Supersymmetry & Grand Unification: Lecture 2

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Supersymmetry & Grand Unification: Lecture 2
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Steiger University so much
so much talk about Turkish supersymmetry has to do with me arms and bows on now and the relationship between them symmetries between them so what actually before we talk about supersymmetry we should talk again about fermions impose on at a summit on and peculiar facts about Jeremy Irons 1st know before we even talk about Iran's let's talk about rotations in space now we always said that a rotation by 2 piety is equivalent to know rotation at all it's not true it's not true let me assure you that if I take my like and I rotate my arrest took part of it is not like doing nothing but now they tell you if I roast headed by former pie which I will do for you in a minute I think if I voted want by its equivalent to doing nothing so you wanna see me what they pay for applied until you that kinda yes I can right now to started this way home up rotate by 2 Piute starts heard Tom up back and this is a topological furor about rotations in space is a topological Thierman tell you explained the topological fear for you I proved it man proved it don't need to prove it by mathematically proved that the by abide by his faith that from the Flathead exactly right but the rough but but they of the appear actually says is the cake a box box has walls it not box good basketball or some sort of object and connect that basketball the walls by strings any number of things that doesn't matter disconnect measuring collected from now I tell you and I think you believe me if I take this ball and rotated by Tupaiidae I'm going to get a hell of a tangle the strings individual all tangled up and the questioners can I untangle them by looping them over the ball by out rotating the ball further rotated around 2 party can I get rid of the tangle and bring it back to this configuration anybody know the answer but they buy took pie no no matter what they provide box is a effects of his theorem about rotations on the ball keep being spatial infinity the box really represent spatial Finley keeping a special effects elaborate pick box so question can I or can I not only due back that rotation abacha parts was we we we do not we simply rotate to party and we as Underwood by moving around the strings wrapping taking them over the years the ball doing whatever we have to do the strains flexible buried in stretchable but there are unbreakable and they connected both the ball and the boundary mathematically it's the same operation trying under Rule this mayors that a rotation by by for what party but you can do it so the answer is for energy rotation by an even number 2 pies you can undo it by moving the strings around picking over the ball and so forth at a topological theorem about the equivalence between 80 rotation by Tupaia no rotation or not equivalent really a rotation by 2 pipe is not equivalent topologically no rotation a rotation by 4 pie is this is kind of a tour of but stroke OK let's now come the properties of waveform churns particles and now I'm thinking simply about their speed imagine nailing down the position of the particle and only thing that's important now it v of a particle and the spin-off particles described by quantum state vertical St spare I'm even thinking about premier arms or bows on in the case of firmly on the spinners have adjourned the case both times 2 chair now the question is what happens to the state of a particle if you rotate the particle by 2 pie that you could imagine for from electron actually doing this in a laboratory how would you actually rotate the spin of an electron Bhutto party but no good way to rotate him whether we hand rotated but that doesn't work so well magnetic field put it in a strong 2 ways you could do it you compose tourist strongly Minnick field and then Rook take the magnetic field around on telecoms back yet are actually do something else if this don't happen still lie in the vertical direction you could put a magnetic field in and just have the process by itself around the lead author of the magnetic you see way will you can rotate the span of a man of of a charged particle simply by grabbing it with a magnetic field the rotating it what happens to the state already been particle when you do rotated by Bhutto party while usually we say has to come back to itself after all rotation by 2 prizes nothing at all but we found that that rotation to party does we can do something so we might suspect and that we rotate the spin of a particle but 2 it gets something happens the way the simplest thing that could happen to a just get multiplied by number why multiplied by a number instead of some of the more complicated operator well that's a real complicated Bell why because we really we secretly believe that no experiment will be kept the rotation by price and if we multiplied the way functional article for example by a phase of my mind 1 that won't change any physics we really secretly believe nothing nothing experimental will be detected by rotating pie 1 possibility is a guest multiplied by 1 of the possibilities circuits multiplied by phase but he is all we do know if we wrote rotate at 4 5 every rotate but to and that gives us some sort of babies the for a rotating again by Paul I will just squared and now we know that rotating by full applies equivalent of doing nothing all day best topological theorem knowing nothing at all had better just goes back the same state cell the mathematical argument says that squared and must equal won his only 2 possibilities tricycle plus 1 or my 1 so we could have either possibility when you rotate a particle but Tupaiidae just been UE the multiplied by plus 1 or you multiplied by minus 1 and interesting question is could you ever imagined would just as a side issue is there ever any experiment both arms observable consequence of the fact the potential factor that the wave function of a particle might change signed when you rotate particles and it was generally considered to be a totally on physical operation you could never detected another words