**Theoretically, the Higgs boson solves a lot of problems. Theoretically, this Higgs boson is a problem.**

Greetings from the good ol’ U.S. of A.

Now that Fall is here, classes are going, holidays are wrapping up, and research programs are in full steam. Unfortunately, all is not well in the Wonderful World of Physics. To refresh, back on 4th of July, the LHC experiments announced the outstanding and historical **discovery of a new particle with properties consistent with the Standard Model Higgs boson**. No doubt, this is a fantastic feat by the experiments, a triumph and culmination of a decades-long endeavor. However, there is deep concern about the existence of a 125 GeV Higgs boson. Being roughly 130 times the proton’s mass, this Higgs boson is *too* light. A full and formal calculation of the Higgs boson’s mass, according to the theory that predicts it, places the Higgs mass pretty close to infinity. Obviously, the Higgs boson’s mass is less than infinite. So let’s talk mass and why this is still a very good thing for particle physics.

For an introduction to the Higgs boson, click here, here, or here (This last one is pretty good).

## The Standard Higgs

The Standard Model of Particle Physics (SM) is the theory that describes, well, everything with the exception of gravity (Yes, this is admittedly a pretty big exception). It may sound pompous and arrogant, but the SM really does a good job at explaining how things work: things like the lights in your kitchen, or smoke detectors, or the sun.

Though if this “theory of almost-everything” can do all this, then when written out explicitly, it must be pretty big, right? **Yes**. The answer is yes. Undeniably, yes. When written out fully and explicitly, the “Lagrangian of the Standard Model” looks like this (click to enlarge):

This rather infamous and impressive piece of work is by Prof. Thomas Gutierrez of Cal Poly SLO. Today, however, we only care about two terms (look for the red circles):

The first term is pretty straightforward. It expresses the fact that the Higgs boson has a mass, and this can represented by the Feynman diagram in Fig 3. (below). As simple and uneventful as this line may appear, its existence has a profound impact on the properties of the Higgs boson. For example, because of its mass, the Higgs boson can *never* travel at the speed of light; this is the complete opposite for the massless photon, which can *only* travel at the speed of light. The existence of the diagram if Fig. 3 also tells us exactly how a Higgs boson (denoted by *h*) travels from one place in the Universe, let’s call is *x*, to another place in the Universe, let’s call it *y*. Armed with this information, and a few other details, we can calculate the probability that a Higgs boson will travel from point *x* to point *y*, or if it will decay at some point in between.

The second term is an interesting little fella. It expresses the way the Higgs boson can interact with other Higgs bosons, or even itself. The Feynman diagram associated with this second term is in Fig. 4. It implies that there is a probability a Higgs boson (at position *w)* and a second Higgs boson (at position *x)* can collide into each other at some point in the Universe, annihilate, and then produce two Higgs bosons (at point *z *and *y*). To recap: two Higgses go in, two Higgses go out.

This next step may seem a little out-of-the-blue and unmotivated, but let’s suppose that one of the incoming Higgs bosons was also one of the outgoing Higgs bosons. This is equivalent to supposing that *w* was equal to *z*. The Feynman diagram would look like Fig. 5 (below).

In words, this “new” diagram states that as a Higgs boson (*h*) at position *x* travels to position *y*, it will **emit and absorb** a second Higgs boson somewhere in between *x *and *y*. Yes, the Higgs boson can and will **emit and absorb** a second Higgs boson.

If you look carefully, this new diagram has the same starting point and ending point at our first diagram in Fig. 3, the one that described the a Higgs boson traveling from position *x* to position *y*. According to the well-tested rules of quantum mechanics, if two diagrams have the same starting and ending conditions, then both diagrams contribute to all the same processes and both must be included in any calculation that has the same stating and ending points. In terms of Feynman diagrams, if we want to talk about a Higgs boson traveling from point *x* to point *y*, then we need to look no further than Fig. 6.

## What Does This All Mean?

Now that I am done building things up, let me quickly get to the point. The second diagram can be considered a “correction” to the first diagram. The first diagram is present because the Higgs boson is allowed to have mass (mH). In a very real sense, the second diagram is a *correction* to the Higgs boson’s mass. In a single equation, the two diagrams in Fig. 6 imply

In Eq. (1), term on the far left is the Higgs boson’s mass that has been experimentally measured, i.e., 125 GeV. Hence the label, “what we measure.” The term just right of that (the “free parameter”) is the mass of the Higgs boson associated with the first term in the SM Lagrangian (Fig. 2 and 3). When physicists talk about the Standard Model not predicting the mass of the Higgs boson, it is this term (the free parameter) that we talk about. The SM makes no mention as to what it should be. We have to get down, dirty, and actually conduct an experiment get the thing. The term on the far right can be ignored. The term “Λ” (the “cutoff scale“), on the other hand, terrifies and mystifies particle physicists.

