The vacuum energy v. Higgs field - discrepancy

[Mordred]

Well at least Chatgp got that part correct as that's precisely what it's used for. The VeV is used in a similar manner just an fyi

Edited April 27 by Mordred

[chron44]

 

Concerning the VeV ("constant"), can one define this 246 GeV amount as some type of needed
minimum "transition" energy when particles are about to acquire its intrinsic mass?

(Probably not that simple, but in an elementary manner?)

[Mordred]

It's a workable descriptive not completely accurate but sufficient for a layman understanding.  Getting into the renormalization aspects would be a bit too advanced it's sufficient to accept that it's a renormalized value.

Edited April 27 by Mordred

[chron44]

I'm further taking deal of.
The Fermi constant plays a crucial role in describing weak interactions. (W and Z boson actions.)

Where electroweak force and the Higgs mechanism are intimately connected within the framework
of the Standard Model.

As shown in the formula of the VeV's effecive_action, presented here earlier.

Therefore the Fermi-constant incorporates into this formula.

[Mordred]

Correct now your getting it  +1 on seeing that connection 

Edited April 27 by Mordred

[chron44]

Uhu.. even a layman in physics may sufficiently grasp somewhat of the Higgs mechanism
with fair and relevant instructions.

Thanks.

 

[Mordred]

your welcome glad to help

[chron44]

This what ChatGPT informs about Higgs field and its VeV:

"The VEV of the Higgs field is fixed at approximately 246 GeV in the vacuum state, providing masses to particles that interact with it. Fluctuations in the Higgs field, if present, would generally occur around this fixed VEV, rather than changing the VEV itself. These fluctuations play a role in various quantum field theory phenomena but do not typically alter the fundamental properties of the Higgs field, such as its VEV."

So, to my understanding:

Higgs field and "its" VeV is merely or mostly a field which applies mass. No more essential physical stances or functions can be connected to this field? Though if this is the situation, this function in physics must be seen for very fundamental. Right?

Furthermore, Higgs field have never been observed in "real life conditions" only indicated at the LHC and Atlas. One cannot "see" the field which is providing mass.

Anyone with any ideas of why this is the situation?

Feel free to speculate, though maybe this isn't the right forum at SF?

/chron44

 

Edited April 28 by chron44
adding text

[Mordred]

Are you familiar with spontaneous symmetry breaking and the Mexican hat potential of the Higgs field ?

Yes the VeV can be described as a fundamental property of the Higgs field in so far as it sets the scale where spontaneous symmetry breaking occurs to give the particles it interacts with their mass terms.

At a certain temperature  is when the spontaneous symmetry breaking occurs ( the precise value depends on the model ) however wiki gives the value 159.5 GeV which I for one do not trust. ( the paper wiki used didnt include the U(1) gauge. The value I have commonly seen is roughly 10^15 GeV which make more sense.  Regardless of the temperature value the VeV describes the temperature where spontaneous symmetry breaking (electroweak symmetry breaking)  occurs. At a higher temperature all particles are massless. At that temperature spontaneous symmetry breaking occurs and particles acquire mass.

Here is a link to spontaneous symmetry breaking and it shows the Mexican hat potential

https://en.m.wikipedia.org/wiki/Spontaneous_symmetry_breaking

https://en.wikipedia.org/wiki/Electroweak_interaction

the second link describes the VeV

"above the unification energy, on the order of 246 GeV,^[a] they would merge into a single force. Thus, if the temperature is high enough – approximately 10¹⁵ K – then the electromagnetic force and weak force merge into a combined electroweak force. During the quark epoch (shortly after the Big Bang), the electroweak force split into the electromagnetic and weak force. "

this link has the correct value. I didn't bother including the link with the incorrect value.

Edited April 28 by Mordred

[chron44]

Being a layman, I have seen it on wiki pages, though never really thought about its more precise function. When you mentioned it here I went to the wiki page and tried to "comprehend". 

It's about the electroweak force, the uniting and separating on both forces involved - depending on temperature. And probably you are right when you notice a far higher value than wiki presents.

This is what I notice, for the moment.

Still, I'm a bit confused. Do we need the Big Bang scale at the LHC for to reach the VeV at Higgs field? I mean does the LHC accelerator really copy the BB condition fort to expose the boson and the VeV in question?

