task. Einstein devoted his last The electromagnetic force would, in fact, push thirty years to unify these two forces without protons violently apart. This paved the way much success. Now, superstring theory is a con- for Yukawa (1935) to suggest a short ranged tender for unifying all the forces. strong nuclear force. The strong nuclear force overcomes the electromagnetic repulsion inside the nucleus and binds nuclei. A short ranged 1.3 The Weak Nuclear Force force requires the exchange of a massive particle. In 1930, Pauli postulated that a massless spin- Yukawa, therefore, predicted the mediator of the 1/2 particle called the 3 must accom- strong nuclear force - the with a mass of pany the emission of the β particle by the nucleus approximately 140MeV . It follows from the un- (more speciflcally by the neutron) if energy, mo- certainty principle (¢t¢E ≥ „h) that the range ' ' „h mentum, and spin statistics are to be conserved, of the strong nuclear force (R c¢t mπc ) Four years later, Fermi (1934) developed the flrst is 1.4 × 10−15m. Feynman diagrams for the quantum theory of weak interaction. This is interaction of nucleons via the exchange of pi- known in the literature as the four{Fermi inter- ons are shown in Figure 3. Besides the pion(s), action. As shown in Figure 2, the interaction many other have been discovered and is represented by a product of four flelds at a continue to be discovered. The Yukawa approach single vertex (a point). Fermi’s theory is still a has been used to develop two- interac- good approximation (up to 100 GeV). According tion models by utilizing various mesons 4 Even to Heisenberg’s uncertainty principle, a point in- 4 Yukawa’s approach lead to the derivation of a one- teraction implies the exchange of a particle of in- pion exchange NN potential (OPEP). Modern NN poten- flnite mass. This was considered unrealistic and tials are based on the exchange of various bosons and was later remedied by Klein (1938) who intro- hence are called OBEPs. Even though they fit world NN duced heavy quanta of spin-one (now known as data below 350 MeV very well, they utilize too many pa- ± ◦ rameters (form factors, coupling constants and masses of ). Figures 2a and 2b display the bosons). Like the original Yukawa OPEP, OBEPs Feynman diagrams for β decay as a four-Fermi are based on linear field theory. When the linear pion (point interaction) and as a W bosons exchange field theory is replaced by a nonlinear field (a solitary wave) theory, a new class of NN potentials (Solitary 3Neitrinos were detected at the Savannah River Labs Wave Exchange Potentials-SWEPs) emerge. SWEPs fit in S. Carolina by Cowan and Reines in the 1950s. For a NN data with a minimum number of parameters. For detailed review of the 1950s neutrino search experiments, a sample SWEP and related papers, retrieve the e-print see Science 203, 1979. xxx.lanl.gov/abs/nucl-th/9409015.

3 4 though the approach is useful at low energy, group theory, and evaluation of complicated in- it is now believed that {exchange forces tegrals related to Feynman diagrams. Our objec- are a manifestation of a more fundamental force tive in this article is to provide a descriptive ac- called the strong color force. In analogy with count of the development of the Standard Model quantum electrodynamics (QED), a theory of with emphasis on the uniflcation framework it strong interactions based on quarks and color ex- provides at the moment and the directions it may change called quantum chromodynamics (QCD) suggest for its future theoretical extensions and has been developed. their experimental tests.