here will be the experiment you take a whole family of electrons prepared identically you take care for them and you stick them into a magnetic field you rotate the magnetic field by 2 pie you think the other half a new the nothing with them at the end of the day is there any experimental difference between the into but that experiment cancers no no you cannot tell the difference which ones that rotated but you could do something else about 20 what it you can delay to slit experiment just just to tell you the meaning of this on mathematical fact you could do it too slick it which you take electronic let's start with a single electron not multiple Elektra arms or 1 by 1 we picked electrons 1 by 1 and we send them through the electronic I those the opera's slid on the laws that we don't know which were not allowed to talk because of we look we will destroy the interference pattern over here some interference pattern over here but now would do without looking at the electrons here a year where Place a magnetic field over here a field over here it will also do the same
thing over here at all
imagined that electron gets temporarily trapped in this region by whatever temporarily trapped and readmitted if we do absolutely nothing for these be fields was still
get some interference pattern here the electron goes up so here and get stuck on the B field and it's readmitted be fields are very interesting or same thing over here but
now we do the following we do that to slit experiment end while only electrons trapped and what these 2 we we rotate 1 of them and not the other rotate 1 of them and not the other Red the wave functions here maybe only get multiplied by a minus sign suppose it does the away function here does not get multiplied by a my side really
is multiplied by a minus sign a plus sign biggest multiplied by a plus sign nothing no detection but gets multiply by minus and this
1 away from coming out of here was not get was at the interference pattern is shifts at it shifts of up Hathaway right a shifts Maxim at minimum so yes you can detect Our signed change but only by splitting the beam of electrons and then rotating half the B B over here being so it is an experiment it's a real phenomenon but he would take the whole experiment and rotate all of it both magnetic field simultaneously then you detect nothing Our it's very similar in mathematical structure of the story that a few rotatable without rotating beat the box are you could detect the fact that you rotate pies if you're allowed to rotate the whole thing ball and a box of course you can't resources similar a similar kind of thing Yahoo tell exactly to rotate the magnetic field by 4 5 the effect goes away right it is it is was not a laboratory experiment or suggested by run myself 1967 there would actually done that Yao OK so far OK so now you could you could you could do experiments with electrons you could do experiments were charged ions of various kinds and you could see which ones fall into the category of getting a minus 1 in which 1 not the ones that don't have a minus 1 other ones where the interference pattern of not shift the ones that don't get a minus sign the ones with interference pattern bus checked the answer is all get a minus sign all bows owns market get that's it 6 1st of all it would be an experimental fact he really did the experiment it's also deeply embedded in the structure of our however mathematics of quiet field theory and acquire mechanics but so that's an interesting distinction between firmly under both on His young after the analogy with the spread of rules where roughly speaking bows arms behave as if they were connected by strings of firmly have some memory of having been rotated by 2 parties they have sort of connections there were 2 things which remembers where rotated by 2 pipe this is just a mathematical wait to see the topology topological factor rotation by compiling not so innocent was replaced by 4 but want you know that we forget about this while which 1 at the while knowing that in this experiment younger 1 of the quantum state of this 1 was localized over here the quantitative this 1 local Ottawa what what's the idea the idea it is you create 1 way or another a superposition of states which the electrons here or its here not to lecture on an electron which is either over here so wave function which consists of 2 bulges probability at half the electron over here probability for half of electron build he both of these electrons now after you've that the 1 electron 1 electron but if the electrodes here or actually putting inside a box to box so we create an electron over here we Split the being which means we create a superposition states where might be here or might be here with probability in half and then we will take this box but a magnetic field we a better ask others electronic or not whether or not there was an electron in it we rotate the box now to start with the wave function was a sum of 2 Sharon's sigh 1 which is the way function in here and site tool which is the wave function he sigh 1 plus I too was the four-way now only rotate the right can box without if rotate both boxes of electrons but charming affirmed than the whole way function changes but the hallway function changes signed all physical quantities are proportional Cloverway function times complex conjugate the minus sign will cancel out but now supposing we rotate 1 box relative to the other then what happens is after the road after the rotation this wave function as change sign this 1 has not real consequence of that if these two-way functions or identical about reflection of our service center here that would say that after the rotation the away function was vanish at the center sigh ones right to have exactly the same shape and let's even supposed after we bring them back together again by symmetry the wave function will vanish the center here if the wave function as odd the wave function is even then after we bring them back together again it doesn't have the vanish shippers so interesting consequence of this is if this is was a friend we rotate by 2 piety and then bring the wave functions back together again we will never find electron and acid example of an interference but the point is that theory it is a difference between sigh 1 might decide to fly 1 offsite to enact that difference Comey experimentally detected a state see it is full shit that is not so we had a slow start while there's something like that broke my job there is if you look for the electron in such a way that to compel the woods which 1 was Ian the knee interference pattern was destroyed right and that was 3 tests call right the result is that a yes or no and 1 actions repair would be a barrel oil still status a collapse is food to fuel its if didn't fare plus I thought it was easy to say that it is serious about interference by aerobic Robocop bleak its Is there a few if you wrote take that's been ne you and destroy but papers the
