arXiv subjects

Nikolai Uraltsev

Publications and source records attributed to Nikolai Uraltsev.

31 records · Page 2Linked to original sources

arXiv2001

A Vademecum on Quark-Hadron Duality

We present an elementary introduction to the problem of quark-hadron duality and its practical limitations, in particular as it concerns local duality violation in inclusive B meson decays. We show that the accurate definition of duality violation elaborated over the recent years allows one to derive informative constraints on violations of local duality. The magnitude of duality violation is particularly restricted in the total semileptonic widths. This explains its strong suppression in concrete dynamical estimates. We analyze the origin of the suppression factors in a model-independent setting, including a fresh perspective on the Small Velocity expansion. A new potentially significant mechanism for violation of local duality in Γ_sl(B) is analyzed. Yet we conclude that the amount of duality violation in Γ_sl(B) must be safely below the half percent level, with realistic estimates being actually much smaller. Violation of local duality in Γ_sl(B) is thus far below the level relevant to phenomenology. We also present a cautionary note on the B->D^* decay amplitude at zero recoil and show that it is much more vulnerable to violations of quark-hadron duality than Γ_sl(B). A critical review of some recent literature is given. We point out that the presently limiting factor in genuinely model-independent extraction of V_cb is the precise value of the short-distance charm quark mass. We suggest a direct and precise experimental check of local quark-hadron duality in semileptonic B->X_c lνdecays.

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arXiv2000

A Few Aspects of Heavy Quark Expansion

Two topics in heavy quark expansion are discussed. The heavy quark potential in perturbation theory is reviewed in connection to the problem of the heavy quark mass. The nontrivial reason behind the failure of the "potential subtracted" mass in higher orders is elucidated. The heavy quark sum rules are the second subject. The physics behind the new exact sum rules is described and a simple quantum mechanical derivation is given. The question of saturation of sum rules is discussed. A comment on the nonstandard possibility which would affect analysis of BR_sl(B) vs. n_c is made.

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arXiv2000

New Exact Heavy Quark Sum Rules

Considering nonforward scattering amplitude off the heavy quark in the Small Velocity limit two exact superconvergent sum rules are derived. The first sum rule leads to the lower bound ρ^2 > 3/4 for the slope of the Isgur-Wise function. It also provides the rationale for the fact that the vector heavy flavor mesons are heavier than the pseudoscalar ones. A spin-nonsinglet analogue \barΣof \barΛ= M_B-m_b is introduced.

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arXiv2000

Topics in the Heavy Quark Expansion

Achievements in the heavy quark theory over the last decade are reviewed, with the main emphasis put on dynamical methods which quantify nonperturbative effects via application of the Operator Product Expansion. These include the total weak decay rates of heavy flavor hadrons and nonperturbative corrections to heavy quark sum rules. Two new exact superconvergent sum rules are derived; they differ from the known ones in that they are finite and normalization point independent in perturbation theory. A new hadronic parameter \barΣis introduced which is a spin-nonsinglet analogue of \barΛ=M_B-m_b; it is expected to be about 0.25GeV. The first sum rule implies the bound ρ^2 > 3/4 for the slope of the Isgur-Wise function. The heavy quark potential is discussed and its connection to the infrared contributions in the heavy quark mass. Among applications extraction of |V_cb| from the total semileptonic and from the B->D^* zero recoil rates is addressed, as well as extracting |V_ub| from Γ_sl(b->u). Practical aspects of local quark-hadron duality are briefly discussed.

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arXiv2000

D^0 - D^0-bar Oscillations as a Probe of Quark-Hadron Duality

It is usually argued that the Standard Model predicts slow D^0-\bar D^0 oscillations with ΔM_D, ΔΓ_D < 10^{-3}*Γ_D$ and that New Physics can reveal itself through ΔM_D exceeding 10^{-3}*Γ_D. It is believed that the bulk of the effect is due to long distance dynamics that cannot be described at the quark level. We point out that in general the OPE yields soft GIM suppression scaling only like (m_s/μ_{hadr})^2 and even like m_s/μ_{hadr} rather than m_s^4/m_c^4 of the simple quark box diagram. Such contributions can actually yield ΔM_D, ΔΓ_D \sim O(10^{-3})*Γ_D without invoking additional long distance effects. They are reasonably suppressed as long as the OPE and local duality are qualitatively applicable in the 1/m_c expansion. We stress the importance of improving the sensitivity on ΔΓ_D as well as ΔM_D in a dedicated fashion as a laboratory for analyzing the onset of quark-hadron duality and comment on the recent preliminary study on ΔΓ_D by the FOCUS group.

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arXiv2000

Analytical Heavy Quark Expansion in the 't Hooft Model

We present a number of exact relations for the heavy quark limit and develop an analytical 1/m_Q expansion for heavy mesons in the 't Hooft model. Among the new results are relation 3μ_π^2=\barΛ^2 - m_{sp}^2+β^2, 1/m_Q corrections to the decay constants, to the kinetic expectation values and 1/m_Q^2 nonperturbative corrections to the B->D amplitude at zero recoil. The properties of the IW functions are addressed and the small velocity sum rules are verified.

