EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-EP-2019-212LHCb-PAPER-2019-031

October 14, 2019

Search for A′→µ+µ− decays

LHCb collaboration†

Abstract

Searches are performed for both prompt-like and long-lived dark photons, A′,produced in proton-proton collisions at a center-of-mass energy of 13 TeV. Thesesearches look for A′ → µ+µ− decays using a data sample corresponding to anintegrated luminosity of 5.5 fb−1 collected with the LHCb detector. Neither searchfinds evidence for a signal, and 90% confidence-level exclusion limits are placedon the γ–A′ kinetic-mixing strength. The prompt-like A′ search explores themass region from near the dimuon threshold up to 70 GeV, and places the moststringent constraints to date on dark photons with 214 < m(A′) . 740 MeV and10.6 < m(A′) . 30 GeV. The search for long-lived A′ → µ+µ− decays placesworld-leading constraints on low-mass dark photons with lifetimes O(1) ps.

Submitted to Physical Review Letters

c© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

†Authors are listed at the end of this Letter.

CERN-EP-2019-21202 October 2019

Substantial effort has been dedicated recently [1–3] to searching for the dark photon,A′, a hypothetical massive vector boson that could mediate the interactions of dark matterparticles [4], similar to how the ordinary photon, γ, mediates the electromagnetic (EM)interactions of charged Standard Model (SM) particles. The dark photon does not coupledirectly to SM particles; however, it can obtain a small coupling to the EM current dueto kinetic mixing between the SM hypercharge and A′ field strength tensors [5–10]. Thiscoupling, which is suppressed relative to that of the photon by a factor labeled ε, wouldprovide a portal through which dark photons can be produced in the laboratory, and alsovia which they can decay into visible SM final states. If the kinetic mixing arises due toprocesses described by one- or two-loop diagrams containing high-mass particles, possiblyeven at the Planck scale, then 10−12 . ε2 . 10−4 is expected [2]. Exploring this few-loopε region is one of the most important near-term goals of dark-sector physics.

Constraints have been placed on visible A′ decays by previous beam-dump [10–26],fixed-target [27–30], collider [31–36], and rare-meson-decay [37–46] experiments. Theseexperiments ruled out the few-loop region for dark-photon masses m(A′) . 10 MeV (c = 1throughout this Letter); however, most of the few-loop region at higher masses remainsunexplored. Decays into invisible dark-sector particles are expected to be dominant ifm(A′) is large enough to allow such decays. Constraints on invisible A′ decays can befound in Refs. [47–59]; only the visible scenario is considered here.

Many ideas have been proposed to further explore the [m(A′), ε2] parameter space [60–80]. For example, Ref. [74] proposed an inclusive search for A′→µ+µ− decays with theLHCb experiment, and showed that such a search will provide sensitivity to large regionsof otherwise inaccessible parameter space with the data collected by the end of Run 3 in2023. The LHCb collaboration first performed this search using Run 2 data correspondingto 1.6 fb−1 collected in 2016 [81]. The constraints placed on prompt-like dark photons,where the dark-photon lifetime is small compared to the detector resolution, were themost stringent to date for 10.6 < m(A′) < 70 GeV and comparable to the best existinglimits for m(A′) < 0.5 GeV. The search for long-lived dark photons was the first to achievesensitivity using a displaced-vertex signature, though only small regions of [m(A′), ε2]parameter space were excluded.

This Letter presents searches for both prompt-like and long-lived dark photons producedin proton-proton, pp, collisions at a center-of-mass energy of 13 TeV, looking for A′→µ+µ−

decays using a data sample corresponding to an integrated luminosity of 5.5 fb−1 collectedwith the LHCb detector in 2016–2018. The strategies employed in these searches are thesame as in Ref. [81], though the three-fold increase in integrated luminosity, improvedtrigger efficiency during 2017–2018 data taking, and improvements in the analysis providemuch better sensitivity to dark photons. The prompt-like A′ search is performed fromnear the dimuon threshold up to 70 GeV, achieving a factor of 5 (2) better sensitivity toε2 at low (high) masses than Ref. [81]. The long-lived A′ search is restricted to the massrange 214 < m(A′) < 350 MeV, where the data sample potentially has sensitivity, andprovides access to much larger regions of [m(A′), ε2] parameter space.

Both the production and decay kinematics of the A′→µ+µ− and γ∗→µ+µ− processesare identical, since dark photons produced in pp collisions via γ–A′ mixing inherit theproduction mechanisms of off-shell photons with m(γ∗) = m(A′). Furthermore, theexpected A′→µ+µ− signal yield is related to the observed prompt γ∗→µ+µ− yield in a

1

small ±∆m window around m(A′), nγ∗

ob[m(A′)], by [74]

nA′

ex [m(A′), ε2] = ε2

[nγ∗

ob[m(A′)]

2∆m

]F [m(A′)] εA′γ∗ [m(A′), τ(A′)], (1)

where the dark-photon lifetime, τ(A′), is a known function of m(A′) and ε2, F is aknown m(A′)-dependent function, and εA′γ∗ [m(A′), τ(A′)] is the τ(A′)-dependent ratio ofthe A′ → µ+µ− and γ∗ → µ+µ− detection efficiencies. For prompt-like dark photons,A′→µ+µ− decays are experimentally indistinguishable from prompt γ∗→µ+µ− decays,resulting in εA′γ∗ [m(A′), τ(A′)] ≈ 1. This facilitates a fully data-driven search where most

experimental systematic effects cancel, since the observed A′→µ+µ− yields, nA′

ob[m(A′)],can be normalized to nA

′ex [m(A′), ε2] to obtain constraints on ε2 without any knowledge

of the detector efficiency or luminosity. When τ(A′) is larger than the detector decay-time resolution, A′→ µ+µ− decays can potentially be reconstructed as displaced fromthe primary pp vertex (PV) resulting in εA′γ∗ [m(A′), τ(A′)] 6= 1; however, only the τ(A′)dependence of the detection efficiency is required to use Eq. (1). Finally, Eq. (1) is alteredfor large m(A′) to account for additional kinetic mixing with the Z boson [82,83].

The LHCb detector is a single-arm forward spectrometer covering the pseudorapidityrange 2 < η < 5, described in detail in Refs. [84,85]. The prompt-like A′ search is basedon a data sample that employs a novel data-storage strategy, made possible by advances inthe LHCb data-taking scheme introduced in 2015 [86,87], where all online-reconstructedparticles are stored, but most lower-level information is discarded, greatly reducing theevent size. In contrast, the data sample used in the long-lived A′ search is derived fromthe standard LHCb data stream. Simulated data samples, which are used to validate theanalysis, are produced using the software described in Refs. [88–90].

