More Examples of Possible Unexpected Higgs Decays

As I explained on Tuesday, I’m currently writing articles for this website that summarize the results of a study, on which I’m one of thirteen co-authors, of various types of decays that the newly-discovered Higgs particle might exhibit, with a focus on measurements that could be done now with 2011-2012 Large Hadron Collider [LHC] data, or very soon with 2015-2018 data.  See Tuesday’s post for an explanation of what this is all about.

On Tuesday I told you I’d created a page summarizing what we know about possible Higgs decays to two new spin-zero particles, which in turn decay to quark pairs or lepton pairs according to our general expectation that heavier particles are preferred in spin-zero-particle decays. A number of theories (including models with more Higgs particles, certain non-minimal supersymmetric models, some Little Higgs models, and various dark matter models) predict this possibility.

Today I’ve added to that page (starting below figure 4) to include possible Higgs decays to two new spin-zero particles which in turn decay to gluon or photon pairs, according to our general expectation that, if the new spin-zero particles don’t interact very strongly with quarks or leptons, then they will typically decay to the force particles, with a rate roughly related to the strengths of the corresponding forces.  While fewer known theories directly predict this possibility compared to the one in the previous paragraph, the ease of looking for Higgs particles decaying to four photons motivates an attempt to do so in current data.

I have a few other classes of Higgs particle exotic decays to cover, so more articles on this subject will follow shortly!

45 responses to “More Examples of Possible Unexpected Higgs Decays

  1. Matt,

    For us non-experts, it is not that clear how spin is conserved in these decay paths that you describe.

    For instance, How a spin-zero particle like the Higgs decays into pairs of spin-one particles, like a pair of photons?

    • First, spin isn’t conserved. Angular momentum is conserved, and that includes both spins of individual particles and motional- (or “orbital-”) angular momentum of particles relative to one another.

      Second, spins don’t add. The rule for the spins of two photons is 1 + 1 = 0 or 1 or 2. For two electrons, the rule is 1/2 + 1/2 = 0 or 1. For an electron and a photon, it is 1 + 1/2 = 1/2 or 3/2. The general rule is S + S’ = anything between |S-S’| and S+S’, spaced by integers.

      On top of that, if two photons have orbital angular momentum L, then when you add the spin and the angular momentum, the rule for the total angular momentum is 1 + 1 + L = L-2 or L-1 or L or (L+1) or L+2 (though ignore any negative numbers; for instance if L=1 then the angular momentum can be 0,1,2, or 3.) Since L can be any integer 0,1,2,3,4,… , two photons can combine to make any integer angular momentum.

      To prove these things requires understanding the rotation group (actually the Lorentz group of rotations and Lorentz boosts) and its algebra. In the U.S., one typically learns this stuff in junior year of university.

      • Spin is one of those things that seems to separate the experts from the rest of us. About all I know (not being anywhere close to expert) is that spin is a key difference between fermions and bosons and that it’s somewhat analogous to physical spin, but has no real classical analogy.

        Your blog has opened the door to so many things for me in how you’ve brought advanced topics down to earth. Would an article on spin for non-experts be possible or is the concept just too lofty?

        I would be very curious to know how spin is measured (the Wiki article doesn’t really explain that in a way I can understand). How does measuring spin result in 1/2 units for fermions and whole units for bosons?

        • In fact, spin is a completely quantum mechanical property with no classical equivalent.

          During the mid 1920s, spin was inserted into the theory as it was not predicted by either Schrodinger’s theory or Heisenberg’s theory, but when Paul Dirac combined Schrodinger’s theory with special relativity, spin emerged from the equations as a natural relativistic consequence, such that Dirac’s theory “postdicted” spin.

          • I just discovered a History section at the end of the Wiki article after all the advanced math (I usually expect the History section up front). It mentions “emission spectrum of alkali metals” (without explaining exactly how that obtained), so apparently there was some experimental evidence that also lead to the discovery.

            It also mentions a Stern-Gerlach experiment in 1922, but that spin was not understood in that context until 1927, I assume due to Dirac’s work you mention beginning in 1924.

            One reason I want to understand spin better is because it’s so crucial to Bell’s theorem. I’m not clear about spin with regard to the x, y and z axes, for example. As I understand it, spin can be measured on any arbitrary axis at any angle, but is spin actually really expressed in terms of x, y and z components contributing to that angle?

