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Standard Model, Higgs Boson and What Next?

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Standard Model, Higgs Boson and What Next? GENERAL ¨ ARTICLE Standard Model, Higgs Boson and What Next? G Rajasekaran One hundred years of Fundamental Physics, start- ing with discoveries such asradioactivity and electron, have culminated in a theory which is called the Standard Model of High Energy Phy- sics. This theory is now known to be the basis of almost all of known physics except gravity. We GRajasekaran is a give anelementary account of this theory in the theoretical physicist at the context of the recently announced discovery of Institute of Mathematical Sciences, Chennai and the Higgs Boson.We conclude with brief re- Chennai Mathematical marks on possible future directions that this in- Institute, Siruseri (near ward bound journey maytake. Chennai). His field of research is Quantum Field 1. Hundred Years of FundamentalPhysics Theory and HighEnergy Physics. The earlier partof the 20th century wasmarked by two revolutions that rocked the foundations of physics: Quantum Mechanics and Relativity. Quantum mechanics becamethebasis for understanding atoms, and then, coupled with specialrelativity, quan- tum mechanics provided the framework for understand- ing the atomic nucleus andwhatliesinside. At the beginningof the 20th century, the quest for the understanding of the atom topped the agenda of fun- damentalphysics. This quest successively led to the unravelling of the atomic nucleus and then to the nu- cleon (the proton ortheneutron). Now we know that the nucleon itself is made of three quarks. This is the level to which we have descended attheendof the 20th Keywords century. The depth (or thedistance scale) probed thus 17 Standard Model, quantum field faris10¡ cm. theory, high energy physics, electromagnetism, gauge theory, Higgs boson discovery, quantum gravity. 956 RESONANCE ¨October 2012 GENERAL ¨ ARTICLE INWARDBOUND Standard Model is now known to be the Atoms Nuclei Nucleons Quarks ? ¡! ¡! ¡! ¡! basis of almost ALL 8 12 13 17 of known physics 10¡ cm 10¡ cm 10¡ cm 10¡ cm except gravity. It is the dynamical theory This inward bound path of discovery unraveling the mys- of electromagnetism teries of matter and the forces holding it together { at and the strong and deeper and ever deeper levels { hasculminated, at the weak nuclear forces. end of the 20th century, in the theory of fundamental forces based on nonabelian gauge ¯elds, for which we have given a rather prosaic name: `The Standard Model of High Energy Physics'. In this theory, the strong forces operating within the nuclei and within the nucleons, aswellas the weak forces that were revealed through the discovery of radioactivity a hundred years ago are understood to be generalizations of the electrodynamics of Faraday and Maxwell. Electrodynamics was formulated around the year 1875 and its applications came in the 20th century. We owe a lot to the Faraday{Maxwell electrodynamics, for the applications of electrodynamic technologyhave become a part of modern life. People take out a small gadget from their pockets and speaktotheirfriends living hun- dreds or thousands of kilometers away; somebody in a spacelab turns a knob of an instrument and controls a spacecraftthat is hurtling across millionsof kilometers to a distant planet. All this hasbeenpossible only be- cause of electromagnetic waves. It turns out that the dynamics of strong and weak forces was formulated around 1975, almost 100 years after the Standard Model has formulation of electrodynamics. We may expect that been constructed by equally profound applications will follow, once the tech- generalizing the nologies of the strong and weak forces are mastered. century-old Thatmay be the technology of the 21st century. electrodynamicsof Faraday and Maxwell. RESONANCE ¨ October 2012 957 GENERAL ¨ ARTICLE The four After this bird'seye view of one century of develop- fundamental ments, we now describe the four forces of Nature and forces govern all then take up the Standard Model. of Nature. 2. FundamentalForcesof Nature The four fundamental forces are the strong, electromag- netic, weak and gravitational forces. Strong forces are responsible for binding nucleons into the nucleus (and for binding quarks into the nucleons). They are charac- terised by a strength parameter which is roughly one and 13 their range is 10¡ cm. Electromagnetic forces bind nu- clei and electronstoform atoms and molecules and bind atoms or molecules to form solid matter. Their strength is measured by the ¯ne structure constant whose value is about 1/137 and their range is in¯nite. Weakin- teractions cause the beta decayof nuclei and also are responsible for the fusion reactions that power the Sun 5 2 and stars. Their strength is 10¡ mp¡ and their range is 14 less than10¡ cm. Here mp is the mass of the proton. Gravity binds the planets into the solarsystem,stars into galaxies and so on. Although gravity is the weak- 40 2 est force { its strength being 10¡ mp¡ { it becomes the dominant force for theUniverseatlarge, because of its in¯nite range and because of it being attractive only (unlike electromagnetism where attraction canbe cancelled by repulsion). In quantum theory the range of a force is inversely pro- portionaltothemass of the quantum thatisexchanged. Since the photon mass is zero, electromagnetic force me- diated by the exchange of photons is of in¯nite range. In quantum theory Since the strong interaction between nucleons has ¯nite the range of a range, it hastobemediated by a quantum (or particle) force is inversely of ¯nite mass. This is how Yukawa predicted the parti- cle thatwaslateridenti¯edas the pion, which we now proportional to the know to be a composite of a quark and an antiquark. mass of the We shall discusslater more about the ¯nite range of quantum that is the weak force and the quantum exchanged. Since grav- exchanged. 