2.1 Symmetry 2 THE STANDARD MODEL Symmetry plays a central, unifying, and sim- In 1979, exactly a century after the uniflcation plifying role in physics. Symmetry implies in- of electricity and magnetism by Maxwell, Steven variance. All the conservation laws of physics Weinberg, Abdus Salam, and Sheldon Glashow are principles of invariance. For example, trans- were awarded the Nobel prize for the uniflcation lational and rotational invariance lead to the of electromagnetic and weak interactions. The conservation of linear and angular momentum electroweak theory they developed predicted the respectively. Symmetry such as that related masses of the W ±, and Z◦ bosons to be about 80 to translational and rotational invariance is ex- GeV and 90 GeV respectively 5. In 1983, physi- pressed by a set of transformations rules that cists at CERN (an European Organization for constitute a mathematical group. Transforma- Nuclear Research) led by Carlo Rubia were able tions of internal symmetries such as the inter- to produce and measure the masses of the W and change of color and avor of quarks can also be Z bosons. The measured masses were in com- described using group theory. "Special Unitary" plete agreement with the predictions of the elec- group represented by a set of 3×3 matrices called troweak theory. The fact that the electroweak SU(3), were used to describe the symmetry of theory was recognized by a Nobel prize before three- (uds) avors. SU(3) is mow used in the W and Z bosons were discovered demon- QCD to represent the symmetry of three-quark strates the confldence the physics community colors(RGB). Similarly, SU(2) can be used to had for it. The electroweak theory is the central describe isospin doublets that interact via the piece of the Standard Model. The incorporation weak interaction. The simplest group is a one- of the symmetry describing the strong force to dimensional unitarity group called U(1. It is the that representing electroweak theory constitutes symmetry associated with QED. QED involves the Standard Model of particles and their inter- one the photon (γ) and a conserved actions. A quantitative description of the Stan- quantity|the total electrical charge (Q). U(1) dard Model can involve quantum fleld theory, is analogous to the symmetry exhibited by a cir-

5 cle rotating on an axis perpendicular to its cen- See e.g. Abdus Salam,“Gauge Unification of Fun- ter. In the language of group theory, the product damental Forces”, Rev. of Mod. Phys. 52, 531 (1980). He gives the range of values MW 77 84 GeV and SU(3)×SU(2)×U(1), represents the underlying ' − MZ 89 95 GeV. symmetry of the Standard Model. This is equiv- ' −

5 alent to saying that the Standard Model incorpo- neutron are isospin doublets that are indistin- rates the electroweak theory that is represented guishable by the strong nuclear force. An isospin by SU(2) × U1) and QCD which is represented group with two members satisfles a symmetry by SU(3). representation|matrix theory called SU(2). SU stand for \Special Unitary". In general we can have SU(N) for N - multiplets. For any SU(N) 2.2 Constituents and Mediators of with N > 1 there are N 2 − 1 gauge bosons. the Standard Model Consequently, for the weakly interacting weak According to the Standard Model, all mat- isospin group SU(2), there must be three gauge bosons. Tentatively these can be identifled as ter in the universe is made up of a dozen + − ◦ fermions| six quarks (u, d, s, c, b, t) and six lep- the weak isovector triplet - W , W , and W bosons. In the 1960s Glashow, Salam, and Wein- tons (e, νe, µ, νµ, τ, ντ ) that come paired up as doublets of three generations. For each quark berg (GSW) were able to unify the weak inter- avor there are three colors (red, green 6, and action with the electromagnetic interaction by blue). All the quarks and are fermions. combining the SU(2) group with i.e., they have spin =1/2. Particles with inte- the U(1) singlet that represents QED. The prod- × gral spin are called bosons. In particular those uct SU(2) U(1) leads to electroweak theory. If × with spin = 1 are called gauge bosons and those the electroweak theory based on SU(2) U(1) with spin = 0 are called scalars. The Standard is to have perfect symmetry the electroweak Model requires the W +, W −, Z, and γ spin- one isospin triplets |the W bosons| and the elec- or gauge bosons to mediate the electroweak force troweak singlet|the photon, must have equal and eight gluons|massless gauge bosons that mass. Since the photon has zero mass, this are color anticolor bound states. The constituent would mean the W bosons will be required to particles of the Standard Model and some of have zero masses as well. However, it was clear their properties are listed in Table 1. The gauge from the outset that the weak interaction has ' −18 bosons and the forces they mediate are listed in an extremely short range R 10 m. This Table 2. Gravity is included for completeness implies masses of W that is of the order of 100 × even though it is not part of the Standard Model. GeV. As it stands, the SU(2) U(1) symmetry is badly broken and requires some justiflcation. The developers of the electroweak theory start 2.3 Unification of the Electromag- with four massless gauge bosons - the triplets netic and Weak Forces. W +, W −, W ◦ and a B◦|an isospin singlet. This would provide a perfect symmetry at very high The grouping of quarks and leptons into pairs of energy (at E ≥ 100GeV ) or equivalently at very three generations suggests that the quarks and high temperatures (1015K). At lower energies or leptons of each generation are weak isospin dou- temperatures, a phase transition occurs and the blets in analogy with the fact that the proton and symmetry is broken (lost or hidden). As a result ± 6 of the spontaneously broken symmetry, the W Some authors, prefer yellow to green. The physics is ◦ ◦ not affected by this. However, most authors are using the obtain mass and the W and B mix and yield primary colors. the massive Z◦ boson and the massless photon

