Short-distance Part Research Articles

Ladder approximation to spin velocities in quantum wires

The spin sector of charge-spin separated single mode quantum wires is studied, accounting for realistic microscopic electron-electron interactions. We utilize the ladder approximation (LA) to the interaction vertex and exploit thermodynamic relations to obtain spin velocities. Down to not too small carrier densities our results compare well with existing quantum Monte-Carlo (QMC) data. Analyzing second order diagrams we identify logarithmically divergent contributions as crucial which the LA includes but which are missed, for example, by the self-consistent Hartree-Fock approximation. Contrary to other approximations the LA yields a non-trivial spin conductance. Its considerably smaller computational effort compared to numerically exact methods, such as the QMC method, enables us to study overall dependences on interaction parameters. We identify the short distance part of the interaction to govern spin sector properties.

Topic and focus at the peripheries: the dynamics of tree growth

In this paper topic and focus effects at both left and right periphery are argued to be epiphenomena of general properties of tree growth. We incorporate Korean into this account as a prototypical verb-final language, and show how long- and short-distance scrambling form part of this general picture. Multiple long-distance scrambling effects emerge as a consequence of the feeding relationship between different forms of structural under-specification. We also show how the array of effects at the right periphery, in both verb-final and other language-types, can also be explained with the same concepts of tree growth. In particular the Right Roof Constraint, a well-known but little understood constraint, is an immediate consequence of compositionality constraints as articulated in this system.

The radiative leptonic decays $D^0 \to e^+ e^-\gamma,\mu^+\mu^-\gamma $ in the standard model and beyond

We present a calculation of the rare decay modes D^0 -> e^+ e^- gamma and D^0 -> mu^+ mu^- gamma in the framework of Standard Model. For the short distance part, we have derived QCD corrections to the Wilson coefficients involved, including C_9. The latter is found to be strongly suppressed by the corrections, leading to diminished values for the c -> u l^+l^- branching ratios in the 10^(-10) range. Within SM the exclusive decays are dominated by long distance effects. Nonresonant contributions are estimated using heavy quark and chiral symmetries to be at the level of 10%, compared to the contributions arising from D^0-> V gamma->l^+ l^- gamma, with V=rho, omega, phi. The total SM branching ratio is predicted to be in the range (1-3) x 10^(-9). We also consider contributions coming from MSSM with and without R parity conservation. Effects from MSSM are significant only for the R-parity violating case. Such contributions enhance the branching ratio D^0-> mu^+ mu^- gamma to 0.5 x 10^(-7), based on appropriately allowed values for C_9 and C_{10}. This selects D^0->mu^+ mu^- gamma as a possible probe of new physics.

Long-distance effects inB→Vγradiative weak decays

A systematic approach to long-distance effects in exclusive radiative weak B decays is presented, based on a combination of the heavy quark limit with perturbative QCD. The dominant long-distance effects, connected with weak annihilation and W-exchange topologies, can be computed in a model-independent way using experimental data on B radiative leptonic decays. Nonfactorizable corrections vanish in the chiral limit and to leading twist. The left-handed photon amplitudes are shown to be enhanced relative to the right-handed ones, both in the long- and short-distance parts of the $\overline{B}$ decay amplitudes. Recent CLEO data on $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma}$ decays are consistent with standard model estimates of the long-distance contributions, and disfavor an enhanced gluonic penguin contribution. We discuss the implications of our results for the extraction of $|{V}_{\mathrm{td}}|.$

