Insights Misconceptions about Virtual Particles - Comments

[DarMM]

Really? I must be an illiterate then...In practice, this means inverting a very large matrix, so that computer time becomes a serious issue. For this reason, most people replace the Dirac operator by the unit operator, which simply corresponds to eliminating all fermion-antifermion loop diagrams. This is, in the lattice-people language, referred to as the quenched approximation. So, you might as well claim that fermions don't exist because we can get rid of them in the quenched approximation! Give yourself a break for goodness sake.

The quenched approximation and the reality of virtual particles aren't remotely analogous, I never claimed the quenched approximation was valid physically. The quenched approximation is a truncation of the theory. Virtual particles appear in the perturbative expansion.

Saying a narrative of the perturbative expansion is invalid, is in no way connected to saying a truncation is equivalent to the full theory.

Also I am aware of the Nielsen-Ninomiya theorem, but this doesn't prevent computers from handling Grassmann numbers, it prevents them from handling Chiral Fermions. Computers can handle Grassmann algebras as easily as they can Complex Numbers, you could code up a Grassmann class in C++, Ruby, Python, e.t.c. in minutes.

Are you accusing me of making up a story?

Really, is that all? Look, I told you something and asked to READ at least one of the 4 paper.
The title of [1] : Improved measurement of the \bar{d}/ \bar{u} asymmetry in the nucleon sea.
From the abstract of [1]:
From these data, the ratio of down antiquark \bar{d} to up \bar{u} antiquark distributions in the proton sea is determined over a wide range in Bjorken-x.These results confirm previous measurements by E866 and extend them to lower x. From these data, \bar{d} - \bar{u} and \int (\bar{d} - \bar{u}) dx are evaluated for 0.015< x < 0.35 .

Did you read this part? Did you ask yourself why should there be a \bar{d} and a \bar{u} in the proton?

Yes, I read that part, and I know it concerns a measurement of the Gottfried Sum observable. This is simply a smeared field difference, even perturbatively it doesn't measure quark-antiquark particle number difference. It's more a difference in field expectation values. I'm not saying observables like this are nonsense, I just don't agree with your interpretation of them. A true observation of a "gluon/quark sea" would be an observation of non-zero particle flux within the proton.

 

[atyy]

(2) In the path integral formulation, which underlies the whole lattice method, the “classical” fermion fields are not true commuting numbers. They are non-commuting numbers, so cannot be directly simulated on a computer.

The path integral formulation does not underlie all lattice methods. There are also Hamiltonian lattice formulations, eg. http://journals.aps.org/prd/abstract/10.1103/PhysRevD.11.395.

 

[A. Neumaier]

QFT deals with on-shell states as well as off-shell states.

Could you please point to a book or paper where off-shell states are given a (nonrigorous but) formal definition? I have never seen any, and I have no idea what could meant by them. All computations involving states are about states created by creation operators and are therefore necessarily on-shell. (See my list of precise definitions in the companion Insight article.)

When experimentalists talk about particle concepts they frequently use concepts without a clear (or only partially understood) formal definition. Sometimes (for example constituent quarks, valence quarks, and sea quarks) these are semiempirical concepts only loosely related to the formal concepts in quantum field theory. But the latter defines the theoretical concepts - in particular the meaning of a virtual (off-shell) particle.

Thus whatever the experimentalists talk about when they talk about states related to a meson cloud or a nucleon sea or a proton sea they are not talking about (off-shell) virtual particles but about (on-shell) bare particles in a simplified description. If they nevertheless use the terminology of virtual particles to talk about sea states as virtual quarks and gluons they are doing it without a sound formal training - they are simply mixing up the concept of a bare particle and that of a virtual particle. Since this confusion makes no difference to their experiments they don't need to care about being accurate.

But trace any experimental statement about virtual particles back to actual formulas involving states and you'll see that all states used are on-shell states. Thus their talk is only due to the loose practices that seem to suggest that virtual particles are real, indirectly observable objects with (nonexistent) off-shell states.

 

[A. Neumaier]

H -> WW* -> whatever? It is one of the standard Higgs decays. The experimental papers have nice collections of references: CMS, ATLAS 1, ATLAS 2

Thanks. The first reference talks about decay, so the decay products must be on-shell - even if they are detected only indirectly though the decay products of the decay products.

