a r X i v :h e p -p h /9806332v 5 15 J a n 1999
Single Top Quark at Future Hadron https://www.doczj.com/doc/492559023.html,plete Signal and Background Study.
A.S.Belyaev 1,2,E.E.Boos 2,L.V.Dudko 2
1
Instituto de F′?sica Te′o rica,Universidade Estadual Paulista,
Rua Pamplona 145,01405–900S?a o Paulo,Brazil.
2
Skobeltsyn Institute of Nuclear Physics,Moscow State University
119899Moscow,Russian Federation
We perform a detail theoretical study including decays and jet fragmentation of all the important modes of the single top quark production and all basic background processes at the upgraded Tevatron and LHC colliders.Special attention was paid to the complete tree level calculation of the QCD fake background which was not considered in the previous studies.Analysis of the various kinematical distributions for the signal and backgrounds allowed to work out a set of cuts for an e?cient background suppression and extraction of the signal.It was shown that the signal to background ratio after optimized cuts could reach about 0.4at the Tevatron and 1at the LHC.The remaining after cuts rate of the signal at the LHC for the lepton +jets signature is expected to be about 6.1pb and will be enough to study the single top physics even during the LHC operation at a low luminosity.
I.INTRODUCTION
The existence of the top quark has been established in March 1995by the CDF and D?collaborations at the
Tevatron collider.[1].Top quark has been discovered in the strong t ˉt
pair production mode.The cross section of electroweak process of single top quark was found to be comparable with the QCD pair top production [2].Single top production mechanism is the independent way of a con?rmation of the top quark existence and straightforward key to measure the V tb CKM matrix element and to study the W tb vertex.Since the mass of the top quark is very large compared to all other quarks one might expect some deviations from the Standard Model (SM)predictions in the top quark interactions [3].The single top quark production rate is directly proportional to the W tb coupling and therefore it is a promising place to look for deviations from the SM.
However one should stress that the task of background reduction is much more serious and important problem in
the case of the single top comparing to the t ˉt
-pair production.It happens because the jet multiplicity of single top quark events is typically less than for t ˉt
-pair production and so QCD W jj and multijet backgrounds are much higher,and the problem of the single top signal extraction is more involved.That is why the detail background study is especially needed in order to ?nd an optimal strategy to search for of single top quark.
Top quark decays into a W -boson and a b quark with the almost 100%branching ratio in the framework of the Standard Model.We consider here the subsequent leptonic decays of the W -boson to a electron (muon)and neutrino,as this signal has much less background and should be easier to ?nd experimentally than channels with hadronic decay of the W boson.
II.MC SIMULATION
In order to study a possibility of the signal extraction from the background we have created the MC generator for complete set of the single top production and backgrounds processes.Generator was designed as a new external user process for the PYTHIA 5.7/JETSET 7.4package [4].This generator is related to PYTHIA 5.7by a special interface and uses FORTRAN codes of squared matrix elements produced by the package CompHEP [5].For integration over the phase space and a consequent event simulation the Monte-Carlo generator uses the kinematics with a proper smoothing of singular variables [6]from the CompHEP and the integrator package BASES/SPRING [7].
The e?ects of the ?nal state radiation,hadronization and string jet fragmentation (by means of JETSET 7.4)have also been taken into account.The following resolutions have been used for the jet and electron energy smearing:?E had
/E =0.5/√E .In our analysis we used the cone algorithm for the jet reconstruction with the cone size ?R =
For all calculations CTEQ3M parton distribution has been used.For the top-quark production we chose the QCD Q2scale equal to the top mass squared,while for W jj background Q2=M W2have been taken.For calculations of jbˉb and jjbˉb processes we chose the invariant bˉb mass for the Q2scale.
Under the assumptions mentioned above the kinematic features of both signatures for signal and background have been studied.
A.Signal
We concentrated on the following set of processes at Tevatron pˉp and LHC pp colliders leading to the single top quark production:
1.pˉp→tqˉb+X,
2.pˉp→tˉb+X,
3.pˉp→tq+X,
4.pˉp→tW+X,
where q is a light quark and X represents the remnants of the proton and antiproton.Basic Feynman diagrams for processes mentioned above are shown in Fig.1.We refer to the paper[8]which consider the whole set of Feynman diagrams for signal subprocesses.
FIG.1.Diagrams for single top production
It is necessary to stress that pˉp→tW+X process contributes only with5%to the total cross section at the2TeV upgraded Tevatron.It could be easily omitted at Tevatron energies but should be taken into account for the LHC energies since as we shall demonstrate below its contribution at the LHC will be about30%of the the total cross section of the single top quark production.
For events analysis we have rescaled the total cross sections of the single top production using the results of the NLO calculations from the papers[9](m t=175GeV):
√
for
σ(tˉb)=0.88±0.05pb,σ(W g=tqˉb+tq)=2.43±0.4pb;
√
and for
FIG.2.Diagrams for W bˉb background
The speci?c feature of the single top production is the high energetic b-jet in?nal state and one additional b-jet for W-gluon and W?processes.It is clear that the only chance to extract the signal from such an overwhelming background is the e?cient b-quark identi?cation.We assume50%of a double b-tagging e?ciency hereafter. However the cross section of the W+2jet process is so large that even with the requirement of a double b-tagging but due to a b-quark jet misidenti?cation it represents an important part of the total background.In our study we chose0.5%misidenti?cation probability which based on the previous MC analysis[15].
