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FCNC Top Quark Decays in Extra Dimensions G.A.Gonz′a lez-Sprinberg ?Instituto de F′?sica,Facultad de Ciencias,Universidad de la Rep′u blica Montevideo,Uruguay R.Mart′?nez ?and J.-Alexis Rodriguez ?Departamento de F′?sica,Universidad Nacional de Colombia Bogot′a ,Colombia Abstract The ?avor changing neutral top quark decay t →cX is computed,where X is a neutral standard model particle,in a extended model with a single extra dimension.The cases for the photon,X =γ,and a Standard Model Higgs boson,X =H ,are analyzed in detail in a non-linear R ξgauge.We ?nd that the branching ratios can be enhanced by the dynamics originated in the extra dimension.In the limit where 1/R >>m t ,we have found Br (t →cγ)?10?10for 1/R =0.5T eV .For the decay t →cH ,we have found Br (t →cH )?10?10for a low Higgs mass value.The branching ratios go to zero when 1/R →∞.
I.INTRODUCTION
Flavor changing neutral currents(FCNC)are very suppressed in the standard model (SM):there are no tree level contributions and at one loop level the charged currents operate with the Glashow-Iliopoulos-Maiani(GIM)mechanism.The branching ratio for top quark FCNC decays into charm quarks are of the order of10?11for t→cg and10?13for t→cγ,(Z)in the framework of the SM[1,2].This suppression can be traced back to the loop amplitudes:they are controlled by down-type quarks,mainly by the bottom quark, resulting in a m4b/M4W factor which can be compared to the enhancement factor that appears in the b→sγprocess where the top quark mass m t is involved instead of m b in this factor. This fourth power mass ratio is generated by the GIM mechanism and is responsible for the suppression beyond naive expectations based on dimensional analysis,power counting and Cabibbo-Kobayashi-Maskawa(CKM)-matrix elements involved.The top quark decay into the SM Higgs boson is even more suppressed[1,2]:Br(t→cH)～10?13?10?15for
M Z≤M H≤2M W.These rates are far below the reach of any foreseen high luminosity collider in the future.The highest FCNC top quark rate in the SM is t→cg,but this value is still six orders of magnitude below the possibility of observation at the LHC.
The discovery of these FCNC e?ects would be a hint of new physics because of the large suppression in the SM.These FCNC decay modes can be strongly enhanced in scenarios beyond the SM,where some of them could be even observed at the LHC or ILC.New physics e?ects in extended Higgs sector models,SUSY and left-right symmetric models were studied in references[1-5].For example,in various SUSY scenarios the branching ratios can go up to the value10?5for the decay t→cg.Also,virtual e?ects of a Z′gauge boson on these rare top quark decays were studied.The decay t→cγhas been analyzed in reference[6],it has been shown that B(t→cγ)is at the10?6level in topcolor assisted technicolor models for m′Z=1T eV,which would allow the detection of this process at future colliders.
On the other hand,the use of e?ective Lagrangians in parameterizing physics beyond the SM has been studied extensively in FCNC top quark couplings and decays[7,8,9].This formalism generates a model-independent parameterization of any new physics characterized by higher dimension operators.Under this approach,several FCNC transitions have been also signi?cantly constrained:t→cγ[10,11],t→cg[11,12],l i→l jγ[13]and H→l i l j [14].
New physics e?ects have also been introduced in models with large extra dimensions(ED)
[15].In recent years,these models have been a major source of inspiration for beyond the
SM physics in the ongoing research.In these scenarios the four dimensional SM emerges
as the low energy e?ective theory of models living in more than four dimensions,where
these extra dimensions are orbifolded.The presence of in?nite towers of Kaluza-Klein(KK)
modes are the remanent of the extended dimensional dynamics at low energies.The size
of the extra dimensions can be unexpectedly large,with1/R at the scale of a few T eV
without contradicting the present experimental data[16].Then,if these KK-modes are
light enough,they could be produced in the near future at the next generation of colliders.
Scenarios where all the SM?elds,fermions as well as bosons,propagate in the bulk are
known as”universal extra dimensions”[17,18].In these theories the number of KK-modes
is conserved at each elementary vertex and the coupling of any excited KK-mode to two
zero modes is prohibited.Then the constraints on the size of the extra dimensions obtained
from the SM precision measurements are less stringent than in the case where there is no
conservation of the KK particles(non universal extra dimensions).
