Search for resonance-enhanced <math display='inline'><mi>C</mi><mi>P</mi></math> and angular asymmetries in the <math display='inline'><msubsup><mi mathvariant='normal'>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy='false'>→</mo><mi>p</mi><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> decay at LHCb aps 05/01/2025 10615062 10.1103/PhysRevD.111.L091102 Physical Review D 2470-0010 111 9 R AaijA_S W AbdelmottelebC Abellan_BetetaF AbudinénT AckernleyA A AdefisoyeB AdevaM AdinolfiP AdlarsonC AgapopoulouC A AidalaZ AjaltouniS AkarK AkibaP AlbicoccoJ AlbrechtF AlessioM AlexanderZ AlioucheP Alvarez_CartelleR AmalricS AmatoJ L AmeyY AmhisL AnL AnderliniM AnderssonA AndreianovP AndreolaM AndreottiD AndreouA AnelliD AoF ArchilliM ArgentonS Arguedas_CuendisA ArtamonovM ArtusoE AslanidesR Ataíde_Da_SilvaM AtzeniB AudurierD BacherI Bachiller_PereaS BachmannM BachmayerJ J BackP Baladron_RodriguezV BalaguraA BalboniW BaldiniL BalzaniH BaoJ Baptista_de_Souza_LeiteC Barbero_PretelM BarbettiI R BarbosaR J BarlowM BarnyakovS BarsukW BarterJ BartzJ M BaselsS BashirG BassiB BatsukhP B BattistaA BayA BeckM BeckerF BedeschiI B BediagaN A BehlingS BelinK BelousI BelovI BelyaevG BenaneG BencivenniE Ben-HaimA BerezhnoyR BernetS Bernet_AndresA BertolinC BetancourtF BettiJ BexIa BezshyikoJ BhomM S BiekerN V BiesuzP BilloirA BiolchiniM BirchF_C R BishopA BitadzeA BizzetiT BlakeF BlancJ E BlankS BluskV BocharnikovJ A BoelhauveO Boente_GarciaT BoettcherA BohareA BoldyrevC S BolognaniR BolzonellaR B BonacciN BondarA BordeliusF BorgatoS BorghiM BorsatoJ T BorsukE BottalicoS A BouchibaM BovillT_J V BowcockA BoyerC BozziJ D BrandenburgA Brea_RodriguezN BreerJ BrodzickaA Brossa_GonzaloJ BrownD BrunduE BuchananL BuonincontriM Burgos_MarcosA T BurkeC BurrJ S ButterJ BuytaertW ByczynskiS CadedduH CaiA CailletR CalabreseS Calderon_RamirezL CaleficeS CaliM CalviM Calvo_GomezP Camargo_MagalhaesJ I Cambon_BouzasP CampanaD H Campora_PerezA F Campoverde_QuezadaS CapelliL CapriottiR Caravaca-MoraA CarboneL Carcedo_SalgadoR CardinaleA CardiniP CarnitiL CarusA Casais_VidalR CasparyG CasseM CattaneoG CavalleroV CavalliniS CelaniS CesareA J ChadwickI ChahrourH ChangM CharlesPh CharpentierE ChatzianagnostouM ChefdevilleC ChenS ChenZ ChenA ChernovS ChernyshenkoX ChiotopoulosV ChobanovaM ChrzaszczA ChubykinV ChulikovP CiambroneX Cid_VidalG CiezarekP CifraP_E L ClarkeM ClemencicH V CliffJ ClosierC Cocha_ToapaxiV CocoJ CoganE CognerasL CojocariuS CollavitiP CollinsT ColomboM ColonnaA Comerma-MontellsL CongedoA ContuN CookeI CorredoiraA CorreiaG CortiJ Cottee_MeldrumB CouturierD C CraikM Cruz_TorresE Curras_RiveraR CurrieC L Da_SilvaS DadabaevL DaiX DaiE Dall’OccoJ DalsenoC D’AmbrosioJ DanielA DanilinaP d’ArgentG DarzeA DavidsonJ E DaviesO De_Aguiar_FranciscoC De_AngelisF De_BenedettiJ de_BoerK De_BruynS De_CapuaM De_CianU De_Freitas_Carneiro_Da_GracaE De_LuciaJ M De_MirandaL De_PaulaM De_SerioP De_SimoneF De_VellisJ A de_VriesF DebernardisD DecampV DeduS DekkersL Del_BuonoB DelaneyH-P DembinskiJ DengV DenysenkoO DeschampsF DettoriB DeyP Di_NezzaI DiachkovS DidenkoS