The b-quark content of the W+2jet processes is fairly small–less then1%.For the cuts mentioned above the total cross section for W±bˉb process(gluon splitting)is8.7pb for Tevatron and30pb for LHC.However,the W+2b?jet process is the irreducible part of the total background which has di?erent kinematical properties from the main QCD W+2jet part,and as will be shown below it depends di?erently on the cuts.
Therefore the W±bˉb background has been considered separately and we have calculated it completely. Complete set of Feynman background diagrams for W bˉb?nal state is shown in Fig.2for u?andˉd-quarks in the initial state.The main contribution comes from subprocess(a)with the gluon splitting into the bˉb quark pair. Diagrams with virtual photon(c)contribute only1%to the total cross section.Contribution from W Z process(c) can be suppressed by applying cut on the invariant bˉb-mass.LO cross section for W Z is2.5pb at Tevatron and about30pb at LHC.For our analysis we apply K-factor=1.33(1.55)for Tevatron(LHC)to rescale this number for the NLO total cross section[16].Cross section of the process(d)of Higgs production(we take as an example m H= 110GeV)is even smaller:0.16(1.8)pb(LO)at Tevatron(LHC),and it means the Higgs is really not an important background for the single top.We apply K-factor=1.25(1.1)for Tevatron(LHC)to rescale the results for NLO one [17].Diagrams(b)give very small contribution due to small value of CKM elements.
process LHC(pb)
1.64·105
1.80·104(
2.50·103)
2.50·104(1.80·104)
9.00·103(3.21·103)
1.97·103(1.97·103)
3.21·103(9.00·103)
1.97·103(1.97·103)
5.67·102(1.25·102)
1.31·103(8.61·101)
Total5.11·105pb
TABLE I.Total cross section for jbˉb process for Tevatron and LHC.The following cuts have been applied at the parton level calculations:?R jj>0.5,p t jet>10GeV for Tevatron and?R jj(ej)>0.5,p t jet>20GeV for LHC
An important background is top-quark pair production:when one of the top decays hadronically and another one–leptonically.One of the cut which helps to reduce the background is the cut on the number of jets which was required to be less than four.At the parton level this cut reduces the top pair rate very strongly.However at the simulation level with a hadronization and jet reconstruction being taken into account the reduction of this background is not so strong anymore.And as a result the top-quark pair represents an important part of the background.This fact will be shown below.NLO total cross section for tt-pair production was taken[13]at Tevatron to be equal to7.56pb and 760pb at LHC.
process LHC(pb)
1.23·102
2.55·100———–
6.61·100———–
6.52·100———–
6.66·100———–
8.70·102———–
2.15·102———–
1.44·102(4.20·101)
9.63·101———–
3.73·102(1.20·102)
9.63·101———–
3.73·102(1.20·102)
9.63·101———–
9.10·101———–
4.20·101(1.44·102)
———–(9.63·101)
6.40·101
9.38·10?1(9.38·10?1)
2.40·100(2.40·100)
2.35·100(2.35·100)
2.24·102(2.24·102)
2.40·100(2.40·100)
7.30·101(7.30·101)
5.10·101
4.23·101———–
4.23·101———–
———–4.23·101
———–4.23·101
7.28·102(7.82·103)
7.82·103(7.28·102)
1.01·103(3.52·103)
7.61·102(7.61·102)
3.52·103(1.01·103)
7.61·102(7.61·102)
9.90·101
4.80·102
4.60·102
3.85·102
3.85·102
3.62·104
Total3.62·105pb
TABLE II.Total cross section for jjbˉb process for Tevatron and LHC.The following cuts have been applied at the parton level calculations:?R jj>0.5,p t jet>10GeV for Tevatron and?R jj(ej)>0.5,p t jet>20GeV for LHC
Another kind of the important reducible background comes from the multijet QCD processes.This happens due to a possible misidenti?cation of jet as an electron in the detector.Though the probability of that is very small(of order of0.01-0.03%)[18],the cross section for such processes is huge and give a signi?cant contribution to the background for single top production.For the analysis we took?fake=0.02%.
We have calculated the total cross section and made MC simulation for jbb and jjbb processes which are relevant for our signature if one the light jet imitates electron.In such a way we could simulate the basic distributions of the expected fake background and understand how strong it could be suppressed by kinematical cuts.The MC simulation of the fake background for the single top study is presented for a?rst time.
The background from the light jets is appeared to be less important despite on the fact the light jet cross sections even with cuts are very large.The light jet background is suppressed by three small factors,by double mistag probability to identify light jet as a b-jet and by the small fake probability to identify light jet as an electron.For instance the gg→ggg subprocess could contribute to the background when two gluon jets fake b-quark jets and a third gluon jet fakes the lepton.The cross section of gg→ggg itself is huge but as was mentioned it’s contribution to the single top background is suppressed by fake probability of gluon multiplied by double mistag probability of two gluons.For example,the cross section of triple gluon production Tevatron is2.7·107pb,double mistag gluon probability is equal to10?6,fake probability of gluon is of order10?4.Therefore the contribution from gg→ggg process is estimated to be equal to?10?2pb(we use combinatoric factor3here)and one can neglect it.
In the Table I and Table II all subprocesses giving jbb and jjbb?nal state signature are shown respectively with the corresponding cross sections for the Tevatron and LHC.In our calculations we neglected the double sea quark and c-sea quark small contributions.Total cross section for jbb at the Tevatron(LHC)is240and70(511and362)nb for jbb and jjbb.
