Addressing Theoretical Uncertainties In Dark Matter Direct .

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Addressing theoretical uncertaintiesin dark matter direct detection experimentsAlejandro IbarraTechnische Universität MünchenBased on works with Andreas Rappelt and Bradley KavanaghIPMUVirtual seminarJune 2020

There is evidence for dark matterin a wide range of distance scalesSolar systempcGalaxieskpcClustersof galaxiesMpcObservableUniverseGpcdistance

There is evidence for dark matterin a wide range of distance scalesSolar systempcGalaxieskpcClustersof galaxiesMpcObservableUniverseGpcdistance

There is evidence for dark matterin a wide range of distance scalesSolar systempcGalaxieskpcClustersof galaxiesMpcAbell 1689ObservableUniverseGpcdistance

There is evidence for dark matterin a wide range of distance scalesSolar systempcGalaxieskpcClustersof galaxiesMpcAbell 1689ObservableUniverseGpcdistance

There is evidence for dark matterin a wide range of distance scalesSolar systempcGalaxieskpcClustersof galaxiesMpcObservableUniverseGpcdistance

There is evidence for dark matterin a wide range of distance scalesSolar systempcGalaxieskpcClustersof galaxiesMpcObservableUniverseGpcdistance

There is evidence for dark matterin a wide range of distance scalesSolar systempcGalaxieskpcAssumption,but well motivatedClustersof galaxiesMpcObservableUniverseGpcdistance

If the DM is made up of WIMPs,the DM population inside theSolar System could be detected

Searching for WIMP DM inside the Solar SystemDMDMNuclear recoilNo significant excess detected so far

Searching for WIMP DM inside the Solar SystemDMDMNuclear recoilNo significant excess detected so far

Searching for WIMP DM inside the Solar SystemDMDMNuclear recoilNo significant excess detected so far

Searching for WIMP DM inside the Solar SystemDMDMNuclear recoilNo significant excess detected so farNo significant excess detected so far

Theoretical interpretationof the experimental results

Theoretical interpretation of the experimental results Differential rate of DM-induced scatterings The neutrino flux from annihilations inside the Sun is, under plausibleassumptions, determined by the capture rate inside the Sun:

Theoretical interpretation of the experimental results Differential rate of DM-induced scatteringsUncertainties from particle/nuclear physics and from astrophysics The neutrino flux from annihilations inside the Sun is, under plausibleassumptions, determined by the capture rate inside the Sun:

Theoretical interpretation of the experimental resultsUncertainties from particle/nuclear physics. Dark matter mass?For thermally produced dark matter, mDM few MeV - 100 TeV Differential cross section?Spin-independent andspin-dependent cross sectionsat zero momentum transferNuclear form factors(In some DM frameworks, other operators may also arise )

Theoretical interpretation of the experimental resultsUncertainties from astrophysics Local dark matter density? “local measurements”:From vertical kinematicsof stars near ( 1 kpc) the Sun “global measurements”:From extrapolations ofρ(r) determined from rotationcurves at large r, to the positionof the Solar System.Read '14

Theoretical interpretation of the experimental resultsUncertainties from astrophysics Local dark matter velocity distribution?Completely unknown. Rely on theoretical considerations If the density distribution follows a singular isothermal sphere profile, thevelocity distribution has a Maxwell-Boltzmann form.

Theoretical interpretation of the experimental resultsUncertainties from astrophysics Local dark matter velocity distribution?Completely unknown. Rely on theoretical considerations If the density distribution follows a singular isothermal sphere profile, thevelocity distribution has a Maxwell-Boltzmann form. Dark matter-only simulations. Show deviations from Maxwell-Boltzmann

Theoretical interpretation of the experimental resultsUncertainties from astrophysics Local dark matter velocity distribution?Completely unknown. Rely on theoretical considerations If the density distribution follows a singular isothermal sphere profile, thevelocity distribution has a Maxwell-Boltzmann form. Dark matter-only simulations. Show deviations from Maxwell-Boltzmann Hydrodynamical simulations (DM baryons). Inconclusive at the moment.Bozorgnia et al'16

Theoretical interpretation of the experimental resultsCommon approach: assume SI or SD interaction only, assume ρloc 0.3 GeV/cm3and assume a Maxwell-Boltzmann velocity beCeIcLUXSuper-KTON1XENCuIceLZ-60PICObe