DingL DittmannV DobishukA D DochevaC DongA M DonohoeF DordeiA C dos_ReisA D DowlingW DuanP DudaM W DudekL DufourV DukP DuranteM M DurasJ M DurhamO D DurmusA DziurdaA DzyubaS EasoE EcksteinU EgedeA EgorychevV EgorychevS EisenhardtE EjopuL EklundM ElashriJ EllbrachtS ElyA EneJ EschleS EsenT EvansF FabianoL N FalcaoY FanB FangL FantiniM FariaK FarmerD FazziniL FelkowskiM FengM FeoA Fernandez_CasaniM Fernandez_GomezA D FernezF FerrariF Ferreira_RodriguesM FerrilloM Ferro-LuzziS FilippovR A FiniM FioriniM FirlejK L FischerD S FitzgeraldC FitzpatrickT FiutowskiF FleuretM FontanaL F ForemanR FortyD Foulds-HoltV Franco_LimaM Franco_SevillaM FrankE FranzosoG FrauC FreiD A FridayJ FuQ FühringY FujiiT FulghesuE GabrielG GalatiM D GalatiA Gallas_TorreiraD GalliS GambettaM GandelmanP GandiniB GanieH GaoR GaoT Q GaoY GaoY GaoY GaoL M Garcia_MartinP Garcia_MorenoJ García_PardiñasP GardnerK G GargL GarridoC GasparA GavrikovL L GerkenE GersabeckM GersabeckT GershonS GhizzoZ GhorbanimoghaddamL GiambastianiF I GiasemisV GibsonH K GiemzaA L GilmanM GiovannettiA GioventùL GirardeyC GiuglianoM A GizaF C GlaserV V GligorovC GöbelL Golinka-BezshyykoE GolobardesD GolubkovA GolutvinS Gomez_FernandezW GomulkaF Goncalves_AbrantesM GoncerzG GongJ A GoodingI V GorelovC GottiE GovorkovaJ P GrabowskiL A Granado_CardosoE GraugésE GraveriniL GrazetteG GrazianiA T GrecuL M GreevenN A GrieserL GrilloS GromovC GuM GuariseL GuerryV GuliaevaP A GüntherA-K GuseinovE GushchinY GuzT GysK HabermannT HadavizadehC HadjivasiliouG HaefeliC HaenG HallettM M HalvorsenP M HamiltonJ HammerichQ HanX HanS Hansmann-MenzemerL HaoN HarnewT H HarrisM HartmannS HashmiJ HeF HemmerC HendersonR_D L HendersonA M HennequinK HennessyL HenryJ HerdP Herrero_GasconJ HeuelA HicheurG Hijano_MendizabalJ HorswillR HouY HouN HowarthJ HuW HuX HuW HuangW HulsbergenR J HunterM HushchynD HutchcroftM IdzikD IlinP IltenA InglessiA IniukhinA IshteevK IvshinR JacobssonH JageS J Jaimes_EllesS JakobsenE JansB K JashalA JawaheryV JevticE JiangX JiangY JiangY J JiangM JohnA John_Rubesh_RajanD JohnsonC R JonesT P JonesS JoshiB JostJ Juan_CastellaN JurikI JuszczakD KaminarisS KandybeiM KaneY KangC KarM KaracsonD KarpenkovA KauniskangasJ W KautzM K KazaneckiF KeizerM KenzieT KetelB KhanjiA KharisovaS KholodenkoG KhreichT KirnV S KirsebomO KitouniS KlaverN KleijneK KlimaszewskiM R KmiecS KoliievL KolkA KonoplyannikovP KopciewiczP KoppenburgM KorolevI KostiukO KotS KotriakhovaA KozachukP KravchenkoL KravchukM KrepsP KrokovnyW KrupaW KrzemienO KshyvanskyiS KubisM KucharczykV KudryavtsevE KulikovaA KupscB K KutsenkoD LacarrereP Laguarta_GonzalezA LaiA LampisD LancieriniC Landesa_GomezJ J LaneR LaneG LanfranchiC LangenbruchJ LangerO LantwinT LathamF LazzariC LazzeroniR Le_GacH LeeR LefèvreA LeflatS LegotinM LehurauxE Lemos_CidO LeroyT LesiakE D LesserB LeveringtonA LiC LiC LiH LiK LiL LiM LiP LiP-R LiQ LiS LiT LiT LiY LiY LiZ LianX LiangS LibralonC LinT LinR LindnerH LintonV LisovskyiR LitvinovF L LiuG LiuK LiuS LiuW LiuY LiuY LiuY L LiuG Loachamin_OrdonezA Lobo_SalviaA LoiT LongJ H LopesA Lopez_HuertasS López_SoliñoQ LuC LucarelliD LucchesiM Lucio_MartinezV LukashenkoY LuoA LupatoE LuppiK LynchX-R LyuG M MaS MaccoliniF MachefertF MaciucB MackI MackayL M MackeyL R Madhan_MohanM J MaduraiA MaevskiyD MagdalinskiD MaisuzenkoJ J MalczewskiS MaldeL MalentaccaA MalininT MaltsevG MancaG MancinelliC MancusoR Manera_EscaleroF M ManganellaD ManuzziD MarangottoJ F MarchandR MarchevskiU MarconiE MarianiS MarianiC Marin_BenitoJ MarksA M MarshallL MartelG MartelliG MartellottiL MartinazzoliM MartinelliD Martinez_GomezD Martinez_SantosF Martinez_VidalA Martorell_i_GranollersA MassafferriR MatevA MathadV MatiuninC MatteuzziK R MattioliA MauriE MauriceJ MauricioP MayencourtJ Mazorra_de_CosM MazurekM McCannT H McGrathN T McHughA McNabR McNultyB MeadowsG MeierD MelnychukF M MengM MerkA MerliL Meyer_GarciaD MiaoH MiaoM MikhasenkoD A MilanesA MinottiE MinucciT MirallesB MitreskaD S MitzelA ModakL MoeserR A MohammedR D MoiseS MokhnenkoE F Molina_CardenasT MombächerM MonkS MonteilA Morcillo_GomezG MorelloM J MorelloM P MorgenthalerJ MoronW MorrenA B MorrisA G MorrisR MountainH MuZ M MuE MuhammadF MuheimM MulderK MüllerF Muñoz-RojasR MurtaP NaikT NakadaR NandakumarT NanutI NastevaM NeedhamN NeriS NeubertN NeufeldP NeustroevJ NicoliniD NicotraE M NielN NikitinQ NiuP NogarolliP NoggaC NormandJ Novoa_FernandezG NowakC NunezH N NurA Oblakowska-MuchaV ObraztsovT OeserS OkamuraA OkhotnikovO OkhrimenkoR OldemanF OlivaM OloccoC_J G OnderwaterR H O’NeilD OsthuesJ M Otalora_GoicocheaP OwenA OyangurenO OzcelikF PaciollaA PadeeK O PadekenB PagareP R PaisT PajeroA PalanoM PalutanX PanG PanshinL PaolucciA PapanestisM PappagalloL L PappalardoC PappenheimerC ParkesD ParmarB PassalacquaG PassalevaD PassaroA PastoreM PatelJ PatocC PatrignaniA PaulC J PawleyA PellegrinoJ PengM Pepe_AltarelliS PerazziniD PereimaH Pereira_Da_CostaA Pereiro_CastroP PerretA PerrevoortA PerroM J PetersK PetridisA PetroliniJ P PfallerH PhamL PicaM PicciniL PiccoloB PietrzykG PietrzykR N PilatoD PinciF PisaniM PizzichemiV PlacintaM Plo_CasasusT PoeschlF PolciM Poli_LenerA PoluektovN PolukhinaI PolyakovE PolycarpoS PonceD PopovS PoslavskiiK PrasanthC ProuveD ProvenzanoV PugatchG PunziS QasimQ Q QianW QianN QinS QuR QuaglianiR I Rabadan_TrejoJ H RademackerM RamaM Ramírez_GarcíaV Ramos_De_OliveiraM Ramos_PernasM S RangelF RatnikovG RavenM Rebollo_De_MiguelF RediJ ReichF ReissZ RenP K ResmiM Ribalda_GalvezR RibattiG RicartD RiccardiS RicciardiK RichardsonM Richardson-SlipperK RinnertP RobbeG RobertsonE RodriguesA Rodriguez_AlvarezE Rodriguez_FernandezJ A Rodriguez_LopezE Rodriguez_RodriguezJ RoenschA RogachevA RogovskiyD L RolfP RoloffV RomanovskiyA Romero_VidalG RomoliniF RonchettiT RongM RotondoS R RoyM S RudolphM Ruiz_DiazR A Ruiz_FernandezJ Ruiz_VidalJ RyzkaJ J Saavedra-AriasJ J Saborido_SilvaR SadekN SagidovaD SahooN SahooB SaittaM SalomoniI SanderswoodR SantacesariaC Santamarina_RiosM SantimariaL SantoroE SantovettiA SaputiD SaraninA SarnatskiyG SarpisM SarpisC SatrianoA SattaM SaurD SavrinaH SazakF SborzacchiL G Scantlebury_SmeadA ScarabottoS SchaelS ScherlM SchillerH SchindlerM SchmellingB SchmidtS