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， 2011.12.17-21。

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Introduction: Higgs naturalness problem

Quadratic divergence in φ4-theory

Our approach

Summary

Z. Wei, L. Bian, arXiv:1104.2735.

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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.

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Measurements of SM Higgs mass from ATLAS and CMS: Exclude: 141—467 GeV; Remain: 114—141 GeV.

12.13 new results discover hint of Higgs. ATLAS MH=126 GeV (3.6σ) excludes: 112-115GeV, >131GeV CMS MH=124 GeV (2.6σ) excludes: 127-600GeV

Higgs naturalness problem

Fine-tuning: bare and counter-term fine-tuning at (102/1019)2~10-34

Higgs is unnatural.5

History

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

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Dimensional regularization is not physical.

He did the first explicit calculation.

= c Λ2

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Some scenarios of solution:

Veltman’s condition:

New symmetry: SUSY, scale invariance, … New particle, dimension: composite Higgs, little Higgs, extra dimension, .…

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A modern review on naturalness: arXiv: 0801.2562.

Naturalness problems in physics: 1. Higgs mass, 2. fermion mass, 3. cosmological constant, …

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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

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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?

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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.

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Pauli-Villas regularization:

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Renormalization scheme

Fujikawa’s idea:

counter-term renormalized quantities

Thus,

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Renormalization group equation for scalar mass

The new mass anomalous dimension is negative.

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Solution for the case with μ2>>m2

m2 decreases as energy scale increase.

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Another way to look at RGE

A new concept

The bare quantities are the renormalized parameters at the UV limit.

m0=m(μ→∞)

Our approach to Higgs naturalness

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The counter-term changes to

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 -mH

2.

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Solution of the RGE

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.

Where mV is called by “Veltman mass”.

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Peculiarity of the SM:

1. The couplings are proportional to masses.

2. The evolutions of coupling constants and masses are correlated with each other.

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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.

End of the naturalness problem?

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But, our start point is wrong:

It is wrong in sign!!!

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Exponential damping becomes growing.

Naturalness problem becomes more serious.