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LHC Dark Matter Searches Describing Dark Matter with Effective Operators ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY Felix Kahlhoefer In collaboration with Rudolf Peierls Centre for Theoretical Physics Mads Frandsen, Ulrich Haisch, Philipp Mertsch, Anthony Preston, Subir Sarkar, Kai Schmidt-Hoberg, James Unwin JHEP 1207 (2012) 123 JCAP 10 (2012) 033 arXiv:1208.4605 Describing Dark Matter with Effective Operators Outline FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 2 • Introduction • Effective operators and their limitations • How to treat resonances at the LHC • Operator mixing and heavy-quark loops • Effective operators for indirect detection • Conclusions Describing Dark Matter with Effective Operators Evidence for dark matter FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 3 Cold dark matter No dark matter Galactic scales Galaxy cluster scales Cosmological scales Conclusive observational evidence for dark matter over a wide range of astrophysical scales Describing Dark Matter with Effective Operators Particle candidates for DM FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 4 • The most popular candidate is the WIMP: A cold thermal relic with weak scale mass and interactions (e.g. the lightest SUSY particle) which naturally has the required relic abundance – the WIMP miracle • The many alternative options include: – – – – Asymmetric dark matter (with same origin as baryons) Warm dark matter (e.g. sterile keV neutrinos) Axion dark matter … Describing Dark Matter with Effective Operators Detecting DM particles FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 5 Dark matter scattering • For most dark matter candidates, we expect some kind of interactions with Standard Model particles Dark matter annihilation leading to thermal equilibrium in the early universe. Dark matter production Describing Dark Matter with Effective Operators DM direct detection FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY Photo: AP PAGE 6 Dark matter particles from the Galactic halo that pass through the Earth will occasionally scatter off nuclei. The resulting recoil energy of the nucleus can be measured in dedicated low background detectors. Dark matter Typical event rates are less than 1 event per kg per year A great experimental challenge! Detector e– heat Dark matter light Recoiling nucleus Describing Dark Matter with Effective Operators DM indirect detection FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 7 Indirect detection experiments look for the products of DM annihilation in regions of high DM density (e.g. the galactic center) with satellites, balloons and ground based telescopes. © Clay Lipsky Difficulties arise from astrophysical backgrounds and the DM density profile. Describing Dark Matter with Effective Operators DM searches at colliders FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 8 Any DM particles produced at colliders will escape from the detector unnoticed. But if other particles (such as jets) are produced in association with a pair of DM particles, we may observe large amounts of missing transverse energy. awkwardatoms.wordpress.com Describing Dark Matter with Effective Operators Detecting DM particles FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY If dark matter particles give a direct detection signal, we also expect to see related processes with distinctive signatures. Experiments searching for these signatures can constrain the direct detection cross section. PAGE 9 Describing Dark Matter with Effective Operators Separation of scales FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 10 Typical momentum transfer - 10 TeV - 1 TeV Collider searches - 100 GeV DM annihilation Dark matter direct detection probes the non-relativistic limit (vDM ≈ 10-3), while the LHC probes the TeV scale. - 10 GeV - 1 GeV Interactions that look very similar at the LHC may look very different in direct detection. - 100 MeV - 10 MeV - 1 MeV Direct detection Describing Dark Matter with Effective Operators Example FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 11 • Assume that DM interacts with quarks via the exchange of a vector mediator R which can couple to the vector current χγμχ or the axial current χγ5γμχ (or a combination). • At the LHC: Impossible to distinguish VC and AC. • In direct detection: Vector couplings Spin-independent Axial couplings Spin-dependent Mixed couplings Momentum suppressed Describing Dark Matter with Effective Operators Effective operators FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 12 To compare bounds from the LHC to direct detection, we describe interactions between DM and quarks with effective operators, e.g. This effective operator could arise from integrating out a vector mediator with mass mR and vector couplings gq to quarks and gχ to DM: Describing Dark Matter with Effective Operators Effective interactions FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY For PAGE 13 the direct detection cross section is