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Thoughts on Higgs naturalness problem

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 。. Z. Wei, L. Bian, arXiv:1104.2735. Introduction: Higgs naturalness problem Quadratic divergence in φ 4 -theory Our approach Summary. Introduction.

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Thoughts on Higgs naturalness problem

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  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，2011.12.17-21。

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

  5. 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

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

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

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

  10. 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

  11. 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

  12. 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.

  13. Pauli-Villas regularization:

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

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

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

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

  18. Our approach to Higgs naturalness • The counter-term changes to

  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. 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.

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

  24. Exponential damping becomes growing. • Naturalness problem becomes more serious.

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