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New Revolutions in Particle Physics: Standard Model | Lecture 9

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again there very quickly and the next tell you what it has to do with masses of quarks and let so far I've explained to you Harold the gage balls hours not fault on the and W bars are on our Ave up clean ministers from this shift of the field away from more symmetric position which field the Higgs field about what I went through it good In a very simple context where they look very much like ordinary electrodynamics I'll continue to do that but keep in mind when not talking about 4 Armed with talking about other particles so let's just go back to electrodynamics which were not really talking about but still mathematics is saying they are these days bars arms the analogs of fault tolerance the mathematics of the maybe a little more complicated the symmetry group may not be you want it astute to arrest 3 but that's not terribly important and there is but a dynamics that leads cool Maxwell's equations and government factor of the simplest way to encapsulate it is in terms of our grungy and you begin where for promote you begin with the field can show images remind you what it is in terms the vector potential giving your back west of coalesced square you make the appropriate rents invariant combination of squares of components electric and magnetic field and that's saw Grosjean notice it only contains derivatives of AT and therefore the photon is mass for us have amassed you have perhaps you have to get an energy amassed corresponds to an energy corresponding to shifting of field homogeneously everywhere as we know the river this no energy or nor nor energy associated with a uniform shift the vector potential because only derivatives come in so far upon by virtue of the massless at most of the speed of light and this simply lead the Maxwell's equation now have something else to wear this Higgs field the Higgs field the field which corresponds to charged particles again I emphasize we're not talking about ordinary electric charge were talking about the the charges the couple from BMW bars on the weak charges tolerant this fight in the form of a row role he really are house complex valued wrote I will write down brands parental Lagrangian in terms of these things that I called called variant derivatives be fine is equal with the river of cost so I can remember plus or minus on May 5 times the vector potential and fight we write your grungy in terms of also things and all of a sudden we have and interesting interaction between the electromagnetic field a majority field it was here the source of the interaction right over here that would be basically that would be electrodynamics ordinary electric ceramics but now something new happens is something new will have happens is energetics the potential energy of favor something unusual namely that fine is the minimum value of 5 are the minimum value of potential energy is not at fight equals 0 barked at the bottom of the Mexican Hat potential somewhere arbitrary position or at a solely right Matt why would be radius of this circle here f the magnitude of the field the magnitude of this score by name the magnitude of the Higgs field is now F shifted away from the origin by amount F and it is also true will drive that could that be curvature of a here is very steep so it cost a lot of energy to shift the field away from the bottom and 1st approximation we can just say that simply equal f the numerical number kinds Ito the RIA of acts only offers a lot of vary and as sort of frozen frozen because it takes too much energy the shifted away from minimum but how far angular variable spilled that while we could write let me tell you what happens that we could take a R this form of fire and figure out what the core area derivative of fight is given fire has this frozen form were only half of varies highlighted for you it's just equal fervor derivative of our class Y 8 now all of that gets multiplied by half times he how fast the covariance derivative of fine derivative of Alpha I'm sorry things I don't know no I hear this may be overall yes because an overall that's what you get when you calculate the Cauvery River now next single revenue is multiplied despite its complex conjugate to compute the action or be low grungy and forceful while fast not just the number we already assumed that F can vary remark grungy and what's your we get s square the number square some number and then organ again derivative of Alpha derivative of alpha with respect space plus that the potential squared and eagerly I offer is going to cancel because from multiplying it by its complex conjugate This is what you get from rural grungy and of the Higgs field if you make the approximation of stock orders better the stock and Morway from minimum viminea Blom assigned available the sign of Excel by Nova was also an ironist and because when you different you get all I can do about both of them have a minor struck out here all we are there now I can't find the site of 1 of your items where are you scared me from whereas I square aside from my side by group but but complex conjugate crew behind bars modified APEC Warley get we get this expression are here that we're remember gage transformation looks like gage transformation which is a cemetery which is supposed to do nothing physics take any
function lets data which is what I call the last time I could be anything we could be anything a gage transformation is AT and shifted by the derivative of fate that's a gage transformation from this this is it a plaster derivative of some of this In a gage transformation This is a gage transformation where a what we have you lose for the gage transformations not arbitrary function later on this half field was off field itself novel we have less redefine aide close to the river of our car that's just a jig gage transformation of 80 but redefine given the name of scored a quorum OK with fourth-quarter crime is squared times a prime square of sources what happens 0 F squared which originally involved 80 why haven't the staff carefully replaced a buy a prime it's completely unchanged because F is gage invariant and so we can also think of about squared or F the sitting over here was making a difference normally find the net upshot that upshot of all this just replaced the original variables by I variables necessary needing as just a name for for something and that a bad a turn or grungy June which is proportional to the square eventual was a mess effect just a had a terms Obama grungy and our the gage field which is proportional a square no derivatives no derivatives and this here is just a prime square that means that few would shift a prime everywhere simultaneously you would get some energy from this tournament is a matter for a it's our fault or cost BMW balls are so here is an example of how this shift of the field from 0 the value OF gives a mass book particle which you might have said is not allow have amassed covered happened vacuum shifted the some rule spontaneously broken vacuum and the excitation of the electromagnetic field that shifted vacuum have a mail so as the Higgs phenomena and furthermore are the athletic field is gone and doughnuts with absorbed into this thing we call prime was no massless particle anymore for gallstone laws on his disappeared it has Leo Messi gage bulls Oregon the matter now not quite