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1 You can hide but you have to run: direct detection with vector mediators Francesco D Eramo CERN Theory Institute - 28 July 2016

2 LHC vs Direct Detection LHC pp! Energy Scale p j s = 13 TeV Energy scales: LHC Direct Detection Direct Detection N! N m2dm MN 2 herecoil i ' 2 v ' 50 kev 2 (mdm + MN ) LUX experiment Xe and mdm = 100 GeV

3 LHC vs Direct Detection L = g A µ µ 5 + g q A µ q µ 5 q ATLAS, arxiv:

4 LHC vs Direct Detection Direct Detection L = g A µ µ 5 + g q A µ q µ 5 q ATLAS, arxiv:

5 LHC vs Direct Detection Direct Detection L = g A µ µ 5 + g q A µ q µ 5 q LHC (mono-jet) ATLAS, arxiv:

6 LHC vs Direct Detection Direct Detection L = g A µ µ 5 + g q A µ q µ 5 q LHC (mono-jet) Complementarity ATLAS, arxiv:

7 LHC vs Direct Detection How are LHC limits translated into the (mdm, σsd) plane? L = g A µ µ 5 + g q A µ q µ 5 q LHC bounds have to be evolved down to the direct detection scale You have to run! (RGE) ATLAS, arxiv:

8 LHC vs Direct Detection How are LHC limits translated into the (mdm, σsd) plane? L = g A µ µ 5 + g q A µ q µ 5 q LHC bounds have to be evolved down to the direct detection scale You have to run! (RGE) ATLAS, arxiv: This line will be affected

9 A well know SM analogy B meson decay: B D π M B!D = hd L SM Bi m W Energy Scale m b

10 A well know SM analogy B meson decay: B D π M B!D = hd L SM Bi m W b c u d Integrate-out heavy SM states (ElectroWeak Hamiltonian) Buras, hep-ph/ H W / G F C1 c µ P L b d µp L u + C 2 c µ P L b d µp L u b c u d Energy Scale m b

11 A well know SM analogy B meson decay: B D π M B!D = hd L SM Bi m W b c u d Integrate-out heavy SM states (ElectroWeak Hamiltonian) Buras, hep-ph/ H W / G F C1 c µ P L b d µp L u + C 2 c µ P L b d µp L u b c u d Energy Scale C 1 (m W )=1 C 2 (m W )=0 m b

12 A well know SM analogy B meson decay: B D π M B!D = hd L SM Bi m W b c u d Integrate-out heavy SM states (ElectroWeak Hamiltonian) Buras, hep-ph/ H W / G F C1 c µ P L b d µp L u + C 2 c µ P L b d µp L u b c u d Energy Scale C 1 (m W )=1 C 2 (m W )=0 g b u c d Renormalization Group Evolution (RGE) m b C 1 (m b ) ' 1.12 C 2 (m b ) ' 0.28

13 A well know SM analogy B meson decay: B D π M B!D = hd L SM Bi m W b c u d Integrate-out heavy SM states (ElectroWeak Hamiltonian) Buras, hep-ph/ H W / G F C1 c µ P L b d µp L u + C 2 c µ P L b d µp L u b c u d Energy Scale C 1 (m W )=1 C 2 (m W )=0 g b u c d Renormalization Group Evolution (RGE) m b Effective couplings C 1 (m b ) ' 1.12 C 2 (m b ) ' 0.28 hd H W (m b ) Bi at the scale mb

14 A well know SM analogy B D π Dark Matter Direct Detection b u c d m W M med b u Energy Scale c d (RGE) g b u c d Energy Scale m b hd H W (m b ) Bi µ N

15 A well know SM analogy B D π Dark Matter Direct Detection m W b c b u d u M med DM DM Med SM SM L SM+DM = 1 M 2 med Integrate-out mediator X c O (6) +... DM DM SM SM Energy Scale c d (RGE) g b u c d Energy Scale m b hd H W (m b ) Bi µ N

16 A well know SM analogy B D π Dark Matter Direct Detection m W b c b u d u M med DM DM Med SM SM L SM+DM = 1 M 2 med Integrate-out mediator X c O (6) +... DM DM SM SM Energy Scale c d (RGE) g b u Energy Scale c (M med ) c d m b hd H W (m b ) Bi µ N