6 Constituent Particles of the Standard Model Table 1. Quarks and Leptons come in three generations of doublets. Each quark has three possible colors red (R), blue(B), green(G). The leptons are colorless. For each quark and lepton there is a correspond- ing antiquark and antilepton. The quark masses given correspond to approximate rest mass energy of quarks conflned in . For exam- ple, the u or d quark mass is one-third that of the nucleon mass and the c quark mass is one-half of the J/ψ meson mass. (Masses as low as 4 MeV and 7 MeV for the u and d quarks respectively are given by some authors.) Since free quarks have not been observed, quark mass estimates are somewhat uncertain. Generation Quarks Leptons First u (up) d (down) e (electron) νe Mass 330 MeV 333 MeV 0.511 MeV < 15 eV Second c (charmed) s(strange) µ () νµ Mass 1.5 GeV 550 MeV 107 MeV < 0.6 MeV Third t (top) b (bottom) τ (tau) ντ Mass 176 GeV 5 GeV 1784 MeV < 250 MeV Charge +2e/3 −e/3 −e 0 Color R G B R G B colorless colorless

Table 1: Constituent particles of the Standard Model|quarks and leptons.

Comparison of Fundamental Forces Table 2. A comparison of the range, relative strength, and some proper- ties of mediators of the fundamental forces. All the given values, except 2 spin, are approximate. Gmp represent the gravitational strength. G is 1 the Newtonian constant and mp is the proton mass. α ' 137 character- 2 izes the electromagnetic strength. GF mp, the product of four{ coupling and square of the proton mass is a measure of the weak force strength. αs ' 1 is the color force strength. Force Range Strength Boson Mass (GeV) Spin Gravity ∞ 10−38 graviton 0 2 E. M. ∞ 10−2 photon 0 1 Weak < 10−18m 10−5 W ±, Z◦ 80, 90 1 Strong < 10−15m 1 gluons 0 1

Table 2: Fundamental forces|range, mediators, and strength.

7 (γ). given below without proof: 7

Familiar examples of spontaneously broken 37.3GeV MW ± = symmetry are the phase transition that occurs sin θW when water freezes to ice below 0◦C and when a red hot bar{shaped ferromagnet regains its mag- MW ± MZ◦ = netism after it is cooled. Water exhibits more cos θW symmetry than ice and the hot iron bar magnet 02 has no polarity and hence no preferred orienta- g 1 1 + 2 = . tion in space. The loss of its magnetism makes it s g cos θW symmetrical. These two, relatively familiar, ex- The constant 37.3 GeV above is related to the amples require exchange of thermal energy with known values { electron charge (e) and the four- their environment to undergo phase transition. Fermi coupling constant (GF ). A current ex- One can thus ask what environmental factors af- perimental value for the Weinberg mixing an- ◦ 2 fect the gauge boson of the electroweak force. It gle (θW ) is about 28 (sin θW ' 0.22). Using is believed that the W and Z bosons obtain their the above relations one can estimate the MW ± mass form Higgs scalar bosons (suggested by pe- and the MZ◦ to be about 80GeV and 90GeV ter Higgs in 1963). At the energy ranges where respectively. As shown in the above equations, perfect SU(2)×U(1) is prevalent a Higgs isospin these predictions are sensitive to the mixing an- + doublet (H , H◦) and its (H−, H„ ◦) gle value. are supposed to exist. The Higgs scalar bosons generate mass due to their mutual self interac- 2.4 Experimental Detection of the tion. When a phase transition or spontaneous W ± and Z◦ bosons symmetry breaking occurs the masses generated by the H± pair is absorbed by the W ± bosons Two groups (known as UA1 and UA2) of interna- and part of the mass from the H◦H„ ◦ pair is tional physicists totaling about 200 detected the used by the Z◦ boson. Since the photon emerges W boson in January 1983 at CERN in Europe. massless, su–cient mass is available for a free A few months later, the same group(s) discov- H◦ boson. A massive neutral ( H ◦) ered the Z boson as well. It was impressive that should, therefore, be available for observation in the masses of these bosons were as predicted by future supercolliders. The search for the neu- the GSW theory. The leaders of these groups| tral Higgs boson is likely to be illusive. Unlike Carlo Rubia and Simon van der Meer|received the W and Z bosons its mass is not constrained a Nobel prize for their remarkable achievement. by theory. An important parameter introduced Their work involved the modiflcation of a Super by the mixing of the W ◦ and B◦ bosons is the Proton Synchrotron (SpS) at CERN in to a Su- 8 θW |the Weinberg mixing angle. This angle re- per Proton Synchrotron (Spp„S) The lates the masses of the W and Z bosons as well as 7For derivations and a list of references, see e.g. H. the electromagnetic (e), charged weak (g), and Frauenfelder and E. M. Henely, Subatomic Physics, 2nd neutral weak (g’) couplings. ed. (1991). 8For details, see D. B. Cline, Carlo Rubia and S. van A summary of these important relations is der Meer, Sci. American, March 1982. See also the Nobel

