Week 8: Lecture 38: CP violation in the K0-K0 and B0-B0 systems

So in this lecture we'll look at uh uh CP violation in two systems the K0 and the K0 bar meison system and the B 0 and the B 0 bar system. So uh just let me uh for completeness say that CP uh is a combined uh symmetry operation. C stands for charge conjugation and P for parity operation. U and the K0 and K0 bar meons have the strange quark in them. Strange and anti-range. Similarly the B 0 and the B 0 bar have the bottom quark in them. So they are heavier obviously. So we'll discuss both these in particular the kison the neutral kons were involved in the so-called tao theta puzzle. We have already seen that in in an earlier lecture. Uh in fact that uh was the uh signal for uh uh Lee and Yang to uh propose that one should look at parity violation in uh other systems other nuclear systems. Uh now these neutral chem also display as I said CP violation and we'll come to that in as we go along. Uh there have also been precision measurements on the beam masons uh using accelerators. Uh of course even the neutral kones were studied using accelerators but in the case of the beamon uh specifically uh collider in kk was built. uh there was already a collider in uh in uh slack and so both these were kind of uh experiments were running in parallel using two different detectors. Of course the slack one was the Babar detector and the KK detector was the ble detector. Um and they looked very closely at uh CP violating processes and all the BK channels and so on. So the K0 K0 bar system uh let's first look at the charged K meon. The charged mezison K plus meison has a strange quark content of uh US I think there's a there's probably a let me see this should be a US bar so that it has a charge of one and it's antiparticle somehow the dashes haven't come I don't know why so the K minus minus is a U bar S. Okay, so this is minus1 charge. The neutral K0 and K0 bar have quarks which are um the D SAR and the D bar S respectively. The mass is uh uh about 498 MV. Isospin is half and the spin parity is 0 minus. The neutral kon is found to decay into two and three pions and that violates parity because if you have two pions each of the pions is a pseudoscaler. So if you have two of them and you have l equal to zero then you just have uh positive parity in the final state. Whereas if you have three pions you have negative parity in the final state. Now the neutral kon is found to decay into either of these channels. So which means that uh the final state can be positive parity negative parity. So the neutral kon is actually the decay is violating parity. [snorts] Now while strangeness is conserved in strong interactions it is not conserved in weak interactions. In fact, when K0 propagates in space, it actually shows a uh two lifetimes. The weaken states are different from the strong states in that the K S K S S standing for short. uh this is equal to K 0 + K 0 bar by 2 whereas K L is K 0 minus K0 bar by 2 and these are states of CP. So it was believed that okay uh parity is violated in K0D case but perhaps CP is a symmetry which is preserved. So these KS and KL are the igon states of CP with igon values of plus 1 and minus1 respectively. So the KS has a CPG value of + one and uh KL has a CPG value of minus1. Now this uh the shortlived uh kon the ks has a lifetime of about 90 picosconds and the long lived one has a lifetime of about 51 nconds. So were you to produce both of these uh let's say you produce k 0 k 0 bar and you look at only k 0 then the uh shortlived one would decay f fast and if you look at long distances which means you look at long times uh as the kon propagates in space then you have a pure k long uh mison Now as we already said the KS has a CPG value of + one uh is that of two pions and two pions is the decated channel. The KL has a CP value of minus1 and that of three pions. Since the phase space for this decay is limited as compared to that for KS obviously it has a longer lifetime. uh however it was found that if KL propagates for a sufficiently long time such that uh there is no contamination of KS and the KS has decayed away it is still found that it sometimes decays into two piles which has the wrong CP and uh at what level is this? This was found to be at a level of about two parts in a thousand and this was the discovery of CP violation in the neutral kon system. Okay. So this was discovered by Cronin and Fitch for which they got the physics Nobel Prize in 1980. uh of course if you uh assume that CPT is conserved and as yet we have no experiment which shows that CPT is violated then of course that implies since CP is violated then it implies that the T invariance is also broken. Uh so both CP and T invariance are broken uh symmetries in the K system. Now Wolfenstein in 1964 proposed that uh since you have mixing of K0 and K0 bar uh he proposed that there are uh some unknown delta S equal to 2 S standing for strangeness which mix these neutral kons and uh this is a paper he wrote in ' 64. uh uh also given here is the uh discovery paper of CP violation in the case system. Uh this paper is was published in ' 64. Uh also same year as BFenstein proposed this uh delta is equal to two interactions. Okay. Uh there is also CP violation in other neutral masonic system with the charmed quark for instance. uh and indeed uh for quir for masonic systems with the uh uh bquark later direct CP violation and t violation was discovered in the barber experiment at slack and the LCB experiment at CERN. Uh this is uh the LCB is one of the smaller experiments at sun. The big ones are uh of course the CMS and Atlas and