17 A well know SM analogy B D π Dark Matter Direct Detection m W b c b u d u M med DM DM Med SM SM L SM+DM = 1 M 2 med Integrate-out mediator X c O (6) +... DM DM SM SM Energy Scale c d (RGE) g b u c d Energy Scale c (M med ) DM DM SM SM SM SM Renormalization Group Evolution (RGE) m b hd H W (m b ) Bi µ N c (d) (µ N )

18 A well know SM analogy B D π Dark Matter Direct Detection m W b c b u d u M med DM DM Med SM SM L SM+DM = 1 M 2 med Integrate-out mediator X c O (6) +... DM DM SM SM Energy Scale c d (RGE) g b u c d Energy Scale c (M med ) DM DM SM SM SM SM Renormalization Group Evolution (RGE) m b hd H W (m b ) Bi µ N c (d) (µ N ) Couplings at the nuclear scale μn ~ 1 GeV hdm N L SM (µ N ) DM N i

19 Why this matters? RGE effects changing size of the effective couplings generating new interactions (operator mixing)

20 Why this matters? RGE effects changing size of the effective couplings generating new interactions (operator mixing) DM-Nucleus scattering: only through couplings to light SM degrees of freedom and very sensitive to the details of the interactions Goodman and Witten, PRD31 (1985)

21 Why this matters? RGE effects changing size of the effective couplings generating new interactions (operator mixing) DM-Nucleus scattering: only through couplings to light SM degrees of freedom and very sensitive to the details of the interactions Goodman and Witten, PRD31 (1985) M med Energy Scale µ N DM SM SM Suppressed interactions between DM and SM DM SM SM Renormalization Group Evolution (RGE) Unsuppressed DM interactions with light SM d.o.f.

22 Why this matters? RGE effects changing size of the effective couplings generating new interactions (operator mixing) DM-Nucleus scattering: Direct detection rates can be orders only through couplings to light SM degrees of freedom This was realized for specific interactions in: and SM Kopp, Niro, Schwetz, Zupan, PRD80 (2009), arxiv: ; SM SM SM Freytsis, Ligeti, PRD83 (2011), arxiv: Frandsen, Haisch, Kahlhoefer, Mertsch, Schmidt-Hoberg, JCAP1210 (2012), arxiv: ; Haisch, Kahlhoefer, JCAP1304 (2013), arxiv: ; Kopp, Michaels, Smirnov, JCAP1404 (2014) arxiv: µ N Crivellin, Haisch, PRD90 (2014), arxiv: Goodman and Witten, PRD31 (1985) very sensitive to the details of the interactions M med Energy Scale DM Suppressed interactions between DM and SM of magnitude larger than the ones computed without RGE effects DM Renormalization Group Evolution (RGE) Unsuppressed DM interactions with light SM d.o.f.

23 Vector Mediators L = L SM + L DM + L V + J µ DM V µ + J µ SM V µ Mediator effects fully accounted for p 2. m 2 V Contact interaction p 2 ' m 2 V q p 2 V Resonant production q g p 2 & m 2 V EFT badly breaks down

24 Vector Mediators L = L SM + L + L V + J µ DM V µ + J µ DM SM V µ Both scalar DM (complex) and fermion DM (Dirac or Majorana) L DM = 2 m 2 2 scalar DM K i/@ m fermion DM K = 1 Dirac 1/2 Majorana

25 Vector Mediators L = L SM + L DM + L + J µ DM V µ + J µ V SM V µ Spin-1 massive mediator L V = 1 4 V µ V µ m2 V V µ V µ

26 Vector Mediators L = L SM + L DM + L V + J µ + J µ DM V µ SM V µ Mediator coupled to spin-1 DM currents V DM DM J µ DM = µ scalar DM K c V µ + c A µ 5 fermion DM

