Master class I with Boris Kayser

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Master class I with Boris Kayser
Neutrino Physics: present and future
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We will review the physics of neutrino oscillation, and summarize what has been learned from oscillation and other data during the last dozen years. We will discuss recent surprises that may point to new interactions and new particles. Then we will turn to the future: What are the open questions, why are they interesting, and how can we answer them through future experiments?
Keywords Neutrino Physics
Neutron Hypothetisches Teilchen Sunlight Force Lepton Kette <Zugmittel> Particle Neutrino Fusion power Model building Reaction (physics) Electron Force Minute Year Weak interaction Power (physics) FACTS (newspaper) Positron Universe Photonics Hour Nuclear fusion Neutrino Neutrino
Analog signal Roman calendar Calendar date Visible spectrum Amplitude Optischer Schalter Mixing (process engineering) Flavour (particle physics) Matrix (printing) Color charge Boson Linear motor Quantum Neutrino Model building Flavour (particle physics) H-alpha Orbit Sensor Electron Short circuit DVD player Ground station Minute Year Visible spectrum FACTS (newspaper) Mixing (process engineering) Current density Cartridge (firearms) Beta particle Mass Mint-made errors Boson Morning Orbit Radioactive decay Hose coupling Neutrino Linear motor RSD-10 Pioneer Gaussian beam Neutrino oscillation Lapping Lepton Standard cell Bahnelement String theory Wednesday Neutrino Mass Hose coupling Mail (armour) Angeregter Zustand Transmission tower Game Matrix (printing) Hour RRS Discovery Semi-trailer truck Neutrino Ground (electricity)
Prozessleittechnik Photocopier Amplitude Negativer Widerstand Klemmverbindung Mixing (process engineering) Particle Disc brake Bird vocalization Roll forming Colorfulness Color charge Semi-trailer truck Linear motor Fuel Model building Flavour (particle physics) H-alpha Sensor Combined cycle Electron Sunlight Year Mixing (process engineering) Julian calendar Annihilation Rolling (metalworking) Beta particle Mass Hose coupling Linear motor Ground state Schubvektorsteuerung Measurement Summer (George Winston album) Lepton Cardboard (paper product) Standard cell Roots-type supercharger Ship class Orbital period Neutrino Nanotechnology Mass Wind Rail transport operations Hose coupling Watercraft rowing Angeregter Zustand Star Cash register Cardinal direction Vakuumphysik Elektronentheorie Measurement Matrix (printing) Plant (control theory) Rutschung Neutrino Analemma
Theory of relativity Prozessleittechnik Rear-view mirror Roman calendar Hull (watercraft) Amplitude Mobile phone Negativer Widerstand Mixing (process engineering) Ladungstrennung Flavour (particle physics) Hall effect Particle Avro Canada CF-105 Arrow Phase (matter) Roll forming Turning Color charge Neutrino CPT-Theorem Renewable energy Flavour (particle physics) H-alpha Speckle imaging Initiator <Steuerungstechnik> Arc lamp Electron Sensor Year Minute Source (album) FACTS (newspaper) Mixing (process engineering) Direct current Cartridge (firearms) Beta particle Mass TARGET2 Antiparticle Morning Homogeneous isotropic turbulence Near field communication Neutrino Spread spectrum Gaussian beam Cosmic distance ladder Grey Neutrino oscillation Lapping Measurement Summer (George Winston album) Vakuumphysik Cardboard (paper product) Ship class Bahnelement C-symmetry Kiln Spare part Orbital period Video Neutrino Nanotechnology On-board diagnostics Mass Coherence (signal processing) Angeregter Zustand Küchenmaschine Heat exchanger Lead Drehmasse Positron Hybrid rocket Interference (wave propagation) Schwache Lokalisation Matrix (printing) Neutrino Stock (firearms)
Photocopier Effects unit Visible spectrum Scale (map) Amplitude Optischer Schalter File (tool) Negativer Widerstand Casting defect Flavour (particle physics) Phase (matter) Bird vocalization Roll forming Turning Ship naming and launching Screw cap Binoculars Quantum Neutrino Flavour (particle physics) H-alpha Sensor Electron Bracket clock Year Black Velvet Evening Source (album) FACTS (newspaper) Mixing (process engineering) Phase (matter) Series and parallel circuits Beta particle Mass Rotation Cosmic distance ladder Gaussian beam Hot working Clock Neutrino oscillation Measurement Force Presspassung Vakuumphysik Angle of attack Band gap Filing (metalworking) Alcohol proof Orbital period Neutrino Nanotechnology Mass Angeregter Zustand Tool Stellar atmosphere Weinberg-Winkel Weak interaction White Map Kopfstütze Measurement Spant Electric generator Angle of attack Gentleman Sizing Interference (wave propagation) Matrix (printing) Water vapor Neutrino
Energiesparmodus Sensor Neutrino oscillation Minute Year Optischer Schalter Negativer Widerstand Source (album) Particle Wavelength Direct current Wavelength Game Cartridge (firearms) Plant (control theory) Neutrino Rückstoß Mass Neutrino Muon Angeregter Zustand Neutrino
Effects unit Klemmverbindung Hawker Hunter Assault rifle Ultra high frequency Separation process Fiat Panda Flavour (particle physics) Tiefdruckgebiet Year Ground station Visible spectrum Crystal structure FACTS (newspaper) Scale (map) Heat Wavelength Missile Universe Beta particle Scattering Solar energy Kelvin Gaussian beam Hot working Neutrino oscillation Basis (linear algebra) Band gap Spare part Mass Hose coupling Ground (electricity) Angeregter Zustand Mikrowellenlandesystem Particle accelerator Collision Ballpoint pen Electronic component Mitsubishi A6M Zero Vakuumphysik Separation process Membrane potential Nuclear fusion Wind wave Neutrino Cosmic ray Acceleration Nuclear reactor Visible spectrum Scale (map) Order and disorder (physics) Negativer Widerstand Flavour (particle physics) Particle Absolute zero Bird vocalization Roll forming Wavelength Gamma ray Limiter Color charge Membrane potential Schwellenspannung Neutrino Ship breaking Bauxitbergbau Number density Electron Sensor Minute Source (album) Circlip Direct current Fermi National Accelerator Laboratory Autumn Ammeter Feldnebel Mass Radioactive decay Neutrino Sensor Cosmic distance ladder Sunlight Measurement Summer (George Winston album) Crystal structure Galaxy Vakuumphysik Weather front Cougar Roots-type supercharger Cluster (physics) Nuclear power plant Steckverbinder Neutrino Video Electron Coherence (signal processing) Mail (armour) Particle accelerator Typesetting Channeling Winter Stellar atmosphere Bending (metalworking) Effects unit Map March (territory) Cogeneration Spant Finger protocol Pattern (sewing) Sizing Gentleman Absolute zero Moving walkway Hour Trade wind Water vapor Week Stock (firearms) Flip (form) Ground (electricity) Demultiplexer
