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L. Oliver

Publications and source records attributed to L. Oliver.

At least 37 records · Page 2Linked to original sources
arXiv2007

Isospin breaking in the yield of heavy meson pairs in e+e- annihilation near threshold

We revisit the problem of interplay between the strong and the Coulomb interaction in the charged-to-neutral yield ratio for $B {\bar B}$ and $D {\bar D}$ pairs near their respective thresholds in $e^+e^-$ annihilation. We consider here a realistic situation with a resonant interaction in the isospin I=0 channel and a nonresonant strong scattering amplitude in the I=1 state. We find that the yield ratio has a smooth behavior depending on the scattering phase in the I=1 channel. The same approach is also applicable to the $K {\bar K}$ production at the $ϕ(1020)$ resonance, where the Coulomb effect in the charged-to-neutral yield ratio is generally sensitive to the scattering phases in both the isoscalar and the isovector channels. Furthermore, we apply the same approach to the treatment of the effect of the isotopic mass difference between the charged and neutral mesons and argue that the strong-scattering effects generally result in a modification to the pure kinematical effect of this mass difference.

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arXiv2006

The Isgur-Wise function in the BPS limit

From sum rules in the heavy quark limit of QCD, using the non-forward amplitude, we demonstrate that if the slope rho^2 = -xsi'(1) of the Isgur-Wise function xsi(w) attains its lower bound 3/4 (as happens in the BPS limit proposed by Uraltsev), the IW function is completely determined, given by the function xsi(w) = [2/(w+1)]^(3/2).

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arXiv2006

Explicit form of the Isgur-Wise function in the BPS limit

Using previously formulated sum rules in the heavy quark limit of QCD, we demonstrate that if the slope rho^2 = -xi'(1) of the Isgur-Wise function xi(w) attains its lower bound 3/4, then all the derivatives (-1)^L xi^(L)(1) attain their lower bounds (2L+1)!!/2^(2L), obtained by Le Yaouanc et al. This implies that the IW function is completely determined, given by the function xi(w) = [2/(w+1)]^(3/2). Since the so-called BPS condition proposed by Uraltsev implies rho^2 = 3/4, it implies also that the IW function is given by the preceding expression.

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arXiv2006

The tensor force in Heavy Quark Effective Theory

We extend the formalism of Leibovich, Ligeti, Stewart and Wise in the 1/m_Q expansion of Heavy Quark Effective Theory for the B semileptonic decays into excited D[(3/2)^+] mesons to the opposite parity states D[(3/2)^-]. For D[(3/2)^+] the 1/m_Q current perturbation dominates over the leading term at zero recoil, while for D[(3/2)^-] the 1/m_Q perturbation due to L_mag dominates also at zero recoil. We show that the corresponding 1/m_Q magnetic coupling is proportional to the mixing between the states D[(3/2)^-] and D[(1/2)^-] induced by the tensor force. We point out some subtleties that appear in this respect in HQET.

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arXiv2005

Memorino on the `1/2 vs. 3/2 Puzzle' in $\bar B \to l \bar νX_c$

After the successes the OPE description has scored in describing $\bar B \to l \bar νX_c$ decays, we need to study what can be said about the composition of the hadronic final state $X_c$. The same OPE treatment yields sum rules implying the dominance of $j_q = 3/2$ charm states in $X_c$ over their $j_q=1/2$ counterparts. This prediction is supported by other general arguments as well as quark model calculations. At present it is unclear to which degree data conform to these predictions. More experimental information is essential. We want to ask our experimental colleagues for a redoubled effort to establish, which hadronic configurations -- $D/D^* + π, D/D^* + 2 π, ...$ -- make up $Γ(\bar B \to l \bar νX_c)$ beyond $\bar B \to l \bar νD/D^*$, what their quantum numbers are and their mass distributions. The latter is most relevant for the determination of hadronic mass moments in $\bar B \to l \bar νX_c$. Since all this will require considerable effort on their part, we want to explain the theoretical issues involved, why they carry `gravitas' -- i.e. are weighty -- and why a better understanding of them will be of significant value. In this brief memo we sketch the underlying arguments based on heavy quark theory, the OPE, a special class of quark models and lattice QCD in a nutshell. After summarizing the experimental situation we conclude with two lists, namely one with measurements that need to be done and one with items of theoretical homework. Some of the latter can be done by employing existing theoretical tools, whereas others need new ideas.

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arXiv2005

Sum rules for leading and subleading form factors in Heavy Quark Effective Theory using the non-forward amplitude

Within the OPE, we the new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/m_Q, using the non-forward amplitude. In particular, we obtain new sum rules involving the elastic subleading form factors chi_i(w) (i = 1,2, 3) at order 1/m_Q that originate from the L_kin and L_mag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (j^P, J^P) = ((1/2)^-, 1^-), ((3/2)^-, 1^-) that enter in the 1/m_Q^2 corrections of the axial form factor h_(A_1)(w) at zero recoil. This allows to obtain a lower bound on -delta_(1/m^2)^(A_1) in terms of the chi_i(w) and the shape of the elastic IW function xi(w). An important theoretical implication is that chi'_1(1), chi_2(1) and chi'_3(1) (chi_1(1) = chi_3(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values rho^2->3/4, sigma^2->15/16. These constraints should be taken into account in the exclusive determination of |V_(cb)|.

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arXiv2005

Lagrangian perturbations at order 1/m$_{\bf Q}$ and the non-forward amplitude in Heavy Quark Effective Theory

We pursue the program of the study of the non-forward amplitude in HQET. We obtain new sum rules involving the elastic subleading form factors $χ_i(w)$ $(i = 1,2, 3)$ at order $1/m_Q$ that originate from the ${\cal L}_{kin}$ and ${\cal L}_{mag}$ perturbations of the Lagrangian. To obtain these sum rules we use two methods. On the one hand we start simply from the definition of these subleading form factors and, on the other hand, we use the Operator Product Expansion. To the sum rules contribute only the same intermediate states $ (j^P, J^P) = ({1 \over 2}^-, 1^-), ({3\over 2}^-, 1^-)$ that enter in the $1/m_Q^2$ corrections of the axial form factor $h_{A_1}(w)$ at zero recoil. This allows to obtain a lower bound on $- δ_{1/m^2}^{(A_1)}$ in terms of the $χ_i(w)$ and the shape of the elastic IW function $ξ(w)$. We find also lower bounds on the $1/m_Q^2$ correction to the form factors $h_+(w)$ and $h_1(w)$ at zero recoil. An important theoretical implication is that $χ'_1(1)$, $χ_2(1)$ and $χ'_3(1)$ ($χ_1(1) = χ_3(1) = 0$ from Luke theorem) must vanish when the slope and the curvature attain their lowest values $ρ^2 \to {3 \over 4}$, $σ^2 \to {15 \over 16}$. We discuss possible implications on the precise determination of $|V_{cb}|$.

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arXiv2005

The decays $\bar{B} \to D^{**}π$ and the Isgur-Wise functions $τ_{1/2}(w)$, $τ_{3/2}(w)$

We perform a phenomenological analysis of the decays $B \to D^{**}π$, where $D^{**}$ is a $P$-wave excited meson with total angular momentum $j = {1 \over 2}$ or ${3 \over 2}$ for the light cloud, recently measured by the Belle Collaboration in the modes $\bar{B}^0\to D^{**+}π^-$ (Class I) and $B^- \to D^{**0}π^-$ (Class III). Making the reasonable assumption of naive factorization, that we test in $B \to D(D^*)π$ decays, Class I decays allow to extract the Isgur-Wise form factors $τ_{1/2}(w)$, $τ_{3/2}(w)$ at $w \cong w_{max}$ ($q^2 \cong 0$). We obtain $τ_{1/2}(w_{max}) < 0.20$, $τ_{3/2}(w_{max}) = 0.31 \pm 0.12$. We discuss the question of the $w$ dependence of these IW functions. We find agreement with the Bakamjian-Thomas quark model of form factors and, extrapolating at $w=1$, with Bjorken and Uraltsev sum rules. We discuss also Class III decays, where the $D^{**0}$ $(j = {1 \over 2})$ emission diagram contributes. We extract the corresponding $f_{D_{1/2}}$ decay constant, that is in agreement with theoretical estimates at finite mass. Finally, we must warn that $1/m_Q$ corrections could be large and upset the results of the present stage of this analysis. On the other hand, we confront present data on the semileptonic rate of $B$ mesons to excited states with theoretical expectations.