27 Vector Mediators L = L SM + L DM + L V + J µ DM V µ + J µ SM V µ Mediator coupled to spin-1 currents of SM fermions V fsm 15 independent SU(2)L x U(1)Y gauge invariant couplings to SM fermions fsm J µ SM = 3X h c (i) q q i L µ q i L + c (i) u u i R µ u i R + c (i) d di R µ d i R + c (i) l l i L µ l i L + c (i) e e i R µ e i R i i=1

28 Vector Mediators L = L SM + L DM + L V + J µ DM V µ + J µ SM V µ Apply EFT techniques: evaluate direct detection rates compare LHC with direct detection for this broad class of models

29 Connecting Scales EMSM χ EFT EW broken SM + χ SM χ EFT SM + χ UV Complete Model SM + χ +Mediators Nuclear Scale Weak Scale Mediator Scale E

30 Connecting Scales EMSM χ EFT EW broken SM + χ SM χ EFT SM + χ UV Complete Model SM + χ +Mediators Nuclear Scale Weak Scale Mediator Scale E STEP 1: Integrate-out mediator L (m V ) EFT = J DM µ J µ SM m 2 V

Connecting Energy Scales dc d ln µ = SM c Crivellin, FD, Procura, Phys.Rev.

31 Connecting Scales EMSM χ EFT EW broken SM + χ SM χ EFT SM + χ UV Complete Model SM + χ +Mediators Nuclear Scale Weak Scale Mediator Scale E STEP II: Connecting Energy Scales dc d ln µ = SM c Crivellin, FD, Procura, Phys.Rev.Lett.112 (2014), arxiv: FD, Procura, JHEP1504 (2015), arxiv:

32 Connecting Scales EMSM χ EFT EW broken SM + χ SM χ EFT SM + χ UV Complete Model SM + χ +Mediators Nuclear Scale Weak Scale Mediator Scale E STEP III: Nuclear Matrix hdm N L SM (µ N ) DM N i Elements Fitzpatrick, Haxton, Katz, Lubbers, Xu, JCAP1302 (2013), arxiv: Cirelli, Del Nobile, Panci, JCAP1310 (2013), arxiv:

rundm: code for RGE Inclusion of RGE effects automatic FD, Kavanagh, Panci, arxiv:1605.

33 rundm: code for RGE Inclusion of RGE effects automatic FD, Kavanagh, Panci, arxiv: INPUT: Effective couplings at an arbitrary energy scale Mathematica and Python versions available at:

34 rundm: code for RGE Inclusion of RGE effects automatic FD, Kavanagh, Panci, arxiv: OUTPUT I: RG evolved couplings at a second arbitrary energy scale (useful for future ID studies) Mathematica and Python versions available at:

35 rundm: code for RGE Inclusion of RGE effects automatic FD, Kavanagh, Panci, arxiv: OUTPUT II: RG evolved couplings for direct detection Mathematica and Python versions available at:

36 RGE Handbook Interested in the RGE-induced currents with light quarks M med V µ f SM µ f SM V µ f SM µ 5 f SM On this slide: approximate solution Energy Scale µ N

37 RGE Handbook Interested in the RGE-induced currents with light quarks M med V µ f SM µ f SM V µ f SM µ 5 f SM On this slide: approximate solution Energy Scale RGE µ N c V ' e ln(m V /µ N )

38 RGE Handbook Interested in the RGE-induced currents with light quarks M med V µ f SM µ f SM V µ f SM µ 5 f SM On this slide: approximate solution Energy Scale RGE RGE µ N c V ' e ln(m V /µ N ) c V,A ' 2 f 16 2 ln(m V /µ N )

39 Results I: quarks vector Flavor universal couplings to quark vector currents L EFT = 1 m 2 V J DM µ 3X hu i µ u i + d i µ d ii i=1

40 Results I: quarks vector Flavor universal couplings to quark vector currents L EFT = 1 m 2 V J DM µ 3X i=1 hu i µ u i + d i µ d ii Mediator mass mv [GeV] Flavor universal: Quarks only µ f µ f LZ projected LUX Dark Matter mass m [GeV] FD, Kavanagh, Panci, arxiv:

41 Results I: quarks vector Flavor universal couplings to quark vector currents L EFT = 1 m 2 V J DM µ 3X i=1 hu i µ u i + d i µ d ii 10 6 Flavor universal: Quarks only µ f µ f RGE: Mediator mass mv [GeV] LZ projected LUX 2014 O(1%) correction to EFT couplings Very strong bounds, meaningful results also Dark Matter mass m [GeV] for loop-induced rates FD, Kavanagh, Panci, arxiv:

42 Results II: quarks axial Flavor universal couplings to quark axial currents L EFT = 1 m 2 V J DM µ 3X hu i µ 5 u i + d i µ 5 d ii i=1

43 Results II: quarks axial Flavor universal couplings to quark axial currents L EFT = 1 m 2 V J DM µ 3X i=1 hu i µ 5 u i + d i µ 5 d ii Flavor universal: Quarks only µ f 5 µ f Mediator mass mv [GeV] LZ projected without RGE with RGE 10 LUX Dark Matter mass m [GeV] FD, Kavanagh, Panci, arxiv:

44 Results II: quarks axial Flavor universal couplings to quark axial currents L EFT = 1 m 2 V J DM µ 3X i=1 hu i µ 5 u i + d i µ 5 d ii Flavor universal: Quarks only µ f 5 µ f Mediator mass mv [GeV] LZ projected LUX 2014 LZ projected without RGE with RGE 10 LUX Dark Matter mass m [GeV] FD, Kavanagh, Panci, arxiv:

45 Results II: quarks axial Flavor universal couplings to quark axial currents L EFT = 1 m 2 V J DM µ 3X i=1 hu i µ 5 u i + d i µ 5 d ii Flavor universal: Quarks only µ f 5 µ f 10 6 Flavor universal: Quarks only µ 5 f 5 µ f Mediator mass mv [GeV] LZ projected LUX 2014 LZ projected Mediator mass mv [GeV] LZ projected 10 LUX 2014 LUX Dark Matter mass m [GeV] Dark Matter mass m [GeV] FD, Kavanagh, Panci, arxiv:

46 Results II: quarks axial Flavor universal couplings to quark axial currents Mediator mass mv [GeV] LEFT = Flavor universal: Quarks only µ f µ 5 f LZ proje cted LUX LZ projec te d Mediator mass mv [GeV] JDM µ 2 mv ui µ 5 i u + di µ 5 i d i=1 i Flavor universal: Quarks only µ 5 f µ 5 f LZ Z pro L projjeeccted ted 103 LUX 2014 LUX Dark Matter mass m [GeV] 3 h X Dark Matter mass m [GeV] 104 FD, Kavanagh, Panci, arxiv:

47 Results III: other cases LZ proje cted 104 LUX LZ proje cted 4 LUX Dark Matter mass m [GeV] Dark Matter mass m [GeV] LZ proje cted 103 LUX Flavor universal: Leptons only $ f µf 104 Third Generation µ f µ 5 f LZ proje cted 4 LUX Mediator mass mv [GeV] 1 10 Flavor universal: Leptons only µ f µ f Mediator mass mv [GeV] Flavor universal: Quarks only $ f µ 5f Mediator mass mv [GeV] Mediator mass mv [GeV] Mediator mass mv [GeV] Dark Matter mass m [GeV] 104 Third Generation $ f µ 5f LZ proje cted LUX Dark Matter mass m [GeV] Dark Matter mass m [GeV] 104 FD, Kavanagh, Panci, arxiv:

48 Comparison with LHC LHC limits on mediator mass translated into limits on direct detection cross section RGE not accounted for! LUX, arxiv: and PICO-2L, arxiv: ATLAS, arxiv: (mono-jet) and arxiv: (mono-photon)

49 Impact of the running N SD = 3µ2 N c A C (N) 2 A m 4 V C (N) A ' g q 2 4 X q=u,d,s (N) q g q 3 t 2 (N) d + (N) s (N) u ln(m V /m Z ) Tree-level Loop-induced

50 Mono-jet Searches SD (DM-neutron) [cm 2 ] LUX 2016 SD (DM-proton) [cm 2 ] LUX 2016 PICO-2L ATLAS monojet g q =0.25,g =1.0 Axial Vector Mediator Dark Matter mass m [GeV] ATLAS monojet g q =0.25,g =1.0 Axial Vector Mediator Dark Matter mass m [GeV] LUX, arxiv: and PICO-2L, arxiv: ATLAS, arxiv: (mono-jet) and arxiv: (mono-photon)

