Transcript if any new physics exists

The Hierarchy Problem
W. Verkerke (NIKHEF)
Wouter Verkerke, NIKHEF
The Standard Model – successes & limitations
• Remarkably successful description of presently known
phenomena
– Experimental frontier moved to few 100 GeV with no confirmed
deviations
– Nevertheless, it is a work in progress
• A new framework is needed at the reduced Planck scale
– MP=(8pGNewton)-1/2 = 2.4 x 1018 GeV
– where quantum gravitational effects become important
• More generally, it would not be surprising if new physics
exists in the 16 orders of magnitude between present
frontier and the Planck scale
Wouter Verkerke, NIKHEF
Influences on SM from beyond the energy frontier
• Even though SM does not describe new particles beyond
energy frontier (other than Higgs) it is sensitive to it
– Specifically Higgs potential is very sensitive to new physics in
almost any imaginable extension of the SM
• How does this happen?
– Neutral Higgs in SM is complex scalar field H with classical
potential
V  mH2 | H | 2  | H | 4
– The SM requires a non-vanishing vacuum
expectation value for H at the minimum of
the potential. This will occur if mH2<0
resulting in
H   mH2 / 2
Wouter Verkerke, NIKHEF
Influences on SM from beyond the energy frontier
• We know experimentally that <H> = 174 GeV
– From measurements of the properties of weak interactions
– So mH2 is roughly of order –(100 GeV)2
H   mH2 / 2
• Theory: mH2 receives non-negligible quantum corrections
– From the virtual effects of every particles which couples directly or
indirectly to the Higgs field
• Can this result in a value consistent with experimental
data?
Wouter Verkerke, NIKHEF
Quantum corrections to the Higgs potential
• Example one-loop corrections
Dirac fermion f with mass mf
Complex scalar s with mass ms
| S | 2 2
2
m 


sm
ln(  UV / mS )  
UV
S
2
16p
2
H


Correction on mH due to diagram contribution
mH2 
|  f |2
16p
2
 2
2
UV

 6m 2f ln( UV / m f )  
UV momentum cutoff used to regulate the loop integral
Interpret cutoff as scale where new physics enters
to alter high energy behavior of theory
Wouter Verkerke, NIKHEF
Quantum corrections to the Higgs potential
• But wait – it is even worse: Problem happens even if
hypothetical new particles do not couple directly to
Higgs
– Example two-loop correction to Higgs mass due to heavy fermion
 | g |2
2
m H  x
2
 16p
2

 a2UV  48m F2 ln(  UV / m F )  



– Numeric factors in  may be small (O(10-5)), but with UV=MP
contribution still enormous
Wouter Verkerke, NIKHEF
Quantum corrections – is it a problem?
• A: yes!
• If you take the MH2 contributions from all SM particles,
mH becomes inconsistent with EW constraints for loop
cutoff values around 1 TeV  Breakdown of SM
– Contribution of top quark the largest (top1)
– Exact breakdown point depends on (accidental) cancellations of
contributions
mH2 
|  f |2
16p
2
 2
2
UV

 6m 2f ln( UV / m f )  
• But also: if any new physics exists between SM and
Planck it will contribute to MH2 proportional to the
mass of those new physics particles
– ‘Natural’ value of mH seems more to be like MP than experimental
value
 ‘Hierarchy problem’ 
Wouter Verkerke, NIKHEF
At what energies does all this become a problem
• ‘Unnatural’ ways out
– ‘Fine tuning’ – A Theory only works for (very) specific set of
parameters for which exists no natural explanation in theory [
though it might happen ]
– Pandora’s box of philosophical arguments here  Anthropic
principle
• You can also turn the hierarchy problem around and
state that it predicts that new physics will appear
around 1 TeV scale to cure SM breakdown
– LHC ‘No-lose’ theorem
• What are you going to see above 1 TeV?
– Production of new heavy particles involved in the solution to the
hierarchy problem
– (Barring fine tuning or accidental cancellations…)
Wouter Verkerke, NIKHEF
Fixing the hierarchy problem
• Classical solution: Find a mechanisms that conspires
that all MH2 terms magically cancel each other
– Physicists favorite conspiracy: a symmetry
– Enter the idea of a ‘super-symmetry’ that accomplishes this
cancellation
fermions
m 
2
H
|  f |2
16p
2
 2
2
UV

 6m 2f ln( UV / m f )  
Note relative minus sign between
fermion and boson contributions
 Exploit this idea
| S | 2 2
2
m 


sm
ln(  UV / mS )  
UV
S
2
16p
2
H
bosons


Wouter Verkerke, NIKHEF
Fixing the hierarchy problem
• Enter the concept of a ‘super-symmetry’
– If each of the quarks and leptons in the SM were accompanied by
two complex scalars with s=|f|2 all one-loop corrections to the
Higgs mass cancel
– If a symmetry between fermions and bosons is postulated all
higher order terms cancel as well
• Some dirty laundry here…
– The supersymmetry transformation turns a boson into a fermion
and vice versa.
– Fixing of the hierarchy problem powerful motivation for the
existence of a supersymmetry
– SuSy kicks in around  of O(1 TeV), below SUSY only SM particles
 explains why we haven’t seen it yet
• Supersymmetry leads to a rich phenomenology of new
‘super’ particles that should be visible at LHC energies
– Subject separate talks in this seminar series
Wouter Verkerke, NIKHEF
Other ways to fix the hierarchy problem
• Recent theory: ‘little Higgs’ (N. Arkani-Hamed et al.)
– Somewhat similar to SuSy, but in LH models are based on a
different symmetry
– In LH models new bosons and fermions are introduced,
but bosons cancel bosons and fermions cancel fermions
– Difficult to construct these models but cancellation of Higgs mass
correction terms doesn’t come as easy as in SuSy
– Higgs in these models is pseudo-Goldstone boson of
spontaneously broken symmetry at energy scale s of P(10 TeV)
– Predicted Higgs masses in the few 100 GeV range
– Predicts vector-like top partner
that can be pair-produced at LHC
(decays cW+b, ch+t, cZ+t)
– Not UV-complete, breaks down
around 10 GeV
Wouter Verkerke, NIKHEF
Other ways to fix the ‘big’ hierarchy problem
• A very different kind of solution: bring down MP
– MP  Scale where gravity becomes strong
• Scenario: postulate existence extra dimensions of finite
size
– MP might be as low as a few TeV
and serve as viable UV in SM
• Example signatures:
Strength
– Change power in running of gravitational coupling constant
Standard Model
uncertain > 1 TeV
– Kaluza-Klein towers
• standing waves in extra dimensions
that appears as massive particles with
uniform mass spacing M(Kn)=n*MKK
1/r2+n
1/r2
– Miniature black hole
production and evaporation
EnergyVerkerke,
(GeV) 
distance
Wouter
NIKHEF
-1
Conclusion
• Hierarchy problem relates mass of Higgs to existence of
physics at energies up to Planck scale through Higgs
self-coupling diagrams
• Constrains on mH from present EW experimental data
suggests a mechanism exists to cancel Higgs selfcoupling terms
• Reversal of above is the ‘no-lose’ for discovery potential
of LHC: Above breakdown scale of SM of O(1 TeV) new
physics involved hierarchy solution must materialize
• Several scenarios exists to accomplish this cancellation
– Supersymmetry (fermion-boson symmetry)
– Little Higgs (Higgs = pseudo-Goldstone boson of broken
symmetry)
– Extra dimensions (lower MP to acceptable energy scale)
Wouter Verkerke, NIKHEF