A decay process happens in time with a well-defined mean lifetime (related to the inverse imaginary part of the mass), which is impossible for a virtual particle (where all masses are real). One can also see it from the approximate [Fermi's golden rule] formula for the decay rate given in the wikipedia reference: It is expressed in terms of a matrix element of the S-matrix, which makes sense only for real particles (extermal lines).

In the light of this, do you still want to uphold your earlier claim?

The W* in H->WW* -> ... appears as intermediate line in a Feynman diagram (unless we have different understandings of "intermediate line")

 

[mfb]

@samalkhaiat: No one doubts that you can describe the proton with sea quarks and gluons, then all the experimental results you quoted apply. But you do not have to choose this description.

Thanks. The first reference talks about decay, so the decay products must be on-shell - even if they are detected only indirectly though the decay products of the decay products.

The W* is not on-shell. Its experimentally reconstructed mass (well, if we could reconstruct the neutrino properly at least...) is at most 45 GeV.

In the light of this, do you still want to uphold your earlier claim?

The W* in H->WW* -> ... appears as intermediate line in a Feynman diagram (unless we have different understandings of "intermediate line")

The W* appears as line in the Feynman diagram, and its line starts and ends within the Feynman diagram. Yes of course I do.

 

[A. Neumaier]

The W* appears as line in the Feynman diagram, and its line starts and ends within the Feynman diagram.

In this case please tell me the pages in the papers you cited for a discussion of this diagram. In particular, what is the formal meaning of the star?

 

[mfb]

The star means it is off-shell.

Here is a Feynman diagram - it is so basic that I doubt the papers include it, but the papers I linked to are exclusively about this process. Pages: all.

 

[A. Neumaier]

The star means it is off-shell.

So one W is on-shell and the other off-shell?? The Feynman diagram you linked to has instead $H\to W^-W^+$ although the text says $H\to WW^*$ which looks inconsistent.

Pages: all.

OK; I'll plough through them until I find the connection to the actual formulas used - which tell the true story. Talk in words is too often too sloppy to be sure what it means. It may take a while before I can present my conclusions.

 

[mfb]

So one W is on-shell and the other off-shell??

Yes.

The Feynman diagram you linked to has instead $H\to W^-W^+$ although the tesxt says $H\to WW^*$ which looks inconsistent.

Just a different notation for the same thing. One time with charge signs and one time with charges omitted and the "off-shellness" explicitely highlighted.

OK; I'll prough through them until I find the connection to the actual formulas used - which tell the true story.

I linked to the experimental papers, the theory papers are the references in those papers.

 

[A. Neumaier]

So one W is on-shell and the other off-shell??

Yes.

But in the Feynman diagram linked to, both W are internal lines, hence off-shell!?

 

[mfb]

One W is as much off-shell as a muon (or even an uranium atom) with its finite lifetime will be. It has a larger decay width, but that is just a quantitative difference.

 

[samalkhaiat]

@samalkhaiat: ... But you do not have to choose this description.

QCD is the underline theory for any description. However, QCD is a gauge theory and, in particular gauge, it is identical to the parton model: The parton model is a picture of the nucleon in the infinite momentum frame, i.e. in a frame where the nucleon moves with almost the speed of light. This picture is particularly useful to understand what is going on in scattering experiments involving high momentum transfer, like e.g. deep-inelastic scattering with no reference to any specific field theory. The light-front gauge is particularly appealing in the infinite-momentum frame, since it relegates dynamical aspects to kinematically suppressed contributions. For this reason, the parton model picture is commonly identified with QCD in the lightfront gauge and in the infinite-momentum frame. Strictly speaking, the light-front gauge is not more “physical” than any other gauge, but turns out to be more convenient for the interpretation of high-energy scattering experiments. One could of course choose to work in a different gauge, but one has to deal with far more complicated expressions and totally unclear physical interpretation.
In short, since thenucleon internal structure is essentially probed in the infinite-momentum frame, the parton model is by far the best model we have to calculate all experimentally relevant quantities in terms of contributions which come from the valence quarks and the sea.
Although the fundamental role of a nonperturbative pion cloud surrounding the nucleon is well understood in QCD as a consequence of the spontaneously broken chiral symmetry, QCD makes no direct definite statement about the violation of the Gottfried sum rule: Based on charge conjugation symmetry it is only possible to say that the quark sea distribution in the nucleon is equal to the antiquark distribution in the antinucleon; plus, the gluon is flavour blind g \to q\bar{q}, so in order to explain the violation, we were led to Sullivan’s old idea that some fraction of the nucleon's anti-quark sea distribution may be associated with non-perturbative processes like the pion cloud of the nucleon. And that seems to work fine.
For those of you who are studying DIS processes, like to dive deeper into the nucleon sea and understand the Gottfried sum rule violation, the PDF below is a good review on the subject.

