Differential Decay Width Research Articles

Form factors for the processes Bc+→D0ℓ+νℓ and Bc+→Ds+ℓ+ℓ−(νν¯) from lattice QCD

We present results of the first lattice QCD calculations of the weak matrix elements for the decays $B_c^+ \to D^0 \ell^+ \nu_{\ell}$, $B_c^+ \to D_s^+ \ell^+ \ell^-$ and $B_c^+ \to D_s^+ \nu \overline{\nu}$. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the continuum limit with physical quark masses. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with three different lattice spacings and including 2+1+1 flavours of sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for all of the valence quarks. The uncertainty on the decay widths from our form factors is similar in size to that from the present value for $V_{ub}$. We obtain the ratio $\Gamma (B_{c}^{+} \rightarrow D^0 \mu^{+} \nu_{\mu}) /\left|\eta_{\mathrm{EW}} V_{u b}\right|^{2}=4.43(63) \times 10^{12} \mathrm{~s}^{-1}$. Combining our form factors with those found previously by HPQCD for $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$, we find $\left|V_{cb}/V_{ub} \right|^2 \Gamma( B_c^+ \to D^0 \mu^+ \nu_\mu )/\Gamma(B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}) = 0.257(36)_{B_c \to D}(18)_{B_c \to J/\psi}$. We calculate the differential decay widths of $B_c^+ \to D_s^+ \ell^+ \ell^-$ across the full $q^2$ range, and give integrated results in $q^2$ bins that avoid possible effects from charmonium and $u \overline{u}$ resonances. For example, we find that the ratio of differential branching fractions integrated over the range $q^2 = 1 \; \mathrm{GeV}^2 - 6 \; \mathrm{GeV}^2$ for $B_c^+ \to D_s^+ \mu^+ \mu^-$ and $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$ is $5.23{\tiny }(73)_{B_c \to D_s}(54)_{B_c \to J/\psi} \times 10^{-6}$. We also give results for the branching fraction of $B_c^+ \to D_s^+ \nu \overline{\nu}$. Prospects for reducing our errors in the future are discussed.

Investigation of Baryons in the Hypercentral Quark Model

In the present study, we consider baryons as three-body bound systems according to the hypercentral constituent quark model in configuration space and solve the three-body Klein-Gordon equation. Then, we analyze perturbative spin-dependent and isospin-dependent interaction effects. To find the analytical solution, we use screened potential and calculate the eigenfunctions and eigenvalues of some baryons. We consider exclusive semileptonic decays of bottom and charm baryons and apply the differential decay width with the Isgur-Wise function and arrive at the rates for some semileptonic baryon decays. The results prove more enhanced compared to recent works and comply well with the experimental data.

The role of right-handed neutrinos in b \u2192 c\u03c4 (\u03c0\u03bd\u03c4, \u03c1\u03bd\u03c4, \u03bc overline{nu} \u03bc\u03bd\u03c4) overline{nu} \u03c4 from visible final-state kinematics

In the context of lepton flavor universality violation (LFUV) studies, we fully derive a general tensor formalism to investigate the role that left- and right-handed neutrino new-physics (NP) terms may have in b → cτ overline{nu} τ transitions. We present, for several extensions of the Standard Model (SM), numerical results for the Λb → Λcτ overline{nu} τ semileptonic decay, which is expected to be measured with precision at the LHCb. This reaction can be a new source of experimental information that can help to confirm, or maybe rule out, LFUV presently seen in overline{B} meson decays. The present study analyzes observables that can help in distinguishing between different NP scenarios that otherwise provide very similar results for the branching ratios, which are our currently best hints for LFUV. Since the τ lepton is very short-lived, we consider three subsequent τ-decay modes, two hadronic πντ and ρντ and one leptonic μ overline{nu} μντ, which have been previously studied for overline{B} → D(*) decays. Within the tensor formalism that we have developed in previous works, we re-obtain the expressions for the differential decay width written in terms of visible (experimentally accessible) variables of the massive particle created in the τ decay. There are seven different τ angular and spin asymmetries that are defined in this way and that can be extracted from experiment. Those asymmetries provide observables that can help in constraining possible SM extensions.

