The study of lepton pair production is an important tool for investigating the properties of hadronic and nuclear collisions as they can leave the strongly interacting system at any stage of its evolution. In order to single out possible medium contributions to the dilepton yield in nucleusnucleus collisions on top of those from hadron decays, studies in hadronic collision systems are instrumental in obtaining a medium-free reference. Recent measurements of dielectron (e þ e -) production at midrapidity in protonproton (pp) collisions at the Large Hadron Collider (LHC) at CERN [1][2][3] and at the Relativistic Heavy-Ion Collider (RHIC) at BNL [4][5][6] are compatible with the expectations from hadron decays, i.e., with the hadronic cocktail, and show no indication of medium effects within the experimental uncertainties. In contrast to this, recent measurements of hadronic observables in small collision systems at the LHC [7][8][9][10] and at RHIC [11][12][13] reveal signs of collectivity and equilibration of the final-state particles at high multiplicities. This suggests that considerable interaction in an intermediate state may, indeed, be at work even in pp collisions, which should also give rise to the emission of electromagnetic radiation.

The production of soft photons in hadronic collision systems was extensively studied in fixed-target experiments at beam momenta ranging from 10.5 to 450 GeV=c. Except for the lowest collision energies [14], most experiments reported an excess of soft photons compared with the expectation from hadron decays that could not be explained by initial-and final-state bremsstrahlung [15][16][17]. The emergence of a photon excess in a transverse momentum (p T ) range far below 0.2 GeV=c was dubbed the softphoton puzzle because bremsstrahlung from initial-and final-state particles should dominate over the radiation from any intermediate state in the soft limit, as stated by the Low theorem [18]. This raised speculations about the existence of a radiating intermediate state with characteristic time and length scales well above 1 fm [19]; a scenario that can be largely ruled out by more recent measurements of the source size in pp collisions from particle interferometry [20][21][22]. Several possible mechanisms were proposed to explain the observations, including the annihilation of soft partons [23][24][25][26][27][28], the production of a cold nonequilibrium state of quarks and gluons [29,30], and the emission of synchrotron radiation off quarks that are accelerated in the chromomagnetic fields of the colliding hadrons [31,32]. A final conclusion on the interpretation of the soft-photon excess has not been reached though [33,34].

In the dilepton sector, an enhancement over the hadronic cocktail was observed for both electron and muon pairs at small invariant masses in pp collisions at the intersecting storage rings (ISRs) [35], and in fixed-target experiments with π and p beams from 10 to 400 GeV=c [36][37][38][39][40][41][42][43][44][45][46]. Similar to the case of real photons, the excess yield could not be reconciled with the expectation from hadronic bremsstrahlung. These observations are supported by findings of an enhanced e þ =π ratio at the ISR [47]. However, the observations in the dilepton sector remained controversial because other experiments reported results that were compatible with bremsstrahlung and hadron decays only [48][49][50]. The question of anomalous softdilepton production in hadronic collisions awaits further experimental input since three decades.

In a dedicated campaign during pp operation at ffiffi ffi s p ¼ 13 TeV, the ALICE central-barrel detectors [51] were operated inside a lower magnetic solenoid field, which increased the sensitivity for electrons at low p T (the term "electron" is used here for electrons and positrons). This makes a reassessment of soft dielectron production possible that could not be performed in a previous analysis at nominal field [2].

A detailed description of the ALICE apparatus and its performance can be found in [52]. The tracking of charged particles is performed by the inner tracking system (ITS) [53] and by the time projection chamber (TPC) [54], which are located in the central barrel and are surrounded by a solenoid, providing a homogeneous magnetic field along the beam direction. The TPC is used for particle identification (PID) via the measurement of the specific ionization energy loss (dE=dx). Additional PID information is provided by the time of flight (TOF) [55] system. Collision events are selected using the V0 detectors located on either side of the interaction point. Furthermore, the events are classified on the basis of the V0 signal amplitude. The event classes are reported in terms of dN ch =dη at midrapidity [56].