 

[samalkhaiat]

Could you please point to a book or paper where off-shell states are given a (nonrigorous but) formal definition?

By on/off shell “states” I ment on/off shell “particles” and that was very very clear and obvious to everybody. So, you don’t need to make a drama out of crices.

(See my list of precise definitions in the companion Insight article.)

The reason of me participating in this thread was to tell you that this thread and your “list of precise definitions” (whatever they are) are unnecessay wast of time.

When experimentalists talk about particle concepts they frequently use concepts without a clear (or only partially understood) formal definition. Sometimes (for example constituent quarks, valence quarks, and sea quarks) these are semiempirical concepts only loosely related to the formal concepts in quantum field theory. But the latter defines the theoretical concepts - in particular the meaning of a virtual (off-shell) particle.

Yeah, why don’t tell the USA and EU governments to stop funding these experiments since they are done by un-trained people. Or, maybe you should write to Weinberg and ask him improve on his understanding of QCD and chiral symmetry, because Weinberg thinks of the physical proton as particle surrounded by a cloud of virtual measons and other hadrons.

Thus whatever the experimentalists talk about when they talk about states related to a meson cloud or a nucleon sea or a proton sea they are not talking about (off-shell) virtual particles but about (on-shell) bare particls in a simplified description. If they nevertheless use the terminology of virtual particles to talk about sea states as virtual uarks and gluons they are doing it without a sound formal training - they are simply mixing up the concept of a bare particle and that of a virtual particle. Since this confusion makes no difference to their experiments they don't need to care about being accurate.

I am a theorist, so if I write |P \rangle_{phy} = C_{3q}|uud\rangle + C_{5q}|uudq\bar{q}\rangle + \cdots , and consider DIS process, does the meson q\bar{q} behave as real or virtual particle? Have you ever calculated or heard of deep virtual Compton scattering from the virtual baryon and meson components of a dressed nucleon?
This is exactly how we explain the violation of Gottfried sum rule: If the proton’s state contains an explicit | \pi^{+} n \rangle Fock state component, a DIS probe scattering from the virtual \pi^{+}, which contains a \bar{d} quark, will automatically lead to an excess of \bar{d} over \bar{u} in the proton. The all theorists Thomas et al.[1] demonstrated ,many years ago, that the nucleon’s pion cloud gives rise to unique terms in the moments of \bar{d} - \bar{u} that are non-analytic in the quark mass. The leading non-analytic behaviour of the excess number of \bar{d} over \bar{u} arises from the infra-red behaviour of chiral loops in chiral effective theories, and is model independent.

[1] A. W. Thomas, W. Melnitchouk and F. M. Steffens, Phys. Rev. Lett. 85, 2892 (2000).

 

[andrew s 1905]

Sorry to interrupt this fascinating debate but, may I ask if virtual photon are just artifacts of the mathematical procedures in QFT in what sense, if at all, do photons mediate the EM interaction?

I am not trying to challenge the point about virtual photon only understand what this then implies wrt the EM interaction?

Regards Andrew

 

[vanhees71]

Photons are states of the electromagnetic field, and the electromagnetic field "mediates" the electromagnetic interaction. I think, the whole debate is much ado about nothing or say about sloppy language in the QFT community. Any practitioner of QFT, however, understands what "virtual particles" are, namely internal lines of Feynman diagrams, representing (in the strict perturbation expansion free) propagators of fields (in vacuum QFT the socalled Feynman propagator). That's it. Case closed ;-)).

Also the debate about the "inner structure of protons" is funny. All there is, is the attempt to describe scattering with protons, and the paradigmatic example in history of the advent of QCD as the fundamental theory of the strong interactions is indeed deep inelastic scattering. Now that we have QCD that can be described by certain approximations like the one described in #132 (light-cone gauge) and #133 ("virtual pion cloud"). These are well understood approximation schemes, and of course one should not take "virtual particles" as particles.