            It’s also interesting to me that you can apparently change spin direction (how?), but never its degree. The amount of spin is part of the particle’s identity.

            Spin reminds me of the weak force in most texts for non-experts. They say something along the lines of, “The weak force contributes to some forms of nuclear decay,” and then move on to the next topic. It’s like spin and the weak force are just too complicated and non-classical to even begin trying to explain in detail.

          • Actually spin isn’t necessary for Bell’s theorem. It’s convenient experimentally, and conceptually if you’re an expert, to use it, but Bell’s theorem operates independently of the concept of spin. The only thing that’s important is to have objects with two or more quantum mechanical states, ones that you can entangle.

            Also the weak force is a lot easier to understand than spin.

            Spin is fundamentally unintuitive. I can tell you facts about spin, I can show you math about spin, but I cannot tell you how to visualize it, because you and I have never see anything “spin” the way particles do. Sometimes particle physicists really have to rely on the math to explain the world we see. We understand spin very well
            (in the sense that we can predict everything about it using math) but that doesn’t mean we can visualize it independently of the math. And that’s the basic problem.

            However: saying a particle has spin 1/2 means that if you align the spin with some direction (say, using a magnetic field) you will find the particle, even when sitting still, has angular momentum along that direction (i.e. is in some sense spinning round that direction) with angular momentum h-bar / 2, where h-bar is Planck’s constant h divided by 2π .

            Now how you should visualize this isn’t so obvious, but it can be done in the case of spin-one particle, and maybe I should try to explain that — after I figure out how also to do it for a spin-two particle…

          • Wow, if the weak force (a topic many popularizing authors won’t even touch) is simpler than spin,… well, just yikes! But if anyone can pull it off, I’m betting you can.

            (For example, I’d already gotten a sense of “curled up” dimensions from the “ant on a garden hose” analogy, but I thought your boats in a canal analogy was brilliant!)

        • This may help, or confuse like Iam confused.
          There is no SPIN without 3D spacetime ? Energy conservation and causality nevertheless prevail, of course, but it requires a changed (or “warped”) metric to do so, and a new understanding of the relation between free and bound electromagnetic energy (E = mcc), and between gravitation, space, and time. Higgs boson gauges the mass-energy of the electroweak unified-force symmetric energy state.
          PHOTONS have energy but not mass at speed c ? Nothing is spinning and/or the word “spin” is caused by some historical inaccuracies or accident. PHOTONS have, zero total angular momentum = ±1. But in classical physics (and common sense!), the energy of a particle must always be a positive number. So the SPIN is 1 ?

          In 1928, Paul Dirac solved the problem: he wrote down an equation, which combined quantum theory and special relativity, to describe the behaviour of the electron. Dirac’s equation won him a Nobel Prize in 1933, but also posed another problem: just as the equation x2=4 can have two possible solutions (x=2 OR x=-2), so Dirac’s equation could have two solutions, one for an electron with positive energy, and one for an electron with negative energy. But in classical physics (and common sense!), the energy of a particle must always be a positive number!

          The equation also implied the existence of a new form of matter, antimatter, hitherto unsuspected and unobserved, and actually predated its experimental discovery. It also provided a theoretical justification for the introduction of several-component wave functions in Pauli’s phenomenological theory of spin. Although Dirac did not at first fully appreciate what his own equation was telling him, …
          “his resolute faith in the logic of mathematics as a means to physical reasoning”,
          ….. his explanation of spin as a consequence of the union of quantum mechanics and relativity, and the eventual discovery of the positron, represents one of the great triumphs of theoretical physics, fully on a par with the work of Newton, Maxwell, and Einstein before him.

          http://scienceblogs.com/principles/2010/07/26/electron-spin-for-toddlers/

          • Thanks for the info and the link!

          • @veeramohan: I’m sorry to differ, but IMHO you are misrepresenting many things in this comment.

            Just to be clear about a a very basic concept: in special relativity, energy, mass (rest mass) and momentum are linked though a pythagorean relationship. That means that, for most situations, these three concepts form a triangle with a rect (perpendicular) angle between rest mass and momentum, but there are certain situations where there is no rest mass term in this relationship, so, in such situations, the energy term is always numerically equal to the momentum term.

