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History of Belle and some of its lesser known highlights StephenLarsOlsen1 CenterforUndergroundPhysics,InstituteforBasicScience Yuseong-gu,DaejeonKorea IreportontheearlyhistoryofBelle,whichwasalmostentirelyfocusedontestingtheKobayashiMaskawamecha- nismforCPviolationthatpredictedlargematter-antimatterasymmetriesincertainBmesondecaymodes.Results reportedbybothBaBarandBelleinthesummerof2001verifiedtheKobayashiMaskawaideaandledtotheir Nobelprizesin2008.InadditiontostudiesofCPviolation,Belle(andBaBar)reportedalargenumberofimpor- 6 1 tantresultsonawidevarietyofothersubjects,manyofwhichthathadnothingtodowithBmesons.Inthistalk 0 Icoverthree(ofmany)subjectswhereBellemeasurementshavehadasignificantimpactonspecificsub-fields 2 ofhadronphysicsbutarenotgenerallywellknow. Theseinclude: thediscoveryofananomalouslylargecross n sectionsfordoublecharmoniumproductionincontinuume+e−annihilation;sensitiveprobesofthestructureof a thelow-massscalarmesons;andfirstmeasurementsoftheCollinsspinfragmentationfunction. J 6 ] x e 1 Introduction - p e Theorganizersofthismeetingaskedmetogiveatalkwiththetitle“BestBelleresultsandhistoryofBelle h [ collaboration.” A talk about the history of Belle is no problem. The intial motivation of the Belle/KEKB project and essentially all of its early work was the study of CP-violation in the B-meson sector, and the 1 workdoneinthisareacertainlyranksamongBelle’s“bestresults.” However, whiletheplaningandfirst v 1 fewyear’sofoperationwerealmostcompletelyfocusedonCP-violationmeasurements,thecollaboration 6 subsequently branched out and studied a wide range of physics subjects that included many unexpected 0 discoveries. To the people involved, each of these rank among the “best Belle results,” and I could not 1 argue with them. So instead of even attempting to identify “best results,” I decided to confine myself to 0 . reportingonBelle’searlyworkonCPviolation,whichcoverstheearly“historyoftheBellecollaboration,” 1 andthendiscussafewotherresultsthatseemtobenotverywidelyknownbuthavehadahugeimpacton 0 6 thespecializedareasofphysicsthattheyaddress. First,somehistoryandBelle’searlyCPVmeasurements: 1 : v i 2 Belle and CP violation X r a TheBelleexperimenttracesitsrootstothe1964discoverythatthelong-livedneutralkaon(K )isnotaCP L eigenstate,asevidencedbyasmallbutnon-zerobranchingfractiontoπ+π−: B(K → π+π−) (cid:39)2×10−3, L which demonstrated that CP is violated, probably by the weak interactions [1]. This inspired Sakharov’s classic1967paper[2]thatpointedoutthatCP-violation(CPV)isanessentialingredientforexplainingthe baryonasymmetryoftheuniverse; i.e.,howamatter-antimatter-symmetricconditionthatprevailedright aftertheBigBang,evolvedintotoday’smatter-dominateduniverse(seeFig.1). [email protected] 1 XXIIndInternationalWorkshop“High-EnergyPhysicsandQuantumFieldTheory”,June24–July1,2015,Samara,Russia Figure1: WhenSakharovcompletedhisfamous1967paperon“ViolationofCPinvariance,Casymmetry,andbaryonasymmetry oftheuniverse,”hegaveLevOkunapreprintwithasmallpoemhandwrittenonitthatidentifiesCPVas“S.Okubo’seffect.” This referstoa1958paperbyOkubothatfirstpointedoutthatwhileCPTinvariancerequiresparticleandantiparticlelifetimestobeequal, CPviolationswouldallowpartiallifetimestobedifferent[3]. Incorporating CPV into the Standard Model (SM) while preserving CPT was not very easy. Wolfenstein proposed a mechanism that expanded the SM by adding a new, ∆S = 2 “superweak” interaction that produceda