The same applies to unstable particles. Strictly speaking they are never particles but resonances and as such appear in the description of scattering matrix elements as internal lines. Of course, sometimes you have very longlived "resonances", which you can treat as particles with a finite lifetime. That's how their width is usually calculated in perturbation theory. You draw an external line of an unstable particle and go ahead. Of course, in fact you can also intepret this calculation also as calculating the imaginary part of the self energy of this unstable particle/resonance, i.e., you dress the free propagator appropriately to describe it as an unstable particle. This applies particularly also to the $W$ boson also discussed in a very bizzarre way in this thread. It's very clear, how the $W$ and $Z$ bosons were famously discovered in the early 80ies at the SPS in proton-antiproton collisions. Of course there you also measure the decay products, what else?

 

[bhobba]

I think, the whole debate is much ado about nothing or say about sloppy language in the QFT community. Any practitioner of QFT, however, understands what "virtual particles" are, namely internal lines of Feynman diagrams, representing (in the strict perturbation expansion free) propagators of fields (in vacuum QFT the socalled Feynman propagator). That's it. Case closed ;-)).

IMHO it indeed is much ado about nothing.

In this case even the Wikipedia article get it right:
https://en.wikipedia.org/wiki/Dyson_series

I think the much more interesting issue is the series is asymptotically divergent. How can we get answers from a divergent series?

Start a new thread about it though.

Thanks
Bill

 

[andrew s 1905]

Photons are states of the electromagnetic field, and the electromagnetic field "mediates" the electromagnetic interaction. I think, the whole debate is much ado about nothing or say about sloppy language in the QFT community. Any practitioner of QFT, however, understands what "virtual particles" are, namely internal lines of Feynman diagrams, representing (in the strict perturbation expansion free) propagators of fields (in vacuum QFT the socalled Feynman propagator). That's it. Case closed ;-)).

So just to absolutely clear then photons do not mediate the EM interaction it is the EM field that does. I assume this is true of the other gauge bosons which seems to make the common description of them as force carriers wrong.

Regards Andrew

 

[mfb]

It is a matter of description.

 

[andrew s 1905]

It is a matter of description.

So if lay people like me misuse the term "virtual particle" it is wrong but physicists can call just dismiss calling particles force carriers (when they don't seem to be) just a matter of description. I would have thought it a simple matter to say if gauge bosons carry force or not.

Regards Andrew

 

[vanhees71]

So just to absolutely clear then photons do not mediate the EM interaction it is the EM field that does. I assume this is true of the other gauge bosons which seems to make the common description of them as force carriers wrong.

Regards Andrew

Sure, it's the field which "mediates" interactions. It was a brilliant insight by Faraday to describe interactions as local via fields. This was long before it became clear that the world is relativistic and that thus "action-at-a-distance models" for interactions are very unnatural and become much more complicated. In fact it was this insight, together with Maxwell's mathematical analysis of the idea in terms of his famous equations which lead to the discovery of relativity.

Of course also the "matter particles" (in the most simple version of QED usually electrons) are described by quantum fields, and if it comes to processes like compton scattering, such a matter field "mediates" the electromagnetic interaction, but also this is a pretty mute discussion. It's usually used in popular-science attempts to explain modern high-energy physics theory to lay people, where you cannot use the appropriate math to explain it right. Then Feynman diagrams are used as if the depict scatterings of particles, where other particles are interchanged (the internal propagator lines). That's legitimate to try to explain the exciting topic to lay people, but it's very misleading to have this picture in scientific discussions. So one should take the Feynman diagrams as what they really are, namely an ingenious notation to shorten otherwise much lengthier calculations of the Dyson series for S-matrix elements.

 

[A. Neumaier]

H -> WW* -> whatever? It is one of the standard Higgs decays. The experimental papers have nice collections of references: CMS, ATLAS 1, ATLAS 2

I found 5, 1, and 0 times the word virtual in these papers. Never is the $W$ or $W^*$ labelled as virtual. Furthermore, CMD never mentions $W^*$. I found not a single occurrence of off-shell, off shell, or offshell in any of the three papers.

Figure 1 in Atlas1 (the only Feynman diagram there) clearly shows that $H\to WW$ and $H\to WW^*$ have the $W$ and $W^*$ as external legs, hence on-shell, hence resonances. Note that Figure 3 is not a Feynman diagram but a space-time diagram, and carefully displayed in a different way!