there is still this thing that we froze In an approximation and approximation we said let's ignore the oscillations of the field back and forth in the other direction if we given the system enough energy you're free really poker hard enough we can start this Higgs field oscillating in a radial direction what's called a radio my reveal actions based its as radial direction field pace bowlers oscillations also on popcorn and then massive Kuiper why they had a lot of energy even at rest oscillate back for those are the Higgs boss hours ours are Griggs post on so we started with firm vessel photons massless Goldstone arms and massive Higgs bars are and how we end up with massive Higgs bars arms null Goldstone bars are and a massive hard at the Higgs off produce this likely a friend squared indicates hello from the answered young reveal Harris they have worked there for supporters of a man's energy up From a field point of view mess of courses of a particle or whatever from a field worker backers have amassed in special relativity is just be energy of a system arrest of a system has no momentum of its arrest of its own reference frame and it's the energy in that reference frame is the rest of us 1st Emogene at rest is called rest now arrest means being arrested means having no momentum From a field fury point of view from the point of view of field offered a point of view of quantum mechanics a particle arrest or particle with 0 momentum corresponds to the quantum of a field of infinite wave infinite means the dozen vary all from point-to-point from Astwood corresponds is in energy stored in a field if you shift the fields simultaneously everywhere would no derivative bro spatial derivative to shift the field everywhere simultaneously if you get some energy that energy is called maps well Our we started with a Lagrangian and also an expression for energy which only involves derivatives of a field Raleigh involves derivatives of fuel means that every shift the field everywhere simultaneously we won't get any energy source accents If this was all that walk for the fault-tolerant then we would say the photon has not a uniform shift of the idea vector potential would not create any energy we say 4 partners from Mayor once the determine like this which doesn't involve derivatives does not involve derivatives ready means if we shift aII simultaneously everywhere the EU response the energy stored and this plan is not 0 we shifted a from 0 with Leonhard Euler 0 something else we got energy factor that energy is called the massive before Carter energy stored in on his in order me by homogeneous homogeneous means everywhere is the same view shift the Photon Field everywhere is the same and you get any energy from it at the massive of before and factor in particle physics are a field theory in general who identified particle energy stored in shifting the field simultaneously everywhere is not just been particle physics all kinds of context I think I've talked about from West time limit is remembered remind you again Our sign waiver crystal sound Crystal corresponds Our motion of a crystal lattice which you could think of as a response to a shift of the position of the molecules if you shift the position of the molecules in a variable way on our way down here you shift and enemies and then halfway down the use leadership role after half a century ago dealership the loss over here I have assimilated right and what you make a longer Waverly Of course phone are a long way away from Honda cut away even the crystal where you were very slowly varying his energy stories that give performed the quest bit that energy is called Gerber farm are now what happens if you shift the
crystal everywhere simultaneously by exactly the same amount would you call out a homogeneous share forgive me energy from that now sorrow a homogeneous shift with Everything is shifted simultaneously altogether back gives no energy they would say phone on some mass on arms have no mass which means that a phone on with 0 momentum for has France for can't spin on things up in arms over there are magnets they have to do with the orientation of moved fundamental magnets ifyou reorient the magnets and variable away from place to place you get a little bit of energy cost where if you rotate or magnets together simultaneously everywhere across North is rotated the magnet for a further example of waves which infinite wavelength for a homogeneous waves have no energy also left earlier stereo this analysis would look Oracle list for library little that NL fluff Yao In reality that that originally before a week coupled with a vector potential energy woes purely Ross squared D Court have squared d alpha squares of Soros or just a square this thing where the vector potential was completely absent from the problem now because of only involved the every shift Alpha everywhere simultaneously everywhere as a space we shift the angle instead of saying the field has a value of year grew over here everywhere space at cost no energy cost or energy because it did make in derivatives saw the question was because I fled will later shifting it THAT helpful and let me loose off but it is a matter of our home where focus that continuously moving a little in a movie about changing it from place to place you changes from place to place Massey Energy of the Goldstone bars are right review shifted everywhere simultaneously then it cost or energy wife because only involves gradients and sorrel backs the idea sir keep them a buzzword that man stands for energy arrests are barred also stands for energy associated with uniform homogeneous shifts fuels fuels or whatever it is report about there is an interesting example the city to get there together the idea of how a man can happen I explained to you if you had crystal and you move or molecules simultaneously but doesn't cost any energy now surpassing your crystal lattice words composed of particles which themselves I have both plus plus charges of some might discharges sorrow these are molecules are ions plus firearms and my or they could just be Adams it could be the protons apparently nuclei of the center and the electrons around supposing you did the foreign you shift did all of these electrons the left uniform and all the protons of the right uniform that would be called a homogeneous ship just a little bit Just a little separation between electron cloud and the nuclei you think that would cost areas you back because you were polio plus charges away from charges that would be or homogeneous shift of not biofuels locations which would cost where you think what happen if you may that shift Burma Road the past particles is where the miners particles as wary were Lappin next we'll sort of library OK you will not behave the way toward yes Everything was more simultaneously from Boeing everything simultaneously that 0 momentum phone mowing the plus charges relative to a minus charges was accordingly applies Martin a plasma arc plasma ones have met former not Our who might not have thought of yes yes yes yes yes which is saying his right from the maddening spatially shifting everything and not inducing in kinder while I we that not the question the by shifting I don't mean an actual process are just mean the mathematical change what you mean by the vacuum that's all you do it extremely slowly very very slowly move from here to here are yet to write these to be the actual energy contains time derivatives also but