SchmittH SchmitzO SchneiderA SchopperN SchulteS SchulteM H SchuneR SchwemmerG SchweringB SciasciaA SciuccatiI SegalS SellamA SemennikovT SengerM Senghi_SoaresA SergiN SerraL SestiniA SeutheY ShangD M ShangaseM ShapkinR S SharmaI ShchemerovL ShchutskaT ShearsL ShekhtmanZ ShenS ShengV ShevchenkoB ShiQ ShiY ShimizuE ShmaninR ShorkinJ D ShupperdR Silva_CoutinhoG SimiS SimoneN SkidmoreT SkwarnickiM W SlaterJ C SmallwoodE SmithK SmithM SmithA SnochL Soares_LavraM D SokoloffF_J P SolerA SolominA SolovevI SolovyevN S SommerfeldR SongY SongY SongY S SongF L Souza_De_AlmeidaB Souza_De_PaulaE Spadaro_NorellaE SpedicatoJ G SpeerE SpiridenkovP SpradlinV SriskaranF StagniM StahlS StahlS StanislausM StefaniakE N SteinO SteinkampO StenyakinH StevensD StrekalinaY SuF SuljikJ SunL SunD SundfeldW SutcliffeK SwientekF SwystunA SzabelskiT SzumlakY TanY TangM D TatA TerentevF TerzuoliF TeubertE ThomasD_J D ThompsonH TilquinV TisserandS T’JampensM TobinL TomassettiG TonaniX TongT TorkD Torres_MachadoL ToscanoD Y TouC TripplG TuciN TuningL H UeckerA UklejaD J UnverzagtB UrbachA UsachovA UstyuzhaninU UwerV VagnoniV Valcarce_CadenasG ValentiN Valls_CanudasJ van_EldikH Van_HeckeE van_HerwijnenC B Van_HulseR Van_LaakM van_VeghelG VasquezR Vazquez_GomezP Vazquez_RegueiroC Vázquez_SierraS VecchiJ J VelthuisM VeltriA VenkateswaranM VerdogliaM VesterinenD Vico_BenetP Vidrier_VillalbaM Vieites_DiazX Vilasis-CardonaE Vilella_FiguerasA VillaP VincentF C VolleD vom_BruchN VoropaevK VosC VrahasJ WagnerJ WalshE J WaltonG WanC WangG WangH WangJ WangJ WangJ WangJ WangM WangN W WangR WangX WangX WangX W WangY WangY W WangZ WangZ WangZ WangJ A WardM WaterlaatN K WatsonD WebsdaleY WeiJ WendelB_D C WesthenryC WhiteM WhiteheadE WhiterA R WiederholdD WiednerG WilkinsonM K WilkinsonM WilliamsM J WilliamsM_R J WilliamsR WilliamsZ WilliamsF F WilsonM WinnW WislickiM WitekL WitolaG WormserS A WottonH WuJ WuX WuY WuZ WuK WyllieS XianZ XiangY XieT X XingA XuL XuL XuM XuZ XuZ XuZ XuK YangS YangX YangY YangZ YangV YeroshenkoH YeungH YinX YinC Y YuJ YuX YuanY YuanE ZaffaroniM ZavertyaevM ZdybalF ZenesiniC ZengM ZengC ZhangD ZhangJ ZhangL ZhangS ZhangS ZhangY ZhangY Z ZhangZ ZhangY ZhaoA ZhelezovS Z ZhengX Z ZhengY ZhengT ZhouX ZhouY ZhouV ZhovkovskaL Z ZhuX ZhuX ZhuV ZhukovJ ZhuoQ ZouD ZulianiG ZunicaLHCb_Collaboration The first measurement of theCPasymmetry of the decay rate (ACP) and theCPaverage (ΣAFB) andCPasymmetry (ΔAFB) of the forward-backward asymmetry in the muon system ofΛc+→pμ+μ−decays is reported. The measurement is performed using a data sample of proton-proton collisions, recorded by the LHCb experiment from 2016 to 2018 at a center-of-mass energy of 13TeV, which corresponds to an integrated luminosity of5.4fb−1. The asymmetries are measured in two regions of dimuon mass near theϕ-meson mass peak. The dimuon-mass integrated results areACP=(−1.1±4.0±0.5)%,ΣAFB=(3.9±4.0±0.6)%,ΔAFB=(3.1±4.0±0.4)%, where the first uncertainty is statistical and the second systematic. The results are consistent with the conservation ofCPsymmetry and the Standard Model expectations.

