Simplified models in collider searches for dark matter. Stefan Vogl

Transcription

1 Simplified models in collider searches for dark matter Stefan Vogl

2 Outline Introduction/Motivation Simplified Models for the LHC A word of caution Conclusion

3 How to look for dark matter at the LHC? experimentally very challenging environment with huge backgrounds need to know something about the expected signal to devise a search strategy dark matter does not interact with detector only one observable directly connected to dark matter: missing transverse energy Emiss T two options: dark matter part of new sector, look for signs of mediators more model independent look for E T miss and something (jet, photon, Z,...) let s try to follow this line of thought for now

4 Monojet searches S. Vogl (MPIK) Colliding Pizza, Heidelberg, 16th of January 2017

5 Monojet searches

6 What does an excess (the absence of an excess) in high Emiss T events tell us? average physicist: not much We need: framework for interpretation of LHC searches framework for interpretation of different experiments provide guide to relevant regions of the parameter space... models for dark matter

7 General BSM models many models for BSM physics at the weak scale can easily accommodate dark matter (supersymmetry, extra dimensions... ) these models offer well motivated candidates, everything is calculable, many experimental signatures BUT: most of the experimental signatures and/or theoretical constraints are not related to DM properties BUT: reinterpretation of experimental results in terms of other model nontrivial

8 Worst case scenario theoretical prejudice should always be treated as a prejudice CDF

9 Effective field theory new physics is heavy Fermi-like theory for DM? L = 1 Λ 2 χγµ χ qγ µ q O(10) possible operators some operators only generated by loops very few parameters (m DM, Λ) easy comparison with other observables

10 Effective field theory g DM g q q 2 M 2 g DMg q M 2 + O(q 2 /M 2 ) +... expansion relies on q < M typical momentum transfer: q = O(100 GeV) typical excluded scale: M = O(100 GeV) unreliable

11 EFT vs model EFT typically does not reproduce distributions correctly BUT: EFT not necessarily inapplicable

12 Not quite as model independent interpretation: Simplified models if new physics is not very heavy we have to keep these degrees of freedom in order to capture the phenomenology dark matter particle and the mediator(s) between dark matter and the Standard Model parameter count: 2 masses, a few couplings... possible ways to think about this: simplification of more complex UV model way to parametrize a differential cross sections/distributions in an experiment could be a viable model in itself (dark matter connected to SM by U(1) B-L etc)

13 Simplified models substantial number of possibilities scalar dark matter, fermionic dark matter, vector dark matter, scalar mediators, fermionic mediators... Warning: Simplicity is in the eye of the beholder the three most widely used simplified models for fermionic dark matter scalar t-channel scalar s-channel vector s-channel

14 Scalar t-channel mediator dark matter couples to a quark and a colored scalar mediator φ L int = y qχφ q + h.c. 3D parameter space: m χ, m φq, y similar to SUSY (neutralino and squarks)

15 Limits run search derive limit map

16 Add more LHC signatures simplified models can predict multiple LHC signatures and different production channels φφ production from pure QCD multi-jet + Emiss T final states mixed χφ production mono-jet

17 Add more experiments simplified models are not limit to LHC searches thermal freeze-out, indirect detection and direct search add valuable information combine available data

18 Compare experiments 500 mχ GeV COUPP Thermal relic Jets MET Λ 1 SD, p Monojet m Φ GeV

19 Scalar s-channel dark matter and quarks interact with a (pseudo-)scalar mediator L int = g χ χχφ + g q qqφ However: qqs = q R q L S + q L q R S, i.e. not gauge invariant typical assumption: coupling proportional to SM Yukawa DM couples mainly to tops g q = y q g q

20 Simplified model for loop induced coupling no top in proton scalar couples to gluon via top loop (similar to Higgs)

21 Loop-induced production simplified model allows consistent treatment of loops

22 LHC limits

23 Vector s-channel mediator fermionic dark matter interacts with SM fermions via a Z boson 2 masses, 2 vector couplings + 2 axial-vector couplings (+ potentially additional flavor structure) L = Z µ [ f g V f γ µ + gf A γ µγ 5] f Z µ ψ [ gdmγ V µ + gdmγ A µ γ 5] ψ. f =q,l,ν DM DM Z f f

24 LHC benchmark models

25 Additional signatures Z also leads to dijet resonance

26 Questions Are results obtained in simplified model reliable? Where does this model come from? Which parts of their parameter space are theoretically motivates?... take Z models as example in the following

27 Let s get out the toolbox

28 Perturbative Unitarity we know from SM that massive vector boson lead to issues with unitarity partial wave analysis of the amplitude M J if (s) = π β if d cos θ dµµ J (θ) M if (s, cos θ) 1 with β if : kinematical factor and dµµ J (θ) : Wigner d-function perturbative unitarity requires check validity of model 0 Im(M J ii ) 1, Re(M J ii ) 1 2.

