**95**, 05015 (2015)

https://doi.org/10.1051/epjconf/20159505015

## The Higgs and top mass coincidence problem

IFT, Dept. of Physics, U. Murcia, Murcia, SPAIN

^{a} e-mail: etl@um.es

Published online: 29 May 2015

On the light of the recent LHC boson discovery, we present a phenomenological evaluation of the ratio *ρ _{t}* =

*m*/

_{Z}m_{t}*m*

^{2}

*, from the LHC combined*

_{H}*m*value, we get ((1

_{H}*σ*))

This value is close to one with a precision of the order ∼ 1%. Similarly we evaluate the ratio *ρ _{Wt}* = (

*m*+

_{W}*m*)/(2

_{t}*m*). From the up-to-date mass values we get

_{H}*ρ*

^{(exp)}

_{wt}= 1.0066 ± 0.0035 (1

*σ*). The Higgs mass is numerically close (at the 1% level) to the

*m*∼ (

_{H}*m*+

_{W}*m*

_{t})/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: *m _{H}*/

*m*≃ 1 + √2

_{Z}*s*

^{2}

_{θW/2},

*m*/

_{H}*m*

_{t}*c*

_{θW}≃ 1 − √2

*s*

^{2}

_{θW/2}. In the limit cos

*θ*→ 1 all the masses would become equal

_{W}*m*=

_{Z}*m*=

_{W}*m*=

_{t}*m*. 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,

_{H}*ρ*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

_{t}*m*

_{s=1}

*m*

_{s=1/2}/

*m*

^{2}

_{s=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*(*g*^{2} + *g*^{′2}) with *κ* ≃ 1 + *o*(*g*/*g _{t}*). Moreover the existence of relations

*m*/

_{i}*m*≃

_{j}*f*(

_{ij}*θ*) could be interpreted as a hint for a role of the

_{W}*SU*(2)

*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*

_{c}*ρ*are so close to one, can we find a mechanism that naturally gives

_{t}, ρ_{Wt}*m*

^{2}

_{H}=

*m*

_{Z}*m*, 2

_{t}*m*=

_{H}*m*+

_{W}*m*?.

_{t}PACS:14.80.Bn,14.80.Cp.

*© Owned by the authors, published by EDP Sciences, 2015*

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.