The online event selection is performed by a trigger [91] consisting of a hardware stageusing information from the calorimeter and muon systems, followed by a software stage thatperforms a full event reconstruction. At the hardware stage, events are required to have amuon with momentum transverse to the beam direction pT(µ) & 1.8 GeV, or a dimuon pairwith pT(µ+)pT(µ−) & (1.5 GeV)2. The long-lived A′ search also uses events selected at thehardware stage independently of the A′→µ+µ− candidate. In the software stage, wherethe pT resolution is substantially improved cf. the hardware stage, A′→µ+µ− candidatesare built from two oppositely charged tracks that form a good-quality vertex and satisfystringent muon-identification criteria, though these criteria were loosened considerably inthe low-mass region during 2017–2018 data taking. Both searches require pT(A′) > 1 GeVand 2 < η(µ) < 4.5. The prompt-like A′ search uses muons that are consistent withoriginating from the PV, with pT(µ) > 1.0 GeV and momentum p(µ) > 20 GeV in 2016,and pT(µ) > 0.5 GeV, p(µ) > 10 GeV, and pT(µ+)pT(µ−) > (1.0 GeV)2 in 2017–2018. Thelong-lived A′ search uses muons that are inconsistent with originating from any PV withpT(µ) > 0.5 GeV and p(µ) > 10 GeV, and requires 2 < η(A′) < 4.5 and a decay topologyconsistent with a dark photon originating from a PV.

The prompt-like A′ sample is contaminated by prompt γ∗→µ+µ− production, variousresonant decays to µ+µ−, whose mass-peak regions are avoided in the search, and by thefollowing types of misreconstruction: (hh) two prompt hadrons misidentified as muons;(hµQ) a misidentified prompt hadron combined with a muon produced in the decay of aheavy-flavor quark, Q, that is misidentified as prompt; and (µQµQ) two muons producedin Q-hadron decays that are both misidentified as prompt. The impact of the γ∗→µ+µ−

2

background is reduced, cf. Ref. [81], by constraining the muons to originate from thePV when determining m(µ+µ−), which improves the resolution, σ[m(µ+µ−)], by abouta factor of 2 for small m(A′). The misreconstructed backgrounds are highly suppressedby the stringent muon-identification and prompt-like requirements applied in the trigger;however, substantial contributions remain for m(A′) & 1.1 GeV. In this mass region, darkphotons are expected to be predominantly produced in Drell–Yan processes, from whichthey would inherit the well-known signature of dimuon pairs that are largely isolated.Therefore, the signal sensitivity is enhanced by applying the anti-kT-based [92–94] isolationrequirement described in Refs. [81,95] for m(A′) > 1.1 GeV.

The observed prompt-like A′ → µ+µ− yields, which are determined from fits tothe m(µ+µ−) spectrum, are normalized using Eq. (1) to obtain constraints on ε2. Thenγ∗

ob[m(A′)] values in Eq. (1) are obtained from binned extended maximum likelihood fits tothe min[χ2

IP(µ±)] distributions, where χ2IP(µ) is defined as the difference in the vertex-fit χ2

when the PV is reconstructed with and without the muon. The min[χ2IP(µ±)] distribution

provides excellent discrimination between prompt muons and the displaced muons thatconstitute the µQµQ background. Since χ2

IP(µ) approximately follows a χ2 probabilitydensity function (PDF), with two degrees of freedom, the min[χ2

IP(µ±)] distributions haveminimal mass dependence for each source of dimuon candidates. The prompt-dimuonPDFs are taken directly from data at m(J/ψ ) and m(Z), where prompt resonances aredominant. Small corrections are applied to obtain these PDFs at all other m(A′), which arevalidated near threshold, at m(φ), and at m[Υ (1S)], where the data predominantly consistof prompt dimuon pairs. Based on these validation studies, a small shape uncertaintyis applied in each min[χ2

IP(µ±)] bin. Same-sign µ±µ± candidates provide estimates forthe PDF and yield of the sum of the hh and hµQ contributions, where each involvesmisidentified prompt hadrons. The µ±µ± yields are corrected to account for the differencein the production rates of π+π− and π±π±, since the hh background largely consistsof π+π− pairs where both pions are misidentified. The uncertainty due to the finitesize of the µ±µ± sample in each bin is included in the likelihood. Simulated Q-hadrondecays are used to obtain the µQµQ PDFs, where the dominant uncertainties are from therelative importance of the various Q-hadron decay contributions at each mass. Examplemin[χ2

IP(µ±)] fits, and the resulting prompt-like candidate categorization versus m(µ+µ−),are provided in Ref. [95]. Finally, the nγ

∗

ob[m(A′)] yields are corrected for bin migrationdue to bremsstrahlung, which is negligible except near the low-mass tails of the J/ψ andΥ (1S), and the small expected Bethe–Heitler contribution is subtracted [74], resulting inthe nA

′ex [m(A′), ε2] values shown in Fig. 1.

The prompt-like mass spectrum is scanned in steps of σ[m(µ+µ−)]/2 searching forA′→µ+µ− contributions [95], using the strategy from Ref. [81]. At each mass, a binnedextended maximum likelihood fit is performed in a ±12.5σ[m(µ+µ−)] window aroundm(A′). The profile likelihood is used to determine the p-value and the upper limit at90% confidence level (CL) on nA

′ob[m(A′)]. The signal mass resolution is determined with

10% precision using a combination of simulated A′→ µ+µ− decays and the observedpT-dependent widths of the large resonance peaks in the data. The method of Ref. [96]selects the background model from a large set of potential components, which includesall Legendre modes up to tenth order and dedicated terms for known resonances, byperforming a data-driven process whose uncertainty is included in the profile likelihoodfollowing Ref. [97]. No significant excess is found in the prompt-like m(A′) spectrum, afteraccounting for the trials factor due to the number of signal hypotheses.

3

1 10

710

810

910

1010

1110

m(A′) [ GeV ]

nA

′ex

[m(A

′ ),ε

2]/ε2

LHCb√s = 13 TeV

⇒ isolationapplied

Figure 1: Expected reconstructed and selected prompt-like A′→ µ+µ− yield divided by ε2,where the displayed uncertainties include the systematic contributions. The gray boxes cover theregions with large SM resonance contributions, where no search for dark photons is performed.The anti-kT-based isolation requirement is applied for m(A′) > 1.1 GeV.

1 108−10

7−10

6−10

5−10

m(A′) [ GeV ]

ε2

LHCbprompt-like A′ search

LHCbLHCb (2016 data)BaBar+KLOE+CMS

Figure 2: Regions of the [m(A′), ε2] parameter space excluded at 90% CL by the prompt-like A′

search compared to the best published [33,36,81] and preliminary [99] limits.

Dark photons are excluded at 90% CL where the upper limit on nA′

ob[m(A′)] is lessthan nA

′ex [m(A′), ε2]. Figure 2 shows that the constraints placed on prompt-like dark

photons are the most stringent for 214 < m(A′) . 740 MeV and 10.6 < m(A′) . 30 GeV.The low-mass constraints are the strongest placed by a prompt-like A′ search at anym(A′). These results are corrected for inefficiency that arises due to τ(A′) no longer beingnegligible at such small values of ε2. The high-mass constraints are adjusted to account foradditional kinetic mixing with the Z boson [82, 83], which alters Eq. (1). Since the LHCbdetector response is independent of which Drell–Yan process produces the dark photonabove 10 GeV, it is straightforward to recast the results in Fig. 2 for other models [98].