The data samples analyzed for this Letter were recorded in 2016-2018 in pp collisions at ffiffi ffi s p ¼ 13 TeV with ALICE, employing a setup where the magnetic solenoid field was reduced from 0.5 T to 0.2 T. This increases the acceptance and efficiency of the tracking and TOF detectors, extending the single electron selection from p T;e ≥ 0.2 GeV=c down to p T;e ≥ 0.075 GeV=c and providing access down to pair transverse momenta p T;ee ≥ 0 for invariant masses m ee > 0.15 GeV=c 2 . The minimum bias (MB) event trigger is constructed using a coincident signal in both V0 scintillators. Interaction vertices are reconstructed by extrapolation of ITS track segments toward the nominal interaction point. Events with multiple reconstructed vertices are tagged as pileup and rejected. The requirement on the vertex position to be within AE10 cm of the nominal interaction point in beam direction is employed to ensure a uniform detector performance.

After event selection, a total of 5.42 × 10 8 MB pp events remain for further analysis, corresponding to an integrated luminosity of L int ¼ 9.38 AE 0.47 nb -1 based on the visible cross section observed by the V0 trigger extracted from a van der Meer scan [57].

The electron candidates used in this analysis are selected in the transverse momentum range p T;e > 0.075 GeV=c and pseudorapidity jη e j < 0.8. Further track and PID selection criteria are identical to those described in [2] with the exception of a stronger requirement on the maximum distance of closest approach (DCA) to the primary vertex in the longitudinal direction (DCA z < 0.3 cm) to remove a contribution of looping tracks in the TPC.

Since pairs of electrons originating from the same source cannot be identified unambiguously, a statistical approach is applied to extract the yield of correlated pairs. To this end, a combinatorial pairing of all electron candidates in an event is performed. Additional photon conversion rejection is achieved by removing pairs based on their characteristic orientation relative to the magnetic field [1].

The combinatorial background estimate is constructed from same-event pairs with the same charge sign, corrected for charge-dependent acceptance effects, and subtracted from the opposite-sign pair distribution, following the approach described in [2]. To correct the signal for the finite reconstruction efficiency, a Monte Carlo (MC) simulation is used as described in [2]. Proton-proton events are generated using the Monash 2013 tune of PYTHIA8.1 [58] to simulate light-hadron decays, while the Perugia 2011 tune of PYTHIA6.4 [59] is utilized to embed heavyflavor hadrons that decay to electrons. The generated particles are propagated through the detector using GEANT3 [60]. The final efficiency as a function of m ee and p T;ee is the average of the efficiencies of the different dielectron sources, weighted by their expected contribution to the hadronic cocktail (see below).

The systematic uncertainties of the data are evaluated as described in [2] by simultaneous variation of the singleelectron tracking and PID selection criteria. The track sample is varied by changing the criteria on the number of space points in TPC and ITS, the χ 2 of the track fits, and the criteria used for electron selection and hadron rejection. These variations imply changes of the pair efficiency by up to about 30%. The systematic uncertainty is calculated as the root-mean-square of the resulting data points. Similar to [2], additional uncertainties related to the conversion rejection criteria, the isolation criterion in the ITS and the requirement of a hit in the first ITS layer, as well as on the TPC-ITS matching efficiency, the V0 trigger efficiency and the vertex reconstruction efficiency are added in quadrature. The resulting total systematic uncertainties are 12% for m ee < 0.04 GeV=c 2 and 11% for larger invariant masses, independent of p T;ee . The global 5% uncertainty resulting from the luminosity measurement is not included in the systematic uncertainties of the data points.

PHYSICAL REVIEW LETTERS 127, 042302 (2021)

The dielectron measurement is compared with the sum of expected contributions from light (π 0 , η, η', ω, ρ, ϕ) and heavy-flavor hadron decays within the kinematic range under study. The hadronic cocktail is constructed as described in [2], with the following exceptions. The p T spectrum of π AE in pp collisions at ffiffi ffi s p ¼ 13 TeV [61] is parametrized using a modified Hagedorn function [62]. The difference between π 0 and π AE due to isospin-violating decays, mainly of the η meson, is estimated using an effective model that describes measured hadron spectra at low p T and includes strong and electromagnetic decays [63]. This leads to a p T -dependent scaling factor applied to the π AE parametrization, which implies an upward shift by 18% AE 6% for p T → 0 that drops monotonically to below 1% at p T > 1 GeV=c. The uncertainty of this correction is estimated from variations of the model parameters and propagated into the final cocktail uncertainty.

