Ideas On Higgs Couplings
    By Tommaso Dorigo | June 28th 2012 08:14 AM | 20 comments | Print | E-mail | Track Comments
    About Tommaso

    I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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    A very interesting paper appeared one week ago in the Arxiv. It is titled "Higgs Self-Coupling Measurements at the LHC", and it is authored by M.Dolan, C.Englert, and M.Spannovsky. The idea is that once and if a Higgs boson is found at the LHC, the next natural step of the research would be its characterization as a pure standard model object or a more complex, or just different, beast.

    Of course, once a signal were established, the LHC experiments would certainly want to measure all its properties as precisely as possible: mass, angular distributions, cross section in all the production mechanisms, and decay modes.

    In theoretical terms, determining angular distributions would answer the question "is this a scalar particle", or "what is its spin-parity", something technically labeled as "0+" in the standard model, much like the blood type of most of us. Definitely a very important theme; but maybe even more important would be to use the production and decay information to decrypt the higgs boson couplings to fermions and bosons, and crucially, its self couplings.

    "Self coupling" means that a particle can split into two copies of themselves (in the simplest realization): definitely not something trivial to do for matter particles, and indeed, fermions cannot do it, for a number of reasons (charge conservation, or angular momentum conservation, come to mind). Bosons instead are not prevented by the conservation of angular momentum rules, so the question is whether they possess or not other quantum numbers that would change in a 1->2 or 1->3 process. Photons cannot split into two photons, for example, because of the conservation of charge conjugation.

    A boson which is perfectly happy to split into copies of itself is the gluon. The presence of a self-coupling of gluons is in fact built into the theory of gluons - Quantum Chromodynamics, QCD - because QCD is based on a non-abelian gauge group, SU(3). For the Higgs, the group-theory reason of the existence of three- and four-particle vertices is to be found in the very electroweak symmetry breaking mechanism, which in the unitary gauge does the miracle of creating mass degrees of freedom to W and Z bosons. I will not bother you with mathematical expressions, but the two things really have the same source in the standard model: the Higgs has self couplings if EWSB works the way it is supposed to. So comparing measured and predicted Higgs boson self couplings is the ultimate dream of the Higgs phenomenologist !

    The paper therefore examines the possibilities to measure these self couplings. What we need to do is find processes whereby two Higgs bosons are simultaneously produced: this would both be due to independent Higgs boson radiation (off a quark line, for instance), and from the production of a single Higgs boson which then materialized a pair, thanks to the self interaction; some possible leading-order diagrams are shown in the figure on the right. One would thus need to measure the production precisely in order to understand how much of the total rate is due to the self interaction diagram. And alas, double Higgs production is predicted to be quite rare at the LHC !

    Theoretical calculations indicate that the rate is of the order of one thousandth of the production of a single Higgs; then of course, if self interaction were much larger (due to some new physics intervening in the double Higgs production, for instance), one would observe more than that. But can such a few-femtobarns-cross-section process be seen ? That is the question to address. One should consider the full powers of a endgame LHC, that is 14 TeV running conditions and hundreds, or even thousands, of inverse femtobarns of integrated luminosity. In that case, it seems that the thing is doable -but only marginally so.

    Having read the article, which deals with details of the most promising signatures (e.g. when the two Higgs bosons are produced "boosted", recoiling against a hard jet, or when the Higgs decay into specific topologies that may beat other standard model backgrounds), I am unsure whether I should be excited by the prospect, or draw home the lesson that if the LHC finds the Higgs we need to build a different machine to study in detail its properties. The latter points to a linear collider as the natural choice: but a linear collider had been advocated for decades as "the" machine to build after the LHC "because LHC would find SUSY particles, and then we'd need to study them in detail in a linear collider". Now using the same argument with only the Higgs boson as a target appears problematic to me...


    Hi Tommaso,

    very nice post! I'd like to point out that the first of the Feynman graphs is zero due to color conservation.
    We forgot to add that to the figure caption ;-)

    Cheers Chris.

    Higgs coupling was already observed in form of top quarks decays or not? According to this interpretation, a top quark bound by to its anti-matter partner, the antitop, would act as a version of the elusive Higgs boson, conferring mass on other particles.