it I apologize for the fact that only 5 minutes later I had planned on more of the story goes if somebody comes up to you a party and then asks you were monitoring of the 4 it is 1 thing you can count Our son generates its power through a chain of fusion reactions begin with this 1 the future of the "quotation mark estimated run a positron and I hear the intrinsic spins of these particles and you see that if we were to take the neutrino away then angular momentum could not be conserved because we're try to go from an integer value to a half integer value that's a problem that means without the neutrino this reaction wouldn't occur and the entire fusion chain which begins with this reaction wouldn't get started so the sun wouldn't have any power output instead of looking like that it would look darker In fact much darker so that's 1 of the things you can tell me now that the party's over we're going it's serious the and photons are while shot the most abundant elementary particles in the universe there about a billion times more abundant than electrons neutrons protons they have comparable numbers in there about 340 neutrinos procured centimeter in the universe everywhere Mike here the neutrinos as we just set our spent half their hour course electrically neutral and they are wiped the only known forces that they experience are the weak force of the Standard Model on gravity which has the consequences very difficult to study neutrinos however we do know that the weak interactions successfully described by the Standard Model In addition in just the last 12 years there's
been a revolution in having been discovered that neutrinos have non-zero masses and that the lap times mix these discoveries came about from the observation that neutrinos can change from 1 flavor to another this is the phenomenon referred to his neutrino oscillation and so I'm going to begin these 2 and a half hours of chit-chat With a discussion of the physics of neutrino flavor change when isolation what is neutral flavor what is the flavor change what is it employs there are at least
3 flavors of neutrinos 3 known the electronic entry on the New wandering along the town string we will define these flavors in terms of what the W does when it decays electronically a W K indicate electronically into an electron from you 1 or a towel plus an accompanying neutrino we will define the new III is the 1 that comes together with an electron the new new is the 1 that comes with a new 1 and the new towers the 1 that comes with the now as far as we know it if you have a neutrino born this way for instance with a new 1 so it's by our definition of 1 Torino and it quickly interacts in a detector before it has time to change into anything else it never creates a charge electron except that the charge leptin has the same flavor as the 1 with which the neutrino was born if a neutrino was born with a view 1 and when it interacts quickly it makes only another you want the new new makes me you know he makes Eatontown makes tapped so far as we know if I use this notation Alford referring to flavor he you worked out his anybody blocked by this box sort of the thing but by box I use Alpha Beta to refer to the new tower flavor so new laughter can be a new union Urinetown L of flavor alpha means a charge lap time of flavor Alpha the charge left town of flavor electron just means the electron 1 of flavor Muenster them you 1 of labor towers that so far as we know when the neutrino flavor Alpha interacts and make charge slept on that charge on is always of the same flavors the neutrino knew makes only he knew only himself on the other hand yeah and by the way interrupt yes question point out the obvious errors that are making deliberately as a player to see viewpoint that is also to a very you Of shortage is on that's a very good question it is possible is it easy not does anyone do it now or not so late the way we we make new 1 neutrino beams usually isn't Pyeongtaek and there is a roughly 1 per cent knew he contamination in such a B the suspect create a problem yes but we have ways proposed ways of making pure beams in the future I will get there roughly 11 30 incidentally I'm going to try to vote very hard on time because of another talk tomorrow morning if it bid the 5th it it so said if neutrinos have mass and if wet tons mix then you can have a scenario like this in which a neutrino born together with a meal on fighting game I a just mentioned so it is by definition of new 1 entry if this is a new 1 and this is a new 1 and I ascended on a long journey like from here to the other end of the the year In such a long journey the neutrino does have time the change its character it can then interact in a detector placed on the far side of the earth making the charge left town and you can have an event in which discharge slept on is not Of the same flavors that 1 for instance it could be a tap now since it is only talent trios that make this howled what that means is that during this journey the new on neutrino has changed into a town neutrino like this and this is the phenomenon which for reasons that will become obvious is called neutrino oscillation it is the change of neutrino flavors and the last decade has brought us really very convincing evidence such for changes do occur as will CDs flavor changes require None 0 neutrino masses that means that there is some spectrum of neutrino mass Eigen states that 1 2 3 maybe more and we like to determine what the spectrum as also see neutrino flavor change requires the tonic mixing and what that means is that the neutrinos that we started out talking about newly New Town each of which is born with the charge slept on of the same flavor are not these new site inspections but instead each of these neutrinos definite flavor is a linear quantum superposition Of the mere sight in states like this I will user Greek subset script as I've already indicated to refer to the neutrinos of definite flavor annually new in town and a Latin subscript higher J to refer to a neutrino definitely Mass a mail site instead the coefficients in this quantum superposition are the elements of what's called the LEP tonic mixing matrix that matrixes electronic analog of the Kobayashi be Court mixing matrix this 1 is referred to as the Pontecorvo lucky Nakagawa said matrix in honor of the electronic mixing pioneers we know that there are and we east 3 different neutrino flavors newly yuan tap that means that there are at least 3 minutes site states because these are orthogonal states they have different flavor and out of 3 orthogonal vectors I can certainly make 3 at least 3 orthogonal no 1 knew to 103 the next thing that we just spoke about as easily incorporated into the standard model description of the coupling of electrons to the W boson before mixing what the standard model says is that here is the coupling the couples the neutrino flavor althought only to the jurors left town of the same flavor corresponding to the experimental facts that I mentioned before the wedding neutrino flavor of