CMA and Atlas2 have no Feynamn diagram. But all three papers frequently refer to $H\to WW$ (without reference to decay products), and the two Atlas papers also frequently refer to $H\to WW^*$ (without reference to decay products), in agreement with the Feynman diagrams they draw.

I also looked at reference [4] suggested by Atlas1, which says on p.8: ''The dominant backgrounds are non-resonant $WW$, $t\bar t$, and $Wt$ production, all of which have real $W$ pairs in the final state.'' Again $W^*$ (here apparently labelled $W^{(*)}$) is not explained.

This means that based on your references it is clear that in the decay process $H\to WW$ or $H\to WW^*$, both $W$ and $W^*$ are on-shell particles (represented by external legs of Feynman diagrams), though I still have no idea what $W^*$ means. Since it seems to occur only in the combination $WW^*$, it looks as if it is perhaps just a joint notation for one of the three $W$'s and its charge conjugate?

I also looked at the particle data group (PDG) entry on the Higgs boson $H^0$. It lists $H\to W^+W^-$ in table 11.2 but not $H\to WW$ (which is however mentioned in the main text on p.19), and $H\to WW^{(*)}$ in Fig.11.16, without explaining the latter either. For the decay they talk of channels, which is standard S-matrix terminology for real particles. This PDG paper uses the word virtual a few times, each time correctly for internal lines mediating a collision process - never for the decay products $WW$ or $W^*$. It uses the word off-shell 4 times, the most relevant two on pp.16-17 in the context of simulations with off-shell bosons, which are described as simulations of the decay $H\to llll$ ''without any on-shell approximation''. This means that this inclusive decay was not simulated as a sequence of three separate decay processes ($H\to WW$ and twice $W\to ll$, which would be inaccurate in view of the other approximations made in the simulation) but as a single decay process (unresolved in space-time). A few more details are given here (in Section 9). They refer to hep-ph/0604011 for details of the simulation mechanism. They say (correctly) in the abstract ''The decay of the Standard Model Higgs boson into four leptons via a virtual W-boson or Z-boson pair is one of the most important decay modes in the Higgs-boson search at the LHC.'' There is no occurrence of $W^*$.

This means that in the simulation calculations done as part of the analysis, both $W$ particles are treated as virtual particles since these concern matrix elements of the 4-lepton decay. As always, the virtual particles appear as a calculational tool, not as a carrier of real physics.

The above shows that those publishing the experimental work were careful (and correct) in their language.

This seems not to be the case in the unpublished summary you linked to here:

Here is a Feynman diagram - it is so basic that I doubt the papers include it, but the papers I linked to are exclusively about this process. Pages: all.

That fourth paper says: ''When the mass of the Higgs boson is greater than 136 GeV the predominant mode of Higgs decay is to a pair of on/off-shell W bosons'', without giving formulas or references. (The only - global - reference given there is another summary, that neither uses the words virtual or off and doesn't mention a $W^*$.) No other usage of off-shell is resent, and the word virtual does not appear. But the Feynman diagram given shows that both $W$ and $W^*$ are virtual in the process displayed. It is one of the contributions to the decay $H\to llll$ discussed already in my analysis above. It does not describe (as claimed) the Higgs decay to a pair of W bosons, which is a different decay process with different S-matrix elements and both W-bosons on-shell.

In the light of the testimony of the three published papers you summoned, do you still want to uphold your earlier claims?

The W* in H->WW* -> ... appears as intermediate line in a Feynman diagram

The star means it is off-shell.

And could you please find a proper (published) reference where the meaning of $W^*$ and/or $W^{(*)}$ (if this is not the same) is explicitly explained?

 

[mfb]

I found 5, 1, and 0 times the word virtual in these papers. Never is the $W$ or $W^*$ labelled as virtual. Furthermore, CMD never mentions $W^*$. I found not a single occurrence of off-shell, off shell, or offshell in any of the three papers.

Those are the experimental papers. They also don't introduce what W bosons are, because they expect the reader to know that.

Figure 1 in Atlas1 (the only Feynman diagram there) clearly shows that $H\to WW$ and $H\to WW^*$ have the $W$ and $W^*$ as external legs, hence on-shell, hence resonances. Note that Figure 3 is not a Feynman diagram by a space-time diagram, and carefully displayed in a different way!

A Higgs cannot decay to two on-shell W bosons. It simply does not have enough mass. This is even more obvious for H->ZZ*->llll where the experiments can reconstruct all 4 leptons.

