# Why top quark mesons must exist

In the previous post I mentioned that one of the failures of the standard model is its inability to explain why top-mesons were not found until today.

Professor Matt Strassler addressed this question in his blog [1] where he offers several arguments regarding this issue. Strassler’s arguments are the well-known arguments of the standard model supporters. My answers below explain why these objections are unjustified.

Argument 1: the top quark decays faster than the time which is required to create a meson.
Answer: a well known phenomenon together with fundamental physical principles put this assertion in question. The particle Δ++ is a baryon which decays into a proton and a pion. The mean lifetime of Δ++ is nearly 5×10-24 sec, which is sufficient for creating pions.

The time required for creating the top-meson is even shorter. The very high energy of the top is followed by a high energy uncertainty. Obviously, the latter is an element of the energy-time uncertainty relations. Thus, the top’s high energy uncertainty indicates that the time needed for the creation of a top-meson is much shorter than the time needed for a pion creation. This argument is supported by the complementary position-momentum uncertainty relations. A higher energy uncertainty entails a higher momentum uncertainty. Therefore the spatial dimension of top-mesons is smaller than that of lighter mesons. Hence, a shorter time is needed for creating a top-meson.

Furthermore, a general rule for a quantum decay process says that the probability of the existence of the initial state decreases exponentially with time. Therefore, there is a probability that several top quarks will live long enough to create a meson. The shorter time needed to create a top-meson implies that non-negligible number of top quarks will create mesons.

Strassler’s argument also violates another important principle of quantum field theory. In a transition between an initial state and a final state, every physically legitimate state can be formed as an intermediate state. Hence, a top-meson can be created by one the following processes:
a) A “bare” top quark is created and if it has not decayed then it captures an anti-quark and produces a top-meson.
b) A bound state of a top quark and an antiquark is produced directly.

Every minute billions of pions are produced in accelerators and in cosmic rays. These pions are produced directly as a bound state of u,d quark-antiquark pair. Therefore, there is no reason to say that this channel is forbidden for the top quark.

Apparently, Strassler misinterprets possibility (a) and ignores possibility (b).

This explains briefly why mesons of the top quark must be found. Therefore, I ask again: where are these mesons?

The standard model doesn’t answer this question. Comay perception, on the other hand, is that the W, Z and the new 125 GeV particle are the missing top-mesons.

There is another strong indication for Comay perception. The W, Z, top quark, and the new 125 GeV particle have a very similar energy width, about 2 GeV. This indicates that their structure may have something in common. According to Comay, the common component of these particles is the top quark and its flavor changing weak decay determines their similar width.

On the other hand, the standard model theoretical prediction of the energy width of the 125 GeV Higgs boson is about thousand of times smaller than the current experimental value which was found by the LHC teams [2]. It is interesting to wait and see if this experimental value will decrease so dramatically after better statistics is accumulated. If it won’t – this will be another proof that the standard model contains serious errors.

Argument 2: the tt meson should have mass around 350 GeV and the new particle is only 125 GeV.
Answer: it is known that the mass of a bound particle is always less than the sum of its constituents’ mass. Let’s see how the meson mass behaves (by the way – Comay’s first work during the 1970s was about building a model that explains meson mass).

The mass of a pion (which consists of a light u,d quark-antiquark pair) is around 135-140 MeV. The mass of another meson, the rho-meson (which consists of a u,d quark-antiquark pair as well), is around 770 MeV. Therefore, we can tell that the sum of the mass of hypothetically free u,d quarks is more than 770 MeV. Furthermore, some mesons that consist of u,d quarks are much heavier than 1 GeV. Therefore, the pions mass is less than 10% of the mass of its constituents. It means that strong interactions consume most of the self-mass of the system’s bound particles.

This mass reduction is typical in the case of strong interactions. It is attributed to the strong bound state of a quark and an antiquark. This binding energy becomes higher with the mass of the quarks. For example, in the case of the electromagnetic force, we know that a muon is bound stronger to the proton compared to the electron in the hydrogen atom, and its radius is smaller. The only relevant difference between the “hydrogen-like muon atom” and a normal hydrogen atom is the mass of the muon relative to the mass of the electron (it is about 100 times heavier). Comay’s strong interaction theory takes the form of electrodynamics. Therefore, if the binding energy of the top-meson is much higher than the binding energy of lighter quarks mesons, the mass reduction of the former should be very significant.

This is why the mass of the top-mesons is significantly smaller than the mass of the top quark.