8 SppS„ enabled them to conduct a pp„ head on col- GSW theory also predicts a free neutral Higgs lision with energies of about 270 GeV per each that is still at large. So far the beam. i.e., A total of 540 GeV per collision. This GSW theory is consistent with all available data. provides su–cient energy for the W ± and Z◦ to A discovery of the Higgs boson will just be the be produced in the reactions: flnal touch it needs to be completely on a flrm ground. In parallel with the GSW theory, there ± p + p„ −→ W + have been developments is quantum chromody- namics (QCD). There is now evidence, albeit cir- cumstantial, for six quark avors. The −→ ◦ p + p„ Z + X has recently (1994) been detected or produced The W and Z produced by the above reactions at Fermi National Lab. The six avors of quark immediately decay as follows: come in thee generations of weak isospin dou- blets. It was this property that enabled GSW ± ± W −→ e + νe(ν„e) to come up with the SU(2) × U(1) symmetry for electroweak theory. Quarks come in three ◦ −→ − + Z e + e colors. This immediately suggests the possibil- Feynman diagrams for the above reaction are ity of SU(3) symmetry based on the color mul- shown in Figure 4. The lifetime of the W and tiples. The SU(3) color symmetry will be ex- Z bosons is about 10−24 seconds. The W ± can act since the three colored quarks of each avor + − ◦ − + decay into e νe or e ν„e and the Z into e e have the same mass. The SU(3) symmetry of pairs. The decay products y away opposite to colored quarks would automatically require eight 2 each other (conservation of momentum dictates (3 − 1 = 8) gauge bosons. These are the eight this) in a direction that is transverse to the beam gluons made of color anticolor quark pairs. The directions while the fragments (X = . . .) dis- construction of gluons is identical to the that perse in the beam directions. The masses of the of obtaining meson multiplets using quark anti- W and Z bosons can be calculated from the mo- quark pairs. The gluons are responsible for me- mentum and energy of the decay products. Fig- diating the strong color force that binds hadrons ure 5 shows a lego plot of the energy deposited [ are of three quarks (qqq in a detector when a Z◦ boson decays in to an states) and bosons are bound states of quarks electron (e−) and a (e+) pair. antiquark (qq„) pairs]. The hadrons are color sin- glets. A readable account of colored quarks and 9 2.5 The Unification of the Strong gluons is given by Sheldon Glashow . Color Force and the Electroweak The Standard Model results when the elec- Force troweak theory group represented by SU(2) × U(1) is extended to include the SU(3) colored The discovery of the W and Z bosons is a very quark group. This is accomplished by multi- strong conflrmation of the electroweak theory de- plying the matrices representing QCD and elec- veloped by Glashow, Salam, and Weinberg. The lectures By C. Rubia and S. van der Meer, Rev. of Mod. 9S. Glashow,“Quarks With Color and Flavor”, Sci. Phys. 57, 689 and 699 (1985). American, Oct. 1976.