For the long-lived A′ search, contamination from prompt particles is negligible dueto the stringent criteria applied in the trigger. Therefore, the dominant backgroundcontributions are: photons that convert into µ+µ− in the silicon-strip vertex detector thatsurrounds the pp interaction region, known as the VELO [100]; b-hadron decay chains thatproduce two muons; and the low-mass tail from K0

S → π+π− decays, where both pions are

4

1

10

250 300 350

10−10

9−10

8−10

m(A′) [MeV]

ε2nA

′ex [m

(A′),ε

2]LHCb

Figure 3: Expected reconstructed and selected long-lived A′→µ+µ− yield.

misidentified as muons. A p-value is assigned to the photon-conversion hypothesis for eachlong-lived A′→µ+µ− candidate using properties of the decay vertex and muon tracks,along with a high-precision three-dimensional material map produced from a data sampleof secondary hadronic interactions [101]. A m(A′)-dependent requirement is applied tothese p-values to reduce conversions to a negligible level. The remaining backgrounds arehighly suppressed by the decay topology requirement applied in the trigger. Furthermore,since muons produced in b-hadron decays are often accompanied by additional displacedtracks, events are rejected if they are selected by the inclusive heavy-flavor softwaretrigger [102,103] independently of the presence of the A′→µ+µ− candidate. In addition,boosted decision tree classifiers are used to reject events containing tracks consistent withoriginating from the same b-hadron decay as the signal muon candidates [104].

The long-lived A′ search is also normalized using Eq. (1); however, εA′γ∗ [m(A′), τ(A′)] isnot unity, in part because the efficiency depends on the decay time, t. The kinematics areidentical for A′→µ+µ− and prompt γ∗→µ+µ− decays for m(A′) = m(γ∗); therefore, thet dependence of εA′γ∗ [m(A′), τ(A′)] is obtained by resampling prompt γ∗→µ+µ− candidatesas long-lived A′→µ+µ− decays, where all t-dependent properties, e.g. min[χ2

IP(µ±)], arerecalculated based on the resampled decay-vertex locations (the impact of backgroundcontamination in the prompt γ∗→µ+µ− sample is negligible). This approach is validatedusing simulation, where prompt A′→µ+µ− decays are used to predict the properties oflong-lived A′→µ+µ− decays. The relative uncertainty on εA′γ∗ [m(A′), τ(A′)] is estimatedto be 5%, which arises largely due to limited knowledge of how radiation damage affectsthe performance of the VELO as a function of the distance from the pp interactionregion. The looser kinematic, muon-identification, and hardware-trigger requirementsapplied to long-lived A′→µ+µ− candidates, cf. prompt-like candidates, also increase theefficiency. This t-independent increase in efficiency is determined using a control datasample of dimuon candidates consistent with originating from the PV, but otherwisesatisfying the long-lived criteria. The nA

′ex [m(A′), ε2] values obtained using these data-

driven εA′γ∗ [m(A′), τ(A′)] values, along with the expected prompt-like A′→µ+µ− yields inFig. 1, are shown in Fig. 3.

The long-livedm(A′) spectrum is also scanned in discrete steps of σ[m(µ+µ−)]/2 lookingfor A′→ µ+µ− contributions [95]; however, discrete steps in τ(A′) are also considered

5

012345678910

250 300 350

10−10

9−10

8−10

m(A′) [MeV]

ε2

90% CL upper limit on nA′ob[m(A′), ε2] / nA′

ex [m(A′), ε2]

LHCb

Figure 4: Ratio of the observed upper limit on nA′

ob[m(A′), ε2] at 90% CL to the expected dark-photon yield, nA

′ex [m(A′), ε2], where regions less than unity are excluded. The only constraints in

this region are from (hashed) the previous LHCb search [81].

here. Binned extended maximum likelihood fits are performed to the three-dimensionalfeature space of m(µ+µ−), t, and the consistency of the decay topology as quantified in thedecay-fit χ2

DF, which has three degrees of freedom. The photon-conversion contributionis derived in each [m(µ+µ−), t, χ2

DF] bin from the number of dimuon candidates thatare rejected by the conversion criterion. Both the b-hadron and K0

S contributions aremodeled in each [t, χ2

DF] bin by second-order polynomials of the energy released in the decay,√m(µ+µ−)2 − 4m(µ)2. These contributions are validated using the following large control

data samples: candidates that fail the b-hadron suppression requirements; and candidatesthat fail, but nearly satisfy, the stringent muon-identification requirements. The profilelikelihood is used to obtain the p-values and confidence intervals on nA

′ob[m(A′), τ(A′)]. No

significant excess is observed in the long-lived A′→µ+µ− search (the three-dimensionaldata distribution and the background-only pull distributions are provided in Ref. [95]).

Since the relationship between τ(A′) and ε2 is known at each mass [74], the upperlimits on nA

′ob[m(A′), τ(A′)] are easily translated into limits on nA

′ob[m(A′), ε2]. Regions

of the [m(A′), ε2] parameter space where the upper limit on nA′

ob[m(A′), ε2] is less thannA′

ex [m(A′), ε2] are excluded at 90% CL. Figure 4 shows that sizable regions of [m(A′), ε2]parameter space are excluded, which are much larger than those excluded by LHCb inRef. [81]. Furthermore, most of the parameter space shown in Fig. 4 would have beenaccessible if the data sample was roughly three times larger. The expected number ofrecorded A′→µ+µ− decays should increase by a factor O(100) in the data sample to becollected in Run 3 by the upgraded LHCb detector.

In summary, searches are performed for prompt-like and long-lived dark photonsproduced in pp collisions at a center-of-mass energy of 13 TeV. Both searches look forA′ → µ+µ− decays using a data sample corresponding to an integrated luminosity of5.5 fb−1 collected with the LHCb detector during 2016–2018. The three-fold increasein integrated luminosity, improved trigger efficiency during 2017–2018 data taking, andimprovements in the analysis result in the searches presented in this Letter achievingmuch better sensitivity to dark photons than the previous LHCb results [81]. The prompt-like A′ search achieves a factor of 5 (2) better sensitivity to ε2 at low (high) masses than

6

Ref. [81], while the long-lived A′ search provides access to much larger regions of [m(A′), ε2]parameter space.

No evidence for a signal is found in either search, and 90% CL exclusion regions areset on the γ–A′ kinetic-mixing strength. The prompt-like A′ search is performed fromnear the dimuon threshold up to 70 GeV, and produces the most stringent constraints ondark photons with 214 < m(A′) . 740 MeV and 10.6 < m(A′) . 30 GeV. The long-livedA′ search is restricted to the mass range 214 < m(A′) < 350 MeV, where the data samplepotentially has sensitivity, and places world-leading constraints on low-mass dark photonswith lifetimes O(1) ps. These results demonstrate the unique sensitivity of the LHCbexperiment to dark photons, even using a data sample collected with a hardware-triggerstage that is highly inefficient for low-mass A′ → µ+µ− decays. The removal of thishardware-trigger stage in Run 3, along with the planned increase in luminosity, shouldgreatly increase the potential yield of A′→µ+µ− decays in the low-mass region comparedto the 2016–2018 data sample, and therefore, greatly increase the dark-photon discoverypotential of the LHCb experiment.

Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments for theexcellent performance of the LHC. We thank the technical and administrative staff at theLHCb institutes. We acknowledge support from CERN and from the national agencies:CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3(France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (Netherlands); MNiSWand NCN (Poland); MEN/IFA (Romania); MSHE (Russia); MinECo (Spain); SNSF andSER (Switzerland); NASU (Ukraine); STFC (United Kingdom); DOE NP and NSF (USA).We acknowledge the computing resources that are provided by CERN, IN2P3 (France),KIT and DESY (Germany), INFN (Italy), SURF (Netherlands), PIC (Spain), GridPP(United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH(Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebted tothe communities behind the multiple open-source software packages on which we depend.Individual groups or members have received support from AvH Foundation (Germany);EPLANET, Marie Sk lodowska-Curie Actions and ERC (European Union); ANR, LabexP2IO and OCEVU, and Region Auvergne-Rhone-Alpes (France); Key Research Programof Frontier Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China);RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); theRoyal Society and the Leverhulme Trust (United Kingdom).

