The Higgs and top mass coincidence problem
IFT, Dept. of Physics, U. Murcia, Murcia, SPAIN
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Published online: 29 May 2015
This value is close to one with a precision of the order ∼ 1%. Similarly we evaluate the ratio ρWt = (mW + mt)/(2mH). From the up-to-date mass values we get ρ(exp)wt = 1.0066 ± 0.0035 (1σ). The Higgs mass is numerically close (at the 1% level) to the mH ∼ (mW + mt)/2. From these relations we can write any two mass ratios as a function of, exclusively, the Weinberg angle (with a precision of the order of 1% or better): (1)
For example: mH/mZ ≃ 1 + √2s2θW/2, mH/mtcθW ≃ 1 − √2s2θW/2. In the limit cos θW → 1 all the masses would become equal mZ = mW = mt = mH. It is tempting to think that such a value, it is not a mere coincidence but, on naturalness grounds, a signal of some more deeper symmetry. In a model independent way, ρt can be viewed as the ratio of the highest massive representatives of the spin (0, 1/2, 1) SM and, to a very good precision the LHC evidence tell us that ms=1ms=1/2/m2s=0 ≃ 1. Somehow the “lowest” scalar particle mass is the geometric mean of the highest spin 1, 1/2 masses.
We review the theoretical situation of this ratio in the SM and beyond. In the SM these relations are rather stable under RGE pointing out to some underlying UV symmetry. In the SM such a ratio hints for a non-casual relation of the type λ ≃ κ(g2 + g′2) with κ ≃ 1 + o(g/gt). Moreover the existence of relations mi/mj ≃ fij(θW) could be interpreted as a hint for a role of the SU(2)c custodial symmetry, together with other unknown mechanism. Without a symmetry at hand to explain then in the SM, it arises a Higgs mass coincidence problem, why the ratios ρt, ρWt are so close to one, can we find a mechanism that naturally gives m2H = mZmt, 2mH = mW + mt ?.
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