1. Loops and loopholes in LHC mono-jet searches
Felix Kahlhoefer
In collaboration with
Ulrich Haisch, Emanuele Re and James Unwin
JCAP 1304 (2013) 050, JHEP 1307 (2013) 125, JHEP 1312 (2013) 007
Rudolf Peierls Centre for Theoretical Physics
4 April 2014, CP3-Origins

2. 4 April 2014, BIDM @ CP3-Origins
Outline
Introduction: Dark matter effective operators
Operator mixing and heavy-quark loops
For spin-independent interactions
For spin-dependent interactions
QCD effects and NLO corrections
Vector operator
Gluon operator
Conclusions
Felix Kahlhoefer
4 April 2014, CP3-Origins

3. Detecting DM particles
For most dark matter candidates, we expect some kind of interactions with Standard Model particles leading to thermal equilibrium in the early universe.
Indirect detection of DM
Direct detection of DM
Collider searches for DM
Dark matter annihilation
Dark matter scattering
Dark matter production
Felix Kahlhoefer
4 April 2014, CP3-Origins

4. Detecting DM particles
If dark matter particles give a signal in one search channel, we also expect to see related processes with distinctive signatures in other channels.
Conversely, we can translate experimental bounds from one kind of search strategy to another.
Direct detection of DM
Indirect detection of DM
Collider searches for DM
Felix Kahlhoefer
4 April 2014, CP3-Origins

5. 4 April 2014, BIDM @ CP3-Origins
Separation of scales
10 TeV
1 TeV
100 GeV
10 GeV
1 GeV
100 MeV
10 MeV
1 MeV
Typical momentum transfer
Collider searches
DM annihilation
Direct detection
While the LHC probes the TeV scale, dark matter direct detection experiments probe the non-relativistic limit (vDM ≈ 10-3).
Interactions that look very similar at the LHC may look very different in direct detection.
Felix Kahlhoefer
4 April 2014, CP3-Origins

6. 4 April 2014, BIDM @ CP3-Origins
Example
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 (SI)
Axial couplings  Spin-dependent (SD)
Mixed couplings  Momentum suppressed
Felix Kahlhoefer
4 April 2014, CP3-Origins

7. 4 April 2014, BIDM @ CP3-Origins
Effective operators
To compare bounds from the LHC to direct detection, we can describe interactions between DM and quarks with effective operators, which arise if the mediator of the interaction can be integrated out:
Vector operator:
Spin-independent (SI) interactions
Axialvector operator:
Spin-dependent (SD) interactions
Anapole operator:
Momentum suppressed interactions
Felix Kahlhoefer
4 April 2014, CP3-Origins

8. Effective interactions
For the vector operator the SI 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 / (M*)4 ~ σp We can directly compare LHC searches for dark matter to direct detection experiments.
Felix Kahlhoefer
4 April 2014, CP3-Origins

9. Monojet searches at the LHC
Search for new physics in monojet events in pp collisions at sqrt(s) = 8 TeV
CMS-PAS-EXO
CMS-PAS-EXO
(based on 20 fb-1)
ATLAS-CONF
(based on 10 fb-1)
Felix Kahlhoefer
4 April 2014, CP3-Origins

10. 4 April 2014, BIDM @ CP3-Origins
Operator mixing
So far, we have neglected an important complication: 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.
Felix Kahlhoefer
4 April 2014, CP3-Origins

11. 4 April 2014, BIDM @ CP3-Origins
Example
Consider the scalar 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:
Felix Kahlhoefer
4 April 2014, CP3-Origins

12. 4 April 2014, BIDM @ CP3-Origins
Example
A similar threshold correction arises for the bottom quark below mb and for the charm quark below mc.
At the scale relevant for direct detection, we need to evaluate and where is the target nucleus state. One finds:
Drees and Nojiri, PRD47, (1993)
Felix Kahlhoefer
4 April 2014, CP3-Origins

13. 4 April 2014, BIDM @ CP3-Origins
LHC bounds
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).
Felix Kahlhoefer
4 April 2014, CP3-Origins

14. 4 April 2014, BIDM @ CP3-Origins
LHC bounds
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.
Felix Kahlhoefer
4 April 2014, CP3-Origins

15. 4 April 2014, BIDM @ CP3-Origins
LHC bounds
Including loop-level processes increases predicted monojet cross sections by a factor of around 500.
Width of the bands reflect scale uncertainties.
Relic density constraint
Loop-level bound
Tree-level bound
Haisch, FK, Unwin, arXiv:
Felix Kahlhoefer
4 April 2014, CP3-Origins

16. How heavy are top quarks?
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 at least a factor of 3.
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.
Felix Kahlhoefer
4 April 2014, CP3-Origins