The impact of the new physics coming from UED models has been widely studied and
constraints on the parameter1/R have been obtained.Analysis of the precision electroweak
observables led to the lower bound1/R 700?800GeV for a light Higgs boson mass and
to1/R 300?400GeV for a heavy Higgs boson mass[19].On the other hand,using the
process b→sγ,the resulting bound on the inverse compacti?cation radius is1/R 250GeV
[20].Moreover,a recent analysis making use of the exclusive branching ratio B→K?γshows
that under conservative assumptions1/R 250GeV[21].And from the inclusive radiative ˉB→X
γdecay,a lower bound on1/R 600GeV at95%C.L.can be obtained and it is s
independent of the Higgs boson mass value[22].Contributions from UED models have been
considered on several FCNC processes,reference[23]has found that the processes K L→π0e+e?,?M s,K+→π+νˉν,K L→π0νˉν,B d,s→X d,sνˉν,K L→μ+μ?,B d,s→μ+μ?,B→X sμ+μ?for1/R≈300GeV are enhanced relative to the SM expectation and the processes B→X sγ,B→X s g,?′/?are suppressed respect to the SM.In general,the present data on FCNC processes are consistent with1/R 300GeV[23,24].Exclusive B→K?l+l?,B→K?νˉνand B s decays[21,25]have been studied in the framework of the UED scenario and also rare semileptonicΛb decays[26].
In this paper we study the FCNC decays of the top quark in a universal extra dimension
theory where all the SM?elds live in?ve dimensions.In particular,we compute the t→cγand t→cH decay modes in a non linear Rξ.This gauge has the advantage of a reduced number of Feynman diagrams as well as simpli?ed Ward identities.These facts facilitates and clarify the calculation.
The paper is organized as follows:in section II we present the general framework for the ?ve dimensional Lagrangian and derive the corresponding four dimensional Lagrangian and Feynman rules.In section III and IV we compute the decays mode t→cγand t→cH respectively,and discuss the hypothesis implicit in the calculation.Finally,in section V we present some conclusions.In the Appendix(section VI)we show the terms in the Lagrangian that are important for the Feynman rules in our calculation.
II.THE MODEL
We begin presenting the SM Lagrangian in?ve dimensions;let x=0,1,2,3be the normal coordinates and x4=y the?fth one.The?fth extra dimension is compacti?ed on the orbifold S1/Z2orbifold of size R which is the compati?cation radius.We consider a generalization of the SM where the fermions,the gauge bosons and the Higgs doublet propagate in the?ve dimensions.The Lagrangian L can be written as
L= d4x dy(L A+L H+L F+L Y)(1) with
L A=?14B MN B MN,
L H=(D MΦ)?D MΦ?V(Φ),
L F= U(iΓM D M)U+
Q Y uΦc U?
gamma matricesΓM areΓμ=γμandΓ4=iγ5with the metric tensor given by g MN=
(+,?,?,?,?).The matter?elds Q,D and U are fermionic four components spinors with
the same quantum numbers as the corresponding SM?elds.To simplify the notation we
have suppressed the SU(2)and color indices.The standard and charge conjugate doublet
standard Higgs?elds are denoted byΦ(x,y)andΦc(x,y)=iτ2Φ?(x,y); Y u,d are the Yukawa matrices in the?ve dimensional theory responsible for the mixing of di?erent families whose
indices were suppressed in the notation for simplicity.We have not included in Eq.(2)the
leptonic sector nor the SU(3)c dynamics because it is not relevant for our proposes.The low
energy theory will only have zero modes for?elds that are even under Z2symmetry:this is
the case for the Higgs doublet that we choose to be even under this symmetry in order to
have a standard zero mode Higgs?eld.The Fourier expansions of the?elds are given by:
Bμ(x,y)=1
πR
B(0)μ(x)+
√
πR
∞
n=1B(n)μ(x)cos ny
2
R ,
Q(x,y)=1
πR
Q(0)
L
(x)+
√
πR
∞
n=1 Q(n)L(x)cos ny R ,
U(x,y)=1
πR
U(0)
R
(x)+
√
πR
∞
n=1 U(n)R(x)cos ny R ,
D(x,y)=1
πR
D(0)
R
(x)+
√
πR
∞
n=1 D(n)R(x)cos ny R .(3)
The expansions for Bμand B5are similar to the expansions for the gauge?elds and the Higgs doublet(but this last one without theμor5Lorentz index).It is by integrating the?fth y component in Eq.(1)that we obtain the usual interaction terms and the KK spectrum for ED models.