interacts makes only a charge slept on flavor helpful this is the semi weak coupling constants the AL reminds us that the weak currents are left-handed all what else W's obviously the W boson to incorporate mixing all you do is you replace the neutrino of definite flavor the linear quantum superposition of Miss Saigon states that we spoke about before now mistakes mixing into account now there are no neutrino masses in the standard Morrow when the standard model was written down it was assumed that neutrinos have no mass no less was known at the time now that we know that they do have non-zero ministers are we have to try to understand those in some way it goes beyond the standard model if neutrino masses or the neutrino masses are described by volume was straightforward extension of the Standard Model then there are no new left on his beyond the ones I've been talking about the EMU tap no 1 to move 3 only 3 of us if that's the case then the amplitude for a W decay intellect tons after which the neutrino makes a left on of a different flavor than the 1 with which the neutrino was born is like this 1st of all it is the amplitude that this neutrino born with this charge left on a flavor is in particular the mass items state New looking up at the Lagrangian the term which makes the neutrino Is this term remember the quantum field like this 1 and I'll it's the
particle that bears its name and creates the anti particle so the field that makes a neutrinos in the war well the amplitude that new Alpha is actually knew why is obviously you helpful I spot apart from this overall due square to which it owes Maryland I will included so here is that 2 that has to be multiplied by the amplitude that this new on when it interacts in the detector makes a charge let time which in particular has the flavor beta the terminal grungy into make L minus His over here and the amplitude that that l minuses of flavor data if the incoming neutrinos new highs obviously you hot that's this factor because neutrino masses are very small if you have a sequence of processes like this you make a neutrino and quickly it interacts no propagating To make an Albania you're not going to know which Miss items they was involved so the amplitudes for them this product for each I have to be added coherently that's this summer this sum is nothing but the dot product between the alpha and beta rose Of the mixing matrix if that mixing matrix is unit Terry then that that product is the dot product between 2 different columns of sorry to different rose in a unitary matrix that 0 on the other hand of data is equal to how far it's the square of the vector which represents 1 wrong the square 1 roll over matrix that unitary use 1 so this is just Delta alpha beta yeah the Standard Model describes neutrino masses buys most straightforward extension and if there are no new laptop then the mixing matrix is Unitarian I want true that true then this piece of arithmetic follows ended In corresponds with what we seem to see experimentally if neutrino was born with a charge that tunnel 1 flavor and it quickly without propagating makes another charge let on that charge looked on as they have the same flavor as the 1 with which the neutrino was born the basic meaning of the mixing matrix going back to the Lagrangian looking in particular at this term apart from this overall factor the the mixing matrix element you Alpha off is nothing but the camp at 2 that when an incoming neutrino a absorbs a W bows on and it is new I makes the charge left on El for so pictorial the amplitude for new ideas to make Elmont itself or by emitting absorbing the W bows on his just due this word 2 times you out on this where you well ideas is the amplitude for this vertex you can write the 3 by 3 presumably unitary matrix in this form so the EU role of you this row by example is just that linear combination of neutrino mass Eigen statesman 1 2 and 3 the couple's 2 electrons namely the linear combination of neutrino Messiah states as couples to electron is you we want started new 1 place you eat to to pursue three-star and 3 and its stars because that's how happened to have defined the matrix and some of you may have noticed that you hear what I want that and I didn't have a star this is not a mistake if some states is a certain winner combination like this of other states then the corresponding field is the same linear combination of the corresponding fields except that there is no star there and you all know the hats of which you don't know that you know lower hopefully you'll be able to see the seasonally lies the pipeline plus state Is this linear combination of Pyrex wife of of of of I trust most people know about yes the field plight plus is the operator which acting on the state .period loss producers the vacuum the ground state that's 0 but the state 0 but only by going to the other blackboard do that you can't seek too dark "quotation mark without help focus all I can see it's quite the now which operator annihilate spent state the operator that annihilate spent state His Pyrex minus prior wife Over the square root of the square root of 2 combine to make a one-half plants annihilating X gives the vacuum minus icons plus sign pie wipe Iwai also gives the vacuum twice the vacuum over this over to his back if I had a plus sign here I have plus items I I get which is not the right answer as this illustrates if you have a complex coefficients in state you have to have the complex conjugate of that coefficient In the field that annihilate that state and it is for that reason but there is no story here this is asylum has nothing to do with which we and now before I go on but I think we're going to make use of it so I'm copy this and put it on the other board using a different color if robbery won't be at the CIA anyway and that I mean I'm not you we all of us but alternative alliance with you this so the Lagrangian this is much better now I the Lagrangian is something or other -minus GAO square to Funds some overall the flavors and all the mass Oregon State neutrino was from call Campbell you out powerful new a lot of don't volume of class the 2nd term of of course just Hermitian conjugated the 1st but it is useful sometimes to have that written out explicit warning and I think now we have the ingredients to talk about the physics of oscillations so fuel
excuse me for just 1 2nd while change the real last year I think there was