9 10 troweak symmetry|SU(3)×SU(2)×U(1). The 3.1 Grand Unified Theories (GUTs) Standard Model can account for all hadronic (strong interaction) and electroweak phenomena. One way to extend the Standard Model and Meson exchange efiects that are still useful in de- unify its coupling constants (g, g’ and e ) is to scribing low energy nuclear phenomena are resid- regard the two lepton doublets in each genera- ual efiects of the strong color force in the same tion as additional indices of color. This results way that molecular forces are consequences of in SU(5) symmetry. Even though the originators the electromagnetic force. The only fundamen- of this idea are Glashow and Georgi (1974), va- tal force missing in the picture portrayed by the rieties of SU(5) based uniflcation theories exist. Standard Model is the gravitational force. The They are called GUTs (grand unifled theories). extension of the Standard Model to include the SU(5) symmetry is supposed to bring quarks and gravitational interaction is an ambitious task. It leptons into a single family. It also suggests 2 has recently generated a urry of activity in the- (5 −1 = 24) two dozen gauge bosons. The Stan- oretical physics. This article will only mention dard Model accounts for half of them. The ad- the basic ideas behind these frontier areas of re- ditional dozen are called X and Y gauge bosons. search. They carry charges of ±4e/3 and ±e/3. These super heavy (compared to W and Z) bosons are rendered massive via a spontaneous symmetry 14 3 BEYOND THE STAN- breaking that takes place at about 10 GeV (1027 K). These energies and temperatures cor- DARD MODEL respond to situations that existed 10−33 seconds after the universe was created by a \a hot big The SU(3) × SU(2) × U(1) gauge the- bang". It is doubtful, therefore, that they can ory with three families is certainly a be achieved in a terrestrial collider of the fu- good beginning, not to accept but to 11 ture . Thus, the X and Y bosons predicted by attack, extend, and exploit. Shelodon SU(5) based GUTs may never be observed di- Lee Glashow 10 rectly. GUTs predict with a life time of 1030 to 1032 years. The Standard Model which is based on SU(3) × Observation of a life time of the order of 1030 SU(2) × U(1) symmetry provides a foundation years may sound ridiculous when the age of the for grander, more inclusive, and, consequently, universe is about 2 × 1010 years. However, if one more speculative uniflcation schemes. Despite starts with 1030 or more protons (about 4000 its impressive success, the Standard Model ex- kg, 4 tonnes, of matter), there is a probability cludes gravity. In the Standard Model, the mass that one of the protons will decay within the difierences of the three generations of quarks and flrst year. Observations of huge (about three the Weinberg angle are parameters that are de- termined by experiment. 11The SSC was expected to attain a 20,000 GeV (20 TeV) of beam energy. The total center of mass energy 10S. Glashow,“Towards a Unified Theory: Threads in when two protons collide will be 40 TeV This is 20 times a Tapestry”, Rev. of Mod. Phys,52, 543, (1980). Nobel the energy available at present. For details on the SSC, lecture. see e.g.; J. D. Jackson et al. Sci. American, March 1986.