by anything except to Tupaia for price you'll lose some parent and treachery rotated by 180 degrees you completely destroyed but that's that's correct you can't interferon ups In would bounce back you could only interfere things which or otherwise saying that right good so we now have some bits of information about firm they change signed the rotation both arms dumps now Webb's come to yet another question let's to question about finding a buyer Graham's but could not find diagrams I have in mind now very very simple they have no external wines at all they're just fine in diagrams in the backyard empty space and they consist of nothing more complicated than a single closed loop a single close look could be an electron or it could be a photon for example could be a fairly or it could be of I am and this final diagram among other things controls but 1st of all among other things the amplitude that you start with nothing you get top so it's part of the vacuum structure but Graham has a value that value is a contribution of the vacuum energy let's not let's not try understand precisely why that sold but just like the diagram which is attached the particle he shifts the energy of the particle a diagram like this and free-floating space would shift the energy of a vacuum the question is does it shifted up or down find out that the answer is different from those arms and fermium so let's think about I'm just a sign of a diagram which looks like there's from Iran's arms amazingly without doing any work at all or we can prove the desired result which will if there a photo here the way we do it let's start With the bombs on Kate let's start and I think both places simultaneously let's begins with 2 loops another words there I was a little but the production of a pair of particles in the subsequent annihilation of it while you could just think of it as a particle going around in a closed loop in space time if you think of particle goes around them a close look in space all are more physically West colorfully production of a pair of particles particle and by particle pair and the annihilation OK here looks and let's ask about the signed but of diagram associated with just 1 who became a positive or negative What about told a separate groups like this we find diagram consisting of 2 separate loops is just the product of refinement diagrams reached loop separately if there's a plus sign tho 1 will then there will be a plus sign but to what about is a minus sign for 1 will still be a plus sign for the loops so they have suffered cyclists disconnected looked like this is always positive whether or not the sign for 1 Lopez negative now let's do the following let's assume that our particles of Fermi on news that break is over here and look at it right in the middle of people 0 while these 2 things in here the but close enough together but they are more sorrow at what happens what happened the amplitude 4 8 1st system if you interchange tool bars are so if you take the tow bows arms and exchange them plus sign the wave function from HBO's arms as always symmetric which means a few interchange then plus I what to take to firmly on the change their mind sign that's a property of Fermi arms embargoes on so firmly on the way functions are enticed and so few interchange at for me and to get a minus sign bows on the plus side self we can't compare to things and the 1st thing we take these and we don't change them that's just too low the 2nd thing before causing it up with change them we just interchange which was which is what happens if the Fermi arms if on we get a minor sign Mr. Bos we get a plus sign from here we married the gold from tool tools to 1 little this 1 will now this is just 1 that's what we went from tool for 1 loop just changing to particles from look necessarily has a plus sign if the involved firm eons vendors assigned change when we interchange 2 particles so we single loop like this me aren't necessarily has a mind sign associated with the single Loper bows aren't has a plus sign near the consequences reverse of profound what it says is that their contribution Of the vacuum energy move on fairly arms is negative contribution Loper both arms as positive that's very interesting we have this very Strange puzzled about the vacuum energy that we talked about last time the vacuum energy whatever it is in nature is very very small would quote dark energy it's extremely small amount of it in this room is extremely negligible and the naive calculation in quantum field theory would give an answer a 123 orders of magnitude larger is at least and minimum interesting that the quantum field theory answered either be positive or negative and that its negative Fermi on positive for bars on the answer depends on all kinds of details about particle depends on the mass of the particle and other things pans out of charge depends on all sorts of things but at least leave encountered a way he to be able to get both plus signs and my besides the fact that they cancel out door 123 orders Best Places bizarre but at least we have the possibility of canceling contribution