Inclusive production of heavy quarkonium ηQ via Z boson decays within the framework of nonrelativistic QCD

In the paper, the inclusive production of heavy quarkonium $\eta_Q$ ($Q=b$ or $c$) via $Z$ boson decays within the framework of nonrelativistic QCD effective theory are studied. The contributions from the leading color-singlet and color-octet Fock states are considered. Total and differential decay widths for the inclusive decays $Z \to \eta_Q+X$ are presented. It is found that the decays $Z\to \eta_Q +X$ are dominated by the $^3S_1^{[8]}$ component, so the decays can be inversely adopted to determine the values of the long-distance matrix elements $\langle {\cal O}^{\eta_{c}}(^{3}S_{1}^{[8]})\rangle$ and $\langle {\cal O}^{\eta_{b}}(^{3}S_{1}^{[8]})\rangle$, respectively. Our numerical results show that at an $e^+e^-$ collider running at the $Z$ pole with a high luminosity around $10^{35}{\rm cm}^{-2}{\rm s}^{-1}$ (a super $Z$ factory), there are about $4.5\times 10^7$ $\eta_c$ meson events and $6.1\times 10^5$ $\eta_b$ meson events to be produced per operation year, and the inclusive decays may be used for clarifying some problems on the heavy quarkonium $\eta_Q$ and nonrelativistic QCD.

Up-down asymmetries and angular distributions in D→K1(→Kππ)ℓ+νℓ

Using the helicity amplitude technique, we derive differential decay widths and angular distributions for the decay cascade $D\to K_{1}(1270,1400)\ell^+\nu_{\ell}\to (K\pi\pi)\ell^+\nu_{\ell} (\ell=e,\mu)$, in which the electron and muon mass is explicitly included. Using a set of phenomenological results for $D\to K_1$ form factors, we calculate partial decay widths and branching fractions for $D^0\to K_1^-\ell^+\nu_{\ell}$ and $D^+\to K_1^0\ell^+\nu_{\ell}$, but find that results for ${\cal B}(D\to K_1(1270)e^+\nu_{e})$ are larger than recent BESIII measurements by about a factor 1.5. We further demonstrate that the measurement of up-down asymmetry in $D\to K_{1}e^+\nu_e\to (K\pi\pi)e^+\nu_{e}$ and angular distributions in $D\to K_{1}\ell^+\nu_\ell\to (K\pi\pi)\ell^+\nu_{\ell}$ can help to determine the hadronic amplitude requested in $B\to K_1(\to K\pi\pi)\gamma$. Based on the Monte-Carlo simulation with the LHCb geometrical acceptance, we find that the angular distributions of MC events can be well described.

Observation of the Mass Difference between Neutral Charm-Meson Eigenstates.

A measurement of mixing and CP violation in neutral charm mesons is performed using data reconstructed in proton-proton collisions collected by the LHCb experiment from 2016 to 2018, corresponding to an integrated luminosity of 5.4 fb^{-1}. A total of 30.6 million D^{0}→K_{S}^{0}π^{+}π^{-} decays are analyzed using a method optimized for the measurement of the mass difference between neutral charm-meson eigenstates. Allowing for CP violation in mixing and in the interference between mixing and decay, the mass and decay-width differences are measured to be x_{CP}=[3.97±0.46(stat)±0.29(syst)]×10^{-3} and y_{CP}=[4.59±1.20(stat)±0.85(syst)]×10^{-3}, respectively. The CP-violating parameters are measured as Δx=[-0.27±0.18(stat)±0.01(syst)]×10^{-3} and Δy=[0.20±0.36(stat)±0.13(syst)]×10^{-3}. This is the first observation of a nonzero mass difference in the D^{0} meson system, with a significance exceeding seven standard deviations. The data are consistent with CP symmetry and improve existing constraints on the associated parameters.