29 DM side: self scattering longitudinal component of vector couples proportional to ga f m f /m Z perturbative unitarity is violated unless π m Z m f 2 gf A DM can not be arbitrary heavy compared to mediator (or is arbitrarily weakly coupled ) A g DM = 1, g A q,l = 0.25 DM overproduction A g DM = 1, g A q,l = 0.25 DM overproduction m Z' [GeV] 10 3 Monojets Direct m Z' [GeV] 10 3 Monojets Direct Perturbative unitarity violation detection detection m DM [GeV] m DM [GeV]

30 DM side: DM DM Z Z matrix element for DM DM Z Z diverges in high energy limit M (ga DM )2 s m DM m 2 Z theory only valid up to 10 4 A m DM = 500 GeV, g DM = 1 scale s < π m2 Z (g A DM )2 m DM thermal dark matter typically requires g A DM of O(1) dangerous s typically low need new physics to unitarize vector boson m Z ' [GeV ] s 1/2 [GeV]

31 A dark Higgs need to restore perturbative unitarity Higgs mechanism break U(1) with scalar singlet S Lagrangian is given by (Majorana dark matter) L DM = i 2 ψ / ψ 1 2 ga DMZ µ ψγ 5 γ µ ψ 1 2 y DM ψ(p L S + P R S )ψ, L S = [( µ + i g S Z µ )S] [ ( µ + i g S Z µ)s ] + µ 2 s S S λ s ( S S ) 2 side remark: vector interaction don t generate these problems (m Z from Stueckelberg mechanism)

32 Shifting benchmark g χ g q = m χ = 100 GeV Perturbative unitarity violation Direct detection Monojets EWPT Dileptons Dijets m Z' [GeV]

33 A look at the SM side: gauge invariance fermionic dark matter interactions with SM fermions mediated by Z boson L = f =q,l,ν Z µ f [ g V f γ µ + g A f γ µγ 5] f Z µ ψ [ g V DM γ µ + g A DMγ µ γ 5] ψ. looks fine but: g V f = 1 2 g (q fr + q fl ), g A f = 1 2 g (q fr q fl ) general Z couplings break SM gauge invariance (SM Yukawa terms)

34 Broken SU(2) invariance broken gauge invariance processes including gauge bosons violate unitarity mono-w harder than QCD QCD cross sections not affected Required level of UV completeness depends on considered signature!

35 Fixing gauge invariance need a consistent picture for SU(2) U(1) U(1) breaking g A f = 1 2 g (q fr q fl ) breaks gauge invariance q H =q ql q ur = q dr q ql = q er q ll restores it leads to following Lagrangian: L SM = f =q,l,ν g Z µ [ q fl fl γ µ f L + q fr fr γ µ f R ] + [ (D µ H) ( i g q H Z µ H) + h.c. ] + g 2 q 2 H Z µ Z µ H H Z interacts with all generations of quarks and with leptons stringent constraints from searches for dilepton resonances off-diagonal mass term δm 2 Z µ Z µ constraints from electroweak precision tests

36 Spot the difference: axial(dm)-axial(sm) A g DM = 1, g A q,l = 0.25 A g DM = 1, g A q,l = 0.25 DM overproduction Electroweak precision tests m Z' [GeV] 10 3 Monojets Direct detection m Z ' [GeV ] 10 3 Dilepton resonances DM overproduction Direct detection Monojets Perturbative unitarity violation m DM [GeV] m DM [GeV] stringent constraints from EWPTs and dilepton resonance substantial part of parameter space inconsistent

37 Conclusion new tools for efficient interpretations of LHC searches necessary simplified models are a useful to map out collider phenomenology of DM interpretation needs care ("naive" simplified models can violate gauge invariance and perturbative unitarity) required level of "UV-completeness" depends on signature