on all things being equal will give equal means same man the same charge all things being equal embargoes on and affirm Iran will give seemed contribution to the vacuum energy except 1 with a plus sign and 1 with the miners now that does not explain why the vacuum and you 0 0 but it does perhaps Crete a fault in your head perhaps there is a lot of cancelations between involves on what it would take that habit exact cancelation would be we'll discussed you would necessarily have perhaps for every bows on a fermionic with exactly the same these diagrams duo depend on the mass of article that we don't have to know the details of how they depend on the rest of the particle but differ every bows on we have a firm armed with exactly the same and the same properties in every other respect then we could imagine we could conceive that the period might exactly cancel I would be back in energy that's 1 of the things that supersymmetric theories can do I will tell you later were supersymmetric theory I have told you yet because 1 of the things of supersymmetric theories could do they can cancel out precisely are the contribution of actor energy now we know in nature we know with absolute certainty that there is not for every particle AT image reflection particle for every bows on there was not a firmly under the same message every Our and vise versa we know that an example would be the electrons Is there a particle in nature with the same electric charge as the electrons but which has the opposite the riches of HBO's Armstead hernia and we would know if they were we would know with certainty and the way we would not is because collisions for example electronic electron-positron electron is a positron what happens to an electronic 89 a C plus what the vaguely Nikolai virtual photo now if their waters a part of its goal of a partner the electrons which was a bows on with exactly the same charge then it could be produced draws a line then it could be produced From the virtual photon with exactly the same probability as electron if it had exactly the same man and we know this doesn't happen just order laboratory scattered electron positron telecoms hours an electron pass or not they are of a ball was armed with the same message are so we know that In fact in nature there is not this symmetry of this reflection symmetry not not reflections based a reflection on both on and on and we know that that's not true but still it's interesting to contemplate the fact that if we had a theory which was sufficiently symmetric will discuss what we mean by sufficiently symmetric but was missed efficiently symmetric between both on Fermi arms we would at least have a chance of canceling out of this vacuum energy release have a chance so it's itself a thought of what to keep in mind another thought to keep in mind can it helpless all with this self energy of both arms we healing have where's bailing out these find diagrams which give rise through quadratic they virgins is in the mail AT boards are even if the myth of the bows on even the bear Mansour both arm was initially 0 with Obama these diagrams create huge masses bows that's a that's a problem that's a problem for the reasons I said we like to get rid of that problem we would like to create a theory in which bows on don't get this huge amount of mass renormalization from what we the we already have a theory in which firmly on don't get these huge amounts of NASA's remember we discussed a few minutes ago that Fermi arms because of this left to right switch firm on In many situations the self energy of a fairly on will not be infinite for example if you start with a firm Young with no manners at all it will not get this big merits Nasup puzzle for some reason your theory was concocted in such a way that even after all this renormalization takes place even after all the worst looking fine Bagram Jakarta magic there was enough symmetry enough structure the theory that meets certain that the firm eons and the bows arms traveled in Perez and always had exactly the same partners then because the firm eons don't get any asks if they didn't start with it must also be true of the bows White while I'm not saying that we can make such a theory in the face of it it seems we can make such a theory because obviously the bowlers arms do get big messes from self interactions and the Fermi on stuff but he is that you could imagine as an example take the various find diagrams which contribute to the south energy of the bows on you might have a final diagram has emerged as an illustration just as illustration for years but you might have a mother father and Raul bows on but you might have another fight diagram where what runs around the center here it is fermionic was going around loop firmly on going around firmly on the HMOs arms always have opposite signs for these little solar can't think then we can imagine that if there was enough symmetry and at every stage at symmetry was correctly preserved in detail the cancelation of a South energies of the both might also be exact art or cancelation of a self energy for the formula and that's exactly it starred 0 in 0 if there was such a symmetry between firm eons and HBO's arms true rigidly enforced by the mathematics of the theory somehow then we might imagine that however there are a series where the ball is on the moon not get these huge self energies that itself is not good enough we know that there is not an exact quote mess equivalence between from Iran's involves on but it's a start that right but sticker break cover human combat of the zeroth
order hypothesis it is not that there is when I see 0 thought I don't mean a mathematical I mean some rough approximation for what the story is that for every day article in Nature there's a partner of the opposite of what something is the opposite of firmly boson composer must be more Uribe Firmiana nature like the electron there's another particle which is a bozo with integer spin with the same now with the same charge yes will In charge electric charges for now I would say with the same mass but we know that's not true or not with the and for every bows on the military and 4 members of Bowe's on this won't pay basic basically doubling the spectrum of all of the elementary particles How about the fact that they don't have exactly the same factor masses are gonna be quite different well if the man's is equality we would discover that all of this bad John cancels out exact Corey supposing misses almost but not quite equal we still