    By the way, the article mistakenly attributes the top quark condensation idea to Christopher Hill. The idea came from Nambu, Jona-Lasino 1961, Nambu 1988, Miransky et al 1989, Tanabashi and Yamawaki.

    The reason of why Higgs field exists is essentially dual to the reason, why in general relativity the flat Universe cannot exist. The space must be always curved, or it couldn't exist at all. The water surface analogy of space-time demonstrates that every space, i.e. the path requiring some time for its passing must be composed of huge amount of tiny gradients, the overcoming of whose requires repetitive acceleration and deceleration. The cumulation of large amount of these gradients is what makes the traveling trough space so slow, i.e. the space so large. But the requirement of these gradients introduces the necessity of some intrinsic inhomogeneity of space-time, i.e. the presence of Brownian noise. Without Brownian noise the water surface is unthinkable and it couldn't be composed of particles. Well, and the Higgs field is the manifestation of this intrinsic inhomogeneity of the space-time at quantum scale. It principally doesn't differ from CMBR noise at the human distance scale.

    The Higgs field therefore manifests in the same way, like the CMBR field: with Yukawa force, which is low-dimensional analogy of Cassimir-Polder force at the microscopic scale and it's responsible for gluing of massive particles into pairs, for example for formation of top-quark pairs. The simplest way, how to detect the Higgs field is therefore the detection of particle pairs, i.e. symmetrical products of particle collisions occurring in particle accelerators. The main problem in interpretation of Higgs boson in this way is, in Standard Model it should manifest preferably with formation of heavier particle pairs rather than with production of gamma ray photons. It's because the massive particles exhibit more intensive Yukawa force than the lightweight ones. We know about dimers of top quarks, but not about dimers of up/down quarks. This is the introductory point of the characterization of LHC collision products as a Higgs boson compliant with Standard Model.

    IMO the most probable explanation of this controversy is in fact, the Standard Model is not complete yet and it allows the forth generation of particles: the superheavy quarks and neutrinos. The pairing of these particles in Higgs field is indeed the most intensive, but because these particles are extremely unstable, they decay directly into shower of gamma ray photons before they can be detected as such. Which is what we are observing by now: the excess of gamma photons pairs over the pions and muon pairs. Therefore the most systematic explanation in context of Standard Model would probably consist from introduction of the fourth mixing angle into Cabbibo matrix and from consideration of quark oscillations between third and fourth particle generation. To prove this model we should detect this oscillation first for example for neutrinos and maybe even for top quarks directly.

    Zephir said, "The reason of why Higgs field exists is essentially dual to the reason, why in general relativity the flat Universe cannot exist. The space must be always curved, or it couldn't exist at all."

    That's not true at all. When the universe 'burns out' and all mass decays into energy, there will be no gravity left to curve spacetime. And furthermore, spacetime was flat before the big bang. And further-furthermore, the entire discussion may be mute because there is ample evidence the big bang didn't happen. And finally-furthermore, I guarantee that either the Higgs particle is not found, or if it is found it is not the 'higgs' particle and it certainly isn't behind the mechanism that endows mass. Hit me up after July 4th and I'll explain it to you in detail.

    > and all mass decays into energy
    > there will be no gravity left to curve spacetime.
    Since when does energy density not have gravitational effects?
    > there is ample evidence the big bang didn't happen.
    > I guarantee that either the Higgs particle is not found, or if it is found it is not the 'higgs' particle
    You better buy a toaster for this guarantee. You will need it.
    > Hit me up after July 4th and I'll explain it to you in detail.
    Do you even know what a complex number is?

    >> and all mass decays into energy
    > Eh?

    Eh what? You seem confused. No worries, I'll restate for your benefit. There will necessarily come a time when the universe expands to a point where all physical matter comprising 'mass' has 'decayed'. The term 'mass' is employed above because people who comprehend the meaning of E=mc^2 understand that 'mass' is rightfully used interchangeably with the term 'matter' when the main context of the discussion revolves around 'matter', and those people would not make the mistake of confusing matter and mass-energy. The term 'decay' is employed above because it more clearly demonstrates the final state that the universe will take, which is a state wherein entropy has increased to a maximum, whereby the totality of invariant mass contained in all matter has been reduced to energy, whereby all particle production has ceased, and whereby this state will become eternal unless the total energy contained in the universe allows it to contract given the radius it will have at the point of total matter-->energy conversion.

