# Higgs field and energy dependence?

• I
asimov42
Hi all,

Basic question that has caused me some confusion: is the Higgs interaction (giving some particles rest mass) energy dependent? (e.g., does the coupling vary with the kinetic energy of the particle involved)

Thanks.

## Answers and Replies

Staff Emeritus
Homework Helper
Gold Member
2021 Award
Are you asking if the Yukawa couplings run with energy? The answer to that question would be "yes". The actual masses of the particles are not affected as the interaction with the vev that gives the position of the pole is evaluated on-shell with zero momentum transfer to the Higgs field. If your question is whether or not masses of particles depend on their energy, the answer would be no. The Higgs vev is a Lorentz scalar.

• vanhees71
asimov42
Ah, thanks - I was asking about the former. In particular (this sounds silly, but just to make sure I'm on track) - there is never momentum transfer to the Higgs field, correct? (already answered but just to make sure I'm crystal clear) I'm actually wondering in the context of a more complicated question related to false vacuums, but I believe the above is all I need to know for now!

Thanks!

asimov42
Is is possible to clarify "zero momentum transfer to the Higgs field"?

asimov42
The reason I ask (which is probably taking this thread too far off track), is related to a metatable vacuum. Let's say the vacuum is metastable, and I'm able create a large number of Higgs bosons (somehow) ... does this excitation of the field, to some small degree, increase the probability of tunneling from the false vacuum state to the true vacuum state?

asimov42
Or am I completely off base?

asimov42
If we live in a metastable vacuum, then concentrating sufficient energy in a small volume may be enough to 'get us over the hump' from the false vacuum to the true vacuum. This much I understand...

Now, if I'm clear, the other possibility is tunneling - where (I am assuming) the Higgs field tunnels to a lower energy true vacuum. My question: is this truly a completely random process? Or are there factors (local excitations of the Higgs field, other things) that influence the tunneling probability?

Standard tunneling of an electron through a barrier depends on the energy of the electron - but I'm completely lost on the relationship between this and the metastable tunneling event (if any).

Mentor
@asimov42 not getting an answer in this thread is not a reason to start a new one. I have moved your new post to this thread.

You might be having difficulty getting an answer because there isn't a known answer; this is an area where physicists are still speculating and we don't have a good confirmed theory.

asimov42
@PeterDonis apologies - my thought in starting a new thread was that I could say something more succinct about the full question, rather than having bits buried in earlier in this thread. Thanks for moving the post.

For the question asked in Post #7, I'm fairly sure there's a known answer, since I've seen estimates bantered about that say things like "the probability is so low that it won't happen for another 10^100 years." But, after looking, I can't seem to find papers pointing to how this calculation is carried out, nor the exact factors involved...

More basically, I'm not clear on whether it's a change in the 'phase' of the Higgs field itself that is involved in the tunnelling process, or whether one needs to create a Higgs boson that would tunnel and then trigger the vacuum decay... (again, given that all the current assumptions hold). The (not very technical) sources I've looked at either point to random fluctuations in the field itself, or to the need to actually create bosons to trigger tunnelling...

Here's an attempt to be more clear and provide an answerable question: I fire up the LHC and generate 1000 Higgs bosons - does doing so ever so slightly increase the probability of vacuum decay? (again, assuming the process would happen at all) Does excitation of the Higgs field matter?

Mentor
Here's an attempt to be more clear and provide an answerable question: I fire up the LHC and generate 1000 Higgs bosons - does doing so ever so slightly increase the probability of vacuum decay? (again, assuming the process would happen at all) Does excitation of the Higgs field matter?

Heuristically, I would think the answer would be yes, since in any metastable state with a finite barrier height, pumping energy into the system should increase the probability of being able to jump the barrier. However, there are a lot of quirks in quantum field theory and I would not trust my intuitions very far.

asimov42
Indeed @PeterDonis, that's what I'd imagine from standard QFT. However, I've read a post on, e.g., Quora (and I know this in not a peer reviewed source, and so probably shouldn't be quoted, but the poster is a Stanford Physics PhD, so...) which says:

"So, now to actually answer the question. The metastability is of the vacuum, not of the Higgs particle. In particular the "thing" that decays is the value of the Higgs field, not the Higgs particle.... If the Higgs potential energy function is like the curve labeled M_0 then there is a very small chance (per unit time) that the field value, at some point in space, could quantum tunnel through the hill in the potential energy function and end up at a new value."

Which is the source of my confusion. Does it matter that the field value at some point in space (x) is excited, changing the tunnelling probability? Since it's the underlying non-zero VEV of the Higgs field that decays, I'm not sure the excitation makes any difference...

Mentor
it matter that the field value at some point in space (x) is excited, changing the tunnelling probability?

I don't know if it would affect the tunneling probability or not. But the total probability of a transition from the "false vacuum" to a "true vacuum" with a lower VEV is the combined probability of tunneling plus jumping over the barrier, so if the latter is affected by exciting the field, then the total probability is affected.

However, as I said, this whole area is speculative at this point.

asimov42
Although speculative, I am very interested in the tunnelling probability - would anyone have suggestions for where to look (or who to ask) for information related to this?

Mentor
Nobody has any information about the tunnelling probability because nobody knows if the Higgs field is currently in a metastable state (we have no evidence to indicate that it is), or if it is, what the relevant potential is that would determine the tunnelling probability. So you're asking for something that doesn't exist.

asimov42
@PeterDonis - thanks, and sorry to beat a dead horse as it were. The latest papers I've seen (I can dig up a reference) do, based only on what we know so far, put us in the metastable regime (there was just one published recently with an analysis of this)...

But even with the above, my question is not about the exact value of the tunneling probability (which is low) - it's whether producing localized field excitations changes that probability by some small amount. We should be able to determine this just from the nature of the Higgs field, regardless of the exact potential involved.

Mentor
The latest papers I've seen (I can dig up a reference)

Please do, since there's no point in just speculating, we need to actually look at what the latest theoretical investigations say.

asimov42
Here is one of the most recent papers which concludes that we're in a metastable region:

A. V. Bednyakov, B. A. Kniehl, A. F. Pikelner, and O. L. Veretin, “Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision,” Phys. Rev. Lett. 115, 201802 (2015).

and another older paper which discusses tunnelling:

A. Kusenko, P. Langacker, and G. Segrè, “Phase Transitions and Vacuum Tunneling into Charge- and Color-breaking Minima in the MSSM,” Phys. Rev. D 54, 5824 (1996); M. Bobrowski, G. Chalons, W. G. Hollik, and U.

However, I still have yet to find any paper or reference which clearly describes whether the tunnelling probability is affected by field excitations (i.e., producing Higgs bosons)... I might be looking in the wrong place, but I would have thought the question would be addressed even in pop-sci literature, since, if the probability did increase, turning on the LHC would always be every so slightly risky (granted that the probabilities are minute, but still...)

Help or pointers would be appreciated!