arXiv subjects

Chi-Keung Chow

Publications and source records attributed to Chi-Keung Chow.

36 records · Page 2Linked to original sources

arXiv1997

Chiral Perturbation Theory for Tensor Mesons

Interactions of $a_2, K^*_2, f_2$ and $f_2'$ tensor-mesons with low-energy $π, K, η, η'$ pseudo-scalar mesons are constrained by chiral symmetry. We derive a chiral Lagrangian of tensor mesons in which the tensor mesons are treated as heavy non-relativistic matter fields. Using $1/N_c$ counting, we derive relations among unknown couplings of the chiral Lagrangian. Chiral perturbation theory is applied to the tensor-meson mass matrix. At one-loop there are large corrections to the individual tensor meson masses, but the singlet-octet mixing angle remains almost unchanged. We argue that all heavy mesons of spin $\ge 1$ share common feature of chiral dynamics.

hep-ph↗

arXiv1997

Comment on ``A new efficient method for calculating perturbative energies using functions which are not square integrable'': regularization and justification

The method recently proposed by Skala and Cizek for calculating perturbation energies in a strict sense is ambiguous because it is expressed as a ratio of two quantities which are separately divergent. Even though this ratio comes out finite and gives the correct perturbation energies, the calculational process must be regularized to be justified. We examine one possible method of regularization and show that the proposed method gives traditional quantum mechanics results.

quant-ph↗

arXiv1996

Qualitative Aspects of Polarization Distributions In Excited Heavy Hadron Productions

Within the context of flux tube models, heavy quark fragmentation takes place through the breaking of flux tubes with the production of a (di)quark-anti(di)quark pair. It is found that the (di)quark produced are more likely to be found in an $L_z=0$ state. This naturally leads to an supression of the polarization distribution parameters $w_{3/2}$ and $\tilde w_1$ for $(D_1, D_2^*)$ and $(Λ_{c1}, Λ_{c1}^*)$ production respectively. The corresponding parameter $w_1$ for $(Σ_c, Σ_c^*)$ production, however, is not suppressed, in agreement with the CLEO results but not the DELPHI one. Implications on the measurements of $Λ_Q$ polarizations are discussed.

hep-ph↗

arXiv1996

Perturbative Scattering Phase Shifts in One-Dimension: Closed-form Results

A simple closed form expression is obtained for the scattering phase shift perturbatively to any given order in effective one-dimensional problems. The result is a hierarchical scheme, expressible in quadratures, requiring only knowledge of the zeroth order solution and the perturbation potential.

quant-ph↗

arXiv1996

Spin Symmetry Without Heavy Quarks: Hyperon Form Factors In The Large $N_c$ Limit

In the large $N_c$ limit, all hyperon decays involving the same quark diagram $Q\to Q'$ are described by a single weak form factor $η_{QQ'}(w)$. No assumption on the mass of $Q$ or $Q'$ is necessary, making our results applicable to both $b\to c$ and $c\to s$ transitions. This same form factor describes both $Λ_Q\toΛ_{Q'}$ and $Σ^{(*)}_Q\toΣ^{(*)}_{Q'}$ transitions. The (non-)commutativity between the heavy quark and the large $N_c$ limits is briefly discussed under the definite example of $Λ_b\toΛ_c$ decay.

hep-ph↗

arXiv1996

Large $N_c$ Universality of The Baryon Isgur--Wise Form Factor: The Group Theoretical Approach

In a previous article, it has been proved under the framework of chiral soliton model that the same Isgur--Wise form factor describes the semileptonic $Λ_b\toΛ_c$ and $Σ^{(*)}_b\toΣ^{(*)}_c$ decays in the large $N_c$ limit. It is shown here that this result is in fact independent of the chiral soliton model and is solely the consequence of the spin-flavor SU(4) symmetry which arises in the baryon sector in the large $N_c$ limit.