Alice. Uh however the LSCB does a kind of precision job and they found uh that CPN is violated in some of these K neutral K and uh Bisonic systems. Of course the bezison system is very well studied uh at both slack and uh kek. Uh the other experiment that also looked at CPNT violation was the CP leer experiment at sun. This is a uh low energy anti-roton ring. Uh and they looked for channels uh where the observable was such that it was CP odd and of course if you find a a a finite value for a CP odd observable then it means that CP is violated just as in the case of uh parity violation. you try to look for a uh p odd observable and if you find that it is non zero then obviously parity is not a good quantum number parity is violated so these are some of the references this is not a complete reference perhaps uh later I will update these slides so as to give you references for uh additional references for these experiments but for instance the barber collaboration uh observed time reversal violation in the B zero system and there was a paper in 2012 uh the LHCB collaboration has found the first evidence for direct CP violation in beauty to charmonium decays. This was a paper published uh fairly recently in 2025. Okay. Now let's go to the B 0 B 0 bar meison system. The B 0 mison has a veence quark structure of DB bar. Uh and of course B 0 bar is its antiparticle. So it would have a veance structure of D bar B. uh the isospin spin and parity has not been measured uh in this B 0 B 0 bars Masonic system but the quark model assigns it a isospin of half and a J pi which means a spin and parity of 0 minus so in that respect it is similar to the K0 system also like the PI0 system pi0 is also a pseudoscalar object the mass is much larger larger than that of the K0 K0 bar mezison. It is about 5280 me and it has a much shorter lifetime since it mass is larger. There are more decay channels and the face space for the decay channels is much more. So the lifetime of the B 0 meon is much shorter uh is only 1.52 picosconds. So as in the neutral kon system the neutral b meons also oscillate just like the k meison k0 meon oscillates similarly the b neutral b meon also oscillates and it shows cp violation. Now Kabibbo before the B meons and the B quark was discovered Kabibbo in 1963 already proposed a quark mixing to explain the weak decays of the strange hedrons. So as you remember uh the we have the U and the D quarks. Then you have the charmed and the strange quarks. And before the discovery or the proposal of the charmed quark, we knew that there are certain uh hedrons which have the strange quark in them. And to understand or to explain their decays, uh he proposed that there is a mixing there's a quark uh mixing matrix a 2x2 m uh mixing matrix with just one parameter theta which mixes the uh UD and S quarks. Now, so Kobayashi and Muscava uh in uh their 73 paper argued that because this was post the discovery of the CP violation, they argued that the 2x2 kabibu matrix mixing mat quark mixing matrix is not enough if you want to understand CP violation uh in the quark sector. So they proposed that you have a 3x3 matrix to understand CP violation because then you have more leeway. There are more angles. There are uh three angles that you have and you also have certain phases that come up and uh that leeway allows you to understand CP violation. Uh, of course this was before uh the the Kabibbo matrix mixing matrix was proposed much before the discovery of the charmed quark. Uh although it was speculated that there is a fourth quark uh it was speculated by Glau and his collaborators in 1970. Uh but uh the discovery of the of course of the charm quark happened in 74. It's known as the September 74 revolution. uh where uh evidence was uh uh gotten by two independent groups groups at uh the uh you know proton induced uh reactions at Brook Haven by uh by the group led by Sam Ting and the E plus E minus collider experiment at slack uh in a team led by RTOR. So that was the charmonium discovery. Uh and uh the there was a prediction or it was speculation by glacial that there has to be a fourth quark but of course there's no prediction of what its mass would be and so on. Okay. So in connection with the B 0B 0 bar and in general CP violation, this was the paper of uh u Kobayashi and Muscava published in 73 where they say CP violation in the renormalizing theory of ren normalizable theory of weak interaction published in the Japanese journal progress in theoretical physics after the discovery of charm and the third generation of charged leptons namely the towel left on that was discovered by Pearl uh somewhere in 75 1975. Uh then the Kobayashi Mascawa paper started started getting some attention. Before that it was not getting uh I mean attention it probably deserved. [snorts] In 1977, Letterman, Leon Letterman uh who if you remember discovered I mean in a collaborative experiment of course who discovered the uh new mu the muon neutrino at Brook Haven in ' 62. Uh he led a collaboration which found evidence for a botonium uh resonance and that was evidence for the bottom quark B. Uh so the CP violation in the neutral beamon system was as I said already measured in two accelerator labs uh at Slack using the Barber detector uh in the US and at KK which is the accelerator laboratory in Japan using the Bell detector and they both used E plus E minus collisions in a collider mode and sitting on the B 0 uh resonance uh not exactly the B 0 resonance. You sit at a place where you produce uh B 0 and B 0 bar. Okay. [snorts] So um uh so you produce actually this is this is probably a a mis you you collider