Quarkonium Feed-Down and Sequential Suppression.pdf
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1、arXiv:hep-ph/0106017v2 11 Jun 2001June 1,2001BI-TP 2001/09Quarkonium Feed-Down and Sequential SuppressionS.Digal,P.Petreczky and H.SatzFakult at f ur Physik,Universit at BielefeldD-33501 Bielefeld,GermanyAbstract:About 40-50%of the quarkonium ground states J/(1S)and(1S)produced inhadronic collisions
2、 originate from the decay of higher excitations.In a hot medium,thesehigher states are dissociated at lower temperatures than the more tightly bound groundstates,leading to a sequential suppression pattern.Using new finite temperature latticeresults,we specify the in-medium potential between heavy q
3、uarks and determine thedissociation points of different quarkonium states.On the basis of recent CDF data onbottomonium production,we then obtain first predictions for sequential suppression innuclear collisions.1.IntroductionThe large values of the charm and bottom quark masses permit potential the
4、ory toprovide a realistic account of quarkonium spectroscopy 1-3.From these studies,it isknown that the intrinsic length scales of quarkonia are much smaller than those of theusual hadrons,with rJ/0.2 fm and r 0.1 fm for the radii of the lowest c c andbb vector mesons,respectively,in contrast to abo
5、ut 1 fm for light q q state radii.This“short-distance”nature of quarkonium states suggests that at least some features of theirproduction in hadronic collisions should be accessible to perturbative QCD calculations,and that indeed turns out to be the case.The simplest and most general model for quar
6、konium production,the color evapora-tion model 4,postulates that the cross-section for the production of a given charmoniumor bottonium state is simply a fixed(energy-independent)fraction of the correspondingperturbatively calculated c c or bb production cross-section.The resulting predictions forth
7、e energy variation of the J/and hadroproduction cross-sections are experimentallyvery well confirmed,for the over a range froms 20 to 1800 GeV 5.The assumedenergy independence of the production ratios of 2S/1S and 3S/1S states is found to holdover the same range 5.Higher quarkonium excitations decay
8、 into lower states with generally known branchingratios and widths.As an example,the=(2S)decays into J/(1S)+anything witha branching ratio of 55%,after a mean life-time of more than 103fm.As a consequence,J/or production in hadronic collisions occurs in part through the production of higher1excited
9、states which subsequently decay into the quarkonium ground states.It is knownexperimentally that for both J/and about 40-50%of the hadroproduction rate isdue to such feed-down from higher excitations 6-10.Quarkonium production through feed-down becomes particularly interesting whenquarkonium states
10、are used to probe the hot and dense medium created in high energynuclear collisions.It was predicted that color deconfinement(quark-gluon plasma for-mation)would lead to J/suppression,since sufficiently hot deconfined media dissolveany c c binding 11.However,different quarkonium excitations will dis
11、solve at differ-ent temperatures of the medium 12,and through a lowering of the open charm(beauty)threshold with temperature,dissociation by DD or BB decay becomes possible for higherexcited states even below the deconfinement point 13.Since the life-time of the exci-tations is much larger than that
12、 of the medium,feed-down production will result in acharacteristic sequential suppression pattern 14,15,with the fraction of J/or pro-duced through the decay of higher excitations becoming suppressed at lower temperaturesthan the directly produced ground states.To fully predict this sequential suppr
13、ession,two prerequisites are needed.We haveto know what fractions of the quarkonium ground state production originate from whichhigher excitations,and we have to know at what temperature or energy density of the hotmedium a given excitation dissolves.The first can be determined either experimentally
14、or through a viable model for quarkonium hadroproduction.The second is a well-definedproblem for finite temperature lattice QCD studies.At present,neither problem is com-pletely solved.However,in the case of charmonium,the production rates of the higherexcitations are experimentally known,and for bo
15、ttonium production,recent Fermilabdata 10,9 provide the basis for fairly reliable estimates.This determines the structure(i.e.,the sequence and the different heights)of the various suppression steps for J/and production,but not the actual positions of these steps as function of the temperatureor ene
16、rgy density.To estimate these,we make use of recent lattice studies calculating thetemperature behavior of the heavy quark potential in full QCD 13,16.As a result,weobtain a modified J/suppression pattern 14,15,including the decay of and cinconfined matter 13,and then first quantitative predictions
17、for the sequential suppres-sion to be studied in forthcoming RHIC and LHC experiments.The structure of this paper is the following.In section 2,we first summarize thehadroproduction cross sections for the different charmonium states and then determinethe corresponding bottonium cross sections from t
18、he mentioned new CDF data.As aresult,we can fully describe the origin of the J/and produced in hadronic collisionsin terms of feed-down from higher excited states.In section 3,we consider the temperaturedependence of the heavy quark potential obtained in recent lattice QCD studies.Solvingthe corresp
19、onding Schr odinger equation,we then determine in section 4 the dissociationparameters for the different states in a deconfined medium.This leads to quantitativeestimates of the sequential J/and suppression patterns.2.Quarkonium Production and Feed-DownA.Charmonium StatesIt is well known that J/prod
20、uction in hadron-hadron collisions is to a considerableextent due to the production and subsequent decay of higher excited c c states 6-8.We2shall here summarize the situation following systematic studies using pion and protonbeams at 300 GeV incident energy 8.In the first two columns of Table 1,we
21、list thecross-sections diobtained for the direct production(excluding feed-down)of the differentcharmonium states(1S),(1P)and=(2S)in-nucleon and p-nucleon interactions,normalized to the overall measured J/cross-section J/,which includes all feed-downcontributions.Hence Ri(N)di(N)/J/(N)for the direct
22、ly produced state iin N interactions,and similarly for p N collisions.Making use of the branching ratios B1(1P)(1S)=0.27 0.02,B2(1P)(1S)=0.14.01,and B(2S)(1S)=0.550.05,one obtains the fractional feed-down contributions fiof the different charmonium states to the observed J/production;these are shown
23、 in the next two columns of Table 1.Also listed are the dissociationenergies Eidis,Eidis 2MD Mi.(1)measuring how far the mass of state i lies below the zero-temperature open charm thresh-old 2MD=3.740 GeV.stateRi(N)Ri(p N)fi(N)%fi(p N)%EdisMeVJ/(1S)0.57 0.030.62 0.0457 362 40.6421(1P)0.72 0.180.60 0
24、.1520 516 40.2292(1P)1.04 0.290.99 0.2915 414 40.183(2S)0.14 0.040.14 0.048 28 20.054J/11100100Table 1:Cross-sections for direct charmonium production in N and pN collisions,normalized to the overall J/production cross section in the corresponding reaction 8;feed-down fractions and mass gap to the o
25、pen charm threshold.From Table 1 it is seen that some 60%of the observed J/are directly produced,about 30%come from and about 10%from decay.According to the color evaporationmodel,feed-down fractions as well as cross section ratios are energy-independent.Theresults shown in Table 1 for the ratio of
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