given by , where f = 3 for gu = gd . Provided the effective operator remains valid at the LHC, we can use it to calculate the cross section for monojet production. σ (j + MET) ~ 1/Λ4 ~ σp We can directly compare LHC searches for dark matter to direct detection experiments Describing Dark Matter with Effective Operators Monojet searches at the LHC FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 14 Search for dark matter candidates and large extra dimensions in events with a jet and missing transverse momentum with the ATLAS detector arXiv:1210.4491 CMS Collaboration, arXiv:1206.5663 See also Goodman et al. arXiv:1005.1286 Bai et al. arXiv:1005.3797 Goodman et al. arXiv:1008.1783 Fox et al. arXiv:1103.0240 Rajaraman et al. arXiv:1108.1196 Fox et al. arXiv:1109.4398 Describing Dark Matter with Effective Operators Problems with perturbativity FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 15 • Current monojet searches at CMS & ATLAS probe Λ ≈ 700 GeV, corresponding to σp ≈ 10-39 cm2. • To have perturbativity, we require gq, gχ < (4π)1/2 • From we then get mR < 2.5 TeV. Fox, Harnik, Kopp, Tsai, arXiv:1109.4398 >Fox, 2.5Harnik, TeV,Kopp, we Tsai, canarXiv:1103.0240 no longer For collisions with √s rely on an effective operator description, because new physics becomes relevant. Describing Dark Matter with Effective Operators Problems with unitarity FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 16 • For a sensible theory, all predicted probabilities should be smaller than unity. • More formally, we require partial wave unitarity • For the effective operator from above leading to √s < 2.7 Λ ≈ 1.9 TeV. Shoemaker, Vecchi, arXiv:1112.5457 For collisions with √s > 1.9 TeV, the effective Fox, Harnik, Primulando, Yu, arXiv:1203.1662 operator makes nonsensical predictions. Describing Dark Matter with Effective Operators Resonant production FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 17 • Effective operators may not be valid at the LHC • It is quite possible that the mediator mass is comparable to LHC energies (mR ~ TeV) • The LHC can produce such a mediator on-shell: σ (j + MET) ~ σ (pp R + j) × BR (R invisible) • As a consequence, the monojet cross section is no longer proportional to the direct detection cross-section and the analysis is more involved. Describing Dark Matter with Effective Operators How to extract a bound FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 18 gq: Coupling to quarks gχ: Coupling to the DM particle mR: Mass of the mediator μχn: Reduced mass More difficult to constrain Constrained by monojet searches Describing Dark Matter with Effective Operators Decay channels FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 19 R can decay into fermions, bosons and new hidden sector states All of these channels can be constrained by the LHC! Describing Dark Matter with Effective Operators Constraints: Fermions FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 20 Frandsen, FK, Preston, Sarkar, Schmidt-Hoberg, arXiv:1204.3839 Updated to include full 7 TeV run in all channels! Describing Dark Matter with Effective Operators Constraints: Bosons FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 21 Frandsen, FK, Preston, Sarkar, Schmidt-Hoberg, arXiv:1204.3839 Updated to include full 7 TeV run in all channels! Describing Dark Matter with Effective Operators Combined Constraints FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 22 • If R decays only into SM particles or invisible states, we can obtain a bound on ΓR. Narrow-width approximation no longer valid Describing Dark Matter with Effective Operators Direct detection limit FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY excluded excluded PAGE 23 Describing Dark Matter with Effective Operators Direct detection limit FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 24 Bound for mR >> 1.1 TeV Bound for mR > 300 GeV mR < 1.1 TeV There are strong constraints on the direct detection cross section for vector mediators with mR < 1.1 TeV. Describing Dark Matter with Effective Operators Non-standard interactions FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 25 • Collider bounds are largely independent of lowenergy effects (e.g. nuclear coherence). • Very strong bounds arise if σp is suppressed. Spin-dependent interactions Isospin-violating interactions Describing Dark Matter with Effective Operators Possible caveats FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 26 1. If the mediator is lighter than 300 GeV it becomes very difficult to constrain BR(R qq). 2. If the DM mass is comparable to the mediator mass, decays of R into χχ are suppressed. 3. If R can decay into new hidden sector states with complicated decay modes, ΓR can be large. 