I was simply the same is true with crystal lattice or the kind derivatives of richer than Connecticut Energy the velocities of molecules so if you're really give Crystal a shift which means it's moving off with possibly that of course is kinetic energy so I suggest that the shift in your marriage a nation where you shift everything simultaneously and start arrest compared where originally was also addressed press report OK let's talk now about family on display electrons new warns us all and where they get their maps from turns out the real electron you want quirks also get their mass from this takes from amount from the spontaneous symmetry breaking but reps discuss what we are marked the 1st thing we go back yeah the basics we are not here but actual experimental data about weak interaction is could be beta decay decay of the neutron probe member our and charm and thereby neutrino OK here's what goes back to are 50 50 earlier in the fifties ever remember exactly half the fact was discovered 1st of all Armed reflections cemetery which means reflection or space West can the right hand is not a good symmetry of nature major fact some fifties was discovered that the reflection of new reflection our process is not another possible process quantum electrodynamics the mirror image of any processes of a possible price that's offers a symmetry it's not a continuous symmetry it's a discrete symmetry you take everything he reflected your rotated you reflect left in the writer whose nor hand which is midway 80 is not continuous where to go from left to and right hand so replacing every left hand by a right-hander every left left the screw
thread with a rights group said so for that's a symmetry of quantum electrodynamics it's also a symmetry of quantum chrome or bear text is not a signatory of the weak interaction left and right are fundamentally different different as they can be so they were experimental factors raft the decay of a neutron you're try which gives a fraught time an electronic and then by neutrino well I trust talk about the handedness of particles 0 any sense in which particles are happy and have a hand in my here yes there is a has been they also on the direction emotion if this thing is along the direction of motion Meridith 2 possibilities the spring can be oriented along the direction of motion it be reorient officer the direction of motion in quantum mechanics of course suspenders oriented some other direction you could build that are part of Super positions of the 2 states along with direction emotional so an electron moving along with a high momentum for example canina habits spilled along the direction emotion that means into rotating with right screws its rotating or spinning off With a right here schools there that's caller right here in that electron an electron can also be a left-hander electron that simply means it is going is he likely going in the opposite direction so kinds of Elektra right-handed and left him they're on what happens in a beta decay like you might think you could even make right here or a left that electron hand left and electrons are as good as each other in every respect in quantum electrodynamics Arundel processes which are not symmetric could make right electrons and processed there was a reflector process which is also a possible process where you could make a left hand or prices possible left as possible nevertheless when they process of beta decay became something where you could really do with precision and study that he had been this of electrons from there always left him never a process it doesn't matter what orientation of spin of the neutron has the matter what you do electrons which corrupt or always left him off Ms. goes Beyond the fury of beta decay any weak interactions process and not always any process where a double both arm for example were W. balls are interact and takes a electron into a neutrino or where you interchange error in or you flip these lines to make go the process is out of it it's always the left-handed Elektra arm which interacts with W. both never arrived here or summer example you could imagine a process where 5 in electron scatters off something changes in the way neutrino something over here that scatters off from promise something else electronic you'll always find the ball left here that electron scanners and the right electron whose car was a fact and the same thing is true of the neutrino automatically it's always a left-handed neutrino it's questionable whether right neutrino existence that this is a question which we not answered followed compact with time time but certainly exist of right and left him electron within that also probably right here left him with treat electron so the something asymmetric left-right symmetric about about the weak interactions and it is what is it is that who left hand that electrons art charged with respect to the W bars on another world we could imagine a situation electrodynamics which would be similar it's untrue situation Mr. right now this is not correct but we Kuhn a match in a world away only left him electrons are charged left in electrons could scatter off for could produce far cons and become left in the electrons and which rightly and electrons could we can imagine it's natural airborne or it is not true unimaginative then you would say that the left electron has an electric charge and the right in the electron was not as bizarre the really bizarre natural boat with respect to the weak interaction it's not the initial default hard but the emission of W bars are is as if you left-handed particles carried charge associated with the emission of indeed both on and the right here particles not that's very strange fact Burkle factor bird or threats also pulled pork is also true of quarks bomb was so we have to move the modified the statement from their bar that's a deeper level that's exactly true OK let's talk about left hand right here particles from your political back to Dirac equation here and I will tell you a little bit about the connection between Dirac equation and that he indebtedness of particles are not going to spend a lot of time is giving you the rough outlines of the idea let's go back to the Dirac equation Dirac equation were some pyrite this on a who signed by saying Barak field which could correspond with electronic correspond with new ones could be a few quirks they all have the same form the Dirac equation we are kind derivative of the Dirac field and remember what a direct fielded visits of 4 Component Object where the I components correspond let's say tool different subdivision of particles can have been all either axis it gives you took components ups and downs spin and the particles could have positive or negative energy particles could have positive or negative energy now we've learned over nor again negative energy particles should be replaced by entire particles positive energy but mathematics Arthur a Dirac field has 4 components ops begins positive energy bounced positive energy up speed negative energy downspin positive energy or you could think of it His ups and downs of particle in an article published over 4 components of the Dirac field and the components takeovers of 4 component column vector beer makers to use for all but 4 matrices called the Dirac matrices Barak called an offer 3 out sorry Serena offers 1 each direction space what's call them How on from 3 directions a space crimes derivative of field with respect to