One more remark: the strong forces provide reasons why the mass of the top-mesons is smaller than the top quark, but that does NOT mean that we don’t need to take the weak forces into account when we try to estimate the mass of top-mesons.

Argument 3: the standard model has a very high predictive success
Answer: I already provided around 20 phenomena that the standard model cannot explain (see here a list and the discussions all over this blog). Some of them blatantly contradict the standard model. When we say something about the predictions of a physical theory, we need to account all the relevant phenomena and not only a partial selection of them.

[1] Search for the word “Larsen” in his blog and see his two replies.
[2] See p. 13, fig. 5 at http://pdg.lbl.gov/2012/reviews/rpp2012-rev-higgs-boson.pdf

## 20 thoughts on “Why top quark mesons must exist”

1. Camila says:

Dear Eliyahu
If the W,Z and the new 125Gev partice are the top quark mesons, then there should be
heavier top quark mesons as it is the case with ud bar mesons (pion and rho meson), right?!
Do you have a calculation or an estimate what the energies these heavier mesons would have? Could the LHC find them?
My last question is: How many different mesons with the same Quark content (for example ud bar mesons) are there and is there a rule or a law that limits their number?
All the best
Camila

2. * As to argument one – you aren’t so far off here. Strictly speaking, the Standard Model does not forbid the creation of top quark mesons or even top quark baryons.

After all, mean lifetime is just that. A bare top quark can last longer or shorter than the mean lifetime. But, because the average time needed for any kind of meson to form is much longer than the mean lifetime of a top quark, the percentage of quark pairs including a top quark that will have time to form a meson before the top quark decays is so vanishingly small relative to that of bottom quarks, for example, that these are events are predicted to be so rare that they are impossible to detect at current experiments, where, keep in mind, top quark production is still always much lower than the production of any other kind of quark anyway.

A bottom quark or charm quark has a mean lifetime that is roughly 10^11 to 10^12 times as long as a top quark (lighter quarks have even longer mean lifetimes). So, the mean time needed to form a meson can be, for example, a million times less than the mean lifetime of a bottom or charm quark (insuring virtually 100% confinement), while still being a million times longer than the mean lifetime of a top quark (insuring virtually 0% confinement).

Suppose that a bottom quark had a mean lifetime of 70 years, like a typical human being. Then, a top quark would have a mean lifetime of something on the order of one hundredth of a second. And, the mean time necessary to form a meson might be something on the order of two and three-quarters hours. Even extreme outlier bottom quarks are almost sure to form hadrons in that time frame, while even extreme outlier top quarks are very unlikely to form hadrons in that time frame.

The likelihood of a top quark living long enough to form a hadron is something whose probability is on the order of a few times over a time frame equal to the age of the universe.

* As to argument two, you are basically wrong about the mass of mesons (and for that matter baryons). The mass of the constituent quarks in a meson and baryon is less than the mass of the composite particle, with the balance attributable to gluonic binding energy.

An up and down quark combined, which are components of the pion and the rho meson have masses on the order of 7 MeV to 10 MeV. Almost all of the balance of the mass is gluon binding energy – about 120 MeV in the pion where the quarks have opposite spins, and 760 MeV in the rho where the quarks have aligned spins.

As a first order approximation, the mass of a hadron equals a gluon binding energy which is the same for all combination of the same number of up and down type quarks with the same spin, plus the sum of the constituent quark mass. This isn’t perfect, because the gluon binding energy rises a bit with heavier constituent quarks, but doesn’t do so very rapidly (the adjustment for constituent quark masses is closer to a natural log of the constituent quark masses than it is to a linear function of the constituent quark masses).

A top-antitop quark meson would have a mass something on the order of 348-351 GeV.

As to argument three – you greatly exaggerate the extent to which the Standard Model is inconsistent with experiment. There are some mild tensions between experiment and its predictions, but as experiments and theoretical calculations are growing more precise, those gaps are growing fewer and fewer rather than getting more common as one would expect if the theory were wrong.