11 thousand tonnes) underground pools of water in- forces. Experimental indication for substrata of dicate that protons are much more stable than leptons and/or quarks is currently non existent. the GUTs predict. GUTs also predict magnetic No body knows, however, what the next gener- monopoles with mass of the order 1016 GeV. ation of super colliders may unfold. Could it be Since they are stable, they should be observed that leptons and quarks have structure? as remnants of the phase transition that pro- duces the X and Y bosons. Neither of these 3.3 The Planck Scale and Quantum prediction have materialized. However, GUTs Gravity yield reasonable values for the Weinberg angle 2 Gravity, the oldest known fundamental force, (sin θW ' 0.21) and the mass (5 GeV). Their major deflciency is the neglect of is also the last to be included in a uniflcation gravity. scheme. An attempt by Einstein, to unify elec- tromagnetism and gravitational forces was un- successful. Part of the reason for the neglect of 3.2 Subquarks (or di–culty in including) gravity in particle in- The Standard Model requires: six avors of teraction is due to the fact that gravity is too fee- quarks and antiquarks each with three colors; six ble to afiect elementary particles. e.g. The ratio leptons and antileptons; a dozen gauge bosons; of the gravitational to electric force an electron and four Higgs bosons. i.e. a total of about feels due to the presence of a proton is of the or- 40 sixty four particles. Guts add a dozen gauge der 10− . In QED, the electromagnetic strength bosons extending the number of fundamental is characterized by the dimensionless constant| particles to at least seventy six. This presents the flne structure constant: a dilemma. Uniflcation of fundamental interac- ke2 1 tions seems to come at the cost of increasing the αf = ' . „hc 137 number of fundamental particles. The desired goal is to unify the forces and build all mat- 1 Where k = 4πε0 is the Coulomb constant. Simi- ter in terms of few fundamental entities. One larly, a flne structure constant for quantum grav- way of reducing the number of particles is to in- ity is deflned as: troduce subquarks or techniquarks that serve as 2 GMP building blocks of quarks and leptons. A simple αg = ' 1 and economical model developed independently „hc 12 by Harari in Israel and Shupe in the U.S. , re- Where, G is the universal gravitational constant 19 quires only two fundamental fermions and their and MP ' 10 GeV , is known as the Planck antiparticles to account for all the leptons and mass. Using this mass in Heisenberg’s uncer- quarks of the Standard Model. This model intro- tainty principle yields: the Planck length, `P ' −35 −43 duces hypercolor and hence involves a more fun- 10 meters, the Planck time and τP ' 10 damental force than the strong color force. Simi- seconds. At the Planck scale gravitational inter- larly, techniquark based model utilize technicolor actions are strong and hence non negligible and 12H. Harari,“The Structure of Quarks and Leptons”, hence must be included in . It Sci. American, April, 1983. becomes necessary, therefore, to introduce a new

12 grand symmetry that provides the framework for called supergravity (SUGRA)13 It is a quantum uniflcation of all the fundamental forces includ- theory of gravity in ten dimensions (9 space + 1 ing gravity. time). The extra six spatial dimensions are sup- posed to be curled up (compactifled) to a region 14 3.4 —SUSY of the order of Planck length. .

The symmetry that extends the Standard Model 3.5 Superstring Theory—A Theory (or GUTs) so that quantum gravity is included of Everything (TOE). is called supersymmetry (SUSY). SUSY is rel- evant at the Planck scale. To achieve a com- In an attempt to unify everything SUSY more plete uniflcation of all the forces, it postulates than doubles the number of fundamental par- that for every fermion there is an associated bo- ticles. Escalation of the number of fundamen- son and vice versa. i.e., for every quark there tal particles is contrary to the goals of theoret- is an squark, for every lepton there is a slepton ical physics. A tentatively promising approach (e.g., an electron should have a SUSY partner is the combination of an old string theory 15 called selectron). Table 3. lists particles of the In superstring theory, the fundamental blocks of Standard Model and their SUSY partners (spar- matter are not particles (points) but line seg- ticles). Introduction of sparticles doubles the ments called superstrings that are of the or- number of fundamental particles. In addition, der of Planck length. Superstrings come in two SUSY requires a total of 496 gauge bosons. The forms|open and closed. Open superstrings have statement that for every particle there is an spar- free ends to which conserved quantities such as ticle is analogous to saying|for every particle charge can be attached. Closed superstrings are there is . Sparticles are supposed to loops. Spin - 1 gauge bosons are vibrational play an important role in canceling divergences modes of open superstrings. Spinning super- that result when calculations of interaction am- 13For a readable account of supergravity see: D. Z. plitudes are attempted at Planck scales. e.g., Freeman and P. van Nieuwenhuizen,“Supergravity and divergences that arise due to graviton exchange the Unification of the Laws of Physics”, Sci. American are taken care ofi by including the exchange of Feb. 1978. 14 a (the SUSY partner of graviton). At The extension of space–time dimensions has its ori- gins in the 1920s when first Kaluza and later Klein sug- a time (or energy scale) when SUSY was an ex- gested adding a hidden fifth dimension could facilitate the act symmetry particles and sparticles would all unification of electromagnetism and gravity. Such theo- have the same mass (possibly zero mass). Cur- ries are now called Kaluza-Klein theories. 15 rently, many of the remnants of these sparticles String theory was developed in the 1960s to explain could be too massive to detect. There should be spectra. It was later given up in favor of the . For a non mathematical discussion of superstring some that are detectable. Thus far, no sparticle theory , see e.g,: M. B. Green,“Superstrings”,Sci. Amer- candidate has been observed. ican, Sept. 1986 and the book by Brian Green: The El- symmetry such as SU(5) with space-time in- egant Universe, Hidden Dimensions, and the Quest for the Ultimate Theory. W. W. Norton 1999. variance (local gauge symmetry). Space-time in- Live web- casts from CERN and guided tours from Fermi Lab on variance is the province of general theory of rel- SM and beyond as well as a variety of superstring web- ativity. The local gauge component of SUSY is sites are available on the Internet.

