#1
Nov406, 03:25 PM

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The helicity of an electron is h=+1/2
The helicity of a photon is h=+1 The helicity of a graviton is h=+2 It seams that all the elementary particles have nonzero helicity. Is there a zero helicity particle? What is the helicity of Higgs Bosons? Thanks for any replies. Max 


#2
Nov406, 03:25 PM

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Max wrote:
> The helicity of an electron is h=+1/2 > The helicity of a photon is h=+1 > The helicity of a graviton is h=+2 > > It seams that all the elementary particles have nonzero helicity. Is > there a zero helicity particle? What do you mean by helicity for massive particles? An electron is massive, so the helicity is not a good (intrinsic quantum number). For massive particles a good quantum number is spin. You can define helicity as the projection of the spin in direction of the momentum of the particle, but that's a framedependent notion, since by a Lorentz transform you can flip the helicity if the particle goes with velocities smaller than c as is the case for massive particles. On the other hand, it can have advantages to describe things in a helicity basis. See, e.g., ON THE GENERAL THEORY OF COLLISIONS FOR PARTICLES WITH SPIN. By M. Jacob, G.C. Wick (Brookhaven),. 1959. Published in Annals Phys.7:404428,1959, Annals Phys.281:774799,2000 doi:10.1006/aphy.2000.6022 > > What is the helicity of Higgs Bosons? Higgs bosons are (massive) scalar particles, and their spin (and thus also their helicity) is 0.  Hendrik van Hees Texas A&M University Phone: +1 979/8451411 Cyclotron Institute, MS3366 Fax: +1 979/8451899 College Station, TX 778433366 http://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu 


#3
Nov406, 03:25 PM

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Hi Max
> The helicity of an electron is h=+1/2 > The helicity of a photon is h=+1 > The helicity of a graviton is h=+2 > > It seams that all the elementary particles have nonzero helicity. Is > there a zero helicity particle? > > What is the helicity of Higgs Bosons? > helicity is a projection of spin vector in the direction of momentum vector. Helicty = spin.momentum/abs(spin.momentum) Higgs boson is scalar particle (spin=0) so Helicity = 0. > Thanks for any replies. > > Max > Boris 


#4
Nov406, 03:25 PM

P: n/a

What is the helicity of Higgs Bosons?
Hendrik van Hees wrote:
"You can define helicity as the projection of the spin in direction of the momentum of the particle, but that's a framedependent notion, since by a Lorentz transform you can flip the helicity if the particle goes with velocities smaller than c as is the case for massive particles." Weyl spinors are eigenstates of helicity. As we know, Weyl spinors are irreducible representations of the Lorentz group. It means that under Lorentz transformations, left and right handed Weyl spinors will NOT change into each other. Max 


#5
Nov406, 03:25 PM

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No elementary spin zero particles have been empirically observed. But
note that neither the Higgs boson nor the gravition have been observed so to be proper we should say: "The spin of a graviton is predicted to be 2" As far as what the most established theory predicts see: http://particleadventure.org/particleadventure/ http://www.hep.net/documents/drell/sec3.html (You should Google "elementary particles" and look there before posting questions here.) The spin of a photon is 1 and thus it can have spin component in a given direction of 1,0,1. But, as there is correlation between spin and the direction of the momentum induced by the maslessness of the photon, this reduces to just +1 and1 when measuring spin about the direction of motion (helicity). A massive spin1 boson such as the Wboson can according to theory be observed to have all three values of 1,0,1 for its helicity. The graviton (should it be observed) would, as a spin 2 particle, have spin component in a given direction of 2,1,0,1, or 2. Again there is correlation between spin and momentum due to the maslessness of the gravitational field so again this reduces the range of values for helicity. However there is still some question as to whether the available values are 2,2 (if GR is correct) or if it is 2,0,2 (possible in other metric theories of gravity). That 0 helicity graviton would correspond to the classical gravity wave whereby space is periodically stretched and compressed radially about the direction of popagation. Regards, James 


#6
Nov406, 03:25 PM

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I think, you should take more attention on the particle mass when you
talk about the helicity. For example, the photon is a massless partilce, so not all the three projections of its spin (in some direction) are physical, and you just need to concern its helicity. But for the massive one , you must consider all the projections. For electron, the spinor representaion is irreducible , because its massive spin1/2 particle. But in other situation, that will not always true. 


#7
Nov406, 03:25 PM

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James wrote:
>However there is still some question as to whether the >available values are 2,2 (if GR is correct) or if it is 2,0,2 >(possible in other metric theories of gravity). That's very interesting. Could you please provide some reference to the 0 helicity graviton theory. Thanks, Max 


#8
Nov406, 03:26 PM

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Max wrote:
> James wrote: > >>However there is still some question as to whether the >>available values are 2,2 (if GR is correct) or if it is 2,0,2 >>(possible in other metric theories of gravity). > > > That's very interesting. Could you please provide some reference to > the 0 helicity graviton theory. These would arize in the quantization of scalartensor (or tensorscalar) theories; e.g., of BransDicke theory. There is a spin 2 graviton with helicity +2, and a scalar graviton with helicity 0. Of course, at present, gravitons are purely hypothetical particles, whether those of sopin 2 or those of spin 0. Arnold Neumaier 


#9
Nov406, 03:26 PM

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Arnold gave the reference but I'll add some speculative thoughts. The
scalar component of the geometric gauge defines the mass scale and reciprocally the propertime scale at each point in spacetime. We can express this in several different ways.  The standard method is to allow the gravitational constant G to become a variable.  One might also consider variation of hbar which relates mass and propertime units.  I also think allowing the cosmological constant to be a variable is another equivalent way of manifesting this scalar gauge field. These choices are ways of picking the gauge condition. They are each ways of fixing the scale of spacetime units to some empirical phenomenon. We specifically like to scale units such that the mass of elementary particles and the speed of light and Plank's constant are fixed over space and time. The existance of massive particles and hence fundamental units of space and time (e.g. the Bohr radius or Compton wavelength or Plank radius) breaks the scaling gauge symmetry. But consider this. The Higgs boson is postulated to be a spinzero quantum. One might speculate (somewhat wildly) that the Higgs boson *is* the scalar graviton. The first difficulty with this proposition is that the Higgs is massive unlike the scalar gravitational field of BransDicke theory. But the Higgs mass is due to self interaction in the quantum theory. We may incorporate into this speculation the explaination that this quantum theoretical selfgenerating mass is exactly what condenses the more general BransDicke theory to the standard Einstein theory (with cosmological constant). Such speculation would require a electroweakgravitational unified theory to formulate rigorously and thence to test. That is unless there are more obvious reasons to reject this notion. I'm not currently well read enough to see where this speculation would fall flat immediately. My intuition tells me that mass is the charge associated with the scalar gauge and so the Higgs mechanism by which particles aquire mass should relate intimately with scalar gravitation. But this is only an intuitive guess and I would not be shocked if someone comes up with (or has already come up with) an obvious reason these two theorized gauge fields should not be identified. Hmmmm.... Regards, James 


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