hep-ph↗

arXiv1995

Self Consistent $1/N_c$ Expansion In The Presence Of Electroweak Interactions

In the conventional approach to the $1/N_c$ expansion, electroweak interactions are switched off and large $N_c$ QCD is treated in isolation. We study the self-consistency of taking the large $N_c$ limit in the presence of electroweak interaction. If the electroweak coupling constants are held constant, the large $N_c$ counting rules are violated by processes involving internal photon or weak boson lines. Anomaly cancellations, however, fix the ratio of electric charges of different fermions. This allows a self-consistent way to scale down the electronic charge $e$ in the large $N_c$ limit and hence restoring the validity of the large $N_c$ counting rules.

hep-ph↗

arXiv1995

Sum Rules for Radiative and Strong Decays of Heavy Mesons

We derive two model-independent sum rules relating the transition matrix elements for radiative and strong decays of excited heavy mesons to properties of the lowest-lying heavy mesons. The sum rule for the radiative decays is an analog of the Cabibbo-Radicati sum rule and expresses the sum of the radiative widths in terms of the isovector charge radius of the ground state heavy meson. Using model-dependent estimates and heavy hadron chiral perturbation theory calculations, we show that this sum rule is close to saturation with states of excitation energies less than 1 GeV. An analog of the Adler-Weisberger sum rule gives an useful sum rule for the pionic widths of heavy excited mesons, which is used to set a model-independent upper bound on the coupling of the P-wave heavy mesons.

hep-ph↗

arXiv1995

Heavy Baryons and Multiquark Exotics in the Large $N_c$ limit

In the large $N_c$ limit, one can describe normal heavy baryons $Qqq$ and heavy pentaquarks $\bar Qqqqq$ as bound states of heavy mesons to chiral (anti)solitons. In this picture, the strong and electromagnetic decay parameters of these hadrons can be calculated from those of the constituent heavy mesons and light baryons, while the weak decay form factors can be evaluated analytically.

hep-ph↗

arXiv1995

Charmed Strange Pentaquarks in the Large $N_c$ Limit

The properties of pentaquarks containing a heavy anti-quark and strange quarks are studied in the bound state picture. In the flavor SU(3) limit, there are many pentaquark states with the same binding energy. When the SU(3) symmetry breaking effects are included, however, three states become particularly stable due to a ``Gell-Mann--Okubo mechanism''. They are the $\bar Qsuud$ and $\bar Qsudd$ states discussed by Lipkin, and a a previously unstudied $\bar Qssud$ state. These states will have $J^P={1\over2}^+$ and their masses are estimated. These states, if exist, may be seen in experiments in the near future.

hep-ph↗

arXiv1995

Radiative Decays of Excited $Λ_Q$ Baryons in the Bound State Picture

It is shown that, in the bound state picture, the $Λ_c(2593) \toΛ_cγ$ and $Λ_c(2625)\toΛ_cγ$ decays are severely suppressed. On the other hand, for their bottom counterparts, which are predicted to have masses 5900 and 5926 MeV respectively, may have significant radiative branching ratio. In particular, the $Λ_b(5926)\toΛ_bγ$ mode may even dominate over the strong decay mode. The isospin allowed $Λ^{**}_Q\toΣ_Qγ$ mode is expected to be small.

hep-ph↗

arXiv1995

More Conservation Laws and Sum Rules in the Heavy Quark Limit

This is the continuation of a previous article, in which the Bjorken and Voloshin sum rules were interpreted as statements of conservation of probability and energy. Here the formalism is extended to higher moments of the Hamiltonian operator. From the conservation of the second moment of the Hamiltonian operator one can derive a sum rule which, in the small velocity limit, reduces to the Bigi--Grozin--Shifman--Uraltsev--Vainshtein (BGSUV) sum rule. On the other hand, the conservation of the third moment of the Hamiltonian operator gives a new sum rule, which is related to the matrix element of the heavy quark counterpart of the Darwin term in atomic physics. The general case of the higher order moments is also discussed.

hep-ph↗

arXiv1994

From Tetraquark to Hexaquark: A Systematic Study of Heavy Exotics in the Large $N_c$ Limit

