Heavy Quark Production Asymmetries
Calculation of the D and B Meson Lifetimes
Abstract Using the expansions of the heavy meson decay widths in the heavy quark mass and QCD sum rules for estimates of corresponding matrix elements, we calculate the D ±,o,s decay widths and the B ±,o,s lifetime differences. The results for D mesons are in agreement with the data, while it is predicted that [Γ(B o ) − Γ(B − )]/ΓB ≃ 4% , and the lifetime difference of the B o and Bs mesons is even smaller. The role of the weak annihilation and Pauli interference contributions to the lifetime differences are described in detail. In the course of self-consistent calculations the values of many parameters crucial for calculations with charmed and beauty mesons are found. In particular, the perturbative pole quark masses are: Mc ≃ 1.65 GeV, Mb ≃ 5.04 GeV , and the decay constants are: fD (Mc ) ≃ 165 MeV , fB (Mb ) ≃ 113 MeV . It is also ¯ o mixing are large, BB ≃ (1 − shown that the nonfactorizable corrections to the B o − B 18%) . The values of the unitarity triangle parameters are found which are consistent with these results and the data available (except for the NA31 result for the ǫ′ /ǫ which is too large): λ ≃ 0.22 , A ≃ 0.825 , ρ ≃ −0.4 , η ≃ 0.2 .
Pentaquark baryon production at the Relativistic Heavy Ion Collider
(1)
∗ On
leave from Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China † On leave from Institute of Physics and Applied Physics and Department of Physics, Yonsei University, Seoul 120-749, Korea
II. COLLISION DYNAMICS AT RHIC
To model the dynamics of central relativistic heavy ion collisions after the end of the quark-gluon plasma phase, we use the boost invariant picture of Bjorken [36] augmented with accelerated transverse expansion. Specifically, the volume of produced fireball is taken to evolve with the proper time according to [37] V (τ ) = π RC + vC (τ − τC ) + a/2(τ − τC )2
PACS numbers: 25.75.-q,25.75.Dw,25.75.Nq
arXiv:nucl-th/0308006v3 23 Sep 2004
I.
INTRODUCTION
In recent experiments on nuclear reactions induced by photons [1, 2, 3, 4, 5], kaons [6], and neutrinos [7], production of baryons consisting of five quarks uudds ¯ has been inferred from the invariant mass spectrum of K + n or K 0 p. The extracted mass is around 1.536 GeV with a width in the range 20-25 MeV except Ref.[6] which gives a width of 9 MeV. All these widths reflect the resolution in the experiments, so the actual width of Θ+ is expected to be smaller. The observed properties of this pentaquark baryon are consistent with those of the Θ+ baryon with spin J = 1/2, isospin I = 0, and strangeness S = +1 that was originally predicted by the chiral soliton model [8] and recently studied using the Skyrme model [9, 10, 11, 12, 13, 14], the constituent quark model [15, 16, 17], the chiral quark model [18, 19], the QCD sum rules [20, 21, 22], and the lattice QCD [23, 24]. Studies of the Θ+ production mechanism in these reactions have also been carried out [25, 26, 27, 28]. Since both kaon and nucleon numbers are not insignificant in the hadronic matter formed in relativistic heavy ion collisions, the Θ+ may also be produced in these collisions. Using a statistical model, which assumes that the Θ+ is in chemical equilibrium with other hadrons, Randrup [29] has estimated its abundance and finds that there is about one Θ+ per unit rapidity in central Au+Au colli√ sions at sN N = 200 GeV available from the Relativistic Heavy Ion Collider (RHIC). As the quark-gluon plasma is expected to be formed in the initial stage of heavy ion collisions at RHIC, and it was suggested that formation of the quark-gluon plasma would enhance the production of hadrons consisting of strange quarks [30], it is of interest to know if this is also the case for Θ+ production and
How Much do Heavy Quarks Thermalize in a Heavy Ion Collision
arXiv:hep-ph/0412346v3 16 Mar 2005
Derek Teaney Department of Physics & Astronomy, SUNY at Stony Brook, Stony Brook, NY 11764, USA
(Dated: February 2, 2008)
it may be difficult to distinguish these two cases [19, 22]. Medium modifications of the heavy quark spectrum RAA flow will be studied experimentally this year and will provide an experimental estimate of this relaxation time [23, 24, 25, 26, 27]. Most recent studies of the medium modifications of the charm spectrum have computed the energy loss of a heavy quark by gluon bremsstrahlung [28, 29, 30, 31]. In weak coupling (which is the framework in which all calculations have been performed), bremsstrahlung is the dominant energy loss mechanism only if the heavy quark is ultra-relativistic, γv ≫ 1/g . (Similarly, for an electron traversing a hydrogen target, bremsstrahlung losses first exceed ionization losses when γv ≃ 700 [32].) For much of the measured momentum range, the heavy quark is not ultra-relativistic, γv < ∼ 4, and in this case it is far from clear that radiative energy loss dominates over collisional energy loss. About two thirds of all heavy quarks are produced with p < ∼ M , and therefore radiative energy loss should be neglected when studying bulk