The cross section of the jbb process in the Table I is only about2times higher at LHC than at Tevatron because higher jet p T cuts for LHC have been used(20GeV at LHC and10GeV at Tevatron).If the equal jet p T cuts are used the cross section at LHC is about50times higher than that at Tevatron.
We performed two ways of calculation of the jjbˉb process,the complete tree level calculation and the splitting approximation when one uses the complete result from jbˉb with an additional jet radiation from the initial and?nal states.In such a way we have checked the validity of splitting approximation.
As it was expected the splitting approximation works reasonably well for the total rate if rather soft cuts on the additional jet are used and the di?erence increases if the more strong cuts are applied.The Table III illustrates such a di?erence in results for the approximation and exact calculations for various cuts on the p T of the second jet(that is the light jet with the smallest p T which is more likely an additional radiated light jet).
1020
[pb]32 1.2σexact
jjbb
σsplit
[pb]220.25 jjbb
TABLE https://www.doczj.com/doc/492559023.html,parison the cross sections for jjbˉb process for exact calculations and the splitting approximation for various p j2T cuts at Tevatron.The following cuts have been applied at the MC level:?R jj>0.5,p t of the?rst jet>10GeV
Indeed one can see that for p j 2T >10GeV cut the di?erence between exact calculation and the splitting approxi-mation is only about 10%:70nb and 64nb respectively.But after p j 2T >40GeV cut those results di?er almost by factor 5:one has 1.2and 0.25nb for exact calculation of jjb ˉb and splitting approximation respectively.
The expected di?erence in the distribution on the momenta transverse of the second jet is illustrated in Figure
3.The distribution in case of the splitting approximation is signi?cantly softer.
p T of the second jet [GeV]
N u m b e r o f e v e n t s
050010001500200025003000350040004500x 104
5
10
15
20
253035404550FIG.3.Distribution for p T of the second jet for jjb ˉb process for exact calculation (solid line)and for splitting from jb ˉb process (dashed line)at Tevatron.
Since we do not apply high p T cut on jet (one of them fakes electron,for which we apply 15GeV p T cut)the di?erence between exact calculation and the approximation is of order of 25%for the fake background simulation.
C.Signal and background kinematical properties
The rate of the signal and backgrounds presented above clearly shows that even after b -tagging the signal is still more than one order less than the background.This fact requires a special kinematical analysis in order to ?nd out a strategy how to suppress the background and extract the signal in an optimal way.
p T jet max [GeV]
N u m b e r o f e v e n t s
5010015020025030035040020406080100120140160180
200
√s ∧ [GeV]
N u m b e r o f e v e n t s
255075100125150175200225150200250300350400450500550
600
H T [GeV]
N u m b e r o f e v e n t s
50100
15020025030035040050100150200250300350
400
di-jet mass [GeV]
N u m b e r o f e v e n t s
100
200
300
400
500
50100150200250300350
400
FIG.4.Distributions for signal and background for the some most spectacular variables at Tevatron.Sketched histogram
stands for signal.
p T jet max [GeV]
N u m b e r o f e v e n t s
1000
200030004000500060007000x 102
50
100
150
200
√s ∧
[GeV]
N u m b e r o f e v e n t s
200400600800100012001400x 103
500
10001500
2000
H T [GeV]
N u m b e r o f e v e n t s
20040060080010001200x 103200
400
600
800
1000
di-jet mass [GeV]
N u m b e r o f e v e n t s
1000
2000300040005000600070008000x 10
2100
200
300
400
FIG.5.Distributions for signal and background for the some most spectacular variables at LHC.Sketched histogram stands
for signal.
The distributions for several sensitive kinematical variables for a separation of the signal and the background are shown in Fig.4for the Tevatron and in Fig.5for the LHC.The mentioned above e?ects of the jet fragmentation,detector resolution and energy smearing are included in the ?gures.Among the kinematical variables for separation of the signal and background the most attractive were found to be:
?p T of leading jet:
p T of leading jet distribution for the signal has a peak around m top /3,while it is much softer for QCD back-ground at Tevatron(Fig.4).The main di?erence between kinematical distributions for signal and background at Tevatron is that jets from W +jj and j (j )bb processes are softer and less central than those for signal with one very hard jet coming from top and another softer jet,accompanying top quark.For LHC there is no such striking di?erence in p T of leading jet distribution between signal and background.It happens because of higher
CM energy and dominating contribution to the background from t ˉt
production (Fig.5)?
√
?p T W:W boson tends to be harder from top-quark decay than from QCD processes.
?scalar transverse energy H T(Fig.4c,5c),H T=|E T(jet1)|+|E T(jet2)|+|E T(lepton)|:
this kinematical variable has peak around150GeV for signal,around300GeV for tˉt background and peaks at the small values for QCD background.
?di-jet mass(Fig.4,5):
It is harder for signal than for QCD background,for which bˉb-pair coming mainly from gluon splitting,in the same time di-jet mass distribution of tˉt background has similar shape with the signal.Di-jet mass cut is also used for a reduction of WZ background.