Theoretical interpretation of the experimental resultsCommon approach: assume SI or SD interaction only, assume ρloc 0.3 GeV/cm3and assume a Maxwell-Boltzmann velocity distributionSI1 is ruled out (by XENON1T, among others)DAMA/LIBRA1Super-KaXPandTON1XENLZubeCeIcLUX

Theoretical interpretation of the experimental resultsCommon approach: assume SI or SD interaction only, assume ρloc 0.3 GeV/cm3and assume a Maxwell-Boltzmann velocity distributionSI1 is ruled out (by XENON1T, among others)DAMA/LIBRA21Super-KaXPandTON1XENLZ2 explains the DAMA results, butubeCeIcLUXis ruled out by other direct detectionexperiments and by neutrino telescopes

Theoretical interpretation of the experimental resultsCommon approach: assume SI or SD interaction only, assume ρloc 0.3 GeV/cm3and assume a Maxwell-Boltzmann velocity distributionSI1 is ruled out (by XENON1T, among others)DAMA/LIBRA21Super-KubeCeIcLUXaXPandTON1XEN2 explains the DAMA results, butis ruled out by other direct detectionexperiments and by neutrino telescopes3 is allowed by current experiments, andwill be tested by LZ.3LZ

Theoretical interpretation of the experimental resultsCommon approach: assume SI or SD interaction only, assume ρloc 0.3 GeV/cm3and assume a Maxwell-Boltzmann velocity distributionSI1 is ruled out (by XENON1T, among others)DAMA/LIBRA21Super-KubeCeIcLUXaXPandTON1XEN2 explains the DAMA results, butis ruled out by other direct detectionexperiments and by neutrino telescopes3 is allowed by current experiments, andwill be tested by LZ.3LZWhat is the impact of the astrophysicaluncertainties on these conclusions?

Theoretical interpretation of the experimental resultsCommon approach: assume SI or SD interaction only, assume ρloc 0.3 GeV/cm3and assume a Maxwell-Boltzmann velocity distributionSI1 is ruled out (by XENON1T, among others)DAMA/LIBRA21Super-KubeCeIcLUXaXPandTON1XEN2 explains the DAMA results, butis ruled out by other direct detectionexperiments and by neutrino telescopes3 is allowed by current experiments, andwill be tested by LZ.3LZWhat is the impact of the astrophysicaluncertainties on these conclusions?

Theoretical interpretation of the experimental resultsCommon approach: assume SI or SD interaction only, assume ρloc 0.3 GeV/cm3and assume a Maxwell-Boltzmann velocity distributionSI1 is ruled out (by XENON1T, among others)DAMA/LIBRA21Super-KubeCeIcLUXaXPandTON1XEN2 explains the DAMA results, butis ruled out by other direct detectionexperiments and by neutrino telescopes3 is allowed by current experiments, andwill be tested by LZ.3LZWhat is the impact of the astrophysicaluncertainties on these conclusions?Do these conclusions hold for arbitraryvelocity distributions?

Addressing astrophysicaluncertainties indark matter detection

Halo-independent approach for DM frameworks is ruled out regardless of the velocity distribution if

Halo-independent approach for DM frameworksis ruled out regardless of the velocity distribution ifRateExcluded

Halo-independent approach for DM frameworksis ruled out regardless of the velocity distribution ifRateExcluded

Halo-independent approach for DM frameworksis ruled out regardless of the velocity distribution ifRateExcluded

Halo-independent approach for DM frameworksis ruled out regardless of the velocity distribution ifRateExcluded

Halo-independent approach for DM frameworks is ruled out regardless of the velocity distribution ifNote: one single direct detection experiment is not sufficient to probea dark matter model in a totally halo-independent mannerf(v)v

Halo-independent approach for DM frameworks is ruled out regardless of the velocity distribution ifNote: one single direct detection experiment is not sufficient to probea dark matter model in a totally halo-independent mannerf(v)Velocity thresholdof the experimentv

Halo-independent approach for DM frameworks is ruled out regardless of the velocity distribution ifNote: one single direct detection experiment is not sufficient to probea dark matter model in a totally halo-independent mannerf(v)Velocity thresholdof the experimentvSome velocity distributions willescape detection in the experiment

Halo-independent approach for DM frameworks is ruled out regardless of the velocity distribution ifNote: one single direct detection experiment is not sufficient to probea dark matter model in a totally halo-independent mannerf(v)Velocity thresholdof the experimentvPossibility 1: consider “distortions” of the Maxwell-Boltzmann distribution

