This video is brought to you by Wondrium. Stay tuned for a special offer for Arvin Ash
viewers. In April, 2022 a big announcement in physics
was made. The mass of the W-boson was measured to a new level of precision.
But this mass was not what the standard model of particle physics predicts. It appears that
our best theory of the way the universe works has failed!
Researchers at Fermilab showed the W-boson mass to be 80.4335 giga electron volts or
GeV plus or minus 0.0094 GeV. It’s the most precise result ever. However,
the predicted mass of the W boson from the equations of the standard model is 80.357
plus or minus 0.006 GeV. Now you might say, what’s the big deal the
measured mass is only 0.1 GeV off. That’s less than a 0.3% difference?
This difference may seem small, but the new measurement is about 7 sigma off the standard
model prediction. Typically in particle physics, anything that is off by 5 sigma or more is
considered a new discovery. So, this difference is way beyond that threshold and is quite
significant. So what the heck is going on? What does the
W-boson do? What difference does this measurement make? And how does it change our view of reality?
That’s coming up right now…
The W boson plays a key role in our understanding of the universe. Together with the Z-boson
it mediates the weak force, which is one of 3 fundamental forces described by the standard
model. It’s a rather heavy particle being about
80 times the mass of the proton which has a mass of about 1 GeV.
This boson is behind the decay of neutrons to protons, and protons to neutrons.
This process is not only important for the stability of large atoms, it is also essential
to how the sun works, and it’s involved in how atoms decay.
The weak nuclear force might not visibly impact our everyday lives like gravity and electromagnetism
does, but without the weak force, countless important nuclear processes wouldn’t
be allowed, and the universe would be completely different. Life would not exist without it.
The problem is that the Fermilab result is not compatible with the standard model, which
is considered our best understanding of how the universe works, and which up until now
has been very accurate in making predictions. So to understand why this is huge, let’s
look more closely at the standard model and in particular the electroweak theory, which
is a key component of this model. The electroweak theory is essential for several
reasons. First, it’s a theory that unites two fundamental forces, the weak nuclear force
and electromagnetism. It tells us how these two forces arise from a single unified force,
and it tells us how this force works. The Higgs field plays a critical role in making
electroweak theory work, because it is responsible for giving mass to the bosons which carry
the weak force. Those bosons are the W and Z bosons. The Higgs boson is an excitation
in the Higgs field. It so happens that the weak force interacts
with all the matter particles of the standard model. So any modification to the standard
model based on new findings, would affect the parameters of electroweak theory. In fact
if anything is wrong with the standard model, it will likely manifest itself in the electroweak
part of the standard model. So let’s look at the electroweak theory
to understand what the new measurement of the W boson means.
Skipping a lot of unimportant math, the electroweak theory specifies a relationship between the
Z and W bosons. The theory doesn’t exactly state what the
mass of these particles should be, but it gives a relationship which must be respected.
That relationship is the following: Where m_W is the mass of the W boson, m_Z
is the mass of the Z boson and theta is called the Weinberg angle. All three parameters including
the Weinberg angle are measured values. The mass of the Z particle and Weinberg angle
are easier to measure than mass of the W particle, so typically scientists measure the mass of
the Z, and theta, and then derive a predicted value for the mass of the W particle from
that. The problem with the new results is that it
is a very precise measurement of Mw, which does not correspond to what it should be based
on the measured values of Mz and Cos(theta). This presents a problem because it appears
to violate the prediction from electroweak theory, which is a critical part of the standard
model. And because until now, the standard model has made so many incredibly
accurate predictions, this new measurement puts a monkey wrench into the situation, because
it calls into question our understanding of the Standard model.
When the W mass was initially calculated based on the standard model, the mass was too low.
The issue is that the mass of all massive particles is affected by the mass of other
particles. These are called quantum corrections. So for example, the W boson is affected by
quantum corrections from its interaction with other particles, like the top quark and the
Higgs boson. These quantum corrections can be expressed in the following equation:
Again, M sub w is the mass of the W boson. m superscript naught is the mass without quantum
corrections, and then we add corrections which depend on
the mass of the top quark and the Higgs boson, two of the heaviest particles in the standard
model. There are also some constants a and b in front
of these terms. There are also more corrections, but these
are the main ones. You might ask why is a mass of one particle
affected by the mass of other particles? This is because at the quantum level, all particles
are excitations in fields. This is the basis of quantum field theory.
The magnitude of these excitations in the field is what we perceive as mass.
And any given field affects other fields. This is why the mass of fundamental particles
is affected by the mass of other particles. In terms of Feynman diagrams these correction
terms can be illustrated as follows, where we see the top-bottom quark contribution,
but since the bottom quark is much lighter it’s not significant. We also see the correction
from the Higgs field, and again there are more terms, but they are less important.