In our analysis we used”e?ective”invariant top quark mass variable which is constructed using the following algorithm.It is clear that mass of the top quark decaying to lepton,neutrino and b-quark can not be unambiguously reconstructed since z-component of neutrino can not be measured.One can construct top quark mass
m2t=(P e+Pν+P b)2(2) using,one of two solutions for p zνof simple quadratic equation1
m2W=(P e+Pν)2=80.122(3) Our Monte Carlo analysis shows that if one chooses p zνto be the|p zν|min from two solutions than it will be in about
70%true p zν.In fact the reason for that is obvious and related to the fact that smaller values of p zνcorrespond in most
√s the e?ective parton-parton cases to smaller values of the total invariant mass
luminosity is larger and therefore the cross section is higher.However anyway if the one solution for p zνis used the invariant”e?ective”mass distribution is broader than real invariant top quark mass and one should apply rather wide window for this kinematical variable in order not to lose too much signal events.We chose±50GeV window in our analysis.
Based on such di?erent behaviors of the signal and background kinematical distributions the following set of cuts for the background suppression has been worked out:
Cut1:?R jj(ej)>0.5,p T jet>10GeV,/E T>15GeV,p t e>15GeV for Tevatron
and?R jj(ej)>0.5,p t jet>20GeV,/E T>20GeV,p t e>20GeV for LHC
which are”initial”cuts for jet separation and W?boson identi?cation
Cut2:p t jet max>45GeV
√
Cut3:
signal W jj j(j)bˉb W H
1.986·102
2.644·102 6.292·1028.428·100 Cut2 1.711·102 1.136·101 4.898·102
1.493·1029.211·101 1.030·102 6.278·100
1Such a method of the single top quark mass reconstruction is known and has been used in the past(see,C.-P.Yuan,Phys. Rev.D41,42(1990))
2The numbers for the LHC could be easily rescaled to the30fb?1of the low luminosity LHC operation.
1.295·102
7.687·1018.910·101 5.145·100Cut 5 1.107·1028.515·100 4.186·1021.249·102 6.649·101 6.961·101 5.013·100Cut 7
1.031·102
7.419·100
1.055·102
1.216·102
6.141·101
3.619·101
4.490·100
signal W jj
j (j )b ˉb W H
1.212·106
1.724·105 1.155·106 6.124·103Cut 2 5.143·104 1.177·104 3.762·1068.764·105 1.015·105 6.053·105 4.854·103Cut 4 3.826·1049.048·103 3.262·1067.401·1057.735·104 4.957·105 3.972·103Cut 6 3.649·104
7.545·103
6.214·1055.370·105
7.408·104
2.411·105
2.740·103
Cut 8
3.177·104 6.030·103
1.886·105
Signal:5.3·105,Background:5.3·105;S/B=1.0
TABLE V.Number of events for single top signal and background at LHC.Cuts numbering correspond to
(4)set of cuts with their consequent application.Window ±50GeV around 175GeV bin was imposed for reconstructed ”e?ective”top mass.
?From the tables one can see that in fact two cuts,Cut 2reducing the QCD +W jj background and Cut 7eliminating t ˉt
background,play the leading role.In the same time all cuts are strongly correlated and one can e?ectively replace Cut 2by Cut3+4or more complicated combination with the same success.
The strong background reduction is clearly illustrated in Fig.6a,b,7a,b for the invariant top mass distribution before (a)and after (b)application of kinematical cuts.After cuts applied the background became about 10times smaller at the Tevatron and 18times at the LHC while approximately 60%(40%)of signal survived at Tevatron (LHC).Signal/background ratio becomes equal approximately to 0.4at Tevatron and 1at LHC.Such a background suppression will allow to measure the signal cross section with the high accuracy.
top mass [GeV]
N u m b e r o f e v e n t s
50
100
150
200
250
50100150200250300350400
top mass [GeV]
N u m b e r o f e v e n t s
5
101520
25303540455050100150200250300350400
(a)
(b)
FIG.6.Distributions for invariant top mass before (a)and after (b)cut application at Tevatron.Sketched histogram stands for signal.
top mass [GeV]
N u m b e r o f e v e n t s
20040060080010001200x 103
100200300400
top mass [GeV]
N u m b e r o f e v e n t s
200400600800100012001400x 102
100200300400
(a)
(b)
FIG.7.Distributions for invariant top mass before (a)and after (b)cut application at LHC.Sketched histogram stands
for signal.
The cross section for single top quarks includes the W tb coupling directly,in contrast to t ˉt
pair production.Therefore,single top production provides a unique opportunity to study the W tb structure and to measure V tb .Experimental studies of this type are among the main goals of the single top https://www.doczj.com/doc/492559023.html,ing the single top quark search one can examine the e?ects of a deviation in the W tb coupling from the SM structure and directly measure the CKM matrix element V tb .Since the signal to background ratio is high after kinematical cuts applied the error of V tb measurement as was shown in [8]is expected to be of order of 10%at the Tevatron RUN2.In the same time much higher statistics and good signal/background ratio at LHC allow considerably improve the measurement of V tb value and test W tb vertex.Since statistical error for 105events is less then 1%,then uncertainty of W tb vertex measurement at LHC depends mostly on the uncertainty of theoretical calculations for single top quark production cross section and for the backgrounds.That is why calculations of the next order corrections to the single top quark production including the corrections to the kinematical distributions but not only to the total events rate and a simulation of main backgrounds at the NLO level are important for the LHC.
Another important source of uncertainties in the W tb vertex measurement comes from parton distribution uncer-tainty as well as from the accuracy of top-quark measurement.In case of Tevatron these uncertainties have been included into consideration [8].However in case of LHC this point is not very clear since one does not know how large those uncertainties would remain when the experiment will start,and the parton distribution functions and the top mass will be measured in separate experiments.That is why at present stage we did not include the pointed uncertainties for the case of LHC.