17. 4 April 2014, BIDM @ CP3-Origins
LHC bounds
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:
Felix Kahlhoefer
4 April 2014, CP3-Origins

18. Pseudoscalar interactions
For the pseudoscalar operator
direct detection cross sections are SD 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.
Felix Kahlhoefer
4 April 2014, CP3-Origins

19. Pseudoscalar interactions
Imposing that DM is not overproduced leads to the bound mψ > 60 GeV (for a Dirac fermion) or mΨ > 85 GeV (for a Majorana fermion).
Relic density
constraint
Allowed
Loop-level bound
Tree-level bound
Haisch, FK, Unwin, arXiv:
Felix Kahlhoefer
4 April 2014, CP3-Origins

20. Spin-dependent interactions
Two operators lead to SD interactions:
Axialvector operator:
Tensor operator:
For SD interactions, direct detection bounds are weak due to the lack of coherent enhancement.
Consequently, monojet searches seem to be superior in constraining the SD cross section.
Felix Kahlhoefer
4 April 2014, CP3-Origins

21. Induced dipole moments
However, loop contributions can significantly boost direct detection bounds, whenever they induce SI interactions.
Most striking example: The tensor operator.
with
SI interactions arise from heavy quark loops, which induce dark matter magnetic dipole moments:
Kopp, Niro, Schwetz, Zupan, arXiv:
Felix Kahlhoefer
4 April 2014, CP3-Origins

22. Induced dipole moments
Because photons are massless, cross sections are strongly enhanced for small momentum transfer.
Consequently, these dipole moments are severely constrained by direct detection experiments.
The resulting constraints can be translated into bounds on the scale M* suppressing the tensor operator.
The resulting bounds are typically much stronger than bounds on M* from LHC monojet searches.
Felix Kahlhoefer
4 April 2014, CP3-Origins

23. Tensor operator bounds
Constraints from LHC monojet searches (width reflects scale uncertainties)
Relic density constraint (overproduction above the line)
Induced bounds from direct detection experiments, which constrain dark matter dipole moments.
Bounds from Fermi-LAT measurements of diffuse gamma-ray emission (with and without background modeling)
Haisch, Kahlhoefer, arXiv:
Felix Kahlhoefer
4 April 2014, CP3-Origins

24. Loop-level vs. tree-level
How do the loop-induced bounds compare to the tree-level cross sections?
Almost the entire parameter region probed by SD searches is excluded by loop-induced SI interactions.
allowed
Haisch, Kahlhoefer, arXiv:
Felix Kahlhoefer
4 April 2014, CP3-Origins

25. QCD effects in mono-jet searches
We have shown in two examples that heavy-quark loops can lead to strong enhancements in both the mono-jet production cross section and the dark matter scattering cross section.
Now we want to study QCD effects in mono-jet searches more systematically, hoping that the resulting corrections lead to an overall increase of the predicted cross sections also for other operators.
In any case, such a study is of great importance, because loop corrections for the signal process are expected to reduce the scale dependencies and hence the theoretical uncertainty of the signal prediction.
Felix Kahlhoefer
4 April 2014, CP3-Origins

26. 4 April 2014, BIDM @ CP3-Origins
POWHEG BOX goes DM
Recent developments: Parton-level mono-jet cross sections can be calculated at NLO using MCFM.
Fox, Williams:
However, a parton-level implementation is insufficient, whenever a full event simulation including showering and hadronisation is required.
In this case , it is necessary to consistently match an NLO computation with parton showers, e.g. using POWHEG.
Alioli, Nason, Oleari, Re:
I will present new results based on an extension of the POWHEG BOX allowing for the generation of mono-jet events at NLO including PS effects .
Felix Kahlhoefer
4 April 2014, CP3-Origins

27. Fixed-order predictions
In agreement with previous analyses, we find that fixed-order NLO corrections increase the monojet cross-section.
For the vector operator the K-factor (ratio of NLO to LO cross section) is approximately 1.1
LO (parton-level)
NLO (parton-level)
CMS cuts
For our choice of the dynamical scale the K-factor is independent of the DM mass.
Felix Kahlhoefer
4 April 2014, CP3-Origins

28. Including parton showering
NLO
(parton-level)
NLOPS
(inclusive)
(jet veto)
CMS cuts
For fully inclusive searches, PS effects are small
See also Bai, Fox, Harnik:
Realistic searches, however, impose a jet veto (Nj ≤ 2).
This restriction reduces the NLOPS cross section by about 40%.
Felix Kahlhoefer
4 April 2014, CP3-Origins