            When in particle physics a given particle is described as massless, we are describing particles that comply with that particular situation where the particle does not have a rest mass term in the pythagorean relationship, which means that the energy term is always equal to the momentum term, like say, with any photon.

            That means that for any photon, the energy it has is completely relativistic, that is, completely due to its momentum.

          • @GEN you are correct, I want to delete my last post, but could not.
            Mathematics is very difficult for me. I would not fix anything – I may land in last days of Nikola Telsa, if I continue. I thank you for the reply.
            But my intuition says, there is something to keep masslessness of radiative photons – in its momentum (or constant speed).

  2. That’s right!

    Good to know how this works.

    Thanks a lot for the heads up.

  3. Looks like you’re a day late on exotics Higgs decays & I was two day early :) At some point I ho

    • (Posted accidentally) I was going to say at some point I would hope we could discuss how I successfully predicted the Higgs decays as detected. It may contribute to your investigation. Either way, I have a working Higgs model that predict the diphoton and ZZ channel w/o leptons or quarks channels. Otherwise, good luck & I wish you the best!

      • The predictions of exotic Higgs decays of the sort I’ve been talking about were made in 2004-2006. They’re all published in the literature. So you’re a few years behind the times… which I’m happy to discuss.

        • Mine are from 2002-2003 :) Regardless, I would love to discuss technical issues insofar as I’m not written off as a crank. I can hang with the big boys :) Maybe its a Rorschach experience, but I’m seeing that the data from both ATLAS and CMS is significantly different from the expectation value of the Higgs decay channels for the ~125GeV predicted by the Standard Model Higgs. I would even refer to one of your article where you show a graph explicitly showing expectation values that are almost the opposite of what was detected. Now I will accept that this is all preliminary and a difficult experiment that needs time, however, I was specifically looking for Higgs decays to be made primarily of neutral bosons. This is part of a new approach to symmetry violation I use called “cross-conjugation”. Furthermore,it appears to me that the ATLAS and CMS data is displaying entanglement. The “mass” of the ZZ and gamma-gamma channels appear to flip-flop between detector (overlap their graphs). This looks like “neutral boson oscillation” similar to neutral meson oscillation. So whats’ oscillation? I’m seeing two Higgs fields displaying explicit symmetry breaking, one field relative to CMS and the other relative to ATLAS. I’m suggesting that we are seeing some sort of “M-Violation” where a massless goldstone Higgs could be intermediating both Higgs fields (H+ and H-) non-locally where these H+ and H- eigenstates represent some form of mass symmetry that is apparently being broken :) This goldstone Higgs (that isn’t being detected) could be the elusive graviton. The scarce leptons and quarks could some form of interference between the two Higgs fields. .. roughly speaking. If you have anything remotely like this I would be very interested in it. Are your papers on exotic Higgs decays available?

          • You’ve just been written off as a crank… as would be anyone who believes that two experiments five miles apart on the Earth as it spins and moves through space would experience two different Higgs fields. Bye.

          • Crank? Isn’t that what starts an engine? You offer a discussion & reference papers you have written. I ask to see your papers regarding exotic Higgs decays and you attempt to insult me… And you represent being an academic or “educatior”? I didn’t realize you were an elitist :) I respect you as a physicist but I am put off by your arrogance. I’ll teapectfully take my physics comments somewhere else. Good day :)

  4. @Wyrd Smythe: The Stern Gerlach experiment brought the first real evidence about spin, but the first theory (a non-relativistic theory of spin) was developed by Wolfgang Pauli. In this theory, Pauli included his now famous exclusion principle, that is intrinsic to spin for fermions in bounded systems.

    • I would not say the exclusion principle is “intrinsic to spin”. It is “intrinsic to fermions”. The fact that particles of spin 1/2 must be fermions is yet another condition, one which can be evaded at least mathematically, but not in a universe of three (or more) spatial dimensions in which special relativity and quantum field theory both apply.

  5. Maybe the phrase was not properly worded: what I was thinkinf of was more in line with “the inclusion or the exclusion principle are related to the value of spin that a particle has: if it is an integer value, the inclusion principle applies, if it is a half-integer value, the exclusion principle applies”.

    It is in that broader sense that I meant that “inclusion/exclusion” is intrinsic to spin, but the phrase presented did not convey that broader concept.

    In the context of the phrase presented, I concur with you that the right thing to say is that exclusion is intrinsic to fermions.