III.CONCLUSIONS
The study of the single top-quark production versus complete background processes has been done.For calculations a special generator has been created based on the CompHEP and PYTHIA/JETSET programs.The computation shows the importance of the QCD fake background which was not taken into account in the previous papers.Study of the e?ects of the initial and ?nal state radiation for jbb process shows that such an approximative method of simulation of higher jet multiplicity process has the accuracy of order 10%or less for the rate and gives signi?cantly softer p T distribution of the radiating jet comparing to the complete calculations.
It was shown that after optimized cuts applied the signal from the single top quark can be extracted from the background with the signal to background ratio about 0.4for the upgraded Tevatron and 1for the LHC.The remaining after cuts single top rate in the lepton +jets mode is expected to be about 120events at the upgraded Tevatron and about 1.6·105events at the low luminosity LHC operation with 30fb ?1accumulated data and assumptions made above.One can expect that Vtb CKM matrix element can be measured at upgraded Tevatron with an accuracy about 10%and hopefully with an accuracy of the order of few %at LHC.
Acknowledgments
Authors are grateful to members of the single top group of the D0collaboration for useful discussions.
A.B.is grateful to S.F.Novaes for fruitful discussions,thank the Instituto de F′?sica Te′o rica for its kind hospitality and acknowledges support from Funda?c?a o de Amparo`a Pesquisa do Estado de S?a o Paulo(FAPESP).
E.B.would like to thank H.Anlauf,P.Manakos,T.Ohl,A.Pukhov,V.Savrin,J.Smith,C.-P.Yuan,and B.-L.Young for discussions of di?erent aspects of calculations used,he wishes to acknowledge the KEK Minami-Tateya (GRACE)collaboration for the kind hospitality during his visit at KEK and his colleagues from the CompHEP group for the interest and support.
E.B.and L.D.acknowledge the?nancial support of the Russian Foundation of Basic Research(grant No96-02-19773a),the Russian Ministry of Science and Technologies,and the Sankt-Petersburg Grant Center.
[14]A.Belyaev,E.Boos,L.Dudko,A.Pukhov“W+2Jets Production at Tevatron:Vecbos and CompHEP Comparison”,
D0-NOTE-2784,(1995),unpublished;hep-ph/9511306
[15]TeV-2000Study Group(D.Amidei et al.),FERMILAB-PUB-96-082.
[16]J.Ohnemus,Phys.Rev.D44,3477(1991)
[17]T.Han and S.Willenbrock,Phys.Lett B273,167(1991)