29. 4 April 2014, BIDM @ CP3-Origins
Ratio of LOPS to NLOPS
The enhancement of the mono-jet cross section found in fixed-order NLO calculations is diminished once the effects of parton showering are included.
NLOPS cross sections are comparable to those at LOPS.
Nevertheless, the inclusion of NLO effects reduces theoretical uncertainties by more than a factor of 2.
LOPS (jet veto)
CMS cuts
NLOPS
(jet veto)
Felix Kahlhoefer
4 April 2014, CP3-Origins

30. Why NLO corrections are small
Because of the large centre-of-mass energy, soft QCD radiation associated to the PS can easily generate additional jets with |ηj| < 4.5 and pT,j > 30 GeV.
For the vector operator, just 35% of the events contain only a single jet. For the gluon operator, the fraction is only 22%.
Only 1-jet events are actually accurate to NLO. Consequently, the large importance of secondary jets reduces the impact of the fixed-order NLO corrections.
Felix Kahlhoefer
4 April 2014, CP3-Origins

31. 4 April 2014, BIDM @ CP3-Origins
Gluon operator
We reach similar conclusions for the gluon operator:
K-factor > 1 at parton level, but reduced to ~ 1 after including PS effects. However, scale uncertainties are reduced.
CMS cuts
CMS cuts
LO (parton-level)
NLO (parton-level)
LOPS (jet veto)
NLOPS (jet veto)
Felix Kahlhoefer
4 April 2014, CP3-Origins

32. 4 April 2014, BIDM @ CP3-Origins
Bounds at NLO level
The K-factors after parton showering can be used to promote experimental LOPS bounds to the NLOPS level, using Λ ~ K1/4 .
CMS cuts
CMS cuts
Felix Kahlhoefer
4 April 2014, CP3-Origins

33. 4 April 2014, BIDM @ CP3-Origins
Resonant production
It is possible that the mediator mass is comparable to LHC energies and effective operators are no longer valid.
The new POWHEG BOX extension includes the case where the mediator of the interaction is on-shell.
mχ = 50 GeV
Γ = M/3
CMS cuts
CMS cuts
LO (parton-level)
NLO (parton-level)
LOPS (jet veto)
NLOPS (jet veto)
Felix Kahlhoefer
4 April 2014, CP3-Origins

34. 4 April 2014, BIDM @ CP3-Origins
Conclusions
Because of the large separation of scales, different interactions may be relevant for different DM searches.
For scalar and pseudoscalar interactions, loop-level processes significantly enhance the monojet cross-section.
For spin-dependent interactions, heavy-quark loops can induce dark matter dipole moments, which are strongly constrained by direct detection experiments.
For most other operators, NLO corrections are small, i.e. NLOPS cross sections are very similar to the LOPS level.
Nevertheless, these corrections significantly reduces scale uncertainties and therefore make these resulting bounds much more reliable.
Felix Kahlhoefer
4 April 2014, CP3-Origins

35. 4 April 2014, BIDM @ CP3-Origins
Backup
Felix Kahlhoefer
4 April 2014, CP3-Origins

36. 4 April 2014, BIDM @ CP3-Origins
Axialvector operator
For the axialvector operator SI interactions are induced from diagrams with two operator insertions: These diagrams give the scalar operator with
Felix Kahlhoefer
4 April 2014, CP3-Origins

37. Loop-level vs. tree-level
For the axialvector operator, loop-level bounds are typically weaker than tree-level bounds.
allowed
Haisch, Kahlhoefer, arXiv:
Felix Kahlhoefer
4 April 2014, CP3-Origins

38. 4 April 2014, BIDM @ CP3-Origins
Experimental details
Consider jet + MET production at the LHC with √s = 8 TeV.
Experimental cuts:
Dynamical determination of the renormalisation and factorisation scale μR = μS = μ on an event-by-event basis:
with
Varied in the range [1/2, 2] to assess theoretical errors in the analysis.
Felix Kahlhoefer
4 April 2014, CP3-Origins

39. 4 April 2014, BIDM @ CP3-Origins
ATLAS cuts
Symmetric cuts on jet pT and MET lead to smaller K-factors, because soft-gluon emission reduces the parton-level cross section.
Parton level NLO calculations may give unrealistically small scale uncertainty. Better estimate are obtained at NLOPS.
ATLAS cuts
ATLAS cuts
LO (parton-level)
NLO (parton-level)
NLOPS (inclusive)
NLOPS (jet veto)
Felix Kahlhoefer
4 April 2014, CP3-Origins

40. 4 April 2014, BIDM @ CP3-Origins
Scalar operator
If we consider the scalar operator ( ) without top quarks, the dominant contribution arises from heavy-quark initial states.
Consequently, theoretical uncertainties are dominated by the uncertainties of the heavy-quark PDFs at large x.
CMS cuts
CMS cuts
LO (parton-level)
NLO (parton-level)
Scale uncertainties
PDF uncertainties
Felix Kahlhoefer
4 April 2014, CP3-Origins