1. Thoughts on Higgs naturalness problem
Zheng-Tao Wei
Nankai University
第十届粒子物理、核物理和宇宙学交叉学科
前沿问题研讨会，三亚， 。

2. Higgs naturalness problem Quadratic divergence in φ4-theory
Z. Wei, L. Bian, arXiv:
Introduction:
Higgs naturalness problem
Quadratic divergence in φ4-theory
Our approach
Summary

3. Introduction The SM is very successful.
Higgs mechanism provides mass for
everything. Higgs—God particle.
The crucial purpose of LHC is to search
and study Higgs.

4. Measurements of SM Higgs mass from
ATLAS and CMS:
Exclude: —467 GeV;
Remain: —141 GeV.
12.13 new results discover hint of Higgs.
ATLAS MH=126 GeV (3.6σ)
excludes: GeV, >131GeV
CMS MH=124 GeV (2.6σ)
excludes: GeV

5. Higgs is unnatural. Higgs naturalness problem
Fine-tuning: bare and counter-term
fine-tuning at (102/1019)2~10-34
Higgs is unnatural.

6. History
The Origins of lattice gauge theory, Kenneth G. Wilson, 2004

8. He did the first explicit calculation.
Dimensional regularization is not physical.
= c Λ2
He did the first explicit calculation.

9. Some scenarios of solution:
Veltman’s condition:
New symmetry:
SUSY, scale invariance, …
New particle, dimension:
composite Higgs, little Higgs,
extra dimension, .…

10. Naturalness problems in physics: 1. Higgs mass, 2. fermion mass,
A modern review on naturalness: arXiv:
Naturalness problems in physics:
1. Higgs mass,
2. fermion mass,
3. cosmological constant, …

11. Is it really a problem, or just an illusion?
SM is renormalizable, mH independent of Λ.
What can the equation tell us?
-----Chuan-Hung Chen’s question
One-loop result may be misleading.
Some examples:
Asymptotic freedom, g->0, large Log
Sudakov form factor, F(Q2)->exp{-c’ln2(Q2/m2)}
large double-Log 11

12. Our idea To study RG evolution of mH with energy
due to quadratic divergence.
What’s the asymptotic behavior of mH
in the short-distance? 12

13. Quadratic divergence in φ4-theory
φ4-theory is simple and provides an ideal place to
study renormalization and RGE.
The mass renormalization is additive, not multiplicative.

14. Pauli-Villas regularization:

15. Renormalization scheme
Fujikawa’s idea:
counter-term
renormalized quantities
Thus,

16. Renormalization group equation for scalar mass
The new mass anomalous dimension is negative.

17. Solution for the case with μ2>>m2
m2 decreases as energy scale increase.

18. Another way to look at RGE
A new concept
The bare quantities are the renormalized
parameters at the UV limit.
m0=m(μ→∞)

19. Our approach to Higgs naturalness
The counter-term changes to

20. RGE for Higgs mass The bare mass is μ-independent,
The evolution is with respect to scale μ,
not lnμ.
The new mass anomalous dimension
is proportional to -mH2.

21. Solution of the RGE The Higgs mass is an exponential damping
Where mV is called by “Veltman mass”.
The Higgs mass is an exponential damping
function when energy scale increases.
The Higgs mass in the UV limit approaches
“Veltaman mass” mV.
The bare mass is not divergent, but finite.

22. Peculiarity of the SM: 1. The couplings are proportional to masses.
2. The evolutions of coupling constants and
masses are correlated with each other.

23. End of the naturalness problem?
The Higgs mass about 100 GeV order is stable.
The Higgs naturalness problem is solved by
radiative corrections themselves within SM.
New symmetry and new particles are
unnecessary.

24. But, our start point is wrong:
It is wrong in sign!!!

25. Exponential damping becomes growing.
Naturalness problem becomes more serious.