ATLAS/CMS Dark Matter Forum meeting

Europe/Zurich
61/1-009 - Room C (CERN)

61/1-009 - Room C

CERN

22
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Antonio Boveia (CERN), Caterina Doglioni (Universite de Geneve (CH)), Sarah Malik (Imperial College Sci., Tech. & Med. (GB)), Stephen Mrenna (FERMILAB), Steve Mrenna (Fermi National Accelerator Lab. (US)), Steven Lowette (Vrije Universiteit Brussel (BE))

Thomas Jacques - On validity of EFT in DM searches
==================

##Literature specifically relevant for this talk:

On the Validity of the Effective Field Theory for Dark Matter
Searches at the LHC:
http://arxiv.org/abs/arXiv:1307.2253
http://arxiv.org/abs/arXiv:1402.1275
http://arxiv.org/abs/arXiv:1405.3101

##Why have EFT been used so far

Collider constraints on theories can go from the EFT, to simplified to full models. The number of parameters (and the dimensionality of parameter space) increases with increasing complexity.

The EFT is convenient since it encapsulates an entire theory in two parameters (M*/lambda, mDM). This allows one to write down all possible operators scanning interactions and particle types. Immediate complementarity with DD/ID is also attractive, but it has so far been employed carelessly: there are limits to the validity of an EFT.

##Minimal limit to validity, in the s-channel:

Initial (7 TeV) results used a validity condition with

- Momentum transfer (Q_tr) larger than 2*m_DM
- Linking the EFT scale lambda to momentum transfer in the s-channel and adding perturbativity of the product of the couplings leads to a limit of lambda>M/4pi.

Discussion: this is a necessary but not sufficient condition: there may be other factors that modify condition. This talk advocates to move on from this approach and consider a more realistic
limit to the EFT validity.

##More realistic limit to validity:

The more realistic limit for the EFT to be valid is to take the momentum transfer larger than the mediator mass (Q_tr > M_Med), coming from the perturbative expansion of the s-channel propagator.

At this point one needs to call in the UV completion of the model, to link the mediator mass to the interaction scale - the validity will depend at least on the couplings and on other possible parameters of the more complicated model used for the completion. For a simple s-channel model with coupling of order unity, this criterion reduces to Q_tr>lambda.

##Quantifying the validity of the EFT

One can calculate analytically the fraction of events passing this criterion, for given choices of lambda and M_DM, for a number of EFT operators. It has been cross-checked that the calculation of this fraction corresponds to the fraction of events not satisfying the condition in simulation.

These curves can be superimposed to current limits, showing that in some of the regions that are claimed to be excluded a potentially large fraction of events is not valid.

##Summary

EFT can be a powerful benchmark, but at the LHC the EFT approximation breaks down, only remaining valid for large couplings/large lambda. A truncation could be implemented to remove the invalid events - details in the next two talks.

Steven Schramm - EFT validity in ATLAS
==================

##Literature specifically relevant for this talk:

ATLAS monojet search, with criteria and assumptions relevant for EFT validity condition, together with the truncation procedures, are explained in the appendix:
http://arxiv.org/abs/1502.01518

##Introduction

When using an EFT, we should only consider events with Q_tr<<Mmed - we want to apply the minimal constraint of Q_tr<Mmed. This is particularly important when comparing to DD, as DD has low Q_tr and it is not affected by EFT considerations - the discussion highlights the bad reputation of collider limits superimposed on the DM-nucleon x-sec plane without any comments on the EFT validity.

##Validity condition and UV matching choices

In an EFT, lambda and mDM are the only parameters available, so in order to evaluate the validity condition we need to make assumptions about:
- the UV completion
- the value of the couplings

The most common examples are the D5, D8 and D9 operators with simple mediators, where one can extract simple validity. In terms of assumptions on the parameters needed to have a validity statement, things get more complicated when considering chirally suppressed operators. E.g. in the case of the C1 operator, there is a Yukawa coupling leading to a dependence on the quark mass---so the question on which quark mass is used for evaluating the validity (ATLAS uses the heaviest quark that dominates in the signal region considered, which is either b or top for heavy flavor models and charm for monojet). Similarly, for gluon operators (D11/C5) one needs to make assumptions on the gluon-gluon-mediator vertex.