CMA and Atlas2 have no Feynamn diagram. But all three papers frequently refer to $H\to WW$ (without reference to decay products), and the two Atlas papers also frequently refer to $H\to WW^*$ (without reference to decay products), in agreement with the Feynman diagrams they draw.

They mention the W decay products everywhere, including two of the three titles, and all three abstracts.

This means that based on your references it is clear that in the decay process $H\to WW$ or $H\to WW^*$, both $W$ and $W^*$ are on-shell particles (represented by external legs of Feynman diagrams), though I still have no idea what $W^*$ means.

It is not, and I don't see how you got that impression.

Since it seems to occur only in the combination $WW^*$, it looks as if it is perhaps just a joint notation for one of the three $W$'s and its charge conjugate?

This is just nonsense. As I said, it is a notation for an off-shell W. The W* decay products have an invariant mass way below the W mass. Calculate the sum of masses for two W and compare it to the Higgs mass, it simply does not add up.
For H->ZZ*->llll this is discussed more clearly in the papers as there the decay products are all detected. As an example, this older publication refers to the Z* as "the lower-mass Z* boson" (page 7, right column) and discusses this lower mass on the next page.

This means that this inclusive decay was not simulated as a sequence of three separate decay processes ($H\to WW$ and twice $W\to ll$, which would be inaccurate in view of the other approximations made in the simulation) but as a single decay process (unresolved in space-time).

Yes of course. It is a single process. For one W you can consider production and decay as separated process if you want, for the W* you cannot as it is not on-shell. You can still calculate the total contribution of Higgs decays via WW* (W+W-, WW, ... all those notations mean the same thing, please don't overanalye who used which notation because there is no deeper meaning in it).

A few more details are given here (in Section 9). They refer to hep-ph/0604011 for details of the simulation mechanism. They say (correctly) in the abstract ''The decay of the Standard Model Higgs boson into four leptons via a virtual W-boson or Z-boson pair is one of the most important decay modes in the Higgs-boson search at the LHC.'' There is no occurrence of $W^*$.

The W* is the off-shell virtual W boson.

This means that in the simulation calculations done as part of the analysis, both $W$ particles are treated as virtual particles since these concern matrix elements of the 4-lepton decay. As always, the virtual particles appear as a calculational tool, not as a carrier of real physics.

The one W acts like a real particle. You could easily imagine a B meson there that moves a few millimeters before it decays, it would not change the situation.

It does not describe (as claimed) the Higgs decay to a pair of W bosons, which is a different decay process with different S-matrix elements and both W-bosons on-shell.

This process does not happen for a 125 GeV Higgs boson. Unless the Higgs itself is off-shell. And there we are again at the problem. Is the Higgs discussed before real? If yes, is it real if we reconstruct a mass 2 MeV away from the actual mass? 10 MeV? 1 GeV? 100 GeV? Is it never real?
How can the W or Z bosons ever be on-shell if we can observe their decay width? Where is the limit?

All those questions have an easy answer if you say "it depends on who calculates those things". But then the classification is purely arbitrary.

In the light of the testimony of the three published papers you summoned, do you still want to uphold your earlier claims?

You confirmed them, where is the problem? The W* is part of a single process H->lvlv.

And could you please find a proper (published) reference where the meaning of $W^*$ and/or $W^{(*)}$ (if this is not the same) is explicitly explained?

See "low-mass Z*" above.

 

[A. Neumaier]

This means that based on your references it is clear that in the decay process $H\to WW$ or $H\to WW^*$, both $W$ and $W^*$ are on-shell particles (represented by external legs of Feynman diagrams)

It is not, and I don't see how you got that impression.

I don't see how you got your impression. My conclusion is clearly visible from the Atlas1 paper you had cited:

Figure 1 in Atlas1 (the only Feynman diagram there) clearly shows that $H\to WW$ and $H\to WW^*$ have the $W$ and $W^*$ as external legs, hence on-shell, hence resonances. Note that Figure 3 is not a Feynman diagram but a space-time diagram, and carefully displayed in a different way!

Moreover, the paper gives numerical characteristics for these processes (in the tables) which make sense only if they are actual processes with an associated S-matrix elements (in terms of which the numbers reported are defined). There is no way in which these numbers can be associated to virtual processes.

