What is not the hierarchy problem (of the SM Higgs)
Matěj Hudec Výjezdní seminář ÚČJF Malá Skála, 12 Apr 2019, lunchtime Our ecological footprint
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2 Our ecological footprint
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3 Our ecological footprint
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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 Energy scales in High Energy Physics TOEs
Strong scale y t i v a r g Electroweak scale m u t n a u Q
16 IR UV Energy scales in High Energy Physics TOEs
Strong scale y t i v a r g Electroweak scale m u t n a u Q
17 IR UV Energy scales in High Energy Physics GUTs TOEs
Strong scale e l y t a i c v s a
r n g o
Electroweak scale i t m a u c t fi n i a n u u
Q d n a r G
18 IR UV Energy scales in High Energy Physics GUTs TOEs
Strong scale e l y t a i c v s a
r n g o
Electroweak scale i t m a u c t fi n i a n u u
Q d n a r G
19 IR UV Energy scales in High Energy Physics GUTs TOEs
Strong scale e l y t a i e l c v s a a
c r n s g
o )
i Electroweak scale I
t m e a u p c t y fi n i t (
a n u w u
a Q d s n e a e r S G
20 IR UV Energy scales in High Energy Physics GUTs TOEs
Strong scale e l y t a i e l c v s a a
c r n s g
o )
i Electroweak scale I
t m e a u p c t y fi n i Great t (
a n u w
dessert u
a Q d s n e a e r S G
21 IR UV Energy scales in High Energy Physics GUTs TOEs
Strong y r t
scale e m e l y m t a i e Y l c v S s a r a
e c r n p s g
o )
U i Electroweak scale I
t S m
e a u y p c t g y fi n r i Great t (
a e n n u w
dessert u
E a Q d - s n w e a e o r L S G
22 IR UV 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 !!!