Edited April 28 by chron44

[Mordred]

well your on the right path

see section 4

https://cds.cern.ch/record/348154/files/9803257.pdf

"(4) In the unitary gauge, the isodoublet is replaced by the physical Higgs eld ! [0; (v+H)=p 2], which describes the uctuation of the I3 = 1=2 component of the isodoublet eld about the ground-state value v=p 2. The scale v of the electroweak symmetry breaking is xed by the W mass, which in turn can be reexpressed by the Fermi coupling, v = 1=qp 2GF 246 GeV. The quartic coupling and the Yukawa couplings gf can be reexpressed in terms of the physical Higgs mass MH and the fermion mass"

it doesn't copy over well from the document please note this is a pre Higgs discovery paper published prior to confirming the Higgs mass so some of the numbers will be off. but it explains the VeV and how its set.

Edited April 28 by Mordred

[chron44]

 

Have to ponder some days or more for to slightly comprehend...

Edited April 28 by chron44
earlier text not accurate

[Mordred]

This is where we have to be careful. You may recall that the VeV is a probability function correct? That probability function will have a probability current. The term "expectation" value denotes this. So it has a weighted average that is described by the 246 VeV value. The other important detail is the Higgs field isn't just one field it is an SU(2) doublet.

\[\phi=\begin{pmatrix}\phi^+\\\phi^0\end{pmatrix}\]

however these are complex fields

\[\phi^+=\frac{1}{2}(\phi_1+i\phi_2)\]

\[\phi^0=\frac{1}{2}(\phi_3+\phi_4\]

now these two statements describe rotations ( matrix, tensor operations) simply put. Yes those two equations do form a matrix but we can ignore that for now.

now fermions have a few properties the Higgs mediates with each has a mass contribution

the Higgs relation to charge Q, weak isospin eigenvalue \(T_3\), and hypercharge Y is related for the Higgs by

\[Q=(T_3+\frac{Y}{2})\phi_0=0\]

only the \(\phi_0\) current that gets a VEV...a probability current giving the weighted average likelyhood

the last equation directly relates to the W, Z and photons gaining mass or not. Unfortunately this is where I'm going to have to turn it up a notch or a dozen notches

 quarks and lepton fields  are organized in left-handed doublets and right-handed singlets:  Matter is left handed, antimatter is right handed

the covariant derivative is given as

\[D^\mu=\partial_\mu+igW_\mu\frac{\tau}{2}-\frac{i\acute{g}}{2}B_\mu\]

\[\begin{pmatrix}V_\ell\\\ell\end{pmatrix}_L,\ell_R,\begin{pmatrix}u\\d\end{pmatrix}_,u_R,d_R\]

The mass eugenstates given by the Weinberg angles are

\[W\pm_\mu=\sqrt{\frac{1}{2}}(W^1_\mu\mp i W_\mu^2)\]

with the photon and Z boson given as

\[A_\mu=B\mu cos\theta_W+W^3_\mu sin\theta_W\]

\[Z_\mu=B\mu sin\theta_W+W^3_\mu cos\theta_W\]

the mass mixings are given by the CKM matrix below

\[\begin{pmatrix}\acute{d}\\\acute{s}\\\acute{b}\end{pmatrix}\begin{pmatrix}V_{ud}&V_{us}&V_{ub}\\V_{cd}&V_{cs}&V_{cb}\\V_{td}&V_{ts}&V_{tb}\end{pmatrix}\begin{pmatrix}d\\s\\b\end{pmatrix}\]

mass euqenstates given by \(A_\mu\) an \(Z_\mu\)

\[W^3_\mu=Z_\mu cos\theta_W+A_\mu sin\theta_W\]

\[B_\mu= Z_\mu sin\theta_W+A_\mu cos\theta_W\]

\[Z_\mu=W^3_\mu cos\theta_W+B_\mu sin\theta_W\]

\[A_\mu=-W^3_\mu\sin\theta_W+B_\mu cos\theta_W\]

this is how the mass terms are generated using eh CKMS mass mixing matrix above. Unfortunately this is a stage where I had to resort to under the math to be accurate enough on how the mass terms apply for W,Z, and why photons do not acquire mass.

