Download Describing Dark Matter with Effective Operators

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
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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
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• 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
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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
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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
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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.
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Describing Dark Matter with Effective Operators
Separation of scales
FELIX KAHLHOEFER
ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY
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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
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• 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
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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
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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
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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
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• 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
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• 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
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• 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
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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
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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
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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
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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
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• 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
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Describing Dark Matter with Effective Operators
Direct detection limit
FELIX KAHLHOEFER
ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY
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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
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• 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
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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
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Describing Dark Matter with Effective Operators
Operator mixing
FELIX KAHLHOEFER
ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY
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• 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
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• 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
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• 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
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• 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
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• 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
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• 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
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• 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
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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
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• 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
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• 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
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• 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
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• 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
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• 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
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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
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• 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
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ROYAL HOLLOWAY, WEDNESDAY, 16 JANUARY
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• 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
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• 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