That further decay products are mentioned in the abstracts (since they were used to deduce the numbers given) doesn't affect the fact that the result of their analysis concerns the processes stated explicitly, for which they have explicitly given the diagrams (rather than something nowhere explicitly stated in the results that you apparently read into the paper).

I'll respond to the remainder of your post after I have read more. But I still would like to see an explicit definition of the meaning of $W^*$ or $Z^*$ rather than casual phrases that assume that the meaning is already known to the reader.

Note that I have a good knowledge of QFT and of its application to QED and QCD phenomenology but I never looked into details of the standard model beyond that. I am using the present discussion to learn to understand the specific issues related to the Higgs sector - assuming that the theoretical concepts involved in its description are the same as elsewhere in QFT.

 

[mfb]

I don't see how you got your impression.

This is really basic experimental particle physics. So basic that the publications don't even bother explaining it in detail because every experimental particle physicist knows it. I am one of those experimental particle physicists.

Did you calculate the sum of two W or Z masses and compared it to the Higgs mass as I asked? This is a really simple check you can do to see that the W/Z cannot be both on-shell.

But I still would like to see an explicit definition of the meaning of $W^*$ or $Z^*$ rather than casual phrases that assume that the meaning is already known to the reader.

Maybe it is explained in even earlier papers, but it is so basic that I really think the authors didn't bother. The star is also irrelevant on its own - you could write WW as well, if you keep in mind that not both W can be on-shell.

(rather than something nowhere explicitly stated in the results that you apparently read into the paper)

I don't read that into the papers, I am part of the people writing papers about LHC results.

 

[A. Neumaier]

every experimental particle physicist knows it.

But they learn it from somewhere. I am sure they didn't learn it by being told (as I effectively was told by you): Here are 220 pages of experimental data discussion plus a thousand references - now try to make sense of it yourself.

From which papers can I learn it in an introductory, fully explained fashion? That was each time my question, and I never got an answer from you.

Did you calculate the sum of two W or Z masses and compared it to the Higgs mass as I asked? This is a really simple check you can do to see that the W/Z cannot be both on-shell.

Yes, I did. But I want to understand what is behind the pure assertion - the relation to the formulas of QFT. Which set of possible states is associated with $W^*$ (whatever you call it)? In which sense is it a $W$ if it hasn't its mass? What is the meaning of the branching ratio reported for a reaction $H\to WW^*$? Is it not defined through a partial width defined by a formula such as the golden section formula in which the particles are represented by external lines of Feynman diagrams - i.e., not as virtual particles? I am trying to figure out this kind of questions and your responses have given me very little help so far.

I am part of the people writing papers about LHC results.

Neither the particle data group nor the CMS and Atlas references you gave used your terminology (though they used the notation $W^*$). Do they speak a different dialect from you? Why don't they talk about virtual particles except when they refer to internal lines in a diagram?

 

[mfb]

But they learn it from somewhere. I am sure they didn't learn it by being told (as I effectively was told by you): Here are 220 pages of experimental data discussion plus a thousand references - now try to make sense of it yourself.

It usually works in a more informal way, indeed. Either you figure it out based on the masses, or you can ask: "Hey what does the star mean?" "It is off-shell".

Anyway, I used google a bit more and found Decays of the Higgs Bosons, discussing "the Higgs boson decay into WW with one off-shell W boson" on page 5. It has references to Higgs-scalar decays: $H \to W^\pm + X$ and "Rizzo Phys. Rev. D22 (1980) 389" where I didn't find a link.

It is a W because it shares its couplings.

 

[Haelfix]

I must admit that I am confused! mfb is completely correct as this is basic particle physics. Or at least if it isn't then I've been doing it wrong for the past 15 years. I also don't understand why this in anyway contradicts your insight article. If you like, you can draw one of the possible reactions as H --> Z l l, where the real Z is treated as an unstable particle that subsequently decays (in another diagram that you draw) and we reconstruct the usual peak (which we can interpret in the usual way as a pole of our S matrix process). The internal Z is a virtual particle as per your own definition!

So again, what is the problem? The whole point of this little exercise and the reason I originally brought it up is that is often convenient (experimentally) to describe things in the other way, precisely b/c there are multiple decay chains that are possible and we like to classify probabilities in a certain way (for instance does the total probability for the myriad final states of WW beat the total probability for the myriad final states of ZZ?