However this table may help visualize what is going on

\[{\small\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline Field & \ell_L& \ell_R &v_L&U_L&d_L&U_R &D_R&\phi^+&\phi^0\\\hline T_3&- \frac{1}{2}&0&\frac{1}{2}&\frac{1}{2}&-\frac{1}{2}&0&0&\frac{1}{2}&-\frac{1}{2} \\\hline Y&-\frac{1}{2}&-1&-\frac{1}{2}&\frac{1}{6}&\frac{1}{6}& \frac{2}{3}&-\frac{1}{3}&\frac{1}{2}&\frac{1}{2}\\\hline Q&-1&-1&0&\frac{2}{3}&-\frac{1}{3}&\frac{2}{3}&-\frac{1}{3}&1&0\\\hline\end{array}}\]

in the above table you also have Yukawa couplings as well for example for a quark

\[\mathcal{L}=q_d\overline{Q}_L\phi d_R+g_\mu \overline{Q}_L\phi_c U_R +h.c\]

h.c. is the hermitean conjugate in QM don't worry about the last equation its just to show that the mass terms isn't strictly due to Higgs. Yukawa couplings also contributes and it uses the same table as above. Also I did not show the right handed singlets in the above. for antineutrinos they have different mixing angles as singlets and will involve Majarona 

what I have shown may likely make your head explode as is lol.

oh forgot to add prior to symmetry breaking the SM model uses the Goldstone bosons

 

 

 

 

 

 

Edited April 28 by Mordred

[chron44]

20 minutes ago, Mordred said:

This is where we have to be careful. You may recall that the VeV is a probability function correct? That probability function will have a probability current. The term "expectation" value denotes this. So it has a weighted average that is described by the 246 VeV value. The other important detail is the Higgs field isn't just one field it is an SU(2) doublet.

 

In some way by earlier theorizing of my own I suspected this situation of Higgs field having two, no more or less, fields.
One with emphasize on "mass" and the other on "electromagnetism".

This is as far as I may comprehend.

All the other formulas you provide are excellent and describing how mass is achieved with the photon remaining massless.
You must be working with these matters professionally. On a high level also. And I'm glad you took time for to guide an interested layman in these matters.

I cannot jump into these formulas. My concern lies more of how and why Higgs field are there in universe permeating all space. Exactly how mass is achieved is a physics professional issue too complex for me, as said.

Hopefully we can continue to discuss in some manner, even if I cannot follow the precise math involved.

/chron44

[Mordred]

11 minutes ago, chron44 said:

 

In some way by earlier theorizing of my own I suspected this situation of Higgs field having two, no more or less, fields.
One with emphasize on "mass" and the other on "electromagnetism".

This is as far as I may comprehend.

All the other formulas you provide are excellent and describing how mass is achieved with the photon remaining massless.
You must be working with these matters professionally. On a high level also. And I'm glad you took time for to guide an interested layman in these matters.

I cannot jump into these formulas. My concern lies more of how and why Higgs field are there in universe permeating all space. Exactly how mass is achieved is a physics professional issue too complex for me, as said.

Hopefully we can continue to discuss in some manner, even if I cannot follow the precise math involved.

/chron44

 

Yes I do work with these on a professional level. Its also one of my primary focusses in regards to my primary expertise in Cosmology. Feel free to ask any questions and I will be glad to help you on it. Most articles including dissertations on Higgs will likely have those equations. Its certainly covered under papers regarding CKMS mass mixing. So resources are readily available to learn how to eventually understand the above.

A big step is knowing vector and spinor relations under math. LIttle hint every SM model for every particle interaction (Feymann path integral) applies the Principle of least action via the Langrangian. Which forms also applies  to the Hamilton 

Edited April 28 by Mordred

[chron44]

 

It looks like the Higgs field consists of two entwined "parts" one- "mass" and one "electromagnetic" related which is shown
from the SU(2) doublet statement.

How is situation derived, I mean originally at the early/mid 20th century's indications of a mass establishing field?
Is it a qualified assumption first theorized and later evolving to the "final" (mid 1960's) Higgs field and its mechanism.
And finally in 2012 proven with the LHC success. How was this interesting "journey" started?

I'm a bit embarrassed asking elementary issues, though it is cosmological crucial issue.
(And I believe that my starting quest caught your attention, though being a bit confused.)

 

2 hours ago, Mordred said:

A big step is knowing vector and spinor relations under math. LIttle hint every SM model for every particle interaction (Feymann path integral) applies the Principle of least action via the Langrangian. Which forms also applies  to the Hamilton 

 

Is the SM and the QFT always to be correct, we know about the cosmological constant problem?

 

[chron44]

For to refine my concern or primary issue we know that VEV is the probabilistic energy amount needed for
mass being established related to Higgs field mechanism. The concern is if this "working" "transition"
"current" mainly is originating from the LHC collision kinetic energy. -Or not, if there are some other
unknown contributing sources involved? This is, to my view a cosmological central issue, besides being
a straight security issue.

Maybe a bit "silly" concern, still the average layman may be wondering.

[Mordred]

Lets put it this way. The SM model including QFT has been so successful that just like the Higgs boson. It was able to predict long before detection over 90 % of the standard model of particles. There is still open questions so it's not complete. However it is simply the best fit for predictability and observational evidence. 