51 Mono-jet Searches SD (DM-neutron) [cm 2 ] ATLAS monojet (with running) ATLAS monojet LUX 2016 g q =0.25,g =1.0 Axial Vector Mediator Dark Matter mass m [GeV] SD (DM-proton) [cm 2 ] ATLAS monojet ATLAS monojet (with running) LUX 2016 PICO-2L g q =0.25,g =1.0 Axial Vector Mediator Dark Matter mass m [GeV] LUX, arxiv: and PICO-2L, arxiv: ATLAS, arxiv: (mono-jet) and arxiv: (mono-photon)

52 Mono-jet Searches LUX SD (DM-neutron) [cm 2 ] LUX 2016 ATLAS monojet (with running) ATLAS monojet g q =0.25,g = Dark Matter mass m [GeV] Axial Vector Mediator ~ factor of 2 10 in 43 σsd SD (DM-proton) [cm 2 ] RGE effects: PICO-2L ATLAS monojet ATLAS monojet (with running) g q =0.25,g =1.0 Axial Vector Mediator Dark Matter mass m [GeV] LUX, arxiv: and PICO-2L, arxiv: ATLAS, arxiv: (mono-jet) and arxiv: (mono-photon)

53 Outlook How well can be constrained by collider and direct detection? µ q µ q µ 5 q µ 5 q µ q µ 5 q µ 5 q µ q

54 Outlook How well can be constrained by collider and direct detection? µ q µ q µ 5 q µ 5 q ~ same as the others ~ same as the others µ q µ 5 q µ 5 q µ q ~ same as the others ~ same as the others

55 Outlook How well can be constrained by collider and direct detection? Standard Lore µ q µ q µ 5 q µ 5 q ~ same as the others ~ same as the others Spin-Independent (SI), no suppression Spin-Dependent (SD), no suppression µ q µ 5 q µ 5 q µ q ~ same as the others ~ same as the others SD with v SI with v

56 Outlook How well can be constrained by collider and direct detection? Standard Lore µ q µ q µ 5 q µ 5 q ~ same as the others ~ same as the others Spin-Independent (SI), no suppression Spin-Dependent (SD), no suppression (large corrections) µ q µ 5 q ~ same as the others Spin-Independent (SI) at one-loop µ 5 ~ same as the others SI with v q µ q But if you run (and you have to run!)

57 Outlook Direct detection rates and comparison with LHC: not always straightforward Flavor universal: Quarks only µ f µ 5 f Flavor universal: Leptons only µ f µ f Mediator mass mv [GeV] LZ projected LUX 2014 SD (DM-neutron) [cm 2 ] ATLAS monojet (with running) LUX 2016 Mediator mass mv [GeV] LZ projected LUX Dark Matter mass m [GeV] ATLAS monojet g q =0.25,g =1.0 Axial Vector Mediator Dark Matter mass m [GeV] Dark Matter mass m [GeV] FD, Kavanagh, Panci, arxiv: Still need to quantify RGE effects for other simplified models

58 Outlook Direct detection rates and comparison with LHC: not always straightforward Flavor universal: Quarks only µ f µ 5 f Flavor universal: Leptons only µ f µ f Mediator mass mv [GeV] LZ projected LUX 2014 SD (DM-neutron) [cm 2 ] ATLAS monojet (with running) LUX 2016 Mediator mass mv [GeV] LZ projected LUX Dark Matter mass m [GeV] ATLAS monojet g q =0.25,g =1.0 Axial Vector Mediator Dark Matter mass m [GeV] Dark Matter mass m [GeV] FD, Kavanagh, Panci, arxiv: Thank You!

Beyond Simplified Models

Pseudoscalar Portal to Dark Matter: Beyond Simplified Models Jose Miguel No King's College London J.M.N. PRD 93 (RC) 031701 (1509.01110) D. Goncalves, P. Machado, J.M.N. 1611.04593 M. Fairbairn, J.M.N.,