By taking these corrections into account this ratio between the Z and W boson matched the
standard model prediction rather precisely. And over decades of W-boson mass measurements,
they have all been within the standard model prediction after taking the error bar or uncertainty
into account…until now. This new result has an unprecedented low combined uncertainty,
so in this case the statistical uncertainties cannot make up for the deviation.
So, what does this mean? There are three possible explanations:
1. The math is wrong. 2. The experiment or analysis is flawed.
3. There is some new unknown physics that affects the mass.
If we look at the first option. Maybe the way we calculate the mass is wrong.
Since the mass of the Higgs and top quark affect the mass of the W boson, could those
values of mass be inaccurate? Well, the masses of the Higgs and top quark
is also measured quite precisely. And we have a pretty good understanding of how to calculate
the W-mass from the standard model, so this prediction is pretty solid.
We can thus be pretty sure, that the predicted mass from the standard model is not the issue.
The second option is that the experiment, or the data analysis is somehow flawed, maybe
by some systemic error. This is more likely than a math error.
The strange thing is that the new result is based on 10-year-old data.
The Fermilab collaboration however argues that this is due to their very careful analysis.
Initially the result seems credible, but now that the result is published, other
scientists will be able to scrutinize the methodology and analysis. So if there is a
mistake someone will find it. Another strange thing is that the previous
results from the same Fermilab collaboration have also not matched the standard model prediction,
but the earlier results had such high error bars that it wasn’t considered an issue.
On the other hand, measurements done at CERN, which is a competitor to Fermilab, more or
less matches the standard model prediction. The Large Hadron Collider could possibly improve
the precision of the Fermilab results, so it would be interesting to see if they independently
obtain the same result as Fermilab or whether it differs.
The current best results from CERN agrees with the standard model but not with the new
measurement from Fermilab, but the CERN results have a higher claimed uncertainty compared
to these new results, so they are not as precise. If in upcoming analyses, CERN reproduces the
new result from Fermilab, then this would leave us with just the last option - new physics.
This could be the most exciting solution. We know that the Standard model is not the
final theory. So this new result could guide us to a new and better theory that could also
fix other problems with the model such as the fact that it doesn’t explain dark matter
and dark energy. Now recall that in electroweak theory things
all depend on each other, and thus in order to measure the W boson, the Fermilab collaboration
have also measured the Z boson in the process. But they find that the Z boson mass is exactly
as expected, it’s only the W mass that is too heavy. The Z mass is right on point.
And again, because the different parameters of the electroweak theory all depend on each
other, it could be that the problem is actually not with the W boson.
Maybe it is supposed to be heavier, but there is a problem with our understanding of the
top quark, Higgs, or Z boson, but we have just happened to have seen the manifestation
of a different problem via the W boson measurement. At the end of the day, it’s just a lot of
different ratios that have to match, not specific values.
If the problem is with the W boson, it could be that there are some further quantum corrections
beyond the standard model that we didn’t take into account.
It could be that some new particle or maybe a dark matter particle is actually also interacting
with the W boson. And this interaction leads to further quantum
corrections to the W mass. So there could be other significant terms in the equation
I showed earlier, pushing the W mass up to the new measured value.
The LHC as of April, 2022 is actually starting up again after a long break when it has been
undergoing many upgrades. So it will start looking for new physics very soon to test
the standard model more rigorously than ever with better detection capability.
I think we shouldn’t jump to conclusions because this new measurement of the W boson
could just be a fluke. But I also think that we might be heading
towards a new and exciting area of particle physics as more and more cracks appear in
our tried and true standard model. So the current and next generation of particle
physicists have a lot of exciting areas to work on. There is no doubt that new discoveries
are waiting to be made which’ll bring us closer to understanding the vast universe
we live in. If you want to go much further into the details
of electroweak theory as well as the standard model,
there’s a fantastic college-level course available on Wondrium, today’s sponsor called,
“The theory of everything: the quest to explain all reality.”
It’s a 24 part course taught by one of my favorite educators, Don Lincoln of Fermilab.
This course gets into just about every subject I’m most interested in.
Don explains everything from fundamental particles and forces, to gravity, to dark matter, dark
energy the big bang, and how they all fit into a potential theory of everything.
You’ll find many other great lecturers like Don Lincoln on Wondrium which has some of
the best educators in the world, and that’s why I have been a member of Wondrium for a
long time. I could not recommend them more. My testimonial is at the bottom of Wondrium’s
home page. It’s really easy to sign up because they are offering a free trial, and you can
cancel at anytime, so you have nothing to lose, and a whole lot to gain.
If you want in-depth knowledge about all the things I talked about in this video, then
be sure to click the special link in the description to take advantage of the free offer. That
link is Wondrium dot com slash arvin. That’s wondrium.com/arvin. And you’ll be supporting
this channel when you sign up. So I really thank you for that.
And if you enjoy content like this, then be sure to hit the subscribe button so you can
be informed the minute I post a new video. And I’d love to hear your comments or questions,
so please leave them in the comment section. I’ll see you in the next video my friend.