Semileptonic Width Research Articles

Three loop calculations and inclusive Vcb

We discuss the impact of the recent O(αs3) calculations of the semileptonic width of the b quark and of the relation between pole and kinetic heavy quark masses by Fael et al. on the inclusive determination of |Vcb|. The most notable effect is a reduction of the uncertainty. Our final result is |Vcb|=42.16(51)10−3.

Higher order corrections to inclusive semileptonic B decays

We describe the computation of the O(αS) corrections to the Wilson coefficients of the kinetic and chromomagnetic operators in inclusive semileptonic B decays. We can thus evaluate the complete correction at order αSΛQCD2/mb2 to the semileptonic width and the first two leptonic moments.

A new contribution to the conventional atmospheric neutrino flux

Atmospheric neutrinos are an important background to astrophysical neutrino searches, and are also of considerable interest in their own right. This paper points out that the contribution to conventional atmospheric νe of the rare semileptonic decay of KS becomes significant at high energy. Although the KS→πeν branching ratio is very small, the short KS lifetime leads to a high critical energy, so that, for vertical showers, the inclusion of KS semileptonic decay increases the conventional νe flux by ≈30% at energies above 100TeV. In this paper, we present calculations of the flux of νe from KS. At energies above their critical energies, the νe fluxes from kaon decay may be simply related to the kaon semileptonic widths; this leads to a near-equality between the flux of νe from K+,KL and KS.

Perturbative corrections to power suppressed effects in semileptonic B decays

We compute the $O(\alpha_s)$ corrections to the Wilson coefficient of the chromomagnetic operator in inclusive semileptonic B decays. The results are employed to evaluate the complete $O(\alpha_s \Lambda^2/m_b^2)$ correction to the semileptonic width and to the first moments of the lepton energy distribution.

Semileptonic width ratios among beauty hadrons

We present predictions based on the heavy quark expansion in QCD. We find SU(3) breaking in B mesons suppressed in the framework of the HQE. B s is expected to have the semileptonic width about 1% lower and Λ b about 3% higher when compared to Γsl(B d ). The largest partial-rate preasymptotic effect is Pauli interference in the b → uℓν channel in Λ b , about +10%. We point out that the Ω b semileptonic width is expected not to exceed that of B d and may turn out to be the smallest among stable b hadrons despite the large mass. The underlying differences with phase-space models are briefly addressed through the heavy mass expansion.

Formula omitted], [formula omitted] and [formula omitted] from (semi-)leptonic [formula omitted]-decays: Signals of New Physics?

We confront the recent improved measurements of the D(s) (semi-)leptonic decays with Lattice QCD (LQCD) with nf=3 flavours and QCD spectral sum rules (QSSR) predictions. D→μνμ leptonic width data compared with theoretical determinations of fD, leads to the value of the CKM mixing angle: |Vcd|=0.230(10)exp(9)th. Measured ratio of the D semi-leptonic widths combined with LQCD and QSSR predictions leads to the average |Vcd|/|Vcs|=0.2175(88), and then to |Vcs|=1.068(47). We consider the previous determinations as improvements of the existing estimates. Using the average data of the Ds→μνμ (respectively Ds→τντ) branching ratios, one obtains: |Vcs|fDsμ=(259±12) MeV (respectively |Vcs|fDsτ=(274±13) MeV), which can be compared with the average of the Standard Model (SM) values from LQCD and QSSR fDs=(240±7) MeV. If one uses the present determination of |Vcs|, there is an agreement with the SM prediction within 1σ. If instead, we impose the unitarity constraint |Vcs|⩽1, or assume (as frequently done) |Vcs|=|Vud|, we would obtain a deviation from the SM expectations ranging from 1.5 to 3σ, therefore, signaling some New Physics beyond the SM.

Progress in computing inclusive B decay spectra

We review the progress in the QCD calculation of inclusive decay spectra. It was recently shown that the inherent infrared finiteness of inclusive spectra extends beyond the level of logarithms. Dressed Gluon Exponentiation makes practical use of this property by computing the Sudakov exponent as a Borel sum. Based on renormalon analysis, infrared sensitivity in the exponent is reflected in power corrections that are inversely proportional to the third power of the mass. Therefore, the parametric enhancement of non-perturbative corrections near the phase–space boundary is effective only in a small region. Consequently, the on-shell decay spectrum provides a good approximation to the meson decay. In particular, it facilitates a precise determination of | V u b | from present measurements of inclusive charmless semileptonic widths without involving a non-perturbative “shape function”.

