Of Particular Significance

Garisto’s Reply to Previous Post

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 10/24/2012

Robert Garisto sent me a reply to my previous post; here it is.  [A “vev” is shorthand for a non-zero value in the vacuum of space, what I call a “non-zero average value”.]

Matt – Thanks for your extensive reply to my comment! Of course I agree that a scalar field without a vev can have a hard mass term. And I do agree that how the Higgs boson gets mass is at least somewhat different than how the W does.

Let’s agree to define a Higgs as a scalar field with a vev. Then I think you agree that the mass of the excitation about the vev, the Higgs boson, is not a hard mass term, one obtains it by finding the minimum of the potential as you did above. Now if there are other scalars with vevs, the mass of the Higgs boson we are concentrating on can depend on those too. But isn’t it correct to say that the mass of such a Higgs boson goes to zero in the limit that all of those vevs go to zero? If so, I would say that the Higgs boson mass is provided by the Higgs fields (all scalars with nonzero vevs).

Anyway, the main reason I made the comment is that for the purposes of explaining to the public electroweak symmetry breaking, I think it makes sense to say that the Higgs boson mass comes from the Higgs field, because it is, in the SM, proportional to the vev.  It’s also kind of neat, I think.

We disagree, that’s all there is to it.  What Garisto says about the Standard Model is a simple consequence of dimensional analysis, not a fundamental relation that applies widely. And no, it is not correct to say that the mass of a Higgs boson always goes to zero in the limit that all vevs go to zero; there can be first order phase transitions in which, as the parameters change, the Higgs field’s vev jumps from non-zero to zero abruptly, and the mass of the Higgs particle is never zero.  So I think to tell the public that the Higgs particle gets its mass from the Higgs field is to confuse them into thinking that the Higgs particle gets its mass the same way the other known particles do — which is false.

But in any case, we agree it’s not that big a deal.  The thing which is important for the public to understand is that the Higgs field does not give mass to all massive objects — such as atomic nuclei and black holes.  And the thing which it is important for particle physics students to understand is that the Higgs mass is not generically proportional to the vev of the Higgs field.

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20 Responses

  1. What an emptry-headed TWIT Garisto is. Is this best the USA can produce? The country of giants like Washington and Jefferson producing such an excuse fot a physicist!! My God help he world! Please Garisto commit suicide: It will be the only honourable thing that you will be able to do in your life!

  2. Would it at least be safe to say that the Higgs is the only particle that we know of with an intrinsic or unexplained mass, and all other masses can be expressed in terms of kinetic energy or interactions between particles?

    1. Neutrinos don’t, I think.
      In that case, Matt, is there any good explanation for the neutrinos masses? Some idea that is ‘liked’ by a good portion of the scientific community?


      1. Neutrinos, like all other known particles, cannot get masses unless the Higgs field is on average non-zero. There are two possible mechanisms for how the masses arise, and either one or a mixture of the two may be operative; we don’t know anything about that yet experimentally. But the Higgs field must be involved; neutrino masses are impossible (because of the type of fundamental obstruction I mentioned on Monday) without it.

    2. [you mean “interactions between fields”; it’s the Higgs field, not the Higgs particle, which is providing masses.]

      It depends what you mean. We know *why* the electron can have a mass — the (or at least, a) Higgs field has to be non-zero; but its mass has two elements: the non-zero Higgs field, and the strength of the interaction between the electron field and the Higgs field. Since we do not know what sets the strength of the interaction between the electron field and the Higgs field, would you say the electron mass is explained? I don’t think I would say so. I would just say that we’ve understood how it can be non-zero, but not why it takes the value it has. However, we do think we know that this is the next question we have to answer.

      As for how the Higgs particle gets its mass — we don’t really know enough to know what the right questions about it are yet, I would say. We need more information from data (and perhaps insights from theory) before we can figure out how to talk about the Higgs mass properly.

  3. Excellent Professor Strassler,
    If I understand, Higgs boson is a “Hard mass” like W bosons provided, it get mass from other source than Higgs Field- like W bosons !- of course, it is in the SM, proportional to the vev.

    Even scalar fields goes to zero, Higgs boson keep its excitation(non-zero) and not generically proportional to the vev of the Higgs field – appears, as “hard mass(parameter)” and getting mass from Higgs field?

    Thank you Professor.

    1. Well — terms like “hard mass” and “soft mass” are very technical. I would rather not use them here.

      There is one mass parameter that goes into the Standard Model’s potential energy. That mass parameter determines both the vev of the field and the mass of the Higgs particle.

      What Garisto wants to say is that this involves two steps: first the mass parameter determines the vev, then the vev [along with the interaction strength of the Higgs field to itself] determines the particle’s mass.

      That seems silly to me: there’s only one step, the mass parameter [along with the interaction strength of the Higgs field to itself] determines both the vev and the mass.

      And the kicker is that outside the Standard Model there are multiple mass parameters, and you can only say that the process involves one step; there’s no way to write the equations so that it would appear that the process involves two steps. Garisto’s statement that this is always possible is simply mathematically wrong; it’s only possible in certain cases.

  4. Is this a problem when translating mathematics into words.

    The maths has precise meaning whereas a phrase like “give mass” is open to interpretation.