Λ is called the “cutoff scale” of the SM. Physically, it represents the energy at which the SM stops working. I mean it: we stop calculating things when we get to energies equal to Λ. Experimentally, Λ is at least a few hundred times the mass of the proton. If Λ is very LARGE, like several times larger than the LHC’s energy range, then the observed Higgs mass gets an equally LARGE bump. For example, if the SM were 100% correct for all energies, then Λ would be infinity. If this were true, then

(the Higgs boson’s mass) = (something not infinity) + (something infinity) ,

which comes out inevitably to be infinity. In other words, *if* the Standard Model of Physics were 100% correct, then the Higgs boson’s mass is *predicted* to be infinity. The Higgs boson is not infinity, obviously, and therefore the Standard Model is not 100%. **Therefore, the existence of the Higgs boson is proof that there must be new physics somewhere.** “Where and at what energy?,” is a whole different question and rightfully deserves its own post.

Happy Colliding

- Richard (@bravelittlemuon)

Tags: @bravelittlemuon, Feynman Diagrams, Higgs, Loop Corrections, new physics

I have a few problems with the lengthy equation above:

Where is the closing bracket corresponding to the bracket after the g-term in line 15 (from top)?

There are 2 closing brackets missing in lines 8 and 9 (counted from bottom up).

And did I miss it or where is the ‘=’ in this “equation”?

Probably there are many more mistakes in there that I did not find.

Looks like you did not expect anybody to read the equation or even check it, huh?

Well, it is a Lagrangian, meaning that it is an expression of a quantity (of energy), not an equation. You seem to be right about the grouping symbols, though.

Hi Suleman,

Let’s take a look:

1. I suspect you may be right about the first “)”.

2. The bracket in four is closed in five; the open bracket in five is closed in seven; the open one in seven is closed in eight; the open bracket in 10 is closed in 11; and the one that opens in 11 also closes in 11. You are 1 for 3, not bad.

The Lagrangian of the Standard Model of Particle Physics is “=” to that whole mess, and the original author makes no guarantee of its accuracy with respect to parentheses, brackets, and curly brackets. http://nuclear.ucdavis.edu/~tgutierr/files/stmL1.html

I fully hoped QD readers would try to go through the Lagrangian and ask questions about it. The equation is very, very rich and describes, for lack of a better phrase, a lot.

- richard

Please explain;If the Higgs Boson is what gives a particle mass, then it seems to me that the Higgs Boson, according to the article, having mass itself doesn’t really make sense as an explanation of what gives mass to that which has mass. It seems that the answer to where does mass comes from, according to this article, is that mass comes from the Higgs Bosons mass… I feel like either im misunderstanding your explanation or the explanation is as it seems, a side stepping of the actual question itself. What is more, if the mass found in a proton is supposed to be contingent on the affect of the Higgs Boson, then why is the Higgs Boson being described as having a substantially greater mass than the protons mass. Shouldn’t the total mass of a proton be the sum of the total effect of the Higgs “particles” that are “responsible” for the protons mass?

Why would one expect that the weak scale mass terms arising of broken symmetry and unique to the Higgs mechanism preclude infinite mass for the Higgs. That is if energy is conserved the Higgs giving mass to all those other particles would make the Higgs field like a heat sink. It would be impossible to impart enough energy to the field because the fields would be stabilized by the almost infinite energy of the entire universe being observed as mass. .?

Hi Rehbock,

In principle, you are right; the Higgs boson’s mass *could* be infinite. However, if we do that, we run into a problem, we violate the “unitarity condition” imposed on quantum mechanics [1]. This puts a strict upper bound on the mass of the Higgs boson roughly at 10 times its mass and not infinity. This is why we expected to see the Higgs boson at the LHC, the collider’s energy is right at the sweet spot needed to detect the boson. Despite how massive the Universe is, there are a finite number of massive particles. The number may not be constant, but it is definitely less than infinity.Therefore, only a finite amount of energy is needed to provide mass to all the massive particles. I hope this clarifies the confusion.