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14

Supplemental Material for LHCb-PAPER-2019-031

Search for A′→µ+µ− decays

Additional details and figures for the prompt-like and long-lived searches are presentedin this Supplemental Material.

Isolation Criterion

For masses above the φ(1020) meson mass, dark photons are expected to be predomi-nantly produced in Drell–Yan processes in pp collisions at the LHC. A well-known signatureof Drell–Yan production is dimuon pairs that are largely isolated, and a high-mass darkphoton would inherit this property. The signal sensitivity for m(A′) > 1.1 GeV is enhancedby applying the jet-based isolation requirement used in Ref. [81]. Jet reconstruction isperformed by clustering charged and neutral particle-flow candidates [94] using the anti-kTclustering algorithm [92] with R = 0.5 as implemented in FastJet [93]. Muons withpT(µ)/pT(jet) < 0.7 are rejected, where the contribution to pT(jet) from the other muonis excluded if both muons are clustered in the same jet, as this is found to provide nearlyoptimal sensitivity for all m(A′) > m(φ).

Prompt-Like Fits

The prompt-like fit strategy is the same as described in detail in the SupplementalMaterial of Ref. [81]. This strategy was first introduced in Ref. [96], where it is denotedby aic-o. The m(µ+µ−) spectrum is scanned in steps of σ[m(µ+µ−)]/2 searching forA′→µ+µ− contributions. At each mass, a binned extended maximum likelihood fit isperformed, and the profile likelihood is used to determine the p-value and the confidenceinterval on nA

′ob[m(A′)]. The prompt-like-search trials factor is obtained using pseudoex-

periments. As in Ref. [96], each fit is performed in a ±12.5σ[m(µ+µ−)] window aroundthe scan-mass value using bins with widths of σ[m(µ+µ−)]/20. Near threshold, the energyreleased in the decay,

√m(µ+µ−)2 − 4m(µ)2, is used instead of the mass since it is easier

to model. The confidence intervals are defined using the bounded likelihood approach, whichinvolves taking ∆ logL relative to zero signal, rather than the best-fit value, if the best-fitsignal value is negative. This approach enforces that only physical (nonnegative) upperlimits are placed on nA

′ob[m(A′)], and prevents defining exclusion regions that are much

better than the experimental sensitivity in cases where a large deficit in the backgroundyield is observed.

The signal models are determined at each m(A′) using a combination of simulatedA′→µ+µ− decays and the widths of the large resonance peaks that are clearly visiblein the data. The background models take as input a large set of potential backgroundcomponents, then the data-driven model-selection process of Ref. [96] is performed, whoseuncertainty is included in the profile likelihood following Ref. [97]. In this analysis, theset of possible background components includes all Legendre modes with ` ≤ 10 atevery m(A′). Additionally, dedicated background components are included for sizablenarrow SM resonance contributions. The use of 11 Legendre modes adequately describesevery double-misidentified peaking background that contributes at a significant level,and therefore, these do not require dedicated background components. In mass regionswhere such complexity is not required, the data-driven model-selection procedure reducesthe complexity which increases the sensitivity to a potential signal contribution. As in

S1

Ref. [96], all fit regions are transformed onto the interval [−1, 1], where the scan m(A′)value maps to zero. After such a transformation, the signal model is (approximately) aneven function; therefore, odd Legendre modes are orthogonal to the signal component,which means that the presence of odd modes has minimal impact on the variance ofnA′

ob[m(A′)]. In the prompt-like fits, all odd Legendre modes up to ninth order are includedin every background model, while only a subset of the even modes is selected for inclusionin each fit.

Regions in the mass spectrum where large known resonance contributions are observedare vetoed in the prompt-like A′ search. Furthermore, the regions near the η′ mesonand the excited Υ states (beyond the Υ (3S) meson) are treated specially. For example,since it is not possible to distinguish between A′→µ+µ− and η′→µ+µ− contributions atm(η′), the p-values near this mass are ignored. The small excess at m(η′) is treated assignal when setting the limits on nA

′ob[m(A′)], which is conservative in that an η′→µ+µ−

contribution will weaken the constraints on A′→µ+µ− decays. The same strategy is usednear the excited Υ masses.

Long-Lived Fits

The long-lived fit strategy is also the same as described in the Supplemental Materialto Ref. [81]. The signal yields are determined from binned extended maximum likelihoodfits performed on all long-lived A′→µ+µ− candidates using the three-dimensional featurespace of m(µ+µ−), t, and χ2

DF. As in the prompt-like A′ search, a scan is performed indiscrete steps of σ[m(µ+µ−)]/2; however, in this case, discrete steps in τ(A′) are alsoconsidered. The profile likelihood is again used to obtain the p-values and the confidenceintervals on nA

′ob[m(A′), τ(A′)]. The binning scheme involves four bins in χ2

DF: [0,2], [2,4],[4,6], and [6,8]. Eight bins in t are used: [0.2,0.6], [0.6,1.1], [1.1,1.6], [1.6,2.2], [2.2,3.0],[3,5], [5,10], and > 10 ps. The binning scheme used for m(µ+µ−) depends on the scanm(A′) value, and is chosen such that the vast majority of the signal falls into a single bin.Signal decays mostly have small χ2

DF values, with about 50% (80%) of A′→µ+µ− decayssatisfying χ2

DF < 2 (4). Background from b-hadron decays populates the small t region andis roughly uniformly distributed in χ2

DF, whereas background from K0S decays is signal-like

in χ2DF and roughly uniformly distributed in t. Figure S3 shows the three-dimensional

distribution of all long-lived A′→µ+µ− candidates.The expected contribution in each bin from photon conversions is derived from the

number of candidates rejected by the conversion criterion. Two large control data samplesare used to develop and validate the modeling of the b-hadron and K0

S contributions. Bothcontributions are well modeled by second-order polynomials in

√m(µ+µ−)2 − 4m(µ)2.

While no evidence for t or χ2DF dependence is observed for these parameters in either the

b-hadron or K0S control sample, all parameters are allowed to vary independently in each

[t, χ2DF] region in the fits used in the long-lived A′ search.Figure S4 shows the long-lived A′ → µ+µ− candidates, along with the pull values

obtained from fits performed to the data where no signal contributions are included.These distributions are consistent with those observed in pseudoexperiments where nosignal component is generated.

S2

Additional Figures

This section provides additional figures from the analysis, and more detailed compar-isons of the new constraints presented in the Letter with previous results.

0

50000

100000

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Can

dida

tes

/ 0.4 LHCb

0 0.5 1 1.5 21/2)]µ(

IP2χmin[

2−02

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dida

tes

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IP2χmin[

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dida

tes

/ 0.4 LHCb µµprompt

QµQµQµh+hh

0 0.5 1 1.5 21/2)]µ(

IP2χmin[

2−02

Pull

Figure S1: Example min[χ2IP(µ±)]1/2 distributions with fit results overlaid for prompt-like

candidates near (left) m(A′) = 0.5, (middle) 5, and (right) 50 GeV. The square root ofmin[χ2

IP(µ±)] is used in the fits to increase the bin occupancies at large min[χ2IP(µ±)] values.