    1. The problem is not mathematics or words but the “precision” itself.

      The non-zero average value of Higgs field is mathematically fine-tuned by renormalization, it appears that there has been a delicate cancellation between the fundamental quantity and the quantum corrections to it.
      Because we do not know the “precise” details of the shortest-distance theory of physics (quantum gravity), we cannot even address how this delicate cancellation between two large terms occurs.

      The Critique of Pure Reason: Kant, Immanuel (1724-1804): “If human reason tries to extend the fundamental concepts and principles of thought beyond the limits of perception for purposes of theoretical knowledge, it yields only illusion”.

      1. The experimental discovery of the formarly only theoretically predicted higgs particle (and the experimental confirmation of GR AFTER its theoretical formulation too for example) nicely falsifies Kant’s Critique of Pure Reason.
        Kant did not fully understand the scientific process, it is perfectly legitimate that theory can be ahead of experiments.

    2. Both Garisto and I agree that the issue here is partly semantic. Also, what are cause and effect inside equations? If I write A = B + C, have B and C caused A? What if I write it as C = A – B? And so on.

      However, some of Garisto’s arguments are simply not right. And my point was that while there are theorems about the masses of the W and Z particles that *require* a Higgs field for them to get a mass — and equally, assure that if there is a non-zero Higgs field, they *will* be massive — there are no such theorems for the Higgs particle’s mass. It’s really different. And that’s not interpretation or semantics. I think this is crucial; Garisto waves it off as a minor detail.

      1. Yes Professor. if humans should not be cheated with mathematics or numbers the problem here is semantic. Kant may indicate as perception this causality- why we think B and C caused A? and C = A – B?.

        If it is science, we should be able to nail the known particles get mass from Standard Model’s potential energy- because SM is mathematically adjusted to Naturalness within Simple symmetry. There should be only one step.
        If we allow numbers or mathematics inside causality, we should tell which is “1” and which is “0”. Mathematics cannot differentiate this because there is no reason or logic involved in it- only perception.

        If “0” and “1” go parallel inside causality, mass parameter get two meaning(s), one must be definitely illusion. SM aim is to fix how matter exist- not whether mass of the particles(or HP) came from potential energy of SM(more blurred, multiple mass parameters beyond SM) or from more “worldly?” Higgs field ?- sorry Iam not an expert.

      2. I understand “worldly” as kinetic energy of Higgs field( like momentum and energy or mass of electron). Known particle is known particle, there is no ambiguity even in Schrodinger’s cat like situation of “quantum” level of reality.
        Here 1 = 0 = 1, where the difference between 1 and 0 is insignificant says our perception or intuition.

        But in SM, both Higgs field and Higgs particle are kinetic energy(mass?) of SM. Both go parallel inside causality of mass parameter. One is experimentally proved inside LHC, another by mathematics(mass) under SM. Here 1 ≠ 0, either one of them must be illusion because both are hypothetical(adjusted to Naturalness) and one is proved experimentally?.

        But for the survival of SM both of them are necessary?. If the definition is blurred(1 = 0) between multiple mass parameters of other fields(beyond SM) and the mass parameter of Standard Model’s potential energy- then there is no existence of matter?

      3. What is true is that the Standard Model Higgs particle — the particle of the simplest possible Higgs field, which involves one and only one elementary field added to the other types of fields we know.

        The finding of Higgs particle is also still consistent with the behavior of the simplest type of Higgs particle — the so-called Standard Model Higgs. The LHC was built to figure out what the Higgs field is (or Higgs fields are), how it works (or they work), and whether it is (or they are) elementary or composite.
        If you try to take the Higgs field out of the mathematics but keep the W and Z particles and the other heavy particles (such as the top quark) that we have already discovered and know are present in nature, you will find that the mathematics of the Standard Model simply makes no sense.

        To restore the theory of the Standard Model to working order, you must add a Higgs field, or something like it, to the fields that we have already discovered experimentally. So start everything from Higgs field’s mass- not from Higgs particles mass?. LHC found a partice, from a field(s) already discovered experimentally?.

      4. (1) Can Higgs field get its “vev” from potential energ(ies)y beyond SM?- then avoid? only SM and not the Higgs field, necessary for existence of matter?- and also solve Strong CP problem(solved within a theory of quantum gravity) and Hierarchy problem ?

        (2) For example: the electric field is a part of nature that is found everywhere. At any given point in space, and at any particular time, you can measure it. If it’s non-zero on average in some region, it can have “physical effects”, such as making your hair stand on end or causing a spark.
        Which cause and effect inside Higgs field equations(“vev”), could make “physical effects” ?

        That’s all from a layperson.

  5. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the value of the scalar field at the same point in space (or spacetime).– Simply a Logos( λόγος)?

  6. Now, if they can only help me find my golf swing, that would be a scientific breakthrough.

    Prof, about my comment (19-Oct)? … I truly believe I found the Z particle and has nothing to do about ripples. It is all geometry, how spacetime stretches and curves under varying temperatures, high temperatures, very high temperatures, temperatures that can only be obtained and contained in a black hole.

    Great website Professor, congratulations.

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