[1] http://www.quantumdiaries.org/2012/02/14/why-do-we-expect-a-higgs-boson-part-ii-unitarization-of-vector-boson-scattering/

Thank you for the reference. The box inset there does address that my naive thought can not be consistent with unitarity

I shall need study this more deeply and thoroughly because I am still feeing the unique non zero expectation value of the Higgs field Is telling something more pointing to the answer to this thani have so far grasped.

Thanks again. Now I shall shut up unless and until I can explain it to a five year old know I do not yet understand a solution that can avoid invoking a not even wrong proposition.

Rehbock,

I face this problem every day. : )

Besides, Higgs logically superfluous. “It is not Higgs” (http://arxiv.org/abs/physics/0302013 )

Dear Gunn,

Let me start by saying that I have not read your paper. Nevertheless, there are a few things that ring crank-bells. For once, your paper is written in Word, which in itself might not mean anything (you might be of a certain age) but is something that immediately makes people suspicious. More than half of your references are to yourself and the rest are mostly textbooks and very old references; I am sure that if you say is true, other people would have gotten hints of it at least. You do not list any association to a university, which makes it difficult to assess whether you have any formal training or not. Finally, there are no acknowledgements, which means that either you did not circulate your results prior to uploading them to the arXiv to other people in the field, or that you did and they dismissed you entirely.

If you like physics, read about it, do calculations, talk to other people. There is no need to get out stuff that at least makes you look like a crank and at worst is plain wrong.

Dear Alberto:

” I have not read your paper”: Well so read. For example, this:

http://www.ptep-online.com/index_files/books_files/quznetsov2011.pdf.

(It is written by LaTex, if you do not like World). Otherwise, there is no sense to argue with you.

What’s up every one, here every person is sharing these kinds of familiarity, thus it’s good to read this

web site, and I used to go to see this web site every day.

Hmm, funny. I commented and see my comment as awaiting moderation, yet this blatant spam comment is here…

Patience my friend, patience.

Hello, thanks for the post!

I was thinking about the last part, I am a bit confuse … I thought the problem was not the infinity thing, there are many infinities in field theory that you need to remove in your renormalization scheme, such as the QED coupling, I thought the only problem was that, if ever the cut-off turns out to be physical (there is new physics at higher energies), then you should specify your theory whith the numbers at the scale of new physics. However, if this scale is high, you may need a huge cancellation of digits to tune your Higgs mass to the electroweak scale. I thought indeed infinity was the only non-problematic scenario. However, is hard to believe there wouldn’t be new physics if gravity is to be included, if you want to explain cosmology, etc…

Could you clarify please?

Thanks a lot!

Hi Pablo,

Good catch. As always, out friend, the devil, is in the details. You brought up a few things so allow me to go down the list:

(a) You are absolutely correct, there are many divergences (infinities) in quantum field theory and they are (mathematically) removed through renormalization [1]. What I discussed above is actually an example of “mass renormalization,” where we require that the physically observed/measured mass is the sum of the mass we find in the Lagrangian (“bare” or “tree-level” mass) + all the quantum mechanical correction terms (“loop effects”).

(b) Briefly regarding gravity: it is unclear quantum gravity can solve this problem with the Higgs’s mass. This is especially questionable because quantum gravity is currently predicted to kick in 17 orders of magnitude in energy higher than the Higgs mass. With such a huge difference in energy scales, the cancellation would have to be due to some physical principle, e.g., loop cancellations by supersymmetric partners, etc.

(c) By definition, if the cutoff is a real number (finite), then there is new physics somewhere. The discovery of the Higgs boson (or something that satisfies its properties) has given the strongest, non-gravity-related indication that the cutoff is indeed finite.

(d) Back to renormalization, the divergence discovered when renormalizing the SM Higgs boson’s mass is different from any other divergence in quantum field theory. All other divergences that are not some mathematical mischief (due to some poorly done transformation) are logarithmically divergent, i.e., they all have a form similar to the far-right term in Eq.(1). The renormalized electron charge, etc., all have logarithmic divergences (they grow logarithmically with the cut-off energy), and have a physical interpretation that is well understood (screening[1,2]). The Λ^2 term grows much more rapidly than any other renormalized parameter and spoils the entire renormalization process. In other words, our usual tricks do not work here. We need a new physical principle to make this divergence go away.

(e) Again, gravity. Yes, the existence of gravity means that the SM must breakdown at some point. However, this is not necessarily “new” physics. : )

(f) I hope this has helped. Please, ask more.

