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Masses of tetraquarks with two heavy quarks in the relativistic quark model

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PACS numbers: 12.40.Yx, 14.40.Gx, 12.39.Ki
I.
INTRODUCTION
Recent experimental studies of the heavy meson spectroscopy revealed several new states, ∗ such as X (3872), Y (4260), Ds 0 (2317) etc., which cannot be simply accommodated in the quark-antiquark (q q ¯) picture [1]. These states can be considered as indications of the possible existence of exotic multiquark states which were proposed long ago, e.g. in [2]. The idea to revisit the multiquark picture using diquarks has been put forward by Jaffe and Wilczek [3]. At present, vast experimental and theoretical evidence of the important role played by diquark correlations in hadrons is collected [4].
R. N. Faustov and V. O. Galkin
Institut f¨ ur Physik, Humboldt–Universit¨ at zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany and Dorodnicyn Computing Centre, Russian Academy of Sciences, Vavilov Str. 40, 119991 Moscow, Russia
HU-EP-07/21 HEPHY-PUB 842/07
Masses of tetraquarks with two heavy quarks in the relativistic quark model
D. Ebert
arXiv:0706.3853v2 [heptitut f¨ ur Physik, Humboldt–Universit¨ at zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany
2 The simplest multiquark system is a tetraquark, composed of two quarks and two antiquarks. Heavy tetraquarks are of particular interest, since the presence of a heavy quark increases the binding energy of the bound system and, as a result, the possibility that such tetraquarks will have masses below the thresholds for decays to mesons with open heavy flavour. If such strong decays are kinematically forbidden, then corresponding tetraquarks can decay only weakly or electromagnetically and thus they should have a small decay width. In this paper we consider tetraquarks with two heavy quarks as bound systems of a diquark and antidiquark. Therefore we assume that both b and c quarks are heavy enough to make the attractive QQ interaction stronger than the Qq ¯ one. For tetraquarks containing c quarks the obtained results crucially depend on this assumption. In particular, the doubly heavy (QQ′ )(¯ qq ¯′ ) tetraquark (Q = b, c and q = u, d, s) is considered as the bound system of the heavy diquark (QQ′ ) and light antidiquark (¯ qq ¯′ ), while the (cq )(¯ bq ¯′ ) tetraquark is the bound state of the heavy-light diquark (cq ) and antidiquark (¯ bq ¯′ ). Masses of heavy tetraquarks with hidden charm (cq )(¯ cq ¯) and bottom (bq )(¯ bq ¯) were calculated in our previous paper [5]. There the dynamical analysis has shown that X (3872) and Y (4260) can be indeed the diquark-antidiquark tetraquarks with hidden charm. It was also argued that the corresponding ground-state tetraquarks with hidden bottom have masses below the open bottom threshold, and thus they should be narrow states. It is important to investigate the possible stability of the (QQ′ )(¯ qq ¯′ ) tetraquarks since they are explicitly exotic states with the heavy flavour number equal to 2. Thus, their observation would be a direct proof of the existence of the multiquark states. Estimates of the production rates of such tetraquarks indicate that they could be produced and detected at present (SELEX, Tevatron, RHIC) and future facilities (LHC, LHCb, ALICE) [6]. To calculate the masses of heavy tetraquarks we use the relativistic quark model based on the quasipotential approach in quantum field theory. Previously we considered in our model the mass spectra of the ground-state and excited doubly-heavy (QQq ) [7] and heavy (qqQ) [8, 9] baryons in the heavy-diquark–light-quark and light-diquark–heavy-quark approximations, respectively. The light quarks and light diquarks were treated completely relativistically. The internal structure of the light and heavy diquarks was taken into account by calculating diquark-gluon form factors in terms of the obtained diquark wave functions. Such scheme proved to be very effective and successful in our calculation of the masses of heavy baryons ∗ in good agreement with experimental data [10]. The predicted masses of the Ω∗ c , Σb , Σb and Ξb baryons proved to be very close to the recently measured ones [11, 12, 13]. Moreover, in Ref. [9] it was shown that currently available experimental data on excited charmed baryons can be accommodated in the picture treating a heavy baryon as the bound system of the light diquark and heavy quark, experiencing orbital and radial excitations. This gives us additional confidence in the reliability of the diquark approximation within our model and motivates the consideration of tetraquarks as diquark-antidiquark bound systems. It is important to note that all parameters of our model were fixed in the previous calculations of meson mass spectra and decays, and we will keep their values in the following analysis of heavy tetraquarks.

