The Higgs Comes Out of its Shell

Title : “First evidence for off-shell production of the Higgs boson and measurement of its width”

Authors : The CMS Collaboration

Link :

CMS Analysis Summary :

If you’ve met a particle physicist in the past decade, they’ve almost certainly told you about the Higgs boson. Since its discovery in 2012, physicists have been busy measuring as many of its properties as the ATLAS and CMS datasets will allow, including its couplings to other particles (e.g. bottom quarks or muons) and how it gets produced at the LHC. Any deviations from the standard model (SM) predictions might signal new physics, so people are understandably very eager to learn as much as possible about the Higgs.

Amidst all the talk of Yukawa couplings and decay modes, it might occur to you to ask a seemingly simpler question: what is the Higgs boson’s lifetime? This turns out to be very difficult to measure, and it was only recently — nearly 10 years after the Higgs discovery — that the CMS experiment released the first measurement of its lifetime.

The difficulty lies in the Higgs’ extremely short lifetime, predicted by the standard model to be around 10⁻²² seconds. This is far shorter than anything we could hope to measure directly, so physicists instead measured a related quantity: its width. According to the Heiseinberg uncertainty principle, short-lived particles can have significant uncertainty in their energy. This means that whenever we produce a Higgs boson at the LHC and reconstruct its mass from its decay products, we’ll measure a slightly different mass each time. If you make a histogram of these measurements, its shape looks like a Breit-Wigner distribution (Fig. 1) peaked at the nominal mass and with a characteristic width .

Fig. 1: A Breit-Wigner curve, which describes the distribution of masses that a particle takes on when it’s produced at the LHC. The peak sits at the particle’s nominal mass, and production within the width is most common (“on-shell”). The long tails allow for rare production far from the peak (“off-shell”).

So, the measurement should be easy, right? Just measure a bunch of Higgs decays, make a histogram of the mass, and run a fit! Unfortunately, things don’t work out this way. A particle’s width and lifetime are inversely proportional, meaning an extremely short-lived particle will have a large width and vice-versa. For particles like the Z boson — which lives for about 10⁻²⁵ seconds — we can simply extract its width from its mass spectrum. The Higgs, however, sits in a sweet spot of experimental evasion: its lifetime is too short to measure, and the corresponding width (about 4 MeV) cannot be resolved by our detectors, whose resolution is limited to roughly 1 GeV.

To overcome this difficulty, physicists relied on another quantum mechanical quirk: “off-shell” Higgs production. Most of the time, a Higgs is produced on-shell, meaning its reconstructed mass will be close to the Breit-Wigner peak. In rare cases, however, it can be produced with a mass very far away from its nominal mass (off-shell) and undergo decays that are otherwise energetically forbidden. Off-shell production is incredibly rare, but if you can manage to measure the ratio of off-shell to on-shell production rates, you can deduce the Higgs width!

Have we just replaced one problem (a too-short lifetime) with another one (rare off-shell production)? Thankfully, the Breit-Wigner distribution saves the day once again. The CMS analysis focused on a Higgs decaying to a pair of Z bosons (Fig. 2, left), one of which must be produced off-shell (the Higgs mass is 125 GeV, whereas each Z is 91 GeV). The Z bosons have a Breit-Wigner peak of their own, however, which enhances the production rate of very off-shell Higgs bosons that can decay to a pair of on-shell Zs. The enhancement means that roughly 10% of H → ZZ decays are expected to involve an off-shell Higgs, which is a large enough fraction to measure with the present-day CMS dataset!

Fig. 2: The signal process involving a Higgs decay to Z bosons (left), and background ZZ production without the Higgs (right)

To measure the off-shell H → ZZ rate, physicists looked at events where one Z boson decays to a pair of leptons and the other to a pair of neutrinos. The neutrinos escape the detector without depositing any energy, generating a large missing transverse momentum which helps identify candidate Higgs events. Using the missing momentum as a proxy for the neutrinos’ momentum, they reconstruct a “transverse mass” for the off-shell Higgs boson. By comparing the observed transverse mass spectrum to the expected “continuum background” (Z boson pairs produced via other mechanisms, e.g. Fig. 2, right) and signal rate, they are able to extract the off-shell production rate.

After a heavy load of sophisticated statistical analysis, the authors found that off-shell Higgs production happened at a rate consistent with SM predictions (Fig. 3). Using these off-shell events, they measured the Higgs width to be 3.2 (+2.4, -1.7) MeV, again consistent with the expectation of 4.1 MeV and a marked improvement upon the previously measured limit of 9.2 MeV.

Fig. 3: The best-fit “signal strength” parameters for off-shell Higgs production in two different modes: gluon fusion (x-axis, shown also in the leftmost Feynman diagram above) and associated production with a vector boson (y-axis). Signal strength measures how often a process occurs relative to the SM expectation, and a value of 1 means that it occurs at the rate predicted by the SM. In this case, the SM prediction (X) is within one standard deviation of the best fit signal strength (diamond).

Unfortunately, this result doesn’t hint at any new physics in the Higgs sector. It does, however, mark a significant step forward into the era of precision Higgs physics at ATLAS and CMS. With a mountain of data at our fingertips — and much more data to come in the next decade — we’ll soon find out what else the Higgs has to teach us.

Read More

“Life of the Higgs Boson” – Coverage of this result from the CMS Collaboration

“Most Particles Decay — But Why?” – An interesting article by Matt Strassler explaining why (some) particles decay

“The Physics Still Hiding in the Higgs Boson” – A Quanta article on what we can learn about new physics by measuring Higgs properties

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