Single Quark Research Articles

The light spectrum near the Argyres–Douglas point

We consider N=2 super Yang-Mills theory with SU(2) gauge group and a single quark hypermultiplet in the fundamental representation. For a specific value of the quark bare mass and at a certain point in the moduli space of vacua, the central charges corresponding to two mutually non-local electro-magnetic charges vanish simultaneously, indicating the possibility of massless such states in the spectrum. By realizing the theory as an M-theory configuration, we show that these states indeed exist in the spectrum near the critical point.

The confining interaction and radiative decays of heavy quarkonia

The radiative spin-flip transition rates of heavy quarkonium states depend sensitively on the matrix elements of the effective confining interaction through the associated two-quark exchange current operator. The Hamiltonian model based on a scalar linear confining interaction with a single gluon exchange hyperfine term is shown to provide an adequate description of the J ψ → η cγ and ψ(2 S) → η c γ decay widths once the relativistic single quark magnetic moment operator is treated without approximation and the exchange current is taken into account. Predictions are given for the radiative spin-flip decay widths of the 1 S, 2 S and 3 S states of the c c , b b and B c + systems. In the B c + system the gluon exchange current also contributes to the spin-flip transition rates.

O(1/M3)effects for heavy-light mesons in lattice NRQCD

The masses of ${}^{1}{S}_{0}$ and ${}^{3}{S}_{1}$ mesons containing a single heavy quark are computed in the quenched approximation. The light quark action and gauge field action are both classically improved and tadpole improved, and the couplings to the heavy quark are organized by the $1/M$ expansion of tadpole-improved NRQCD. At each of two lattice spacings, near 0.22 fm and 0.26 fm, meson masses are obtained for heavy quarks spanning the region between charmed and bottom mesons. Results up to $O(1/M),$ ${O(1/M}^{2})$ and ${O(1/M}^{3})$ are displayed separately, so that the convergence of the heavy quark expansion can be discussed. Also, the effect of each term in the ${O(1/M}^{3})$ contribution is computed individually. For bottom mesons the $1/M$ expansion appears to be satisfactory, but the situation for charmed mesons is less clear.

HEAVY BARYONS IN THE QUARK-DIQUARK PICTURE

We describe heavy baryons as bound states of a quark and a diquark. For this purpose we derive the Faddeev equation for baryons containing a single heavy quark from a Nambu–Jona–Lasinio type of model which is appropriately extended to include also heavy quarks. The latter are treated in the heavy mass limit. The heavy baryon Faddeev equation is then solved using a static approximation for the exchanged quark.

Quark confinement in C-periodic cylinders at temperatures above Tc

Due to the Gauss law, a single quark cannot exist in a periodic volume, while it can exist with C-periodic boundary conditions. In a C-periodic cylinder of cross section A = L_x L_y and length L_z >> L_x, L_y containing deconfined gluons, regions of different high temperature Z(3) phases are aligned along the z-direction, separated by deconfined- deconfined interfaces. In this geometry, the free energy of a single static quark diverges in proportion to L_z. Hence, paradoxically, the quark is confined, although the temperature T is larger than T_c. At T around T_c, the confined phase coexists with the three deconfined phases. The deconfined-deconfined interfaces can be completely or incompletely wet by the confined phase. The free energy of a quark behaves differently in these two cases. In contrast to claims in the literature, our results imply that deconfined-deconfined interfaces are not Euclidean artifacts, but have observable consequences in a system of hot gluons.

The constituent quark as a soliton in a linear σ-model

We study a stable, soliton-like solution in the linear σ-model where the chiral fields are coupled to a single massless nonstrange quark. We investigate a possibility that this solution represents the constituent quark of Georgi and Manohar. We show that its properties are indeed consistent with nucleon observables. Furthermore, we derive chiral meson exchange potentials between such objects which are similar to recently used potentials in the constituent quark models.

Heavy baryon masses in the 1/mQ and 1/Nc expansions.

The masses of baryons containing a single heavy quark are studied in a combined expansion in 1/{ital m}{sub {ital Q}}, 1/{ital N}{sub {ital c}}, and SU(3) flavor symmetry breaking. Heavy quark baryon mass splittings are related to mass splittings of the octet and decuplet baryons. The {Sigma}{sub {ital c}}{sup {asterisk}}, {Xi}{sub {ital c}}{sup {prime}}, and {Omega}{sub {ital c}}{sup {asterisk}} are predicted to the level of a few MeV. A number of bottom baryon mass splittings are predicted very accurately. {copyright} {ital 1996 The American Physical Society.}

Heavy baryon spectroscopy from the lattice.