4. If gq << gχ the production of R at LHC is insufficient to constrain ΓR. Describing Dark Matter with Effective Operators Operator mixing FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 27 Describing Dark Matter with Effective Operators Operator mixing FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 28 • To calculate direct detection cross sections, we must evolve all effective operators from the TeV scale down to the hadronic scale. • In the process, new interactions may be induced at loop-level, leading to additional operators, which are absent (or small) at the TEV scale. • A full calculation should include the mixing of all relevant effective operators under Renormalisation Group evolution. Describing Dark Matter with Effective Operators Example FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 29 • Consider the operator which may arise from integrating out a scalar mediator with quark couplings proportional to the quark mass mq. • For energies below the top quark mass mt, the top quark can be integrated out to give an effective interaction between DM and gluons: Describing Dark Matter with Effective Operators Example FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 30 • More formally, the operator induces the operator with δt = 11αs(mt)/(4π) • A similar threshold correction arises for the bottom quark below mb and for the charm quark below mc. Drees and Nojiri, PRD47, (1993) Describing Dark Matter with Effective Operators Direct detection cross-section FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 31 • To calculate the direct detection cross-section, we now need to evaluate and where is the target nucleus state. One finds and • Literature: Lattice QCD finds the much smaller value with Describing Dark Matter with Effective Operators LHC bounds FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 32 • What is the correct procedure to analyse bounds from monojet searches for the scalar operator? • Tree-level cross section are small, because there are no heavy quarks in the initial state. • We cannot use effective DM-gluon interactions, because the typical energies (√s, pT, …) are large compared to mt (not to mention mb and mc). Describing Dark Matter with Effective Operators LHC bounds FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 33 • For an accurate analysis, we must include the full energy dependence of the heavy quark loops using FormCalc + LoopTools (or MCFM). • While charm and bottom quarks are negligible, top quark loops give the dominant contribution. Describing Dark Matter with Effective Operators Implementation in MCFM FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 34 • Our analysis is based on analytical results for the process p + p H + j τ + τ - + j . Ellis et al., Nucl.Phys. B297, 221 (1988) • These results can be extended to the case of an offshell mediator by replacing mH with the invariant mass of the DM pair (equal to s + t + u). • Because the primary jet has very large pT, effects of parton showering and hadronisation are expected to be small. Bai, Fox, Harnik, arXiv:1005.3797 Choudalakis, arXiv:1110.5295 Describing Dark Matter with Effective Operators LHC bounds FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 35 Relic density constraint Loop-level bound Tree-level bound Haisch, FK, Unwin, arXiv:1208.4605 • Including loop-level processes increases predicted monojet cross sections by a factor of around 500. • Width of the bands reflect scale uncertainties. Describing Dark Matter with Effective Operators How heavy are top quarks? FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 36 • It is tempting to consider only the limit of infinitely heavy top quark and use the effective DM-gluon interaction • We find that this approximation overestimates cross sections by a factor of 3 for small DM masses. • For large DM masses, the error grows rapidly, reaching a factor of 40 at mψ = 1 TeV. • For accurate results it is essential to allow on-shell top quarks with finite mass in the loops. Describing Dark Matter with Effective Operators LHC bounds FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 37 Including loop processes improves the bounds by more than two orders of magnitude Heavy top quark limit overestimates the bound significantly. Haisch, FK, Unwin, arXiv:1208.4605 Describing Dark Matter with Effective Operators Pseudoscalar interactions FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 38 • For the pseudoscalar operator detection cross sections are spin-dependent and in addition suppressed by q4 / mN4. • Consequently, no relevant constraints on Λp arise from direct detection experiments. • At the LHC scalar and pseudoscalar interactions look very similar, so we obtain strong constraints on Λp. Describing Dark Matter with Effective Operators Pseudoscalar interactions FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY Allowed for asymmetric dark matter PAGE 39 Relic density constraint Loop-level bound Tree-level bound Haisch, FK, Unwin, arXiv:1208.4605 • Imposing that DM is not overproduced leads to the bound mψ > 60 GeV (Majorana fermion: mΨ > 85 GeV). Describing Dark Matter with Effective Operators How about indirect detection? FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY Weniger, arXiv:1204.2797 PAGE 40 “In regions close to the Galactic center, we find a 4.6σ indication