    >> there will be no gravity left to curve spacetime.
    >Since when does energy density not have gravitational effects?

    Don't quite understand that one. Maybe you meant to ask, 'since when does a gravitational field not have an energy density'?

    And since when was there a quantum theory of gravity?

    Regardless, I'll answer your 'question'. At the precise and potentially discontinuous time (discontinuous in the case the universe is allowed to contract when it reaches the expansion/contraction interface radius), when all matter has been transformed to energy such that the total rest mass of the universe is zero (i.e. total mass of particles which are _allowed_ to be put at rest so that they can have their mass measured in the first place), such that spacetime has its metric converted to a form equipped with a tensor which does not provide for the curvature which is necessary for gravity to arise.

    > there is ample evidence the big bang didn't happen.

    Sorry, I don't speak 'Idiot'. Would you please translate? And if you get a chance to take a break from that, read up a little on the galaxies that exist which are older than the universe itself (where the big-bang necessarily defines a time zero). But that's only if you have the energy to translate all that text you need to read from English into your native tongue of Idiot.

    >> I guarantee that either the Higgs particle is not found, or if it is found it is not the 'higgs' particle
    > You better buy a toaster for this guarantee. You will need it.

    Now, why did you truncate the most important part of my quote? I was conveying that if 'a' particle is found, it won't possess the function that the higgs boson is theorized to have.

    >Do you even know what a complex number is?

    Yes, I think I can maybe remember if I try real hard?? Do you even know the most basic principles geometry, let alone general relativity?

    You know, I can be just as rude as you, if not more. And I'll fire back harder than you'll ever be able to fire in the first place. But if your method is to demean and ridicule people who have a different opinion than yours, or a level of intelligence that you incorrectly "perceive" to be lower than your "high-functioning" level, then that's your choice and your problem. But for the record, I ain't playin' that game with you.


    In dense aether model the universe is steady state and infinite and the red shift is a product of light scattering with density fluctuations of vacuum. The galaxies are condensing and evaporating randomly in this model like giant fluctuations of dense gas. The vacuum fluctuations are independent on gravitational field created with massive objects, until space-time exists at long distance scale, this noise must exist too at the small scale. You may consider Mach principle in this regard: the bucket filled with water will "recognize" its rotation in the Universe even without any massive objects in its neighbourhood.

    Already a century long, an equivalent of a Higgs field is hidden in the Dirac equation. It is hidden because the alpha, beta and gamma matrices together with the spinors hide that this equation in fact stands for a pair of quaternionic balance equations. This insight can be obtained in two steps. First the complex quantum state function must be extended to a quaternionic quantum state function. The basic functionality of the quantum state function as a probability amplitude distribution stays the same. However, the extension introduces the real part as a "charge" density distribution and the imaginary part as a "current"density distribution. The second step concerns the conversion of the spinors into pairs of quaternionic probability amplitude distributions (QPAD's). Now the equation for the electron runs as:

    ∇ψ = m φ

    Here ∇ is the quaternionic nabla. ψ is the quantum state function of the particle. m is the coupling factor. m φ is the source term. ∇ψ is the corresponding drain.

    It is a full quaternionic balance equation. Usually only the real part is taken as a balance equation. The Dirac equation also covers the imaginary part.
    The source part φ can be interpreted as a QPAD that consists of the local superposition of the tails of the quantum state functions of distant particles. In that way it acts as an anchor that couples the quantum state function of the electron to all particles that exist in universe. This coupling establishes inertia. The principle of this coupling is treated in "The origin of inertia" by Denis Sciama
    The factor m can be computed by multiplying both sides of the equation with the conjugate of φ and then taking the integral over the whole universe.
    According to this view the QPAD φ has the functionality of the Higgs field.
    See the manuscript at: for more details.
    If you think, think twice
    Hi Tommaso,

    Thank's for clarifying particle self-coupling in the Standard Model.

    Joe P.

    ""0+" in the standard model, much like the blood type of most of us" -- NO,
    the universal donor, not the majority blood type unless you are Hispanic. See
    percentages at


    the page you link shows that indeed, O+ is the most common blood type of all,
    regardless of ethnicity. It is not the majority, though, so what I wrote is not
    perfectly accurate either...