might have a lot of cancelation perhaps not a complete cancelation but an approximate cancelation of masses were not exactly equal we don't care for example Matt had there might be some energy for these bows are we just don't want to be healed orange so I diagram like this in the like that will not exactly canceled unless the masses running around the look pure exactly the same but if not exactly the same but closest we might expect a good deal of cancelation approximate cancelation enough cancelation to keep from getting this explosively large cancer back we will talk about supersymmetry supersymmetry is nothing but but it is in fact much more but among other things it is this idea that every particle has partner Of the opposite statistics is the the right word statistics means I mean this boson as what supersymmetry is at a cemetery which relates firmly on the bows arms in such a way that every bows on hazardous fermionic partner it's fermionic super part the common super partner Paris end With a precise Mesic wounds of the particles partners we would have precise cancelation of this kind of thing of the vacuum energy and so forth with almost be generously be generously means a quorum we can have approximate cancelation that's the working hypothesis that these things which controlled and keep these phenomena from running away in being enormously large is cancelation between from beyond the bars on now were not so we we are going to say more about it than perhaps even do a little bit of the mathematics of it it's extremely abstract as I said that doesn't mean difficult just means abstract about but that's the zeroth lawyer idea every particle comes equipped very sober partner those super partners I have never been discovered in laboratory not 1 of them a single 1 of them has ever been discovered the laboratory the implication is that must be of good deal heavier I showed you how you might detect the super partner of electrons you collided pair of electrons you create a virtual 4 times and then you create no charged particles which are the partners of the electrons the fact that they've never been discovered after means that no experiment has ever had enough energy to create these particles these particles must be quite massive promises basically at sea Agent detectability beyond the edge of detectability that means hundreds of EVE hundreds of times the mass of the proton that is this really and far-fetched that sounds very far-fetched that we just by accident all the particles all the partners I happened to be cool heavy to be seen as a about really sounds like really not so not a good they're practice well it's not really that bad because when you look at these supersymmetric theories what you discover what you discover is that some of the particles have a natural can not natural tendency of the property natural property that he only way that they can get mass from The Hague phenomena others can have made without their eggs from around it turns out new series just mathematically but exactly half the particles some of them fermions some of on necessarily all the demands of the Higgs phenomena which is another way of saying they must be massless until their spontaneous symmetry breaking of electroweak of the Higgs boson phenomena and the other half are allowed that mass without that so it's almost natural to say that have the particles might be of good deal more massive than the other half hour is for most of us it's a it's a little bit of a stretch the supersymmetry idea Mr. tho little bit who were lucky that we just haven't seen it yet on the other hand there is some rationale for why the particles that we've seen happen to be the ones which have low enough may ask to be seen and why the ones we haven't seen could conceivably have hired us so we have to wait and find out but that's that's kind of what LHC was designed to find out our originally was designed to to detect expose but by now is generally conceded that our Higgs boson I've gotta be there and it turns out to be the hardest thing discovering a list of things that you might want discovered be much easier things and more profound and much more around our interesting interesting and a point from point of view that we don't know of there or not is supersymmetry so gotta be studied collisions at high enough energy to produce these super partners if the super partners are low enough man who were to be detected now 1st question had only known that they're not way off at enormous man what what happens through this cancelation if half of the particles
were at an enormously large mass How the survival of the plant commenced then the cancelation would be extremely bad at Blix said it would be just as bad as not having these heavy particles of all of practically is bad and instead of having if it itself energies you would have a self energies which were as big as the park so if you want this supersymmetry to play the role of somehow protecting you against enormously large self energy correction the main difference between the bows on the permanent cannot be who in fact a couple of hundred GUV beyond that cancelation would be 2 they have a decent explanation of why the self energy of the Higgs boson on was not too big too big for for experimental reasons if the role of supersymmetry it is to keep the Higgs balls on from getting much much too much then the difference between the masses of the particles and super partners cannot be all that date that has to be roughly speaking within the experimental range of the LHC that's a lot that's a logical what's going on super partners in this symmetry To protect against having the Higgs blows on dragged up to enormously high energy and everything else with it but role super partners after the masses of the particles in the Super partners were unknown not to be equal how different can they be and still do the job that they were intended to to do and he answers not too far from experiment Boer detectability Yap questioners was Robert we had to go that far off statistics earlier because I was wrong about there that is well that energy is not really up robbery gift illustrated vacuum energy is 1 thing the supersymmetry could do were