In general, given a choice one can have an unique validity criterion per operator (see monojet paper) given
- the relation between Mmed and M*
- coupling term range
Still there can be arbitrary factors related to the completion chosen, e.g. the VEV scale factor for C1/C5.

##Implementation of the validity in ATLAS papers

EFT validity has been implemented in the 8 TeV DM+heavy flavor/monophoton/monojet search results from ATLAS. There was also an early, slightly different version in the ATLAS 14 TeV monojet prospects note.

Two methods of truncation or rescaling the limits are available, providing compatible results in the limit of high statistics. The difference between the two methods is at the level of 1%, given sufficient statistics. There is some concern that the effect of the choices made for the truncation is itself larger than this difference.

##Presentation of results including EFT validity statements

Since the EFT validity depends on many factors, there are many options for plotting this informations. The choices made in ATLAS have been:

- the ratio of valid/non valid events in the plane sqrt(couplings) vs m_DM, with explicit marks where M*valid/M*exp > 99%.
- the truncated limits, in the plane sqrt(couplings) vs m_DM,

It can be observed that at large couplings the EFT have fewer validity problems, and that some operators have more validity problems than others (e.g. D11: no points where EFT is >99% valid).

If one wants to show those limits in comparison with ID and DD on the DM-nucleon plot, the choices ATLAS made were:
- showing nominal limits, corresponding to maximum couplings, up to the point where the EFT has valid events
- showing truncated limits, with the choice of couplings = 1
This reflects that some operators are in better shape than others.

##Conclusions

The EFT are useful benchmarks but have limitations. One cannot ignore the validity problem if comparing to DD/ID. A procedure for truncation that depends on the UV matching conditions and on the coupling is available.
Simplified models however provide better long-term solution.


Davide Racco - EFT validity
=====================

##Literature specifically relevant for this talk:

Robust collider limits on heavy-mediator Dark Matter
http://arxiv.org/abs/1502.04701

##Introduction

An EFT intrinsically contains three parameters:
- dark matter mass m_DM
- effective scale (lambda/M*)
- cut-off scale for the validity of the EFT, Mcut

The proposal from the authors of this paper is to only consider signal events where the *total* center-of-mass energy is below the cut-off scale of the EFT. This proposal is more conservative and more general than what outlined in previous talks. This limit is consistent: when Mcut is chosen properly the limit is strictly weaker than any limit one would obtain with a particular UV completion.

##Recasting the ATLAS monojet analysis (10 inv pb)

The ATLAS monojet analysis has been recast, obtaining limits on the M*/m_DM plane when fixing M_cut or when linking the M_cut values to the effective coupling strength of the EFT (g*^2=M_cut^2/M*^2, following the EFT Lagrangian) and fixing g*. The lower limit on the excluded region that was not shown in the previous procedure (but was still present) can be understood as a combination of acceptance and kinematic threshold. This definition and scan of the values of the M_cut (g*) parameter space have been discussed for the D8 operator. Other operators may have different definitions and scan values that make the results easier to recast.

##Comparing to simplified models (s-channel vector/t-channel scalar mediators)

The options for the limits in the M*/m_med plane can be compared:
- for a naive EFT without truncation
- for the EFT truncation assuming M_cut = m_med
- for the full simplified model
This shows that there is a region in this plane where the EFT is a good approximation (high m_med), a region in which the simplified model limit is stronger due to the resonant mediator production, and a region at low mediator masses in which the naive EFT limit is too aggressive. This is consistent with earlier comparisons, e.g. arXiv:1109.4398. Showing results in this plane has limitations, as curves of fixed width cannot be shown consistently.

##Q&A:

Q: Should we consider the lower M* limit of validity as "unconstrained regions"?
A: This is somehow an artifact: if we had lower pT we would still set a limit there.

Q: Is the criterion presented in the last talk also valid in models with loops?
A: Yes, this is a universal bound (more conservative than the simplified model approach).

Q: How do we find Mcut in practice?
A: For tree-level processes, we can set this to the mediator mass.