something missing In theory the you want know as I said more than that I said if the I would without saying what I was saying what I said was that the standard model is extended In the most straightforward way To conclude neutrino masses of then the mixing matrix is and if there were no new electrons that limiting His unitary now not go ahead and continue but was the 2nd of see you in the morning as enemy and explained that the more could I don't know if this stock if there are additional let then probably there is 8 mixing matrix which is unitary which includes those additional times but that mixing matrix is not accessible and may not be accessible experimentally and that part of the big bigger than 3 by 3 mixing matrix that is accessible experimentally that is not overall the overall there is there is something which is unitary board the experiments that you do may not reveal that that's the case so it will look to you like you're dealing with a 3 by 3 non-unitary you're welcome so now here's if theorists theorists view moreover the neutrino oscillations we have some source of nutrients all 3 W exchange it emits a charge that time flavor out from you for instance also trio the neutrino goes down some being line and then it hits the target in a detector and it makes again by W. exchange the 2nd charge conferences town the electric charges here are are not important for the moment we will come back to that what matters at the moment is just the flavors alpha and beta now since it is by definition a new Alpha which is admitted with El and since the only neutrino flavor which can make elevated isn't new later this experiment is what we conventionally be cold knew out new Alpha to new data oscillations experiment on the other hand if neutrinos have non-zero masses of their new offers superposition of neutrinos definitely us and so in the mass I can state bassist went close down the beam line is 1 or another of those reciting states New Orleans and because the masses are so small were not going to know we're nowhere near being able to make the measurements that will tell us richness Oregon State went down the beam line as a result just like in the double slit electoral interference experiments the difference the contributions of the different Ms states have to be added coherently with 1 another and consequently the amplitude the new Alpha to go to New Baden is a coherent superposition however ,comma contributions of the various Mexican states now the contribution of a particular Miss Saigon state knew has several factors 1st of all there is the probability ample that the neutrino made with Alpha was in particular the Masai against a new high while we have here the Lagrangian we're making an Alfa class so that this term I None of this the absorbs this is the worst of no this absorbs know this observes elephant minors that's right it's this term so the amplitude is simply you start for once the Ms they get to the detector and makes charge electron Albania with that charge that's this term with offer equal beta so the amplitude is you better finally there is some impetus for this neutrino to propagate the arithmetic of getting a cellphone is very trivial but conceptually it is very very tricky and people still argue about it they've been doing next this is broadly agreed to this legislation the amplitude for new Ida propagate from the source to the detector Over a distance L if the being energy is and the massive new lies Is this phase factor OK know this just repeats that it says the amplitude for new offered a golden beta is this coherence some in now taking it out from the picture that's the amplitude this simple expression and if you now take the absolute square of the sample to To get the probability and then you make some sneaky use of the sooner Unitarian rhetoric you can write the answer in this form where fancy are and I refer to the real and the imaginary part of what follows and Delta squared I J is just the difference between the squared masses of new and right now if you go back and you do look at the electric charges that we started with you will see that we have been talking about a neutrino rather than an antineutrino should there be any difference there may not be differences will discuss but if there is a difference we've been talking about a inventory because the neutrinos and a negatively charged electrons like an electron are defined to be lap times and the antineutrino the positively charged like of positrons are defined to be in the and if elected Members conservative then the neutral thing which can make an minus is a neutrino 90 antineutrino and neutral thing which is born with an plus from a W which is not elect on is again neutrino so we have been talking about neutrino propagation to talk about antineutrino propagation you don't have to repeat the whole thing you can make use of CPT invariants and in fact our formalism has already assumed that because we used that Standard Model ranching and this comes from the standard model which is a local relativistic Lee invariant quantum field theory any such quantum field theory is of automatically CPT in invariant that's the secretive here now it's always you want to
calculate the probability not renew efforts in New Baden but from new Alpha Botany about the CPT mirror image of this process is no better going to new wealth see charge conjugation just replaces a particle by its anti particle In the case of neutrinos neutrinos they're given to us by nature to study are always left-handed the antineutrinos the things we call antineutrinos was right-handed the difference between a left-handed or right-handed thing is parity so to go from what's called the the new outflow a left-handed particles 2 it's called the new offer bar all right and antiparticles you have to apply not see CP because you have to reverse spread finally we apply tea and that reverses the direction of time so that arrow pointing this way points the other way or another words we interchange Alpha Beta final initial state so this is the CPT mirror image of that and if nature as we assume this CPT invariant then these 2 probabilities have to be equal this probability is the probability we just arrived I just repeated year bought with alpha and beta interchange and we see that when you interchange alpha and beta all you do is review replace you buy you spot so if CPT invariance holds the probability for this process is the same as the probability for on-board processors with the same initials on the same final flavor but would be replaced by its complex so I just do that the probability for the bars is the same as before but Of course the imaginary part changes Sciences a minus sign here now since these 2 processes as we said just a minute ago RCP mirror images of each other this is the CPE mirror images back this is seeking the image of back if there should be a difference between the probabilities for these 2 seeping near and processes that would mean that there is a violation of invariants under CP so complex faces In the mixing matrix lead to CP violation in neutrino oscillation through this imaginary part 5 k now I wanna write that 1 down to because we're going to be using it you see the red from over there because it's it's dark I can see it from here and I used to I you for goes to New Baden it's antineutrino