The dominant contribution to the hadronic cocktail in the kinematic region of interest is given by the η meson. Therefore, a parametrization of the ALICE measurement of η=π 0 ratio as a function of p T in pp collisions at ffiffi ffi s p ¼ 7 TeV [64], 8 TeV [65], and in p-Pb collisions at a center-of-mass energy per nucleon-nucleon collision ffiffiffiffiffiffiffi ffi s NN p ¼ 5.02 TeV [66] is performed and extended to low p T , using data from CERES/TAPS [67] below p T ¼ 0.4 GeV=c and assuming energy independence of the ratio. The estimated uncertainty is about 15% at p T > 0.5 GeV=c, where data from LHC exist. At smaller p T , a conservative p T -dependent uncertainty of up to 40% is assigned, covering the full spread of the data points and a possible weak energy dependence of the η=π 0 ratio. The resulting η=π 0 parametrization including the estimated uncertainties is shown in Fig. 1. It also illustrates that m T scaling [68] fails to describe the measured η=π 0 ratio at low p T , as reported earlier [65,69].

The contribution from correlated semileptonic decays of open charm and beauty hadrons is estimated based on the decay distributions from the Perugia 2011 tune of PYTHIA 6.4, normalized to the measured cross sections at midrapidity, dσ cc =dyj y¼0 ¼ 974 AE 138ðstatÞAE140ðsystÞ μb and dσ b b=dyj y¼0 ¼ 79 AE 14ðstatÞ AE 11ðsystÞμb, from the dielectron analysis in pp collisions at ffiffi ffi s p ¼ 13 TeV at nominal field [2]. Finally, the detector resolution in p T;e , η e and azimuthal angle φ e is extracted as a function of p T;e from the same MC simulation and applied to all decay electrons [70]. To construct the cocktail in intervals of dN ch =dη, the light-flavor p T spectra of the MB cocktail are scaled by the ratio of the charged-particle p T spectra measured in multiplicity intervals to all events having at least one charged particle produced in the pseudorapidity interval jηj < 1 (INEL > 0 events) [61]. The open-charm contribution is weighted according to the measured enhancement of D mesons at p T > 1 GeV=c in pp collisions at ffiffi ffi s p ¼ 7 TeV [71]. The overall systematic uncertainties of the hadronic cocktail are estimated by adding in quadrature the uncertainties of the following contributions: the input data parametrizations as a function of p T , the π 0 =π AE correction factor, the uncertainty of the η=π 0 , ω=π 0 [58], and ρ=π 0 [58] ratios, the scaling parameters used for η 0

[59] and ϕ [72], the branching fractions of the different light-flavor decay channels, the measured cross sections, as well as the estimation of dN ch =dη. This results in a systematic uncertainty of the hadronic cocktail between 13% in the π 0 -Dalitz region and up to 24% in the mass region dominated by the η meson. The dielectron cross section as a function of m ee in the range p T;ee < 0.4 GeV=c and within the ALICE single- The ratio η=π 0 as a function of p T , measured in pp and proton-nucleus collisions at different center-of-mass energies [64][65][66][67]. Also shown is the parametrization used for the construction of the hadronic cocktail (solid line), its uncertainty (dotted line), and the expectation from m T scaling (dashed line). electron acceptance is shown in the left panel of Fig. 2. The data points are compared to the hadronic cocktail. Within the uncertainties, data and cocktail are in good agreement at m ee < m π while an excess over the hadronic cocktail is observed at larger masses. The representation of the data as a function of p T;ee in the invariant mass region 0.15 < m ee < 0.6 GeV=c 2 (right panel of Fig. 2) illustrates that the excess is most pronounced at p T;ee < 0.4 GeV=c, while the hadronic cocktail agrees well with the data at higher p T;ee . In the mass region 0.15 < m ee < 0.6 GeV=c 2 and for p T;ee < 0.4 GeV=c, the enhancement factor amounts to 1.61 AE 0.13ðstatÞ AE 0.17ðsyst; dataÞ AE 0.34ðsyst; cocktailÞ. The systematic uncertainty is dominated by the uncertainty of the η contribution to the hadronic cocktail.