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A Relativistic $O(a^2)$ Improved Action for Heavy Quarks

A Relativistic $O(a^2)$ Improved Action for Heavy Quarks

1
A Relativistic O(a2 ) Improved Action for Heavy Quarks
M. B. Oktaya ∗ , A. X. El-Khadraab , A. S. Kronfeldb , P. B. Mackenzie b , and J. N. Simoneb
a b
j
sion five, to obtain a lattice action for fermions, improved to O(a), and valid for quarks with arbitrary mass. In this work we extend the analysis of Ref. [2] to include operators of dimension six for O(a2 ) improvement. 2. THE ACTION At dimension six we have to consider both fermion bilinears and four-fermion operators. For these proceedings, we concentrate on determining the bilinear interactions. The five dimension-six bilinears that satisfy axis-interchange symmetry are given in Ref. [4]. Without axis-interchange symmetry, these operators become the seventeen operators listed in Table 1. (The lower dimensional operators are given in Ref. [2].) Following Refs. [4,2], we use field transformations to expose the redundant directions for on-shell improvement. Since we are considering dimension-six operators in the action we must include dimension-two operators in the transformations, and we must also consider gauge field transformations. Writing ψ → eJ ψ, we have J = aǫ1 (D / + m) + aδ1 γ · D + a2 ǫ2 (D / 3; ǫ2 δ2 + δ 2 δ2 − δ 2 δu − δ u δu + δ u ǫF + ǫF ǫF − ǫF * δB + δ B (6) (7)
Baryon-Number Nonconservation and the Stability of Strange Matter

Baryon-Number Nonconservation and the Stability of Strange Matter

UCRHEP-T160 August 1996
Baryon-Number Nonconservation and
arXiv:hep-ph/9609211v1 30 Aug 1996
the Stability of Strange Matter
E. Keith and Ernest Ma Department of Physics University of California Riverside, California 92521
1
Introduction
Matter containing a large number of strange quarks may have a lower energy per baryon than ordinary nuclei and be absolutely stable[1, 2]. This intriguing possibility has generated a great deal of interest across many subfields of physics. A crucial implicit assumption for the stability of this new kind of matter, called strange matter, is that the baryon number B is exactly conserved. Of course, we know nuclei are stable against ∆B = 0 decays. The best mode-independent experimental lower limit to date is 1.6 × 1025 years[3]. However, there may be effective ∆B = 0 interactions which are highly suppressed for nuclei but not for strange matter. We examine such a hypothesis here and show that whereas such exotic decays are possible, the relevant lifetime should be longer than 105 years. In Sec. 2 we review briefly the present experimental constraints on ∆B = 0 interactions. These come mainly from the nonobservation of proton decay and of neutron-antineutron oscillation. We then point out the possible consequences of an effective ∆B = 2, ∆Ns = 4 operator (where Ns denotes the number of s quarks) on the stability of strange matter. We proceed to discuss some possible theoretical origins of such an operator in Sec. 3 and Sec. 4. We deal first with the supersymmetric standard model with R-parity nonconserving terms of
the masses of atoms molecules and ions