x some light this would be the Dirac equation F particle had no maps now could you see that you could see that because the equation or only involves derivatives of field if the field me Hall dynamics field only involves derivatives of a few we seen in previous situations that when the dynamics of the field only involves derivatives feel matchless is normal restoring force tendency for the field oscillate aired on West it has a gradient not time derivative I'm West as a space derivative sought to shift the field sigh everywhere simultaneously it does not create an oscillation was not creative energy Wadi upon the right hand side if you want that amassed for the the field well there was a fall Barak matrix called Bader you put mass Beta times sigh that's a Viereck equation now electron could be moving along with a momentum momentum means is a gradient of the field sigh of playing way of our pets and this being can either be all along the direction of motion or opposite direction abortion foes to components reconfigure Battisto left the components of the Dirac field right here or let right these equations for you for equations 1 for each compartment what's right and the left and right here the components separately is also applied are times the derivative of a right-handed component of the Dirac four-year-old describing right here in the electrons plus ii Alpha I derivative of a right-handed video is equality where you might think that the right thing but here is something involving the right-handed field but it turns out is bathe is matrix interchanges right in the left him saw a man's term over here corresponds to a cop white between right-handed and left-handed likewise user equation for left or left-handed by DT things out Martinez ii how officer these I left him read by VXI His equal that can sigh right-handed but other lawyers a funny equation awards a right-handed and left-handed components Our completely independent if the masses but the mass makes his mark broadly speaking you can think of a Dirac electron as 1 which as it moves along oscillate between left and right what the oscillations semester but works for about which 2 are quite right on the master couples pulls together the left-handed and right compile this is for a Dirac particle were masters thing which couples together it served it's a Madsen energy which is only the error of both the left and the right components of both sides OK now we can see what on art let's the poems that only the left him to Dirac particles have a charge which is true with respect to the weak interactions not true with respect to electromagnetic of let's just prepared only the left-handed electron has charged a right hand that I left arm has no charge a friend a fictitious world is isn't quite enough allowable rent well it's not because the meaning of this equation is that AT right-handed particle along will turn into a left-handed particles are going nowhere 2nd left in the particle Morgan along with current or write article or this means and means that charge conservation would be violated a left our right here in this field becoming a left-handed field would violate charge conservation another way to say it is to remember that a charge field the field has charged it gets multiplied under a gage transformation around their armies are you 1 transformations it gets multiplied by the way I played has not charged because not multiply by the yard greater now we look at this equation this equation carefully right in this field is neutral Fresno charge then under a U 1 transformations nothing will happen the left hand side but the right hand side would pick up a factor VIII figure likewise over here left inside would pick up a factory to yard favor right-hand side would not these equations cannot be symmetric if only sigh left is multiplied by the way I favor and not sire right some another way of saying that charge conservation would not permit a mixing of left them right like there's if calm if only the left-handed electron were charged although them are charged in reality beers both of them carry the same charge you go back and forth from left to to right without firing a shot all I ask is a following are no probably not old nor sorry that you're right enough consistent the article overhaul why are on the outside of your right now the film is a basic charge conservation would for beard the possibility of a mess of your life electrons if only left-hander electrons had charge for if only right intellect fortunately for the real world of structural electron right here in the charm and left in charge electron amassed the world will be very different electron they have amassed and a chemistry wouldn't exist now there would be a happy world judo F right it could be that we pulled right in the and left him Will contour will Crumpler your very different but from little comfort broke a strong food but come a week and I got quite the measure the state of electron vertically unless it's like what the point of it if you accelerate those in that direction they have failed I think you're a fan of this question is it possible that it would only be 1 kind of our charmingly only left and electron yes it is but only if the massless dominated by white supposing was only are
left in the electron that means it only cover laughed when wolves because a left-handed Dracula Goh emotion right now if electron has In you could imagine swallowing it can read arrest Brietta asked in a way that doesn't change its angular momentum Yukon bring a real good exert a force army which doesn't her changes angular momentum sorrow in that case you would select from which is moving along with rotating be left with a left in the motion bring it arrest and even go past that bring back the other way it's rotations sense of rotation hasn't changed its just angular momentum conservation but its direction of velocity has changed it is turned into a right electron if I judged by my farm was is moving in that direction directions my fingers and there's rotating that way and moving that way it's left him but there is rotating that way and moving that way is right here south of the particle has amassed you could always bring it arrest and Over decelerated center or from the opposite direction and you're guaranteed then you've taken a left-handed electron and turned it into right here if it has a mail why has no matter where you simply can't bring it arrest you simply cannot do this process of taking it moving in that direction soaring Obama bring it arrest what you can do is rotated around but that does not change our change my left hand my right hand right rotate around barked about I can bring it arrest you could be sure that both cars have effect breathed arrests sure the postcards necessarily have to exist Yoogali bring object arrest it has amassed so there's another way of thinking about yacht 2 the circularly polarized OK it changes polarization of the rotating that whereabouts of the mirror local theater wrote that we were going the opposite direction that means a change from circular polarization right-handed circular polarization left him so the photon was also the bill or have us right came arrest OK if DOI if you'll have a particle which only could have warned who was sitting in his hand the and you could have a mirror reflect that word there a gap in America all Rugby callers Ok be cause real electrons have a mail it means the electron we'll elect charm is a mixture of