really more interested in In the south energy of the bows out of hand both arms where's be here but all the other will have to be they all have to be close to them also the set the man's splitting is between the particles in the Super partners cannot less the this same he have had the overall ruled that in order I know 1 possibility is that in the aggregate canceled that would not require our inexact matching between reruns of both on which is required of the sum of firmly so approximately cancel against the sum of all bows on right that's being To be an accidental cancelation our as uncomfortable and Evans a surprising and fine-tuned as the original problem was you could say the formulas give you the opportunity perhaps have some negative signs an extra there is giving the opportunity but it was just a question of Ind In an aggregate cancelation then you would say well this was an extraordinary exceptionally lucky accident but if you could build series if you could build series with this cancelation was more natural given below series with a higher at the moment the way I stated it's not very natural so the question is is there a mathematical framework that contains these kind of symmetries between fermions of embargoes on which also could explain the fact that they're not exactly equal and natural wary and which these are in which the symmetry between them by natural nobody knows exactly what natural means natural means it's sort of mathematical consequence of some reasonable postulates that these things approximately cancel each other that would be much much more satisfactory just saying the whole bunch of them accidently cancel against a whole bunch of your warns that if Dutch the vagaries of the I think I think that just means we don't really understand them know what's natural what's not this is true this is true whether who is no question that were groping around for answers to these things 100 officers is the mathematics of supersymmetry and spontaneously broken supersymmetry we haven't discussed that was emotional spontaneously broken supersymmetry which will create mass differences particles the mathematics of that conceivably could be something which would not conceivably and we know areas where it really will do the job are the only question is the right theory end is the only theory were told that the moment yes but that doesn't mean it will stay that way topped by a court that was slap the roots the measured yields the articles that I would like to get cause where was the power would tell Khan that was discovered yet yet but the that was the 3rd of the well follow but I think it for it's not the sum of all that duties measures what I call is accuracy this is a OK good good that's question Frazer question a bit differently on that that is a very very good question has come back to this electron-positron story and super partners as an illustration all I said it wasn't enough energy or at least it had better be would that the use the partners a heavy enough that current experiments have not had enough energy to work to create them but you might expect you might ask others possibly direct evidence the kind of indirect evidence might be something like that is a fine and diagram With his electron the positron Corrie create I'm out of drove a super partly reversed a strong super partners would bottom lines but there really isn't enough energy to create the file super partners so they
have to annihilate again and that means we just think of this as a virtual process which violates energy conservation a little bit for a short time they might as well as doesn't this diagram of modify slightly what electron-positron process like and kid to detect that this difference so it becomes a question of high precision called high-precision electroweak a high-precision of phenomenology particle physics where you don't actually look for the particles but you look in very high precision experiments already done you look for evidence of this kind of thing well what I can tell you it is to some extent the answer is that these high precision experiments dual constrained things and they really are pushing you be edge of the parameter space nor observed it's getting a little dicey as to whether you could really fit supersymmetric supersymmetry symmetric particles theory it's still abide by no means ruled out by no means ruled out by these high-precision electroweak experiments but it's a very good question I think we answer is if we would have an electron positron called light where known for wider animal energy of maybe and I'm not sure I'm about my numbers here but a few times larger than slack we might be able to do very high precision experiments and rule out supersymmetry basis of high precision experiments our we don't have that why an electron-positron collider incidentally a wise said that if a high-precision electrons and positrons is believed collide with EU collided Allante collide a drama have but time basically protons our necks they consist of several quarks and when you trailer trying to do was collide quarks together and the it's a mess it's a message of much Mondesi things then to elementary particles colliding together like an electron-positron so electron-positron collider is a much better machine a high-precision if we had such a machine now at all I 1 GUT or something like that we could probably do business with a high precision but we don't know what we have done Rumsfeld said we go with the a machine that we have hurt and roamed build Mel muon known not only that but if all but also a lot of time to see a lot of the other way be BY but they would have to get the Super particles before going to the extent that it had a loss of that got on a silver particles are not expected to be stable they're expected to be rather unstable they will decay know things fairly quickly the likelihood that is written in the Super partners of electron floating around the space not likely they will long ago after so I think the answer is that there was good reason to believe that there are no freely floating around you have to make them somehow how you make them by having enough energy to make them Tulkarm the maps I'm not a witch