equivalent of user Delta alpha beta minus for this summer on the mayor's Oregon State's Real part the other 2 helpful livestock are you can tell by the fact that I'm not looking and must encountered formula few times before plus warfare for the case of the antineutrinos -minus some mild hybrid J. the imaginary part of the same product review matrix elements times sign not squared hello virtually but now there's a bunch of prominent someone make about the formula all of you the on the other thank you suppressed as very kind words for I had to isn't going to matter but it may well be right 1st Bosnia or Marsalis then in particular all these mass differences would be 0 all the signed functions would vanish this probability would collapse the Delta alpha beta itself if the probability for new offer going to New Baden With had different from is 9 0 for which you need these other terms that tells you that the neutrino masses at least some of them must be non-zero so the 1st thing the implication is that flavor change implies 0 neutrino mass and that's the most important thing about this for that's the big deal the observation that neutrinos really do change flavor taught that they have non-zero ministers 2nd .period suppose there were no Mexico what that would mean is that when dubs the same neutrino signs not sometimes in 1 sometimes 2 sometimes 3 but I always knew 1 said I wanted the case to a different charge left flavor better differ from this is again always the same science state but a different 1 than over here new to say consequently if there is no mixing a product of you matrix elements involving the same but different Alpha and Beta would be 0 if I go from here to there and I change Alpha into a different data this new it has to be in the absence of mixing a different objective so this product would be 0 0 here too so once again the oscillation probability would collapse 2 Delta half of it consequently if you see an actual change of flavor from 1 Alpha to a different beta so that this probabilities not Delta alpha-beta that tells you that there is non-trivial mixing
3rd 1 can detect neutrino oscillation in 2 ways 1 way is to build of being all the known flavor like me the 1 neutrinos let's say we have that have developed a technique for making a pure New Deal and then you observing this being the flavor that wasn't there at the beginning like an electron neutrino that tells you that flavor has changed and that for obvious reasons is called all appearance experiment appearance of a new flavor the other thing you can do is you can make of flocks of neutrinos of a certain initial flavor like new again and if you know just how big that flux is then you can look to see if some of it disappears presumably by oscillating into other flavors a practical way to do that is you have to detectives 1 it's very near the source before the neutrinos have a chance possibly and 1 that's much farther away and then you compare the new fluxes in those 2 detectives if they're not related to 1 another simply by 1 over distance squared that's a disappear so this is calling disappearances forthcoming start I have written factors like this in form Delta and scored all over for it but I have been suppressing explicit factors of each foreign see taking them to be 1 if you insert the missing factors than this expression is really bad expression and then if you insert the known value of age policy which everyone knows is approximately 280 for me and that that's about all you need ah this becomes this expression 1 . 2 7 Delta and squared measured in electoral squared the distance between source and detector America kilometers and the beam energy the European Union now this will factor which is really this wittily factory is going to become appreciable when the argument in the square brackets becomes an appreciable fraction of what the pirated typically when you do an experiment is characterized by a certain typical distances traveled health and a certain typical beam energy he is so your experiment has a certain elderly you're experiment will be sensitive to Delta and square all the way down to the inverse of velvety so that this product is awarded 1 so for example if the beam energies 1 GB which is typical for a oscillation experiments if the distances to the diameter of the Earth which is weightiest for atmospheric neutrino oscillation experiments then he over a all in these units is 10 to the minus 4 because the diameter of the Earth is about 10 thousand kilometers In consequently year experiment is sensitive to Delta and square all the way down to the water 10 to the minus 4 electoral votes were really very very tiny explains compared let's say to the electron mass for any heavier .period so what has happened is that through the quantum interference effects which give rise to these oscillations neutrino oscillation is sensitive to the very tiny mirrors would you just have to make L. over you big enough so that this phase becomes a water 1 even Delta was quoted as a response next .period an obvious point the probability for neutrino to change flavor oscillates as a function of well over me that's the reason this thing called neutrino oscillation they actually supposed that this behavior it has been observed that area and incidentally the reason that the variable With respect to which this oscillates L over In 9 times or something held without the whatever is that neutrino oscillation is something that the neutrino going by itself what the neutrinos does depends on how much the clock has advanced in its own rest frame the proper time that has elapsed between production and detection apart from a constant if the neutrino travels the distance L in your laboratory frame with an energy E in your laboratory frames then the proper time that has elapsed in its own frame is overrated that's why the variable His salary and that's something else and surely that oscillation actually depends on over each showing experimental but it depends on over here not something else is 1 way of telling yourself that oscillation is something that the neutrino doing by itself rather than as a result of interacting with matter through which it may be passing something like this has been done to next .period you see that the way that oscillation probability depends on neutrino masses is by depending on the mass squared splitting not the individual investors that the absolute mere scale so oscillation experiments can tell you what the splitting czar between different members of the spectrum but not how far above 0 the whole spectrum is now if you're serious like mean you wanna build the fury of entry as it would help to lobby that masses isolation experiments can I tell you next when neutrinos change from 1 flavor to another that doesn't change the number of neutrinos in the beam it's just changing again From 1 flavor to it the toll number of neutrinos in the is still the same N he there by using this formula or by going back in using the amplitude from which this formula came you can prove explicitly that if you some the neutrino oscillation probability over all possible final flavors including the original file flavor flavor with which the neutrino was born that's something 1 where to put it another way the probability that a neutrino changes flavor plus the probability that it does not His wife and these forms it better be right these formulas explicitly conform to that particularly if I include the fact too on the other hand some of these flavors into which the neutrino can oscillate from whatever was initially could be
