What is the helicity of Higgs Bosons?

[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 non-zero helicity. Is
there a zero helicity particle?

What is the helicity of Higgs Bosons?

Thanks for any replies.

Max

[Hendrik van Hees]

Post by 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 non-zero 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 frame-dependent 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.7:404-428,1959, Annals Phys.281:774-799,2000
doi:10.1006/aphy.2000.6022

Post by Max
What is the helicity of Higgs Bosons?

Higgs bosons are (massive) scalar particles, and their spin (and thus
also their helicity) is 0.

[Max]

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 frame-dependent 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

[Boris Bralo]

Hi Max

Post by 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 non-zero 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.

Post by Max
Thanks for any replies.
Max

Boris

[jambaugh]

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 and-1 when measuring spin about the
direction of motion (helicity).

A massive spin-1 boson such as the W-boson 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

[Max]

Post by jambaugh
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

[Arnold Neumaier]

Post by Max

Post by jambaugh
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 scalar-tensor (or
tensor-scalar) theories; e.g., of Brans-Dicke 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

[mgao]

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 spin-1/2 particle. But in other situation, that will not
always true.

[jambaugh]

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 proper-time scale at each point in space-time.

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
proper-time 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 space-time 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 spin-zero
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 Brans-Dicke 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 self-generating mass is exactly what condenses the more
general Brans-Dicke theory to the standard Einstein theory (with
cosmological constant).

Such speculation would require a electro-weak-gravitational 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