Connecting low-energy Dark Matter searches with high-energy physics: the role of operator mixing Bradley J. Kavanagh - LPTHE (Paris) F. D’Eramo, B. J. Kavanagh , P. Panci, JHEP (2016) 2016: 111, arXiv:1605.04917 F. D’Eramo, B. J. Kavanagh , P. Panci, PLB 771 (2017) 339-348, arXiv:1702.00016 IRN Terascale, Montpellier - 4th July 2017 bkavanagh@lpthe.jussieu.fr @BradleyKavanagh NewDark
Complementarity of Dark Matter searches: Direct detection vs Indirect detection vs LHC Bradley J. Kavanagh - LPTHE (Paris) F. D’Eramo, B. J. Kavanagh , P. Panci, JHEP (2016) 2016: 111, arXiv:1605.04917 F. D’Eramo, B. J. Kavanagh , P. Panci, PLB 771 (2017) 339-348, arXiv:1702.00016 IRN Terascale, Montpellier - 4th July 2017 bkavanagh@lpthe.jussieu.fr @BradleyKavanagh NewDark
Collider searches Indirect direction Direct direction Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
UV this way E Collider searches ∼ 10 TeV m V ∼ 2 m χ Indirect direction m Z m N Direct direction ∼ 1 GeV Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Connect scales carefully and consistently [ RUN DM code] accounting for RG and operator mixing in the SM sector e.g. Gives corrections to Gives bounds you never direct detection bounds thought were there e.g. mapping from e.g. leptophilic DM LHC to DD Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Outline RG effects in Simplified Models Crivellin, D’Eramo, Procura [1402.1173]; D’Eramo, Procura [1411.3342] Direct detection constraints on Simplified Models D’Eramo, Procura [1411.3342]; D’Eramo, BJK, Panci [1605.04917] LHC vs Direct Detection D’Eramo, BJK, Panci [1605.04917] Leptophilic Dark Matter D’Eramo, BJK, Panci [1702.00016] Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Simplified Models Review: De Simone, Jacques [1603.08002] EFT Simplified Model c q c χ m χ , Λ c q , c χ , m χ , m V For direct detection, momentum transfer is small, q ~ 100 MeV: EFT okay For colliders, momentum transfer is large, q ~ O(TeV): EFT may break down! Frandsen et al. [1204.3839], Buchmueller et al. [1407.8257], Malik et al. [1409.4075], Abdallah et al. [1506.03116], and many others… Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Our Simplified Model Assume fermion Dark Matter and a new (massive) vector mediator V χ L = L SM + L DM + L V + J µ DM V µ + J µ SM V µ Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Our Simplified Model V Assume fermion Dark Matter and a new (massive) vector mediator χ L = L SM + L DM + L V + J µ DM V µ + J µ SM V µ J µ DM = c χ V χγ µ χ + c χ A χγ µ γ 5 χ Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Our Simplified Model V Assume fermion Dark Matter and a new (massive) vector mediator χ L = L SM + L DM + L V + J µ DM V µ + J µ SM V µ 3 h i R + c ( i ) R + c ( i ) J µ X c ( i ) L + c ( i ) L + c ( i ) L γ µ q i R γ µ u i R γ µ d i L γ µ l i R γ µ e i q i u u i d i l i e i SM = q e R d l i =1 15 independent, SU(2) L x U(1) Y gauge-invariant couplings Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Direct detection Look for low energy - O(keV) - recoils of detector nuclei… Detector N N m χ & 1 GeV χ χ v ∼ 10 − 3 χ Rate driven by coupling of DM to light quarks (u, d, s): χγ µ χ q γ µ γ 5 q χγ µ χ q γ µ q χγ µ γ 5 χ q γ µ γ 5 q χγ µ γ 5 χ q γ µ q Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Direct detection Look for low energy - O(keV) - recoils of detector nuclei… Detector N N m χ & 1 GeV χ χ v ∼ 10 − 3 χ Rate driven by coupling of DM to light quarks (u, d, s): χγ µ χ q γ µ γ 5 q χγ µ χ q γ µ q Standard SI χγ µ γ 5 χ q γ µ γ 5 q Standard SD χγ µ γ 5 χ q γ µ q Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Direct detection Look for low energy - O(keV) - recoils of detector nuclei… Detector N N m χ & 1 GeV χ χ v ∼ 10 − 3 χ Rate driven by coupling of DM to light quarks (u, d, s): χγ µ χ q γ µ γ 5 q χγ µ χ q