Steve Smith Tuition: Physics Notes

Transcription

1 Steve Smith Tition: Physics Notes E = mc 2 F = GMm r 2 sin θ m = mλ hν = φ mv2 Particle-opoly! Contents 1 Getting Reay to Play e Broglie s Formla Einstein s Mass-Energy Eqivalence Thingy Particles an Anti-Particles Particle Annihilation an Creation Heisenberg s Uncertainty Thingy Spontaneos Particle Creation Qantm Nmbers Pali s Exclsion Thingy The Game The Pieces The Leptons The Qarks The Bosons The Rles Bil-Yor-Own-Particle Kit Particles Bilt from,,, an Qarks Mesons Baryons Particles Bilt from,, s,,, an s Qarks Mesons Baryons Particles Bilt from All the Qarks Forces The Electromagnetic Force Replsive Forces Attractive Forces The Weak Nclear Force β Decay β + Decay Electron Captre The Strong Nclear Force The Strong Nclear Force Within a Haron Glons Can Create Qarks! Annihilation Can Create Glons! The Strong Nclear Force Within a Ncles So - How Do Yo Know If an Interaction is Strong, or Weak? Smmary of Particle Forces 22 6 Smmary of the Rles 22 1

2 A Reqire Particle Knowlege by Exam Boar an Syllabs 23 B Playing the Game 24 C Particle Decays 24 D Things I ve Left Ot 24 D.1 The Z 0 Boson D.2 W Boson Decays D.3 Other Qantm Nmbers D.4 Wave-Particle Dality Stff D.5 Grop Theory Stff Prereqisites None. Notes In orer to try an give yo an iea of what topics are reqire on which A-Level syllabi, I have pt inicators in the margin by section heaers. So, for example, if yo see this in the margin, it is esigne to inicate that the topic is reqire in the Eexcel syllabs (green for reqire), bt not reqire in the an syllabi (re for not reqire). The problem I ve been having in writing this ocment, of corse, is that in orer to tell a coherent story, I ve ha to talk abot things that aren t in any of the syllabi... A more etaile breakown of what topics are incle on which syllabs can be fon in Appenix A. Another point I like to make is that in this ocment I have not mentione anywhere anything to o with the history of particle physics. I ve only presente a glimpse of the Stanar Moel as it crrently stans. If yo want to fin ot more abot the history of particle physics, there are a nmber of very goo books on the sbject, sch as (Close, 2004), (Hesketh, 2016), or (Ne Eman et al., 1996). Docment History Date Version Comments 5 May Initial creation of the ocment. References Close, F. (2004). Particle Physics: A very Short Introction. OUP Oxfor. Hesketh, G. (2016). The Particle Zoo. Qercs. Ne Eman, Y., Kirsh, Y. et al. (1996). The Particle Hnters. Cambrige University Press. Smith, S. (2017a). Particle Decays. Smith, S. (2017b). Playing Particle-opoly! 2

3 1 Getting Reay to Play... Before we start to learn how to play Particle-opoly, I have to mention a few really weir things that yo nee to know abot. If yo thoght that opening a tin of bake beans with nothing bt a banana was ifficlt, well, that s nothing to trying to nerstan this stff. So hol on to yor hat e Broglie s Formla In 1905 Einstein pblishe a paper that explaine the observations from experiments on the photoelectric effect. Up ntil that point, light was consiere to be waves. Unfortnately, Einstein showe that the only way of explaining the reslts of the photoelectric effect experiments was to consier light to be mae of particles (which we now call photons), each carrying an energy given by h is a constant, with a vale of J s. E = h f (1) This was the start of moern physics, as it was realise that sometimes things behave like particles, an sometimes they behave like waves. Light can be shown to act like particles (sch as in the photoelectric effect experiments), an sometimes like waves (in Yong s oble-slit experiment, for example). Similarly, things we ve always thoght of as particles, like electrons, say, can exhibit wave behavior too! Electrons were se in Yong s oble slit experiments, an yes, iffraction patterns reslte. So particles can behave like waves. Ma. In 1923, e Broglie sbmitte a PhD thesis, which ha one iea in it. That iea is, what if : mv = h λ (2) On the left of this eqation we have mass, m an velocity, v (an when yo mltiply m an v yo get a qantity calle momentm). Stanar particle-like stff. On the right han sie of the eqation is wavelength, λ. Now yo can t get mch more wave-y than a wavelength. So essentially, e Broglie was saying that: a particle a wave an Eqation (2) shows yo how to convert information from one form of the thing to the other. h being the same constant as in Eqation (1). e Broglie gave no proof of Eqation (2). There is is no erivation. No theory nerpinning the eqation. It jst works, so we se it. The significance of Eqations (1) an (2) for s in this ocment is that photons have energy, an photons have momentm. 1.2 Einstein s Mass-Energy Eqivalence Thingy Particles have their own associate mass, which is measre in kg. Physicists seem to prefer to talk abot the mass of particles in terms of energy, thogh. To o that yo jst se the E = mc 2 relationship that Einstein showe s meant that energy an mass were eqivalent, an that c 2 is the conversion factor. So, for example, the mass of a qark (whatever that is) is often qote as 2.3 MeV. Why? The mass of a qark is actally kg. Now that s what I call a proper nit of mass. Kilograms. Yo can t arge with that! Bt becase of E = mc 2, this mass will have an energy eqivalent of E = mc 2 = ( ) 2 = J 3

