Standard Model Part 8: Spicing Up the Standard Model
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- Опубліковано 17 тра 2024
- In the last installment of the standard model series, we round out the discussion by covering the fermions and the fascinating world of flavor physics!
00:00 - Intro/recap
01:33 - Lepton Flavor Universality
02:24 - Another Charged Lepton?
04:50 - Isospin and Decays
06:58 - Kaons and Strangeness
09:22 - Proceed at Own Risk!
09:41 - Rare Kaon Decays
12:45 - Quark Mixing: Cabibo Matrix
19:03 - Complex Phases: CP Violation
20:38 - Neutral Kaon Mixing
25:00 - Quark Recap
26:20 - Outro
As a recent particle physics graduate, I sincerely commend you for this brilliant exposition of the SM, it has been a pleasure rewatching this series as my own knowledge grew, and contrast it to the often lackluster explanations I see online or in the classroom. This is an exquisite outreach piece I will be sure to recommend to future students. Though I am sad to see this series end, I presume you could always extend it with the many topics you still haven’t covered about the SM (like lattice qcd, anomalies, etc), or even BSM physics (Majorana neutrinos, multihiggs, etc), if ever you feel the desire to do so. I will be sure to keep my eyes peeled :)
you know its a good day when zap physics uploads
I'm so glad to see you back!
Great video! Awesome to see you back!🎉
"Scary math" was fine, as a layman I could follow the matrices easily. Feel free to add more background stuff like that.
Amazing video
Hello I just want to say thank you im just a normal young 15 years old guy But I really like things like that
for me this series is amazing. How you explain things etc. I like how you do your presentations becuase you say about a math of this and about many other things I just like to know details. Thank you for your work Really big thanks❤
You have been gone for a while. Welcome back.
Surprize! See whos back🎉
Here are 4 more examples showcasing how non-contradictory infinitesimal/monadological frameworks can resolve paradoxes across various scientific domains:
17) Thermodynamics and Foundations of Statistical Mechanics
Contradictory Paradoxes:
- Gibbs Paradox about distinguishability of particles
- Maxwell's Demon paradox regarding information/entropy
- Loschmidt's Paradox about time-reversal asymmetry
Non-Contradictory Possibilities:
Infinitesimal Ergodic Realizations
S = -kB Σi pi ln(pi) (entropy from realization weights)
pi = Ni/N (weights from monadic distinctions)
N = Πj mj^nj (total realization monadology)
Representing entropy as a measure over distinct infinitesimal monadic realizations subjectivized via the pi probability weights could resolve classical paradoxes while reconciling information and time's arrow.
18) Foundations of Logic
Contradictory Paradoxes:
- Russell's Paradox about sets/classes
- Liar's Paradox about self-reference
- Berry's Paradox about definability
Non-Contradictory Possibilities:
Pluriverse-Valued Realizability Logics
⌈A⌉ = {Ui(A) | i ∈ N} (truth values over monadic realizations)
A ↔ B ⇐⇒ ⌈A⌉ = ⌈B⌉ (pluriverse-valued equivalence)
Representing propositions as pluriverses of realizable monadic interpretations Ui(A), rather than binary truth values, could avoid diagonalization, circularity and definability paradoxes.
19) Interpretation of Quantum Mechanics
Contradictory Paradoxes:
- Measurement Problem
- Schrodinger's Cat paradox
- Einstein's "Spooky Action at a Distance" paradox
Non-Contradictory Possibilities:
Monadic Relational QM
|Ψ> = Σn cn Un(A)|0> (superposition of monadic perspectives)
Un(A) = ΠiΓn,i(Ai) (integrated monad of relational properties)
Representing quantum states as superposed monadic perspectives Un integrated over the relational algebraic properties Γn,i(Ai) could resolve paradoxes by grounding phenomena in coherent relational pluralisms.