CP-violatingnon-diagonalcontributiontotheneutralkaonmassmatrixandnothingelse[4]. However, the superweak interaction was ruled out by the observation of direct CPV decays of neutral kaonsbytheNA31experimentatCERN[5]and,later,theKTeVexperimentatFermilab[6]. ToincorporateCPVintotheSMproper,oneneedsanamplitudethathasacomplexphaseangleφ thathas CP oppositesignsforparticleandantiparticleprocesses. Sincemeasureableprocessesareproportionaltothe absolutevaluesquaredoftheamplitude,thisCPVphaseisunmeasureableunlessitinterfereswithanother processthathasanon-zerostrong,orcommonphaseφ ,thathasthesamesignforparticleandantiparticle 0 processes [7]. This isillustrated inFig. 2a, where a CP violatingprocess X0 → π+π− (X0 → π+π−) has a complex amplitude A = |A|exp(iφ ) (A = |A|exp(−iφ )). Differences in the decay rates can be be CP CP measured if the CP-violating amplitude interferes with a CP-conserving amplitude for the same process C = |C|exp(iφ ) = C. InthatcasetheX0 → π+π− andX0 → π+π− ratesdifferbyatermproportionalto 0 2|A||C|sinφ sinφ ;notethatthisinterferencetermiszeroifφ =0. 0 CP 0 In1972,KobayashiandMaskawa(KM)showedthatanon-trivialCP-violatingphasecouldbeintroduced into the weak interaction quark-flavor mixing matrix, but only if there were at least three generations of quarkdoublets,i.e.,atleastsixquarkflavors(seeFig.2b)[8].Thiswasremarkablebecauseatthattime,only threequarkflavorshadbeenestablished. Ina1980paper,CarterandSandasuggestedthatiftheb-quark- related flavor mixing parameters were such that B0 ↔ B0 was substantial and the B-meson lifetime was relativelylong,largeCPviolationsmightbeobservableinneutralBmesondecaysandprovideconclusive 2 XXIIndInternationalWorkshop“High-EnergyPhysicsandQuantumFieldTheory”,June24–July1,2015,Samara,Russia b) imag. a) A φ 0 C φ X0π+π-‐ CP -φ real CP _ Page 1: A … φ 0C Page 12: 3 Euler angles: θ θ & θ, plus 1 CP-‐viola7ng phase: δ 1 2 3 Figure 2: a) The amplitude A represents a CP-violating contribution to a hypothetical process X0 → π+. Differences in the X0→π+π−andX0→π+π−decayratescanonlybeobservedifitinterfereswithaCP-conservingprocess(amplitude=C)thathas anon-zerocommonphaseφ0.b)Excerptsfrompage1(above)andpage12(below)oftheclassicKobayashi-Maskawapaper[8]. testsoftheKMidea[9].However,theteststhatCarterandSandaproposedwouldrequiredatasamplesthe containedseveralhundredsofexclusiveB0decaystoCPeigenstates,suchasB0 → K J/ψandB0 → K ψ(cid:48). S S In1983,CLEOreportedtheworld’sfirstsampleofexclusiveB-mesondecaysshowninFig.3a,wherethere are 18 events in the B-meson mass peak, divided equally between neutral and charged B-mesons with a backgroundthatisestimatedtobebetween4and7events[10].NoexclusivedecaystoaCPeigenstatewere observed. Thus,intheearly1980’s,whenthestate-of-the-arte+e− colliderluminositywas∼ 1031cm−2s−1, the possibility for checking the KM idea seemed hopeless, except for a few super-optimists who could foreseeluminositiesgreaterthan1033cm−2s−1bytheendofthecentury. Forthe1973KMideatoberelevantandtestable,therehadtobe:sixquarksinsteadofthree;arelativelylong B-mesonlifetimeandsizable B0 ↔ B0 mixing(correspondingto|V | < |V | < 0.1);andathousand-fold cu cb ormorecombinedimprovementine+e− luminosityanddetectorperformance. In1974,thefourthquark, thec-quark,wasdiscoveredatBrookhaven[12]andSLAC[13]andthefifthquark,theb-quark,wasfound in1977byaFermilabexperiment[14]. Then,in1983,along(τ (cid:39) 1.5ps) B-mesonlifetimewasmeasured B at PEPII [15,16] and, in 1987, a substantial signal for B0 ↔ B0 mixing was