Is spin of tau conserved in lab/rest frame?

[studnte]

if p_{tau}>>m_{tau} and we boost along the lab momentum of tau to go to its rest frame and defining this boost direction as Z-axis and looking at its decay product nu_tau and pi^- coming back-to-back along this Z-axis.
here, the question is whether the tau spin in the rest frame is the same as in lab frame?

 

[mormonator_rm]

if p_{tau}>>m_{tau} and we boost along the lab momentum of tau to go to its rest frame and defining this boost direction as Z-axis and looking at its decay product nu_tau and pi^- coming back-to-back along this Z-axis.
here, the question is whether the tau spin in the rest frame is the same as in lab frame?

Yes, the spin is indeed conserved. It will be conserved in any reference frame. I know this because I have simulated millions of events for proton-antiproton annihilation, and the reference frame does not affect the spins of the proton or antiproton, nor does it ever effect the spins of the resultant pions. The particle's spin will always be the same in the lab frame as it is in the rest frame, or any other reference frame for that matter. This is because the irreducible representation of a particle's wave-function is Lorentz-invariant. Now, you must always take care to calculate the momentum, which does vary from frame to frame. The center-of-mass reference frame has always been my favorite because I find it easiest to be able to cancel all momenta to zero before I begin treatment of the problem.

If anyone else has something to add or correct, please contribute!

 

[studnte]

Yes, the spin is indeed conserved. It will be conserved in any reference frame. I know this because I have simulated millions of events for proton-antiproton annihilation, and the reference frame does not affect the spins of the proton or antiproton, nor does it ever effect the spins of the resultant pions. The particle's spin will always be the same in the lab frame as it is in the rest frame, or any other reference frame for that matter. This is because the irreducible representation of a particle's wave-function is Lorentz-invariant. Now, you must always take care to calculate the momentum, which does vary from frame to frame. The center-of-mass reference frame has always been my favorite because I find it easiest to be able to cancel all momenta to zero before I begin treatment of the problem.

If anyone else has something to add or correct, please contribute!

Thanks mormonator_rm . So:
if the tau is right-hand in lab fram, its spin should has the same direction as its mementum (the angle between spin and momentum <90 degree, here orbital angule mementum is 0). because the spin is conserved (the value and direction), in tau's rest frame (boosting as what I mentioned and
tau_R^{-} --->pi^- + neu_{tau}), because the angular mementum conservation (spin of pi is 0) and momentum of pi and neu_{tau} should back to back in tau's rest fram, according to these i could conclude pi^- is forward w.r.t the boost direction.
am I right? thanks

 

[mormonator_rm]

I am slightly confused by what you are asking here... my gut feeling is to say "not necessarily". The only thing that is garaunteed is the isotropy of the decay. In other words, whichever direction the pi- goes, the tau neutrino will go in the opposite direction with equal magnitude of momentum in the rest frame of the source tau- particle. The direction of the tau neutrino and pi- emission is not biased to the spin of the particles involved, as I understand it. Would anyone else like to comment or correct?

 

[Meir Achuz]

Thanks mormonator_rm . So:
if the tau is right-hand in lab fram, its spin should has the same direction as its mementum (the angle between spin and momentum <90 degree, here orbital angule mementum is 0). because the spin is conserved (the value and direction), in tau's rest frame (boosting as what I mentioned and
tau_R^{-} --->pi^- + neu_{tau}), because the angular mementum conservation (spin of pi is 0) and momentum of pi and neu_{tau} should back to back in tau's rest fram, according to these i could conclude pi^- is forward w.r.t the boost direction.
am I right? thanks

I think you mean s_z when you say "spin".
The spin of the tau is 1/2 no matter what you do to it.
You also must mean L_z when you say "orbital angule mementum is 0".
s_z is conserved for a boost in the z direction. The helicity of the
neutrino will be negative, which means it will tend to go forward wrt the direction of the original tau momentum. But there will be an angular distribution (1+cos\theta)^2 due to a mixture of L=0 and L=1.
"Helicity", s_z, and "spin" are three different things.

 

[studnte]

I think you mean s_z when you say "spin".
The spin of the tau is 1/2 no matter what you do to it.
You also must mean L_z when you say "orbital angule mementum is 0".
s_z is conserved for a boost in the z direction. The helicity of the
neutrino will be negative, which means it will tend to go forward wrt the direction of the original tau momentum. But there will be an angular distribution (1+cos\theta)^2 due to a mixture of L=0 and L=1.
"Helicity", s_z, and "spin" are three different things.

Thanks, you are right. but one point, "neutrino tend to go backward wrt the direction of the original tau momentum"(because I assumed tau is right hand).

 

[Meir Achuz]

The tau lepton is left handed, which means that a tau from weak decay will generally have average helicity=-v/2c. There will be a small probability of a tau with positive helicity. Is that what you mean?

 

[mormonator_rm]

I wasn't sure I should comment on that right away, but Meir confirmed my gut feeling on this one. Tau's are always left-handed in nature, never right-handed, although the helicity may be different on rare occasion like Meir said.

 

[studnte]

in MSSM, if charged higgs H^(-)->tau^(-)+anit-\tau_{neu}, tau is right-hand, it is different from that of tau decay from W-. and then, the momentum of 1-prong tau jet(here only means pion) decaying from tau are also different. (btw, it does not work very well due to the poor jet energy resolution of hadronic calorimeter).

tau could be left/right-hand