a flea flicker we go over the top for former roosters good if were to all Brooker Gerber Reich the co-op the Pansy depends on our work exactly was focused their way to a good approximation left-handed and right-handed particles in electric or magnetic field behave the same way they have the same trajectories not quite because of the difference over magnetic moment soft magnetic moment just war remarked on and alike and if you are a gradient of an electric field gradient magnetic field awhile magnetic fields in general are they would is saying a magnetic field will affect the left-hander right electrons differently now who would cool yah your Brooks right toe 0 2 but stem With wary you OK so how now Haley are win a world our visits left right if if if they should 1st as a deaths said nature probably not accident of nature it's not an accident of nature or from a moment but treated as a maximum of major empirical fact that we know from all price if strolled mathematical Dirac equation left-handed article right here the particle have different charge in the Dirac equation or the symmetry of the year system will not allow us to mix right and left-handed like that then the question is how might be electron give a charge regular mass Excuse me how perhaps it is weak world In which left in right-hander electrons have different electric charge a use electric charges because familiar winemaker by through the weak interaction forces that were arrested by let's imagine that there's another field that make it a bows on field a bars on-field 5 and this was our field why is also charged but says plus charge was on-field means it's quanta have Hauser charge let's right down the rules of transformation from movies you 1 symmetries for assault I refer over here you want transformations sigh laugh grows Ito ARE later sigh wear West white because left him with your charms are charged for Abbas's I write from Rio it just goes desire right because transformer however suffice it's charge right charms by assumptions depending on the sign of the charge but said because the same way as this 1 needs to I made fine locate Ellis comeback that equation over here clearly requires a stand it is not invariant under this operation the left-hand side of the top equations was not transform the right hand side has transformed same thing with glory quaking soap operas where Fred West take this mess throw the mess out for the moment and put in here on armored constant some unknown constant which will fix later numerical constant kind fight see left in the warned transforms crimes of fight Star and this 1 kind of it is a legal now this 1 thousand transformer alright for about theirs left gets a phase by 5 gets if I started gets the phase salt we haven't violated the symmetry the U 1 symmetry have 1 nor are North good nor bad is good let's say sigh right does not
transform role and I think sigh left them fight transformed the same way right so fine right the transformer or sigh left picks up the factory because I've played a
certified so both of these equations are now consistent with the cemetery this is a perfectly good arm alteration of the Dirac equation which does not violate charge conservation those normally think about it you can't think about this picture saying a right he handed the left-hand side represents the propagation of a
right-handed particle and the right hand side represents the splitting into a left-handed particle and I guess it's a fight particle fire off a 5 nearby fight so a neutral particle breaks up into a left-handed particles which has charged a right here the article which has the opposite charge that's what this equation means particle propagating along makes a transition Kudo particles wanders left-handed mourners of a 5 star prize considers charge and the status of the same amount this 1 over here a left him particle along and becomes a fine right-hander article about also considers charge so that's the way you could think about this it is describes on you'll kind of processed here which left and right and turn into each other but only at the cost of remaining charged particles to compensate the charge what the the probability for committing such a particle the strength of the interaction the constant heat the GE is called a coupling constant it's not be electromagnetic charges none of the of the coupling constants River a already described its quota you Carla cup wine comeback defied let's suppose is 1 of these magical Higgs fields of causing fires were magical Higgs field remember the Higgs field is also a charge carrying four-year-old suppose it has the former role would he How far too In addition something which is definitely not true of electrodynamics let's suppose this 5 field has a spontaneous urges rice store spontaneous symmetry breaking so that in fact it has a magnitude death let's forget Alpha to a moment remember Alpha where valve for gap eaten by the Higgs armor and disappeared the system by Raul itself off I was just proportional lose F quantity was F F was just the shift of the field away from the origin want happens over here right body issues full rigid get excited very easily and source just approximated by a constant this just be becomes approximately GE half sigh left this becomes approximately Gene F. sigh right GE is as the number of stores at those bad well OK here's how we separate and we go back remember what happened to the before autonomous fake world it has amassed a quarter at so we look at the Photon growers say the photon not the real far really museum w we were busy in the W and that tells us what effort mainly look act we firmly arms Stuart G. years but what is this combination this combination play exactly the same role as the original In the Dirac equation so I'm not some magical example of how a shift in the Higgs field gives rise masses of particles masses for particles simply means coupling between left and right and left Costa right-handed we identify batters mess and here we see that can happen but only if the symmetry is spontaneously broken Salt Higgs phenomena has a mullah role it gives the Fermi met probably is a mess of firmly on a massage Firmiana is a quote some GE Times f now there are different from eons of our world is electron you want their various quirks that only means but there are a collection of different G use and the world these genes accord you Carla couple and 1 for each kind of Fermi arm as an electron you call coupling bus estimate how big is electron you or cropland remember that the massive busy Mossad Robert W. bars on is essentially F anybody know what a mess with W. bars on this as about 900 GEV right to retain much 5th a cesarean 90 g of roughly 100 what a