unexpectedly discovered by the ARGUS experiment at DESY [17]. Taken together, these results indicated that the CKM mixing-angle valueswerefavorableforexperimentaltestsoftheKMidea. (The B0 ↔ B0 mixingfrequencyisnowwell measured to be ω (cid:39) 0.5ps−1, and not much different than 1/τ .) In addition, the luminosity of e+e− 0 B colliderskeptincreasinginaMoore’s-law-likefashionwithadoublingtimeofabout2.5years(seeFig.3b). In2001,lessthantwentyyearsaftertheCLEOreportofan18eventexclusiveB-mesondecaysignalwithno CPeigenstatemodes,theBelleexperiment’sdiscoverypaperonCP-violationintheB-mesonsystemused the∼ 700neutral BmesonstoCPeigenstatedecayswithCPeigenvalueξ = −1(mostly B → K J/ψ)in f S thesignalpeakshowninFig.3c[11]. 3 XXIIndInternationalWorkshop“High-EnergyPhysicsandQuantumFieldTheory”,June24–July1,2015,Samara,Russia b) c) a) Belle 2001 Figure 3: a)(Figure2fromref.[10].) ThefirstreportedsignalforexclusiveB-mesonsdecays,foundbyCLEOina40pb−1data samplerecordedoverathree-yeartimeperiod. b)A“Livingstonplot”fore+e− luminositiesvs. year. c)(Figure1fromref.[11].) The2001B→KS(cc),ξf =−1CPeigenstatedecaysignalfroma29fb−1Belledatasample,containing∼700signalevents,mostly B→KSJ/ψdecays,witha92%signalpurity. a) J/ψ b) Flavor-‐tag decay Vcb (B0 or B0 ?) fCP B0 e+ J/ψ e-‐ K + S Δz KS V*td Vtb Vcb J/ψ BB -‐+ B––B more B’s B0 B0 more B’s t=0 tCP ≈ Δz/c β γ Vtb Vt*d KS = (1-‐2w)sin2φ1 Figure4: a)AB0-mesoncandecaytoaCPeigenstatedirectlyorbyfirstmixingintoaB0thatinturndecaysthesameCPeigenstate. Theinterferencebetweenthetwoprocessesis∝V∗2(not|V∗|2).b)AcartoonthatillustrateshowtheB-factoryexperimentsmeasure td td φ1,theCP-violatingphaseofVt∗d. CarterandSandasuggestedthatφ ,theCPV phaseofV ,couldbemeasuredbytheinterferencebetween 1 td thetwoB0-mesonquark-lineprocessesshowninFig.4a.HerethetopdiagramisthedirectB0-mesondecay to a CP eigenstate (chosen here as K J/ψ for illustration). In the lower diagram, the B0 first mixes into a S 0 0 B and the B decays to the same CP eigenstate. The amplitude forthe upper diagram isproportional to V , which has no CPV phase; that for the lower diagram is proportional to V2V∗2V , where, in the KM cb tb td ub formalism,onlyV∗ hasaCPV violatingphase. Thus,theinterferencetermis∝V∗2 ∝sin2φ . td td 1 The way this interference is measured is illustrated in Fig. 4b. An asymmetric energy e+e− collison pro- duces a boosted B0 and a B0 in a “entangled” JPC = 1−− quantum state. After some time, one of the B meson decays to a “flavor specific” final-state, i.e. a final state that allows one to distinguish whether the flavorofdecayingBmesonisaB0oraB0.Atthattime,whichistakenast =0,theaccompanyingBmeson has to have the opposite flavor. Then this accompanying B meson evolves with time, mixing as it goes along(eitherforwardorbackwardintime!) intotheoppositeflavorwithafrequencyω ,andeventually mix 4 XXIIndInternationalWorkshop“High-EnergyPhysicsandQuantumFieldTheory”,June24–July1,2015,Samara,Russia decaysattimetintoaCPeigenstate. Whatismeasured,istheasymmetryA asafunctionoft,where CP N −N A = B0 B0 = ξ (1−2w)sin2φ sinω t, (1) CP N +N f 1 B B0 B0 N (N )isthenumberoftimestheflavor-taggedBisaB0 (B0),ξ istheCPeigenvalueofthestatebeing B0 B0 f studied (for B → K J/ψ, ξ = −1), w is the probability that the flavor-tagged B meson is assigned the S f wrong flavor, and t is inferred from ∆z, the measured separation of the two B-meson decay vertices: t = ∆z/(cγβ). Inthismeasurement,therequiredcommonphasethatwasdiscussedaboveinconjunctionwith Fig. 2a