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arXiv2005

Subleading form factors at order 1/m_Q in terms of leading quantities using the non-forward amplitude in HQET

We consider the non-forward amplitude within the Heavy Quark Effective theory. We show that one can obtain new information on the subleading corrections in 1/m_Q. We illustrate the method by deriving new simple relations between the functions Xsi_3(w) and Lambdabar Xsi(w) and the sums Sum_n DeltaE^(n)_j tau^(n)_j(1) tau^(n)_j(w) (j=1/2,3/2), that involve leading quantities, namely the Isgur-Wise functions tau^(n)_j(w) and the level spacings DeltaE^(n)_j. The simplicity of our results follows from the fact that, for the non-forward amplitude B(v_i)->D^(n)(v')->B(v_f), there are three variables (w_i,w_f,w_if)=(v_i.v',v_f.v',v_i.v_f) independent in a certain domain, and we consider the zero recoil frontier (w,1,w) where only a finite number of j^P states contribute (1/2^+,3/2^+). These sum rules reduce to known results at w=1, for Lambdabar obtainted by Voloshin, and for Xsi_3(1) obtained by Le Yaouanc et al. and by Uraltsev, and generalizes them to all values of w. We discuss phenomenological applications of these results, in particular the check of Bakamjian-Thomas quark models and the comparison with the QCD Sum Rules approach.

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arXiv2004

Sum rules in the heavy quark limit of QCD and Isgur-Wise functions

Using the OPE, we formulate new sum rules in the heavy quark limit of QCD. These sum rules imply that the elastic Isgur-Wise function $ξ(w)$ is an alternate series in powers of $(w-1)$. Moreover, one gets that the $n$-th derivative of $ξ(w)$ at $ w=1$ can be bounded by the $(n-1)$-th one, and an absolute lower bound for the $n$-th derivative $(-1)^n ξ^{(n)}(1) \geq {(2n+1)!! \over 2^{2n}}$. Moreover, for the curvature we find $ξ''(1) \geq {1 \over 5} [4 ρ^2 + 3(ρ^2)^2]$ where $ρ^2 = - ξ'(1)$. We show that the quadratic term ${3 \over 5} (ρ^2)^2$ has a transparent physical interpretation, as it is leading in a non-relativistic expansion in the mass of the light quark. These bounds should be taken into account in the parametrizations of $ξ(w)$ used to extract $|V_{cb}|$. These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for $ξ(w)$. The method is extended to the subleading quantities in $1/m_Q$, namely $ξ_3(w)$ and $\barΛξ(w)$.}]

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arXiv2004

Bounds on the derivatives of the Isgur-Wise function with a non-relativistic light quark

In a preceeding study in the heavy quark limit of QCD, it has been demonstrated that the best lower bound on the curvature of the Isgur-Wise function Xsi(w) is Xsi"(1) > (4rho2+3(rho2)2) > 15/16. The quadratic term (rho2)2 is dominant in a non-relativistic expansion in the light quark, both Xsi"(1) and (rho2)2 scaling like (R2m2)2, where m is the light quark mass and R the bound state radius. The non-relativistic limit is thus a good guide-line in the study of the shape of Xsi(w). In the present paper we obtain similar bounds on all the derivatives of XsiNR(w), the IW function with the light quark non-relativistic, and we demons- trate that these bounds are optimal. We formulate a general method, based on the positivity of matrices of moments of the ground state wave function, that allows to bound the n-th derivative XsiNR(n)(w) in terms of the m-th ones (m < n). We argue that this method can be generalized to the true Isgur-Wise function of QCD Xsi(w).