I'm there the tell yet gets that it's as if it is possible that 1 super partner might be stable are the reason 1 because Airport may have to vacate some friend in miniseries they have to Decatur something which is still a superpower you King during war super partners so yes but those of the partners might and very likely would be electrically neutral the reason is because any kind of electric charges likely to make make it even heavier so it's quite likely that that revenues whatever the stable supra partners for the lightest super partner ELS P supra partner but less of a problem very likely is electrically charged that doesn't mean it's undetectable you detected in the laboratory but it wouldn't be thing here are the lightest super primary may will be stable and may well be a year of dark energy but most likely will be 1 of them which would be stable so all the remnant particles in the universe or super partners would just be for that 1 and that wonderful world not electrically charged would not be so easy to that but you would but it principal years E out starts a cuts its key did they have only 1 of the things which is very very important case that's an interesting question on Web Strawser Byram's let's take talk diagram Bob with the vacuum energy but we could also do it principle for a although stood yet those laughter duty is defined in diagrams 1 of them involving Inc the the electron going a little and the other involving these super partner of electrons normal they will have opposite sign and they will cancel each other if we if they're well matched the paper well matched match the now that's another fine which a photon goes here and the photon goes he Will they match and will they cancel each other yes they will still cancel each other but only if the electric charge of electron electric charge of the Super partner equal otherwise it will be a discrepancy between East tool numerical discrepancy between them which would lead again into a big divergent dancer so it's important in these arguments that you follow through with every level and make sure that cancelation takes place in that typically requires electric charge of partners 0 drug particles the real partner of man now column what is I'm telling you we do not have a
collection of articles which have the same number down so supersymmetry is not a precise figure at best bits of approximation it's an approximation in which an exact supersymmetric theory that existed super partner on the photon would be nasalis it's not that these particles of names incidentally typically if you have any of the ordinary particle is but was on the super partners is an e-mail for example the photon partner would be a Filipino W bows on its partner would be a wine or we know our busy particle so busy now supposed the army is not such a neat named for the Super partners over both arms there typically scalar particles and you put ass in front of their name so that leaves the disgusting but the select you don't nice the super partners have peculiar names our Gravitt Tino would be a fermionic version of the Graduate our world remains of the peculiar name a hate Zeno were to be a fermionic version of the Higgs particle he knows are always except when they're ordinary Fermi on thin and that he knows it just electrons quirks whether what would you expect the bows ionic partner Ovibos on Committee a squat what was caught us quarks and all kinds and none I have ever been Deepak yet I think be detected my guess is that this work but now we will find out just their guessing let's talk about 1 last thing before we go home a a a super particles if they if the ordinary particles Our borrows arms and super particles are always turning around half of the a particle is bows on that typically the super partners half and that's true whether it be a year with the original particles scalar or a deed goes on to meet partner perhaps the particle if he would particle is perhaps the particle typically the partner of it it is a scalar particle which means no spend but so is this interplay they always differ by half a unit of us so the ordinary particles have been the usual pea-souper partner would be spin 0 ordinary particle is 0 like Higgs bows on and the corresponding fermium on would be half of it always differ by Have you now please use for so did well we would want to see a for a spontaneous parade and principle Eds it could be yes in fact that would be a very bad idea yet so we ordered that must not happen our right to treachery repeat the question the question is that all these additional scalar particles around that means scalar fields a scalar fields of things which we see can have the spontaneous symmetry breaking phenomena could we tolerate having an additional some other so spontaneous symmetry break and now we could do that would be a bad a bad things can happen so that that would be good but also has all kinds a special properties but nothing to part of experimental particle physicist and show we could conjure up all sorts of special properties but nothing nothing is able at what remember the fort however as simply another way of talking about a fine Bagram with 2 particles committed particles go out so there will be matching interaction is 1 of the things that has been match interactions of particle have talked about all so they will be matching of phenomena take the place of the 5 4 terms young but it won't be exactly what to think but if yet you have a little bit there's protest he said the by Asian you're asking whether a higher and lower demand versions of it the on our d answers yes there are I think it's an island even mentioned businesses peculiar discrepancy between on even dimensions were users of are on there can be analog if a a little dimensions doesn't happen on until dimensions there are things which are in between on HBO's arms accord any arms any means any value of the spin photo dimensions to spatial dimensions there was very generalizations in each game called any eons and they have condensed matter physics uh expectations in certain condensed matter systems have basically arbitrary spin arm but this is not for us the discussed now OK I was good our 1 more thing just about whether we will lowered the world be like if it were exactly supersymmetric did think questions supposing was exactly supersymmetric how different would the world be how different would we be have differ would biology a different chemistry be theaters very different so let me just show you want it not possible certainly we don't live in a supersymmetric world supersymmetric meaning exact be generous exact equal loans between masses of particles and the soup pot as we do not have such a world could we live in such a world with such a world be 1 in which ordinary chemistry lit exist for example biology anything else we're familiar with I think not mystery will happen chemistry among other things Adams of course have electrons if there was a super partner