The interaction terms relevant for our calculation will be written in a non-linear Rξgauge(see for details[27]and the?rst reference in[5]).For example,in this gauge there is no mixing between the gauge bosons and the charged and neutral unphysical Higgs?elds. Besides,the interaction terms are simpli?ed in such a way that there are no trilinear terms
such as W+μG?
W Aμ,where G?
W
is an unphysical Higgs?eld.We are interested in the third
family of quarks and Q(n)t and Q(n)
b
are the upper and lower parts of the doublet Q.Similarly,
the U(n)t and D(n)
b
are the KK modes of the usual right-handed singlet top and bottom quarks, respectively.There is a mixing between the mass and gauge eigenstates of the KK top quarks
(Q(n)t and U(n)t)where the mixing angle is given by tan(2αn t)=m t/m n with m n=n/R.For the b quark the mixing is quite similar,but at leading order the only masses that remain are m t and m n and in this limit the mixing angle is zero.This leads to the spectrum
m Q n
b =m n and m Q n
t
=m U n=
M W 4
1?m2V
Γ(t→cγ)SM?
( n(M W/m n)2)2
The sum on the KK tower of excited states can be evaluated as we will explain later in the text and we obtain
Γ(t →cγ)ED
36 (M W /(1/R ))
26c 2W π2m 2t
??αk μ(2 F R 2m t )ˉu c σαμP R u t (11)where c W is the cosine of the weak mixing angle and the form factors F R 2and F R 2
are related by F R 2m t =
eg 229π2s 4w c 4w
|F R 2|2≈4.8×10?7|F R 2|2.(13)
In order to perform the one loop calculation,we consider two scenarios.The?rst one, when the mass of the excited states associated to the quarks from the three low-energy families are quasi-degenerated at tree level,without any kind of radiative corrections to KK masses.In this case,when the excitations coming from the other quarks are taken into account,the transition amplitude for the process t→cγtakes the form
∝ i=d,s,b V ti V?ci1
m2b
(n/R)2
FIG.1:Diagrams contributing to the t→cγdecay in the non linear Rξgauge.
Diagrams with G?(n)
W ˉD(n)
b
t(0)
L
in the loop are proportional toλ2b and then to m2b and can be
neglected.
The leading contributions of type1diagrams(see?gure1)to the decay come from the following particles circulating in the loop:
W(n)
5Q(n)
b
Q(n)
b
,W(n)
μ
Q(n)
b
Q(n)
b
,G(n)
W
Q(n)
b
Q(n)
b
,G(n)
W
D(n)
b
D(n)
b
.(15)
where the external photon is coupled to the fermion in the loop.The sum of all these diagrams gives,for the form factor F R2,the following expression
2F R2=2
16π2 10dz
1?z0dw1?w?z
M2
W ,(16)
where the factor X comes from the dimensional regularization tricks of the product of inverse propagators of the particles circulating in the loop
X=m2t z2+m2t wz?m2t z+m2n.(17) The main contribution of type2diagrams(see?gure1)is the one with KK excitation of the standard model gauge boson or a scalar?eld circulating in the loop which are coupled to the external photon:
W(n)
μW(n)
μ
Q(n)
b
,W(n)
5
W(n)
5
Q(n)
b
,G(n)
W
G(n)
W
D(n)
b
,G(n)
W
G(n)
W
Q(n)
b
,
(G(n)
W W(n)
μ
Q(n)
b
+W(n)
μ
G(n)
W
Q(n)
b
).(18)
These terms contribute to the F R 2form factor with the following expression
2F R 2=?g 2e i
X
4(2?3w ?4z +2wz +2z 2)?(1?w ?z ) (w +z )?(w +z ?1/2)m 2b
m 2n :m 2b M 2W .(20)
The numerical estimation of all these contributions is straightforward.All the excited mass terms are proportional to n/R ,except for the electroweak correction coming from the sym-metry breaking.From the numerical point of view this correction does not change the results and can be neglected without modifying the ?nal estimates.Based on these hypothesis,we
can also take X ?m 2n
and,then,the sum over all the KK excited states can be easily done,as
n 1 n 61R 2(21)
where in any numerical estimate 1/R ?O (1)TeV.Thus,within this approximation,the sum over all the excited KK states is equivalent to multiply the results obtained for the ?rst KK excited state by the factor π2/6.The sum of all contributions using equations
(16)and (19)gives,
2F R 2=g 2e 16π2 10dz 1?z 0
dw 12M 2W ≈g 2e
16π2 ?5
M 2W .