Decay constants of heavy-light mesons in Bakamjian-Thomas heavy quark models

In quark models \`a la Bakamjian and Thomas, that yield covariance and Isgur-Wise scaling of form factors in the heavy quark limit, we compute the decay constants $f^{(n)}$ and $f^{(n)}_{1/2}$ of S-wave and P-wave mesons composed of heavy and light quarks. Heavy quark limit scaling $\sqrt{M} f = Cst$ is obtained, and it is shown that this class of models satisfies the sum rules involving decay constants and Isgur-Wise functions recently formulated by us in the heavy quark limit of QCD. Moreover, the model also satisfies the selection rules of the type $f^{(n)}_{3/2} = 0$ that must hold in this limit. We discuss different Ans\"atze for the dynamics of the mass operator at rest. For non-relativistic kinetic energies ${p^2 \over 2m}$ the decay constants are finite even if the potential $V(r)$ has a Coulomb part. For the relativistic form $\sqrt{p^2 + m^2}$, the S-wave decay constants diverge if there is a Coulomb singularity. Using phenomenological models of the spectrum with relativistic kinetic energy and regularized short distance part (Godfrey-Isgur model or Richardson potential of Colangelo et al.), that yield $\rho^2 \simeq 1$ for the elastic Isgur-Wise function, we compute the decay constants in the heavy quark limit, and obtain $f_B \simeq$ 300 MeV, of the same order although slightly smaller than in the static limit of lattice QCD. We find the decay constants of $D^{**}$ with $j =1/2$ of the same order of magnitude. The convergence of the heavy quark limit sum rules is also studied.

1/Nccorrections to the hadronic matrix elements ofQ6andQ8inK→ππdecays

We calculate long-distance contributions to the amplitudes ${A(K}^{0}\ensuremath{\rightarrow}2\ensuremath{\pi},I)$ induced by the gluon and the electroweak penguin operators ${Q}_{6}$ and ${Q}_{8},$ respectively. We use the ${1/N}_{c}$ expansion within the effective chiral Lagrangian for pseudoscalar mesons. In addition, we adopt a modified prescription for the identification of meson momenta in the chiral loop corrections in order to achieve a consistent matching to the short-distance part. Our approach leads to an explicit classification of the loop diagrams into non-factorizable and factorizable, the scale dependence of the latter being absorbed in the low-energy coefficients of the effective theory. Along these lines we calculate the one-loop corrections to the $\mathcal{O}{(p}^{0})$ term in the chiral expansion of both operators. In the numerical results, we obtain moderate corrections to ${B}_{6}^{(1/2)}$ and a substantial reduction of ${B}_{8}^{(3/2)}.$

Higher Fock states and power counting in exclusive $P$ -wave quarkonium decays

Exclusive processes at large momentum transfer $Q$ factor into perturbatively calculable short-distance parts and long-distance hadronic wave functions. Usually, only contributions from the leading Fock states have to be included to leading order in $1/Q$ . We show that for exclusive decays of $P$ -wave quarkonia the contribution from the next-higher Fock state $|{\rm Q}\bar{\rm Q}{\rm g}\rangle$ contributes at the same order in $1/Q$ . We investigate how the constituent gluon attaches to the hard process in order to form colour-singlet final-state hadrons and argue that a single additional long-distance factor is sufficient to parametrize the size of its contribution. Incorporating transverse degrees of freedom and Sudakov factors, our results are perturbatively stable in the sense that soft phase-space contributions are largely suppressed. Explicit calculations yield good agreement with data on $\chi_{{\rm c} J}$ decays into pairs of pions, kaons, and etas. We also comment on $J/\psi$ decays into two pions.

Higher Fock states and power counting in exclusive

Exclusive processes at large momentum transfer $Q$ factor into perturbatively calculable short-distance parts and long-distance hadronic wave functions. Usually, only contributions from the leading Fock states have to be included to leading order in $1/Q$ . We show that for exclusive decays of $P$ -wave quarkonia the contribution from the next-higher Fock state $|{\rm Q}\bar{\rm Q}{\rm g}\rangle$ contributes at the same order in $1/Q$ . We investigate how the constituent gluon attaches to the hard process in order to form colour-singlet final-state hadrons and argue that a single additional long-distance factor is sufficient to parametrize the size of its contribution. Incorporating transverse degrees of freedom and Sudakov factors, our results are perturbatively stable in the sense that soft phase-space contributions are largely suppressed. Explicit calculations yield good agreement with data on $\chi_{{\rm c} J}$ decays into pairs of pions, kaons, and etas. We also comment on $J/\psi$ decays into two pions.