20) The Unification of Physics
Contradictory Barriers:
- Clash between quantum/relativistic geometric premises
- Infinities and non-renormalizability issues
- Lack of quantum theory of gravity and spacetime microphysics
Non-Contradictory Possibilities:
Algebraic Quantum Gravity
Rμν = k [ Tμν - (1/2)gμνT ] (monadic-valued sources)
Tμν = Σab Γab,μν (relational algebras)
Γab,μν = f(ma, ra, qa, ...) (catalytic charged mnds)
Treating gravity/spacetime as collective phenomena emerging from catalytic combinatorial charge relation algebras Γab,μν between pluralistic relativistic monadic elements could unite QM/QFT/GR description.
The key theme is using infinitesimal relational monadological frameworks to represent phenomena that appear paradoxical under classical separability assumptions as perfectly coherent manifestations of integrated pluralistic structures.
Whether statistical mechanics, logic, QM or unified physics - the contradictions all stem from erroneous premises that:
1) Observers are separable from observations
2) Properties/events are independently existing entities
3) Time evolution is fundamentally deterministic
4) Reality can be fully represented in a single mathematical model
By centering infinitesimal monadic perspectival interactions as primitives, these paradox-generating premises are all circumvented in favor of irreducible relational pluralisms.
The monadic "zero" subjects and their combinatorial algebras become the SOURCE of coherent interdependent plurality, not a paradoxical separable ontic realm. Deterministic laws emerge as statistically regulated boundary patterns on a vaster potential pluriverse.
In essence, the monadological frameworks realign our descriptive representations with the inescapable facts of first-person experience - allowing our physics and logics to resonate with the intrinsic integrated structure of reality we comprise, rather than segregating it into hopeless contradictions.
This pluralistic Renaissance offers the path toward renovating humanity's knowledge bases and reason architectures - restoring consilience by deriving all phenomena as cohesive relational aspects of a monadic metaphysics, rooted in irreducible first-person facts.
❤
If the only difference between the flavors of charged leptons is their mass, are they the same object before electroweak symmetry breaking?
Is it then useful to think of them as different kinds of excitations of the same quantum field, which behave differently under the Higgs?
Or is it possible to distinguish them, because the corresponding neutrinos will behave differently, regardless of the Higgs?
And is this different for the quarks? Since the Strangeness seems to indicate that these interact fundamentally differently in some way?
Lastly is it possible, within the standard model, that there are quarks with masses in between the charm and top, but they are somehow suppressed?
Also welcome back and thank you so much for making this series!
Hi Narf! Thank you for the insightful questions as always.
The first thing to note is that, before electroweak symmetry breaking, even though the particles themselves are massless, they still interact with the Higgs, and this interaction is what ends up giving them their mass after EWSB. So, all the flavors of both the leptons and quarks are always distinguished from each other by their interactions with the Higgs. However, for pretty much all of the particles aside from the top (really, the left-handed quark doublet and right-handed up-like singlet of the third generation), these interactions are very small, so there is actually quite a large approximate flavor symmetry of the standard model: U(2)^2 x U(3)^3 (the U(2)^2 comes from the first two generation quark doublets and up singlets while the U(3)^3 comes from the down singlets, the lepton doublets and the charged lepton singlets). The smaller U(2)^5 symmetry disregarding all third-generation particles is actually an even better approximation. These approximate symmetries allow us to essentially build flavor multiplets exactly like you suggest, and can be very useful for model-building in new physics scenarios.
The fundamental difference between the quarks and the leptons is that in the standard model, the neutrinos are massless, while both the up- and down-like quarks are massive. The key feature of this is that when one of the two particles in the weak doublets is massless after EWSB, the particle is always a physically propagating state with definite-energy, no matter how one rotates it with a unitary transformation (this is just because there is no mass matrix that needs to be diagonalized to give definite masses to the particles). So, one can always rotate the massless particles (neutrinos in this case) in the opposite direction of the massive particles (charged leptons) so that the weak eigenstates are aligned with the mass eigenstates and no off-diagonal interactions arise. However, since we now know that neutrinos are massive, we need to include this mixing effect into the neutrino sector as well which is accomplished using an analog of the CKM matrix, known as the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix, and is the reason we end up with neutrino oscillations.