    Without the use of equations, we have to be even more precise with scientific ideas expressed in words.

  6. @Wyrd Smythe: as far as I can tell, the spin of electrons is related to spectral measurements when you consider the fine structure of spectra, that is, the splitting of spectral lines due to the effect of spin of the electrons involved.

    Per se, spin that has nothing to do with Bell’s theorem, just as Matt has already mentioned, that theorem is theoretically important to study and understand quantum entanglement.

    The very concept of quantum entanglement was brought to center stage by an influential paper published by Einstein, Podolsky and Rosen (EPR) in 1935.

    What they wanted to demonstrate was that the most accepted interpretation of the Uncertainty Principle at the time, the so-called Copenhagen Interpretation, was not the only plausible explanation, and they proposed the existance of “hidden variables”.

    To describe their idea, they proposed a thought experiment (gedanken) with a special type of quantum system that, according to the predicted behaviour by QM, it would present two entangled particles.

    But since this thought experiment was an argument on how to interpret the Uncertainty Principle, it focused its attention on conjugated properties, that is, the properties associated with non-commuting operators, like say, momentum and position, so, it is clear that per se, quantum entanglement has no particular relationship to spin.

    • Thank you for writing all this. I am familiar with the EPR paper, and I do understand that spin is just one way to demonstrate quantum entanglement providing different results than random statistics (I believe other experiments have used photon polarization, for example).

      A thing I’m not clear on is as I mentioned above. If spin is measured on non-orthogonal axes, is the measurement a superposition (if that’s the right word here) between orthogonal axes, or do particles literally have a spin direction on any arbitrary axis? I’ve gotten the sense that it’s the former.

      • You’re on the right track with “superposition”, but it needs to be formulated differently. Also it does not really matter whether the different axes you look at are orthogonal or not, you just get simpler numbers if you use right angles.

        Let’s say you have a spin 1/2 particle in a state U that is definitely “up” in the up-down direction (say “z”). Now there is nothing special about the “z” axis itself, you may as well use the “x” axis (left-right, say) to describe the very same state U. There are formulas you can look up that tell you that U = aL + bR, where L is a state of spin pointing “definitely left” and R of “definitely right”, and “a” and “b” are two particular (complex) numbers. In this sense you could say: “The state U with spin definitely up is a particular superposition of (the states of) spin definitely left and definitely right.”

        This tells you that when you actually measure the spin in the “x” direction, you will sometimes get “left” and sometimes “right”, the probabilities being proportional to the square of the absolute values of “a” and “b” respectively. (The numbers depend on the angle between the axes you chose. In this particular case you will get 50% left and 50% right.) Note that after the measurement in the “x” direction, the state will be either L or R, so you have destroyed your original “definitely up” state U.

        It is important to understand that “being a superposition” is not an absolute property of a state. It’s not like there are states that “are superpositions” and states that are not. I think this is not emphasized enough in many popular presentations of quantum mechanics. The statement above just says something about the relation of the state U to the states L and R. You can as well say that L is a particular superposition of “up” (U) and “down” (D), or of the two possibilities along any other arbitrary direction you choose – just the numbers a and b will vary.

        • Thank you for this. Let me see if I can say it back correctly and sensibly. A particle has a quality, spin, that if measured about any arbitrary axis will have a CW or CCW direction about that axis. Three orthogonal axes merely provide a mathematically convenient way to assess the probabilities given a previous measurement on an axis (or in EPR experiments, given the measurement of the entangled particle).

          I think maybe the light bulb is finally starting to be fully on wrt to Bell. If p1 and p2 are entangled, and if p1 is measured to be in state U, p2 is still undetermined for L and R per “a” and “b” although it would be determined for D (anti-U). This particular measurement would be 50/50, which does not eliminate classical probabilities, but the math of “a” and “b” along non-orthogonal axes involves the complex number math of quantum mechanics and not the math of classical statistics.

          • I think you are at a point of your inquiries where it may be worthwhile to pick up a good introductory book with the real equations. It is near impossible to convey these things correctly without math.

            Yes, if you have a single spin 1/2 particle and you measure the projection of its spin onto a chosen axis there are only two possible results: +1/2 (“up”) and -1/2 (“down”) in units of h-bar, which you may call CCW and CW. The general state before the measurement can be written as aU + bD (with complex numbers a,b) and from that you can calculate the probabilities for results along any arbitrary axis, but you can do only one of these measurements on this state. If you take subsequent measurements along three different axes, the second and the third one will no longer probe the same original state!