thermalization. When γv > ∼ 4, calculations do suggest that radiation dominates the average energy loss rate [33, 34]. However, as has been repeatedly emphasized [35, 36], the average energy loss is insufficient to describe the medium modifications of the spectrum RAA . Collisions have a different fluctuation spectrum than radiation and therefore might contribute more to the suppression factor than was at first anticipated [37]. Since we are primarily interested here in heavy quarks with typical momenta γv ∼ 1, we will concentrate exclusively on elastic collisions. Considering these points, we will re-examine collisional energy loss of a heavy quark in the perturbative QGP. Our tools are Hard Thermal Loop (HTL) perturbation theory and a heavy quark expansion (M ≫ T ). The average energy loss rate was first computed by Braaten and Thoma [38] and we will independently verify their results. (Recently this calculation was extended to anisotropic plasmas by Romatschke and Strickland [39].) We will also compute the rates of longitudinal and transverse momentum broadening which are essential to a complete calculation of the modification factor RAA . We will relate all of these rates to the diffusion coefficient which we will compute. (In principle the diffusion coefficient of a heavy quark could have been gleaned from the results of Braaten and Thoma [38] and Svetitsky [40].) In perturbation theory, we can compare the diffusion coefficient of the heavy quark to the hydrodynamic time scale η/(e + p) which was calculated previously [41, 42, 43]. Many of the ambiguities of perturbation theory cancel in the ratio of transport coefficients and we therefore hope to be able to extrapolate smoothly into the non-perturbative domain. Following this ideology, we express all of our phenomenological results in terms of the diffusion coefficient which may ultimately be determined from lattice QCD calculations. With these transport properties in hand, we adopt a Langevin model for the equilibration of heavy quarks in heavy ion collisions. The Langevin equations correctly describe the kinetics of a heavy particle in a thermal medium and therefore naturally interpolate between a hydrodynamic regime at small momentum and a kinetic regime at large momentum. The model is similar to old work by Svetitsky [40] and was later used without fluctuations to estimate RAA [34]. The model is strictly valid for non-relativistic quarks and for all velocities to leading logarithm in T /mD . The corresponding Fokker-Planck equation is solved analytically in Section V for a Bjorken expansion. The solution provides a simple estimate for the modification factor RAA and further elucidates the dynamics of equilibration. Then we solve the Langevin equations numerically in a hydrodynamic simulation of the heavy ion reaction. The results of the simulation are the medium modification factor RAA and the corresponding elliptic flow v2 (pT ) as a function of the diffusion coefficient. 3
Two lectures on heavy quark production in hadronic collisions
Abstract These lectures present a pedagogical introduction to the physics of heavy-flavour production in hadronic collisions. The first lecture gives the theoretical background, with a discussion of leading-order calculations and of the effects of next-to-leading-order corrections. The origin and implications of the large logarithmic corrections appearing at this order are presented in an elementary way. The second lecture provides a survey of current experimental data on charm and bottom production, and describes their comparison with theoretical predictions. We emphasize the role played by some non-perturbative effects in the determination of charm distributions, and study the theoretical systematic uncertainties which affect our predictions.
CERN-TH/97-328 hep-ph/9711337
Test of the heavy quark-light diquark approximation for baryons with a heavy quark
The set of coordinates more adequate for a heavy quark-light diquark description are the Jacobi coordinates (See Fig. 1)
PACS numbers: 12.39.Jh,14.20.Lq,14.20.Mr
I. INTRODUCTION
Heavy quark symmetry [1, 2, 3, 4, 5, 6] (HQS) predicts that in baryons with a heavy quark, and up to corrections in the inverse of the heavy quark mass, the light degrees of freedom quantum numbers are well defined, in particular the total spin of the light degrees of freedom is well defined. This prediction has been taken in different calculations as the basis for treating the light quark subsystem as a diquark, and the baryon as a heavy quark-light diquark (HQLD) system [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. This HQS prediction does not imply though that the orbital motion of the two light quarks is not affected by the presence of the heavy quark as it seems to be implicit in the HQLD approximation 1. Very recently the diquark structure of heavy baryons have been analyzed in Λc production in heavy ion collisions [17] where its enhanced yield is seen as a signal for the existence of light diquark correlations both in the quark gluon plasma and the heavy baryon.