• Ofer Comay says:

There are several claims in your comment:
Claim 1: You say that the probability of creating a top-meson is tiny.
You can see the answer in this post. A simple calculation shows that the mean life time of the top quark is not very different from the time to create a top-meson (see the first part of this post). In fact, it shows that it is reasonable that top-mesons decays should be more frequent than top-quark decays.
Claim 2: You say that the mass of top meson is greater than its constituents. As claimed here, the mass of a bound particle is always lower than the mass of its constituents. This is a well known physical property which is derived from energy conservation.
Claim 3: You say that the standard model doesn’t contain severe inconsistencies with experiments. Look here for twenty phenomena which are inconsistent with QCD, an important part of the standard model:
https://nohiggs.wordpress.com/2012/01/03/to-continue-as-usual/

3. […] According to the Standard Model the top-quark mesons do not appear in experiments because the time required to form a top meson is greater than the mean lifetime of the top-quark. However, this doesn’t explain why the tt meson is never created in one step (like the pi-0 meson) (unexplained #5). Furthermore, considering the uncertainty principle, this Standard Model claim doesn’t explain why some top quarks do not live long enough to form a top meson (unexplained #6). See discussion of these problems in the article top quark mesons must exist. […]

4. IIRC there is no pure uū meson. Instead, there is mixed π₀. Shouldn’t top-antitop state mix with another state as well?

5. Valery says:

Can you explain the statement: “The shorter time needed to create a top-meson implies that non-negligible number of top quarks will create mesons”? Is there any computation that shows that this is “non-negligible” indeed?

• Dear Valery,

This site and the book that is shown on the right hand panel describe many different kinds of experiments that disprove QCD and support the idea that strong interactions theory takes an electromagnetic-like form. An Article that discusses this issue can be found in the following link http://www.ejtp.com/articles/ejtpv9i26p93.pdf and the theory is called RCMT which is the acronym for Regular Charge Monopole Theory. The main difference between electrodynamics and RCMT is that in RCMT the elementary unit charge is much greater. Evidently, a description of the underlying principles that serve a discussion is not repeated time and again in every specific case.

A calculation of a hadronic state is a very difficult assignment. The direct measurement of antiquarks in the proton proves that the system is extremely relativistic and that additional quark-antiquark pairs must be included in the set of configurations that describe a hadronic state. QCD has been recognized for more than two decades before an attempt to carry out a calculation has been undertaken. The RCMT deserves a similar attitude.

The lack of calculations does not prohibit an application of general principles of electromagnetic-like bound states. This is done in the text that contains your quotation. Here the higher mass of the top quark is used. Furthermore, the similar width of the top quark, the W,Z and the new 125 GeV particle is consistent with the idea that all these particles contain a top quark. (BTW, Standard Model Higgs calculations predict for the new 125 GeV particle a width that is about 1000 times smaller than the present LHC experimental value.)

Cheers, Eli

6. Valery says:

I understand that top quark decays into W and b-quark. Can you explain that? Why it does not decay into other things (or maybe it does?)

• Dear Valery,

Everybody agrees that a conservation of baryonic number means a conservation of quark number. Hence, a single top quark is produced by weak interactions together with an antiquark. Now there is an interesting feature of weak interactions which prefer flavor changing processes that occur within the given generation (see below). Now, the t-quark and the b-quark belong to the same generation. For this reason the weak interactions production of a t-quark is associated with a production of an anti-b quark and a W meson comes out.

The existence of the generation preference effect of weak interactions is supported by the following properties of mesons which are reported by the PDG (see http://pdg.lbl.gov/2012/listings/contents_listings.html ).
1. The hadronic decay of a charged kaon into pions is an example of a generation changing weak process. In the hadronic decay of a charged kaon, an s-quark goes into a lower generation quark of the u,d family. The data show that the life-time of the charged kaon is similar to the life-time of a charged pion. It means that the larger phase-space of the kaon decay and the increase of the number of available decay channels do not boil down into a shorter life-time because the transition matrix element is smaller. On the other hand, in the case of the charged and the neutral D mesons, the weakly decaying processes take place within the quark’s generation. Here a c-quark goes into an s-quark and K mesons are produced. Thus, the life-time of the weakly decaying D mesons is shorter by several orders of magnitude than the life time of the K meson.
2. This effect is also seen in the life-time of weakly decaying B mesons. Here a b-quark decays into quarks of a lower generation and, in spite of the larger phase space, the life-time of B mesons is of the same order of magnitude as that of the D mesons. (As a matter of fact, the lifetime of B mesons is a little bit longer than that of the lighter D mesons.) This effect corresponds to the life-time similarity of charged kaons and charged pions. In both cases a transition into a lower generation has a smaller matrix element and the contribution of the increased phase space disappears.
3. The weak interactions processes of the top quark take place within the generation. Namely, a top quark goes into a bottom quark. This effect together with the large increase of the phase space are the reasons for the very short life-time of the top-quark itself and of the W,Z and of the new 125 GeV particle, where the three latter are top quark mesons. This effect is analogous to the large decrease in the life-time of c-quark mesons which is pointed out above.