Halo-independent approach for DM frameworks is ruled out regardless of the velocity distribution ifNote: one single direct detection experiment is not sufficient to probea dark matter model in a totally halo-independent mannerf(v)Zero velocity thresholdvPossibility 2: Design an experiment with zero velocity threshold

Halo-independent approach for DM frameworks is ruled out regardless of the velocity distribution ifNote: one single direct detection experiment is not sufficient to probea dark matter model in a totally halo-independent mannerf(v)velocity threshold forcapture in the SunvNeutrino telescopes probe low dark matter velocities. In combination withdirect detection experiments, one can probe the whole velocity space

Halo-independent approach for DM frameworks is ruled out regardless of the velocity distribution ifPossibility 1:Possibility 2:Optimization problem with constraints

Halo-independent approach for DM frameworksTechnically complicated.

Halo-independent approach for DM frameworksExpress the velocity distribution as a superposition of many many streams:Minimization problem. For given DM mass and cross-section:The parameters σ and mDM are excluded in a halo independent manner if :

Halo-independent approach for DM frameworksExpress the velocity distribution as a superposition of many many streams:Minimization problem. For given DM mass and cross-section:The objective function and the constraintsare linear in the weights of the DM streams Optimize using linear programming techniques.

A tour in linear programmingAn automobile company produces cars and trucks. For each car obtains400 profit, and for each truck, 700 . What should be the strategy of thecompany to optimize the weekly profit?

A tour in linear programmingAn automobile company produces cars and trucks. For each car obtains400 profit, and for each truck, 700 . What should be the strategy of thecompany to optimize the weekly profit?Answer: produce only trucks, if there are no constraints.

A tour in linear programmingAn automobile company produces cars and trucks. For each car obtains400 profit, and for each truck, 700 . What should be the strategy of thecompany to optimize the weekly profit?Answer: produce only trucks, if there are no constraints.In real life, the production is subject to constraints- It takes 4 hours to assemble the engine of a car, and 3 hours for a truck- It takes 2 hours to paint a car, and 4 hours to paint a truck- The assembling chain operates 14 hours a day, and the paintworkshop operates 10 hours a day, 5 days a week.

A tour in linear programmingAn automobile company produces cars and trucks. For each car obtains400 profit, and for each truck, 700 . What should be the strategy of thecompany to optimize the weekly profit?Answer: produce only trucks, if there are no constraints.In real life, the production is subject to constraints- It takes 4 hours to assemble the engine of a car, and 3 hours for a truck- It takes 2 hours to paint a car, and 4 hours to paint a truck- The assembling chain operates 14 hours a day, and the paintworkshop operates 10 hours a day, 5 days a week.Linear programming problem:

A tour in linear programmingAn automobile company produces cars and trucks. For each car obtains400 profit, and for each truck, 700 . What should be the strategy of thecompany to optimize the weekly profit?Answer: produce only trucks, if there are no constraints.In real life, the production is subject to constraints- It takes 4 hours to assemble the engine of a car, and 3 hours for a truck- It takes 2 hours to paint a car, and 4 hours to paint a truck- The assembling chain operates 14 hours a day, and the paintworkshop operates 10 hours a day, 5 days a week.Linear programming problem:“Objective function”“Constraints”“Decision variables”

A tour in linear programmingeassmblyNt“feasible region”Ncpa int

A tour in linear programmingNt500075001000012500Nc15000

A tour in linear programmingNc 13Nt 6Profit 9400 /weekNt50007500100001250015000940Nc0

A tour in linear programmingNc 0Nt 16.7Profit 11700 /week11700Nt500075001000012500Nc15000

A tour in linear programmingNtNtNcNcLessons:1) The solution lies at one of the vertices of the feasible region (polygon)2) For two constraints there are:- two non-vanishing decision variables, when the two constraints are saturated- one non-vanishing decision variable, when one of the constraints isnot saturated

A tour in linear programmingSuppose that the company also produces motorbikes. The profit is 100 per motorbike, it takes 1 hour to assemble the engine of the motorbike,and it takes 30 minutes to paint the motorbike.NtNcNb

A tour in linear programmingSuppose that the company also produces motorbikes. The profit is 100 per motorbike, it takes 1 hour to assemble the engine of the motorbike,and it takes 30 minutes to paint the motorbike.Nb 0Nc 13NtNt 6Profit 9400 /weekNcNb

A tour in linear programmingNtNcNbFor three decision variables and two constraints, the optimizedsolution necessarily has at least one vanishing decision variable(or, alternatively, at most two non-vanishing decision variables).(Three non-vanishing decision variables would correspondto a point singled-out by the intersection of three planes,but we only have two constraints!)

