Effective theories and simple applications - iitg.ac.in · There is some new physics above a scale ¤. Construct the leading observable virtual effects ... DM paradigm The Universe

Effective theories in the era of the LHC and LUX

J. Wudka UCR

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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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Effective Lagrangians

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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known unknown

Renormalized Slight

Observable heavy physics

effects

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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

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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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Application

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V. Gonzalez-Macias JW

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

©

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Z

ª

ª nucleon nucleon

Nucleonic weak current

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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mª = 5.6 GeV mª = 9.9 GeV

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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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Large mo:

© Á

N ª `

`⊗

⊗

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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