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What Is Not the Hierarchy Problem (Of the SM Higgs)

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What Is Not the Hierarchy Problem (Of the SM Higgs) What is not the hierarchy problem (of the SM Higgs) Matěj Hudec Výjezdní seminář ÚČJF Malá Skála, 12 Apr 2019, lunchtime Our ecological footprint he FuFnu wni twhit th the ggs AbAebliealina nH iHiggs mmodoedlel ký MM. M. Maalinlinsský 5 (2013) EEPPJJCC 7 733, ,2 244115 (2013) 660 aarrXXiivv::11221122..44660 12 pgs. 2 Our ecological footprint the Aspects of FuFnu wni twhith the Aspects of ggs renormalization AbAebliealina nH iHiggs renormalization of spontaneously mmodoedlel of spontaneously broken gauge broken gauge theories theories ký MM. M. Maalinlinsský MASTER THESIS MASTER THESIS M. H. M. H. 5 (2013) supervised by M.M. EEPPJJCC 7 733, ,2 244115 (2013) supervised by M.M. iv:1212.4660 2016 aarrXXiv:1212.4660 2016 12 pgs. 56 pgs. 3 Our ecological footprint Aspects of Fun with the H Fun with the Aspects of ierarchy and n Higgs renormalization AbAebliealian Higgs renormalization dHecoup of spontaneously ierarclhing mmodoedlel of spontaneously y and broken gauge decoup broken gauge ling theories theories M. Hudec, M. Malinský M M. Malinský MASTER THESIS .M M. alinský MASTER THESIS Hudec, M. M M. H. alinský M. H. (hopeful 5 (2013) supervised by M.M. ly EPJC) EEPPJJCC 7 733, ,2 244115 (2013) supervised by M.M. arX (hopef iv:190u2lly. 0EPJ 12.4660 2016 4C4) 70 aarrXXiivv::112212.4660 a 2016 rXiv:190 2.04470 12 pgs. 56 pgs. 17 pgs. 4 Hierarchy problem – first thoughts 5 Hierarchy problem – first thoughts In particle physics, the hierarchy problem is the large discrepancy between aspects of the weak force and gravity. 6 Hierarchy problem – first thoughts In particle physics, the hierarchy problem is the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 1024 times stronger 7 than gravity. Hierarchy problem – first thoughts In particle physics, the hierarchy problem is the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 1024 times stronger 8 than gravity. Energy scales in High Energy Physics 9 IR UV Energy scales in High Energy Physics Electroweak scale 10 IR UV Energy scales in High Energy Physics Electroweak scale 11 IR UV Energy scales in High Energy Physics Strong scale Electroweak scale 12 IR UV Energy scales in High Energy Physics Strong scale Electroweak scale 13 IR UV Energy scales in High Energy Physics Strong scale Electroweak scale 14 IR UV Energy scales in High Energy Physics Strong scale Electroweak scale 15 IR UV Electroweak scale Electroweak Strong Strong scale Energy scales inH scales Energy IR igh igh E UV nergy nergy P hysics 16 TOEs Quantum gravity Electroweak scale Electroweak Strong Strong scale Energy scales inH scales Energy IR igh igh E UV nergy nergy P hysics 17 TOEs Quantum gravity Electroweak scale Electroweak Strong Strong scale Energy scales inH scales Energy IR igh igh E UV nergy nergy P hysics GUTs Grand unification scale 18 TOEs Quantum gravity Electroweak scale Electroweak Strong Strong scale Energy scales inH scales Energy IR igh igh E UV nergy nergy P hysics GUTs Grand unification scale 19 TOEs Quantum gravity Electroweak scale Electroweak Strong Strong scale Energy scales inH scales Energy IR igh igh E UV nergy nergy P Seesaw (type I) scale hysics GUTs Grand unification scale 20 TOEs Quantum gravity Electroweak scale Electroweak Strong Strong scale Energy scales inH scales Energy IR dessert Great igh igh E UV nergy nergy P Seesaw (type I) scale hysics GUTs Grand unification scale 21 TOEs Quantum gravity Electroweak scale Electroweak Strong Strong scale Energy scales inH scales Energy IR Low-Energy SUperSYmmetry dessert Great igh igh E UV nergy nergy P Seesaw (type I) scale hysics GUTs Grand unification scale 22 TOEs Quantum gravity More scales – why people care (1) 23 More scales – why people care (1) Example: SU(5) Grand Unified Theory “Doublet – triplet splitting” 24 More scales – why people care (1) Example: SU(5) Grand Unified Theory “Doublet – triplet splitting” 25 More scales – why people care (1) Example: SU(5) Grand Unified Theory “Doublet – triplet splitting” Fine tuning needed iff mX and mΔ are independent input parameters. 26 More scales – why people care (1) Example: SU(5) Grand Unified Theory “Doublet – triplet splitting” Fine tuning needed iff mX and mΔ are independent input parameters. Based on “Bayessian feelings”! 