γ µ q χγ µ γ 5 χ q γ µ γ 5 q χγ µ γ 5 χ q γ µ q Velocity suppressed Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Connecting high and low scales Define couplings at high energy scale (mediator mass), but need to calculate direct detection rate at low energy Running can change the DD rate by orders of magnitude. Examples in specific models: Kopp et al. [0907.3159], Frandsen et al. [1207.3971], Haisch, Kahlhoefer [1302.4454], Kopp et al. [1401.6457], Crivellin, Haisch [1408.5046] • Use EFT techniques and RG flow to study the effects for general interactions • Include all relevant DD interactions (not just naive ‘leading order’) Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
E Fix couplings at high energy (~m V ) m V SM χ m Z EW SM χ ⇠⇠ m N NREFT D’Eramo, Procura [1411.3342] Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
E Fix couplings at high energy (~m V ) Integrate out vector mediator m V SM χ m Z EW SM χ ⇠⇠ m N NREFT D’Eramo, Procura [1411.3342] Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
E Fix couplings at high energy (~m V ) Integrate out vector mediator m V Run down to electroweak scale SM χ m Z EW SM χ ⇠⇠ m N NREFT D’Eramo, Procura [1411.3342] Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
E Fix couplings at high energy (~m V ) Integrate out vector mediator m V Run down to electroweak scale SM χ Match onto EW-broken theory m Z EW SM χ ⇠⇠ m N NREFT D’Eramo, Procura [1411.3342] Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
E Fix couplings at high energy (~m V ) Integrate out vector mediator m V Matching at EWSB V,A u = ± c ( i ) + c ( i ) Run down to electroweak scale c ( i ) q u SM χ + c H g V,A u 2 V,A d = ± c ( i ) + c ( i ) Match onto EW-broken theory c ( i ) q d m Z + c H g V,A d 2 V,A e = ± c ( i ) + c ( i ) c ( i ) e l + c H g V,A e EW SM χ ⇠⇠ 2 m N NREFT D’Eramo, Procura [1411.3342] Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
E Fix couplings at high energy (~m V ) Integrate out vector mediator m V Run down to electroweak scale SM χ Match onto EW-broken theory m Z EW SM χ Run down to nuclear scale ⇠⇠ m N NREFT D’Eramo, Procura [1411.3342] Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
E Fix couplings at high energy (~m V ) Integrate out vector mediator m V Run down to electroweak scale SM χ Match onto EW-broken theory m Z EW SM χ Run down to nuclear scale ⇠⇠ Match onto nucleon couplings m N NREFT Calculate direct detection rate σ ∼ | c ( m V ) | 2 /m 4 D’Eramo, Procura [1411.3342] V Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
RG effects As we move between the different scales, we have to take into account the running of the couplings, due only to loops of Standard Model particles, e.g. Self-renormalisation Operator mixing The running doesn’t depend on the properties of the Dark Sector. Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
RG effects As we move between the different scales, we have to take into account the running of the couplings, due only to loops of Standard Model particles, e.g. ! N U R O T E V A H U O Y Self-renormalisation Operator mixing The running doesn’t depend on the properties of the Dark Sector. Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
runDM - a code for the RGE Mathematica and Python versions available at: https://github.com/bradkav/runDM/ Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
Results I - quarks vector 3 L EFT = − 1 h u i γ µ u i + d i γ µ d i i X J DM µ m 2 V i =1 10 6 Flavor universal: Quarks only χγ µ χ ¯ f γ µ f ¯ LZ projected Mediator mass m V [GeV] 10 5 LUX 2014 10 4 10 3 10 2 10 2 10 3 10 4 10 Dark Matter mass m χ [GeV] LUX 2014 [1310.8214] LZ (projected) [1509.02910] Bradley J Kavanagh (LPTHE, Paris) Dark Matter - operator mixing IRN Terascale@Montpellier - 4th July 2017
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