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arXiv2003

Lower bounds on the curvature of the Isgur-Wise function

Using the OPE, we obtain new sum rules in the heavy quark limit of QCD, in addition to those previously formulated. Key elements in their derivation are the consideration of the non-forward amplitude, plus the systematic use of boundary conditions that ensure that only a finite number of $j^P$ intermediate states (with their tower of radial excitations) contribute. A study of these sum rules shows that it is possible to bound the curvature $σ^2 = ξ''(1)$ of the elastic Isgur-Wise function $ξ(w)$ in terms of its slope $ρ^2 = - ξ'(1)$. Besides the bound $σ^2 \geq {5 \over 4} ρ^2$, previously demonstrated, we find the better bound $σ^2 \geq {1 \over 5} [4 ρ^2 + 3(ρ^2)^2]$. We show that the quadratic term ${3 \over 5} (ρ^2)^2$ has a transparent physical interpretation, as it is leading in a non-relativistic expansion in the mass of the light quark. At the lowest possible value for the slope $ρ^2 = {3 \over 4}$, both bounds imply the same bound for the curvature, $σ^2 \geq {15 \over 16}$. We point out that these results are consistent with the dispersive bounds, and, furthermore, that they strongly reduce the allowed region by the latter for $ξ(w)$.

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arXiv2003

Sum rules in the heavy quark limit of QCD

In the leading order of the heavy quark expansion, we propose a method within the OPE and the trace formalism, that allows to obtain, in a systematic way, Bjorken-like sum rules for the derivatives of the elastic Isgur-Wise function $ξ(w)$ in terms of corresponding Isgur-Wise functions of transitions to excited states. A key element is the consideration of the non-forward amplitude, as introduced by Uraltsev. A simplifying feature of our method is to consider currents aligned along the initial and final four-velocities. As an illustration, we give a very simple derivation of Bjorken and Uraltsev sum rules. On the other hand, we obtain a new class of sum rules that involve the products of IW functions at zero recoil and IW functions at any $w$. Special care is given to the needed derivation of the projector on the polarization tensors of particles of arbitrary integer spin. The new sum rules give further information on the slope $ρ^2 = - ξ'(1)$ and also on the curvature $σ^2 = ξ'' (1)$, and imply, modulo a very natural assumption, the inequality $σ^2 \geq {5\over 4} ρ^2$, and therefore the absolute bound $σ^2 \geq {15 \over 16}$.

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arXiv2002

Bounds on the derivatives of the Isgur-Wise function from sum rules in the heavy quark limit of QCD

Using the OPE and the trace formalism, we have obtained a number of sum rules in the heavy quark limit of QCD that include the sum over all excited states for any value $j^P$ of the light cloud. We show that these sum rules imply that the elastic Isgur-Wise function $ξ(w)$ is an alternate series in powers of $(w-1)$. Moreover, we obtain sum rules involving the derivatives of the elastic Isgur-Wise function $ξ(w)$ at zero recoil, that imply that the $n$-th derivative can be bounded by the $(n-1)$-th one. For the curvature $σ^2 = ξ''(1)$, this proves the already proposed bound $σ^2 \geq {5 \over 4} ρ^2$. Moreover, we obtain the absolute bound for the $n$-th derivative $(-1)^n ξ^{(n)}(1) \geq {(2n+1)!! \over 2^{2n}}$, that generalizes the results $ρ^2 \geq {3 \over 4}$ and $σ^2 \geq {15 \over 16}$.