Q: What could be improved about this procedure?
A: We can apply this to higher-dimensional operators (e.g. EW EFT operators where the UV completion is different)

Discussion and Q&A on EFT validity
=====================

Q: Is a truncation a long-term solution to keep using the EFT, or a temporary fix before we fully transition to simplified models?
A: The proper long-term solution is to use simplified models. However there is interest in part of the community to keep providing results for EFT benchmarks. When they can be used correctly, the EFT interpretation involves fewer model assumptions. EFT limits presented in terms of the EFT parameters for a range of Mcut values or for varying amounts of truncation are useful to theorists.

Q: Which benchmark should we use for collider/DD comparison?
A (part of the audience): Not the EFT, this is theoretically unsafe and has caused problems in the past - it might be one of the reasons why collider limits on DM are not taken seriously by other communities. Presenting EFT limits on the DD cross section is a dangerous exercise, even with caveats. We should at most keep the EFT limits as benchmark to be used to compare amongst LHC results, nothing else.
A (another part of the audience): EFT with truncation, as this is the only model-independent mapping. If there is a straight-forward mechanism to reinterpret those limits (e.g. limits as a function of MCut) then these can still be useful as they are sufficiently abstract and robust to be universally usable. Theorists can worry about doing the comparisons.

Q: why not have both options (truncated EFTs and simplified models) as comparisons? This way we would have both conservative model-independence and strength of colliders in a more model-dependent way.

Q: when we discuss Q_tr or M_cut prescriptions on EFT truncation, we assume that the theory prediction is absolute. Once we include reasonable theory systematic estimates (done in analysis and interpretation both), how much difference remains? This includes PDF uncertainty, alpha_s(pTjet) and potentially Sudakov suppression.
Furthermore, EFT validity considerations should be split in two possible points:
- the EFT does not make sense if the approximation behind the operator is violated: the mediator mass is too low to be integrated out or the coupling is too large.
- the validity of the QCD part should also be considered. If one of the incoming quark lines is off-shell more than the factorization scale, then the eikonal approximation for the gluon emission will only be reliable up to a factor of a few. In many/most cases, it overestimates the tail of the pT distribution (this was studied extensively for Pythia). But, it isn't zero, so QCD may predict a lower bound on the high-pT tail.

## Discussion Summary:

There is some disagreement within the meeting on how much emphasis to be put on EFTs, and especially whether it's worth ever comparing any of the EFT limits to DD/ID. An alternative option is to keep EFTs only as simple benchmarks, to compare within an experiment or between ATLAS and CMS. Part of the audience reckons that the use of EFT has lead to other experiments not considering LHC limits on their plots. This does not mean that there is no interest from the DD/ID community in doing this or in discussing it.  A third use of EFTs limits is for reinterpretation, if there can be a scheme that parameterizes the model-dependence.

According to the Forum’s mandate, discussing how to compare truncated collider EFT results with DD/ID results should be a lesser priority than an agreement on the truncation itself. This truncation procedure will also need to be discussed within ATLAS and CMS before a final agreement, as will the other recommendations of the Forum.

If we have settled on how to treat the EFT, as well as achieved the other goals of the Forum, recommendations could be given on what could/should be done if an experiment wants to translate EFT limits to non-collider experiments. Care is needed because being conservative is generally considered a merit, but when it does not convey the true information (colliders can be more or less sensitive than these limits, depending on the underlying UV completion) one might draw the wrong conclusions from the comparison plots.

There are minutes attached to this event. Show them.
    • 15:00 16:15
      Discussion on EFT validity
      • 15:00
        EFT validity truncation in ATLAS: theory considerations 15m
        Speakers: Thomas David Jacques (Universite de Geneve (CH)), Thomas Jacques (U)
        Slides
      • 15:15
        EFT validity truncation in ATLAS: procedure and implementation 15m
        Speaker: Steven Randolph Schramm (University of Toronto (CA))
        Slides
      • 15:35
        EFT validity truncation procedure from http://arxiv.org/abs/1502.04701 20m
        Speaker: Davide Racco (CERN)
        Slides
    • 16:15 17:15
      Monojet grid point scan: Monojet and DM+HF parameter scan
      • 16:15
        Monojet parameter scan 20m
        Speaker: David Salek (NIKHEF (NL))
        Slides
      • 16:45
        Studies of pseudoscalar simplified model 15m
        Speakers: Deborah Pinna (Universitaet Zuerich (CH)), Deborah Pinna (E)
        Slides