4 Now since the Jole is sch a big nit of energy for tiny sb-atomic particles, physicists have come p with another (profonly non-metric!!) nit of energy: the electron-volt (symbol ev). What is an electron-volt? Well, the efinition of an electron-volt is 1 ev J So that means that the mass of or qark wol be or 2.3 million electron-volts, in energy nits. E = J = = ev = 2.3 MeV 19 ev So 2.3 MeV is the energy eqivalent of the mass of the qark. Sometimes yo see the mass of a thing expresse as 2.3 MeV/c 2 (so that it incles the mass energy conversion constant). Bt the mass of something being written as 2.3 MeV an 2.3 MeV/c 2 mean the same thing. Physicists are jst lazy when they say that the mass of a qark is 2.3 MeV. Well, that s certainly not confsing at all, is it?? 1.3 Particles an Anti-Particles Before we can talk abot particle annihilation an creation, we nee a efinition of an anti-particle. Every particle has an anti-particle. Particles an their anti-particles have the same mass, bt they have opposite charges. So, for example, an electron an a positron are anti-particles. One thing that I in t nerstan (ntil I learne abot qarks) was that: by this efinition of antimatter, how on earth can there be an anti-netron? I mean, if a particle has zero charge, how can it have an anti-particle?? This, I hope, will be answere later... Some particles, like the photon, are their own anti-particles. That s qite interesting! 1.4 Particle Annihilation an Creation After the iscssion abot particles an anti-particles, we can talk abot particle annihilation. An yo may have come across the iea of particle annihilation alreay: it s where yo get two particles coming together, one a particle an the other its anti-particle, an when they meet, they estroy each other an completely convert their mass to energy (in the form of photons) 1. The amont of energy the mass is converte into will be given by E = mc 2, of corse. For example, if we have an electron an a positron meeting, e + e + 2γ they can estroy each other to proce two γ photons, which carry away the energy-eqivalent of the mass of the two particles. The reverse of this process also occrs. If yo have a photon of exactly the right energy, then this col happen: γ e + e + The mass for the new particles coming from the energy of the photon, accoring to E = mc 2. 1 Interestingly, there are always two photons create in this process. That trns ot to be in orer to conserve the momentm of the collision. 4

5 1.5 Heisenberg s Uncertainty Thingy To be precise, this is actally calle Heisenberg s Uncertainty Principle. Bt becase no-one can be qite sre what it s calle (becase it s a bit ncertain), I m going to call it Heisenberg s Uncertainty Thingy (or HUT for short). So...what is HUT? Well, as far as we are concerne in this ocment, HUT boils own to this kin-of-eqation: E t h 2π Bt what are all these symbols, an what oes it all mean? Well, as for the symbols: E means a change in energy. always means change in in physics an maths. So t means a change in time. h is known as Planck s constant, an has a vale of J s, which is pretty small. We ve seen this h thing before, somewhere, haven t we? Now where was that...? Now, what oes this eqation tell s? Let s take an example. Let s say that at some point in space, there was crrently no energy. Now what HUT tells s, via eqation (3), is that it is possible to create a small amont of energy, ot of nothing, if it was only to last a small amont of time. E energy t 0 t 1 t 2 time Check ot Figre 1. (3) We start off, at t = 0, with no energy. Time rolls inexorably on, ntil we get to t = t 1. Senly, an amont of energy appears! Wow! Ot of nothing! Wow!! An it stays there ntil we get to t = t 2, where, jst as senly, it isappears again! Wow!!! Weir? Absoltely. This sort of thing can t possibly happen, can it? Absoltely. It oes. All the time. If yo fin that har to swallow, how abot this Figre 1: Heisenberg s Uncertainty Thingy perfectly reasonable alternative explanation. How can yo not nerstan this: at t = t 1, the small amont of energy E is borrowe from the ftre, an then pai back when we get to t = t 2. Ah! that clears it all p. An of corse, becase of eqation (3), the more energy we borrow, the smaller the time we can borrow it for. For example, let s say that we wante to borrow 80 GeV. That s 80 giga electron-volts. Yes: electron-volts. How mch time can we borrow this for? Well, from (3) Not very long. t h 2π E π (converting the energy into Joles) s The thing is thogh, now it is possible to borrow an amont of energy for a short while, what can we o with it? Well... 5

6 1.6 Spontaneos Particle Creation Now becase of HUT, there is another way to proce particles. Becase of this borrowing-energy-otof-nowhere thing, we can borrow a bit of energy, trn it into mass (sing E = mc 2 of corse) an make a particle ot of it! The only problem with this is that the particle won t be able to last very long. Remember the example from earlier? Let s say that there was a particle that ha a mass of 80 GeV. Let s call it a W boson. Stpi name, I know. Bt hey. Then if we wante to create one of these things, we col jst borrow the 80 GeV from the ftre, an create or own W boson! Ot of nothing! Bargain! The only problem is that we woln t have very long at all to play with it. We ll have to give it back after only s. Harly enogh time to make friens Qantm Nmbers Energy, ev 0.85 n= n= n= gron state n=1 Figre 2: Electron Energy Levels in Atoms of Hyrogen Qantm nmbers are jst important characteristics that particles have. Do yo remember Bohr s iea that electrons can only exist in particlar energy levels within atoms of Hyrogen (see Figre 2)? Well, the vales of n for the electrons (their energy level) is one of the qantm nmbers that electrons can have when they re insie atoms. There are others: charge, for example, is another. Particles can have ifferent vales of a set of qantm nmbers. An these qantm nmbers essentially tell yo everything yo want to know abot a particle. In fact, the big problem that physicists have ha over the years is to iscover what all the qantm nmbers for particles were. This qest is essentially the same as iscovering the rles of the game that we are playing here. In this ocment we are concerne with particles in the nclei of atoms, an not flying aron the otsie of the ncles. It trns ot that the set of qantm nmbers that nclear particles have that we are intereste in are: charge, Q lepton nmber, L baryon nmber, B strangeness (!!), S color (!!!), C Don t worry abt what all these things are yet. I ll introce them later. 1.8 Pali s Exclsion Thingy To be slightly less ncertain, this is actally calle Pali s Exclsion Principle, bt I think PET sons a bit better than PEP. It makes me think of something soft, warm an frry. Wolfgang Pali came p with this iea in An here is the iea: In any system 2, no two particles can have the same set of qantm nmbers. It s a bit like the rle that at a party, no two women are allowe to have the same hair-o an the same ress. 2 Whatever that means! 6