mess of electron could be talking about electrons here this would be the EU Carla coupling for the electron half a meteorite sorrow electron here must be of a very small number what is your the ratio of electron passed through Izzy maps and 100 Versus half of MTV a house or a big number prejudice about on a much broader White a hundred GTV Vs half of em difference between MTV and Jedi is a factor of thousands dollars roughly a factor of 10 that his numbers about change the minus 5 very very small number Hi we know it we not from knowing book a massive W. both on and mess of electric next what's the next 1 the next 1 the new armor of it up corporate downcourt and was a variety of different numbers what's the heaviest of the year quirks the top quark awards at which Meris Eds about a factor of 1 and a half of tow times are somewhere between 1 and a half to times primed a mass of the W so that means for the top quark this number he is a number of water 1 so the whole spectrum of these different you couplings brings that nobody understands but 1 thing that's interesting is you say stock a story you've done Is it hour collection of numbers the masses of the Fermi but Nell you could hope for experimental conservation of experimental confirmation of these numbers let's go back through the coupling of a right-handed and left-handed particles fear and remember that F was simply the the frozen value of the Higgs field but I feel is not really frozen you really can shift around was thinks feel the Higgs field is the fluctuation away from the frozen value real Higgs particle re-elect particle is a fluctuation away from Seoul in fact will we should really right if we do it correctly is right f cost the Higgs field I'm sorry West was is us this is telling us that sorry was right the right or left Yahoo this is telling us that process can happen where are right here in the Fermi concerned a left-handed firmly on and the Higgs particle a real process left right in the particle can be calm or left article and the Higgs particle and watch the amplitude for that miss seeing you call or cop the Yukawa your call was a Japanese physicists sorry you Carlisle Yo call what it calls a Japanese physicist 3rd a forties are among other things wrote down the mathematics of the couplings between now firmly on both on won the Nobel Prize for 1st 19 forties for different physics of nuclear physics applications of these ideas many case point is that this same coupling cards which appears in the mass Of the Fermi eons also governs the process of a fermionic becoming a Higgs balls on and another fermionic so or why firmly on left-handed becomes firmly on right-handed legs balls on now would not be packed could expose here were not detected earlier so it becomes a very very important thing once they goes on the pact bid the study a different process season in which Higgs bows answer produced to see that the relative probabilities of producing a Higgs blows on by an electron and by a top quark or another kind of work that they have the same ratios Arabs these constants here for example it tells us but in the decay of the Higgs both on the committee registered became Higgs bows on into a pair Fermi arms that it prefers to carried the heaviest fifa has enough energy to do so yeah preferentially Tecate heavier formulas rather white and about That's a consequence of the coupling a larger so that's 1 of the things that I will become important and study properties of Higgs borrows around and see if we can take evidence from these coupling constants dog follow this sometimes it 4th group to probabilities the highly family square prefers my vary with the probabilities near but there's associated Chris only for such fateful so I have made the assumption was only 1 pack or in various more complicated theories beyond the standard model often more than 1 and then much of what I have to say for example there are Higgs boson our Yao errors supersymmetric models to usually to exposed by revenue just modified accordingly and across much of what I say the has been modified harbor costs the weak interactions arrest you to not you 1 so I'm going is giving you a kind of a simplified version of what pigs from about as much thus far taking into account all of these various gage interactions here's an interesting fact all of the particles that have seen the standard model could not have amassed war not for abuse show performers shift of Higgs field the gay bars on they normally do not have rest the only way to give them a masterly way to give them mass users from amount of spontaneous symmetry breaking associated with 6 field then asked his typically proportional just this act His Ian W. on all of the Fermi R & B class Of the peculiar property that the weak interactions are purely left-handed symmetries of the gage theories do not allow you to just write down your postulate a mathematical mass refer Iran is the only way that they get smashed through this shift of the field to say yet another way of all of the masses of the known particles are such that they are proportional for this symmetry breaking parameter f the shift of the Higgs field that curiosity which may be deepened but if you have a particles and they became better with the direction the opposite merit of the good therefore from electron is purely left-handed letter sent by particles prudery right Berwyn arrest continued the court work pandas are equal sorcery electrons like him if I he also saw I Rimmer rip positron which directs would be but if we all your game is not and his fur it's just rip your convention we have a lot more experience of electron do with positron we can't name things fiber we can't say the electron meaning the full complex of objects that go together and with electron called left him nevertheless the positron right if I have a flow of electrons and positrons collide together could make for example a easy balls so I guess it would be a left-handed electron manner right here how's it from our could make a photo that Hall the a
normal Marie agree borrowed from the brokered you do you hit any particle hard enough with anything and I will make among other things pass certainly for positrons Richard of a good and you could make a part of positrons by just colliding electron with photon you have tried hard enough for the photon you make electron disappear but I will calm electro electron America positron perjure What's your work capped a fine and by I ran the describes that case finally diagrams basic find diagram for the basic vertex ears electron electronic photon but if we football lines around contenders electron costly minors it last of positron and folk art war better yet let's story West a we said electronic collides with photons and makes an extra electron-positron OK so here's the uh photons colliding with electron them another photons emitted and that photon turning into an electronic past as a fine and diagram of fairly complicated find an offer that would take an electron a photo armed and turn it into an electron electrons and positrons was all kinds of prosecutors Otto E. Tito U.S. team practice how much newer not at March so yes you can nuke in there you could change you view your bearing magnetic field for thought full if this last fall as a follow-up County are hard to make polarized electron what would you make them you could accelerate of electrons are made in the so are charms of which a polarizer arrest report remember but there have been no accelerators or for a share of the vote a a flat details of how accurate it's it's not easy to do we need he big magnetic fields and took a while for to generate technology do were polarized electron beams colored there is a further trade talk a freely 5 or 0 in these standard model and old good prime we before recent years it was not known whether the trader was that was thought that the the neutrino was massless now the massive tree was very very small number there are several different neutrinos electron neutrinos your neutrinos very small Arthur within experimental error remove the speed of light and that means that possible for them have only a single handed the Standard Model neutrinos for are left-hander to withstand model was not even contain