The background categories, as described in the Letter, are as follows: (hh) two prompt hadronsmisidentified as muons; (hµQ) a misidentified prompt hadron combined with a muon producedin the decay of a heavy-flavor quark, Q, that is misidentified as prompt; and (µQµQ) two muonsproduced in Q-hadron decays that are both misidentified as prompt.

210

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m(µ+µ−) [ GeV ]

Can

did

ates

/σ

[m(µ

+µ−

)]/

2

101

LHCb√s = 13 TeV

prompt µ+µ−

µQµQ

hh+ hµQ

⇒ isolationapplied

Figure S2: Prompt-like mass spectrum, where the categorization of the data as prompt µ+µ−,µQµQ, and hh+ hµQ is determined using the min[χ2

IP(µ±)] fits described in the text (examplesof these fits are shown in Fig. S1). The anti-kT-based isolation requirement is applied form(A′) > 1.1 GeV.

S3

0

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250 300 350

) [MeV]−µ+µ(m

1

10

[ps

]t

DF2χ

LHCb

Figure S3: Three-dimensional distribution of χ2DF versus t versus m(µ+µ−), which is fit to

determine the long-lived signal yields. The data are consistent with being predominantly due tob-hadron decays at small t, and due to K0

S decays for large t and m(µ+µ−) & 280 MeV. Theremaining few candidates at large t and small m(µ+µ−) are likely photon conversions.

3−

2−

1−

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) [MeV]−µ+µ(m

1

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250 300 350

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1

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[ps

]t

< 8DF2χ6 <

LHCb

Pull

Figure S4: Long-lived A′→µ+µ− candidates (black points) showing t versus m(µ+µ−) in binsof χ2

DF, compared to the pulls from binned fits performed without a signal contribution (coloraxis). Positive pulls denote an excess of data candidates.

S4

2−10 1−10 1 106−10

5−10

4−10

3−10

2−10

m(A′) [ GeV ]

ε (g − 2)e

E774

E141

E137

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KEK

NA64

ν-CAL ICHARM

PS191NOMAD

NA48/2 BaBarBaBar

KLOE

KLOE

A1APEXHPS

LHCb

LHCb

LHCb

CMS

Figure S5: Comparison of the results presented in this Letter to existing constraints from previousexperiments in the few-loop ε region (see Ref. [98] for details about previous experiments).

0.1 0.2 0.3 0.46−10

5−10

4−10

3−10

2−10

m(A′) [ GeV ]

ε

LHCb

BaBarNA48/2

Beam Dumps

Figure S6: Comparison of the results presented in this Letter to existing constraints from previousexperiments in the few-loop ε region (see Ref. [98] for details about previous experiments),restricted to the mass region motivated by self-interacting dark matter [4].

S5

LHCb collaboration

R. Aaij31, C. Abellan Beteta49, T. Ackernley59, B. Adeva45, M. Adinolfi53, H. Afsharnia9,C.A. Aidala79, S. Aiola25, Z. Ajaltouni9, S. Akar64, P. Albicocco22, J. Albrecht14, F. Alessio47,M. Alexander58, A. Alfonso Albero44, G. Alkhazov37, P. Alvarez Cartelle60, A.A. Alves Jr45,S. Amato2, Y. Amhis11, L. An21, L. Anderlini21, G. Andreassi48, M. Andreotti20, F. Archilli16,J. Arnau Romeu10, A. Artamonov43, M. Artuso67, K. Arzymatov41, E. Aslanides10, M. Atzeni49,B. Audurier26, S. Bachmann16, J.J. Back55, S. Baker60, V. Balagura11,b, W. Baldini20,47,A. Baranov41, R.J. Barlow61, S. Barsuk11, W. Barter60, M. Bartolini23,47,h, F. Baryshnikov76,G. Bassi28, V. Batozskaya35, B. Batsukh67, A. Battig14, V. Battista48, A. Bay48, M. Becker14,F. Bedeschi28, I. Bediaga1, A. Beiter67, L.J. Bel31, V. Belavin41, S. Belin26, N. Beliy5,V. Bellee48, K. Belous43, I. Belyaev38, G. Bencivenni22, E. Ben-Haim12, S. Benson31,S. Beranek13, A. Berezhnoy39, R. Bernet49, D. Berninghoff16, H.C. Bernstein67, E. Bertholet12,A. Bertolin27, C. Betancourt49, F. Betti19,e, M.O. Bettler54, Ia. Bezshyiko49, S. Bhasin53,J. Bhom33, M.S. Bieker14, S. Bifani52, P. Billoir12, A. Bizzeti21,u, M. Bjørn62, M.P. Blago47,T. Blake55, F. Blanc48, S. Blusk67, D. Bobulska58, V. Bocci30, O. Boente Garcia45,T. Boettcher63, A. Boldyrev77, A. Bondar42,x, N. Bondar37, S. Borghi61,47, M. Borisyak41,M. Borsato16, J.T. Borsuk33, T.J.V. Bowcock59, C. Bozzi20, S. Braun16, A. Brea Rodriguez45,M. Brodski47, J. Brodzicka33, A. Brossa Gonzalo55, D. Brundu26, E. Buchanan53,A. Buonaura49, C. Burr47, A. Bursche26, J.S. Butter31, J. Buytaert47, W. Byczynski47,S. Cadeddu26, H. Cai71, R. Calabrese20,g, L. Calero Diaz22, S. Cali22, R. Calladine52,M. Calvi24,i, M. Calvo Gomez44,m, A. Camboni44, P. Campana22, D.H. Campora Perez47,L. Capriotti19,e, A. Carbone19,e, G. Carboni29, R. Cardinale23,h, A. Cardini26, P. Carniti24,i,K. Carvalho Akiba31, A. Casais Vidal45, G. Casse59, M. Cattaneo47, G. Cavallero47,R. Cenci28,p, J. Cerasoli10, M.G. Chapman53, M. Charles12,47, Ph. Charpentier47,G. Chatzikonstantinidis52, M. Chefdeville8, V. Chekalina41, C. Chen3, S. Chen26, A. Chernov33,S.-G. Chitic47, V. Chobanova45, M. Chrzaszcz47, A. Chubykin37, P. Ciambrone22, M.F. Cicala55,X. Cid Vidal45, G. Ciezarek47, F. Cindolo19, P.E.L. Clarke57, M. Clemencic47, H.V. Cliff54,J. Closier47, J.L. Cobbledick61, V. Coco47, J.A.B. Coelho11, J. Cogan10, E. Cogneras9,L. Cojocariu36, P. Collins47, T. Colombo47, A. Comerma-Montells16, A. Contu26, N. Cooke52,G. Coombs58, S. Coquereau44, G. Corti47, C.M. Costa Sobral55, B. Couturier47, D.C. Craik63,J. Crkovska66, A. Crocombe55, M. Cruz Torres1, R. Currie57, C.L. Da Silva66, E. Dall’Occo31,J. Dalseno45,53, C. D’Ambrosio47, A. Danilina38, P. d’Argent16, A. Davis61,O. De Aguiar Francisco47, K. De Bruyn47, S. De Capua61, M. De Cian48, J.M. De Miranda1,L. De Paula2, M. De Serio18,d, P. De Simone22, J.A. de Vries31, C.T. Dean66, W. Dean79,D. Decamp8, L. Del Buono12, B. Delaney54, H.-P. Dembinski15, M. Demmer14, A. Dendek34,V. Denysenko49, D. Derkach77, O. Deschamps9, F. Desse11, F. Dettori26, B. Dey7,A. Di Canto47, P. Di Nezza22, S. Didenko76, H. Dijkstra47, F. Dordei26, M. Dorigo28,y,A.C. dos Reis1, L. Douglas58, A. Dovbnya50, K. Dreimanis59, M.W. Dudek33, L. Dufour47,G. Dujany12, P. Durante47, J.M. Durham66, D. Dutta61, R. Dzhelyadin43,†, M. Dziewiecki16,A. Dziurda33, A. Dzyuba37, S. Easo56, U. Egede60, V. Egorychev38, S. Eidelman42,x,S. Eisenhardt57, R. Ekelhof14, S. Ek-In48, L. Eklund58, S. Ely67, A. Ene36, S. Escher13,S. Esen31, T. Evans47, A. Falabella19, J. Fan3, N. Farley52, S. Farry59, D. Fazzini11, M. Feo47,P. Fernandez Declara47, A. Fernandez Prieto45, F. Ferrari19,e, L. Ferreira Lopes48,F. Ferreira Rodrigues2, S. Ferreres Sole31, M. Ferrillo49, M. Ferro-Luzzi47, S. Filippov40,R.A. Fini18, M. Fiorini20,g, M. Firlej34, K.M. Fischer62, C. Fitzpatrick47, T. Fiutowski34,F. Fleuret11,b, M. Fontana47, F. Fontanelli23,h, R. Forty47, V. Franco Lima59,M. Franco Sevilla65, M. Frank47, C. Frei47, D.A. Friday58, J. Fu25,q, M. Fuehring14, W. Funk47,E. Gabriel57, A. Gallas Torreira45, D. Galli19,e, S. Gallorini27, S. Gambetta57, Y. Gan3,M. Gandelman2, P. Gandini25, Y. Gao4, L.M. Garcia Martin46, J. Garcıa Pardinas49,