Measurement of lepton momentum moments in the decayB¯→Xlν¯and determination of the heavy quark expansion parameters and|Vcb|

We measure the primary lepton momentum spectrum in B-bar to X l nu decays, for p_l > 1.5 GeV/c in the B rest frame. From this, we calculate various moments of the spectrum. In particular, we find R_0 = [int(E_l>1.7) (dGam/dE_sl)*dE_l] / [int(E_l>1.5) (dGam/dE_sl)*dE_l] = 0.6187 +/- 0.0014_stat +/- 0.0016_sys and R_1 = [int(E_l>1.5) E_l(dGam/dE_sl)*dE_l] / [int(E_l>1.5) (dGam/dE_sl)*dE_l] = (1.7810 +/- 0.0007_stat +/- 0.0009_sys) GeV. We use these moments to determine non-perturbative parameters governing the semileptonic width. In particular, we extract the Heavy Quark Expansion parameters Lambda-bar = (0.39 +/- 0.03_stat +/- 0.06_sys +/- 0.12_th) GeV and lambda_1 = (-0.25 +/- 0.02_stat +/- 0.05_sys +/- 0.14_th) GeV^2. The theoretical constraints used are evaluated through order 1/M_B^3 in the non-perturbative expansion and beta_0*alpha__s^2 in the perturbative expansion. We use these parameters to extract |V_cb| from the world average of the semileptonic width and find |V_cb| = (40.8 +/- 0.5_Gam-sl +/- 0.4_(lambda_1,Lambda-bar)-exp +/- 0.9_th) x 10^-3. In addition, we extract the short range b-quark mass m_b^1S = (4.82 +/- 0.07_exp +/- 0.11_th) GeV/c^2. Finally, we discuss the implications of our measurements for the theoretical understanding of inclusive semileptonic processes.

The bound state corrections to the semileptonic decays of the heavy baryons

We present an investigation of the lepton energy distributions in the inclusive semileptonic weak decays of heavy baryons performed within a relativistic quark model formulated on the light front (LF). Using the heavy-quark LF distribution functions related to the equal time momentum wave functions taken from the Kalman-Tran-D'Souza model we compute the electron energy spectra and the total semileptonic widths of the Λ Q and Ξ Q ( Q = c, b) baryons and confront the results with existing data.

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 the 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. The 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 Vcb 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→ Xcℓν decays.

Hadronic mass moments in inclusive semileptonic B meson decays.

We have measured the first and second moments of the hadronic mass-squared distribution in B-->X(c)l nu, for P(lepton)>1.5 GeV/c. We find <M(2)(X)-M macro(2)(D)> = 0.251+/-0.066 GeV(2), <(M(2)(X)-<M(2)(X)>)(2)> = 0.576+/-0.170 GeV(4), where M macro(D) is the spin-averaged D meson mass. From that first moment and the first moment of the photon energy spectrum in b-->s gamma, we find the heavy quark effective theory parameter lambda(1) (in the modified minimal subtraction renormalization scheme, to order 1/M(3)(B) and beta(0)alpha(2)(s)) to be -0.24+/-0.11 GeV(2). Using these first moments and the B semileptonic width, and assuming parton-hadron duality, we obtain absolute value of V(cb) = 0.0404+/-0.0013.

The bound state corrections to the leptonic decays of the B meson: The light-front approach versus ACM model

A generalization of the parton-like formula is used for the first time to find the differential distributions in the inclusive semileptonic weak decays of the B meson. The main features of this new approach are the treatment of the b quark as an on-mass-shell particle and the inclusion of the effects arising from the b-quark transverse motion in the B meson. Using the b-quark light-front (LF) distribution function related to the equal time momentum wave function taken from the ACM model, we compute the electron energy spectra and the total semileptonic widths of the B meson. We find an impressive agreement between the electron energy spectra calculated in the LF approach and the ones obtained in the ACM model, provided the b-quark mass is identified with the average of the floating b-quark mass in the ACM model. In spite of the simplicity of the model, we obtain a fairly good description of the CLEO data for | V cb | 0.042.

Bottom quark mass and | Vcb| matrix element from [formula omitted] and Γs1( b → clνl) in the next-to-next-to-leading order

We present a consistent analysis of ϒ sum rules and B-meson semileptonic width in the next-to-next-to-leading order in the strong coupling constant. The analysis is based on the analytical result for the heavy quark vector current correlator near threshold in the second-order in perturbative and relativistic expansion around the non-relativistic Coulomb approximation.

Next-to-next-to-leading order relation between [formula omitted] and Γsl( b→ clνl) and precise determination of | Vcb|

We present the next-to-next-to-leading order relation between the moments of the ϒ system spectral density and the inclusive B-meson semileptonic width. The perturbative series for the width as an explicit function of the moments is well convergent in three consequent orders in the strong coupling constant that provides solid and accurate theoretical estimate. As a result, the uncertainty of the value of | V cb | Cabibbo-Kobayashi-Maskawa matrix element is reduced.