is provided by the mixing term exp(iω t), which changes sign at t = 0. Thus the time integrated B asymmetryiszeroandtheboost(γβ)providedbytheenergyasymmetryofthebeamsisessential. Atthetimetheflavored-tagged B-mesondecays,theaccompanying Bmesonisinapureflavorstate,and theinterference(andasymmetry)iszero; asthismesonpropagates,itsflavormixesand,afterabout3ps, the B0 and B0 amplitudes are nearly equal and the asymmetry is maximum. However, this 50:50 mixing occurs for a decay-time difference of about two B0 meson lifetimes, and only ∼13% of the B mesons live this long. This, and the small branching fractions for B0 decays to measureable CP eigenstates (typically ∼0.1%),explainwhysuchahugeincreaseine+e−colliderluminositywascriticalforthesemeasurements. The K J/ψ final state has ξ = +1 and a CPV asymmetry that is opposite in sign to that for K J/ψ final L f S states. Thus, both BaBar and Belle instrumented their magnet return yoke to make it suitable for recon- structing K J/ψfinalstates. A K canproduceasplashofenergyintheinstrumentedreturnyoke,either L L bydecayingorinteractinginoneoftheyoke’sironplates,asshowninthetoppanelofFig.5a,thatcanbe usedtodeterminetheK direction. That,withtheassumptionoftwo-bodydecaydynamics,canbeusedto L infer pcms,the Bmeson’sthree-momentuminthecenterofmass(c.m.) system. Belle’s2001 pcms distribu- B B tion,showninthelowerpanelofFig.5a,exhibitsadistinct,∼346-eventsignalpeakforB → K J/ψdecays L at pcms (cid:39)0.33GeV/c(witha61%signalpurity)thatwerealsousedforCPV asymmetrymeasurements. B a) b) Belle c) combined Belle 2001 asymmetry 2001 sin2φ1=0.99±0.15 “raw” distribu9ons q.(cid:106)f = +1 KL 0.20 q.(cid:106)f = (cid:60)1 t)(cid:54) d( N/ Belle .Nd0.10 2001 1/ 0.00 -8 -4 0 4 8 (cid:54)t (ps) Figure5: a)(top)AcomputerdisplayofB→KLJ/ψeventscandidateinBelle,wheretheJ/ψdecaysintoaµ+µ−pairandtheKL producesanenergyclusterinthemagnet’sinstrumentedfluxreturn. (bottom)ThepcBmsdistributionforcandidateKLJ/ψevents. b) Thet-dependentCPVasymmetryforξf =−1(top),ξf =+1(center)andnon-CPeigenstatedecays(bottom). c)Thetdependence ofeventsorganizedaccordingtoqξf values,whereq=+1(−1)correspondstoataggedB0(B0)(bottom). Thecombinedqξf =−1 minusqξf =+1asymmetries,togetherwiththefitresults(top). The 2001 Belle result, sin2φ = 0.99±0.15 [11], was 6σ from zero and conclusively confirmed the KM 1 prediction for a non-zero CPV complex phase in the V element of the quark-flavor mixing matrix. The td 5 XXIIndInternationalWorkshop“High-EnergyPhysicsandQuantumFieldTheory”,June24–July1,2015,Samara,Russia oppositeasymmetriesfor ξ = +1and −1decaysamples, showninthecenterandtoppanelsofFig.5b, f respectively,providedacheckonpossiblesystematiceffectsonthesin2φ measurements.Anothervalidity 1 checkisillustratedinthelowerpanelofFig.5b,whichshowstheresultsofthesameanalysisappliedtonon- CP eigenstatedecaymodes,wherenoasymmetryisexpected; thefitresultfortheseeventsis0.05±0.04. Atthesametime,theBaBarexperimentreporteda4σnon-zerovalue: sin2φ =0.59±0.15[18]. 1 The combined average of the 2001 BaBar and Belle φ results is compared with constraints from other 1 measurements in Fig. 6a [19], where good agreement with expectations is evident. Eventually BaBar and Belleeachaccumulatedahugeamountofadditionaldataandsignificantlyimprovedtheprecisionontheir φ measurements and other quantities that now constrain the 2015 allowed region of the same plane [20] 1 asshowninFig.6b,whichdemonstratesthattheconsistencyoftheCKMpictureisamazinglygood. This successresultedinKobayahiandMaskawasharingthe2008PhysicsNobelprize(withYoichiroNambu). a) b) c) Figure 6: a)TheunitaritytriangleplotfromtheCKM-fittergroupwiththeaverageofthe2001BaBarandBellesin2φ1 results (labeledassin2βWA). HereρandηaretheWolfensteinCPVparameters[21]. b)The2015versionoftheCKM-fittergroup’sunitary triangleplot.c)(left)Kobayashiand(right)MaskawameetingtheKingofSwedeninDec.2008. 