7 2...The Game Right. Now we have everything in place for me to be able to start to explain how to play Particle-opoly. An to o that, we have to learn what pieces we can move aron the boar, an what the rles of the game are. Let s start with the pieces. 2.1 The Pieces The Leptons Leptons 3 were the first elementary particles to be iscovere. J. J. Thompson iscovere the electron in That s before there was conclsive evience for atoms! Since then, frther leptons have been iscovere. It is now thoght that there are six of them (an six corresponing anti-particles). Three of them are: the electron e, the mon, µ an the taon, τ. These particles can all be thoght of as jst electrons. Energy (MeV) τ µ e The mon an the taon are jst electrons in higher energy levels (or alternatively: electrons with more mass, becase that s the same thing, right?). See Figre 3. Note the logarithmic scale p the energy axis! Associate with these electrons are three other particles calle netrinos 4. Netrinos have no charge an almost no mass. So, the netrinos are: the electron-netrino, ν e, the mon-netrino, ν µ, an the taon-netrino, ν τ. An of corse, jst to jazz things p a bit, all these electrons an netrinos have anti-particles. These are enote by: e +, µ +, τ +, ν e, ν µ an ν τ. Figre 3: Electron Energies/Masses Table 1 shows all the leptons, together with their qantm nmbers. We haven t talke abot anything other than charge yet. That comes later. The colmns that are greye ot correspon to qantm nmbers that the particles on t have, so their vales are zero. Particle name, Symbol Q L B S C Mass (MeV) Electron, e Mon, µ Taon, τ Electron-netrino, ν e Mon-netrino, ν µ < 0.2 Taon-netrino, ν τ < 16 Positron, e Anti-mon, µ Anti-taon, τ Electron-antinetrino, ν e Mon-antinetrino, ν µ < 0.2 Taon-antinetrino, ν τ < 16 Table 1: Leptons an their Qantm Nmbers So here, as leptons aren t baryons, then they won t have a baryon nmber. Or, we col say that their baryon nmber is zero. Leptons on t have strangeness or color, either (whatever they are). Leptons are all fnamental particles: they can t be split p into anything smaller. 3 The name comes from the Greek wor λɛπτoσ (leptos), meaning light ones. That was appropriate when the electron was iscovere, bt not any more! 4 Name becase they are electrically netral, an that they have very little mass (-ino is often se to mean small.) 7

8 2.1.2 The Qarks There are six qarks, calle p, own, strange, charm, top, an bottom 5. An then there are their antiparticles. So we also have anti-p, anti-own, anti-strange, anti-charm, anti-top, an anti-bottom. So there are twelve in all. These are all fnamental particles: they can t be split p into anything smaller. The symbols se for the ifferent qarks are:,, s, c, t, b for the qarks, respectively, an,, s, c, t an b, respectively, for the anti-qarks. These ifferent types of qarks are calle ifferent flavors of qarks. Energy (MeV) Q = 1 Q = Q = t τ b c 10 2 µ s e 10 1 Figre 4: Electron an Qark Energies/Masses So, bearing that in min, Figre 4 is a chart showing the masses of the six ifferent qarks (the respective anti-qarks have exactly the same masses as their normal matter twins). I ve also incle the electron masses for comparison. Note again the logarithmic energy-axis. Very important!! Jst as with the leptons, where we consiere the mon an taon as being electrons in a higher energy state (or electrons with more mass), well yo can think of qarks in the same way. Becase, s an b qarks all have a charge of 3 1, yo can think of s an b qarks as being qarks in higher energy states; an becase, c an t qarks all have a charge of + 2 3, yo can think of c an t qarks as being qarks in higher energy states. Thinking of the electrons an qarks like this, we can grop these particles in a ifferent way: by generation. See Table 2. Generation Particles Anti-particles First e,, e +,, Secon µ, s, c µ +, s, c Thir τ, b, t τ +, b, t Table 2: Generations of Electrons an Qarks So thir generation particles have more energy (or mass) than secon generation particles, an secon generation particles have more energy (or mass) than first generation particles. Table 3 lists all the qarks, an the anti-qarks, giving all their qantm nmbers. As qarks aren t leptons, then their lepton nmber is zero. Particle flavor, Symbol Q L B S C Mass (MeV) Up, R, G or B 2.3 Down, R, G or B 4.8 Charm, c R, G or B 1275 Strange, s R, G or B 95 Top, t R, G or B Bottom, b R, G or B 4180 Anti-p, R, G or B 2.3 Anti-own, R, G or B 4.8 Anti-charm, c R, G or B 1275 Anti-strange, s R, G or B 95 Anti-top, t R, G or B Anti-bottom, b R, G or B 4180 Table 3: Qarks an their Qantm Nmbers 5 These names on t mean anything. They re jst wors that are se to enote the ifferent qarks, jst so that we can talk abot them behin their backs. 8