Semileptonic Meson Decays in the Quark Model An Update
Nathan Isgur Continuous Electron Beam Accelerator Facility 12000 Jefferson Avenue, Newport News, Virginia 23606
We present the predictions of ISGW2, an update of the ISGW quark model for semileptonic meson decays. The updated model incorporates a number of features which should make it more reliable, including the constraints imposed by Heavy Quark Symmetry, hyperfine distortions of wavefunctions, and form factors with more realistic high recoil behaviors.
2
I. OVERVIEW
It has been nearly ten years since the ISGW model [1] was introduced [2,3] so it is not surprising that the heavy quark semileptonic landscape now looks very different. At that time, for both theoretical and experimental reasons, inclusive decays were the main focus of attention, and the ISGW model, which studied exclusive decays and approximated the inclusive semileptonic spectra by summing over resonant channels, was considered quite eccentric. Today, improvements in both theory and experiment have made exclusive semileptonic decays a main focus of attention. Such decays seem very likely to provide the most accurate determinations of the weak mixing angles Vcb and Vub . They also provide excellent probes of hadronic structure via precision tests of Heavy Quark Symmetry (HQS) [4-7]. The ISGW model was in many respects a stepping-stone to Heavy Quark Symmetry: it is a model which respects the symmetry in the heavy quark limit near zero recoil. It also played a role in the discussion of the reliability of the free quark decay model (and its derivatives) for the endpoint region in b → u semileptonic decay. Indeed, the model had its origin in that discussion, and was designed to provide the minimum reasonable prediction for the decay rate in this region for a fixed Vub . In this paper we present an updated version of ISGW, which (with the permission of the ISGW authors) we call ISGW2 to emphasize that it is not a new model but rather an improved version of an old one [8]. The new features are described in detail in Section III, but briefly they are:
On the B_{c} leptonic decay constant
Sameer M. Ikhdair∗
∗ Department
of Electrical and Electronic Engineerinsity, Nicosia, North Cyprus, Mersin-10, Turkey PACS NUMBER(S): 12.39.Pn, 12.39.Jh, 13.25.Jx, 14.40.-n
arXiv:hep-ph/0504107v1 14 Apr 2005
(February 2, 2008)
Typeset using REVTEX
∗ Electronic
address (internet): sameer@.tr
1
Abstract
We give a review and present a comprehensive calculations for the leptonic constant fBc of the low-lying pseudoscalar and vector states of Bc -meson in the framework of static and QCD-motivated nonrelativistic potential models taking into account the one-loop and two-loop QCD corrections in the short distance coefficient that governs the leptonic constant of Bc quarkonium system. Further, we use the scaling relation to predict the leptonic constant of the nS-states of the bc system. Our results are compared with other models to gauge the reliability of the predictions and point out differences.
Production of (super)heavy quarkonia and new Higgs physics at hadron colliders
G.A. Kozlov, A.N. Sissakian, J.I. Khubua, G. Arabidze and G. Khoriauli Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia e-mail: kozlov@thsun1.jinr.ru and T. Morii Div. of Sciences for Natural Environment, Faculty of Human Development, Kobe University, Kobe, Japan e-mail: morii@kobe-u.ac.jp
arXiv:hep-ph/0305006v2 6 May 2003
ห้องสมุดไป่ตู้
¯ ) composed of a (super)heavy quark Q and an antiquark A study on quarkonia T (QQ ¯ Q (a possible and interesting candidate of Q is the up(U )- and/or down(D )-quarks in the fourth generation family) is required in current particle physics for testing the standard model (SM) and/or searching for signals for physics beyond the SM. It is nowadays one of the most interesting subjects since the subject can be studied, with high priority, in the forthcoming experiments at high energy hadron colliders, i.e. the Tevatron and LHC. In particular, no theoretical arguments are seen to rule out the (super)heavy quarks and the (super)heavy quarkonium states with the masses around hundred GeV or even a few TeV (see, e.g. [1]). As the recent example, in one of the extended models, the little Higgs model [2], there could be an additional heavy quark q ˜ with a mass of order O(1 TeV) to promote the quark doublet q to quark triplet under the global SU(3), Q = (q, q ˜). By preserving the global symmetry of the coupling, the one-loop quadratic divergence to the top quark is removed. In fact, the SM and its extensions, e.g., the Minimal Supersymmetric Standard Model (MSSM), do not explain the family (generation) structure of the quark masses. Each quark has an arbitrary Yukawa coupling and hence is independent of the family to which it belongs. It is required to explain the family structure and the Cabibbo-Kobayashi-Maskawa (CKM) matrix for the quark sector in any extension of the SM or even in the SM. 1