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arXiv2001

Remarks on sum rules in the heavy quark limit of QCD

We underline a problem existing in the heavy quark limit of QCD concerning the rates of semileptonic B decays into P-wave $D_J(j)$ mesons, where $j = {1 \over 2}$ (wide states) or $j = {3 \over 2}$ (narrow states). The leading order sum rules of Bjorken and Uraltsev suggest $Γ[ \bar{B} \to D_{0,1} ({1 \over 2}) \ell ν] \ll Γ[ \bar{B} \to D_{1,2} ({3 \over 2}) \ell ν]$, in contradiction with experiment. The same trend follows also from a sum rule for the subleading $1/m_Q$ curent matrix element correction $ξ_3(1)$. The problem is made explicit in relativistic quarks models à la Bakamjian and Thomas, that give a transparent physical interpretation of the latter as due, not to a $L \cdot S$ force, but to the Wigner rotation of the light quark spin. We point out moreover that the selection rule for decay constants of $j = {3 \over 2}$ states, $f_{3/2} = 0$, predicts, assuming the model of factorization, the opposite hierarchy $Γ[ \bar{B} \to \bar{D}_{s_{1,2}} ({3 \over 2}) D^{(*)} ] \ll Γ[ \bar{B} \to \bar{D}_{s_{0,1}} ({1 \over 2}) D^{(*)} ]$.

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arXiv2001

On P-wave meson decay constants in the heavy quark limit of QCD

In previous work it has been shown that, either from a sum rule for the subleading Isgur-Wise function $ξ_3(1)$ or from a combination of Uraltsev and Bjorken SR, one infers for $P$-wave states $|τ_{1/2}(1)| \ll |τ_{3/2}(1)|$. This implies, in the heavy quark limit of QCD, a hierarchy for the {\it production} rates of $P$-states $Γ(\bar{B}_d \to D ({1 \over 2}) \ell ν) \ll Γ(\bar{B}_d \to D ({3 \over 2}) \ell ν)$ that seems at present to be contradicted by experiment. It was also shown that the decay constants of $j = {3 \over 2}$ $P$-states vanish in the heavy quark limit of QCD, $f_{3/2}^{(n)} = 0$. Assuming the {\it model} of factorization in the decays $\bar{B}_d \to \bar{D}_s^{**}D$, one expects the opposite hierarchy for the {\it emission} rates $Γ(\bar{B}_d \to \bar{D}_s ({3 \over 2}) D) \ll Γ(\bar{B}_d \to \bar{D}_s ({1 \over 2}) D)$, since $j = {1 \over 2}$ $P$-states are coupled to vacuum. Moreover, using Bjorken SR and previously discovered SR involving heavy-light meson decay constants and IW functions, one can prove that the sums $\sum\limits_n ({f^{(n)} \over f^{(0)}})^2$, $\sum\limits_n ({f_{1/2}^{(n)} \over f^{(0)}})^2$ (where $f^{(n)}$ and $f_{1/2}^{(n)}$ are the decay constants of $S$-states and $j = {1\over 2}$ $P$-states) are divergent. This situation seems to be realized in the relativistic quark models à la Bakamjian and Thomas, that satisfy HQET and predict decays constants $f^{(n)}$ and $f_{1/2}^{(n)}$ that do not decrease with the radial quantum number $n$.

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arXiv2001

Uraltsev Sum Rule in Bakamjian-Thomas Quark Models

We show that the sum rule recently proved by Uraltsev in the heavy quark limit of QCD holds in relativistic quark models à la Bakamjian and Thomas, that were already shown to satisfy Isgur-Wise scaling and Bjorken sum rule. This new sum rule provides a {\it rationale} for the lower bound of the slope of the elastic IW function $ρ^2 \geq {3 \over 4}$ obtained within the BT formalism some years ago. Uraltsev sum rule suggests an inequality $|τ_{3/2}(1)| > |τ_{1/2}(1)|$. This difference is interpreted in the BT formalism as due to the Wigner rotation of the light quark spin, independently of a possible LS force. In BT models, the sum rule convergence is very fast, the $n = 0$ state giving the essential contribution in most of the phenomenological potential models. We underline that there is a serious problem, in the heavy quark limit of QCD, between theory and experiment for the decays $B \to D^*_{0,1}(broad) \ell ν$, independently of any model calculation.

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