© 2025 CERN, for the LHCb Collaboration2025CERN]]>

Rare decays that are sensitive to transitions between c and u quarks in association with the simultaneous emission of a pair of oppositely charged leptons (l þ l -) offer the opportunity to explore flavor-changing neutral-currents (FCNCs) in the up-type quark sector. In the Standard Model (SM), FCNC transitions are only generated by looplevel processes and suppressed by the Glashow-Iliopoulos-Maiani (GIM) mechanism [1]. In the charm system, the GIM mechanism leads to a particularly strong suppression with respect to the down-type quark sector. Thus, studies of rare charm decays are sensitive probes of beyond-Standard-Model phenomena and constitute a complementary testing ground with respect to studies of rare beauty and strange hadron decays. New particles and interactions extending the SM can lead to modifications of branching fractions, modify angular distributions of final-state particles, or introduce additional sources of charge-parity (CP) asymmetry [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The LHCb collaboration has previously succeeded in measuring branching fractions of rare charm meson decays at the level of 10 -7 and recently published the first angular analysis and a search for CP violation in rare decays of neutral D 0 mesons [16][17][18][19]. However, measurements of rare baryonic charm decays comprising two charged leptons in the final state remain far less explored in the experimental landscape [20][21][22].

The decays of Λ þ c baryons to pμ þ μ -final states 1 proceed at short distances via c → ul þ l -transitions, which in the SM lead to branching fractions below Oð10 -8 Þ [23][24][25][26][27]. However, the total decay width is dominated by intermediate resonant contributions of the form Λ þ c → pXð→ μ þ μ -Þ, where X can be a short-lived η, ρ 0 , ω, or ϕ meson that subsequently decays into two muons. These long-distance contributions increase the branching fraction to Oð10 -6 Þ. Recently, the LHCb collaboration has published an updated measurement of the branching fractions of Λ þ c → pμ þ μ - decays in different regions of the dimuon mass, mðμ þ μ -Þ [22]. The measurement is performed relative to the branching fraction in the mðμ þ μ -Þ region around the known ϕ-meson mass [28], which is the dominant contribution to the total decay rate. An upper limit on the branching fraction

where the influence of intermediate resonances is minimal and sensitivity to beyond-SM contributions is largest. Further separation of short and long-distance contributions can be reached by studying angular distributions and CP asymmetries, which complement searches for new phenomena in decays of D 0 and D þ mesons because of the nonzero spin of the Λ þ c baryons [25][26][27]. However, to date, no measurements of CP or angular asymmetries in

This letter presents the first measurement of the direct CP asymmetry, as well as the CP average and CP asymmetry of the forward-backward asymmetry in the lepton system, in Λ þ c → pμ þ μ -decays. The analysis uses proton-proton (pp) collision data recorded by the LHCb experiment at a center-of-mass energy of 13 TeV in the years 2016, 2017, and 2018, which correspond to an integrated luminosity of 5.4 fb -1 . The analysis uses Λ þ c baryons produced directly in the primary p p interaction and the same data as used in Ref. [22]. However, the signal candidate selection is reoptimized for the measurement of asymmetries. The CP asymmetry, A CP , is defined in terms of the difference of decay rates for Λ þ c and Λc decays to pμ þ μ -and pμ þ μ -final states as

where Γ is the decay rate. The forward-backward asymmetry, A FB , is defined as

where θ is the angle between the direction of the positively charged lepton in the dimuon rest frame and the flight direction of the dimuon system in the rest frame of the Λ þ c baryon. In contrast, for Λc baryons the angle is measured relative to the flight direction of the negatively charged lepton. The forward-backward asymmetry is measured separately for Λ þ c and Λc baryons and referred to as

FB , respectively, which allows the CP average, ΣA CP FB , and the CP asymmetry, ΔA CP FB , to be defined as

These observables further enhance the sensitivity of the measurement to the real and imaginary parts of beyond-SM couplings [26].

Given the current experimental sensitivity, the asymmetries measured in this letter are null tests of the SM. Interference effects between SM resonant and beyond-SM amplitudes can produce asymmetries as large as Oð%Þ [25], referred to as resonance enhanced asymmetries. The measurement is performed in the mðμ þ μ -Þ region which is dominated by the intermediate ϕ meson, where the signal yield is sufficiently high to measure CP and angular asymmetries. To be sensitive to variations of the asymmetries over the phase space, the observables are determined in two regions, which are defined symmetrically below and above the known mass of the ϕ meson [28].

The LHCb detector [29,30] is a single-arm forward spectrometer designed for the study of particles containing b or c quarks. It includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 T m, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The polarity of the magnetic field is reversed periodically throughout the data-taking. Particle identification is provided by two ring-imaging Cherenkov detectors, an electromagnetic and a hadronic calorimeter, and a muon system composed of alternating layers of iron and multiwire proportional chambers. Events are selected online by a trigger that consists of a hardware stage, which is based on information from the calorimeter and muon systems, followed by a software stage which performs a full event reconstruction [31]. Simulation is required to model the effects of the detector acceptance, the imposed selection requirements and to describe the signal and backgrounds. In the simulation, pp collisions are generated using Pythia [32] with a specific LHCb configuration [33]. Decays of unstable particles are described by EvtGen [34], in which final-state radiation is generated using Photos [35]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [36] as described in Ref. [37]. The underlying pp interaction is reused multiple times, with an independently generated signal decay for each [38].