The short answer to the question of more quarks between the bottom and top masses is that no, this is not really possible. The reason is actually quite interesting: we know that the coupling constant of QCD runs with the energy scale, and this running can both be calculated as well as measured (of course, "measured" has a loose meaning here since couplings aren't totally physical objects. However, the parametric dependence of physical observables on these couplings can be determined by the theory, allowing one to extract them from data). This running has a strict dependence on the number of quarks with masses below the energy scale at which one is determining the coupling constant. And it turns out that, below the top mass scale, a five-quark-flavor running agrees with the experimental determination remarkably well (see Fig. 9.1 in pdg.lbl.gov/2006/reviews/qcdrpp.pdf, where the theory prediction is the Spectroscopy (Lattice) point). If there were additional quarks in nature, we would have to see an additional effect here since all quarks interact with via QCD with the same strength.
Hope that answers your questions!
@@zapphysics Hi Zap! :) Thank you, for the interesting answers!
The neutrino part and another one of your replies here gave me a thought. If we think of lepton, and quark generations as doublets, should we not expect the neutrinos to be electrically charged, just like the quarks? Or is this just about flavor?
Is the charge of the neutrino predicted, or is it a measured value?(of course we needed it to be neutral to match observation in the first place)
Is there a relationship between the massiveness and the neutral charge of the neutrino?
The fact that we see no charged particles without mass seems "suggestive". There is nothing that forbids this, right?
And an unrelated question. I have been (slowly...)working my way down to the fundamentals of General Relativity and Differential Geometry and I am *struggling* with the concept of a connection, and how to rigorously define one.
Then I remembered that Sean Carroll said that, in QFT, the boson fields are connection fields, just like the ones in GR, which tell us how to parallel transport the charged vectors.
What is the bundle in this formulation? And is the "Photon Connection" just given by Maxwell's Equations?
Fun anecdote: I had just happily accepted that "connection", "parallel transport", and "covariant derivative" mean the same thing. Today I started a lecture that opened with "in general relativity these are often used synonymously. You need to forget all that." ... Math is hard.
@@narfwhals7843 I'll start with your first question, mainly because it is much easier to answer.
So the main thing to remember is that electric charge is really a combination of a particle's weak isospin (T3) and its hypercharge (Y) after EWSB as e = T3 + Y (sometimes there will be some extra factors of 1/2 thrown in, but this is just how you normalize the generators of the group). Just like regular spin, for doublets under SU(2), the isospin values take either +1/2 or -1/2. Also remember that, since these are doublets, both elements of the doublet must have the same weak hypercharge. So, we know experimentally that the up quark has electric charge +2/3 while the down quark has electric charge -1/3. The only way to put these into a doublet in a consistent way is to have T3u = +1/2, T3d = -1/2 and Yquark = +1/6. For the case of the leptons, if we measure an electron with electric charge -1, we have two options: T3e = +1/2, Ylepton = -3/2 or T3e = -1/2, Ylepton = -1/2. The first choice then includes a particle with T3=-1/2 which would then have electric charge -2 and the other choice has T3=+1/2 and zero electric charge. The distinction is then made by the fact that we observe electrically neutral neutrinos.
However, this isn't all experimental, there is a theoretical aspect to it, namely in terms of the relative choices of hypercharge of the quarks and leptons. This has to do with the fact that, whenever you have a gauge theory which talks to left- and right-handed fermions differently, quantum corrections to the theory can actually induce a non-conservation of the corresponding current and therefore break the gauge symmetry. This is known as an anomaly, and it is really important that for any chiral gauge theory, these anomalies cancel. As it turns out, this is actually quite restrictive in terms of the allowed charges your fermions can take in the theory. In the case of the standard model, once you include all of the lepton and quark doublets as well as the singlets, it actually pretty much completely fixes the allowed choices of the hypercharges of the particles in order to preserve the symmetries of the SM. Weinberg actually has a really good discussion of this in Chapter 22 of his second QFT volume.
