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Solution to the Higgs naturalness problem

Solution to the Higgs naturalness problem. Zheng-Tao Wei Nankai University, Tianjin. Seminar at National Tsing Hua University, 2011.6.7. Beijing ↔ Tianjin, ½ hour by train. The highest building in the north China. Tianjin Binhai New Area: the most admired industrial park;

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Solution to the Higgs naturalness problem

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  1. Solution to the Higgs naturalness problem Zheng-Tao Wei Nankai University, Tianjin Seminar at National Tsing Hua University, 2011.6.7.

  2. Beijing ↔ Tianjin, ½ hour by train. 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.

  3. Nankai University 我 是 愛 南 開 的 看 门 I love Nankai I am gardener of south gate 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, ….

  4. Z. Wei, L. Bian, arXiv:1104.2735. • Introduction: • Higgs naturalness problem • Quadratic divergence in φ4-theory • Our solution • Summary

  5. Introduction • The SM is very successful. • Higgs mechanism provides mass for • everything. • The crucial purpose of LHC is to search • and study Higgs.

  6. Higgs naturalness problem Fine-tuning: bare and counter-term fine-tuning at (102/1019)2~10-34; or Hierarchy: MP>>mH. Higgs is unnatural.

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

  8. Dimensional regularization is not physical. = c Λ2 • He did the first explicit calculations. 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, .…

  10. A modern review on naturalness: arXiv: 0801.2562. Naturalness problems in physics: 1. Higgs mass, 2. fermion mass, 3. cosmological constant, …

  11. 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.

  12. Pauli-Villas regularization:

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

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

  15. Solution for the case with μ2>>m2

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

  17. 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?

  19. 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.

  20. Solution of the RGE 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.

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

  22. Summary • 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.

  23. 人体是一个 自我调节系统。 Human body is a self-tuning system. SM

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