3 It wasn’t only about CP, or even B mesons 3.1 Double cc production in e+e− annihilation One of the earliest measurements in Belle was a study of inclusive J/ψ production in continuum e+e− annihilation at c.m. energies near 10.6 GeV. Studies of J/ψ production is a common activity for the early stages of an experiment because they are a prolific source of tagged muons and electrons that are useful for calibrating lepton identification systems, validating triggers and tuning up charged particle tracking algorithms. Theoretically, inclusive and exclusive J/ψ production is supposed to be described accurately (andrigorously)bynon-relativisticquantumchromodynamics,NRQCD[22]. In2002,Bellereportedatotalcrosssectionfortheinclusive,continuumannihilationprocesse+e− → J/ψ+ Xof1.47±0.16pb[23].ThiswasinreasonableagreementwithNRQCD[24],whichhadpredicteda∼1.1pb crosssectionthatis∼(1/3)rd duetoe+e− → gg(cc) and∼(2/3)rds duetoe+e− → g(cc) ,where(cc) and 1 8 1 (cc) refertocolor-singletandcolor-octetcharmed-quarkanticharmed-quarkconfigurations,respectively. 8 However,Belle’smeasured J/ψmomentumdistribution,showninFig.7a,hasnosignificanteventsignal in the highest kinematically allowed momentum region, 4.5-4.84 GeV/c, where the dominant color-octet contributionwasexpectedtobestrongest. AMCestimateforthenumberofexpectedsignaleventsinthis 6 XXIIndInternationalWorkshop“High-EnergyPhysicsandQuantumFieldTheory”,June24–July1,2015,Samara,Russia highmomentumregionusingaspecialNRQCD-inspiredeventgeneratorincorporatedintoPYTHIA[25] predicteda∼300eventsignalinthetwohighestbinsofFig.7a,wherenosignalisseen. a) b) c) Belle e+e-‐  J/ψ D D_ Belle Belle e+e-‐  J/ψ D D_* √ Figure7: a)TheJ/ψc.m.three-momentumdistributionforinclusivee+e−→J/ψXreactionsnear s=10.6GeV(fromref.[23]). b)ThedistributionofmassesrecoilingfromtheJ/ψininclusivee+e− → J/ψXannihilations. Theshadedhistogramisbackground estimatedfromtheJ/ψmasssidebands;theopenhistogramisthefeeddownfromψ(cid:48) → J/ψ+X(fromref.[26]).c)TheJ/ψrecoil massdistributionsfore+e− → J/ψDD(upper)ande+e− → J/ψDD∗(lower)events(fromref.[26]). Thehatchedhistogramshows thebackgroundestimatedfromtheD-masssidebands.(Theinclusionofcharge-conjugatestatesisimplied.) A2007Bellestudyofthesameprocesswithmoredata,reportedresultsintermsofthemassrecoilingfrom (cid:113) thedetected J/ψ(i.e. M (J/ψ) = (E −Ecms)2−pcms )showninFig.7b[26]. Thisdistributionhas recoil cms J/ψ J/ψ anumbernoteworthyfeatures: • therearenoobvioussignaleventsbelowtheη peak,wherecontributionsfromcolor-octetproduction c areexpectedtobestrongest; • the ∼500 event η signal corresponds to a cross section for the exclusive process e+e− → J/ψη of c c 25.6±4.4fb[27],morethananorderofmagnitudehigherthanNRQCD-basedexpectations[28,29]; • the∼300eventη (2S)signalprovidedthebestconfirmationofthisstateatthattime; c • thethreelower-masspeaksallcorrespondtoestablished,spin=0charmoniumstates; • thereisstrongproduction(σ (cid:39)10fb)ofapreviouslyunknownstatewith M (cid:39)3940MeV. Belle found that the J/ψcc component corresponds to (59±0.18)% of the total inclusive J/ψ production (cid:46) cross section [30] in