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arXiv1999

Heavy Quark Expansion and Preasymptotic Corrections to Decay Widths in the 't Hooft Model

We address nonperturbative power corrections to inclusive decay widths of heavy flavor hadrons in the context of the 't Hooft model (two-dimensional QCD at N_c->oo), with the emphasis on the spectator-dependent effects sensitive to the flavor of the spectator. The summation of exclusive widths is performed analytically using the `t Hooft equation. We show that the 1/m_Q expansion of both the Weak Annihilation and Pauli Interference widths coincides with the OPE predictions, to the computed orders. Violation of local duality in the inclusive widths is quantified, and the new example is identified where the OPE prediction and the actual effect are completely saturated by a single final state. The qualitative aspects of quark hadronization emerging from the analysis in the 't Hooft model are discussed. Certain aspects of summation of spectator-independent hadronic weak decay widths are given in more detail, which were not spelled out previously. We also give some useful details of the 1/m_Q expansion in the 't~Hooft model.

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arXiv1999

Theoretical Uncertainties in Gamma_sl(b->u)

I review the existing theoretical uncertainties in relating the semileptonic decay width in b->u transitions to the underlying Kobayashi-Maskawa mixing element |V_ub|. The theoretical error bars are only a few percent in |V_ub|, with uncertainties from the impact of the nonperturbative effects nearly negligible.

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arXiv1999

Pauli Interference in the 't Hooft Model: Heavy Quark Expansion and Quark-Hadron Duality

Pauli Interference in decays of heavy flavor mesons, a genuinely nonleptonic nonperturbative effect, is considered in the 't Hooft model. Analytic summation of the exclusive decay widths yields the same expression as obtained in the OPE-based approach. Threshold-related violations of local duality in PI are found to be suppressed. A novel case is identified where the OPE effect is completely saturated by a single final state.

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arXiv1998

Four-fermion heavy quark operators and light current amplitudes in heavy flavor hadrons

We introduce and study the properties of the "color-straight" four-quark operators containing heavy and light quark fields. They are of the form (\bar bΓ_b b)(\bar qΓ_q q) where both brackets are color singlets. Their expectation values include the bulk of the nonfactorizable contributions to the nonleptonic decay widths of heavy hadrons. The expectation values of the color-straight operators in the heavy hadrons are related to the momentum integrals of the elastic light-quark formfactors of the respective heavy hadron. We calculate the asymptotic behavior of the light-current formfactors of heavy hadrons and show that the actual decrease is 1/(q^2)^3/2 rather than 1/q^4. The two-loop hybrid anomalous dimensions of the four-quark operators and their mixing (absent in the first loop) are obtained. Using plausible models for the elastic formfactors, we estimate the expectation values of the color-straight operators in the heavy mesons and baryons. Improved estimates will be possible in the future with new data on the radiative decays of heavy hadrons. We give the Wilson coefficients of the four-fermion operators in the 1/m_b expansion of the inclusive widths and discuss the numerical predictions. Estimates of the nonfactorizable expectation values are given.

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arXiv1998

Heavy quark expansion in beauty and its decays

I give an introduction to the QCD-based theory of the heavy flavor hadrons and their weak decays. Trying to remain at the next-to-elementary level and skip technicalities, I concentrate on the qualitative description of the most important applications and physical meaning of the theoretical statements. The numerical results of the dedicated theoretical analyses of extracting V_cb are given and the possibilities to determine V_ub in future are discussed. At the same time I describe in simple language subtle peculiarities distinguishing actual QCD of heavy quarks from naive quantum mechanical treatment often applied to heavy flavor hadrons. These subtleties are often mistreated. Particular attention is paid to the concept of the heavy quark mass and its evaluation, to the kinetic operator and the question of the 1/m_Q corrections to inclusive widths of heavy flavor hadrons. I argue that the properly defined b quark mass is known with a good accuracy from the \bar{b} b threshold cross section.

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arXiv1997

Complete O(alpha_s^2) Corrections to Zero-Recoil Sum Rules for B-->D* Transitions

We present the complete O(alpha_s^2) corrections to the Wilson coefficient of the unit operator in the zero-recoil sum rule for the B-->D* transition. We include both perturbative and power-suppressed nonperturbative effects in a manner consistent with the operator product expansion. The impact of these corrections on |V_cb| extracted from semileptonic B-->D* decays near zero recoil is discussed. The mixing of the heavy quark kinetic operator with the unit operator at the two loop level is obtained. O(alpha_s) corrections to a number of power-suppressed operators are calculated.

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arXiv1996

BLM-Resummation and OPE in Heavy Flavor Transitions

An all-order resummation is performed for the effect of the running of the strong coupling in the zero recoil sum rule for the axial current and for the kinetic operator \vecπ^2. The perturbative corrections to well-defined objects of OPE turn out to be very moderate. The renormalization of the kinetic operator is addressed.

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