water called step we'll say more about that later but a sterile Atorino is 1 that does not interact like any of the known forces of nature including the weak force of the standard model except gravity while its gravitational interaction with any detective you can build is not likely to be the detectable so if neutrino become sterile you're never going to see it should write to the Director they'll go right through the effective mostly anyway even if they're not start it's odd enough to detect announced their launching of Estero 1 forget it after you start with the muon neutrino let's say and the muon neutrinos oscillate into other flavors but some of those flavors Estero that if you build the detector the best detector candle this to detect the active neutrinos the 1 that interact with the ones that interact with the W bows on that's new union Uniontown you can get the total flux of effective neutrinos but this still fluxes can be less than the original flocks because some of the neutrinos became sterile the total number of neutrinos has not changed but some of them have become completely invisible so they will look to you like the flux went out finally ,comma we know that there are yes yeah you look uncomfortable with that Everything so fine that the man yes that's was the only you may get it back again if you move you detect father of the year year all under the No no no no no and that they don't necessarily away oscillation is isolation an Israeli where if you focus on a particular flavor you put a detective series uses number you produce detected see less it which is detected using more again will look at that it is that's how works has been observed to work their way it's not just a foreigner was on a blackboard but White Water evidence so I can say that stick around and coming back to that point but about 1 AM we'll get there I want to make sure we get there I will skip other things to make sure we get if necessary we know that there are at least 3 neutrino mass items that and 3 corresponding however 2 a very good approximation if you're just trying to describe 1 experiment it is a very good approximation to take just 2 neutrinos into account 2 states although no 1 into so there's only 1 Delta and scored into square by someone's work and tool flavored neutrinos call avenue Bader made up out of you 1 to buy this quantum superposition when you do that the mixing matrix becomes just the 2 by 2 matrix it's not really in history because the real matrix is bigger but to a good approximation of might be in area and the most general expression for it to buy 2 unitary matrix that takes into account that certain phases don't have any meaning because what I call electron you can call the to the 37 degrees times electronic and remove phases that 1 the most general expression theirs the 2 by 2 rotation matrix depending on a rotation angle theta which is called the mixing angle times a matrix which has a face in it but this phase does not affect between oscillation and when you plug this mixing matrix and the approximation that there's only 1 adult and squared into this formula the collapses to something very simple the probability for new Alpha to go new beta or the other way around or the antineutrino just sign scored twice this mixing angle times the size square of this 1 tore factor that is still left and the probability that new Alpha does not change its flavor is just 1 minus the probability that it does and the simple formulas have been used to describe numerous experiments and I'm the copy them onto black portals White people OK so this is tune the the introduction to the general warned me that some animals or 1 the latter I would put it the other way around some were smaller than others it exactly so this collapse is a piece of walk it it comes about actually because of 2 things 1 of them is what you just said and the other I suppose the spectrum as users will see a while looks like this is 1 small cap and a much bigger gap if I do an experiment that is just adequate to see the big gap is not going to be able to see the small gaps so for this experiment these 2 neutrinos look like the generator they look like 1 Atorino so this looks like a tomb neutrino spectrum you know it's not that's the other Peace Walk because of those 2 things together we have this possibility and I mean this is it's it's nurses that the formula simple is that it's a function of true parameters just do instead of this which is relatively a map it's so and the other piece of good luck is that those Delta and squares although they are very small they were big enough to be observed experimentally and that you know that's call claims
Anderson now I have to change the real again it's 1 now I
mentioned but when talking about the propagator From the source of the detector that people still argue about the quantum mechanics however neutrino oscillation and recently there was some excitement when it was suggested that everything I have said so far is wrong this talk about neutrinos may environment most of those the case we the result of 1 in and for a given parent plant energy for example upon arrest the neutrino and the new 1 with which it was produced are killing manically entangled that is to say the chemical properties are correlated with 1 another because of energy momentum conservation the energy of the new 1 is going to depend In the pirates preying on how much this neutrino ways so it's going to depend on which means I can stay was minutes that's what you mean by quantum entanglement never the games into particles they opposite direction the properties of this are entangled with the poverty that they're not in so you can ask when that is taken into account which I did not do in the writing is do we still expect neutrinos oscillate like this function With an isolation which is defined that way you can just solve equating 2 things for party or at all times well I'm within the last year I an approach taking entanglement into account was constructed and the wavelength that was derived for the oscillation looked very different and the usual 1 like a 50 per cent there however that New
