I often hear people say that the Higgs field gives things mass. How can I understand that with out going deep in quantum mechanics, field theory, and the standard model?
thanks in advance,
Farah, my opinion and answer would be on the similar spirit as Dr. Nicolas F. Lori although I would like to furnish the need for a Higgs field.
Weak interaction traditionally manifesting through nuclear beta decay has the oldest theoretical understanding via four-fermion interaction due to Fermi. Its strength is the experimentally determined Fermi coupling constant. This is a contact interaction which has mass dimension 6 and not " renormalizable". It has a great disadvantage that this interaction predicts second and third etc. orders of interaction to be larger than the first order interaction.
By 1940'-50 it was known that QED can be described with high precision to all higher orders through its "renormalizability". The cdarrier or quantum of QED is the photon. The gauge symmetry associated with QED is the local abelian group U(1)_{em} which remains unbroken at all energy scales. This predicts photon to have zero mass or infinite range of emj interactions.
Attepts were made to bring weak interaction under the similar footing and precision as QED.
Weinberg, Salam, and Glashow found this to be possible if weak and electromagnetic interactions are combined via gauge symmetry SU(2)_L\times U(1)_Y who arrived at their predictions by combining the ideas of Higgs, Englert, Brout, Gourlanik, Kibble....
The associated number of gauge bosons in SU(2)_L\times U(1)_Y would be 3+1 =4 which are W+, W-, W_3, and B bosons.
At first when Higgs mechanism was not known was noted that, like QED, this theory
is renormalisable when all four gauge bosons are mass less. This would predict weak interaction to be of infinite range against experimental fact. Weak int has
range \sim 10^-{14} cm . Since range is inversely proportional to mass, weak interaction needs order 10 GeV mass for W^{\pm} gauge bosons.
On the other hand if direct mass terms are added to the Lagrangian , it would spoil the attractive property of renormalisability.
The problem faced by the proponents of SU(2)_L\times U(1)_Y theorists was to give mass to weak bosons to agree with experimental facts while safeguarding renormalisabiliy.
It is the Higgs mechanism which achieved this objective. In the process of giving mass to the gauge bosons by spontaneous symmetry breaking mechanism through
the non-vanishing VEV of its neutral component, it does not destroy the underlying gauge symmetry of the Lagrangian thereby guranting renormalisability , Gauge bosons get masses via gauge interactions of the Higgs field. Fermions get masses by Yukawa interaction.
To start with, when people talk about mass what they refer to is rest mass. Meaning the mass measured when you weight it. The mass is equal to the rest mass divided by the square route of 1 minus the square of the division between the velocity of the object v and the speed of light in vacuum c:
mass="rest mass"/sqrt(1-(v/c)^2)
This obtains for v much smaller than c:
mass="rest mass"+ (1/2)X"rest mass"X(v/c)^2
Using the Einstein relation E=mc^2, for low velocities the equation above becomes:
Energy="rest Energy"+(1/2)X"rest mass"Xv^2
The last term on the left is the low velocity kinetic energy known from classical Physics.
The rest mass of everyday objects is almost completely provided by the rest mass of the proton and the neutron. Although the proton and the neutron are both made with 3 quarks (up+up+down for proton, up+down+down for neutron) the rest masses of the proton and neutron are almost completely generated by the kinetic energy of the quarks, not by the rest mass of the quarks which is very low.
So, the question is not what generates rest mass in general, but what generates the rest mass of the fundamental particles like the masses of the quarks, or the electron. There are only 12 fundamental particles that one needs to care about, the 6 quarks and the 6 leptons. The 6 quarks are: up, down, strange, charm, top, bottom. The 6 leptons are: electron, muon, taon, neutrino of electron, neutrino of muon, neutrino of taon.
This is a question because the equation that describes the interactions between them by gauge symmetries assumes these fundamental particles are massless. The equation is called a Yang-Mills Lagrangian and there is one for each gauge symmetry. The U(1) gauge symmetry obtains the electromagnetic force, the SU(2) obtains the weak nuclear force, and the SU(3) obtains the strong nuclear forces.
What the Higgs mechanism allows is for massless fundamental particles to gain mass by the spontaneous symmetry breaking of the vacuum state. The Higgs field is the field generated by that spontaneous symmetry breaking, and the Higgs particle is the quantized particle associated to that Higgs field. In the same way that the photon is associated to the electromagnetic field.
A spontaneous symmetry breaking occurs when a system is prepared in a state that has a symmetry similar to the Lagrangian symmetry, but that symmetry is then broken because the non-symmetric state has lower energy (thus higher probability) than the symmetric state. Like a pencil put on the vertical above an horizontal surface, when the pencil falls down that is a spontaneous symmetry breaking.
