Heavy WIMP Effective Theory: Formalism and Applications for Scattering on Nucleon Targets

188 Pages·2016·3.336 MB·English

by  Mikhail P. Solon (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
Mikhail P. Solon

Heavy WIMP
Eff ective Theory
Formalism and Applications for Scattering
on Nucleon Targets
Springer Theses
Recognizing Outstanding Ph.D. Research
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Mikhail P. Solon
Heavy WIMP Effective
Theory
Formalism and Applications for Scattering
on Nucleon Targets
Doctoral Thesis accepted by The University of Chicago,
Chicago, Illinois, USA
123
MikhailP.Solon
UniversityofCalifornia,Berkeley
Berkeley,CA,USA
ISSN2190-5053 ISSN2190-5061 (electronic)
SpringerTheses
ISBN978-3-319-25197-4 ISBN978-3-319-25199-8 (eBook)
DOI10.1007/978-3-319-25199-8
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To OrvilleandSophiaSolon

Supervisor’s Foreword
MikhailSolon’sexcellentthesisformulatesthenewheavyWIMPeffectivetheory.
ThistheoryallowsprecisedeterminationofWIMP-nucleonscatteringcrosssections
in the absence of detailed knowledge about underlying dark sector dynamics,
essential for planning and interpreting the results of future dark matter direct
detectionexperiments.
ExploringthepossibleinteractionsbetweenWIMPsandstandardmodelparticles
has exposed gaps in our understandingof effective quantum field theory. Besides
explicit computations of dark matter properties, Solon’s thesis addresses several
basictheoreticalquestions.ItdescribesanewformalismforimplementingLorentz
invariance constraints in nonrelativistic theories with unknown, or unspecified,
ultravioletcompletion.ThethesisalsoprovidesnewperturbativeQCDresultsthat
determinetheimpactofheavyquarksonthehadronicmatrixelementsinvolvedin
WIMPdirectdetection.
Solon’s thesis is a technical tour de force, with impacts in dark matter phe-
nomenology,field theory formalism, and precision hadronic physics. His compu-
tationof scatteringratesforheavyelectroweak-chargeddarkmatterhasbecomea
benchmarkforthe fieldof directdetection,and histhesishasalso spawneda new
field of investigation in dark matter indirect detection, determining heavy WIMP
annihilation rates using effective field theory methods. The systematic treatment
of renormalization and heavy quark threshold matching conditions, the review of
backgroundfield methods, and the survey of hadronic matrix elements should be
useful to students and researchers interested in a variety of new physics searches
andprecisionmeasurementsinvolvingweakprobesofthenucleon.
Chicago,IL,USA RichardJ.Hill
vii

Preface
The discovery of a standard model-like Higgs boson and the hitherto absence of
evidence for other new states may indicate that if WIMPs comprise cosmological
dark matter, they are heavy compared to electroweak scale particles, M (cid:2)
mW±,mZ0.Inthislimit,theabsolutecrosssectionforaWIMPofgivenelectroweak
quantum numbers to scatter from a nucleon becomes computable in terms of
standardmodelparameters.Extendingaspectsofheavyparticleformalismfamiliar
from heavy quark effective theory, we develop heavy WIMP effective theory to
isolateuniversalbehaviorwithintheWIMPparadigm.
We presentingredientsnecessaryforthiseffectivetheoryframework,including
the formalism for bottom-upconstructionof heavy particle Lagrangiansbased on
inducedrepresentationsoftheLorentzgroup,thecompletecalculationofone-and
two-loopweak-scalematchingamplitudes,aconsistentrenormalizationschemein
thepresenceofnontrivialresidualmasses,andtheQCDframeworkforpassingfrom
thetheoryrenormalizedattheelectroweakscaletothetheoryofquarksandgluons
belowthecharmscale.
WeanalyzetheheavyWIMPlimitofWIMP-nucleonscatteringandpresentthe
firstcompletecalculationoftheleadingspin-independentcrosssectioninstandard
modelextensionsconsistingofoneortwoelectroweakSU(2) ×U(1) multiplets,
W Y
includingacarefultreatmentofperturbativeandhadronic-inputuncertainties.The
standardmodelexhibitsasurprisingtransparencyofnucleonstoWIMPscattering,
duetoacancellationbetweenscalarandtensoramplitudecontributions.Theresult-
ing cross-section predictions and their fractional uncertainties depend sensitively
on parameter inputs, and we investigate the impact of model-independentinputs,
such as perturbativeQCD corrections and nucleon scalar matrix elements, and of
model-dependentinputs,suchasWIMPquantumnumbers,additionalelectroweak
multiplets,andextendedHiggssectors.
Berkeley,CA,USA MikhailP.Solon
ix