I might be able to help a little bit with the topic of gauge fields as connections, but I will warn you that this topic has always confused me as well, so my help will be limited.
I think that the best way to get a more intuitive grasp on what these things mean is to just look at the flat, Euclidean plane described in polar coordinates. Something that I find is not necessarily emphasized enough is that this choice of coordinates *depends on where you are in the plane*, or in other words, if you start at one point in the plane and move to another, your basis vectors have changed their orientation.
This is obviously going to be an issue when we try to compare two points using e.g. a partial derivative, which takes the difference of some object evaluated at two neighboring points. The problem is that how I describe that object actually changes between the two points because the basis vectors are not aligned (think of defining the vector (1, 0) where the first component is radial and the second is azimuthal at the two separate points: the vector looks different at each point even though it should be the "same" object!). So, in order to actually reasonably take the difference of this object evaluated at two points, I need some way of consistently accounting for this additional change coming from the rotation of the basis vectors at the two points.
The way to do this is to introduce some new object that "connects" the two points by "transporting" the basis vector information at one point to the other point. As this would suggest, this object is exactly the connection, while the action of this connection is parallel transport. I can then define an operation which consistently compares two neighboring points by introducing this connection into the derivative to account for the rotation of the basis vectors. This combination, of course, is the covariant derivative.
Now, in spacetime, this has a fairly concrete meaning: the choice of coordinates can be spacetime dependent, so we have to account for the way that the components of spacetime tensors change as the basis vectors are varied from point to point. Remember that each component of a tensor is contracted with a set of basis vectors to define the true, coordinate-independent tensor object, so the number of indices that we need to describe these components will change the way that we need to compensate the variation of the basis vectors. This is why Christoffel symbols have three indices: they eat one spacetime index (how one piece of the tensor components change with the basis vectors), they have to replace this index for consistency between the right and left sides of the equation, and it has to have an additional spacetime index that tells us along which spacetime basis vector we are changing.
When we are working with gauge theories in QFT, the story is quite similar, except the variations no longer happen in spacetime (we always work in flat spacetime, so we can simply use Cartesian coordinates), but instead some internal space which depends on the symmetry group of the theory. When we make this symmetry local (i.e. spacetime dependent), the field's orientation in the internal space is going to change as we move in spacetime. So again, when we try to compare the field at two points in spacetime, the field has a different internal orientation at these two points, and we are trying to compare two inequivalent objects. So we do the same thing: we introduce an object which transports us from spacetime point to another in a consistent way in the *internal* space. So by analogy to the Christoffel symbols, this connection will need two internal indices to "eat" and replace the internal space information of the field at the two points, and a spacetime index to give the information of the path through spacetime. So, we always have a spacetime vector which serves as a connection, though its internal structure depends on the representation of the field under the symmetry group (this turns out to be exactly proportional to the generators of the representation). This connection is the spacetime vector gauge field that we introduce to preserve local symmetries. Of course, when we add this connection into the derivative to properly compare the spacetime points, we end up with a gauge-covariant derivative.
Unfortunately, I don't think I'll be much help with the bundles...this is usually the point where my eyes glaze over a bit seeing the mathematical definitions, theorems, etc. (I agree that math is hard.) However, maybe this review of the subject will be more useful to you:
arxiv.org/pdf/1607.03089
@@zapphysics Thank you _very_ much!
So the vector we are transporting is not the state vector in Hilbert space, but a vector in this "internal space", given by the symmetry group. This should make it clear what the bundle is. I'll check that paper!
The first paragraph is already fascinating.
woah, ur back
In a different question, may I ask what research field do you specialize in?
Thank you so much for the kind words, I really appreciate it and I'm glad you enjoyed the series! Yes, I am absolutely planning to cover anomalies and lattice calculations, and want to start a whole separate series on BSM in the future!