The hardware trigger requires the presence of a muon with large transverse momentum, p T , which is compatible with one of the two muons of the signal candidate. Furthermore, candidates where a positive trigger decision is caused by the presence of muons with high p T , or a hadron, photon or electron with high transverse energy in the calorimeters due to other particles produced in the pp collision, are also considered. The subsequent software trigger selects in a first stage events where a pair of tracks satisfies a multivariate classifier based on geometric and kinematic criteria that identifies candidates consistent with the displaced decay of a charm hadron, or alternatively events with a reconstructed dimuon vertex which is displaced from any primary vertex (PV). In the second software-trigger stage, candidate Λ þ c baryons are constructed by combining three charged tracks that form a good-quality secondary vertex. Each of the tracks is required to be inconsistent with originating from a PV, to satisfy p T > 0.3 GeV=c and to have a minimum momentum p of 3 GeV=c. The scalar sum of the p T of the three tracks has to exceed 0.5 GeV=c. The Λ þ c candidate must have a decay vertex significantly separated from any PV, and compatible with originating from one of the PVs. Therefore, only Λ þ c candidates with a reconstructed momentum vector that aligns with the vector connecting the secondary and primary vertices are further considered.

Additional selection criteria are applied offline. The reconstructed mass of the Λ þ c candidates, mðpμ þ μ -Þ, is limited to the range ½2147; 2486 MeV=c 2 . Stringent particle identification criteria are placed on the particles identified as protons to suppress background from misidentified

, where the pion is wrongly identified as a proton. The selection is further optimized to reduce the contributions of two major sources of background. The first comprises random associations of unrelated tracks that coincidentally fulfill the selection criteria. To reduce this combinatorial background, a multivariate selection based on a boosted decision tree (BDT) classifier [39,40] as implemented in the TMVA toolkit [41] is employed. The BDT classifier is trained using simulated candidates as proxies for the signal, and data candidates with

5 MeV=c 2 for the background. The AdaBoost algorithm [42] is used when training the BDT classifier in ten disjoint training subsamples, which is subsequently applied using a k-fold cross-validation [43]. The choice of features that are used in the training has been based on the selection described in Ref. [22] and comprises kinematic and topological features of the Λ þ c candidates, as well as features related to the isolation of the signal candidates with respect to other tracks in the event. The variables are chosen to minimize the correlation with the Λ þ c mass to avoid artificial sculpting of the mass spectrum of Λ þ c candidates. The second major background arises from hadronic Λ þ c baryon decays to pπ þ π -final states, where two oppositely charged pions are identified as muons. Despite the low pion to muon misidentification probability [44], the large branching fraction of Λ þ c → pπ þ π -decays [28] causes a peaking background. This is further suppressed by a multivariate muon-identification discriminant that combines the information from the Cherenkov detectors, the calorimeters, and the muon chambers.

The threshold on the muon-identification discriminant is simultaneously optimized with the requirement on the BDT classifier output by minimizing the uncertainty on the asymmetries. This is achieved by randomly splitting the data samples into two halves, simulating a vanishing asymmetry in the samples as expected in null-test measurements.

If after the full selection an event contains more than one Λ þ c candidate, only one is randomly selected. This requirement removes less than one percent of candidates. To avoid potential biases on the measured quantities, all asymmetries were shifted by a random offset and only examined after the analysis procedure had been finalized.

The reconstruction and selection requirements result in efficiency losses that correlate with the decay kinematics and vary as a function of mðμ þ μ -Þ and cos θ. A correction for relative efficiency variations across the phase space is applied using simulated samples to ensure an unbiased determination of the measured asymmetries. The simulation samples are corrected for known differences with respect to data in particle identification response [44]. A two-dimensional correction map is employed to assign weights to each candidate that account for relative efficiency variations and can be found in the Supplemental Material [45].

To determine A CP , the so-called raw asymmetry, A raw , is measured, which also receives contributions from nuisance asymmetries of approximately 4%. These asymmetries are caused by the different production cross sections of Λ þ c and Λc baryons, quantified as the production asymmetry, A prod ðΛ þ c Þ, and a nonequal detection efficiency of protons and antiprotons which leads to a detection asymmetry, A det ðpÞ. The detection asymmetry from the pair of oppositely charged muons is estimated to be negligible. For small asymmetries, the raw asymmetry can be approximated as

The CP asymmetry is obtained by subtracting the raw asymmetry measured in a control data sample of Λ þ c → pK 0 S decays, where effects of CP violation are assumed to be negligible and which is subject to the same nuisance asymmetries, as

Since A det ðpÞ and A prod ðΛ þ c Þ depend on the kinematics of the p and Λ þ c particles, a weighting scheme is developed to match the final-state kinematics of the control mode to that of the signal mode using a BDT algorithm with gradient boosting [39][40][41].