[1] http://en.wikipedia.org/wiki/Renormalization

[2] http://en.wikipedia.org/wiki/Screening_effect

Nice answer

Also found this on QD

http://www.quantumdiaries.org/2012/07/01/the-hierarchy-problem-why-the-higgs-has-a-snowballs-chance-in-hell/

thanks for the enlightening

The Higgs boson at 125 GeV/c^2 is an exceptionally

short rangecarrier, re the Weak force via W and Z bosons at 80.4 GeV/c^2 and 91.2 GeV/c^2. Is that behavior observed in conferred mass? No.The Standard Model has 26 manually inserted tuning parameters. It is a curve fit. SM predictions fail. Introduction of mass (the Higgs, CP-even) unleashes furies of parity violations followed by hierarchies of manually inserted symmetry breakings to further curve fit. SUSY has no empirical validation. Fundamental vacuum mirror symmetry, f(x) = f(-x), cannot be rigorously correct toward fermionic mass.

“

Therefore, the existence of the Higgs boson is proof that there must be new physics somewhere” Yes! Euclid and Newton are both rigorously derived. Euclid failed via Bolyai. Newton failed via Einstein and quantum mechanics. Validating internally does not find the problem. One must falsify externally.Observed vacuum has a trace chiral background toward mass, f(x) = -f(-x). Probe ONLY the chiral background. Chemically and macroscopically identical, enantiomorphic atomic mass distributions will insert with trace different energies. They will vacuum free fall along trace non-identical minimum action trajectories. That is your SM-gravitation connection. It is testable to 5×10^(-14) difference/average sensitivity within 90 days in existing apparatus as a geometric Eotvos experiment.

A pseudoscalar field will do everything a scalar field does, plus whistle. Neither “elegant” nor “derived” demands “empirically true.” The only way to know is to look.

“The LHC state at 125.5 GeV and FNAL data as an evidence for the existence of the new class of particles — $W$-hadrons” http://arxiv.org/abs/1209.2831

$W$-hadron much closer corresponds to the LHC data than Higgs.

Too much white noise around this Richard’s blog although his blog is highly sensible. It clearly cuts through: Higgs Boson discovered is “too light” to be theoretical Higgs. So from where does neutrons, and all other nucleons generate their mass from? Does this higgs borrow from other neighboring but unsensed / undetected Higgs lying around? or does depending on the particle to be formed, Higgs lable 125TeV shares with some other Higgs, but then what happens to the residual Higgs? inifinite number of questions, not infinite mass exist! exist. we could go on and on.

To me no matter how we look at it, higgs boson has one of the short life spans in the universe, (less than 1.0 X 10-33sec) which makes its decay stages impossible to observe with CMS / ATLAS… There is difference between what CERN has discovered and celebrated the higgs particle, and what higgs theory celebrates to be the higgs particle. The particle discovered can be given any name, including higgs.

I agree with Richard, but on a different scale or dimension. Scientist all over will find out someday that the solution to our SM model is there when we consider that all matter is in the pure liquid state (Brookhaven… discovery) with low viscosity. I add that high and ultra high densities of liquid matter is what makes matter behave like particles to detectors because it is observed like single moving shot, single compact mass, single object (virtual particle) at the quantum leve, and real solid particle at the macrolevel.

“So from where does neutrons, and all other nucleons generate their mass from?”

Neutrons and all other nucleons generate their mass from Dirak’s improved equation:

http://arxiv.org/pdf/physics/0302013

Prof Gunn: I browsed thru your state-of-the art paper… and thank you it is very illuminating and instructive to read what you referenced.

The problem is I believe that probabilistic quantum physics is not the answer to our real physical world. May be Einsteinist in this sense.

I also think that time generate whiace and not as commonly understood, because time was up and running when there were nothing at all of existence. so to me space is generated by time which may seem hard to conceptualize by scientists for different reasons.

sorry! there was typo errors, so it is repeated.

Prof Gunn: I browsed thru your state-of-the art paper… and thank you it is very illuminating and instructive to read what you referenced.

The problem is I believe that probabilistic quantum physics is not the answer to our real physical world. May be Einsteinist in this sense.

I also think that time generates space and not as commonly understood, because time was up and running when there were nothing at all of existence. so to me space is generated by time which may seem hard to conceptualize by scientists for different reasons.