    I am a bit confused on the terminology. Strike that -- I'm very confused on the terminology.
    The 'mexican hat' potential, which it often used to illustrate what is the spontaneous symmetry breaking of the ground state --- is this potential the "higgs field", and then the low energy field excitations in this potential are the "higgs bosons"? And is the shape of this potential the higgs "self-coupling"?

    How are all these concepts related, and what precisely are the potential vs. field vs. non-zero vacuum expectation of the field vs the actual higgs bosons being measured, etc?

    Isn't the form of the potential already affect the non-zero vacuum expectation, and thus do we really need a direct higgs boson to measure this? And why do we need two-higgs to see the self-coupling? Can't the self-coupling be seen with the interaction of a higgs-boson with the non-zero vacuum expectation?

    For an essentially beginner physics student, I can never keep straight what the particle physicists mean by all these terms they seem to use interchangeable because of an (unrealistic in my opinion) hope that we can tell what they mean from the context what was actually meant.

    I'd appreciate it very much if you could help clarify all this for me and others.

    Hi CR,

    the self coupling of course affects the phenomenology of the particle, but the only way
    to measure it directly is by observing the diagram on the right in the post above, or
    similar ones.

    To really understand where that arises from, you need to look at the electroweak
    lagrangian and then apply the choice of vacuum, breaking the symmetry, and developing
    the product of terms - you will get h^3 and h^4 expressions in the new lagrangian.
    These are responsible for three- and four-particle vertices. I have no simpler way
    to explain this unfortunately... It requires the math.

    One imagines that a year or two more of LHC data would greatly refine both the predicted background and the predicted SM Higgs coupling event predictions, allowing analysis of older LHC combined with new LHC looking for evidence of a Higgs self-coupling to be conducted with greater power. For example, Higgs branching fractions appear to be quite sensitive to the Higgs boson mass even within a 123 GeV-127 GeV range, so pinning this and other details down could reduce the uncertainty in everything else and increase the significance of any detections of Higgs self-couplings. One also ought to be able to reduce systemic error as well as theoretical error at LHC by the tail end of the run through calibration of the results to date against theoretical benchmarks.

    There oughts to be something on the order of 600,000+ Higgs events when the LHC is finished with its initial planned run, so getting a statistically significant result (even if it is not a 5 sigma result) once the parameters are tightened up on the SM v. non-SM hypothesis seems fairly doable. And, even a mere 2-3 sigma confirmation of a SM result is probably still good enough to rule out of lot of BSM theories to a much higher level of significance and with pretty narrow error bars.

    to get a better feeling for sigmas, could you answer a question: when the W boson (or the Z boson) was discovered in the 1980s, roughly how many sigma did the data show at the time?

    Hi Clara,

    I am afraid I do not know the answer to that question; it might even be that the number of standard deviations was not quantified. I know that when Rubbia made his announcement he only had a handful of W events; however, they were very clean and backgrounds were very small to non-existent.

    In the old days, one event could make a discovery: if you have zero background, one event has infinite significance in principle... The Omega minus, for instance, is a clear example: one event was sufficient to discover it (back in 1964).



    thank you. Your answer suggests that the sigma number required/common for a discovery was much higher in the past. Why then do we only ask for 5 sigma now?

    Hmmm, no - you got it backwards. The fact that in old bubble chamber experiments backgrounds were non-existent does not mean that the threshold was higher. Indeed, many particles have been claimed and then found to be flukes in the sixties and seventies, and less so from the eighties onwards. Notable exception, the top quark by Rubbia and Denegri in 1984 (curious thing, the anniversary of the false announcement is July 4th, again a Main Auditorium CERN announcement as the one in two days).

    5 sigma are not "only" - they are a pretty tough level to reach for a signal. I thnk it would be much more sensible to go down to 4 sigma once one has corrected for the look-elsewhere effect, in fact, and I have been trying to converge on that in common meetings of the ATLAS and CMS statistics committees. But twenty intelligent physicists will have about 20 different opinions on such matters ;-)

    Don't rule out the idea of a muon collider as the successor to the LHC.