(22)By using equations (13)and (12),the numerical value for the decay width is
Γ(t →cγ)=1.65×10?10GeV ,
(23)
for R?1=0.5TeV,and the branching fraction is
Br(t→cγ)≡
Γ(t→cγ)
u c(p)(F L P L+F R P R)u t(k),(25) where F L and F R are form factors.In our notation we identify the external scalar Higgs H with the zero mode Higgs?eld h(0).From this amplitude we can compute the decay width
Γ(t→cH)=m t
m2t 2 |F L|2+|F R|2 .(26)
FIG.2:Feynman diagrams for the t→c H decay in extra dimensions.
The leading diagrams that contribute to the decay are shown in Figure2.The leading group of type1diagrams in?gure2is the one with KK excitations of the SM quarks circulating in the loop which are coupled to the external higgs:
W(n)
μQ(n)
b
D(n)
b
,G(n)
W
Q(n)
b
Q(n)
b
,W(n)
5
Q(n)
b
D(n)
b
.(27)
In this case,the external Higgs is coupled to the excited quark Q b generating a ?avor
changing ˉQ
(n )D b h (0)(see the appendix),which is proportional to the bottom quark mass m b .The contributions to the F L ,F R form factors are of the order of zero at leading order,i .e .F L =F R ≈0.The leading diagrams of type 2in ?gure 2is the one with KK excitations of the standard model gauge bosons and scalar ?elds circulating in the loop which are coupled to the external higgs boson h (0):
W (n )5W (n )5Q (n )b ,G (n )W G (n )W Q (n )
b ,W (n )μW (n )μQ (n )
b ,W (n )μG (n )W Q (n )
b ,
G (n )W W (n )μQ (n )b ,(W (n )5G (n )W Q (n )b +G (n )W W (n )5Q (n )
b ),
(28)
and these contribute to the form factor with the following expressions:
F L =g 3V tb V ?
cb i
X
{2(1?w )m t M W ? (z ?1)(w +z )m 2t +w (z ?2)m 2h
m t
16π2 10dz 1?z 0
dw 1
6m 2n V tb V ?cb i M W
+7
m 2h m t
6m 2n V tb V ?
cb i
important contribution to the loop correction comes from the excited KK states associated to the third generation.The results show a branching ratio that is above the SM one.The branching ratios for these two decay widths are of the order of10?10.
There is a strong dependence on top quark mass m t in the amplitude of the t→cH process,it is coming from the type2diagrams in?gure2with an excited scalar in the loop, resulting in a m3t/M3W factor.When we take the limit m n?m t,we?nd that the decay
widths for the t→cγ,(H)processes are decoupled respect to the new scale1/R and they go to zero.Considering that the excited states of the quarks are quasi-degenerated and the unitarity of the CKM matrix,the amplitudes for the?avor changing decay t?c due to the contribution of the excited states of the quarks,are suppressed by the factor(m b/(n/R))2, and the predicted values are smaller than the SM predictions.
VI.ACKNOWLEDGEMENTS
R.Martinez acknowledge the?nancial support from Fundacin Banco de la Republica. VII.APPENDIX
The Lagrangian can be separated in di?erent terms as in the following sum:
L= m=1,2,3∞ n=1L(n)m.(31) After symmetry breaking the interaction terms are included in the terms L(n)1up to L(n)3. The?rst one,L(n)1is
L(n)1=gm t
2M W
ˉQ(n)
bL
t(0)
R
G?(n)
W?
gm b
2M W
ˉD(n)
bR
t(0)
L
G?(n)
W
+h.c.(32)
The second term,L(n)2has the excited gauge boson-fermion interactions:
L(n)2=2
√
√
R
A(0)μ W?(n)μW+(n)5?W+(n)μW?(n)5 +h.c. (33)
And the third term has the neutral Higgs boson interactions:
L (n )3=?gm t
2M W
ˉQ (n )b D (n )b h (0)+gM W W +(n )5W ?(n )5h (0)+gM W W +(n )μW ?(n )μh
(0)?gm 2h
2n
2W +(n )μh (0)?μG ?(n )W +h.c. (34)
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［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/2f11791369.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
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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