i

B. Garcia Plana45, F.A. Garcia Rosales11, J. Garra Tico54, L. Garrido44, D. Gascon44,C. Gaspar47, D. Gerick16, E. Gersabeck61, M. Gersabeck61, T. Gershon55, D. Gerstel10,Ph. Ghez8, V. Gibson54, A. Gioventu45, O.G. Girard48, P. Gironella Gironell44, L. Giubega36,C. Giugliano20, K. Gizdov57, V.V. Gligorov12, C. Gobel69, D. Golubkov38, A. Golutvin60,76,A. Gomes1,a, P. Gorbounov38,6, I.V. Gorelov39, C. Gotti24,i, E. Govorkova31, J.P. Grabowski16,R. Graciani Diaz44, T. Grammatico12, L.A. Granado Cardoso47, E. Grauges44, E. Graverini48,G. Graziani21, A. Grecu36, R. Greim31, P. Griffith20, L. Grillo61, L. Gruber47,B.R. Gruberg Cazon62, C. Gu3, E. Gushchin40, A. Guth13, Yu. Guz43,47, T. Gys47,T. Hadavizadeh62, G. Haefeli48, C. Haen47, S.C. Haines54, P.M. Hamilton65, Q. Han7, X. Han16,T.H. Hancock62, S. Hansmann-Menzemer16, N. Harnew62, T. Harrison59, R. Hart31, C. Hasse47,M. Hatch47, J. He5, M. Hecker60, K. Heijhoff31, K. Heinicke14, A. Heister14, A.M. Hennequin47,K. Hennessy59, L. Henry46, J. Heuel13, A. Hicheur68, R. Hidalgo Charman61, D. Hill62,M. Hilton61, P.H. Hopchev48, J. Hu16, W. Hu7, W. Huang5, W. Hulsbergen31, T. Humair60,R.J. Hunter55, M. Hushchyn77, D. Hutchcroft59, D. Hynds31, P. Ibis14, M. Idzik34, P. Ilten52,A. Inglessi37, A. Inyakin43, K. Ivshin37, R. Jacobsson47, S. Jakobsen47, J. Jalocha62, E. Jans31,B.K. Jashal46, A. Jawahery65, V. Jevtic14, F. Jiang3, M. John62, D. Johnson47, C.R. Jones54,B. Jost47, N. Jurik62, S. Kandybei50, M. Karacson47, J.M. Kariuki53, N. Kazeev77, M. Kecke16,F. Keizer54, M. Kelsey67, M. Kenzie54, T. Ketel32, B. Khanji47, A. Kharisova78, K.E. Kim67,T. Kirn13, V.S. Kirsebom48, S. Klaver22, K. Klimaszewski35, S. Koliiev51, A. Kondybayeva76,A. Konoplyannikov38, P. Kopciewicz34, R. Kopecna16, P. Koppenburg31, I. Kostiuk31,51,O. Kot51, S. Kotriakhova37, L. Kravchuk40, R.D. Krawczyk47, M. Kreps55, F. Kress60,S. Kretzschmar13, P. Krokovny42,x, W. Krupa34, W. Krzemien35, W. Kucewicz33,l,M. Kucharczyk33, V. Kudryavtsev42,x, H.S. Kuindersma31, G.J. Kunde66, A.K. Kuonen48,T. Kvaratskheliya38, D. Lacarrere47, G. Lafferty61, A. Lai26, D. Lancierini49, J.J. Lane61,G. Lanfranchi22, C. Langenbruch13, T. Latham55, F. Lazzari28,v, C. Lazzeroni52, R. Le Gac10,R. Lefevre9, A. Leflat39, F. Lemaitre47, O. Leroy10, T. Lesiak33, B. Leverington16, H. Li70,X. Li66, Y. Li6, Z. Li67, X. Liang67, R. Lindner47, F. Lionetto49, V. Lisovskyi11, G. Liu70,X. Liu3, D. Loh55, A. Loi26, J. Lomba Castro45, I. Longstaff58, J.H. Lopes2, G. Loustau49,G.H. Lovell54, Y. Lu6, D. Lucchesi27,o, M. Lucio Martinez31, Y. Luo3, A. Lupato27, E. Luppi20,g,O. Lupton55, A. Lusiani28, X. Lyu5, S. Maccolini19,e, F. Machefert11, F. Maciuc36, V. Macko48,P. Mackowiak14, S. Maddrell-Mander53, L.R. Madhan Mohan53, O. Maev37,47, A. Maevskiy77,K. Maguire61, D. Maisuzenko37, M.W. Majewski34, S. Malde62, B. Malecki47, A. Malinin75,T. Maltsev42,x, H. Malygina16, G. Manca26,f , G. Mancinelli10, R. Manera Escalero44,D. Manuzzi19,e, D. Marangotto25,q, J. Maratas9,w, J.F. Marchand8, U. Marconi19, S. Mariani21,C. Marin Benito11, M. Marinangeli48, P. Marino48, J. Marks16, P.J. Marshall59, G. Martellotti30,L. Martinazzoli47, M. Martinelli24, D. Martinez Santos45, F. Martinez Vidal46, A. Massafferri1,M. Materok13, R. Matev47, A. Mathad49, Z. Mathe47, V. Matiunin38, C. Matteuzzi24,K.R. Mattioli79, A. Mauri49, E. Maurice11,b, M. McCann60,47, L. Mcconnell17, A. McNab61,R. McNulty17, J.V. Mead59, B. Meadows64, C. Meaux10, G. Meier14, N. Meinert73,D. Melnychuk35, S. Meloni24,i, M. Merk31, A. Merli25, M. Mikhasenko47, D.A. Milanes72,E. Millard55, M.-N. Minard8, O. Mineev38, L. Minzoni20,g, S.E. Mitchell57, B. Mitreska61,D.S. Mitzel47, A. Modden14, A. Mogini12, R.D. Moise60, T. Mombacher14, I.A. Monroy72,S. Monteil9, M. Morandin27, G. Morello22, M.J. Morello28,t, J. Moron34, A.B. Morris10,A.G. Morris55, R. Mountain67, H. Mu3, F. Muheim57, M. Mukherjee7, M. Mulder31, D. Muller47,K. Muller49, V. Muller14, C.H. Murphy62, D. Murray61, P. Muzzetto26, P. Naik53, T. Nakada48,R. Nandakumar56, A. Nandi62, T. Nanut48, I. Nasteva2, M. Needham57, N. Neri25,q,S. Neubert16, N. Neufeld47, R. Newcombe60, T.D. Nguyen48, C. Nguyen-Mau48,n, E.M. Niel11,S. Nieswand13, N. Nikitin39, N.S. Nolte47, C. Nunez79, A. Oblakowska-Mucha34, V. Obraztsov43,S. Ogilvy58, D.P. O’Hanlon19, R. Oldeman26,f , C.J.G. Onderwater74, J. D. Osborn79,A. Ossowska33, J.M. Otalora Goicochea2, T. Ovsiannikova38, P. Owen49, A. Oyanguren46,