To measure the asymmetries, the data are split in four disjoint subsamples, which are defined by the flavor of the Λ þ c baryon and the sign of cos θ. The measurement is performed separately in the two mðμ þ μ -Þ regions ϕ low and ϕ high , defined as ½979.46; 1019.46 MeV=c 2 and ½1019.46; 1059.46 MeV=c 2 . In the following, these dimuon-mass regions refer to ranges in the reconstructed dimuon mass, without correcting for effects due to a finite experimental mass resolution of approximately 8 MeV=c 2 [45]. Figure 1 shows the background-subtracted dimuonmass spectrum of Λ þ c → pμ þ μ -candidates using a sideband subtraction, with the boundary between the two mðμ þ μ -Þ ranges also indicated.

The asymmetries are then determined through unbinned extended maximum-likelihood fits to the weighted mðpμ þ μ -Þ distribution of selected candidates, where the weights correct for the phase-space-dependent efficiency variations. The asymmetries and yields are determined from simultaneous fits, in which they are treated as free parameters. The total fit function consists of three components: the Λ þ c → pμ þ μ -signal, combinatorial background and background from misidentified Λ þ c → pπ þ π -decays. The signal component is described by the sum of a Johnson S U function [46] and a Gaussian function, to account for asymmetric tails of the distribution. The parameters of the model are determined by a fit to simulated candidates which are selected with the same requirements as the data candidates. The peak position of the distribution is allowed to vary in the fit to the data separately for the two dimuon-mass regions and baryon flavors. The mass shape of the combinatorial background is parametrized using a fourth-order Chebyshev polynomial with parameters determined by a fit to a control data sample, where all three final-state particles carry the same electric charge. These candidates are entirely made of random combinations of tracks and used as a proxy for the combinatorial background. The misidentified Λ þ c → pπ þ π -background is also described by a Johnson S U function [46] whose parameters are determined using simulated candidates of Λ þ c → pπ þ π -decays assigning the muon mass hypothesis to both pions. Due to limited simulation sample sizes, not all selection criteria can be applied and the requirement on muon particle identification is applied to only one of the two pions. The CP and forward-backward asymmetries of misidentified background are determined using high-yield data control samples of Λ þ c → pπ þ π -decays and are fixed in the baseline fit that is used to measure the asymmetries. Assumptions in the background modeling give rise to systematic uncertainties which are described later in this letter.

In the fit, the free parameters are the yields of each fit component, the asymmetries of signal and combinatorial background, and the signal peak position. The fits are performed separately in the two dimuon-mass regions. The fits are validated to return unbiased estimates of the asymmetries and their uncertainties using large samples of pseudoexperiments. The resulting signal and background yields, as well as the asymmetries A CP , A Λ þ c FB , and 2, together with the fit projection.

The dominant systematic uncertainties affect all asymmetries and arise from limited knowledge of the models used in the mass fits and possible imperfections in the correction for phase-space-dependent efficiency variations. To evaluate the systematic uncertainty related to the fit model, pseudoexperiments are performed, where alternative parametrizations of the signal and background components are tested against the baseline fit model. For the signal component, a Crystal Ball function [47] and a Gaussian function are chosen as alternatives. In addition, the requirements used to select the control sample to

The red line indicates the known mass of the ϕ meson, which marks the boundary between the two considered dimuon-mass regions. Weights are assigned to correct for efficiency variations as described in the main text. FIG. 2. Distribution of mðpμ þ μ -Þ for efficiency-weighted candidates, together with the fit projection. TABLE I. Yields after correcting for relative efficiency variations and measured asymmetries for Λ þ c → pμ þ μ -decays in the two dimuon-mass regions. For the asymmetries the first uncertainty is statistical and the second systematic.

Efficiency-weighted yields

Asymmetries

%] ϕ low 346 AE 22 57 AE 21 437 AE 26 -0.8 AE 6.2 AE 0.6 11.7 AE 8.5 AE 1.1 2.2 AE 8.7 AE 1.4 ϕ high 435 AE 22 35 AE 17 390 AE 25 -1.4 AE 5.3 AE 0.6 3 .5 AE 7.2 AE 0.9 -0.3 AE 7.4 AE 1.1

determine the shape of the combinatorial background are varied, and an alternative shape is obtained from a fit, where the shape parameters are left free to vary when fitting

To address the inability to apply the signal muon particle-identification requirements on the simulated Λ þ c → pπ þ π -decays, an alternative shape is determined on a sample where muon particle identification requirements are not applied. The asymmetries of the misidentified background component, which are fixed in the baseline fit, are determined in control samples with modified selection requirements and varied within the observed deviations from the baseline values. The studies are performed separately for both dimuon-mass regions. For all tested alternatives, the mean bias with respect to the baseline model is determined for the measured asymmetries, and the largest observed bias over the set of shape variations in each dimuon-mass region is taken as the corresponding systematic uncertainty.