contradiction to NRQCD expectations that it would be 10% of the J/ψgg component[31,32]. Thecrosssectionsforexclusivedouble-charmoniumprocesses(suchas J/ψη )arewellabove c lowest-order NRQCD-based predictions [28,29]. This inspired studies of the corrections due the next-to- leadingorder(NLO)[33–35], andthesewerefoundtobelarge(largeenoughtoexplainthediscrepancy), butsuchlargecorrectionsatNLOraisesuspicionsabouttheconvergenceoftheNRQCDexpansion[36]. Belle’sexperimentalresultsondoubleccproductionhavehad(andarestillhaving)ahugeimpactonthe development of NRQCD and, although they are not well known outside of this specialty, they are very importantto,andhighlycitedby,practionersinthisfield. (Attheendof2015,refs.[26],[27]and[30]had 271,155and320citations,respectively.) 7 XXIIndInternationalWorkshop“High-EnergyPhysicsandQuantumFieldTheory”,June24–July1,2015,Samara,Russia 3.1.1 Themasspeakat3940MeV In order to study the peak at 3940 MeV in the J/ψ recoil mass spectrum, Belle selected events with a reconstructed J/ψ and D meson[26]. Intheseeventsthedistributionofmassesrecoilingfromthe J/ψ-D ∗ ∗ system exhibit clear and distinct signals for recoil D and D mesons. The DD and DD invariant mass distributions for these events are shown in the upper and lower panels, respectively, of Fig. 7c, where a ∗ clearpeakat3.94GeVisevidentintheDD spectrumbutnotintheDDchannel. Theabsenceofanysignalsforknownspin=1orspin=2charmoniumstatesinthe J/ψrecoilmassspectrum ofFig.7b,andthelackofanysignificantsignalforthethe3940MeVpeakinthe DD massdistributionin Fig.7C(upper),providecircumstantialevidencethatthe JPC quantumnumbersforthisnewstateare0−+, whichwouldmakeitacandidatefortheη (3S)charmoniumstate. However,inthiscaseits3942±9MeV c masswouldbe∼100MeVbelowitshyperfinepartner,theψ(3S) = ψ(4040),implyingahyperfinesplitting that is about twice as large as the ψ(2S)-η (2S) splitting. This is contrary to expectations from potential c modelsinwhichthehyperfinesplittingdecreaseswithincreasingradialquantumnumber.Forstatesabove opencharmedthresholds, naïvepotentialmodelresultsaremodifiedbytheinfluenceofcoupledpairsof ∗ open-charmed mesons. The nearest open charmed pair relevant to the η (3S)-ψ(3S) doublet is a DD c systeminarelative P-wave,andthisshouldnothaveaverylargeeffectonthehyperfinesplitting,which isprimarilysensitivetotheccwavefunctionattheorigin. Theseissuesarediscussedinref.[37]. 3.2 Probing the f (980) and a (980)scalar mesons 0 0 The nature of the scalar mesons with mass below 1 GeV is one of the most long-standing mysteries of hadron physics. Although they have been studied for more than four decades, they continue to remain controversial[38,39]. Ithasbeensuggestedthattheyarenot“standard”qqmesonsbut,instead,fourquark stateseitherofthediquark-diantiquark[40],ormeson-mesonmolecule[41–43]variety. Awaytodistinguishbetweendifferentsubstructuresproposedforthescalarmesonsisbythedetermina- tionsofthetwo-photonwidths(Γ )oftheelectricallyneutral f (980)anda0(980)statesviameasurements γγ 0 0 oftheirproductioncrosssectionsinγγcollisions. Figure8aillustrateshowthisworksforqqmesons. Both photonscoupletotheinternalquarkpairandthepartial-widthsareproportionalthee4. Thus,forexample, q intheqqpicturefortheisoscalar f (980)meson,(whereq = uandd),theexpectationforΓ (f (980))isin 0 γγ 0 therange1.3to1.8keV[44];forafour-quarkKKmoleculeitismorecomplicatedandmuchsmaller,inthe 0.2-0.6keVrange[45];forssitisexpectedtobeintherange0.3-0.5keV[46]. The measurement of γγ → f (980) → π+π− is