27 More scales – why people care (1) Example: SU(5) Grand Unified Theory “Doublet – triplet splitting” Fine tuning needed iff mX and mΔ are independent input parameters. Explain macroscopic phenomena in terms of microscopic laws Based on “Bayessian feelings”! 28 More scales – why people care (1) Example: SU(5) Grand Unified Theory “Doublet – triplet splitting” Fine tuning needed iff mX and mΔ are independent input parameters. Explain macroscopic phenomena in terms of microscopic laws Based on “Bayessian feelings”! Hierarchy problem = naturalness problem 29 More scales – why people care (1) Example: SU(5) Grand Unified Theory “Doublet – triplet splitting” Everything was TREE LEVEL! Fine tuning needed iff mX and mΔ are independent input parameters. Explain macroscopic phenomena in terms of microscopic laws Based on “Bayessian feelings”! Hierarchy problem = naturalness problem 30 More scales – why people care (2) Example 2: Loop corrections in simple models 31 More scales – why people care (2) Example 2: Loop corrections in simple models 32 More scales – why people care (2) Example 2: Loop corrections in simple models If , fine-tuning of large negative . 33 More scales – why people care (2) Example 2: Loop corrections in simple models If , fine-tuning of large negative . Common wisdom: scalars are more sensitive on higher-energy scales than fermions. 34 More scales – why people care (2) Example 2: Loop corrections in simple models If , fine-tuning of large negative . Common wisdom: scalars are more sensitive on higher-energy scales than fermions. → Hierarchy problem of the Higgs mass 35 More scales – why people care (2) Example 2: Loop corrections in simple models If , fine-tuning of large negative . Common wisdom: scalars are more sensitive on higher-energy scales than fermions. → Hierarchy problem of the Higgs mass 36 This can be solved by SUSY, unlike Example 1. Dark side of the internet “If the Standard Model is used to calculate quantum corrections to Fermi’s constant, it appears … surprisingly large, closer to a Newton’s constant.” 37 Dark side of the internet “If the Standard Model is used to calculate quantum corrections to Fermi’s constant, it appears … surprisingly large, closer to a Newton’s constant.” FALSE 38 Standard Model 39 Standard Model 40 Standard Model Higgs potential: 41 Standard Model Higgs potential: Single dimensionful parameter in the Lagrangian! 42 Standard Model Higgs potential: Single dimensionful parameter in the Lagrangian! Tree level: Vaccum Expectation Value of the Higgs field = “the VEV” 43 Standard Model Higgs potential: Single dimensionful parameter in the Lagrangian! Tree level: Vaccum Expectation Value of the Higgs field = “the VEV” 44 Standard Model Higgs potential: Single dimensionful parameter in the Lagrangian! Tree level: Vaccum Expectation Value of the Higgs field = “the VEV” Quantum (loop) level: only more complicated prefactors 45 Effective potential - crash-course Analogue to scalar potential (e.g. Higgs) but with quantum loops incorporated. 46 Effective potential - crash-course Analogue to scalar potential (e.g. Higgs) but with quantum loops incorporated. Vaccuum Expectation Value of the scalar field is determined by minimum condition. Mass of the corresponding particle given by curvature in the minimum 47 2 What if Veff = Veff(ф ) Examples: - SM - SM with UV-cuttof - SM + heavy neutrino 48 2 What if Veff = Veff(ф ) Examples: - SM - SM with UV-cuttof - SM + heavy neutrino 49 2 What if Veff = Veff(ф ) Examples: - SM - SM with UV-cuttof - SM + heavy neutrino Symmetric phase Broken phase Def Extremum condition Scalar mass 50 2 What if Veff = Veff(ф ) Examples: - SM - SM with UV-cuttof - SM + heavy neutrino Symmetric phase Broken phase Def Extremum condition Scalar mass Higgs boson mass always proportional to electroweak VEV! 51 2 What if Veff = Veff(ф ) Examples: - SM - SM with UV-cuttof - SM + heavy neutrino Symmetric phase Broken phase Def Extremum condition Scalar mass Higgs boson mass always proportional to electroweak VEV! Even for BSM people mH = 125 GeV should have been no surprise!52 Hierarchy problem is not a problem of the SM alone as it is a single scale theory caused solely by loop corrections tree-level fine-tuning issues are also common resolved fully in SUSY GUTs, tree level fine tuning still there a problem of smallness of mH= 125 GeV but rather of the whole electroweak scale a problem at all for “totally unBayessed” people. 53 LUNCH !!! .
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