mode uh producing B 0 bar uh resonances. Okay. Now there is another uh uh additional uh trick that was used by both these collaborations. Namely, uh since the you want to tag these uh B 0 resonances, B 0 as well as the B 0 bar resonances uh and they have a very short uh uh lifetime. Then these colliders were operated not in the symmetric mode which is uh which was done for instance in LEP where you had the same energy uh uh uh where you had the same energy uh electron and positron moving in opposite direction colliding to produce the Z0 bzon. Uh so what they did was at uh I mean roughly similar kind of energies uh as symmetry uh for instance at KK Japan they used a 8 GV E minus colliding with a 3.5G E+ at slack they used a 9 GV uh electron colliding with a 3.1 GV+ plus such that you could produce these B 0 and B 0 bars and uh the idea was that you want to have a vertex uh for decay of the beam as on which is different from the vertex of interaction. Okay. So that you can separate out B 0 uh from other uh prompt uh promptly produced particles in the collision. So a typical event at uh for instance uh Babar or Bell is that you populate the uh oopsilon 4s uh state and then that decays to the B 0 uh and B 0 uh bar for instance uh and then that further decay. The blue lines indicate an invisible track because of course both are being neutral particles. They won't ionize uh anything in the detector and they can only be seen through their decays and for instance they decay to a JSI which quickly decays into a E plus E minus for example or it decays into a K0 strange uh object which then decays to a pi plus and pi minus. So anyway the idea is that this uh v 0 uh which is produced uh it then decays and there is a certain decay length which you can use as a handle to separate out the b 0 uh decay events. So uh for instance you see this uh one of the I haven't defined this but there is a uh CP uh you know observable CP odd or even observable and as a function of uh uh the uh decay uh time and uh you see that this shows a oscilly behavior which uh using these 529 events as a function of time and this is one depiction of that. Uh, of course there are detailed papers. I think I might have occasion to actually discuss this in some subsequent lecture where uh direct CP violation and direct T violation uh will be discussed. Anyway, this is just to give you a flavor of the kind of measurements that you do with this asymmetric uh uh collider. Okay. So all this data is kind of summarized in this mixing matrix quark mixing matrix. So the uh the igen states of the full Hamiltonian uh are d prime, s prime and b prime and they are connected by a 3x3 matrix here uh which has nine elements to it and that connects this uh the vectors with the full Hamiltonian with uh another description where you have the uh strong uh uh you know vectors. Uh so uh this this is similar to the neutrino mixing matrix as we shall see later except that uh this matrix the moduli of each of these elements here is given in this uh uh matrix and uh you can see that the magnitude of the diagonal elements. So the diagonal elements are this this and this and they differ uh they're very close to one but they differ by less than 2 and a half%. There's a small deviation but not very large. Uh the offdagonal elements are these uh this one this one this this and similarly the these two. Okay, they are small unlike in the case uh of the neutrino mixing matrix as we shall see later. Now for this work uh Kobayashi and Muskava uh got the shared the Nobel Prize. So half the Nobel prize in 2008, the Nobel Prize in physics went to Kobayashi Muscawa and uh Yoiro Nambu. Uh the citation for Yoir Nambu was that he got the Nobel he got half the share of the Nobel prize for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics. and uh Kobayashi and Muskava uh got the Nobel Prize. They shared half of their Nobel Prize, so one quarter each for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature. uh of course there is a limit to the number of Nobel prize winners and so these already exhausted the total number of Nobel laureates that Nobel uh that the Nobel foundation could give but surprisingly and Kabibbo was left out of this share of the Nobel Prize. So some people thought that Kabibbo should have shared this Nobel prize with Kobayashi and Muskava because uh he actually introduced this uh park mixing matrix. Of course it was a 2x two because this was done very early when uh the uh even CP violation was not yet discovered. Uh perhaps Namboo could have got a separate Nobel prize. Uh anyway that that uh these these things happen and uh so anyway Kobayashin Muskawa got the Nobel Prize for uh this uh CP violation basically CP violation uh which needed a 3x3 matrix. So in summary the K0 and the anti-K0 strange mezison show some interesting properties such as mixing. uh they also show CP violation. Uh similarly the neutral uh beamons also show mixing and CP violation. Uh and uh there are now accelerators which are looking at this very closely using asymmetric E plus E minus colliders. In fact, uh the there has been an upgrade of both the detector and the accelerator to get luminosities of the order of 10^ the 35 or 10 the 36 to enable even higher precision measurements to be made at KK. Uh so the direct measurements of CP and T violations have been done. uh uh direct uh measurements of CPA have been done in the K0 and the B 0 uh meison systems. uh maybe in a future lecture I might discuss these separately because uh these are beautiful experiments and uh I I I hope to do that in some later uh lecture. Thank you. [music] >> [music]