Solution to the Higgs naturalness problem

Zheng-Tao Wei

Nankai University, Tianjin

Seminar at National Tsing Hua University, 2011.6.7.

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The highest building in the north China.

Tianjin Binhai New Area: the most admired industrial park; the most attractive investment area in China and even Asia as a whole.

Beijing ↔ Tianjin,½ hour by train.

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Primier En-Lian Zhou (周恩来 ), Xing-Shen Chen (陈省身 )； Tao Han (韩涛 ), T.D. Lee, C.N. Yang, Ta-You Wu, ….

Nankai University

我是愛南開的

I love Nankai

看

门

I am gardener of south gate

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Introduction: Higgs naturalness problem

Quadratic divergence in φ4-theory

Our solution

Summary

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

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Introduction The SM is very successful. Higgs mechanism provides mass for everything.

The crucial purpose of LHC is to search and study Higgs.

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Higgs naturalness problem

Fine-tuning: bare and counter-term fine-tuning at (102/1019)2~10-34; orHierarchy: MP>>mH.

Higgs is unnatural.

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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 calculations.

= c Λ2

To do is better than to say!9

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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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

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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 solution to Higgs naturalness

Is it really a problem, or 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 18

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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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.

Summary

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人体是一个

自我调节系统。

Human body is a

self-tuning system.

SM

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