difficult with Belle because of a huge background from 0 the QED process γγ → µ+µ−. In the π+π− invariant-mass region of interest for this measurement, the pions and muons have low laboratory momenta and do not reach the Belle muon identification system. Nevertheless,thedifferentresponsesoftheCsIcrystalsinBelle’selectromagneticcalorimetertopionsand muons and the huge luminosity of KEKB allow for a mass-bin by mass-bin statistical separation of the pionandmuoncontributions. ThebluetrianglesandblacksquaresinFig.8bshowresultsfromprevious measurementsbyCello[47]andMarkII[48],wherethereisnosignofanyresonance-likebehaviorinthe 980 MeV region. The small red dots in the same figure are not a theoretical curve or the results of MC calculations;theseare,instead,Bellemeasurementswithstatisticalerrorbarsthatareaboutthesizeasthe datapointsthemselves[49]. TheupperpanelofFig.8cprovidesanexpandedviewoftheBelleresultsnear the f (980)mass,whereadistinctstructurenear980MeVisevident. Thisstructuredoesnothaveasimple 0 BreitWignerlineshapebecauseofstronginterferencewiththehelicity=0,non-resonantπ+π−background andadistortioncausedbytheopeningofthe f (980) → KK atthe2m threshold. The f (980) isfitwith 0 K 0 acoherentFlattè-likelineshape[50,51]usingparametersdeterminedbyBESII[52]thattakestheseeffects 8 XXIIndInternationalWorkshop“High-EnergyPhysicsandQuantumFieldTheory”,June24–July1,2015,Samara,Russia a) b) c) Belle f0(980)? Figure 8: a)Acartoonthatillustratestherelationbetweenγγproductionmeasurementsandtheinternalstructureofneutral mesons. b)σ(γγ → π+π−)measurementsfromCello(triangles),MarkII(opensquares)andBelle(reddots). Thedashedredline indicatesthesizeofBelle’ssystematicerrorsc)(upper)AnexpandedviewoftheBellemeasurementsinthevicinityofthef0(980)with fitresultsshownbythecurvedline. (lower)The f0(980)componentsofthefit: total f0(980) → π+π−(solidcurve); f0(980) → KK (shortdashes);effectof f0(980)interferenceofthenon-resonantπ+π−background(longdashes). into account. The components of the resulting fit are shown in the lower panel of Fig. 8c. The fit gives an f (980) mass and ππ partial width of M = 985.6+1.2+1.1 MeV and Γ = 34.2+13.9+8.8 MeV and a 0 −1.5−1.6 ππ −11.8−2.5 γγ partial width of Γ = 205+95+147 eV, where the first errors are statistical and the second systematic. γγ −83−117 The main systematic error on Γ is from the cross section normalization that, in turn, is sensitive to the γγ modelingofthenon-resonantπ+π− background. Bellealsostudied f (980)productionintheγγ → f (980) → π0π0channel,whereµ+µ−andnon-resonant 0 0 π0π0 backgrounds are not an issue. In Fig. 9a, Belle results [53] for σ(γγ → π0π0) are shown as red di- amonds (with invisible statistical error bars) together with previous results from the Crystal Ball experiment [54] shown as black solid circles with error bars. Here again the Belle results represent a huge im- provement in statistical precision. The results of Belle fits to the differential cross section measurements are shown in Fig. 9b, where a distinct signal for an S-wave resonance near 980 MeV is found with mass 982.2±1.0+8.1 MeV and Γ (f ) = 286±17+211 eV; these values agree well with Belle’s results from the −8.0 γγ 0 −70 π+π− channelbutwithdifferentsourcesofsystematicerrors. a) b) c) f0(980)? Figure9: a)Belle(reddots)andCrystalBall(solidcircles)resultsforσ(γγ→π0π0). ThedashedlineindicatesthesizeofBelle’s systematicerrors. b)Belleresultsforσ(γγ → π0π0)withtheresultsoftheBellefit: totalfit(solidcurve); S-wave(shortdashes); helicity=2 D-wave (dash-dot); helicity=0 D-wave (long dashes). c) Belle σ(γγ → ηπ0) measurements (solid dots) together with previousCrystalBallresults.ThedashedcurveindicatesthesizeofBelle’ssystematicerrors. 