J.Ohnemus and W.J.Stirling,Phys.Rev.D47,2722(1993)
H.Baer,B.Baiely and J.Owens,Phys.Rev.D47,2730(1993)
[18]D0Collaboration(S.Abachi et al.),Phys.Rev.D52,4877(1995)
［摘要］夸克－胶子等离子体是当今粒子物理领域的重要研究课题，它不仅能揭示微观粒子的物理性质，还能帮助人们认识宇宙的演化过程。本文对夸克－胶子等离子体的研究现状进行了概述。［关键词］夸克－胶子等离子体；高能重离子碰撞浅谈现代粒子物理前沿问题———夸克－胶子等离子体 傅永平 郗勤 （临沧师范高等专科学校数理系，云南临沧 ６７７０００） 1研究夸克-胶子等离子体的科学意义 按照目前的实验观测结果，已知的物质最小构成单元是夸克和轻子，比如质子和中子就是由上夸克和下夸克组成的三夸克色禁闭束缚态，而介子则是双夸克色禁闭束缚态。我们熟知的电子就是轻子的一种。如果用质量来标度，夸克和轻子可以分为三代，每一代有２种夸克和轻子，其中夸克包括上夸克、下夸克、奇夸克、璨夸克、顶夸克和低夸克，轻子包括电子、电子中微子、μ子、μ子中微子、τ子和τ子中微子。 夸克－胶子等离子体是区别于强子的一种新的物质形态，夸克不再是以强子型的双夸克或三夸克色禁闭束缚态形式存在，夸克－胶子等离子体中的夸克是色相互作用渐近自由的，夸克与夸克之间，夸克与多夸克之间存在自由的色相互作用，这是一种多体夸克凝聚的新物质形态。 宇宙大爆炸初期宇宙的温度约为１０２８ ｅＶ，按照标准模型，当时可 能存在的物质只有轻子和夸克，此时夸克的色自由度是解禁的，就会形成夸克－胶子等离子体。之后随着宇宙不断膨胀，温度下降到１００ＭｅＶ时，夸克物质发生对称性破缺，开始冻结成为质子和中子。从夸克物质演化的意义来讲，研究夸克－胶子等离子体不仅对基本粒子物理研究意义重大，而且对于宇宙演化的研究来讲也具有重要意义。 2实验概况 实验表明，高能重离子碰撞有可能产生核子的多重碰撞，使能量主要集中在质心附近。也即一个核的核子有可能和另一个核的不同核子发生多次碰撞，而不是仅发生一次碰撞便飞离质心区域，这样在一个很短的驰豫时间内，能量可以集中在质心附近，从而产生夸克－胶子等离子体。为更好地解释在高能重离子碰撞过程中，能量如何主要聚集在质心附近，引入核阻塞能力的概念，它表征重离子碰撞过程中一个入射核子与另一个核碰撞时所受到核物质的阻塞程度，如果多重碰撞程度越高，阻塞能力也就越大，出射核子所携带的能量就越小，那么聚集在质心附近的能量就越高，也就越容易产生夸克－胶子等离子体。多重碰撞及核阻塞能力的研究，在高能重离子碰撞产生夸克－胶子等离子体方面具有重要作用。 实验物理学家们正在尝试着利用高能重离子碰撞实验装置，把物质的温度和密度在一个很小的时空区域内提升到大爆炸的初始阶段，即把“历史”退回到存在自由夸克物质的宇宙初期。美国布鲁海文国家实验室（ＢＮＬ）的相对论重离子对撞机（ＲＨＩＣ）能够将金原子核加速到每核子１００ＧｅＶ，碰撞的质心系能量可达３９．４ＴｅＶ。 此外，欧洲核子研究中心（ＣＥＲＮ）的大型强子对撞机（ＬＨＣ）可以把铅原子核加速到每核子２．７６ＴｅＶ的质心系能量。那么碰撞的质心系能量可达到５７４．０８ＴｅＶ。未来ＬＨＣ的质心系能量还将提升到每核子５．５ＴｅＶ，碰撞的质心系能量将达到１１４４ＴｅＶ。ＲＨＩＣ能将金原子核加速到光速的９９．９５％，核粒子束迎头相撞时，每秒钟将会出现上千次的碰撞，每一次碰撞都能在相撞点上产生很高的温度，大约能产生超过１０１２Ｋ的温度，这相当于太阳温度的１万倍。 3探测夸克-胶子等离子体 夸克－胶子等离子体一旦产生就会迅速冷却膨胀，所以其寿命是很短暂的。对于实验物理学家而言，观察其冷却过程中的粒子产生才是观测夸克－胶子等离子体的有效途径。夸克－胶子等离子体在冷却过程中将有大量新粒子产生，其中包括光子、轻子和夸克碎裂产生的强 子。标准模型预言，夸克－胶子等离子体的粒子产生多重数将远大于核子－核子深度非弹性散射的粒子产生，所以通过比较实验结果和理论预言将成为又一检验标准模型正确与否的关键。 如何观测夸克－胶子等离子体不仅是实验关心的问题，也是理论研究的热点。比如研究夸克－胶子等离子体的动力学特征。而要了解它，就必须依赖于从中心区域出射的、且未被其损坏的粒子。这些粒子的最佳候选者就是光子和轻子，因为光子和轻子只参与电磁相互作用和弱相互作用，它们都不会与夸克物质发生强相互作用，对于以强相互作用为主导的过程而言，它们几乎可以不受阻碍地从碰撞中心区域出射并被探测器捕捉到，所以光子和轻子都可以携带中心区域夸克物质的动力学信息，通过研究它们便可以了解自由夸克物质的动力学特征及规律。 在高能重离子碰撞过程中有以下三种主要的光子产生源，首先是初始冷组分部分子碰撞产生的快光子，它们包括夸克、胶子之间的湮灭和康普顿过程产生的直接光子，还包括由末态部分子在真空中碎裂产生的光子。还有喷注通过热媒介时，与热部分子相互作用也会产生光子。由于初始部分子碰撞过程中的转移动量很高，强相互作用跑动耦合常数小于１，这些光子的产生机制可以利用微扰量子色动力学和量子电动力学来处理。此外，在热夸克物质的平衡相中，热光子将由热夸克和热胶子的湮灭和康普顿过程产生，由于夸克－胶子等离子体的热光子主要集中在低横动量区域，所以微扰论很难处理。 只能依靠有限温度场论以及有效热质量截断等技术来解释夸克－胶子等离子体的热光子产生。最近，有的学者提出了一种新的理论来解释热光子的产生机制，称为共形反常。在夸克－胶子等离子体中存在共形不变对称性的破缺，这种破缺机制直接导致了色单态热部分子之间的相互作用产生热光子。光子产生的最后一个主要来源是碰撞演化末态的强子物质，热强子气体之间主要通过介子相互作用产生热光子，其中介子主要是轻介子，目前关于强子气体模型已经把奇异介子也包含进来了。