9 Table 3 also introces a very strange qantm nmber inee: strangeness. Only strange particles have strangeness. That s strange. As a final cople of remarks abot qarks, let me jst say that the an syllabi teach that there are the six qarks:,, s,,, an s. However, OCR-B (Avancing Physics) an Eexcel syllabi teach that there are all twelve. Also, OCR-B is the only syllabs to mention the color qark qantm nmber, C The Bosons Now here s a thing. In or Stanar Moel, there are particles an there are forces, an the forces act on the particles, casing them o o stff. Right? Bt in the crrent theory, there s a very big iea inee: the forces between particles are case by the exchange of other particles!!! So really, there aren t particles an forces, there are jst particles. Bt some of those particles are prely responsible for giving the illsion that forces exist. Sch particles are calle bosons, an theories that se particles as force-carriers are calle gage theories (for some reason). So bosons are also calle gage bosons. When Newton formlate his three laws of mechanics, his secon law was written as force = rate of change of momentm so a change in a particle s momentm is eqivalent to the particle experiencing a force. This means that we can view forces by the exchange of particles that carry momentm, so that the momentm of the interacting particles are both change in the process: they both experience a force e to each other! Force Boson(s) Mass (MeV) Really strong nclear (between qarks) glons 0 Strong nclear (between ncleons) π + π π Weak nclear W W Electromagnetic γ 0 Table 4: Forces an their Bosons Table 4 shows all the exchange particles that we are intereste in here, together with their masses. One thing that s really confsing when yo rea books is that there seems to be something o abot the strong nclear force. Sometimes yo see that the bosons responsible for the strong force are glons, an sometimes yo see that pions are sppose to be responsible for it. So which is it? Glons or pions? Well, it trns ot that it s both. There s more abot this later, bt for now, jst think of it like this: glons are the force-carriers between qarks (within a single baryon or meson), so glons hol single harons together; pions are the force-carriers between ncleons in a ncles, so pions provie the force that hols protons an netrons together in a ncles. 2.2 The Rles The rles of the game are going to be bilt p in the next section. Can t wait, eh? 9

10 3 Bil-Yor-Own-Particle Kit Now we know what all the fnamental matter particles 6 are (the leptons an qarks), how can we bil bigger particles ot of them? Here s where we start learning some of the rles of the game. Rle 1: Particles can only be bilt sing qarks Rle 2: Particles can only have integer charge Rle 3: Particles can only have integer baryon nmber Now then: let s have a look at the conseqences of these three rles. These rles mean that we can never fin a qark on its own. Since qarks have charges of ± 1 3 or ± 2 3, an baryon nmbers of ± 3 1, then yo can never get one withot at least one mate to keep her company. 3.1 Particles Bilt from,,, an Qarks Becase of Rles 1-3, it is only possible to bil particles that have either two qarks in them (so they wol have to have a baryon nmber of 0: these are calle mesons), or three qarks, so that the baryon nmber is ±1 or ±2 (which are calle baryons) Mesons Let s have a look at the possible particles we col bil ot of two qarks. An to get a feel for the thing, let s start by only consiering sing,,, an qarks, the first generation qarks, as or biling blocks. It makes some sense to o this: the first generation qarks are going to be the most stable, as they have the least energy. We ll learn later that more energetic qarks are nstable, an ecay own to less energetic ones. Yo might expect this: the same sort of thing happens with electron energy levels in atoms. Q B S Name Symbol Mass (MeV) Pion π Pion π Pion π Pion π Table 5: All Possible Mesons Bilt From,,, an Qarks Table 5 shows all the possibilities sing first generation qarks. The greye rows inicate possibilities that violate Rle 2 an/or Rle 3. The table shows that there are only for particles it is possible to make: these particles have been calle pions. Notice that the only possible particles that it is possible to make with two qarks are mae of a qarkantiqark pair. This is becase of the charges on the ifferent types of qarks. This is an important reslt. 6 First off, there s a major ifference between fnamental particles, the leptons an the qarks, an other non-fnamental particles that can be bilt from the fnamental ones, sing them as biling blocks. From now on, I m going to call all nonfnamental particles jst particles, an if I want to refer to leptons or qarks, I ll se those names. 7 I m slightly lying here. Accoring to these first three rles, there s nothing to stop s biling particles ot of for, or six qarks, is there? Don t worry abot oing this for A-Level, thogh! 10

11 Now there s one very interesting thing here: look at the masses of these pions. An then look at the masses of the qarks that make them p. What o yo notice? When yo start biling particles ot of qarks, the masses of the particles are always greater (mch greater), than the masses of the qarks that make them p. Why on earth is this? This is not at all easy to explain. I m going to have a bash, bt yo ll have to wait ntil later! Baryons Now let s have a look at the possible particles we col bil ot of three qarks. An again I m only going to se first generation qarks in the biling process. Q B S Name Symbol Mass (MeV) Delta Proton p Netron n Delta Delta Proton p Netron n Delta Table 6: All Possible Baryons Bilt From,,, an Qarks Table 6 shows all the possibilities sing first generation qarks. The greye rows inicate possibilities that violate Rle 2 an/or Rle 3. The table shows that there are only eight particles it is possible to make: an these particles have a variety of names! This time notice that when we make baryons, particles mae ot of three qarks, it is only possible when either all three are qarks, or all three are anti-qarks. This is another important reslt. An note also that the masses of these baryons, mae of three qarks, are mch greater than the masses of mesons, which are only mae of two qarks. In fact, the proton, with a mass of aron 938 MeV, is almost exactly a hnre times more massive than the qarks that make it p. Wow. 11