ii

P.R. Pais48, T. Pajero28,t, A. Palano18, M. Palutan22, G. Panshin78, A. Papanestis56,M. Pappagallo57, L.L. Pappalardo20,g, C. Pappenheimer64, W. Parker65, C. Parkes61,47,G. Passaleva21,47, A. Pastore18, M. Patel60, C. Patrignani19,e, A. Pearce47, A. Pellegrino31,M. Pepe Altarelli47, S. Perazzini19, D. Pereima38, P. Perret9, L. Pescatore48, K. Petridis53,A. Petrolini23,h, A. Petrov75, S. Petrucci57, M. Petruzzo25,q, B. Pietrzyk8, G. Pietrzyk48,M. Pikies33, M. Pili62, D. Pinci30, J. Pinzino47, F. Pisani47, A. Piucci16, V. Placinta36,S. Playfer57, J. Plews52, M. Plo Casasus45, F. Polci12, M. Poli Lener22, M. Poliakova67,A. Poluektov10, N. Polukhina76,c, I. Polyakov67, E. Polycarpo2, G.J. Pomery53, S. Ponce47,A. Popov43, D. Popov52, S. Poslavskii43, K. Prasanth33, L. Promberger47, C. Prouve45,V. Pugatch51, A. Puig Navarro49, H. Pullen62, G. Punzi28,p, W. Qian5, J. Qin5, R. Quagliani12,B. Quintana9, N.V. Raab17, R.I. Rabadan Trejo10, B. Rachwal34, J.H. Rademacker53,M. Rama28, M. Ramos Pernas45, M.S. Rangel2, F. Ratnikov41,77, G. Raven32,M. Ravonel Salzgeber47, M. Reboud8, F. Redi48, S. Reichert14, F. Reiss12, C. Remon Alepuz46,Z. Ren3, V. Renaudin62, S. Ricciardi56, S. Richards53, K. Rinnert59, P. Robbe11, A. Robert12,A.B. Rodrigues48, E. Rodrigues64, J.A. Rodriguez Lopez72, M. Roehrken47, S. Roiser47,A. Rollings62, V. Romanovskiy43, M. Romero Lamas45, A. Romero Vidal45, J.D. Roth79,M. Rotondo22, M.S. Rudolph67, T. Ruf47, J. Ruiz Vidal46, J. Ryzka34, J.J. Saborido Silva45,N. Sagidova37, B. Saitta26,f , C. Sanchez Gras31, C. Sanchez Mayordomo46,B. Sanmartin Sedes45, R. Santacesaria30, C. Santamarina Rios45, M. Santimaria22,E. Santovetti29,j , G. Sarpis61, A. Sarti30, C. Satriano30,s, A. Satta29, M. Saur5, D. Savrina38,39,L.G. Scantlebury Smead62, S. Schael13, M. Schellenberg14, M. Schiller58, H. Schindler47,M. Schmelling15, T. Schmelzer14, B. Schmidt47, O. Schneider48, A. Schopper47, H.F. Schreiner64,M. Schubiger31, S. Schulte48, M.H. Schune11, R. Schwemmer47, B. Sciascia22, A. Sciubba30,k,S. Sellam68, A. Semennikov38, A. Sergi52,47, N. Serra49, J. Serrano10, L. Sestini27, A. Seuthe14,P. Seyfert47, D.M. Shangase79, M. Shapkin43, T. Shears59, L. Shekhtman42,x, V. Shevchenko75,76,E. Shmanin76, J.D. Shupperd67, B.G. Siddi20, R. Silva Coutinho49, L. Silva de Oliveira2,G. Simi27,o, S. Simone18,d, I. Skiba20, N. Skidmore16, T. Skwarnicki67, M.W. Slater52,J.G. Smeaton54, A. Smetkina38, E. Smith13, I.T. Smith57, M. Smith60, A. Snoch31, M. Soares19,L. Soares Lavra1, M.D. Sokoloff64, F.J.P. Soler58, B. Souza De Paula2, B. Spaan14,E. Spadaro Norella25,q, P. Spradlin58, F. Stagni47, M. Stahl64, S. Stahl47, P. Stefko48,S. Stefkova60, O. Steinkamp49, S. Stemmle16, O. Stenyakin43, M. Stepanova37, H. Stevens14,S. Stone67, S. Stracka28, M.E. Stramaglia48, M. Straticiuc36, S. Strokov78, J. Sun3, L. Sun71,Y. Sun65, P. Svihra61, K. Swientek34, A. Szabelski35, T. Szumlak34, M. Szymanski5, S. Taneja61,Z. Tang3, T. Tekampe14, G. Tellarini20, F. Teubert47, E. Thomas47, K.A. Thomson59,M.J. Tilley60, V. Tisserand9, S. T’Jampens8, M. Tobin6, S. Tolk47, L. Tomassetti20,g,D. Tonelli28, D.Y. Tou12, E. Tournefier8, M. Traill58, M.T. Tran48, C. Trippl48, A. Trisovic54,A. Tsaregorodtsev10, G. Tuci28,47,p, A. Tully48, N. Tuning31, A. Ukleja35, A. Usachov11,A. Ustyuzhanin41,77, U. Uwer16, A. Vagner78, V. Vagnoni19, A. Valassi47, G. Valenti19,M. van Beuzekom31, H. Van Hecke66, E. van Herwijnen47, C.B. Van Hulse17, J. van Tilburg31,M. van Veghel74, R. Vazquez Gomez44, P. Vazquez Regueiro45, C. Vazquez Sierra31, S. Vecchi20,J.J. Velthuis53, M. Veltri21,r, A. Venkateswaran67, M. Vernet9, M. Veronesi31, M. Vesterinen55,J.V. Viana Barbosa47, D. Vieira5, M. Vieites Diaz48, H. Viemann73, X. Vilasis-Cardona44,m,A. Vitkovskiy31, V. Volkov39, A. Vollhardt49, D. Vom Bruch12, A. Vorobyev37, V. Vorobyev42,x,N. Voropaev37, R. Waldi73, J. Walsh28, J. Wang3, J. Wang71, J. Wang6, M. Wang3, Y. Wang7,Z. Wang49, D.R. Ward54, H.M. Wark59, N.K. Watson52, D. Websdale60, A. Weiden49,C. Weisser63, B.D.C. Westhenry53, D.J. White61, M. Whitehead13, D. Wiedner14,G. Wilkinson62, M. Wilkinson67, I. Williams54, M. Williams63, M.R.J. Williams61,T. Williams52, F.F. Wilson56, M. Winn11, W. Wislicki35, M. Witek33, G. Wormser11,S.A. Wotton54, H. Wu67, K. Wyllie47, Z. Xiang5, D. Xiao7, Y. Xie7, H. Xing70, A. Xu3, L. Xu3,M. Xu7, Q. Xu5, Z. Xu8, Z. Xu3, Z. Yang3, Z. Yang65, Y. Yao67, L.E. Yeomans59, H. Yin7,