来自ＲＨＩＣ的ＰＨＥＮＩＸ实验组和ＬＨＣ的ＣＭＳ实验组得到的光子实验数据能较好地与理论计算结果相吻合。 对于高能重离子碰撞中双轻子的产生机制，与光子产生过程完全类似，只需要将实光子变换为虚光子即可，因为双轻子主要由虚光子衰变而来。理论表明来自于夸克－胶子等离子体的热双轻子在低不变质量区域产率最大，但是热双轻子在这个区域的贡献被众多的强子衰变谱所掩盖，热双轻子唯一占主导的区域是在中间不变质量区域。但中间不变质量区域的双轻子数据同样能用粲粒子衰变来解释。不过来自ＮＡ６０实验组的数据表明较之粲粒子衰变谱，中间不变质量区域的双轻子数据有一个抬高，这个抬高有可能是来自热双轻子的贡献。 除此之外，对于ＲＨＩＣ的双轻子实验而言，仍存在着不少公开问题。其中之一就是低横动量双轻子数据在低不变质量区域较之强子衰变的理论预言有一个２到３倍的抬高现象。这种抬高现象可以通过热媒介中矢量介子由于手征部分恢复而发生质量移动来部分地得到解释，但仍无法完全解释抬高现象。最近，ＰＨＥＮＩＸ实验组得到的高横动量双轻子不变质量谱也存在实验值高于现有理论预言的抬高现象。来自热双轻子的贡献仍无法解释现有数据。 4小节 本文就目前粒子物理的前沿热点，夸克－胶子等离子体，进行了概述。现有的夸克－胶子等离子体的光子产生实验数据能够与理论计算结果较好地吻合，但是双轻子产生的实验数据在理（下转第４２页）
原子核和强相互作用物质的相变1 刘玉鑫，穆良柱，常雷 1．北京大学物理系, 北京100871 2．北京大学重离子物理教育部重点实验室，北京100871 3．重离子加速器国家实验室理论核物理中心，兰州730000 摘要：简要回顾原子核和强相互作用物质的相结构及相变研究的现状。说明原子核和强相互作用物质的相结构和相变的研究是原子核物理、粒子物理、天体物理、宇宙学和统计物理等领域共同关心重要前沿领域，到目前为止已取得重大进展，但无论是具体实际问题还是研究方法等方面都需要系统深入的研究。 关键词：原子核物理；强相互作用物质；相与相变 1 引言 100年前，爱因斯坦通过分析充满空腔的辐射系统的熵与充满空腔的气体系统的熵，提出电磁辐射由光量子组成[1,2] ，从而建立了光子的概念，吹响了引导人们探索微观世界的冲锋号。进一步的深入研究表明，组成物质世界的粒子可以分为强子和轻子两类，粒子间的相互作用可以分为引力作用、电磁作用、弱作用和强作用4类。参与强相互作用的粒子或具有强相互作用的系统统称为强相互作用物质（包括强子物质、夸克物质等）及其特殊形式——原子核（由有限个强子组成的系统），对原子核和强相互作用系统的相结构及相变的研究，对于认识强相互作用系统的相结构、相变，了解宇宙的起源和演化至关重要，并且可能是有限系统的统计物理的检验平台。因此，近年来关于原子核和强相互作用系统的相变的研究不仅是原子核物理、天体物理、宇宙学及粒子物理等领域研究的重要前沿课题，还引起了有限量子多体系统领域和统计物理学界的极大关注。本文简要介绍原子核及强相互作用系统的相及相变研究的现状。 2 原子核的相及相变 2.1 原子核的单粒子运动与集体运动 原子核是有限数目的强子组成的束缚系统，其中的核子（质子和中子）自然具有单粒子运动，并建立壳模型成功的描述原子核的相应性质。实验上对原子核的能谱和电磁跃迁等的研究表明，原子核还具有整体运动，并建立了原子核具有形状和振动、转动等集体运动模式的概念。人们通常利用将核半径按球谐函数),(?θlm Y 展开来描述原子核的形状，并将相应的形变称为l 2极形变（如图1所示）。已经观测到和已经预言的原子核形状多种多样[3,4]，比较重要的是四极形变，实验上已经观测到的最高极形变是16极形变[3,4]。按照壳模型和集体模型的观点， 幻数核多为球 1基金项目：国家自然科学基金（10425521, 10135030）、国家重点基础研究发展规划（G2000077400）、教育部优秀青年教师奖励计划项目、教育部博士点专项研究基金（20040001010） 作者简介：刘玉鑫，男，博士，北京大学物理系教授，主要研究方向为原子核理论、强相互作用物质理论及QCD 相变、物理学中的群论方法及计算物理等方面的研究工作；中国物理学会会员（S020001000M ）,E-mail: liuyx@https://www.doczj.com/doc/492559023.html, 。
核子结构论文夸克论文 基于强子袋模型的核子特征参数 摘要：我们把高能核碰撞环境下的核子质量看作是它的整个静止能量，它可以分为分别来自内部夸克和胶子的两部分。我们采用袋模型的本质意义去讨论核子的结构，发现我们计算得出的温度、核子半径、袋常数等参量均是可以接受的，如果我们把这样环境下的核子看成是一个由夸克和胶子组成的局域热平衡系统的话。 Abstract: We treat the mass of a proton as the total static energy which can be separated into two parts that come from the contribution of quarks and gluons respectively. We adopt the essential meaning of the bag model of hadron to discuss the structure of a proton and find that the calculated temperature, proton radius, the bag constant are acceptable if a proton is a thermal equilibrium system of quarks and gluons. 关键词：高能碰撞；核子；半径；夸克；袋模型 Key words: high-energy collision；nucleon；radium；quark；bag model 1概述 探索核子的内部结构一直是人们了解强相互作用的一个最重要课题之一。它也有助于人们去寻找强相互作用下新的一种物质形态-夸克胶子等离子体（QGP）。对这一问题的理论研究主要集中在量子色动力学（QCD）[1]。当然，也存在一些关于核子结构和其特征参