anything you call right here neutrinos half generalizations of the Standard Model have right-handed neutrinos but those right-handed neutrinos typically have a very large mass and Vera too complicated story will make will come to it but in the simple standard marble columns neutrinos are massless now doing all are really massless not we know they're not we they're not because of neutrino oscillation so we know they're not prepare mess of very small and the right of free electron volts or smaller shares were sold In approximately a cost matchless quite Wetteland as neutrino was really curious member man's tournament here a thing which turns left him with a right here of the process in which left him with can make a transition right now are were happens with military neutrino there are left-handed neutrinos and of course they go along with the right here in the in the tree From trio was left him with me in the tree was right here and 1 way of having amassed for the neutrino used hammer or left-handed neutrino make transitions right he he banditry masses always prefer it's always left-hand turns and the right-hand turns the left in terms of right processes which involve when the train was curiously the right here in particle which the neutrino can make a transition to argues the entire particle of OF arrest him trees so that's thrusting go back White code why could be electrons real electron why could the real electron not get amassed by mixing by go left here the electron with the right here positron frankly I believe pretty amazed to see AT electron turned for positron because of which charge conservation so that some options for for the electrons wise allowed for the neutrino as our charged over charge that the buzzword terminology for a particle which gets on from a Dirac equation for a curious fate and the right-hand side here is the impact article of the left-hand side for a trio of particle which gets masked by mixing in this way with its impact particle called minor particle my airliner it was my are we saw a younger Italian physicist America's what are the model at Torrey my around I who disappeared shortly after things my a particle was heard of again was academically heard army was never murder Norwood nor have I smile after the flood area outside fire back yard and talk about so that the mass of the Higgs particle was also generated by the Higgs particle was also ordered the same at so we more or less expect the Higgs particle will have the same order of magnitude W. people's on somewhat heavier but said but OK so let's think about how we found this is somewhat striking formal masters in the Standard Model traced back to this parameter F F 4 0 0 they would all be nasalis all the particles of the Standard Model With the possible exception of bombs on itself for all the particles of the Standard Model all the familiar guise and many of the on familiar ones C. W. so forth top or bottom quarks store works are all of their masters are respond to this proportional F In the former of particle physics why he's that why and then no particles in nature was messes on might not be much much larger than half or maybe not particles with masses much larger and therefore just haven't discovered that he had warned that because they are the limits of our energy use all roughly at about that level this number a half in order to agree with the masses is Ian W. bows on this number F thought as a man is about 150 GUV if what particles in nature Was may ask for much larger than 200 GVO so we would not have discovered their surpassing particles that we give you an example of particle in this context in this Our slightly fictitious but but still a qualitatively correct context where a particle could get a man that was not due the expose are supposedly have particles in this weak interaction context where both the left and the right here in components both had the same charge With respect to weak interactions supposed such a particle
existed then that it would be no ob structure having a maps which had nothing whatever to do with it could have a mess which would be arbitrarily big thing could be much much bigger F it could be handled the 16th thailand's bigger and bigger f it would be no obstruction to it having amassed having nothing to do with this are there or other kinds of particles that could have messes which are not due to the thinking now is the natural scale of elementary particle physics wherever it comes from and we could talk about where it comes from his much much bigger than ever any particle that can have amassed will have a amassed and that s will be much much bigger than is only those particles for which there are symmetries which of deep underlying reasons why in absence of spontaneous symmetry breaking making have met the gage bows on themselves photon was 1 of them are these particles which are purely left-handed they are forbidden from having S on the last spontaneous symmetry breaking so maybe it's not so surprising that all the particles which have long enough energy could be be packed with all are the ones who was masses are coming from the same origin mainly on small amount of spontaneous symmetry breaking all the other particles which could have masses independent of the staff simply up apparently have masses from scale which is much larger busses thinking are so it's not a mess and be particle spectrum as we know it consists of a particles which would have been matters worse if the symmetry was not spontaneously broken all responses who a small amount of spontaneous symmetry breaking par that's the thinking in any case may regard for that a shot on therefore we could mean that and of course with me by rail a tough game with which forms or weird raw of awards which can have no cure they do not play much role in ordinary physics now 1 exception is the possibility of dark matter their best guesses about theories of dark matter is that the masses of them are much significantly larger than this possibly by a factor of 10 more arduous path for such particles on reasonable for various reasons the thing that that they get a mass in this way and so dark matter particles may be the 1st indication of a spectrum of particles was masses do not come from but as printing risk this particular spontaneous Richard Burt are not would wear cosmic rays electrons are year of protons the photons repair matters is the matter of particles energy massed means energy arrest or to grasp was energy of cosmic rays are basically anything pop 2 of our tent 21 electron volts of the 21 21 my mind 12 hour remembers years 12 10 of the 12 which is very very high I accelerator answered every cosmic-ray coalition and Minnesota sense will not be High in energy probe has accelerated world and the reason is because the cosmic rays particle arrest me collider will call together particles and it's you may think of twice the energy but much more pulled that we can't Hawaii are heading a particle arrest with high energy it is not the program's potent was heading 2 particles over a head-on with a good deal Lauren G. soul work will be measured and Stern will be processed easily energies Our nor storm hard storm a hard as cosmic word how she thought a she did if the merger that a Rob you have some value could cast by what magic is it that nurse shark parents these expressions In the Dirac equations and so forth correspond to the same physical idea and more complicated but you go back to base a basic relativity