The VeV is part of that for the Higgs. If it weren't for the VeV range prior to Higgs detection. CERN wouldn't have known what range to look for to calibrate it's detectors.

[chron44]

Thanks for your replies, it's over midnight here, so good night.

 

[Mordred]

Night

[chron44]

Citing again from ChatGPT:

"As the temperature of the universe decreases from the time of the Big Bang (BB), certain phase transitions occur in the early universe that lead to spontaneous symmetry breaking (SSB), including the emergence of non-zero vacuum expectation values (VEVs) of certain fields, such as the Higgs field."

And, my own "statement":
The energy "sources" in average temperatures, for example of the VEV of Higgs field, are mainly the remaining's of Big Bang and kinetic and potential energy. (Where the residuals of BB include all novel types of particles and fields, their virtual components and so on...)

And, even if there are parallel ideas/ways of the origin of the "matter/energy" involved, the QFT and SM have been proven about at 90% all time since these physics models was introduced. I.e. the accuracy of QFT and SM are not dependent of the origin of all the novel existing matter/energy. (Representing a non-BB universal evolution idea.) (Which may correct the cosmological constant problem.)

I understand that these latest statements or ideas are not at all common in the physics community. Forgive me if I as an interested layman am trying to promote some new/odd cosmological evolutionary theories.

/chron44

Edited April 29 by chron44
grammar

[Mordred]

The first two paragraphs are accurate enough. It's more accurately described by 

As a result of expansion particle fields including the Higgs field drop out of thermal equilibrium in accordance to thermodynamic ideal gas laws involving tempersture/ density/ pressure and volume relations.

  Once the Higgs field drops out of equilibrium particles acquire mass leading to electroweak symmetry breaking. All particles and particle fields has a temperature contribution 

As for any personal proposals this isn't the section for that. If you choose to pursue personal ideas and a personal hypothesis our rules require that gets done in our Speculation forum.

We may not currently know the cause of the cosmological constant. It may be quantum fluctuations due to the Heisenburg Uncertainty principle of the quantum harmonic oscillator which all fields are effected by.

Or it may be the Higgs field. There is plenty of research papers suggesting either possibility however nothing is conclusive enough to make any determination between those two possibilities 

[chron44]

 

59 minutes ago, Mordred said:

As a result of expansion particle fields including the Higgs field drop out of thermal equilibrium in accordance to thermodynamic ideal gas laws involving tempersture/ density/ pressure and volume relations.

  Once the Higgs field drops out of equilibrium particles acquire mass leading to electroweak symmetry breaking. All particles and particle fields has a temperature contribution 

OK, I notice your comment. All seems fair and representing today's cosmological physics. Also very distinct and compact expressed.

For my own ideas of the cosmological evolution, I'll express them in the Speculation section.

Just very interesten in cosmology and physics in general, and in a "layman" level.

[exchemist]

1 hour ago, IlyaGeller said:

Take a look at the photos in the articles "In-situ Imaging of a Single-Atom Wave Packet in Continuous Space" and "This Stunning Image Is The Highest Resolution We've Ever Seen Atoms." Do you see the volumes of the atoms and their increases?

https://arxiv.org/html/2404.05699v1

https://www.sciencealert.com/this-stunning-image-is-the-highest-resolution-weve-ever-seen-atoms

In Higgs theories the volumes of particles, such as the volume of the Higgs boson, are ignored. Therefore, his theory is incorrect.

Take a look at the photos in the articles "In-situ Imaging of a Single-Atom Wave Packet in Continuous Space" and "This Stunning Image Is The Highest Resolution We've Ever Seen Atoms." Do you see the volumes of the atoms and their increases?

https://arxiv.org/html/2404.05699v1

https://www.sciencealert.com/this-stunning-image-is-the-highest-resolution-weve-ever-seen-atoms

In Higgs theories the volumes of particles, such as the volume of the Higgs boson, are ignored. Therefore, his theory is incorrect.

What do you mean by the "volume" of a particle? Such a concept requires objects with sharply defined edges, doesn't it? 

[Mordred]

Particles are not little bullets with defined boundaries. That is not the modern understanding. Nor is the Bohr model of the atom. 

 The electron cloud in modern treatment is a probability cloud which is what those images are showing.. You also won't see a Higgs boson in those images.

The Higgs theory does not predict nor describe the atom with a volume or changes in volume for good reasons. 

 The second paper discusses the probability aspects 

Edit looks like IlyaGeller deleted his post 

Edited September 17 by Mordred