12 3.2 Particles Bilt from,, s,,, an s Qarks Mesons Now let s incle the s an s qarks as biling blocks. What can we make now? This time, I m only incling particles that it is possible to make in or tables. That s becase the nmbers of possible particles is going p very fast! Incling the s an s qarks gives s the Kaon mesons! s s Q B S Name Symbol Mass ()MeV Pion π Pion π s Kaon K Pion π Pion π s Kaon K s Kaon K 494 s Kaon K s s Pion π Table 7: Mesons Bilt From,, s,,, an s Qarks Notice how mesons mae with secon generation qarks are mch more massive than mesons mae with only first generation qarks Baryons An incling the s an s qarks gives s a whole host of new baryons. s s Q B S Name Symbol Mass (MeV) Delta Proton p s Sigma Netron n s Sigma ss Xi Cascae Ξ Delta 1232 s Sigma 1197 ss Xi Cascae Ξ 1322 sss Omega Ω Delta Proton p 938 s Sigma Netron n s Sigma ss Xi Cascae Ξ Delta s Sigma ss Xi Cascae Ξ sss Omega Ω Table 8: Baryons Bilt From,, s,,, an s Qarks 12

13 3.3 Particles Bilt from All the Qarks There will be too many to list in table. In fact, if we worke ot how many ifferent particles yo col make sing Rles 1-3, yo wol fin: Qarks Use Nmber of Mesons Nmber of Baryons,,, 4 8,, s,,, s 9 20,, s, c,,, s, c 16 40,, s, c, b,,, s, c, b 25 70,, s, c, b, t,,, s, c, b, t Table 9: Nmbers of Particles Mae from Different Combinations of Qarks 4 Forces Right. Now let s start looking at all the forces. What we re intereste in here is what effect the forces will have on ifferent types of particles. Now becase we now know that there are two types of particles: matter particles (mae of qarks an leptons), an force particles (the bosons), then what we re trying to o here is iscover how the matter particles an force particles interact with themselves an each other. To help with this, a famos physicist calle Richar Feynman invente a way to raw pictres of the interactions of all these particles. They have become known, perhaps nsrprisingly, as Feynman iagrams. Here s a cople of examples: B time e time B γ A A space (a) An electron stays in the same place as time passes. space (b) A photon travels from one place to another as time passes. Figre 5: The Basic Feynman Diagram There are two axes in a Feynman iagram. In my iagrams, the vertical y-axis will be time, with time increasing p 8. The horizontal x-axis will be space. I ll always mark which is which in my iagrams to avoi confsion. Check ot Figre 5. In (a) we have an electron which stays in the same place as time passes. How o we know that it stays in the same place? Becase its trajectory is vertically p. That means time will go by, bt it s space coorinate will stay the same. [A particle will never actally stay in the same place in practice. This example is jst to try an help yo nerstan the iagrams!] In (b) we have a photon which moves throgh space as time passes. How o we know that? Becase ring its trajectory, both the time an space coorinates change. Get the iea? 8 Annoyingly, yo will sometimes fin that people raw Feynman iagrams with time along the x-axis, where time increases to the right. Watch ot for this. The reason for this apparent absrity that people raw Feynman iagrams in ifferent ways, with the time axis going in ifferent irections, is actally becase one of the things that came ot of Special Relativity theory is that space an time sholn t be thoght of as separate things. We shol be combining them into what is now known as spacetime. Get this: that means we can o things like rotate Feynman Diagrams to see what conseqences of interactions col be in ifferent circmstances!!!!! Now, for example, particles can be fon going back in time... My hea hrts. 13

14 By the way: what wol yo say the points A an B represente in these iagrams? They re actally what physicists call events: that is: a point in both space an time. Right. Now we know abot Feynman iagrams, let s get starte trying to nerstan forces. An the first one I m going to choose is the electromagnetic force. 4.1 The Electromagnetic Force Replsive Forces The electromagnetic force is the force that acts between charge particles. An if two particles have the same charge, the force pshes them apart, an if the two particles have opposite charges, then the force plls them together. In the Stanar Moel, the boson that s responsible for transmitting the electromagnetic force is the photon. Let s see how this is one with the help of a Feynman iagram! time A e e γ space B e e Figre 6: The Replsive Electromagnetic Force In Figre 6 we have a Feynman iagram of the replsive force between two electrons. The electron on the left is travelling along, moving towar the electron on the right initially, ntil the event A occrs. At A the left electron emits a photon. As photons have momentm (see Section 1.1), then the left electron s momentm will change, an its irection of motion will change (away from the right electron). The photon travels towar the electron on the right, ntil at B the photon hits the right electron. This cases the momentm of the right electron to change too, an it moves away from the left electron. So initially (towar the bottom of Figre 6) the two electrons are moving towar each other, an later (towar the top of Figre 6) the two electrons are moving away from each other. An the case of the changes in irections of the electrons is the transmission an absorption of the photon Attractive Forces It is mch more ifficlt to explain the Feynman iagram for the attractive electromagnetic force (between a proton an an electron, say), so I m going to avoi trying to o it. At A-Level, yo woln t be expecte to be able to raw to the Feynman iagram for electromagnetic attraction. So, after that nifty sie-step, I m going to move swiftly on to the weak nclear force... 14