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a r X i v :h e p -p h /9909437v 1 20 S e p 1999LU TP 99–28September 1999Heavy Quark Production AsymmetriesE.Norrbin 1Department of Theoretical Physics,Lund University,Lund,SwedenAbstractIn the hadroproduction of charm (or heavy flavours in general)in the con-text of string fragmentation,the pull of a beam remnant at the other end of a string may give a charm hadron more energy than the perturbatively produced one.The collapse of a low-mass string to a single hadron is the extreme case in this direction,and gives rise to asymmetries between lead-ing and non-leading charm hadrons.We study these phenomena within the Lund string fragmentation model and improve the modelling in part by a consideration of hadroproduction data.Applications include heavy quark production in any collision between hadron-like particles such as γp at HERA and pp at HERA-B or the LHC.1IntroductionSeveral experiments atfixed-target energies have observed asymmetries between leading and non-leading charmed hadrons inπ−p collisions[1].In[2]we study this effect in the context of the Lund string fragmentation model[3]andfind that it is possible to improve the model to obtain a good description of the asymmetry data.In this model,collapses of light colour singlets mainly account for the asymmetry.We also study single charm spectra and particle/anti-particle correlations andfind good agreement between the model and single charm spectra,but fail to describe the cor-relation data from E791[4].This is in contrast to NLO calculations[5],which adequately describe single charm spectra for non-leading particles and some correlations,but fail to describe the asymmetry and leading-particle single charm spectra.A related effect included in the string model is the non-perturbative’beam drag’.In this model the produced heavy quarks are connected to the beam remnants by colour singlet strings.Through soft interactions with the beam remnant the charm quark can gain energy and momentum to produce a heavy hadron at a larger rapidity than that of the heavy quark.2Model aspectsThe asymmetry between D+and D−is described by the asymmetry parameterσ(D−)−σ(D+)A=A(x F,p⊥)=c-d string masses near threshold is shown infig.3,both using the default parameters and with some modifications.Depending on the mass of a string,different hadronization mechanisms are used: Large mass(M string>m c+m q+1GeV)Ordinary string fragmentation with a contin-uum of phase-space states.Low mass The colour-singlet system forms a cluster that undergoes two-body decay into two hadrons.Very low mass If the invariant mass of a cluster is so small that two-body decay is not possible,the cluster is forced to collapse into a single hadron with compatible flavour contents.This gives rise to an asymmetry favouring leading particles.The qualitative nature of the asymmetry is thus described by the string model.How-ever,the quantitative behaviour depends on the parameters of the model.The model aspects considered are described in more detail in[2],so here we just give a brief sum-mary:Figure 1:Experimentalresults on asymmetries compared to the modified version of Pythia 6.1described in this note.Data is from π−p fixed-target experiments,where x F >0is the pion fragmentation region.p +π−cud d ¡Figure 2:String configuration in a π−p collision with quark fusion charm production.Figure 3:Distribution ofuFigure4:The ud diquark of the proton remnant has,at least in the average,a larger energy/momentum than the lone u quark.Because the diquark is in a colour singlet with the c-quark,in average,we will have y D > y c and y D > y00.511.522.533.5400.51 1.52d σ/d y (p b )|y|p t> 0 GeV-1-0.8-0.6-0.4-0.200.200.20.40.60.81 1.2 1.4 1.6 1.8A s y m m e t r y|y|p t> 5 GeV102030405060701234567d σ/d y (n b )|y|p t> 0 GeV-0.3-0.25-0.2-0.15-0.1-0.0500.050.101234567A s y m m e t r y|y|p t> 5 GeVFigure 5:B 0(dashed)andB 0))/(σ(B 0)+σ(p.This sections gives just a few examples.Asymmetries in the B 0q pair it can interact as ameson and therefore you need to know the parton distribution of the photon.These two0.010.1110100100010000-6-4-2024d σ/d y (n b )y(a) DirectHadrons QuarksHadrons, p T > 4 GeV Quarks, p T > 4 GeV0.010.1110100-6-4-2024y(b) Resolved0.010.1110100100010000-6-4-2024d σ/d y (n b )y(c)Hadrons, direct Hadrons, resolved Direct+Resolved0.0010.010.11101001000012345678910d σ/d p T (n b )p T(d)Figure 6:Charm cross section for direct and resolved photons with different p ⊥cuts.classes of events give rise to fairly different event structures,see fig.6.The drag effect shifts the hadron spectrum in the direction of the proton beam remnant.5SummaryWe have studied some non-perturbative effects in heavy quark production within the framework of the Lund string fragmentation model.We find some agreement with data if specific parameters are used.We also apply the model to pp and γp physics and arrive at predictions of bottom-asymmetries at HERA-B and the LHC.References[1]WA82Collaberation,M.Adamovich et al.,Phys.Lett.B 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