Electromagnetic corrections for pions and kaons: masses and polarizabilities

The unknown constants in Chiral Perturbation Theory needed for an all orders analysis of the polarizabilities and electromagnetic corrections to the masses of the pseudo-Goldstone bosons are estimated at leading order in 1 N c . We organize the calculation in an 1 N c expansion and separate long- and short-distance physics contributions by introducing a Euclidean cut-off. The long-distance part is evaluated using the ENJL model and the short-distance part using perturbative QCD and factorization. We obtain very good matching between both. We then include these estimates in a full chiral perturbation theory calculation to order e 2 p 2 for the masses and p 6 for the polarizabilities. For the electromagnetic corrections to the masses, we confirm a large violation of Dashen's theorem getting a more precise value for this violation. We make a comparison with earlier related work. Some phenomenological consequences are discussed too.

Nonperturbative effects in polarization phenomena for [formula omitted] and B → K + π + γ decays

Polarization characteristics of γ-quanta, produced in decays B → K ∗ + γ and B → K + π + γ are studied in a general parity non-conserving framework. Polarization characteristics of γ quanta for perturbative (i.e. short distance) part of the matrix element of these decays are shown to be universal, independent of the process. Nonperturbative effects however violate such universality.

Calculation of the renormalized charmed-quark mass in lattice QCD

The correlator of heavy-quark currents is calculated in quenched Lattice QCD on a 16 3 × 32-lattice for β = {6,6.3}. The renormalized charmed quark mass is extracted from the short-distance part of that correlator: m c MS (m c) = 1.22(5) GeV . We study the sensitivity of our data to the strong coupling constant.

Determination of the renormalized heavy-quark mass in lattice QCD

We study on the lattice the correlator of heavy-quark currents in the vicinity of vanishing momentum. The renormalized charmed quark mass, the renormalized strong coupling constant and gluon condensate can be defined in terms of the derivatives of that correlator at zero momentum. We analyze quenched Monte Carlo data on a small 8 3 × 16 lattice for β = 6. We generalize dispersion relations to the lattice theory in a simple way and use them successfully to fit both the short-distance part and long-distance part of the correlator in such a small volume.

Systematics of quarkonium production

Quarkonium production in high-energy reactions is found to exhibit a behaviour more universal than that expected from velocity scaling. Total rates of quarkonia produced in hadronic interactions as well as Feynman- x and transverse momentum distributions can be described over the full range of accessible energies ( 15 ≲ s ≲ 1800 GeV ) by two-stage processes. The quarkonium production cross section factors into a process-dependent short-distance part and a single long-distance matrix element. The first part describing the production of a free quark-antiquark pair is the perturbatively calculated subthreshold cross section. The non-perturbative factor turns out to be universal, giving the model great predictive power. Furthermore we estimate the fraction of the heavy-quark cross section leading to quarkonium for both the charm and bottom systems. Finally, we comment on quarkonium photoproduction.

Study of long distance contributions to K-->n pi nu nu -bar.

We calculate the long distance contributions to $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\nu}\overline{\ensuremath{\nu}}, \ensuremath{\pi}\ensuremath{\pi}\ensuremath{\nu}\overline{\ensuremath{\nu}}, \mathrm{and} \ensuremath{\pi}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ modes within the framework of chiral perturbation theory. We find that these contributions to decay rates of $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ and $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ in the chiral logarithmic approximation are at least seven orders of magnitude suppressed relative to those from the short distance parts. The long distance effects in this class of decays are, therefore, negligible.

Nuclear dependence in direct photon production.