15 4.2 The Weak Nclear Force The weak nclear force is a force that acts on qarks. It is transmitte via two bosons: the W + an the W (W for weak) bosons. Only one of these bosons will be involve in any given interaction. time A e W B ν e The weak nclear force changes the flavor of qarks. That means, for example, that a qark col change into a qark ring a weak interaction. The weak interaction is the only force that can change the flavor of a qark. An to o that, the interaction has to se either the W + or W boson β Decay space Figre 7: A Weak Interaction: β Decay Talking abot charge changing introces s to another rle: Here s an example. In Figre 7 a qark is going abot its bsiness qite happily, ntil at A, it spontaneosly emits a W boson. Wow! W bosons have mass (an conseqently momentm) an so the momentm of the qark will change. W bosons also carry a negative charge of 1. That charge can only come from the qark, an so the charge of the qark mst change. Rle 4: Charge is conserve in interactions. In the interaction at A therefore, charge mst be conserve. At A we mst have an eqation like this: + W Q: Since charge nees to be conserve, the total charge on each sie has to be the same. This is the case: ( 1 3 ) = (+ 2 3 ) + ( 1). That means that the qark that the qark changes into mst have a charge of The best caniate for sch a qark wol be the qark (since that s the qark with a charge of with the least mass/energy, an so is easiest to make). In the interaction at A (as in all interactions) baryon nmber mst also be conserve. Rle 5: Baryon nmber is conserve in interactions. So at A or eqation nees amening a bit: + W Q: B: At B the W qark ecays. As it s carrying a charge of 1, the W particle ecays into an electron. That s the particle with a charge of 1 that has the least mass/energy, an so is easiest to make. However, there s a problem. Rle 6: Lepton Nmber is conserve in interactions. An electron has a lepton nmber of +1. Since none of the stff that participate in the interaction at A ha a lepton nmber (becase none of them are leptons!), then the interaction at B has no lepton nmber coming in. That means there has to be zero lepton nmber going ot of B as well. W e + ν e Q: L:

16 That s the reason why yo always get an electron antinetrino when yo get an electron proce in this kin of interaction. By the way, this particlar interaction is known as β ecay: this is the interaction responsible for β raiation in raioactivity. It trns ot that any of the negatively charge qarks can change into any of the positively charge qarks by emitting a W boson. An hh! By symmetry, it trns ot that any of the positively charge qarks can change into any of the negatively charge qarks by emitting a W + boson. So yo col sm p the weak interaction by: {, c, t} {, s, b} This has an interesting conseqence. If one of the qarks involve in the weak interaction was a strange qark, an the other one isn t, then strangeness won t be conserve in a weak interaction! Bt if that happens, it will only change by ±1: Rle 7: Strangeness changes by 0 or ±1 in interactions. An another interesting thing: I mentione earlier that W bosons have mass. How mch mass? Well, it trns ot the the mass of the W bosons is aron 80 GeV!! That s abot times the mass of a qark!! So, for the interaction at A in Figre 7, where i the energy come from to make the W boson? Well, Heisenberg s Uncertainty Thingy, of corse. An remember the calclation we i in Section 1.5? If we borrow 80 GeV of energy from the ftre, we can only have it for abot s before we have to pay it back. So these W bosons on t get very far before they ecay into an electron an electron antinetrino. This is why the weak interaction is a very short range force β + Decay Here s another example of the weak nclear force in action: β + ecay. B e + This col be, for example, where a proton interacts with an anti-netrino. Figre 8 shows the Feynman iagram. time A W + ν e It is only one of the proton s qarks that actally gets involve in this process: it emits a W + boson in the interaction at A, trning itself into a qark: + W + Q: space B: Figre 8: β + Decay The W + boson then interacts with the anti-netrino at B, trning themselves into a positron: W + + ν e e + Q: L:

17 4.2.3 Electron Captre Here s another example of the weak nclear force in action: electron captre. time A W + B e ν e This is where an electron in an inner shell of an atom is rawn into the ncles of the atom an interacts with a proton, trning the proton into a netron an a netrino in the process. It s actally a mechanism whereby an nstable ncles can make itself more stable. Figre 9 shows the Feynman iagram. It is only one of the proton s qarks that actally gets involve in this process: it emits a W + boson in the interaction at A, trning itself into a qark: space Figre 9: Electron Captre + W + Q: B: The W + boson then interacts with the electron at B, trning themselves into a netrino: W + + e ν e Q: L: The Strong Nclear Force If the ncles of an atom only has positively charge protons an netral netrons in it, how can it be stable? A qick calclation of the (Colomb) electromagnetic force between two ajacent protons in a ncles, each of iameter m an charge C sitting next to each other yiels F = qq 4πɛ 0 r 2 Two Ajacent Pro- Figre 10: tons m = π ( ) 2 = 230 N That s two hnre an thirty newtons!! Jst to pt that in perspective, a typical apple has a weight of abot a newton. So the force pshing two ajacent protons apart in a ncles is eqivalent to several bags of very heavy shopping. An that s acting on two particles that have a iameter of m!! An most nclei have more than two protons in them... How can protons possibly stay together ner that amont of replsive force? There mst be some other, even stronger, force acting, plling the protons together! An another thing: how o the qarks stay together insie baryons an mesons? Drm roll...enter the Strong Nclear Force. An here s an interesting twist: the strong nclear force nees to be thoght of in two ways. Firstly as a really, REALLY strong force (acting on the qarks within a haron), an seconly as a not qite sch a strong force acting between harons (especially in a ncles of an atom). Yo coln t make this stff p, col yo? 17