物质的形态有几种
————————————————————————————————作者：————————————————————————————————日期：
物质的形态有几种 在生活中，我们常见到的物质的形态有三种，分别为固态、液态和气态。其特性如下：固体具有一定的形状，不容易被压缩; 液体没有固定的形状，具有流动性; 气体没有一定的形状，容易压缩，具有流动性。 那么，是不是物质的形态只有这三种呢？答案是否定的。 物质的形态有许多种，除了常见的固态、液态和气态外，还有等离子态、“夸克—胶子”等离子态、超流态、凝聚态、费米子凝聚态、“波色——爱因斯坦”凝聚态、超固态、简并态、中子态、超导态等，一般只有在实验室环境内才能见到这些另类的形态。 各种另类形态的介绍 等离子态 将气体加热，当其原子达到几千甚至上万摄氏度时，电子就会被原子"甩"掉，原子变成只带正电荷的离子。此时，电子和离子带的电荷相反，但数量相等，这种状态称做等离子态。 “夸克—胶子”等离子态 夸克-胶子等离子体顾名思义含有夸克与胶子，如同普通（强子）物质。这两种QCD的相态不同处在于：普通物质里，夸克要不是与反夸克成双成对而构成介子，或与另两个夸克构成重子（例如质子与中子）。在QGP，相对地，这些介子与强子失去了身分，而成为更大一坨的夸克与胶子。在普通物质，夸克是呈现色约束的；在QGP，夸克则不受约束。 超流态 超流体是一种物质状态，特点是完全缺乏黏性。如果将超流体放置于环状的容器中，由于没有摩擦力，它可以永无止尽地流动。它能以零阻力通过微管，甚至能从碗中向上“滴” 出而逃逸。 凝聚态 所谓“凝聚态”，指的是由大量粒子组成，并且粒子间有很强相互作用的系统。自然界中存在着各种各样的凝聚态物质。固态和液态是最常见的凝聚态。低温下的超流态，超导态，玻色- 爱因斯坦凝聚态，磁介质中的铁磁态，反铁磁态等，也都是凝聚态。
高能核物理前沿：探寻夸克－ 胶子等离子体 马余刚 对于我们身处的物质世界，现代物理学认为它是起源于约150亿至200亿年前的一次宇宙大爆炸。在宇宙的早期，物质的温度和密度都相当大，整个宇宙体系达到平衡。初始的宇宙间只有正反夸克、轻子、胶子等一些基本粒子形态的物质。宙间的物质主要是质子、电子、光 子和一些比较轻的原子核。当温度 降到几千度时，辐射减退，宇宙间 主要是气态物质，气体逐渐凝聚成 气云，再进一步形成各种各样的恒 星体系，成为我们今天看到的宇宙。 宇宙大爆炸学说是现代宇宙 生指出：20世纪物理学存在两大 疑难，其一是对称性丢失，其二是 夸克禁闭，疑难的解决，可能与真 空的结构有关。人们预期通过相对 论重离子碰撞形成高温高密极端条 件，改变真空的性质，从而解除夸 克禁闭产生出一种在夸克层次上的 图1 宇宙演化的示意图 （引自：D. E. Groom et al., Particle Data Group, The European Physical Journal C15 （2000））
图2 位于RHIC对撞机上的STAR探测器图示
3Λ）的衰变产物。 (a)(b) 得到碰撞顶点之后,对与碰撞顶点图3 STAR-TPC上探测到的粒子径迹。其中反氦3（3He）和p+是超氚核（H
4 高能重离子碰撞中产生的热密物质的化学势（a）、温度（b）随碰撞的质心系能量的关系 强作用物质的相图：数据点来自（a）、（b），曲线分别表示了宇宙早期的演化、格点QCD和口袋模型的计算得到的相边界。圆点代表数据。三角点代表可能的相变临界终点（引自：P. Braun-Munzinger，J.Stachel，The quest for the quark–gluon plasma，Nature448 302（2007））
冷夸克物质中的“夸克凝聚”现象 来小禹徐仁新 中国，北京，北京大学物理学院，核物理与技术国家重点实验室 100871 摘要：有人提出，冷夸克物质中，在几个核密度下，由于强相互作用夸克会聚在一起形成“夸克簇”。这是因为在那里夸克间的弱耦合相互作用会显不足。如果簇间的势足够深，以至于能局部化晶格集群，那么我们可以推测冷夸克物质将会以固体状态出现（即形成晶体结构）。冷夸克物质这样的一种固体状态对于我们理解脉冲星那样的小体积的星体的不同表现形式是十分必要的，它并不服从第一原则。 关键词：夸克物质，中子星，脉冲星，核物质，量子色动力学。 PACS21.65.Qr, 97.60.Jd, 97.60.Gb 一、超核密度下物质物理性质的介绍 一方面，在超核密度下，对于冷物质的物理性质，脉冲星那样的小体积星体是绝好的实验室，它们无疑和夸克间基本的色相互作用有着密切联系。然而，对今天的物理学家来说，其中的挑战之一就是如何理解低能级下的强相互作用。尽管量子色动力学（QCD）被认为是描述初级强相互作用的基础理论，在高能级也已经被很好地检验，但是其在低能级下的非微扰性质使得我们在处理强相互作用下的粒子系统时非常棘手，尤其是几个核密度尺度下的冷物质情况。 另一方面，对于天体物理学家，理解脉冲星那样的小体积星体也是一个挑战，尽管第一颗脉冲星已经发现40多年了。特别关心的是这样的小体积星体的密度是否足够的高以至于导致非禁闭夸克（夸克物质）的出现。对比那些主导自由度为强子的中子星，由去掉禁制的夸克（及可能的胶子）作为主导自由度而组成的星体被称为夸克星（或者叫做奇异星体——因为奇夸克的存在）。存在可能的观测证据指出，脉冲星这样的星体就是夸克星。制作（形成）夸克星取决于冷夸克物质在超核密度下的状态，然而不幸的是，由于量子色