The study of the multiplicity dependence of the observed excess may help to unravel the nature of the underlying dielectron production mechanisms [26]. To this end, four intervals of the event multiplicity are selected, based on the V0 signal, and the dielectron data are integrated over different regions of m ee and p T;ee . The upper part of Fig. 3 shows the dielectron yield per event in the interval 0.15 < m ee < 0.6 GeV=c 2 and p T;ee < 0.4 GeV=c compared with the hadronic cocktail, integrated over the same m ee and p T;ee interval, as a function of the relative charged-particle multiplicity at midrapidity, ðdN ch =dηÞ=hdN ch =dηi INEL>0 , where hdN ch =dηi INEL>0 ¼ 7.6 AE 0.5 is the mean multiplicity in INEL > 0 pp collisions at ffiffi ffi s p ¼ 13 TeV [56]. The dielectron yield is systematically above the cocktail in all multiplicity intervals. The enhancement of the data over the cocktail is shown in the lower part of Fig. 3. Within the experimental accuracy, no clear trend for the multiplicity dependence is found. Figure 3 also shows the multiplicity dependence in control regions at smaller m ee or larger p T;ee , where no excess is observed. To further characterize the observed dielectron enhancement, the hadronic cocktail is subtracted from the measured m ee and p T;ee spectra. The extracted excess spectra are corrected for the single-electron acceptance in p T;e and η e , assuming isotropic decay in the pair center-ofmass frame, which enables the measurement of the excess cross section in m ee > 0.15 GeV=c 2 and p T;ee > 0 at midrapidity. The corresponding excess spectra as a function of m ee and p T;ee are shown in Fig. 4. The data points are compared with a calculation of bremsstrahlung from initial-and final-state hadrons following the approach in [73] using a mean charge transfer hΔQ 2 i ¼ 1.32 in units of the electric charge e squared and the inelastic hadronic cross section [57]. Also shown is a calculation of the thermal dielectron yield from a hadronic many-body model [74][75][76], assuming a fireball lifetime of 2 fm=c, an initial temperature of 216 MeV=c and a freeze-out temperature of 170 MeV=c. While the hadronic manybody approach is successful in describing the dilepton production in heavy-ion collisions at the SPS [77,78], at RHIC [79][80][81], and at the LHC [82], it fails to describe the present dielectron results in pp collisions. An enhancement of dielectrons at very low p T;ee in peripheral Au-Au collisions at ffiffiffiffiffiffiffi ffi s NN p ¼ 200 GeV, reported by the STAR collaboration [83], could be explained by coherent twophoton production of lepton pairs in the strong electric fields of the colliding nuclei [84][85][86]. Owing to the strong Z dependence, this mechanism is not sufficient to describe the present enhancement in pp collisions. The results reported here are expected to encourage further theoretical work.

In conclusion, an excess of soft dielectrons over the expectation from hadron decays is observed in pp collisions at ffiffi ffi s p ¼ 13 TeV. The enhancement factor shows no dependence on the event multiplicity, and the acceptance-corrected excess yield cannot be explained by bremsstrahlung from initial-and final-state hadrons or by thermal dielectron production. The excess of soft dielectrons in pp is an intriguing observation, although its significance is presently limited to 1.6σ, mostly by the uncertainty of the hadronic cocktail. Forthcoming precision measurements with the upgraded ALICE detector will help to further elucidate this finding, including a possible connection to earlier observations of anomalous softphoton and soft-dielectron production at lower collision energies.

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I.