18 4.3.1 The Strong Nclear Force Within a Haron The strong nclear force acts between qarks within a haron. It keeps the qarks together. Now the electromagnetic force acts between objects that have charge; the weak force acts between objects that have flavor; what property of an object makes it ssceptible to the strong nclear force? It s an object s color. Why o we nee this new color qantm nmber? Well, remember Pali s Exclsion Thingy? Imagine that yo ha a proton. A proton consists of two qarks an a qark. Up to now, the two qarks wol be ientitcal - they wol have the same set of qantm nmbers: the same charge ( + 2 ) 3, lepton nmber (0), baryon nmber ( ) an strangeness (0). Bt PET tell s that no two qarks in the same haron can have the same set of qantm nmbers. So we nee another qantm nmber to istingish them. Hence the nee for qark color. Color is absoltely nothing to o with what we think of as color. It s jst a name that physicists have given to a property of a qark, that can be in one of three possible states. They col have calle the property Gibb, an the three states Barry, Marice an Robin. Or Spice, with the states given by Scary, Sporty an Baby. Bt they in t. Possibly becase there were actally five Spice girls. Everyone forgets Ginger, on t they? An who s the other one? Anyway, the powers that be chose color as the name of the property, an the three states that an object with this property can be in are re, ble an green. Any given qark has to have one of these colors, an it can only have one of them at any one time. Oh - an anti-qarks have the colors of anti-re, anti-ble or anti-green, of corse! So in a proton, one of the qarks col be re, an the other one col be ble. Then we can tell them apart! They wol obey the PET. Right. The strong nclear force acts between objects that have color. Of the particles we have come across so far, only qarks have color, so this is a force that acts between qarks. The particle that transmits the force is calle a glon. An what the glon oes when it leaves one qark, or hits another, is to change the qark s color. time b A r space r b B b r Figre 11 is an example of a Feynman iagram showing how this happens. At A a re qark emits a glon an trns into a ble qark. At B that glon hits a ble qark an trns it re. How oes it o this? Glons also have color! Bt in a really weir way! Glons have both a color an an anti-color!! So when the re qark trns ble, it oes this by creating an emitting a re/anti-ble glon, thereby conserving total color in the interaction! An when the re/anti-ble glon hits the ble qark in the interaction at B, it changes the qark s color from ble to re, again conserving total color in the interaction! Figre 11: A Strong Interaction So we have another rle: Rle 8: Color is conserve in interactions. Another way of looking at this transmission an reception of the re/anti-ble glon between the re an ble qarks is shown in Figre 12. The big balls represent the qarks, each one having it s own color. For this process, we on t care what flavor the qarks are (,, etc.), as the strong force oesn t care what flavor the qarks are, only their color. The arrow,, represents the glon. The hea of the arrow represents the color of the glon, the tail the anti-color. So, in pictre (a), we are in a state immeiately prior to the transmission of the glon. We have two qarks, one re, the other ble. Total color: r + b. 18

19 (a) Two qarks: one re, the other ble. (b) The re qark emits a re/anti-ble glon, trning ble in the process. (c) The glon hits the other ble qark an trns it re. Figre 12: Transmission an Reception of a Glon In (b) the re qark has emitte the r b glon, trning ble in the process. Total color of qarks an glons: b + r b + b = r + b (as one of the bs an the b cancel ot!). In (c) the glon hits the other ble qark, trning it re. Total color: r + b. Color has been conserve throghot! Now, how can ifferent combinations of color exist within harons? It trns ot that free particles can only have qarks whose colors a p to white. How oes that work? Well: Another rle: re + ble + green = white re + anti-re = white ble + anti-ble = white green + anti-green = white Rle 9: Free particles can only be white. So that means we can t ever get a qark otsie of a haron (as it has color), an we can t get glons otsie of harons either (as they have color) Glons Can Create Qarks! It is also possible for glons to create qarks. Check ot Figre 13. (a) A re qark. (b) The re qark emits a re/anti-ble glon, trning ble in the process. (c) The glon oesn t hit anything: it creates a re/anti-ble qark pair. Figre 13: Glons Creating Qarks In (a) we have a re qark. Total color: r. In (b) the re qark has emitte a re/anti-ble glon, trning the qark ble. Total color: b + r b = r. In (c), the glon ecays before hitting another qark. The glon has ecaye into a qark/anti-qark pair (which wol have to have corresponing flavors: e.g. ū,, etc), converting the glon colors into the qark colors. The qark wol take the glon color, an the anti-qark wol take the glon anti-color. Total color: b + r b = r. 19