to electronically would be a bows on right would be a bows on who have exactly the same Mass charge of electrons if we live in such a supersymmetric world there will also be a part of photon recalled the 14 R & B class the photons Mass was the protein or would also have to be exactly massless so let me tell you what would happen to like that I'm not dead another hydrogen or a helium madam but let's start with Adams with the free electrons a 4 electrons of 5 times in a hydrogen atom of course be a single electron moving it moves in lowest order was for orbit in helium we have to electrons also both moving in orbit so of hydrogen and helium electrons 0 moved in the lowest order stable form of these let's go next lithium let him as an extra lectern extra electrons and in the next orbit out because of me what what's a principle which says the video lithium atom can have 3 electrons in the same orbit Ali exclusion principle Polly exclusion principle is most definitely associated with the fact that the electrons affirming now what would happen if this outer electron Remember the outer electron has more energy inner electrons it wants to go down to the lowest level but I can't get here because because being blocked by the other ones and just the normal allow another lecture nearby the Paoli exclusion principle how could be a how would consider how would it get down to the lowest level lead down to the lowest level by admitting a photon which would carry awesome energy and electron dropped down to lower levels but block it can happen now imagine there was also a faux Tino which was also massless what could have entered this electron not what would have could have don't but what happened is useless review electron moving around would be a full not photon missiles field of exactly the same properties of similar properties photo and then what would become With electron has the change this a literary it is a fairly from is projected out what has to be left over from right if a friendlier and comes in and a formula has become a bows on board that goes on beat it would be the super partner of electrons which is called the select this electron now this electron bows on it has no trouble getting into lowest orbit so it drops them the most I bet and you would not have a lithium Madam you would have paid so lithium Matamoros of something where but the main thing is that we electron would be replaced by something drops the laws nothing about began chemistry Was chemistry due to chemistry is due to the physics Of the valence electrons valence electrons what happened to the valence electrons and a big they would all just dropped down by the same mechanism they were all dropped down list energy or that and all crowd in on the lowest energy orbit the extent that they can in nearly would not be blocked by Fermi statistics and so they all In the lowest energy they could get into what kind of thing would you have at the center here at the center you would have a HBO's condensation of electrons rather than an Adam with valence electrons to have entirely different thing I don't know what the world would be like I just know whatever would be like it would not have conventional chemistry would have nothing like conventional chemistry weather you couldn't carry you lose such Adams take good toys to create molecules and so forth rather out our their mobility crowded in the that there at small distances near the nucleus around about that anything resembling ordinary chemistry of molecules so forth but I don't think will work out what the world would be like in such a stupid but would not live resemble our salicylate delivers a gave it a a a leader from would if there was an electron if there was number was a start it was something would look awfully much like AT lithium that it would very quickly become was lithium battery with a 14 0 he not with that eye yes yes he could you we know what coupling constant electric charge so we know it's not hard compute what would be the life time with if the electron could drop than will be short it would be just a microsecond or something 1 King calculating these would not be terribly small numbers that would not be canceled now you not to get away from it that way so some interesting fact that why is the world's supersymmetric I don't know but I know that we strike could be here but were Caffrey Alexis of yours truly a bit of a mess but the question is what to begin with smaller we compared with the compare with the best of protons big we compare with unification scale plants terribly kind of odd go for a long time if if if a toe on possible answers the symmetry were broken we would be a basket right I did Sebastien so we have other couldn't see other could right on the other hand is not very hard to break these trees it's not mathematically terribly hard to break rather generic but not that American in this certainly are completely supersymmetric theories the ones we understand best and eventually the mathematical theories and the course over visa we use of weak interaction issues just as mathematical fact the quantum field theories about Best understood other supersymmetric 1 they have sold much special structure them that they often could be almost exactly solved Mum much more is known about them and the others loss of fabulous special low structure OK the click more on personal supersymmetry for more please
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