Re: Lorentz violation of the Standard Model

J.C. Yoon wrote:

> The SM is written as a Lorentz-invariant action,but that
> of a massive fermion with massless property.

Is there a typo in that sentence? Did you omit a "not"?

A massive fermion cannot be written as
$\psi_{L}$, $\psi_{R}$ as if they are massless.

And it is why its obserbable outcomes such as
Left-Right asymmetry in E158 is not Lorentz
invariant; the cross section of Left-handed
Helicity electron is different from that of
Right-handed Helicity electron, i.e., the
cross section of a particle with one spin
direction along its momentum can be different
from when the spin direction is opposite to
its momentum, which can be obtained by
Lorentz transformation.

This sounds like the old confusion between helicity
and chirality which inevitably recurs on spr.
Below is an (edited) copy of a posting I wrote some
time ago when a person named "Starblade Darksquall"
had the same problem...

---------------------------------------------------
Starblade Darksquall wrote:

Dr Tim wrote:

>> [...] So the weak force is dependent on your
>> frame of reference. (Howard Georgi comes
>> close to admitting this: "The value of the
>> weak charge depends on the way the electron
>> is moving...") How can that be!?! Can a
>> neutron decay in one frame yet remain whole
>> in another?!?

That's a good point. Why isn't anyone
adressing this issue?

Because it was actually addressed satisfactorily
long ago, though it is still a source of confusion
when one is first learning the subject.

I think you may have asked a question which
nobody here has a good answer to. Proove me
wrong, people! Proove me wrong!

As others have mentioned, there's an important
distinction between helicity and chirality. When
textbooks say that only left-handed fermions
participate in the weak interaction, they mean
left-handed chirality, not left-handed helicity.

Helicity is not a Lorentz-invariant concept for
massive fermions. You can Lorentz boost into a
frame where the helicity is different. This is not
true for chirality - which *is* invariant under
Lorentz boost. For massless particles however, the
two concepts happen to coincide.

So just to be clear: whenever textbooks speak of
handedness in connection with weak interactions,
they mean chirality, not helicity. And whenever
people talk about boosting into another frame to
change the handedness, they're talking about
helicity.

The weak interaction terms in the SM Lagrangian
are indeed Lorentz-invariant - because of this
distinction between helicity and chirality.

- MikeM.

.

Relevant Pages

  • Re: Lorentz violation of the Standard Model
    ... is different from that of Right-handed Helicity electron, i.e., the ... not stated it in this way, it is a Lorentz violation. ... For a massless particle, it so happens that the L ... Whenever interacting fermions are present, ...
    (sci.physics.research)
  • Re: Lorentz violation of the Standard Model
    ... I think what you meant chirality, not helicity in the following. ... right handed helicity will NOT change into each other under Lorentz ... boost, because left and right handed Weyl spinors are irreducible ...
    (sci.physics.research)
  • Re: Lorentz violation of the Standard Model
    ... Dirac spinor is an irreducible representation of the Lorentz group ... doesn't commute with. ... Helicity commutes with the Lorentz boost. ...
    (sci.physics.research)
  • Re: Lorentz violation of the Standard Model
    ... also changed in addition to the sign of momentum. ... It makes clear your point that the orientation of spin becomes reversed ... the helicity is conserved under Lorentz transformations. ...
    (sci.physics.research)