20 Figre 14: The Sea of Qarks Within a Proton Jst a minte: glons on t have mass. So how can they possibly create a meson (qark/anti-qark pair) that oes have mass? Oh stpi me! Heisenberg s Uncertainty Thingy. Imagine that the re qark in (a) is in a proton. HUT tells s that the meson in (c) won t be aron for very long. Bt it will be aron long enogh for the proton to have significantly more mass than before the meson was create! That s becase the proton now has, temporarily, five qarks in it!! An it gets worse: mesons are being create within a haron by the ecay of glons like crazy, thereby increasing the nmbers of qarks in the haron enormosly. If, at any one instant, instea of there being not three qarks, bt three hnre qarks in a proton, that wol explain where all that extra mass of the proton comes from, compare to the mass of the three component qarks!!! Check ot Figre 14 9 This pictre is esigne to illstrate the mayhem that s going on insie a baryon. The three particle qarks (the large prple balls) are srrone by a sea of glons (the springs), photons (the wavey lines - we get photons exchange between charge particles, remember!) an mesons (the small green an prple balls). If I ha rawn this pictre, I wol have colore the qarks properly: either re, green or ble. Bt I hope yo get the iea Annihilation Can Create Glons! It is also possible for qark/anti-qark pairs to annihilate to create glons. Check ot Figre 15. (a) A pair. (b) The pair annihilate... (c)...procing a gr glon. Figre 15: Annihilation Creating Glons Again, color has to be conserve (Rle 8). An this sort of thing is happenning continally insie all harons (see Figre 14 again) The Strong Nclear Force Within a Ncles We now have everything we nee to nerstan how two ncleons are attracte together by the strong nclear force. Or to pt it another way, how two ncleons can exchange particles that case an attraction between them. Check ot Figre 16 as an example of this inter-ncleon particle exchange process. [By the way: in orer to try an keep this as simple as I can, I have omitte all the glons that are continally flying abot between the qarks within the proton an the netron in the iagrams.] In (a) we have a proton, consisting of qarks own in the bottom left, an a netron, consisting of qarks, in the pper right. For both particles we have one re, one green an one ble qark, accoring to Rle 9. In (b) the ble qark in the proton has emmitte a ble/anti-green glon. This trns the ble qark green. In (c) the glon exploes! No it oesn t. Bt it oes cease to exist, an......in () the glon trns into a qark/anti-qark pair, sing pair-proction (see Section 4.3.2). This pair have to be a qark/anti-qark pair: in this case, they happen to be a pair. An their colors have to come from the glon (color conservation in the interaction: Rle 8). So the qark takes the glon color, an the anti- qark takes the glon anti-color. This qark/anti-qark pair forms a pion, an leaves the proton. As this pion has color, it can t leave the ncles. 9 Which is a pictre I ve shamelessly nicke from the Physics Toay website. 20

21 (a) (b) (c) () (e) (f) (g) (h) (i) Figre 16: Force Acting Between Two Ncleons In (e) the pion emitte by the proton arrives at the netron. Meanwhile, back at the proton, the green qark emits a green/anti-ble glon. This trns the qark ble. This glon wol then form another pion by pair proction which wol fly off somewhere. Bt to keep Figre 16 as simple as possible, I m not going to follow that one throgh... In (f) something interesting happens! The anti-green qark in the pion annihilates with the re qark in the netron......which creates a re/anti-green glon (color has to be conserve, Rle 8) in (g). In (h) the glon hits the green qark in the netron, trning it re. In (i) one of the ble qarks in the netron emits a glon, trning the qark green, so that the netron as a whole trns white (Rle 9). This will then form a pion which will fly off an hit another ncleon So - How Do Yo Know If an Interaction is Strong, or Weak? Well, if an interaction involves a W as the exchange particle, changes the flavor of a qark, an/or proces a pair of leptons, it s weak; if an interaction involves a glon (or a pion) as the exchange particle, conserves the flavor of qarks, an proces no leptons, it s strong. 21

22 5 Smmary of Particle Forces Force Boson(s) Property Really strong nclear (between qarks) glons qark color Strong nclear (between ncleons) π +, π, π 0 qark color Weak nclear W +, W qark flavor Electromagnetic γ charge Table 10: Smmary of Particle Forces 6 Smmary of the Rles Rle 1: Particles can only be bilt sing qarks Rle 2: Particles can only have integer charge Rle 3: Particles can only have integer baryon nmber Rle 4: Charge is conserve in interactions. Rle 5: Baryon Nmber is conserve in interactions. Rle 6: Lepton Nmber is conserve in interactions. Rle 7: Strangeness changes by 0 or ±1 in interactions. Rle 8: Color is conserve in interactions. Rle 9: Free particles can only be white. 22

23 A Reqire Particle Knowlege by Exam Boar an Syllabs Matter an Antimatter AQA Eexcel OCR e Broglie s formla an wave-particle ality Yes Yes Yes Heisenberg s ncertainty principle No No No Annihilation an pair-proction Yes Yes Yes Spontaneos particle creation No No No Every particle has its own anti-particle Yes Yes Yes Leptons an their antiparticles Yes Yes Yes Is knowlege of E = mc 2 reqire? Yes Yes Yes Is E = mc 2 reqire in calclations? No Yes Yes The anti-particles of the electron, proton, netron an netrino Yes Yes Yes Two classes of harons: baryons an mesons Yes Yes Yes Comparison of particle an anti-particle masses in GeV Yes Yes No Which Qarks?,, s All,, s Qarks combine in threes to make baryons Yes Yes Yes Qarks combine in twos to make mesons Yes Yes No Ncleon (mass) nmber an proton (atomic) nmber Yes Yes Yes Table 11: Matter an Antimatter Particle Interactions AQA Eexcel OCR Knowlege of the for interaction types: gravity, electromagnetic, weak, strong Yes Yes Yes Exchange particles are se to explain forces Yes Yes No Knowlege of the glon, Z 0 an graviton No Yes No Virtal photons are the exchange particle for the electromagnetic force Yes Yes No Harons are sbject to strong interactions Yes Yes Yes Pions are the exchange particles for the strong nclear force Yes No No Weak interaction limite to β an β + ecay, electron captre an electron-proton collisions Yes Yes Yes W an W + particles are the exchange particles for the weak interaction Yes Yes No Conservation of energy an momentm in interactions Yes Yes Yes Strange particles are create via the strong interaction an ecay via the weak interaction Yes No No Qark types change in weak interactions Yes No No Table 12: Particle Interactions Particle Decay AQA Eexcel OCR Kaons can ecay into pions Yes No No Proton is the only stable baryon Yes No No Feynman Diagrams Yes No No Decay of a netron into a proton Yes No No Table 13: Particle Decay 23