nuclear vests special wrote you could ask the same question definition so different definitions Of met 1 of them is Anderson our Hargrave to get accelerating and the other is energy at rest why is the the energy of an object at rest related to be and are sure of how much how hard it is to accelerate that is contained in the rules as pressure relativity but once you know back then you might as Well focused on the definition of May as energy arrest so the question is not have to do with particle physics at both have rest but if so low that at the 0 exactly why couples yacht yes that's right on good sorrow that's correct once it gets messed it starts to couples were gravity field now that's a little bit not quite accurate fault on Star photons do coupled with with the gravity field but what is it about photons there wasn't really couples gravity field Energy Energy Energy is a thing which really couples the gravitational field how we know the photons coupled with a gravitational field they abandoned their trajectories of photon Robbie Fleck gravitational field actually equals reaction so that means that the orbit of the sun is slightly perturbed every time pop on those pastor but that's pretty negligible but just the fact that the photons of deflected where McGraw around the sun means that the messed was particles do Koppel gravity bogged down to our articles at rest their energy is simply mass you have to particles more arrest the gravitational interaction between the West for this it exact resist say a a a a a a here to correct our resistance acceleration of iron particle is bigger than a particle arrest of the only the only subtlety is that the resist caught a resistance the resistance to acceleration of particles moving back z-axis then a different effective Charlotte if you make a force along the c-axis are make force perpendicular z-axis so there's no universal concept of mass unique man's rock particle which is more in terms on which way you push a ownership that's why people spot talking about massive particles which left stop talking about that and defined mass to be the energy of the thing arrest but yes charm that is correct or more Genicom object used the harbor or rose to blood and it's not left-hander arrived here on our electron arrest breath candidate this is relationship between the momentum was particularly well-defined behind them momentum the definition of a right he the particles 1 whose screen heroes all along its
momentum and the left-handed particles were In his operas so the answer is that there is no definition write him and left him for particle where it is mostly useful for high energy particles north of here 1st so I that a yes a flood that has a flaw this now you really pushed me to be be a juror who are at odds with the subtlety which I have told you about that's the difference between what is called car ready and he was to be Iike promised about a little bit loose in what I mean by here so let's go back but uh lead ID of handedness as I've defined is especially useful for high-energy particles particles from momentum a lot when the particle was very small from the handedness are issues most of God are losing money it's getting too late for combat will auto a 1st case of aid not bad for 250 g the Higgs particle is good evidence of good a wider all our high-precision noon experimental and theoretical comparisons between the properties the masses of but both they would have they would respond to changes in the mass of the Higgs balls on the way and from experimental knowledge of the masses of these W boats are because research bound by the Higgs masses probably its West 160 years plus less than the 250 years but not by an order of magnitude F look at our report but purchased earlier possible it hold of a fan favorite that if you had for which she didn't see a generation and that valid away having both of them the beatable at 1 of your articles didn't the generation that would food is back we'll talk maybe next quarter Greek knew about more Bable demurred what kind of different physics Compte Place in different on but simply stated you could have anything happened most anything happened and of a minimum of the potential so I didn't wanna get into that getting tired you could see as is more questions if the energy level would required more than 1 class 8 for next not a value of course but the guys are was my work look I suppose we lower-class and or I have to be away at some point but I don't think that's a retail all year young while we don't have that to classes we all have to classes for Serbia for the year before the 11th week but from the 10th week where which lets me when I get Church you have share OK yeah if I AFI recover from my said you know there are various
scenarios for the value of the Higgs hours on merits and some of them with a range of energies is quite echoed is easy it's the rate the things of things decay sometimes it became distant visible things so far the Higgs boson arm will not be the 1st thing discovered that a coarser may be the 1st in discovery also discovered by there's a lot of land for Discovery before we export particularly but I will say that they are there because there were no nor has it does not have to do where the match it has to do with their absence of having any kind of charge to distinguish the particle from me and article the photon is are charged with respect any kind of charm that we know about doesn't participate in weak interactions it's now electrically charged ghetto trio of and that if they also their age our fold that were ah vary nurturing hours on well now some people would say there's only 1 kind of neutrino and both left-handed and right-handed other people would say there on neutrinos tree was appointed as the neutrinos mix together with me and banditry euros and form a massive my Aronoff article which is owned by Article why because it's a superposition of upon corners of that article Sobel corn beef birthday while a I say Yahoo Yahoo Yahoo Rick to home but only with them on remember that neutrinos have weak charges they interact and the weak interactions star 0 Our EU weak interactions provide this collection of charges that we've been discussing neutrino was not charged with respect to a weak interaction with respective busy W. bars on the particulars being neutrino or and treenail interact differently with gazebo so are you might say that with respect to Izzy bows on the neutrino and neutrino have opposite charge they also have left Palm removed Brook is brought a fair of 1st thought that you should we restore poor members work but after that OK I am not in my head yes but I know people my heart no role and the reason is that left on number is not really thought because right it's connected with my and the massive neutrinos or retrieve also of the tree for more please
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Titel New Revolutions in Particle Physics: Standard Model | Lecture 9
Serientitel Lecture Collection | Particle Physics: Standard Model
Teil 9
Anzahl der Teile 10
Autor Susskind, Leonard
Lizenz CC-Namensnennung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/15081
Herausgeber Stanford University
Erscheinungsjahr 2010
Sprache Englisch

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Fachgebiet Physik
Abstract (March 30, 2009) Leonard Susskind explains how the Higgs phenomenon interacts masses of quarks and leptons.

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