            If you measure along the same axis twice, you will get the same result the second time (in an ideal experiment where nothing messes with the particle). If you tilt the axis the second time a little you get e.g. 99% of the time the orientation closer to the first one. The more you change the angle, the less correlation you get, up to a right angle where you completely loose it (as you would expect from symmetry considerations).

            With two spin 1/2 particles it gets more tricky. The key point is that it is not two states, it is one state describing two particles. The general state can be written like aUU + bUD + cDU + dDD. Depending on the numbers a,b,c,d you can have varying degrees of entanglement. The full treatment is much too long for a comment, however.

        • @Edwin Steiner: IMHO, the fact that all quantum mechanical theories as well as all QFTs support superposition is just the simple result that nature has sistematically favored a mathematical truth that is “all over the place” when we deal with differential equations: any linear combination of particular solutions of a given differential equation could also be a solution (a more general solution) of said equation.

          We know that it can be proven that the complete set of particular solutions of a given differential equation are orthogonal to each other in the sense that they are linearly independent, so, they can form the basis for a space of functions, which means that a linear combination of all these functions that behave like “eigen vectors” of a space of functions can define a general solution for that given differential equation.

          Kind regards, GEN

          • @GEN: Yes, the superposition principle is merely the statement of the linearity of the equations. For people familiar with the math there is no risk of confusion, because they know that the coordinates of a vector depend on the arbitrary choice of basis they make.

            My worry is that people who have not seen the math could walk away from some popular expositions with the impression that there are “ordinary” definite states like “spin up” on the one hand and “crazy” states like a “superposition of spin up and spin down” on the other hand. It is not like that, there is no such distinction. What looks definite with respect to one basis (e.g. projection of spin onto the z-axis) can look “crazy” with respect to another basis (e.g. projection of spin onto another axis).

            Of course – without math you can never completely avoid confusion. However I feel that this one is a crucial point, confusion about which can cause deep misunderstandings of quantum mechanics. I know because I had this confusion myself before I learned the math.

          • Speaking as one of the potentially confused, the key (at least for me) seems to lie in the “dreaded trig.” Below, @GEN draws a line from 3D space thru spherical coordinate systems (so very useful for rotations of things) to the sine function (which is just a ratio over an angle). That certain axes give “sane” answers (like 0.5) while others give “crazy” ones is just due to how the sine function behaves.

            Maybe it helps to have dabbled in 3D CGI, and the need to rotate things with the helpful trig, but the discussion here makes it crystal clear to me. (So thanks!) It might be a harder reach for those who “hate math” (let alone trig). Pity; trig is one place math becomes beautiful.

      • Spin, like angular momentum of any sort, can only be specified by two numbers: (1) the total amount of spin, and (2) the amount of that spin along one and only one axis. The answer to both (1) is an integer or half-integer L; the answer to (2) can only be L, L-1, L-2 … down to -L. Why? When you understand that “particles” are quanta, that is, ripples of minimal size, and thus are more like waves, it becomes easier to understand how this works for ordinary rotational angular momentum, but not simple. All of atomic physics is determined by this property of angular momentum; it’s not special to spin.

        But for spin it remains very difficult to visualize. You can’t think of this in terms of a whirling object; you simply have to calculate it.

  7. Spin has handedness, in the sense of left-handed spin or right-handed spin. In Physics, things that have handedness are vectors, so it is no wonder that spin is a vector.

    The handedness of spin of a particle can be exposed in some ways, like for instance, through a property called helicity, which is the projection of the spin of a particle onto the linear momentum of said particle.

    In Physics, a projection implies the inner product of two vectors, in this case, the inner product of the vector of spin with the vector of linear momentum. Since the result of any inner product is a scalar, it means that helicity is a scalar.

    Equations in Physics are described with variables that represent the dimensions of a certain space. In can be proven that out of the infinite combinations of possible dimensions that can be chosen, the combinations that make most sense are those that contain dimensions that are orthogonal to each other.

    For a system like an atom, which has spherical symmetry, it makes most sense to use spherical coordinates, but no matter what convention of coordinates you choose, they will always be orthogonal to each other.