The Higgs field also helps explain how the photon does not have mass but the 3 particles carrying the weak nuclear force do. These particles are the W-,W+, and W0. The W 0 is als. called Z0. This occurs through a joining of the SU(2) (weak nuclear force) and U(1) (electromagneitism), thus describing a SU(2)xU(1) electroweak force.
The weak nuclear force and the electromagnetic force are two simplifications of this electroweak force.
thank you for helping. I am trying to understand and study what you mentioned up there.
But is the neutrino of electron and that of muon and taon different than the neutrino that is emitted with beta particles to quantize the total spin change in decay?
Farah, my opinion and answer would be on the similar spirit as Dr. Nicolas F. Lori although I would like to furnish the need for a Higgs field.
Weak interaction traditionally manifesting through nuclear beta decay has the oldest theoretical understanding via four-fermion interaction due to Fermi. Its strength is the experimentally determined Fermi coupling constant. This is a contact interaction which has mass dimension 6 and not " renormalizable". It has a great disadvantage that this interaction predicts second and third etc. orders of interaction to be larger than the first order interaction.
By 1940'-50 it was known that QED can be described with high precision to all higher orders through its "renormalizability". The cdarrier or quantum of QED is the photon. The gauge symmetry associated with QED is the local abelian group U(1)_{em} which remains unbroken at all energy scales. This predicts photon to have zero mass or infinite range of emj interactions.
Attepts were made to bring weak interaction under the similar footing and precision as QED.
Weinberg, Salam, and Glashow found this to be possible if weak and electromagnetic interactions are combined via gauge symmetry SU(2)_L\times U(1)_Y who arrived at their predictions by combining the ideas of Higgs, Englert, Brout, Gourlanik, Kibble....
The associated number of gauge bosons in SU(2)_L\times U(1)_Y would be 3+1 =4 which are W+, W-, W_3, and B bosons.
At first when Higgs mechanism was not known was noted that, like QED, this theory
is renormalisable when all four gauge bosons are mass less. This would predict weak interaction to be of infinite range against experimental fact. Weak int has
range \sim 10^-{14} cm . Since range is inversely proportional to mass, weak interaction needs order 10 GeV mass for W^{\pm} gauge bosons.
On the other hand if direct mass terms are added to the Lagrangian , it would spoil the attractive property of renormalisability.
The problem faced by the proponents of SU(2)_L\times U(1)_Y theorists was to give mass to weak bosons to agree with experimental facts while safeguarding renormalisabiliy.
It is the Higgs mechanism which achieved this objective. In the process of giving mass to the gauge bosons by spontaneous symmetry breaking mechanism through
the non-vanishing VEV of its neutral component, it does not destroy the underlying gauge symmetry of the Lagrangian thereby guranting renormalisability , Gauge bosons get masses via gauge interactions of the Higgs field. Fermions get masses by Yukawa interaction.
In summary the introduction of the Higgs field and the HIggs mechanism has been able to give electroweak scale masses to W^{\pm} and Z bosons, while safe guarding
renormalizability of the ew theory and the Dirac theory.
Having mass is having the capability to deform the environment of the owner of that mass. That environment is a field. In fact that field is our living space. This field can be described by a mostly continuous multidimensional function and that function has a flat (not deformed) parameter space. The Higgs particle and the Higgs field are part of a specific model. Other models exist that do not require the equivalents of the Higgs particle and the Higgs field, but that still support an equivalent of mass carrying particles and a deformed embedding field. Besides of that, the Higgs model only gives mass to a subset of the mass carrying objects. The Hilbert Book Test Model does support mass and a correspondingly deformed embedding field, but it does not discern the Higgs field and the corresponding particle.
http://vixra.org/abs/1603.0021
Direct mass term will spoil renormalizability. So masses are to be produced indirectly. Then you add a new scalar sector in the theory, which has self interaction. Symmetry is broken (spontaneously) by the VEV of scalar field, then it is communicated to fermions and gauge bosons by the interaction terms. In this way, gauge bosons and fermions become massive, photon remains mass less and the theory remains renormalizable. Best part is that Higgs field has really been observed. That is the end of almost a fairy tale. It is noticeable that the existence of Higgs boson was theoretically postulated in the decade of 1960s, much before it's experimental discovery in 2015.
http://home.cern/topics/higgs-boson
Theoretical caveat in this successful model is that nobody knows how to stabilize the mass of a Higgs particle (in a quantum field theory) against large radiative corrections. This is also known as hierarcy problem. See for example this interesting talk by J. Lykken,
http://www.slac.stanford.edu/econf/C040802/lec_notes/Lykken/Lykken_web.pdf
No one at LHC has proved that the detected particle is elementary.
No one at LHC has proved that the detected particle or its field provides mass for other elementary particles.
Thanks all....