A systematic study of multiquark exotics with one or $N_c-1$ heavy quarks in the large $N_c$ limit is presented. By binding a chiral soliton to a heavy meson, either a normal $N_c$-quark baryon or an exotic $(N_c+2)$-quark baryon is obtained. By replacing the heavy quark with $N_c-1$ heavy antiquarks, exotic $(2N_c-2)$-quark and $2N_c$-quark mesons are obtained. When $N_c = 3$, they are just the normal triquark baryon $Qqq$, the exotic pentaquark baryon $Q\bar q\bar q\bar q\bar q$, tetraquark di-meson $\bar Q \bar Q qq$ and the hexaquark di-baryon $\bar Q \bar Q \bar q \bar q\ bar q \bar q$ respectively. Their stabilities and decays are also discussed. In particular, it is shown that the ``heavy to heavy'' semileptonic decays are described by the Isgur--Wise form factors of the normal baryons.

hep-ph↗

arXiv1994

Semileptonic Decays of Heavy Tetraquarks

There exist heavy tetraquark states $QQ \bar q \bar q$ in the heavy quark limit. These states are stable with respect to strong interactions and hence must decay weakly. It is shown that the semileptonic decay depends on a single Isgur--Wise form factor, which can be expressed in term of the Isgur--Wise form factors which govern the semileptonic decays of the $Qqq$ and $QQq$ baryons.

hep-ph↗

arXiv1994

Conservation Laws and Sum Rules in the Heavy Quark Limit

In the heavy quark limit, hadrons appear as eigenstates of the light degrees of freedom under the static color field of the heavy quark. In this formalism, the weak form factors appear naturally as the overlaps of the initial and final wavefunctions of the light degrees of freedom, and the Bjorken and Voloshin sum rules are statements of conservation of probability and energy. Moreover, parity conservation can lead to a sum rule which relates weak form factors at different kinematic points. {}From this sum rule, model independent lower bounds on Isgur--Wise form factors can be obtained analytically.

hep-ph↗

arXiv1994

New Universality of Baryon Isgur--Wise Form Factor in the Large $N_c$ limit

New universality appears for the baryon Isgur--Wise form factor in the large $N_c$ limit. It is found that the semileptonic $Λ_b \rightarrow Λ_c$ and $Σ_b^{(*)} \rightarrow Σ^{(*)}_c$ decays are described by the same form factor, which can be calculated analytically. In the exact chiral $SU(3)$ limit, the same form factor is applicable to semileptonic $Ω_b^{(*)} \rightarrow Ω^{(*)}_c$ decays.

hep-ph↗

arXiv1994

Excited $Λ_Q$ Baryons in the Large $N_c$ Limit

The spectrum of excited $Λ_Q$-type heavy baryons is considered in the large $N_c$ limit. The universal form factors for $Λ_b$ semileptonic decay to excited charmed baryons are calculated in the large $N_c$ limit. We find that the Bjorken sum rule (for the slope of the Isgur--Wise function) and Voloshin sum rule (for the mass of the light degrees of freedom) are saturated by the first doublet of excited $Λ_Q$ states.

hep-ph↗

arXiv1993

Corrections from Low Momentum Physics to Heavy Quark Symmetry Relations for $B\rightarrow De\bar ν_e$ and $B\rightarrow D^*e \bar ν_e$ Decay

Heavy quark symmetry relations for $B\rightarrow De\bar ν_e$ and $B\rightarrow D^*e \bar ν_e$ form factors receive corrections suppressed by powers of the charm quark mass. For small up and down quark massed the leading corrections of order $(1/m_c)^{n+2}~n = 0,1,2,...$ have a nonanalytic dependence on the light quark masses of the form $\ell n m_π^2$ for $n = 0$ and $(1/m_π)^n$ for $n = 1,2, ...$~. These corrections arise from very low momentum physics (i.e., well below the chiral symmetry breaking scale) and are computed using chiral perturbation theory. They are typically of order a few percent.

hep-ph↗