Fingerprinting the Higgs

This blog post title stolen from Christophe Grojean and his collaborators.

With Thursday's mammoth Angband post finally finished, I figure it might be a good time to talk about physics instead.  And what better thing to talk about than what the theory community has been up to in the last three and a half weeks?  Yes, as expected there have been an abundance of Higgs-related papers of varying quality since the discovery announcement back on the 4th.  Thankfully, since many of them tread over similar ground I can cover multiple papers at once!

Ambulance Chasing

The basic question is: is this thing we've found the Standard Model Higgs?  To understand the nature of this question, we need to go back to 2009, just before the LHC was due to turn on for the second time.  At that point, we knew a lot about the Standard Model.  We had found all the particles except the Higgs, including finding the predicted W and Z bosons and top quark.  Given that knowledge, the Standard Model Higgs was a very predictive theory in the following sense: all the phenomenology of the Higgs depended on only a single unknown, the Higgs mass.


This fact was used by the experimental collaborations to aid in their searches, both initially to rule out certain possible masses for the Higgs, and then in their discovery.  Contrast that with, for example, searches for Supersymmetry.  There are so many unknowns in SUSY that it is difficult to rule it out.  The experiments at the LHC presented nice exclusion bounds based on not seeing any signal, only for theorists to turn around and point out regions of parameter space not bound by those observations.  (In fairness, it's worth pointing out that the experimentalists began by looking at the parameters that theorists had talked about the most.)  SUSY, with over a hundred new parameters, is a bit of a perverse case, but most extensions of the Standard Model suffer from this type of problem.


So to return to the Higgs, now that we have a mass we know what all its interactions should be.  Thus by measuring those interactions we can test our hypothesis.  What is particularly exciting is that if any of those interactions does differ from the prediction, it implies the existence of further new physics to discover.


This program of measurement is a long term goal, that will require the experimental collaborations to carefully push their machines to the limit.  It will probably demand a specialised collider, a Higgs Factory, built to resonantly produce the Higgs and get better than percent-level accuracy.  So why are theorists writing papers about it?  Well, if lawyers are ambulance-chasers, theorists are citation-chasers.  They who publish first will get lots of citations, even if what is published is crap.


The basic idea of all these papers was to make some assumptions about how our putative Higgs might differ from the Standard Model, and then use the limited data we currently have to constrain those differences.  Despite my snarky tone, I do think this is useful, since it helps us prepare for possible future experimental results and see what types of new physics are preferred by the data.  The only danger is that of drawing too many conclusions from the currently data, which is limited and has large uncertainties.

The Data

Before considering the theoretical models that people have looked at, it's worth reviewing the actual data we have.  The Higgs, of course, is far too short-lived to be directly seen; rather, what is observed are its decay products and other things produced alongside the Higgs.  In particular, there are two main ways that the Higgs is produced at the LHC.  In one, you do not typically expect anything interesting alongside the Higgs; but in the other you expect two roughly jets of hadronic particles, roughly back-to-back and close to the beam.


The actual observation is some number of events in each of the different possible final states: each different possible decay mode, and the presence or absence of extra stuff.  These numbers by themselves are not too helpful, so experimentalists normally present a quantity called the cross section, which is roughly the probability for each different process to occur.

The Models

With the data outlined, let's talk about the theory.  While there have been several different approaches, the most common idea is to introduce new parameters determining the strength of the Higgs couplings.  When those parameters equal one, the interaction has the Standard Model strength; for other values the interaction is stronger or weaker as appropriate.  The main difference between papers is what relations are imposed a priori among those parameters.


The simplest useful possibility was done by John Ellis and Tevong You, almost immediately after the initial announcement.  They reduced the additional parameters to only two: one giving the strength of the Higgs coupling to the W and Z bosons, and the other the coupling to the Standard Model fermions (the various quarks, plus the electron, muon and tau).  The extremely important couplings of the Higgs to two photons and to two gluons are not varied separately.  Instead they are assumed to be generated in the same way as in the Standard Model, through higher order corrections involving intermediate tops and Ws.  Changing the Higgs-top and Higgs-W interaction strengths then indirectly changes the Higgs-photon and Higgs-gluon couplings.


Their main result is as follows:

In this plot, the horizontal axis (a) is the Higgs-W coupling, and the vertical axis (c) the Higgs-fermion. The light regions are preferred by the data, and we see that the Standard Model is included.  The yellow lines correspond to various more complete theories that have been advanced; the fermiphobic Higgs, that only couples to the W and Z, is disfavoured while theories where the Higgs is a composite object remain allowed.


A more general study was done by Dean Carmi and collaborators.  They allowed almost all the Higgs couplings to very independently; the only exception was that they imposed the Higgs couplings to W and Z be equal.  This is preferred by precise measurements of the two gauge boson masses.  Another extension was the inclusion of a possible invisible Higgs decay; that is, events where the Higgs would be produced but would decay to some other new particle that is not seen.  Invisible decays can only be constrained indirectly; their existence would lower the number of visible events.

With a much larger parameter space, it is no longer possible to show what is allowed and forbidden as easily, so their plots show only sections of parameter space:

A selection of results from Carmi et al.  Each plot fixes some set of Higgs couplings and  shows for the couplings allowed to vary which regions are preferred by the data.  The green regions correspond to including all data, the other regions to only accounting for the listed process.

These plots are also nice because they break down which channels are giving what constraints.  As before, we see two preferred regions, thanks to an insensitivity to the sign of the couplings.  Also, not shown here is the upper limit on the invisible width; less than 20% of Higgses decay unseen.


As noted, the previous work assumed equal Higgs couplings to the W and Z.  It should come as no surprise that someone extended that; those someones were Shankha Banerjee et al.  Apart from that, their work and findings agree with pretty much everyone else.  They do find a small preference for a stronger coupling of the Higgs to the Z than the W, but at this point it's hardly compelling.

The Higgs-W and Higgs-Z coupling strengths on the horizontal and vertical axes respectively.  The intersection of the dotted lines marks the Standard Model; the red cross the best fit point; and the blue and red regions are preferred.

Finally, I want to mention the work of Dan Hooper and Matt Buckley.  Their paper, which also came out very soon after the original announcement, does something different to the above.  It claims that the data is inconsistent with the Standard Model.  The money plot is this one:

The preferred regions for the Higgs-photon and Higgs-gluon couplings, on the vertical and horizontal axes  respectively. The intersection of the dashed lines marks the Standard Model, while the cross is the best fit to the data.

The closed loops correspond to the best-fit regions at various confidence levels, and the Standard Model is outside the 99% contour.  To get this, they only vary the Higgs-photon and Higgs-gluon couplings.  This is a reasonable approach for two reasons.  Theoretically, in the Standard Model these couplings arise from higher order effects, and so they are more vulnerable to the effects of new physics; and Matt and Dan tested varying other couplings, and it did not noticeably improve their fit.

They suggest that this might be a hint for the existence of new particles, which would have to be relatively light to have this effect.  However, as much as I respect these two I think they are engaging in wishful thinking here.  I find it hard to give their results credence when most of the data is within one or two standard deviations from the Standard Model, and when almost everyone else finds consistency.

Concluding Comments

So, what does all this tell us?  The newly discovered particle does look quite a bit like the Standard Model Higgs.  In particular, it's couplings to the gauge bosons is right in line with what we would expect, and remember that that interaction underpins the Higgs's raison d'etre.  It looks most likely that we have an essentially Standard Model Higgs, but one with different photon and gluon couplings due to the presence of something else.  And that something else could be a lot of fun.