Semileptonic decay of Bc to ηc and J/ψ on the light front

We study the semileptonic decay of the $B_c (0^-)$ to charmonia through the bottom-to-charm-quark electroweak current in the framework of basis light-front quantization. Explicitly, we calculate the weak transition form factors for processes of $B_c$ decaying into $\eta_c$ or $J/\psi$ based on the corresponding initial and final valence light-front wave functions both obtained from the basis light-front quantization. We also present the corresponding differential decay width and branching ratios, as well as the branching ratios for decays into the $\eta_c'$ and the $\psi'$. We observe unphysical frame dependence of the calculated form factors, which is attributed to only including the valence light-front wave functions. Based on the analysis of current component, we propose a preferred set of frames to calculate these form factors.

Parametrizations of the spin density matrix

We propose for the spin density matrix two parametrizations which automatically fulfill the non-negativity conditions, without setting any bound on the parameters. The first one relies on a theorem, that we prove, and it is rather simple and easily adaptable to some specific reactions, where, for example, parity is conserved or angular momentum conservation entails selection rules. Moreover, in the case when the rank is less than the order of the density matrix, we show how to improve the fits to the data, either by implementing previous suggestions, or by elaborating an alternative method, for which we prove a second theorem. Our second parametrization is a variant of previous treatments, it appears suitable for some particular processes. Moreover, we discuss about the possibility of inferring the elements of the density matrix from the differential decay width. Last, we illustrate various examples of current interest, both in strong and weak decays; some of them may be helpful in the investigation of physics beyond the standard model.

Measurement of the CP-violating phase ϕs in the [formula omitted] channel in proton-proton collisions at [formula omitted

The CP -violating weak phase ϕs and the decay width difference ΔΓs between the light and heavy Bs0 mass eigenstates are measured with the CMS detector at the LHC in a sample of 48500reconstructed Bs0→J/ψϕ(1020)→μ+μ−K+K− events. The measurement is based on a data sample corresponding to an integrated luminosity of 96.4fb−1, collected in proton-proton collisions at s=13TeV in 2017–2018. To extract the values of ϕs and ΔΓs, a time-dependent and flavor-tagged angular analysis of the μ+μ−K+K− final state is performed. The analysis employs a dedicated tagging trigger and a novel opposite-side muon flavor tagger based on machine learning techniques. The measurement yields ϕs=−11±50(stat)±10(syst)mrad and ΔΓs=0.114±0.014(stat)±0.007(syst)ps−1, in agreement with the standard model predictions. When combined with the previous CMS measurement at s=8TeV, the following values are obtained: ϕs=−21±44(stat)±10(syst)mrad, ΔΓs=0.1032±0.0095(stat)±0.0048(syst)ps−1, a significant improvement over the 8 TeV result.

Angular analysis of bottom-flavored hadron production in semileptonic decays of polarized top quarks

We study the inclusive production of bottom-flavored hadrons from semileptonic decays of polarized top quarks at next-to-leading order in QCD using fragmentation functions recently determined from a global fit to $e^+e^-$ data. We provide the relevant differential decay widths at parton level in analytic form. These results fill an important gap in the theoretical interpretation of recent measurements of the top-quark polarization and the $t\bar{t}$ spin correlations using dilepton final states in proton-proton collisions at the CERN Large Hadron Collider. As an illustration, we study the distributions in the scaled bottom-hadron energy of the polarized-top-quark decay widths for different $W$-boson helicities.

Measurement of the weak mixing phase ϕs through time-dependent CP-violation in Bs0 → J/ψϕ decays in the ATLAS detector

A measurement of [Formula: see text] decay parameters using data collected by the ATLAS detector in [Formula: see text] collisions at 13 TeV in 2015–2017 is performed. Integrated luminosity of this sample is 80.5 fb[Formula: see text]. The measurement of physical parameters are statistically combined with results obtained from Run 1 data at 7 and 8 TeV. The measured value of CP-violating phase [Formula: see text] is obtained, which has significantly better precision in comparison with Run 1 result. Precision of other physical parameters is also improved, including the decay width difference [Formula: see text]. Further improvement is expected from the use of full Run 2 statistics, as well as from modifications in the analysis.