The results of an exploratory lattice study of heavy baryon spectroscopy are presented. We have computed the full spectrum of the eight baryons containing a single heavy quark, on a $24^3\times 48$ lattice at $\beta=6.2$, using an $O(a)$-improved fermion action. We discuss the lattice baryon operators and give a method for isolating the contributions of the spin doublets $(\Sigma,\Sigma^*)$, $(\Xi',\Xi^*)$ and $(\Omega,\Omega^*)$ to the correlation function of the relevant operator. We compare our results with the available experimental data and find good agreement in both the charm and the beauty sectors, despite the long extrapolation in the heavy quark mass needed in the latter case. We also predict the masses of several undiscovered baryons. We compute the $\Lambda-\mbox{pseudoscalar meson}$ and $\Sigma-\Lambda$ mass splittings. Our results, which have errors in the range $ 10-30\%$, are in good agreement with the experimental numbers. For the $\Sigma^*-\Sigma$ mass splitting, we find results considerably smaller than the experimental values for both the charm and the beauty baryons, although in the latter case the experimental results are still preliminary. This is also the case for the lattice results for the hyperfine splitting for the heavy mesons.

Photonic decay widths of some heavy pseudoscalar mesons.

The photonic decays of the heavy pseudoscalar mesons ${B}_{L}$, ${B}_{\mathrm{sL}}$, and ${D}_{L}$ are studied in the single loop quark model. The contribution to the two $\ensuremath{\gamma}$ decays of the heavy pseudoscalar mesons are computed in the standard model as a function of the quark mass. It is interesting to note the equality of the order for the two $\ensuremath{\gamma}$ decay amplitudes of ${B}_{L}$, ${B}_{\mathrm{sL}}$, and ${D}_{L}$.

Baryon magnetic moments and the quark model reexamined.

The baryon magnetic moments are considered within the framework of the constituent quark model assuming charge symmetry ${\mathrm{\ensuremath{\mu}}}_{\mathit{d}}$=-${\mathrm{\ensuremath{\mu}}}_{\mathit{u}}$/2. The baryons on the perimeter of the octet have two quarks of the same flavor, and a single quark of different flavor. The effective moments of the single flavor quarks were allowed to vary with I and Y. The resulting formulas predict eight magnetic moments in terms of four parameters. The average discrepancy is 〈\ensuremath{\Vert}${\mathrm{\ensuremath{\mu}}}_{\mathrm{fit}}$-${\mathrm{\ensuremath{\mu}}}_{\mathrm{expt}}$\ensuremath{\Vert}〉=0.024${\mathrm{\ensuremath{\mu}}}_{\mathit{N}}$. \textcopyright{} 1996 The American Physical Society.

Single inclusive heavy quark production at high-energy hadronic colliders

Theoretical uncertainties in the calculation of single inclusive b-quark and B-meson cross sections at high-energy p p colliders and the agreement between new experimental data and theory are studied in detail taking into account recent results on α s( M z ). Possible implications for the gluon distribution g( x, μ 2) in the proton are discussed. The need for high-energy resummation techniques is examined by analysing the perturbative stability of the cross sections. For completeness, results for total t t pair production are briefly presented.

Is B-->Xs gamma equal to b-->s gamma ? Spectator contributions to rare inclusive B decays.

In $B \to X_s \gamma $ there are perturbative $QCD$ corrections at order $\alpha_s$ not only to the single quark line process $ b \to s \gamma$ but also coming from a set of diagrams where the weak interaction vertex involves a gluon which interacts with the spectator quark in the B hadron. We discuss the impact of the full set of these diagrams. These can influence the decay rate and also the line shape of the photon spectrum as they favor a softer photon energy than does the pure spectator decay $b \to s \gamma$. A subset of these diagrams generate differences in the decay rates for charged and neutral B's , $B^+ \to X_s \gamma$ vs. $B^0 \to X_s \gamma$ which can be searched for experimentally, although our calculation indicates that the effect will be hard to observe. Bound state effects turn out to be required to give rise to spectator corrections to the decay rate at order $\alpha_s$. The resulting contribution to the total rate is rather small (of about $5 \% $ ), although the effect is somewhat larger on portions of the photon spectrum.

Mass splittings and matrix elements of mesons and baryons containing a single heavy quark

We present a study in the quenched approximation of the $B$ parameter $B_B$ and the decay constant $f_B$ using heavy-quark propagators implemented in the static approximation, and light-quark propagators computed using an $O(a)$-improved fermion action. We find a value of $\Bbstat$ close unity, and discuss the systematic errors entering into the calculation. $\fbstat$ is extracted using a variational fitting technique in order to obtain a reliable estimate of the ground state. In the second part of the talk, we describe an exploratory study of baryons containing a single heavy quark, computed using the $O(a)$-improved fermion action. We obtain masses generally in good agreement with experiment in both the charm and beauty sectors. We also report preliminary results for the form factor $G_1$ in the semi-leptonic $\Lambda_b \rightarrow \Lambda_c$ transition.

Fragmentation production of doubly heavy baryons.

Baryons with a single heavy quark are being studied experimentally at present. Baryons with two units of heavy flavor will be abundantly produced not only at future colliders, but also at existing facilities. In this paper we study the production via heavy quark fragmentation of baryons containing two heavy quarks at the Fermilab Tevatron, the CERN LHC, DESY HERA, and the NLC. The production rate is woefully small at HERA and at the NLC, but significant at pp and pp\ifmmode\bar\else\textasciimacron\fi{} machines. We present distributions in various kinematical variables in addition to the integrated cross sections at hadron colliders. \textcopyright{} 1996 The American Physical Society.