Also, to answer your question, I actually am mainly a flavor physicist (I do some BSM stuff here and there though), so this video has a special place in my heart!
📍16:39
So could there be more quarks?
This is certainly the natural question to ask after the discovery of all of the generations of quarks. In principle, yes, but they would likely have to behave quite differently than the standard model quarks.
The issue is that new quarks would have to be quite a bit heavier than the top quark, otherwise we would have seen their effects in e.g. FCNC decays (or perhaps even direct production at the LHC). The main problem with this is that, if they couple to the Higgs (which is the only way in the standard model that particles can get masses to begin with), quantum corrections coming from interactions should drive the Higgs mass up to the scale of the heaviest quark. Since the Higgs mass is already very close to the top mass, it is theoretically very difficult to come up with a model with additional quarks where the new quarks are heavy, but the Higgs keeps its top-like mass. Now, one could just suppose that the new quarks don't talk to the Higgs, and get their mass from some other mechanism, but these new quarks would have to behave very weirdly compared to the ones we have observed. In particular, if we decompose them into left- and right-handed pieces, these pieces would have to interact the same way according to standard model interactions (otherwise the masses would violate the symmetries of the standard model). Compare this to the standard model quarks whose left- and right-handed components behave very differently, particularly with weak decays. Nonetheless, these new quarks can arise in some theories and there are active searches at the LHC for these so-called heavy "vector-like" quarks.
@@zapphysicsand what about additional leptons? ;)
@Firedragon9898 the charged leptons are pretty much the exact same story since the known charged leptons get their masses from the Higgs, and if there were additional charged leptons lighter than the Higgs/top, then we would have seen them in similar decays to those where we measured the tau. So, there isn't too much room for additional charged leptons aside from similar, vector-like leptons where the left- and right-handed pieces are treated the same by the standard model.
Neutrinos are a bit of a different story, since they already don't have mass in the standard model. There are several ways that neutrinos can get a mass (which we know they do, in reality, have) and some of these require some additional neutrinos for it to work. But in some sense, the standard model already only has "half" the number of neutrinos as charged leptons since we have only observed left-handed neutrinos, so one way to give neutrinos mass is by adding a right-handed neutrino basically allows the neutrinos to talk to the Higgs in the first place. This isn't the only way to give neutrinos mass, but it is perhaps the simplest, so again there are several experiments working on trying to find evidence for right-handed neutrinos.
Neil turoks work on right handed nuetrinos looks promising, imho.
why can't neutrinos have mass in the standard model?
This has to do with the fact that we can split fermions into two pieces: a left-handed piece and a right-handed piece (the "handedness" is somewhat related to the two spins, up/down, of the fermions, but not exactly). Typically, in order for a complex fermion (like the charged leptons or the quarks) to have a mass in the standard model, it needs to have a left- and a right-handed component, which allows it to couple to the Higgs. However, since neutrinos are neutral under electromagnetism and QCD, they only interact via weak interactions, which only talk to the left-handed pieces of the fermions, so we have only ever observed left-handed neutrinos. Without a right-handed counterpart, neutrinos can't interact with the Higgs in the standard model and so don't get a mass.
We know that in nature neutrinos have mass, so you might wonder why don't we just add a right-handed neutrino to the standard model, have it couple to the Higgs, get a mass and call it a day? The issue is that, unlike the other fermions, the neutrino is neutral under all conserved gauge symmetries of the standard model, so there is a possibility that it is a *real* fermion, not complex, typically called a Majorana fermion. If we are allowed to extend the standard model (which we have to do anyway to add a right-handed neutrino), there are ways to give a real, left-handed neutrino a mass WITHOUT adding a right-handed component. So, without knowing for sure which scenario actually describes nature, we don't know yet how to extend the neutrino sector to explain the neutrino masses.
@@zapphysics so there are multiple ways to do it, but we don't know which matches reality?
"You can't learn anything by watching youtube videos." -Warren pinkard
brain hurt