13 Particles and their SUSY Partners Table 3. A list of constituent particles and gauge bosons of the Standard Model with their supersymmetric partners. For completeness, the graviton (spin = 2) has the SUSY partner 3 gravitino (spin= 2 ). Constituent Particles Gauge Bosons 1 1 Spin 2 Spin 0 Spin 1 Spin 2 quark(q) squark(q~) photon(γ) (γ~) lepton(l) slepton(~l) W, Z, bosons wino(W~ ), zino(Z~) higgisimo(φ~) higgs(φ) (g) (g~)

Table 3: Particles and sparticles.

strings may be equivalent to fermions. Super- and of the very large|cosmology have merged. strings can join and form closed ones. A gravi- Early cosmology has become synonymous with ton arises as a vibrational mode of a closed su- high energy physics. Superstring theory, though perstring. In general, the fundamental particles highly speculative, has generated a lot interest can be regarded as a spectra of the excitations and activity among high energy physicists, astro- of the superstrings. The tension (mass/length) physicists, and mathematicians. Even though a of the superstrings sets the vibrational modes. large number of superstring theories’ predictions Superstrings have a rich structure and many ex- may never be accessible to any man-made super citational modes. They have lead to a variety collider, there could be some cosmic remnants of possible theories. All versions unify the fun- and less massive (mass of the order of 10 TeV damental forces, they provide a means for gen- or less) sparticles waiting to be discovered. It erating the fundamental constituent particles as would also exciting if some light sparticles show well as the gauge bosons (including the illusive up. The discovery of an sparticle would make graviton) of the standard model and beyond| SUSY, SUGRA, superstring theory etc. cred- they are the theory of everything (TOE). With- ible and more exciting It is not clear when one out the usual interplay between experiment and can expect to have a unifled theory (TOE). Even theory, the only check we have on superstring when we have a Theory of Every thing it does theories is to demand they be internally consis- not mean the end of physics. TOEs may not tent. TOEs are supposed to be transparent only solve for us practical problems. Fundamental is- at the planck scale. i.e. at a times of the or- sues related to the anticipation of unifled theory der of 10−43 seconds after the "hot big bang". in the next century and what to expect from it Today we live at a time that is three broken is addressed by S. Weinberg. 16. symmetries (phase changes) removed from the era of TOE. At the extremely high energy limit, the study of the very small, particle physics, 16S. Weinberg, ”A Unified Physics by 2050?”, Sci. Am, Dec. 1999

14 15 3.6 Summary The journey physics has taken in the last four centuries and may continue to do so in the next century in the quest for a unifled theory{a The- ory of Every Thing (TOE)is summarized by the line drawings in Figure 6. Gravity will be the last one to join the Elecroweak and Strong nuclear forces. Superstring theory promises to unify SUGRA(quantum gravity) with GUTs( a combi- nation of Electoweak (GSW) Theory and QCD). This is supposed to be realized at extremely high energies of the order 1019 GeV. Unfortunately, this will not be accessible to any man-made su- per collider. The interplay between experiment and theory will be lost. To evaluate TOEs, One has to rely on their internal mathematical consis- tency and their low energy limit predictions. It will not be unreasonable, for example, to expect TOEs to enable us to calculate the seemingly ar- bitrary parameters of the Standard Model such as the quark and lepton masses.

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