9 XXIIndInternationalWorkshop“High-EnergyPhysicsandQuantumFieldTheory”,June24–July1,2015,Samara,Russia Belle also studied two-photon production of the isovector a0(980) scalar in the γγ → a0(980) → ηπ0 0 0 channel[56]. Belle’sσ(γγ → ηπ0)resultsareshownasblackdotsinFig.9cwithpreviousmeasurements fromtheCrystalBallshownasopencircleswitherrorbars.[57]. Belleresultsagreewellwiththeprevious measurements but with substantially improved precision. The Belle results for the a0 mass, total width 0 andγγpartialwidthare: M = 982.3+0.6+3.1 MeV;Γ = 75.6±1.6+17.4 MeV;andΓ ×B(a → ηπ0) = −0.7−4.7 tot −10.0 γγ 0 128+3+502 eV. The large positive systematic error on the γγ partial width is associated with uncertain −2−43 interferenceeffectswithhigherηπ0resonances,whichwerenotconsideredinpreviousmeasurements. TheBelleΓ (f )resultsareinconsistentwithexpectationsforapureqqmesonandconsistentwiththefour- γγ 0 quarkmodelpredictionof270eVprovidedinref.[55]. TheimpactofBelleresultsontheunderstandingof thelightscalarmesonsisdiscussedinrefs.[58]and[59]. Belle published ten papers on γγ production of six light meson channels: π+π−, π0π0, ηπ0, ηη, K+K− and K K . These papers all include game-changing improvements in statistical precision over previous S S work (similar to the examples given above) and include analyses of twenty well identified meson states thatinclude,usuallyforthefirsttime,considerationofangulardistributionsandtheeffectsofinterference. 3.3 Spin polarimetry for quark jets The strongly interacting particles in the SM are quarks and gluons. The strongly interacting particles in Nature are hadrons. Presumably the transition of quarks and gluons into hadrons is described by long- distance QCD, but calculations of the processes that are involved are hopelessly complicated. Attempts tocopewiththesedifficultiesbyusing“QCD-motivated”modelshavehadonlymodestsuccess. Usually, thetransitionsbetweenquarksandhadronsareparameterizedbyexperimentallymeasuredfragmentation functions Dh(z,p2 ), which are probability densities for a quark of flavor q to produce a hadron h with q h⊥ a fraction z of the quark’s original momentum and with a transverse momentum relative to the quark directionof |ph⊥|, asillustratedintheupperpartofFig.10a. Measuringthesefragmentationfunctionsis animportant(butunsung)partoftheresearchprogramofmostexperiments(seee.g.,ref.[60]). a) b) unpolarized quarks: use quark-‐spin correla2ons in e+e-‐  q _q  hadrons q Dz e=n Pshi/tk y oafn fidn d p i hn ⊥ gin a a h jaedt rporno dh uwcietdh beyn ear pgya rftroanc: qo n ϕ2 ϕ1 € € polarized quarks: q dσd(Ωe+dez−1d→z2dh12hq2TX)=B(y)cos(ϕ1+ϕ2)H1⊥[1](z1)H1 ⊥[1](z2) quark spin analyzing power B(y)=y(1−y)c=m1sin2Θ 4 € Figure 10: a)Illustrationofunpolarized(upper)andpolarized(lower)quarkfragmentationfunctions. b)Theprincipleofmea- surementoftheproductoftwoCollinsspinfragmentationfunctionsusinge+e− →qqannihilations. Heretheblueplaneisdefined bythethrustaxisoftheevent(purpleline)andtheincominge+e−direction(blueline). Ifthequarkispolarized,thefragmentationdensitycanalsodependontheazimuthalanglearoundthethe quark’sinitialmomentumdirectionasillustratedinthelowerpartofFig.10a. Thiswasfirstdiscussedby Collins[61],whointroducedasecondterminthefragmentation,H⊥h(z,p2 ),asafirst-ordercharacteriza- 1,q h⊥ 10