for a gamma-ray line at Eγ ≈ 130 GeV. When taking into account the look-elsewhere effect the significance of the observed excess is 3.2σ. If interpreted in terms of dark matter particles annihilating into a photon pair, the observations imply a dark matter mass of mχ = 129.8 ± 2.4 GeV and a partial annihilation cross-section of <σv>χχ→γγ = (1.27 ± 0.32) ×10−27 cm3 s−1 when using the Einasto dark matter profile.” See also: Bringmann et al., arXiv:1203.1312 Ackermann et al., arXiv:1205.2739 Describing Dark Matter with Effective Operators Annihilation into photons FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 41 • To interpret the claimed 130 GeV γ-ray signal at Fermi, we use effective operators to describe the interactions between dark matter and photons. • Here: Consider only the case where DM is a Majorana fermion (M) or a Dirac fermion (D). p-wave s-wave p-wave as well as operators with M replaced by D. Rajaraman, Tait, Whiteson, arXiv:1205.4723 Describing Dark Matter with Effective Operators “Rayleigh” Dark Matter FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 42 • The most interesting operator is because it gives rise to a direct detection signal. Weiner, Yavin, arXiv:1206.2910 • Photons interact coherently with the entire nucleus. • Similar to Rayleigh scattering: use heavy-quark effective theory. • Amplitude proportional to Z2, cross section proportional to Z4. Describing Dark Matter with Effective Operators Operator mixing FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 43 • At the same time, the operator mixes under QED into the operator Frandsen, Haisch, FK, Mertsch, Schmidt-Hoberg, arXiv:1206.2910 • At low energies, obtain standard spin-independent interactions. • Amplitude proportional to target nucleus mass, cross section proportional to A2. Describing Dark Matter with Effective Operators Loop-induced direct detection FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 44 The two contributions interfere destructively. Rayleigh scattering dominates because of Z4 enhancement. Operator mixing Mixing contribution dominates Interference leads because of form factor suppression. to dip in event rate XENON100 Interference Rayleigh scattering Describing Dark Matter with Effective Operators Sensitivity of XENON FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY Official Fermi bound PAGE 45 Claimed Fermi γ-ray signal XENON100 XENON1T (projected) Frandsen, Haisch, FK, Mertsch, Schmidt-Hoberg, arXiv:1207.3971 • If DM annihilation into photons proceeds via pchannel, it can be tested with XENON1T. Describing Dark Matter with Effective Operators Conclusions FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 46 • At typical LHC energies effective operators may be insufficient to interpret monojet bounds, because the intermediate particles can be on-shell. • Example 1: Resonant production of vector mediators Heavy mediators (mR ≥ 300 GeV) can be tested and constrained by current LHC data. • Example 2: Heavy-quark loops for scalar mediators Loop-level processes significantly enhance the monojet cross-section, but one needs to include the full top-mass dependence for accurate results. Describing Dark Matter with Effective Operators Backup FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 47 Describing Dark Matter with Effective Operators Monojet searches at the LHC FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 48 • For our analysis, we use the CMS search for jets + MET with an integrated luminosity of 5.0 fb-1 (7 TeV). • Cuts: MET > 350 GeV Primary jet (j1) with pT > 110 GeV and η < 2.4 Secondary jet (j2) with pT > 30 GeV permitted, provided Δφ(j1, j2) < 2.5 Events with high-pT tertiary jets, electrons or muons are vetoed • The results exclude new contributions to the cross section in excess of 0.032 pb at 95% CL. • Similar results are found using data from ATLAS. Describing Dark Matter with Effective Operators Scale uncertainties FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 49 • We evaluate αs(μ) on an event-by-event basis. • Varying μ between 0.5pT and 2pT allows to estimate scale ambiguities. • Resulting cross sections change by up to 50%, corresponding to an uncertainty of 15 GeV in Λ. • These observations indicate that next-to-leading order (NLO) corrections might be large. • For p + p H + j the ratio between the NLO result and the LO result is roughly 1.5 and we expect a similar K-factor for monojet signals. Describing Dark Matter with Effective Operators Importance of secondary jets FELIX KAHLHOEFER ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY PAGE 50 • Secondary jets are allowed in the CMS analysis, provided the two jets are not back-to-back. • We estimate the relevance of secondary jets by studying the process p + p H + 2j in the limit of infinitely heavy top quark. • In this case, the total cross sections increases by a factor of 2 when secondary jets are included. • A similar enhancement is expected in the case of finite top quark mass. Del Duca, Kilgore, Oleari, Schmidt, Zeppenfeld, arXiv:hep-ph/0108030