the masses of atoms molecules and ions

The masses of atoms, molecules and ionsT: Ok, let’s begin our class. In our daily life, we can weight our body, the basketball. Now I have one thing. The atom, can you weight it? Do you have some ideas?S: No.T: Because it’s too small, you can’t use scales to weight it. Right?S: Right.T: So today, we’ll learn the masses of atoms, molecules and ions. We don’t know how to weight the atoms, but the scientists do. First, they choose an atom of carbon-12 to be the standard atom. They fix its masses as exactly 12 units. Look at the carbon atom. How many protons, neutrons and electrons in it?(Write down the title on the blackboard)S: It has 6 protons, 6neutrons and 6 electrons.T: Right. The scientists ignore the electrons’ weight, because the electrons are negligible which are compared with the protons and neutrons. Then they compared all the other atoms with this standard atom, in a machine, called a mass spectrometer, and found values for their masses. Like this:C This is the standard atom 126C, its mass is exactly 12.Mg magnesium is twice as heavy as the standard atom, so its mass must be 12*2=24.Now it’s your turn. I’ll give you the hydrogen atom. And it is 1/12 as heavy as the standard atom. What’s the mass about it? Give me the answer.S: Its mass is 12*1/12=1.T: Good, sit down, please. Then we can say that the mass of an atom found by comparing it with 12C atom is called its relative atomic mass or Ar. So the Ar of hydrogen is 1, the Ar of magnesium 6is 24.As we have learned, the atoms of an element are not always identical, just like the isotopes, which have the same number of protons but the different number of neutrons. Then how can we know the relative atomic mass of this kind of atoms?We’ll solve this problem. As the Cl is an example. It has two isotopes. One is chlorine-35. Another is chlorine-37. 75%of chlorine atoms are chlorine-35, 25% of chlorine atoms are chlorine-37. How we can calculate the Ar of Cl? We can use this formula:Relative atomic mass of an element=(%*nucleon number for the first isotope)+(%*nucleon number for the second isotope)and so on for all its natural isotopes.Then we can calculate the Ar of the chlorine:Ar of chlorine = 75%*35+25%*37=75/100*35+25/100*37(changing % to fractions)=26.25+9.25=35.5Then we can get a more clearly definition of the relative atomic mass. The relative atomic mass(Ar) of an element is the average mass of its isotopes compared to an atom of caebon-12. Now do an exercise. Naturally occurring neon is 90.9% neon-20, 0.3% neon-21 and 8.8% neon-22. Use these figures to calculate the relative atomic mass of naturally occuring neon. Use the formula that we have learned.S:The Ar of neon=90.9%*20+0.3%*21+8.8%*22=18.18+0.06+1.93=20.2T: Very good. This table shows us Ar values for some common elements. If you want to know more, you can look at the Periodic Table. In it, you can find the Ar of each element. But this is not enough for our calculation. What about the mass of Na, NaCl, H2? Maybe you can have a try. We want to know more about the mass of the molecule or group of ions. We’ll find the masses of molecules and ions together.We can use Ar values, it is easy to work out the mass of any molecules or group of ions. First, we should know a rule: we know the mass of an atom, but the ions? Do you know? For example: Mass of sodium atom=23, because the mass of one electron is negligible, so the Ar of sodium ion is equal to the mass of sodium atom, it’s also 23.As a molecule, for example:The hydrogen gas is made of molecules. Each molecule contains 2 hydrogen atoms, so its mass is 2.Another one, the formula of water is H2O. A water molecule contains 2 hydrogen atoms and 1 oxygen atom. So the mass is 2*1+16=18.Like the hydrogen and water, are made of molecules, its mass found in this way is called the relative molecular mass or Mr. So the Mr for hydrogen is 2, for water is 18.Different from the hydrogen and water, the sodium chloride is made of ions, sodium chloride forms a giant structure with one sodium ion for every chloride ion. So the mass of a ‘unit’of sodium chloride is 35.5+23=58.5.Like the NaCl, the substance is made of ions, its mass is called the relative formula mass. The short form for this is also Mr. So the Mr for NaCl is 58.5.Understand? Now, Let’s do some exercises.(on PPT)Work out the Mr of these, and say whether it is the relative molecular mass or the relative formula mass.a.oxygen O2b.copper sulphate CuSO4c.methane CH4d.sodium carbonate Na2CO3e.chlorine Cl2Do more exercise after class, and review what we learn today. Class is over.5.2 The masses of atoms molecules and ions1.Relative atomic mass 3.the masses of molecules and ionsAr of hydrogen=1 a. the mass of ionsAr of magnesium=24 the No. of ions=the No. of atoms2.Ar and isotopes b. the relative molecular massCl-35 75% Mr for water=18Cl-37 25% c. the relative formula massAr= 75%*35+25%37=35.5 Mr of NaCl= 58.5。

Two lectures on heavy quark production in hadronic collisions

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