Dr. Amrit thanks again, I have downloaded your book "the physics of now" I will read it as soon as I finish my final exams.
Dr. Hans I am interested in your point of view....
Most physicists repeat without criticism what was lectured to them at their universities. Students must also be told that their lecturers are not omniscient and that the great physicists that guided the development of physics are all fallible. That does not mean that all of physics is wrong. Most of it is proper. But current physics contains items that can easily be disproved. Physics is not a self-consistent theory. In that respect mathematics is far more trustworthy. However, also that branch of science is not perfect and it is certainly not complete. On the other hand you must be a damn good scientist in order to be able to improve the current state of physics and mathematics. Many scientists are able to improve this situation a little bit. Only a few can contribute a significant amount. Most of them lived in the first decades of the last century. For science that was a turbulent period. Not everything occurred in the proper order. Learning lessons of what happened in that period can be very advantageous.
Personally I am very curious about how the foundation of reality is configured. In the first decades of the twentieth century lived several great scientists like Einstein, Hilbert, von Neumann and Dirac that showed that same curiosity. Today the trend is to earn as much as is possible by applying the achieved knowledge. Hardly anyone is interested in foundations. Those that are, often miss the required knowledge of advanced mathematics.
My message to students and young scientists is: "Do not take everything that is lectured for granted. Take care that you get a sufficient knowledge of advanced mathematics. Keep seeking for a proper foundation of everything that you learned. Dare to take an unconventional and/or controversial point of view."
"Do not take everything that is lectured for granted. Take care that you get a sufficient knowledge of advanced mathematics. Keep seeking for a proper foundation of everything that you learned. Dare to take an unconventional and/or controversial point of view." ~ Hans Van Leunen ~
I will always keep that in mind ... :)
Farah,
In the main time one must earn bread and feed one's family. Only after my retirement I got sufficient time in order to take a deep dive into the foundations of reality. I am convinced that reality contains several of the structures and phenomena that are quite similar to comparable structures and phenomena that we usually assign to mathematics.
I have started a Wikiversity project that treats the foundation and the lower levels of the structure of physical reality. The project introduces new mathematics and new physics.
https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project
Dear Farah,
Although you have not gone deep into quantum mechanics , field theory, or standard model (SM), I hope you know Fermions which carry half integral spin =1/2, ...and Bosons which carry zero or integral spin such as 0,1,... Examples: electron and neutrino have spin half. Composite particles p and n also have spin 1/2, their constituents the quarks have also spin 1/2. Photon the carrier of electromegnetism, has spin 1. It is called a gauge boson of e.m. interaction between any two particles having charge. In this case charge defines the strength of e.m. interaction and you know fine structure constant =e^2/(4\pi). Popular examples of e.m. interaction: emissio and absoption of light by atoms, e^-+e^+ \to photons ,or matter + anti-matter \to e.m.radiation. Photon is massless. This is because of well known popular connection:
Range of a force is inversely proportional to the gauge boson mass. Using this and the fact that e.m. int. has infinite range you say photon is massless.
Similarly the carriers of weak interactions must be massive because weak int has range of the order of few fermi. Note that one fermi =10^{-13} cm. The W, Z, bosons discovered at CERN LEP collider have masses about 80 GeV and 91 GeV respectively. All these masses are generated by interaction through Higgs boson.
Higgs Boson has zero spin. Popularly the mass generation mechanism of the SM can be stated as:
Any particle (leptons, quarks, gauge bosons etc) which interact with Higgs boson get mass. If this interaction is stronger or weaker, the mass aqured by the interacting particle with Higgs boson is more or less.
All fermions (e, quarks, .) interact with Higgs by Yukawa interaction. An example of original Yukawa interaction for which Yukawa got Nobel prize is : Y\times p n\pi^- ,whre \pi^- is the spin zero negatively charged pion of mass 140 MeV. Y is Yukawa coupling strength. p= proton, n=neutron. Similarly the Yukawa interaction of HIggs particle h with electron is Y_e \times e .e h. Since Y_e=10^{-7} elctron is ithe lightest charged lepton. Top quark has similay Yuk int. Y_{top}\times t .t . h . Since Y_{top}=1 top quark is the most massive fermion of mass \sim 170 GeV among SM partricles..
Similarly W, Z bosons get masses through their gauge interctions with Higgs boson.
Photon remains mass less because it has no interaction with Higgs.
Please let me know how much do you gather from this stuff.
Best Wishes,
M. K. Parida
Quite a good alternative exists that offers all elementary particles their mass by constituting their footprint.
http://vixra.org/abs/1708.0233
Better to persue or propose ideas which can explain most if not al of the obseebed facts and predict experimentally testable quantities. Falsifiability is a highly desirable chracteristic feature of a model.
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