Constraints on light quark masses from the heavy meson spectrum.

We use the observed SU(3) breaking in the mass spectrum of mesons containing a single heavy quark to place restrictions on the light quark current masses. A crucial ingredient in this analysis is our recent first-principles calculation of the electromagnetic contribution to the isospin-violating mass splittings. We also pay special attention to the role of higher-order corrections in chiral perturbation theory. We find that large corrections are necessary for the heavy meson data to be consistent with ${\mathit{m}}_{\mathit{u}}$=0.

Leptonic and semileptonic decays of charm and bottom hadrons

The authors review the experimental measurements and theoretical descriptions of leptonic and semileptonic decays of particles containing a single heavy quark, either charm or bottom. Measurements of bottom semileptonic decays are used to determine the magnitudes of two fundamental parameters of the standard model, the Cabibbo-Kobayashi-Maskawa matrix elements ${V}_{\mathrm{cb}}$ and ${V}_{\mathrm{ub}}$. These parameters are connected with the physics of quark flavor and mass, and they have important implications for the breakdown of $\mathrm{CP}$ symmetry. To extract precise values of $|{V}_{\mathrm{cb}}|$ and $|{V}_{\mathrm{ub}}|$ from measurements, however, requires a good understanding of the decay dynamics. Measurements of both charm and bottom decay distributions provide information on the interactions governing these processes. The underlying weak transition in each case is relatively simple, but the strong interactions that bind the quarks into hadrons introduce complications. The authors also discuss new theoretical approaches, especially heavy-quark effective theory and lattice QCD, which are providing insights and predictions now being tested by experiment. An international effort at many laboratories will rapidly advance knowledge of this area of physics during the next decade.

HEAVY QUARK PRODUCTION IN pp COLLISIONS

A systematic study of the inclusive single heavy quark and heavy-quark pair production cross sections in pp collisions is presented for RHIC and LHC energies. We compare with existing data when possible. The dependence of the rates on the renormalization and factorization scales is discussed. Predictions of the cross sections are given for two different sets of parton distribution functions.

Heavy-meson electromagnetic mass differences from QCD.

We compute the electromagnetic mass differences of mesons containing a single heavy quark in terms of measurable data using QCD-based arguments in heavy-quark effective theory. We derive an unsubtracted dispersion relation that shows that the mass differences are caculable in terms of the properties of lowest-lying physical intermediate states. We then consider the problem in the large-N limit, where N is the number of QCD colors. In this limit, we can write a kind of double-dispersion relation for the amplitude required to determine the electromagnetic mass difference. We use this to derive analogues of the Weinberg sum rules for heavy-meson matrix elements valid to leading order in 1/N and to O(1/${\mathit{m}}_{\mathit{Q}}$) in the heavy-quark expansion. In order to obtain our final result, we assume that the electromagnetic mass differences and sum rules are dominated by the lowest-lying states in analogy with the situation for the ${\mathrm{\ensuremath{\pi}}}^{+}$-${\mathrm{\ensuremath{\pi}}}^{0}$ mass difference. Despite the fact that some of the matrix elements appearing in our final result have not yet been accurately measured, we can obtain useful estimates of the electromagnetic mass differences: for example, we obtain (${\mathit{M}}_{\mathit{B}}^{+}$-${\mathit{M}}_{\mathit{B}}^{0}$${)}^{\mathrm{EM}}$\ensuremath{\simeq}+1.8 MeV. We argue that our results are accurate to about 30%.

Neutron electric dipole moment in the minimal supersymmetric standard model

The neutron electric dipole moment (EDM) due to the single quark EDM and to the transition EDM is calculated in the minimal supersymmetric standard model. Assuming that the Cabibbo-Kobayashi-Maskawa matrix at the grand unification scale is the only source of CP violation, complex phases are induced in the parameters of soft supersymmetry breaking at low energies. The chargino one-loop diagram is found to give the dominant contribution of the order of 10 −27 ∼ 10 −29 e·cm for the quark EDM, assuming the light chargino mass and the universal scalar mass to be 50 GeV and 100 GeV, respectively. Therefore the neutron EDM in this class of model is difficult to measure experimentally. The gluino one-loop diagram also contributes due to the flavor changing gluino coupling. The transition EDM is found to give dominant contributions for certain parameter regions.

BROKEN SU(8) AND HADRONIC MASS RELATIONS IN HEAVY QUARK EFFECTIVE THEORY

Mass relations for hadrons containing a single heavy quark (charm or beauty) are studied from the viewpoint of a quark model with broken SU(8) symmetry, developed by Hendry and Lichtenberg some time ago, in comparison to that of the heavy quark effective theory. The interplay of the two approaches is explored and spectroscopic consequences derived.