958 RESONANCE ¨October 2012 GENERAL ¨ ARTICLE ity has in¯nite range, quantum theory of gravity (if it Electrodynamics is constructed) will have its quantum, called graviton, and weak forces with zero mass. have been unified The above textbook classi¯cation of the four fundamen- into electroweak tal forces has broken down. We now know thattheweak dynamics. Further force and electromagnetism are two facetsof one entity unification may be called electroweak force. Canonegofurther and unify achieved in future. the strong force with the electroweak force? It is possi- bletodosoand it is called `grand uni¯cation', but that is a speculative step which maybecon¯rmedonlyin the future. The grander uni¯cation will be uni¯cation with gravitation which we maycall `TotalUni¯cation' which was the dreamof Einstein. Perhaps that will be realized by string theory and in the future. For the present we have the Standard Model which is a theory of the electroweak and strong interactions andis based on a generalization of elecrodynamics. So let us start with electrodynamics. 3. Laws of Electrodynamics The laws of electrodynamics are expressed in termsof the following partialdi®erentialequations: ~ E~ =4¼½ ; (1) r¢ 1 @B~ ~ E~ + =0; (2) r£ c @t ~ B~ =0; (3) r¢ 1 @E~ 4¼ ~ B~ = ~j : (4) All laws of Nature are r£ ¡ c @t c written in the These laws were formulated by Maxwell on the basis language of of earlier experimentaldiscoveriesbyOersted, Ampµere, mathematics. But Faraday and many others. Actually, from his obser- they can be vations and extensive experimentalstudies of the elec- discovered and tromagnetic phenomena,Faradayhad built up an in- establishedtobetrue tuitive physical picture of the electromagnetic ¯eld and only by experiment. RESONANCE ¨ October 2012 959 GENERAL ¨ ARTICLE Maxwell's laws have Maxwell made this pictureprecisebyhismathematical stood the test of time formulation. Once Maxwell wrote down the complete for much more than a and consistent system of laws, very important conse- century. But the quences followed. He could show thathisequations ad- classical picture of mitted the existence of waves thattravelled with a ve- the electromagnetic locity thathecould calculate purely from electricalmea- surements to be 3 1010 cm per sec. Since the velocity field has to be £ replaced by quantum of light wasknown tobethis number, Maxwell proposed field theory. thatlightwas an electromagnetic wave. This was a great discovery since until thattimenobody knew whatlight was. Subsequently Hertz experimentally demonstrated the existence of the electromagnetic waves prediced by Maxwell. Maxwell's laws have stoodthetestof time for much more than a century. Even the two revolutions of rel- ativity and quantum mechanics havenotinvalidated them. In fact, Einstein resolved the confrontation be- tween Newton's laws of particle dynamics and Maxwell's laws of ¯eld dynamics in favour of thelatter. He had to modifyNewton's laws to be in conformity with the space{time picture of Maxwell's laws and this is how specialtheoryof relativity wasborn.Evenquantum me- chanics lefttheform of Maxwell's equations unchanged. However, there was a profound reinterpretation of the continuous Faraday{Maxwell¯eldwithitscontinuous energy distribution in space{time. It wasreplaced by Standard Model is discrete ¯eld-quanta or discrete packets of energy. This wascalled ¯eld quantization and this was the birth of written in the Quantum Field Theory. language of quantum field theory. All Let us brie°y compare the Faraday{Maxwell picture with forces or interactions quantum ¯eld theory. In the former, a charged particle, are mediated by say, a proton is surrounded by an electromagnetic ¯eld quanta, like the existing ateverypointinspace{time. If another charged photon which particle, anelectron is placed in this ¯eld, the ¯eld will mediates interact with the electron and that is how the electro- electromagnetic magnetic interaction between proton and electron is to interactions. be understood in the classical electromagnetic theory. 960 RESONANCE ¨October 2012 GENERAL ¨ ARTICLE In quantum ¯eld theory, the proton emits an electro- magnetic quantum which is called the photon and the electron absorbs it and this is how the interaction be- tween the proton and electron is to be understood. Ex- change of the ¯eld-quanta is responsible for the interac- tion. This is depicted in the `Feynman diagram' shown in Figure 1.
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