higgs rain model It is understood that the vacuum is the state with minimum energy, otherwise the extra energy could be used to create a particle, and the state would cease to be vacuum. The vacuum expectation value of the Higgs field h i = v is the crucial quantity that gives mass to the gauge boson Aμ, as we will see.

2. Why the Higgs Field is Non-Zero on Average | Of ...

profmattstrassler.com/...higgs-field.../2-why-the-higgs-field-is-non-zero-...

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Oct 14, 2012 - (Bottom Right) A non-zero value for the Higgs field does not change the ... where a and b are constants (whose squares are positive! notice the plus ..... of why the Higgs vev (vacuum expectation value) has the particular value ...

[PDF]Physics of Higgs Bosons - UW High Energy Physics

www.hep.wisc.edu/~sheaff/.../Higgs.p...

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University of Wisconsin‑Madison

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Mar 8, 2012 - expectation value of the Higgs field 〈Φ〉 = v is the crucial quantity that gives mass to ... 2: Higgs potential in the complex plane of the Higgs field.

The lagrangian is taken as,
L =

(∂μ − iqAμ) †

[(∂μ + iqAμ) ] −
1
4
FμνFμν − V
􀀀
†

(2)
where Aμ is the gauge field, with Fμν = ∂μAν − ∂νAμ and
Aμ −→ A′μ = Aμ + ∂μθ (3)
is the U(1) transformation of the gauge field. For the Higgs potential we take,
V
􀀀
†

= μ2 † + λ
􀀀
†
2 (4)
where μ2 has units of mass squared and λ is a dimensionless parameter that accounts for the
quartic Higgs self interaction. The Higgs potential is shown in Fig. 1 for two different values of
the sign of μ2.
It is understood that the vacuum is the state with minimum energy, otherwise the extra energy
could be used to create a particle, and the state would cease to be vacuum. The vacuum
expectation value of the Higgs field h i = v is the crucial quantity that gives mass to the gauge
boson Aμ, as we will see. Therefore, the situation μ2 > 0 at the left of Fig. 1 is not useful, and
we need a non zero value for v, thus
μ2 < 0 (5)
In fact, the Higgs field is complex, thus the minimum of the Higgs potential is a circle in this
complex plane, as indicated in Fig. 2. This vev though can always be chosen as real because
gauge invariance allow us to choose a gauge where ′ = exp(−iqθ) is real. Since the vev is
not gauge invariant, it is said that the gauge symmetry has been spontaneously broken.



--------------

The Higgs field is like rain, and there is no place you can go to keep dry. Just like there’s no way to shield yourself from gravitation, there’s no way to hide from the rain that is the Higgs field.
If there were no Higgs field, all the fundamental particles would be like dried-out sponges. Massless, dried-out sponges.

How the Higgs gives Mass to the Universe

Posted by Ethan on July 4, 2012

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Higgs Event

“This is evidently a discovery of a new particle. If anybody claims otherwise you can tell them they have lost connection with reality.” -Tommaso Dorigo

You’ve probably heard the news by now: the Higgs boson — the last undiscovered fundamental particle of nature — has been found.

The fundamental types of particles in the Universe, now complete.

Indeed the news reports just keep rolling in; this is easily the discovery of the century for physics, so far. I’m not here to recap the scientific discovery itself; I wrote what to expect yesterday, and that prediction was pretty much exactly what happened, with CMS announcing a 4.9-σ discovery and ATLAS announcing a 5.0-σ discovery, of a Higgs boson at 125-126 GeV. You can watch a recording of the press conference announcing the official discovery here, and all observing scientists were thoroughly convinced of both the quality and veracity of the work.

Screenshot from the original, live webcast of the seminars leading up to the presentation. Taken at the moment the CMS team first said the words "5-sigma," long known as the gold standard for discovery in the field.

So, the Higgs boson has been discovered! That’s good news. You may have also heard that the Higgs gives mass to everything in the Universe, and that it’s a field.
The odd thing is that all of these things are true, if not intuitive. There are some attempts to explain it simply, but as you can see, even the top ones are not very clear. So let’s give you something to sink your teeth into: How do fundamental particles, including the Higgs boson, get their mass?

Image credit: Highway Man of WhiteBlaze.net.

The Higgs field is like rain, and there is no place you can go to keep dry. Just like there’s no way to shield yourself from gravitation, there’s no way to hide from the rain that is the Higgs field.
If there were no Higgs field, all the fundamental particles would be like dried-out sponges. Massless, dried-out sponges.

You have to use your imagination, if only slightly, for the massless part.

But you can’t keep these sponges out of the rain, and when you can’t stop them from getting wet, they carry that water with them. Some sponges can only carry a little bit of water, while others can expand to many times their original size, carrying very large amounts of water with them once they’re fully expanded.

Image credit: GNI Phoenix International, via DIYTrade.com.

The most massive fundamental particles are the ones that couple most strongly to the Higgs field, and are like the sponges that expand the most and hold the most water in the rain. Of all the particles I’ve shown you, atop, there are just two that are truly massless, and hence don’t couple to the Higgs at all: the photon and the gluon.
They can be represented by massless sponges, too, except they are water repellent.

Image credit: CETEX Water Repellent, from Waltar Enterprises; photo by © Gregory Alan Dunbar.

So, the Higgs field is rain, all the particles are like various types of sponges (with various absorbancies), and then… then there’s the Higgs Boson. How can the field — the rain — be a particle, too?

Image credit: stockmedia.cc / stockarch.com.

If it weren’t raining — if there were no source of water — your intended water balloon would be a sad failure. If there were no Higgs field, there wouldn’t be a Higgs boson; at least, not one of any interest, and not one with any mass.
But the water comes from the Higgs field, and it also fills the balloon that is the Higgs boson: the Higgs field gives mass to all the particles that couple to the Higgs field, including the Higgs boson itself!

Image credit: Laura Williams from SheKnows.com.

Without the water, the balloons and the sponges would be far less interesting, and without the Higgs field, the Higgs boson and all the other fundamental particles would have no intrinsic mass to them.

"I've found the Higgs boson! And I'm very, very wet!"

So now you not only know that we’ve found the Higgs Boson, but how the Higgs field gives mass to all the particles in the Universe, including the newly-discovered boson itself. Just like water can seep its way into almost anything, making it heavier, the Higgs field couples to almost all types of fundamental particles — some more than others — giving them mass.
And the great new find? We’ve been able to create and detect enough Higgs Bosons at the Large Hadron Collider to confidently announce — for the first time — that we’ve discovered it, that we’ve determined its mass (around 133 times the mass of a proton), and that it agrees perfectly with what our understanding of the Universe currently is.

Image credit: A Higgs creation, decay and detection event, courtesy of CERN.

Like I told you yesterday, keep up with the latest Particle Physics news here, and if you want to see/hear me on TV talking about the discovery of the Higgs in all its glory, you get to, tonight!
I’ll be talking about the discovery of the Higgs Boson at CERN later today, July 4th, at 7PM (Pacific Time) live on Portland, OR’s own KGW NewsChannel 8 on The Square: Live @ 7! If you missed my last appearance on the show, talking about the Higgs, you can watch it anytime.

But if you want to catch tonight’s show? Tune in to channel 8 if you’re in Portland, otherwise you can watch the live stream from anywhere in the world at 7PM Pacific at this link. See you then, and enjoy your Higgs-Discovery/Independence Day!