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This might be a silly question. When the mass of a spin 1 meson is measured, is there a way to check whether it is the same for all polarizations? Is such a meson mass the same for longitudinal and for transverse polarizations?

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The mass of all polarizations of a massive particle is the same because of the rotational symmetry. The rotational symmetry of the laws of physics is equivalent via Noether's theorem to the angular momentum conservation law which is easily checked in all particle physics processes, indeed. The difference between the transverse and longitudinal polarization only makes sense relatively to a chosen direction of motion i.e. it depends on the reference frame but the laws of physics don't, so there can't be any dependence of this sort, either. –  Luboš Motl May 2 '12 at 19:00
    
Related question from OP: physics.stackexchange.com/q/22182/2451 –  Qmechanic May 2 '12 at 19:13
    
@LubošMotl: even if it does follow from rotational symmetry, we still ought to check, shouldn't we? Else we risk the parity embarrassment... –  Emilio Pisanty May 2 '12 at 19:46
    
In the question of "is it measureable" I'd venture an unambiguous "yes". What existing data sets to look at is rather harder –  dmckee May 2 '12 at 19:52
    
I wonder whether ether type suppositions are involved in this question . –  anna v May 3 '12 at 4:06
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1 Answer

This is your second effort to get a response on this question.

As far as I know, there has not been a reason to expect that the mass of an elementary particle is a function of its polarization , We implicitly accept that an elementary particle has one rest mass, as it has one spin and one charge. You have not given a justification for the question.

Here is the abstract of one experimental study by L3

Events from the e+e− -> Z + gamma process with hard initial-state radiation collected with the L3 detector at centre-of-mass energies between 183 GeV and 209 GeV are used to measure the mass of the Z boson. Decays of the Z boson into hadrons or muon pairs are considered and the Z mass is determined to be 91.272 +/-0 0.032 (stat.) +/- 0.033 (syst:) GeV, in agreement with the value measured at the Z resonance. Alternatively,assuming this measured value of the Z mass, the method determines the LEP centre-of-mass energy, found to be 175 +/-68 (stat.)+/-68 (syst) MeV lower than the nominal value.

In the center of mass system this sample has Z polarized with the opposite polarization to the gamma. If the longitudinal mass were different than the averaged mass already studied there would be no agreement with the standard value.

Here is also a preprint with a study of the polarization of the rho meson. The mass is a given.

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Dear Anna, just a detail: the OP asked about mesons. The Z-boson isn't a meson because it's not strongly interacting (like in QCD). Not that this difference between the 1st and 2nd question by the OP makes any difference for the question. ;-) –  Luboš Motl May 2 '12 at 19:07
    
@LubošMotl Well, I tried to find a link for the rho meson but it was too hard, because those studies happened a long while ago. –  anna v May 2 '12 at 19:08
    
I will not edit so as not to bring it up to first page again, but should like to point out that as far as the Z mass is concerned there is no difference within the errors measured between longitudinal and average masses, even if rotational invariance would not be a given for some far fetched reason. –  anna v May 3 '12 at 6:25
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