Introduction
State of the field:
• Half filled glass: done with the SM, energy will reach the NP threshold, perhaps see hints now?
• Half empty glass: noting will come from the LHC; we see DM & DE, but what are they?
Effective theories are a good tool for situations like these:
“parameterizing ignorance”.
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Assumption:
There is some new physics above a scale ¤.
Construct the leading observable virtual effects of the heavy physics at scales below ¤.
Two interesting cases
• Light physics non-renormalizable Lagrangian
• Light physics renormalizable Lagrangian
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O generated at tree level by
some types of new physics
O generated at loop level
by all types of new physics
PTG operators
LG operators
Parameterize all NP effects
Made of light fields & obey the light local symmetries
Thinning the herd
• The higher the dimension the smaller the effect
• LG subdominant ) look for PTG-generated effects
• O can also be generated by
SM loops ) look for SM-suppressed effects
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The equivalence “theorem”: if {Oi} and O’ satisfy
Then, if we add b’ O’ to L eff the S matrix changes:
S[ bi ] S[ bi + b’ ui ]
the effect on all observables is just a shift in the bi
) drop O’
N.B. non-observables can depend on bi and b’ ui separately
Equivalence: a property of the light theory Loop order: a property of the heavy theory
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For SM (1 scalar doublet & no ºR) after using the equiv. them:
• 1 dim 5 operator: (ÁT L)2 º L Majorana mass
• 59 dim 6 operators • 23 dim 7 operators • VERY MANY dim 8 operators • FEWER, BUT STILL VERY MANY dim 9 operators Etc.
Effective operators for the pure SM
Hiding new physics
All PTG operators have a vertex of the form
If all heavy fields carry a symmetry under which the SM fields are singlets:
• These vertices are forbidden
• No PTG operators
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light
light
heavy
Example: eeuu 4-fermion interaction
Many successful paradigms use this:
– SUSY! R-parity
– Gauge-Higgs ! 5th dim. momentum
Those that don’t can have problems (e.g. Technicolor)
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Defective Lagrangians
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The formalism fails if: • Energies considered are above ¤
• Redundant operators are dropped when calculating non-observables
• Operator coefficients are unnaturally large
• One eliminates some terms using field redefinitions, but ‘forgets’ to
do this everywhere.
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Eliminate redundant ops. Estimate effects Use finite renormalizations
• Drop non-redundant ops • Use non-observables • Consider energies > ¤
• Renormalize only some terms
Else, bad things happen
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DM paradigm
The Universe
SM (~4%)
DM (~23%)
DE (~73%)
Assumptions:
• standard & dark sectors interact via the exchange of heavy mediators
• DM stabilized against decay by some symmetry GDM
• SM particles: GDM singlets
• Dark particles: GSM singlets
• Weak coupling
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Within the paradigm:
Mediator mass
OSM ODM mediator
Mediator fields; singlets under DM & SM symmetries
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N-generated:
• ≥ 2 component dark sector
• Couple DM (©, ª) to neutrinos
• (©,ª)-Z,h coupling @ 1 loop
Higgs portal
Leading interactions: Lowest dimension (smallest M suppression) Weak coupling ) Tree generated (no loop suppression factor)
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Dark sector: at least © & ª
m© > mª ) all ©’s have decayed: fermionic DM. ª
©
º
Important loop-generated couplings
Z
ª
ª
h
h
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The Planck constraints fix
¤eff = ¤eff(mª)
NB: Large ¸ ) small mª
Small ¾ ) small mª
ª
ª
º
º
©
If I ignore the Higgs couplings:
LUX constraints require mª ≲ 10 GeV
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mª (GeV)
¾D
D (cm
2 )
LUX excluded
m©/mª = 2
1.5 1
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If ª - anti ª asymmetry is not small:
expect monochromatic neutrinos of energy mª (below » 10 GeV)
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Add neutral fermions N to the SM:
Mass eigentsates: nL (mass=0), and  (mass=M)
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Neutrino portal scenario works well for light DM (a few GeV), but difficult to confirm.
Several items left to investigate (in progress): – full direct-detection calculation
– º mass generation (model)
– indirect detection calculation
– phenomenology
Other possible dark-standard interactions besides Higgs and neutrino portals might also be of interest