iii

J. Yu7,aa, X. Yuan67, O. Yushchenko43, K.A. Zarebski52, M. Zavertyaev15,c, M. Zdybal33,M. Zeng3, D. Zhang7, L. Zhang3, S. Zhang3, W.C. Zhang3,z, Y. Zhang47, A. Zhelezov16,Y. Zheng5, X. Zhou5, Y. Zhou5, X. Zhu3, V. Zhukov13,39, J.B. Zonneveld57, S. Zucchelli19,e.

1Centro Brasileiro de Pesquisas Fısicas (CBPF), Rio de Janeiro, Brazil2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil3Center for High Energy Physics, Tsinghua University, Beijing, China4School of Physics State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing,China5University of Chinese Academy of Sciences, Beijing, China6Institute Of High Energy Physics (IHEP), Beijing, China7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China8Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France9Universite Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France10Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France11LAL, Univ. Paris-Sud, CNRS/IN2P3, Universite Paris-Saclay, Orsay, France12LPNHE, Sorbonne Universite, Paris Diderot Sorbonne Paris Cite, CNRS/IN2P3, Paris, France13I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany14Fakultat Physik, Technische Universitat Dortmund, Dortmund, Germany15Max-Planck-Institut fur Kernphysik (MPIK), Heidelberg, Germany16Physikalisches Institut, Ruprecht-Karls-Universitat Heidelberg, Heidelberg, Germany17School of Physics, University College Dublin, Dublin, Ireland18INFN Sezione di Bari, Bari, Italy19INFN Sezione di Bologna, Bologna, Italy20INFN Sezione di Ferrara, Ferrara, Italy21INFN Sezione di Firenze, Firenze, Italy22INFN Laboratori Nazionali di Frascati, Frascati, Italy23INFN Sezione di Genova, Genova, Italy24INFN Sezione di Milano-Bicocca, Milano, Italy25INFN Sezione di Milano, Milano, Italy26INFN Sezione di Cagliari, Monserrato, Italy27INFN Sezione di Padova, Padova, Italy28INFN Sezione di Pisa, Pisa, Italy29INFN Sezione di Roma Tor Vergata, Roma, Italy30INFN Sezione di Roma La Sapienza, Roma, Italy31Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands32Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam,Netherlands33Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland34AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,Krakow, Poland35National Center for Nuclear Research (NCBJ), Warsaw, Poland36Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania37Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI), Gatchina, Russia38Institute of Theoretical and Experimental Physics NRC Kurchatov Institute (ITEP NRC KI), Moscow,Russia, Moscow, Russia39Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia40Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS), Moscow, Russia41Yandex School of Data Analysis, Moscow, Russia42Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia43Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI), Protvino, Russia,Protvino, Russia44ICCUB, Universitat de Barcelona, Barcelona, Spain45Instituto Galego de Fısica de Altas Enerxıas (IGFAE), Universidade de Santiago de Compostela,Santiago de Compostela, Spain46Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain

iv

47European Organization for Nuclear Research (CERN), Geneva, Switzerland48Institute of Physics, Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland49Physik-Institut, Universitat Zurich, Zurich, Switzerland50NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine51Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine52University of Birmingham, Birmingham, United Kingdom53H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom54Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom55Department of Physics, University of Warwick, Coventry, United Kingdom56STFC Rutherford Appleton Laboratory, Didcot, United Kingdom57School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom58School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom59Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom60Imperial College London, London, United Kingdom61Department of Physics and Astronomy, University of Manchester, Manchester, United Kingdom62Department of Physics, University of Oxford, Oxford, United Kingdom63Massachusetts Institute of Technology, Cambridge, MA, United States64University of Cincinnati, Cincinnati, OH, United States65University of Maryland, College Park, MD, United States66Los Alamos National Laboratory (LANL), Los Alamos, United States67Syracuse University, Syracuse, NY, United States68Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria, associated to 2

69Pontifıcia Universidade Catolica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2

70South China Normal University, Guangzhou, China, associated to 3

71School of Physics and Technology, Wuhan University, Wuhan, China, associated to 3

72Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia, associated to 12

73Institut fur Physik, Universitat Rostock, Rostock, Germany, associated to 16

74Van Swinderen Institute, University of Groningen, Groningen, Netherlands, associated to 31

75National Research Centre Kurchatov Institute, Moscow, Russia, associated to 38

76National University of Science and Technology “MISIS”, Moscow, Russia, associated to 38

77National Research University Higher School of Economics, Moscow, Russia, associated to 41

78National Research Tomsk Polytechnic University, Tomsk, Russia, associated to 38

79University of Michigan, Ann Arbor, United States, associated to 67

aUniversidade Federal do Triangulo Mineiro (UFTM), Uberaba-MG, BrazilbLaboratoire Leprince-Ringuet, Palaiseau, FrancecP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, RussiadUniversita di Bari, Bari, ItalyeUniversita di Bologna, Bologna, ItalyfUniversita di Cagliari, Cagliari, ItalygUniversita di Ferrara, Ferrara, ItalyhUniversita di Genova, Genova, ItalyiUniversita di Milano Bicocca, Milano, ItalyjUniversita di Roma Tor Vergata, Roma, ItalykUniversita di Roma La Sapienza, Roma, ItalylAGH - University of Science and Technology, Faculty of Computer Science, Electronics andTelecommunications, Krakow, PolandmLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, SpainnHanoi University of Science, Hanoi, VietnamoUniversita di Padova, Padova, ItalypUniversita di Pisa, Pisa, ItalyqUniversita degli Studi di Milano, Milano, ItalyrUniversita di Urbino, Urbino, ItalysUniversita della Basilicata, Potenza, ItalytScuola Normale Superiore, Pisa, ItalyuUniversita di Modena e Reggio Emilia, Modena, ItalyvUniversita di Siena, Siena, Italy

v

wMSU - Iligan Institute of Technology (MSU-IIT), Iligan, PhilippinesxNovosibirsk State University, Novosibirsk, RussiaySezione INFN di Trieste, Trieste, ItalyzSchool of Physics and Information Technology, Shaanxi Normal University (SNNU), Xi’an, ChinaaaPhysics and Micro Electronic College, Hunan University, Changsha City, China

†Deceased

vi