A tour in linear programmingTake-home lessons from linear programming:1) The solution lies at one of the vertices of the “feasible region”2) For N constraints, there are between 1 and N non-vanishingdecision variables(when r of the constraints are not saturated, then theoptimal solution consists of N - r decision variables)

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK.Express the velocity distribution as a superposition of many many streams:Minimization problem. For given DM mass and cross-section:1) The solution lies at one of the vertices of the “feasible region”2) The optimized velocity distribution contains either one or twostreams (depending on the number of constraints that are not saturated).

GeneralizationCalculate the maximum/minimum outcome in a direct detection experiment A,given the upper limits on the outcome of p experiments Bα, α 1., p , and thelower limits on the outcome of q experiments Bα, α p 1., p q (and therequirement that the velocity distribution is normalized to 1).1) The solution lies at one of the vertices of the “feasible region”.2) The optimized velocity distribution contains between 1and p q 1 streams (depending on the number of constraintsthat are not saturated).

Distorting the Maxwell-Boltzmann distributionCalculate for a given Δ the minimum of the scattering rate among all thevelocity distributions within the band. A point in parameter space is excluded if:

Distorting the Maxwell-Boltzmann distributionCalculate for a given Δ the minimum of the scattering rate among all thevelocity distributions within the band. A point in parameter space is excluded if:Ruled out by XENON1T assumingthe SHM, and ruled out unless oneallows distortions Δ 10x

Distorting the Maxwell-Boltzmann distributionCalculate for a given Δ the minimum of the scattering rate among all thevelocity distributions within the band. A point in parameter space is excluded if:xNo signal at XENON1T assumingthe SHM, but may produce signalsif Δ 100

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK.Calculate the minimum of the scattering rate among all the velocitydistributions giving a capture rate in agreement with the constraints fromneutrino telescopes. A point in parameter space is excluded if:

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK.Calculate the minimum of the scattering rate among all the velocitydistributions giving a capture rate in agreement with the constraints fromneutrino telescopes. A point in parameter space is excluded if:AI, Rappelt’17

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK.Calculate the minimum of the scattering rate among all the velocitydistributions giving a capture rate in agreement with the constraints fromneutrino telescopes. A point in parameter space is excluded if:AI, Rappelt’17

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK.Calculate the minimum of the scattering rate among all the velocitydistributions giving a capture rate in agreement with the constraints fromneutrino telescopes. A point in parameter space is excluded if:AI, Rappelt’17

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK.Calculate the minimum of the scattering rate among all the velocitydistributions giving a capture rate in agreement with the constraints fromneutrino telescopes. A point in parameter space is excluded if:1 is ruled out by PandaX assuming the SHM,but allowed for some velocity distributions1AI, Rappelt’17

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK.Calculate the minimum of the scattering rate among all the velocitydistributions giving a capture rate in agreement with the constraints fromneutrino telescopes. A point in parameter space is excluded if:1 is ruled out by PandaX assuming the SHM,but allowed for some velocity distributions22 is ruled out from combining PandaX andneutrino telescopes, for any velocitydistribution.1AI, Rappelt’17

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK.Calculate the minimum of the scattering rate among all the velocitydistributions giving a capture rate in agreement with the constraints fromneutrino telescopes. A point in parameter space is excluded if:31 is ruled out by PandaX assuming the SHM,but allowed for some velocity distributions22 is ruled out from combining PandaX andneutrino telescopes, for any velocitydistribution.13 is ruled out by neutrino telescopes only,for any velocity distribution.AI, Rappelt’17

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK: extensionCalculate the minimum of the scattering rate among all the velocity distributionswithin the band of width D giving a capture rate in agreement with theconstraints from neutrino telescopes. A point in parameter space is excluded if:AI, Kavanagh, Rappelt’18

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK: extensionCalculate the minimum of the scattering rate among all the velocity distributionswithin the band of width D giving a capture rate in agreement with theconstraints from neutrino telescopes. A point in parameter space is excluded if:AI, Kavanagh, Rappelt’18

Upper limit on the scattering cross section fromcombining PandaX and IceCube/SK: extensionCalculate the m

Neutrino telescopes probe low dark matter velocities. In combination with direct detection experiments, one can probe the whole velocity space v f(v) Note: one single direct detection experiment is not sufficient to probe a dark matter model in a totally halo-independent manner

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