Wave like the right by that approach is not for oscillation as a function of the distance between the source that is to say where the aplomb decays and the detector where the neutrinos detected rather when look at closely this new oscillation wavelength is for oscillation as a function Of the lab frame separation S between the neutrino and the new 1 at the time within the planned restoration when the neutrinos detected that sounds like the most ridiculous variable you've ever heard of but it's not actually from the point use this approach you supposing you have a palm it decays into a neutrino which goes our way and it's frustrating 1 which goes in the other directions the entangled so the natural variable is the separation between them not the distance that either 1 of them has traveled a long and at what time well at the same time in the Pyron frame obviously that's where they just came from the buyer was their parents however in the land that looks really we in the lab 1st of all this plan has a lot of energy the new trade on the view are both going in the direction of the neutrinos going into the ball going in this direction and the separation between them is less then the source of the detected distance but now if you work out the relativistic kinematics you find that the new wave that was derided by the entangled approach is to the usual wavelength the 1 that's in here as this new variable it is to the usual variable another words the New Wave like this actually physically equivalent to the usual 1 letter refers to a different variable is so it has to be bigger than usual 1 by the amount or smaller by the amount that that new variable was smaller than the usual 1 and that's exactly what 1 finds itself yet another threat To the usual results has been defeated but more threats will come home now without my explicitly mentioning it we had been talking so far about neutrino oscillation in backing I never talked about the neutrinos interacting with stuff while the undergoing their journey but any experiment thing you do is going to have the neutrinos traveling through some matter or other for example if you use an accelerator to make your neutrinos and then you fire them at a distant detector because the earth's surface is curved in the neutrinos follow a straight line they will be traveling through birth matter like this now on the way they will encounter electrons lots of money if the beam is neutrinos opposed antineutrinos the new heat component had been can exchange a W with an electron in the matter like this if what's going down the beam line is anti neutrinos newly bar component can make this diagram again exchanging a W this time in this channel rather than that 1 with an electron the map it's only the newly new Reebok component that can do this because according to this formula when you write it in the form premixed saying it's only the electron neutrino the couple's to W and an electron and we don't have new ones and housing earth we have just elected so this affects just a new era in the remark upon me however they can affect it in a big way because lots of electrons in the earth and the coherence forward then forward scattering fire this aware that diagram leads to an act in extra interaction potential energy on the part of newly or of newly bar as it travels through matter and how big is this extra interaction potential energy while it's going to be awarded the Fermi constant because that constant measures the size of either of these impotence it's going to be proportional to how many electrons there are around to interact with solely electoral number density and the coefficient out front we cannot Dubai and waving at the Standard Model tells us that it's plus the square root of 2 4 and note that neutrino beam and mine set for an antineutrino being so this is a matter of fact because that's a possible raises the energy of a new inside matter and lowers the energy of a newly the fractional the importance for that matter effect on oscillation involving a vacuum splitting dolphin words can be gaged by this parameter that I'll call X This is the interaction energy again .period and the thing with which that has to compete Is is the vacuum energy splitting that governs the assault torrid behavior of oscillation and the beef before I change this into a science word function from the co-signed than it was before that was quarrel over 2 weeks so this is X and now some comments about acts it grows with the neutrino energy because this is in the denominator of the denominator so the bigger the energy is the bigger the matter importance it is sensitive to the sign of Delta squared what I mean by the side of dolphins word was suppose yet to minutes state senior something from from elsewhere about the like this 1 couple's a lot electrons about 1 thousand the site of Delta and square can tell you whether the 1 the couple's 2 electrons is heavier than the other guy where the other way around finally remember that this interaction potential flip side when you go from the dreary antineutrino so the effect of matter correspondingly flip side when you go from the Trinity antineutrino and FX's of water 1 the matter affected important effects is 100 it's very important effects is very small compared to what the matter effect is negligible there have been experiments but both kinds when the matter was important the matter was negligible the young the canonical coffee break hours at 2 a quarter to 9 we started a 5 minutes later maybe between imported and I intend to 9 we have few minutes I'll keep going short time and will break I'm not going to take the time to tell you about the really beautiful experiments which have demonstrated that neutrinos really do of but I will summarize where we stand we have we believe very strongly convincing evidence for flavor change on the part of neutrinos made by the sun In fusion reactions like the 1 I talked about the very beginning neutrinos that are emitted by nuclear power plants and are allowed to travel a few hundred kilometers neutrinos made in the Earth's atmosphere by incoming cosmic rays and there you do an experiment where you study not just the neutrinos coming from overhead but the ones coming from the Earth's atmosphere of far earth so they travel through the whole earth to get to detectives neutrinos made by particle accelerators like the 1 at Fermilab where I work in the travel a few hundred kilometers and there's even some evidence to which we will return From an experiment called Ellison the which reports that perhaps the neutrinos from stopped new plastic a oscillate already when they travel 30 meters not kilometers meters and there's an experiment running at Fermilab which is called neighborhood which is supposed to confirm or refute Ellison the and I will talk about what the later here there is a question of very interesting questions there is no question these neutrinos change was so what yes but that only in the fall of the data did not mean that the people of the year of I came here to the people that were there alive said who
