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In the standard model, Higgs particles have negative mass squared term in the SM lagrangian and hence, the Higgs is tachyonic in nature. This isn't a problem since -at low energy (temperature)- the Higgs particle will stay close to the local minima of the the Mexican hat potential and by doing so, it breaks $SU(2)$ gauge and acquires a non-negative real mass. But if we consider the high energy situation (assuming that the energy regime is higher than the unstable maximum of the higgs potential), the gauge symmetry should be restored and - as far as I understand - the higgs should have an imaginary mass.

Can Higgs particles move faster than light if the temperature/energy is high enough?

Qmechanic
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Eslam Sabry
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    A tachyonic field represents an instability, and does not have modes that superluminally; see, eg, https://en.wikipedia.org/wiki/Tachyonic_field – Andrew Apr 21 '22 at 02:55
  • As far as I understand, the instability leads to phase transition and at zero temperature, we have real mass. But if the temperature is above the critical temperature, shouldn't the system retain its imaginary mass? – Eslam Sabry Apr 21 '22 at 03:22
  • What matters is the effective mass squared parameter, which has a negative contribution from the intrinsic potential energy, and a positive contribution from thermal fluctuations. At high temperatures, the thermal contribution is larger than the intrinsic potential energy contribution, and the effective mass squared is positive. As the temperature decreases, the thermal contribution becomes smaller, until the negative potential energy term dominates. At that point, you get the tachyonic instability described in the article I linked above. – Andrew Apr 21 '22 at 03:28
  • oh, I see. This makes sense. Thank you. By the way, do you have a reference on this topic? – Eslam Sabry Apr 21 '22 at 03:31
  • This is a pretty broad topic. A good starting point is to learn about Ginzburg-Landau theory, see eg Section 1.3 of Tong's statistical field theory notes. His course page and the beginning of his notes contain some other recommended sources. If you want to know about thermal corrections to quantum field theory, this review looks good (I haven't read it though). If you want to know about the electroweak phase transition, here's a review: https://arxiv.org/abs/2006.12614 (see Section 2.3.2) – Andrew Apr 21 '22 at 03:42
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    It seems to me you are mixing up the concept of the Higgs field with the concept of particle . The Higgs particle is the particle sought at LHC to validate the standard model's Higgs field.. As the electron is the particle generated on the electron field. – anna v Apr 21 '22 at 04:09
  • Essentially a duplicate of Do tachyons move faster than light? – Qmechanic Apr 21 '22 at 04:32

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Can Higgs particles move faster than light if the temperature/energy is high enough?

No.

hft
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