THE STANDARD MODEL AND BEYOND: A descriptive account of fundamental particles and the quest for the uni¯cation 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, signi¯cant progress has equivalent to having a complete theory of every- been made in the identi¯cation of fundamental thing (TOE). Currently, a contender for a TOE particles and the uni¯cation 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 con¯dently 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 matter in the universe is made up of a dozen fermions|six quarks and six lep- tons. The quarks and leptons interact by ex- 1 HISTORICAL INTRO- changing a dozen gauge (spin|one) bosons| DUCTION eight gluons and four electroweak bosons. The Standard Model provides a framework for the Our job in physics is to see things sim- uni¯cation of the electroweak and strong nu- ply, to understand a great many com- clear forces. A major de¯ciency of the Standard plicated phenomena in a uni¯ed 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|simpli¯cation 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 Uni¯ed Theory of Weak and Electromag- couraging him to participate in the PHYSNET/CUPLE netic Interactions", 52, 515 (1980). This is the ¯rst sen- project. tence of his Nobel lecture. 1 ¯cation 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 graviton (¡) 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 deflected 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 ¯eld creates an elec- force and the Strong Nuclear force. tric ¯eld. In addition, Amp`ere 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 ¯rst fundamental force (interaction) to be magnetic forces culminated in the development de¯ned 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 uni¯cation of electricity and his Principa. Using his law, Newton was able magnetism{electromagnetism. This is the ¯rst to show that the force of gravity was responsi- example of a uni¯cation of forces. At any point ble for motions of planets around the sun as well in space a change in electric ¯eld (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 ¯eld. This is characteristic of lestial and terrestrial motions were believed to vector ¯elds called gauge ¯elds were local sym- be caused by two di®erent forces2 His gravita- metry is preserved via a compensating change tional law was re¯ned by Albert Einstein in 1916 in the ¯eld components. A relativistic quantum (almost three centuries later). According to Ein- theory (quantum ¯eld 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 e®ort 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 ¯rst example of uni¯cation of forces and a exchange of gravitons -a massless particle 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 ¯eld theory, the electromag- 2 netic interaction is mediated by a massless gauge interactions. (spin{one) boson|the photon (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 electron{proton (ep) The neutron was discovered in 1932. This meant scattering. Despite the similarity between Fig- that the nucleus is made up of protons and neu- ures 1a and 1b, and the similarity between the trons (nucleons). Using the then known forces, formulas for the Newton's gravitational law and primarily the electromagnetic force, it was im- Coulomb's law, uni¯cation 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 neutrino 3 must accom- strong nuclear force - the pion with a mass of pany the emission of the ¯ particle by the nucleus approximately 140MeV . It follows from the un- (more speci¯cally by the neutron) if energy, mo- certainty principle (¢t¢E ¸ ¹h) that the range ' ' h¹ mentum, and spin statistics are to be conserved, of the strong nuclear force (R c¢t m¼c ) Four years later, Fermi (1934) developed the ¯rst 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 mesons have been discovered and is represented by a product of four ¯elds 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-nucleon 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- ¯nite 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 ¯t 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 W and Z bosons). Figures 2a and 2b display the bosons). Like the original Yukawa OPEP, OBEPs Feynman diagrams for ¯ decay as a four-Fermi are based on linear ¯eld theory. When the linear pion (point interaction) and as a W bosons exchange ¯eld theory is replaced by a nonlinear ¯eld (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 ¯t 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.