Conclusion: the transition of the top quark into W and the decay of the top quark mesons fit well documented phenomena of weak interactions processes and the W,Z as well as the new 125 GeV particle are top quark mesons.

Cheers, Eli

• It does decay into other kinds of quarks, but at very low probabilities. The probability that a top quark will decay into a W and an s-quark is about 160 per 100,000. The probability that a top quark will decay into a down quark is about 7 per 100,000. The probability that a top quark will decay into a bottom quark is about 99.833% (the values are derived from squaring the Vts, Vtd and Vtb elements of the CKM matrix using the Particle Data Group world average experimental values for those CKM matrix elements in a global fit of all nine of the elements to the unitary matrix).

7. Dear Santiago,
Matt Strassler refuses to discuss the Standard Model (SM) obvious errors. Indeed,
1. QCD is a part of the SM. Now, QCD is inconsistent with many different kinds of experimental results. This evidence is described in many places of this blog and in the accompanying book which is shown on the right hand panel of this page. You can also see the items marked by an asterisk at this link http://www.tau.ac.il/~elicomay/OVERVIEW.html .
2. Experiment shows that the width of all particles having a mass greater then 80 GeV is about 2 GeV. Taking the SM point of view, it is a quite strange coincidence that the W, Z, Higgs and the top quark that belong to three different kinds of elementary particles, share this property. Note also that the width of the SM Higgs boson is predicted to be orders of magnitude smaller than the present LHC value. Now, these particles decay by weak interactions and a width of 2 GeV is much greater than the typical width of lighter hadrons that decay strongly. It means that in this very high energy environment, weak interactions become very strong. For this reason, both weak and strong interactions should be considered in cases where the state of the heavy particles is examined. Now, it is proved in the following link that the electroweak theory has theoretical errors. See http://ptep-online.com/index_files/2012/PP-31-03.PDF .
Considering these facts, you may agree with me that there is no reason why should I discuss details of Strassler’s arguments that are based on these erroneous theories. Furthermore, it is Matt Strassler who has blocked my attempt to open a discussion, by hiding my Comment of 28 September 2012 on his blog here http://profmattstrassler.com/new-start-here/#comment-19933 . You are invited to ask him why he hides my response from readers of his blog.
Cheers, Eli

• The LHC simply isn’t precise enough to measure the SM with for the Higgs boson width of about 1 MeV. Its results are not inconsistent with the SM value but the precision of the experimental measurement is simply hundreds of times more crude than the theoretically expected value.

8. Valery says:

“…such a particle would have specific decay modes, incompatible with the decay modes observed for the new boson and for the W and Z bosons…”
Can you answer this comment? Thanks!

• Dear Valery,

I really wonder about the answer of Prof. Gagnon. In the following lines I explain why the data support my point of view.

1. The Particle Data Group (PDG) is the institute that is authorized to define particle properties. In their report (see http://pdg.lbl.gov/2012/listings/contents_listings.html ) one finds information on particle properties like decay channels, width etc. Thus, one can compare W, Z decay channels with those of B mesons which are mesons of the b quark – namely, the heaviest mesons below the W,Z. Here the following similarity is found: both have leptonic and pure hadronic decay channels and the leptonic part is smaller than the pure hadronic part. These particles also have many decay channels and the W,Z have a larger number of decay channels than those of the B mesons. The reasons for this difference are explained as follows. The acceptable decay channels of the W,Z have more particles that have more flavor types. Another reason is that the b-quark makes distinct mesons, depending on the flavor of its antiquark companion. On the other hand, the large width of the W,Z indicates that it is impossible to distinguish between mesons made of a top quark and an antiquark of different flavor. Therefore, the W,Z decay mode is a superposition of decay modes of several flavors whereas in the case of the B mesons they are shown separately.
2. The W,Z, the top quark and the new 125 GeV particle have a similar and large width of about 2 GeV. All these particles decay due to flavor changing weak interactions processes. The similar width indicates a common physical reason which is the weak decay of the top quark that is a component found in all these particles. By contrast, the Standard Model prediction of the width of the 125 GeV Higgs boson is smaller by about 3 orders of magnitude – namely, it is completely inconsistent with the present data.

