I have one question which I need to verify as a thought.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose I have a particle collider for symmetric energies [itex]e^\pm[/itex], that give as a result the [itex]Y(4S)[/itex] resonance which later decays in [itex]B[/itex] mesons. Then the lab-frame is equivalent to the rest frame of the [itex]e^\pm[/itex] system and the [itex]Y(4S)[/itex] is at rest in the lab. In that case I was able to determine the momentum [itex] |p|= \sqrt{\frac{m_Y^2-4m_B^2}{4}}[/itex] and velocities [itex]u=\frac{p}{E}[/itex] of the [itex]B[/itex]-mesons and derive their travel length [itex]d_{lab}=\gamma(u) u c \tau[/itex]...

If on the other hand the energies of the [itex]e^\pm[/itex] are not equal, say [itex]E_+ \ne E_-[/itex], then the [itex]Y(4S)[/itex] will not be at rest for the lab but have some velocity [itex]\beta[/itex] relative to it.

If I want to derive the length the [itex]B[/itex] mesons travel before decaying, could I boost the result of the symmetric energies ([itex]\beta=0[/itex]) to the new lab frame ([itex]\beta \ne 0[/itex]) to get the [itex]B[/itex]-mesons "new" speed (boost the [itex]d_{lab}[/itex] by [itex]\beta[/itex])?

I am not sure about the directions however...since the B meson result can have any kind of velocity orentation at the first case -with only constraint to be in P-wave - (Y(4S) rest frame= lab frame) , while at the second (Y(4S) boosted relative to the lab) the Y(4S) speed is boosted along the beam's direction alone.

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# Lab frame symmetric/asymmetric energies

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