 

[A. Neumaier]

I also don't understand why this in anyway contradicts your insight article.

It shouldn't but on the surface it does - when I see Feynman diagrams with off-shell external legs, which shouldn't exist according to the textbook picture, and the corresponding branching ratios don't make sense in the standard way. So for me there is something more to be understood clearly enough that I can explain it in my own words. I am still reading, but gradually the confusion clears.

If you like, you can draw one of the possible reactions as H --> Z l l, where the real Z is treated as an unstable particle that subsequently decays (in another diagram that you draw) and we reconstruct the usual peak (which we can interpret in the usual way as a pole of our S matrix process). The internal Z is a virtual particle as per your own definition!

Thanks. Yesterday night I discovered the first paper http://arxiv.org/abs/hep-ph/9807536 that describes it this way. Before that I had to guess the meaning from the context, which was never clear enough. The diagram that mfb had claimed as being equivalent to $H\to WW^*$ is in fact a diagram for $H\to W^*W^*$, while I had taken the equivalence at face value. I could see that these are different only after having finally read a precise enough explanation (Figures 2 and 3 in the cited paper). I am somewhat surprised that the PDG account doesn't mention these conventions but uses the star notation without comment - at least I haven't found any explanatory comment.

 

[vanhees71]

It usually works in a more informal way, indeed. Either you figure it out based on the masses, or you can ask: "Hey what does the star mean?" "It is off-shell".

Yep, this notation you find everywhere. E.g., sometimes you confuse your experimental colleagues by talking about "virtual photons", writing $\gamma^*$, when you in fact mean dileptons, but that's just slang again. I'd not say that there's any problem with it in the scientific community. The same is true for $W^*$. I guess it just means a $W$ line that is far off-shell (in the sense of the pole mass or peak mass of the $W$ meson, where only the former is of course a well-defined gauge-invariant object). What's of course observed is not such a far-off-shell W boson but the stable decay products showing up as signals from the detectors. Puristically speaking any resonance is never on-shell, because it has not a well-defined mass but a mass distribution given by its spectral function (i.e., the imaginary part of its (retarded!) propagator). So with some right you should put a star on every resonance, when you write a short-hand reaction like $H \rightarrow WW$. The two W's decay further anyway, and you detect the stable endproducts.

The same thing you have in the heavy-ion dilepton context with $\rho$ mesons way below the "mass shell", where it appears in Dalitz-decay diagrams as a vectorm-meson resonance model for the electromagnetic transition form factor, e.g., in the decay of baryon resonances or other mesons (like the $\omega$ or $\eta$). The $\rho$ meson has a low-mass tail down to $2m_{\text{e}}$, and thus it has even spectral strength there, but what goes into the rates is anyway the squared $\rho$ propagator in the em. current-current correlation function.

I think, you fight against windmills, if you try to get rid of the usual slang in the HEP/HI community. Sometimes you have confusion, and then you can clarify it by reminding the confused colleagues about the meaning of resonances vs. particles, which are defined as asyptomptic free states (external lines of Feynman diagrams) and that a resonance with finite width around its pole mass can only occur as external lines in a very specific sense when calculating decay rates in an approximate way.

Where you really have still a lot of unnecessary confusion is when it comes to oscillations (particularly neutrino oscillations). There you must explicitly take care of the production and detection mechanism to make proper sense of the hand-wavingly derived "plane-wave oscillation formula", but that's another topic.

 

[A. Neumaier]

Puristically speaking any resonance is never on-shell, because it has not a well-defined mass but a mass distribution given by its spectral function (i.e., the imaginary part of its (retarded!) propagator).

It is on-shell in the analytic continuation with a well-defined complex mass. Otherwise it would be impossible to compute cross section for processes associated with them, without taking into account all their decay products. It would not even be possible to give it an unambiguous meaning! And it has a state with a well-defined dynamics in time since it is (almost, ignoring very tiny tails at negative masses) equivalent to a state in the undeformed, physical Hilbert space involving contributions from the scattering spectrum with a mass distribution given by its spectral function. None of these can be said of a virtual particle.

I think, you fight against windmills, if you try to get rid of the usual slang in the HEP/HI community.

I never tried to do that. My goal is to fully understand what they say and do, in clear and unambiguous terms, and pointing out where and how sloppy terminolgy is used and what the latter really means. I want to have for myself a clear mental picture and a precise way of talking about it.