RESUMMATION ANALYSIS OF THE τ-DECAY WIDTH USING THE FOUR-LOOP β-FUNCTION

We extract the strong coupling constant [Formula: see text] from the semileptonic τ-decay width taking into account resummation effects from the running of the strong coupling constant. In the [Formula: see text] scheme. The result reads αs=0.375±0.007 to third-order and αs=0.378±0.007 to fourth-order in the β-function, respectively, where we use the recently computed four-loop coefficient β3. These values for the coupling constant have to be compared with the value αs=0.354±0.005 derived from a third-order analysis of τ-decays. We determine the exact value of the convergence radius of the perturbation series by analyzing the singularity structure of the complex coupling constant plane.

High powernofmbinb-flavored widths andn=5→∞limit

The leading term in the semileptonic width of heavy flavor hadrons depends on the fifth power of the heavy quark mass. We present an analysis where this power can be self-consistently treated as a free parameter n and the width can be studied in the limit n -> oo. The resulting expansion elucidates why the small velocity (SV) treatment is relevant for the inclusive semileptonic b->c transition. The extended SV limit (ESV limit) is introduced. The leading terms in the perturbative alpha_s expansion enhanced by powers of n are automatically resummed by using the low-scale Euclidean mass. The large-n treatment explains why the scales of order m_b/n are appropriate. On the other hand, the scale cannot be too small since the factorially divergent perturbative corrections associated with running of alpha_s show up. Both requirements are met if we use the short-distance mass normalized at a scale around m_b/n \sim 1 GeV. A convenient definition of such low-scale OPE-compatible masses is briefly discussed.

ASPECTS OF HEAVY-QUARK THEORY

▪ Abstract Recent achievements in heavy-quark theory are critically reviewed. The emphasis is put on those aspects that either did not attract enough attention or cause heated debates in the current literature. Among other topics we discuss (a) basic parameters of the heavy-quark theory; (b) a class of exact QCD inequalities; (c) new heavy quark sum rules; (d) the virial theorem; (e) applications (|Vcb| from the total semileptonic width and from the B → D* transition at zero recoil). In some instances new derivations of previously known results are given, or new aspects addressed. In particular, we dwell on the exact QCD inequalities. Furthermore, a toy model is considered that may shed light on the controversy regarding the value of the kinetic energy of heavy quarks obtained by different methods.

What are the right values of [formula omitted] and the heavy quark kinetic energy?

The values of two important parameters of the heavy quark effective theory, Λ and μ π 2 (the mean value of the heavy quark three momentum squared), have been determined recently by Gremm et al. [M. Gremm, A. Kapustin, Z. Ligeti, M. Wise, CALT-68-2043, hep-ph/9603314 (original and revised versions)] from the precise CLEO data on the shape of the electron spectrum in semileptonic B meson decays. The values obtained by Gremm et al.: Λ = (0.55 ± 0.05) GeV , μ π 2 = (0.35 ± 0.05) GeV 2, disagree with the result obtained earlier by Chernyak [Nucl. Phys. B 457 (1995) 961] from the D meson semileptonic width. The purpose of this note is to show that the main reason for a disagreement is the secondary electron background present in the data, which influences strongly the extracted values of Λ and μ π 2. We determine the amount of this background from the selfconsistency conditions, and subtract it out. As a result, the values of Λ and μ π 2 become a factor two smaller and agree with Chernyak (q.v.).

Erratum: Operator product expansion sum rules for heavy flavor transitions and the determination of ||Vcb||

We derive a model-independent upper bound for the axial-vector form factor of the $B\ra D^*$ transition at zero recoil, $F_{B\ra D^*}$. The form factor turns out to be noticeably less than unity. The deviation of $F_{B\ra D^*}$ from unity is larger than previously anticipated. Using our estimate we extract $|V_{cb}|$ from the measured exclusive rate of $B\ra D^* l\nu$ extrapolated to the point of zero recoil. The central `` exclusive" value of $|V_{cb}|$ is in agreement with the value obtained from the inclusive semileptonic width $\Gamma (B\ra X_c l\nu)$. We argue that the theoretical uncertainty in determining $|V_{cb}|$ from the total inclusive width is significantly reduced if a constraint on the quark mass difference $m_b - m_c$ stemming from the heavy quark expansion is taken into account.

Calculation of 1/mc3 terms in the total semileptonic width of D mesons.

We calculate the 1/${\mathit{m}}_{\mathit{c}}^{3}$ corrections in the inclusive semileptonic widths of D mesons. We show that these are due to the novel penguin-type operators that appear at this level in the transition operator. Taking into account the nonperturbative corrections leads to the predicted value of the semileptonic width significantly lower than the experimental value. The 1/${\mathit{m}}_{\mathit{c}}^{3}$ corrections worsen the situation or, at the very least, within uncertainty, give a small contribution. We indicate possible ways out of this problem. It seems most probable that violations of duality are noticeable in the energy range characteristic to the inclusive decays in the charm family. Theoretically these deviations are related to divergence of the high-order terms in the power expansion in the inverse heavy quark mass.