Systematic uncertainties related to the correction for efficiency variations are evaluated by creating alternative correction maps targeting aspects of the selection which might be subject to residual differences in simulation and data. The alternative maps are obtained by applying weights to the simulated candidates to match the number of reconstructed tracks and the BDT output distribution observed in data, and by placing requirements on particle identification for the final-state particles neglecting the corrections that are applied in the baseline analysis. Using the alternative correction maps, the measurement is repeated on resampled datasets which are obtained by bootstrapping the original sample [48]. The root mean square among the variations of the results that are observed with the alternative maps is taken as the systematic uncertainty. The uncertainty related to the limited simulation sample size is also propagated and considered as systematic uncertainty on the measured asymmetries.

Additionally, the following three sources of systematic uncertainty are only relevant for the measurement of A CP . The first source arises from the instrumental asymmetry correction due to limitations of the kinematic equalization procedure. A systematic uncertainty is assigned by evaluating the effect of residual discrepancies of the kinematic distributions of signal and control mode candidates after the weighting. The root mean square among the variations of the results obtained after a second one-dimensional weighting of the Λ þ c and proton kinematic distributions is taken as a systematic uncertainty. The second source arises from the combined effects of CP violation and mixing in the neutral kaon system and the different interaction probabilities of K 0 and K0 particles with the detector material [49,50] and a systematic uncertainty is evaluated following the method described in Refs. [51,52]. Finally, the fraction of Λ þ c baryons arising from decays of b -flavored hadrons is determined for signal and control mode candidates by studying the distribution of the impact parameter, which is defined as the minimum distance of the Λ þ c trajectory to the PV. The difference of these fractions for signal and control mode candidates, together with the difference in asymmetries for Λ þ c baryons produced in the primary interaction and from b -hadron decays, are translated into a systematic uncertainty related to an imperfect cancellation of production asymmetries.

The finite angular resolution of the LHCb detector is relevant for the measurement of the forward-backward asymmetry, and a systematic uncertainty is assigned by estimating the fraction of candidates where the sign of cos θ changes due to the finite detector resolution in simulations.

A summary of the systematic uncertainties, together with the correlations of the measured asymmetries due to the systematic uncertainties, can be found in the Supplemental Material of this letter [45]. The size of the systematic uncertainty depends on the considered asymmetry and dimuon-mass region but typically constitutes between 10% and 15% of the corresponding statistical uncertainty.

The analysis is repeated on statistically independent data subsets to check for biases from specific instrumental effects. The criteria to split the subsets include the number of PVs and reconstructed tracks in the event, the datataking year, the magnetic-field orientation, the trigger classification, the Λ þ c baryon transverse momentum and the impact parameter significance of the Λ þ c candidate with respect to the PV, which is defined as the difference in the vertex-fit χ 2 of a given PV, reconstructed with and without considering the candidate. The resulting variations of the measured asymmetries are consistent with statistical fluctuations.

Using Eq. ( 3) and considering correlations between the systematic uncertainties [45], ΔA FB and ΣA FB are computed from the measured asymmetries listed in Table I and the results can be found in Table II. Correlations between the statistical uncertainties of the measured asymmetries are negligible. Furthermore, the dimuon-mass integrated values are determined, following the procedure described in Ref. [53], and found to be

1.1 AE 4.0 AE 0.5Þ%; ΣA FB ¼ ð3.9 AE 4.0 AE 0.6Þ%; ΔA FB ¼ ð3.1 AE 4.0 AE 0.4Þ%;

TABLE II. CP average and asymmetry of the forward-backward asymmetry for Λ þ c → pμ þ μ -decays in the dimuon-mass regions. The first uncertainty is statistical and the second systematic. mðμ þ μ -Þ ΣA FB [%] ΔA FB [%] ϕ low 6.9 AE 6.1 AE 1.0 4 .8 AE 6.1 AE 0.8 ϕ high 1.6 AE 5.2 AE 0.8 1 .9 AE 5.2 AE 0.6

where the first uncertainty is statistical and the second systematic. All results are also shown in Fig. 3 and are consistent with zero, confirming the SM expectation. In summary, a search for resonance-enhanced angular and CP asymmetries in Λ þ c → pμ þ μ -decays in two mðμ þ μ -Þ regions near the ϕ-meson mass is presented. The results are based on the analysis of pp collision data recorded by the LHCb experiment in the years 2016, 2017, and 2018 at a center-of-mass energy of 13 TeV, which correspond to an integrated luminosity of 5.4 fb -1 . The asymmetries are measured in two regions of dimuon mass to enhance the sensitivity to beyond-SM effects. The results confirm the SM prediction and will help to constrain the parameter space of models extending the SM [25,26]. Future datasets recorded by the upgraded LHCb detector [54] with significantly increased yields will allow the statistical uncertainties to be further reduced, and the measurement to be extended to additional dimuon-mass regions.