    The original Schrodinger equations (the time independent equation and the time dependent equation) were capable to predict many of the aspects of quantum mechanics already known, but these equations did not predict the spin in a very direct way, but in a rather indirect way.

    To start with, when these equations where used to describe the Hydrogen atom, the predictions and description were perfect when compared to the experiments. Up to this point, no clues and no evidence about the spin.

    When these equations were used to describe a atomic system with two electrons, this is when something weird with the wave function showed up: there were more possible mathematical answers to the equation than the number of possible answers that made sense.

    When these mathematical answers were analyzed in detail, some of these answers did not make any sense at all, mainly because they implied that the electrons could be distinguishable from each other, which happens to be anathema for any quantum mechanical theory.

    This was the way out of this problem: if you discard the mathematical solutions that do not support the principle of indistinguishable particles, you get the “right” number of solutions with the “right” properties.

    The first physicist that came up with a right explanation for all this weid behaviour was Wolfgang Pauli: he introduced a theory for spin, the exclusion principle and how to discard the “excess” solutions to the equations.

    • Spin does *not* have handedness; this is wrong. Helicity is about handedness, but that is about the correlation between spin and motion. For an electron one can speak of handedness relative to a particular axis, but the spin does not intrinsically have any handedness.

      Please be careful not to mislead my readers!!! this subject is confusing enough without misinformation appearing on my own site!!!

      • /“particles” are quanta, that is, ripples of minimal size, and thus are more like waves, it becomes easier to understand how this works for ordinary rotational angular momentum./
        The photons are responding to the curvature in space-time, not directly to the gravitational field.
        At this curvature, photom mass will remain as 4 x 10^-48 grams or it will start to increase ?

      • Confusing indeed. Principally the earth has no specific welldefined axis. Whatever the axis of rotation, after a turn of 360 degrees the earth looks the same. Is this how I can visualize spin-1?

      • I apologize for such a stupid mistake.

  8. I have simplified the descriptions of all the math work needed to come up with the right solutions.

    To be able to “bump into” the “supernumerical” amount of solutions, we have to consider an particular kind of operation with the wave function for the system with two electrons: what happens if we exchange one electron with the other? what happens if we do that again?

    With the first “exchange” of electrons, certain things in the solution will suffer an “inversion”.

    If we do a second “exchange”, there will be another “inversion” of certain things in the solution, but we should also consider that, affer two consecutive “exchanges”, we will get back to the original situation.

    So, that gives us some clues regarding what “inversions” of things after each “exchange” are valid: we can only accept as valid those inversions that after an even number of exchanges can give us a solution that is identical to the solution of the original state with no exchanges.

    The Schrodinger equations are mathematical equations with complex variables, and it requires to be fluent in the math with complex numbers, in this case, partial differential equations with complex numbers.

    It is because of this particular fact, equations with complex numbers, it is a natural consequence of this that the solutions very frequently (most often than not) contain sines and cosines, as well as the exponential functions with negative exponents.

    The Sine function and the Cosine function are periodic functions, and periodic functions offer many mathematical “tricks” were integer numbers are just a natural consequence. This is a very important aspect of the importance of the Schrodinger equation regarding QMs and QFTs in general.

    • I’m going to have to chew on this for a while, but thank you! (I knew actually liking trig would come in handy!)

    • Thank you Mr.Gastón E. Nusimovich, the “inversion” shows the spin 1/2 of fermions ?
      Can we say all that have rest mass is resistant to space time and experience this inversion – and zero mass not, which “discard the mathematical solutions that do not support the principle of indistinguishable particles, we get the “right” number of solutions with the “right” properties.” ?
      The hidden variable which give “excess” solutions to the equations – cancels out – except some non zero jitter ?

      How this fermion definition in equations, behave – when two photons roar in a closed system ?

  9. @Edwin Steiner: Indeed, you have a point with that.

  10. Pingback: Visualizing the quantum ‘spin’ | The Great Vindications

  11. Since we now have a theory of continuous spin particles (Schuster & Toro, 2013: http://arxiv.org/pdf/1302.3225v2.pdf), how do i calculate the probability that a Higgs decays into 2-off, spin 2^1/2 or 2-off, spin 2^-1/2 (root 2 and 1/(root 2)). Is it via Fermi’s Golden Rule or another route? :ask:

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