was that of a I think the a massive I'm not a collider however the because probably not collider because the masses are so small you have to do if you want to do that you have to do something that is sensitive to the very very very small masses not miss splitting with masses which means probably a better offer very low winter peas where the energies are not enormous compared to the Mass welcome back today so what we learned from all the oscillation data we know that there are at least 3 science states who want to free 2 of them are separated by this quite small so-called solar Delta and squared and it's called that because this tribes flavor change on the part of neutrinos from the sun the 3rd neutrino separated from this costly space pair by roughly 30 times bigger atmospheric Delta and square which describes what neutrinos made in the Earth's atmosphere do as they travel through the whole we don't know whether the closely spaced pairs at the bottom of the spectrum or at the top if it's at the bottom then neutrino spectrum would resemble qualitatively the charge court spectrum the the positively charged court spectrum the negatively charged with spectrum the charge that the inspector they all look qualitatively this way a small gap at the bottom end of big gap at the top Princeton's and the upward the Trump again the talk work with the heck of on the other hand it could look like this and if the neutrino spectrum looks like that it would be "quotation mark inverted it it looks like the other spectrum it would be called normal budget means looks like your respect this is an interesting question earlier the cause of oscillation experiments measure only spleens we also don't know How far above 0 the whole matter is the absolute scale now oscillation do oscillation best-seller something wherever I don't know the spectrum exist where upside down it doesn't matter somebody is at the bottom of the spectrum and wherever the guy at the bottom of the spectrum is it's not below 0 so whichever status at the top of the spectrum must have a mail squared which is no small then the bigger of the 2 Delta and squares and that means it's menace must be no smaller than the square root of that number and the square root of that number is about . 0 4 electron so whoever is at that top of the spectrum ways and we that much we already know that cosmology on the other hand gives us an opera limit all those neutrinos in the universe of fact large-scale structure on the scale of galaxies clusters of galaxies clusters of clusters of galaxies the the masses effect large-scale structure in a way that depends on how big the mayor's what you can get from cosmology depends on which data you are willing to you and what cosmological assumptions you're willing to make but for reasonable use of data and assumptions you get an upper bound on the son of the masses of the mere sight in states which is somewhere between . 1 7 in something like 1 electron volt so we have the the back yes the upper bound can't be taken to be this more aggressive value and if there are only 3 neutrinos looking either this way or that way Venice the upper bound on the sum of their masses translates into that upper bound on whichever is the heaviest particles on the other end of the cosmological bound really 1 then the corresponding bound on the basis of the heaviest is 0 . 4 something like that so if the . 1 7 can be believed then we already know the mass of the heaviest member of perspective it's something like . 0 5 0 electron volts with between . 0 4 . 0 7 and once you know the heaviest mess we do know this blames we terminal tho on the other hand if it's this more conservative and then as an order of March to difference between these 2 not present knowledge is wonderful black there are no loopholes in the cosmological argument that connects you From cosmological observations on the 1 to statement about neutrino masses on the other so I think in the end Is there be no substitute for an absolute neutrino mass measurement In the laboratory using the kind of technique you were asking about and the technique the people are pursuing mouse there's nothing like a collider experiments the opposite in some sense you look at tritium beta this is 1 of the baby with the smallest energy release of any beta decay solely about 17 killed electoral votes it's not only and what you measure Is the spectrum on the outgoing natives going electric now when tritium decays the electron is accompanied by 1 or another of the residing states new 1 and 2 and 3 it happens to be a new Barca's as electron but the bars not the point it's no wonder it's new to new 3 and the branching ratio for making a particularly new is the probability of making that new Line connection with electron in other words From this Lagrangian is the square UGI so there are 3 different decay modes here 1 of which produces new 1 box 1 produces toolbox 1 producers 3 and obviously for a particular outgoing assigned state the heavier than me as I can state is the less energy is left over for the electron so electron spectrum is going to be affected and there are 3 separate thresholds in that electron energy spectrum as you start with a high electron energy and you moved down 1st you reach a point where the lightest nearsighted state neutrino can be admitted that's where the decay stock as you move down further eventually the next heavy amid signs that neutrino could be admitted and there is a threshold as you move down for still the heaviest of all the 3 minutes I can states can be admitted and there's another version 1 finds that in the presence of masses on the part of the mere sight in states the spectrum that you would have in the absence of man gets modified into this specter as I said it is this summer of 3 separate spectrum so it's the incoherent some like this each spectrum has its threshold where the energy becomes low enough to admit Minnesota Mining and there is this factor times that replacing this factory in the missiles now present experimental energy resolution is insufficient 2 separate those 3 threshold so what is measured is actually an average a weighted average Over the words miss work because that's what occurs there of the different nearsighted states each 1 waited by the branching ratio for e-mailing that nearsighted state and they haven't measured that Eva they just got monopoly limited so far on it and then opera librettist to electoral votes so it's done around the same places the upper bound 1 electron ball from cosmology but this 1 does not involve any cosmological assumption that's the answer to your question this is how you go about it is the 9 collided with the are I think this might be a suitable place to break


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