We calculate the nuclear dependence of direct photon production in hadron-nucleus collisions. In terms of a multiple scattering picture, we factorize the cross section for direct photon production into calculable short-distance partonic parts times multiparton correlation functions in nuclei. We present the hadron-nucleus cross section as $A^{\alpha}$ times the hadron-nucleon cross section. Using information on the multiparton correlation functions extracted from photon-nucleus experiments, we compute the value of $\alpha$ as a function of transverse momentum of the direct photon. We also compare our results with recent data from Fermilab experiment E706.

Meson-gluon interaction and ΔI=1/2 problem in the standard model

In the present paper we study the new K→ππ decay channel with the gluons being an intermediate state which is neglected within the factorization framework. Both short-distance (perturbative) and long-distance (non-perturbative) part of the corresponding amplitude are calculated To obtain the long-distance contribution the chiral Lagrangian approach is used as a low-energy model of strong interactions and a relevant chiral coupling is derived via QCD sum rules. We find that non-perturbative contribution being dominant, gives additional enhancement of the K→ππ decay amplitude with the isospin transfer ΔI=1/2 what improves the rather undetermined situation with the ΔI=1/2 problem. The scale of this new contribution allows us to conclude that there is a sizable violation of the factorization hypothesis in theO(p4) order of the chiral expansion.

The rare decays [formula omitted] beyond leading logarithms

We analyze the branching ratio for the FCNC mode K + → π +ν ν in the standard model with QCD effects taken into account consistently to next-to-leading order. This involves a two-loop renormalization group analysis for the charm contribution, presented in this paper, and the calculation of O( α S) corrections to all orders in m t/ M W for the top-quark case that we have described elsewhere. The inclusion of next-to-leading corrections reduces considerably the theoretical uncertainty due to the choice of the renormalization scales, inherent in any calculation to finite order in perturbation theory. For K + → π +ν ν this point has not been discussed previously. In particular, the related uncertainty in the determination of | V td| from B( K + → π +ν ν) is reduced from ∼ 30% to ∼ 7% for typical values of the parameters. Simultaneously also the dependence of B( K + → π +ν ν) on the choice of m c is considerably reduced. We also give the next-to-leading order expression for the short-distance part of K L → μ + μ −. Impacts of our calculations on the determination of the unitarity triangle are presented.

Testing the CKM parameters with parity violating longitudinal muon polarization in K + → π+μ+μ−

We point out that the parity violating longitudinal muon polarization P L in the decay K +→ π + μ + μ − is closely related to the short-distance part of the decay amplitude in K L → μ + μ −. M Measuring such polarization would provide not only a rather clean test on the CKM parameter ϱ, but also a check on the short-distance contribution to K L → μ + μ −. The possible ranges of P L in the standard and two-Higgs doublets models are presented. We find that P L is not sensitive to extensions of the Higgs sector when taking into account all the experimental data.

Power corrections in hadronic scattering (I). Leading 1/ Q2 corrections to the Drell-Yan cross section

We review the leading 1/ Q 2 corrections to hadronic structure functions measured in deeply inelastic scattering, and we calculate the leading 1/ Q 2 corrections to Drell-Yan cross section. We find that the leading 1/ Q 2 corrections to a Drell-Yan cross section is given by the convolution of a calculable short-distance hard part, a twist-2 matrix element and a twist-4 matrix element. At leading order in α s, the normalization of the 1/ Q 2 longitudinal structure functions for Drell-Yan cross sections are determined by higher-twist longitudinal structure functions in deeply inelastic scattering. Other experimental tests of 1/ Q 2 corrections are also discussed.

On the double penguin-like contributions to the $$B^0 - \bar B^0 $$ mixing

We investigate double penguin-like diagrams for the\(B^0 - \bar B^0 \) mixing, a missing piece in the literature. We find that the short-distance part of these diagrams contributes ≲5% and thus is unimportant in reconciling the value of poorly determined parameters of the standard model and most recent experimental information. We also point out the long-distance hadronic complications which leave the\(B^0 - \bar B^0 \) mixing issue to some extent open.