These arguments show the similarity of the decay channels of the W,Z and of lighter mesons and also the similar width of all heavy particles. These effects support my point of view about the W,Z and the new 125 GeV particle which regard all these particles as top quark mesons. I also advise you to read below my Reply to Santiago, which discusses related issues and the Reply of Ofer Comay as well.

Cheers, Eli

9. Santiago Sinelnicof says:

Doctor Comay,

I’m following your exchange with Dr Strassler with much interest because when one is starved of responses then any response, no matter how unpleasant, will do.

In reading his arguments and your response, I found a particular comment by Dr Strassler left unanswered (at least in my uneducated understanding). The comment is the following:

“…if the top quark had such strong forces acting on it that it could form the W and Z and Higgs by binding to other quarks, then many other things about the top quark — including the rate at which it is produced at the Tevatron and the LHC — would have been way off from the Standard Model prediction. In fact, they agree with the Standard Model at the 10% level.”

I would very much appreciate if you could clarify this issue, either because it is derived from your article above, and I’ve missed it, or by adding additional explanations.

Thank you very much for your time.

• Eliyahu Comay says:

Dear Santiago,

Matt Strassler refuses to discuss the Standard Model (SM) obvious errors. Indeed,

1. QCD is a part of the SM. Now, QCD is inconsistent with many different kinds of experimental results. This evidence is described in many places of this blog and in the accompanying book which is shown on the right hand panel of this page. You can also see the items marked by an asterisk at this link http://www.tau.ac.il/~elicomay/OVERVIEW.html .

2. Experiment shows that the width of all particles having a mass greater then 80 GeV is about 2 GeV. Taking the SM point of view, it is a quite strange coincidence that the W, Z, Higgs and the top quark that belong to three different kinds of elementary particles, share this property. Note also that the width of the SM Higgs boson is predicted to be orders of magnitude smaller than the present LHC value. Now, these particles decay by weak interactions and a width of 2 GeV is much greater than the typical width of lighter hadrons that decay strongly. It means that in this very high energy environment, weak interactions become very strong. For this reason, both weak and strong interactions should be considered in cases where the state of the heavy particles is examined. Now, it is proved in the following link that the electroweak theory has theoretical errors. See http://ptep-online.com/index_files/2012/PP-31-03.PDF .

Considering these facts, you may agree with me that there is no reason why should I discuss details of Strassler’s arguments that are based on these erroneous theories. Furthermore, it is Matt Strassler who has blocked my attempt to open a discussion, by hiding my Comment of 28 September 2012 on his blog here http://profmattstrassler.com/new-start-here/#comment-19933 . You are invited to ask him why he hides my response from the readers of his blog.

Cheers, Eli

• ofercomay says:

The summary of the above is that the standard model has much higher error rate than the 10% that Prof. Strassler declared. In the case of the width of the 125 GeV particle – it is 1000 times higher than the SM expectations (100,000% error and not 10%) and in the case of the bb decay which was expected to be 300 times more than the photon-photon decay but didn’t occur at all – the SM error is infinite.

• drou says:

This is a misunderstanding of what the experimental width of a particle is. The experimental width is NOT the experimental measurement of the (true) width of a particle, it is the observed width of the particle, which is a convolution of the true one, and detector effects. Up to now, there is no evidence the width of the particle is not due solely to detector effects, i.e. the data is consistent with the Monte-Carlo simulation with null true width.
For example a back of an envelope calculation for the decay Higgs to gamma gamma, neglecting angular resolution, the mass resolution is from simple error propagation : sigma M/M = sqrt(2)*sigma E/E. In atlas the photon energy resolution is sigma E/E=0.1/sqrt E. E is of order M/2 => this gives a resolution of 2 GeV.
Now looking at the papers from the two experiments http://webshop.elsevier.com/campaigns/higgsParticle/ , it is funny there is no statement on the width of the new particle. You could say they are hiding something. But it is just that the statement would have been something like “width<0.5 GeV" which is so far above the standard model that it does not constrain anything. Most likely such statement will be in future publications.

• A reply to drou: you are right – I didn’t use accurate language.

It is possible that the large width is due to detector errors. This is why we need to wait and see whether the error will be reduced after more statistics is gathered.

The reason that I used such language is because so many people jump to conclusions and based on the current experimental data decide that they found the Higgs… Therefore, based on the current data – this is not the Higgs, yet. All of us need to wait for better stats. One thing is sure – a new particle was found. Is it elementary? This is the question, and as you could see, I do not believe it is.