The most interesting thing that I want focus on here, is the fact that you were implying that nucleons get their mass from Dirak’s improved equation. This directly means that if we could assume theoretically (only) Dirak’s improved equations to be correct, then we are really saying that there are no nucleons at all in atoms substructures or in matter before Dirak’s improved equation is triggered or kicked off to generate masses for these unexisting particles? WAHOO! Great! because this helps me kick off my view (or framework) which conjectures that matter is pure liquid (what experimentally RHIC detected recently) and that particles are formed or masses are generated by Dirak’s improved equation on exit from matter. Whether collision or any simple chemical, physical, thermal, entropical, strain, stress, nuclear, whatever surrounding field exists that forces changes in matter to spit an electron, a proton, a neutron, etc…???

Please illuminate me, Professor Gunn?

Dear Prof. Maximal:

“The problem is I believe that probabilistic quantum physics is not the answer to our real physical world. May be Einsteinist in this sense.”

But all modern physical experimental data are statistical.

“I also think that time generates space and not as commonly understood, because time was up and running when there were nothing at all of existence. so to me space is generated by time which may seem hard to conceptualize by scientists for different reasons.”

Yes, I agree with it (see ref. p.21-49).

“The most interesting thing that I want focus on here, is the fact that you were implying that nucleons get their mass from Dirak’s improved equation. This directly means that if we could assume theoretically (only) Dirak’s improved equations to be correct, then we are really saying that there are no nucleons at all in atoms substructures or in matter before Dirak’s improved equation is triggered or kicked off to generate masses for these unexisting particles? WAHOO! Great! because this helps me kick off my view (or framework) which conjectures that matter is pure liquid (what experimentally RHIC detected recently) and that particles are formed or masses are generated by Dirak’s improved equation on exit from matter. Whether collision or any simple chemical, physical, thermal, entropical, strain, stress, nuclear, whatever surrounding field exists that forces changes in matter to spit an electron, a proton, a neutron, etc…???”

No, here the elementary particle (a lepton, a quark) is an ensemble of dot events (ref. p.37-80). The behavior of probabilities of such events is defined by Dirak’s equation (ref.p, 80-101). Masses, moments, energies, spins of such particles represent parameters of their probabilities distributions. Hadrons, atoms and molecules are constructed of elementary particles standardly (in standard textbooks).

Thank to you

Thank you Professor Gunn.

You are right from a probabilistic viewpoint. YES, all modern physical experimentation data are statistically based which gears all experimental designs, setups, and result-interpretations from a probabilistic angle. To me, probabilitic analysis is one of our most advancing and pioneering sciences that is able to solve or psuedo-solve (pareto-feaible solution) some of complex intractible nature’s problems like simple weather predictions or next customer incoming and service times, let’s say at some bank queue or movie queues. Hoewever, I would like to add that if we can reformulate some quantum physics models in deterministic environment, or couple the 2 models together one can solve some prediction problems possible much better. Then, we can rest assured of improved results with over 99.999 %confidence levels.

But these models (superstrings, dark matter, dark energy, etc.) don’t prove to be true experiment. And my probabilistic analysis doesn’t use any ontologic hypotheses – only property of probabilities.

When quaternionic quantum physics is considered (Constantin Piron, ~1960) , then the quantum state function becomes a quaternionic probability amplitude distribution. This can be split in a real scalar field and a 3D vector field. These fields describe (charge) density distributions and current density distributions of lower order charge carriers that do not yet have a name. Having mass now gets a new interpretation because these lower order objects will certainly play a role in the explanation.

Given the spurious inventions of Black holes, Dark Matter, Big Bang, superstrings and long and abstract dictats about how the universe is – when it isn’t, why would it surprise anyone to learn that the Higgs Boson has been made a cash cow and will never be found? Why, each time they “find” it, it turns out to become a “Higgs-like” boson? Why is it possible that A level students are reviewing EGR and finding all the glaring errors that predict such things and yet their forebears never questioned it? – Never bothered to check? Never bothered to do their job as scientists? Why are $billions being spent on bogus science? …Answer these questions and we can move on to proper knowledge.

The evidence strongly supports Black holes, Dark Matter, and the Big Bang, plus the evidence is consistent with what we understand from superstrings (M-Theory). So saying they are spurious is a little silly, to put it politely.

If anyone thinks there are better explanations than that provided by Black holes, Dark Matter, Big Bang, and superstrings – then they should provide better alternatives that are consistent with the evidence!

I blog quite often and I truly appreciate your content.

Your article has truly peaked my interest. I’m going to take a note of your blog and keep checking for new information about once a week. I subscribed to your Feed as well.