B¯c→ηc , B¯c→J/ψ and B¯→D(*) semileptonic decays including new physics

We apply the general formalism derived in N. Penalva et al. [Phys. Rev. D 101, 113004 (2020)] to the semileptonic decay of pseudoscalar mesons containing a $b$ quark. While present $B\to D^{(*)}$ data give the strongest evidence in favor of lepton flavor universality violation, the observables that are normally considered are not able to distinguish between different new physics (NP) scenarios. In the above reference we discussed the relevant role that the various contributions to the double differential decay widths $d^2\Gamma/(d\omega d\cos\theta_\ell)$ and $d^2\Gamma/(d\omega dE_\ell)$ could play to this end. Here $\omega$ is the product of the two hadron four-velocities, $\theta_\ell$ is the angle made by the final lepton and final hadron three-momenta in the center of mass of the final two-lepton system, and $E_\ell$ is the final charged lepton energy in the laboratory system. The formalism was applied there to the analysis of the $\Lambda_b\to\Lambda_c$ semileptonic decay showing the new observables were able to tell apart different NP scenarios. Here we analyze the $\bar B_c\to \eta_c \tau\bar\nu_\tau$, $\bar B_c\to J/\psi\tau\bar\nu_\tau$, $\bar B\to D\tau\bar\nu_\tau$ and $\bar B\to D^*\tau\bar\nu_\tau$ semileptonic decays. We show that, as a general rule, the $\bar B_c \to J/\psi$ observables, even including $\tau$ polarization, are less optimal for distinguishing between NP scenarios than those obtained from $\bar B_c \to \eta_c$ decays, or those presented in N. Penalva et al. for the related $\Lambda_b \to \Lambda_c$ semileptonic decay. Finally, we show that $\bar B\to D$ and $\bar B_c\to \eta_c$, and $\bar B\to D^*$ and $\bar B_c\to J/\psi$ decay observables exhibit similar behaviors.

Hadron and lepton tensors in semileptonic decays including new physics

We extend our general framework for semileptonic decay, originally introduced in N. Penalva et al. [Phys. Rev. D100, 113007 (2019)], with the addition of new physics (NP) tensor terms. In this way, all the NP effective Hamiltonians that are considered in lepton flavour universality violation (LFUV) studies have now been included. Besides, we now also give general expressions that allow for complex Wilson coefficients. The scheme developed is totally general and it can be applied to any charged current semileptonic decay, involving any quark flavors or initial and final hadron states. We show that all the hadronic input, including NP effects, can be parametrized in terms of 16 Lorentz scalar structure functions. In the second part of this work, we use this formalism to obtain the complete NP effects in the $\Lambda_b\to \Lambda_c \tau\bar\nu_\tau$ semileptonic decay, where LFUV, if finally confirmed, is also expected to be seen. We stress the relevance of the center of mass (CM) $d^2\Gamma/(d\omega d\cos\theta_\ell)$ and laboratory (LAB) $d^2\Gamma/(d\omega dE_\ell)$ differential decay widths. While models with very different strengths in the NP terms give the same differential $d\Gamma/d\omega$ and total decay widths for this decay, they predict very different numerical results for some of the $\cos\theta_\ell$ and $E_\ell$ coefficient-functions that determine the above two distributions. Thus, the combined analysis of the CM $d^2\Gamma/(d\omega d\cos\theta_\ell)$ and LAB $d^2\Gamma/ (d\omega dE_\ell)$ differential decay widths will help clarifying what kind of NP is a better candidate in order to explain LFUV.

The decay τ → K⁎−(892)ηντ in the NJL model

The branching fraction of τ→K⁎−(892)ηντ was calculated in the Nambu–Jona-Lasinio model in the mean field approximation, which corresponds to considering quark loops in the leading order of 1/Nc. Four channels were taken into account: the contact channel (the final states are directly producted from the lepton current without any intermediate meson states), the axial-vector channel with two intermediate physical states K1(1270) and K1(1400), the vector channel with intermediate K⁎(892) meson and the pseudoscalar channel with intermediate K meson. It is shown that the first two channels give the dominant contribution to the decay width. Of the remaining two channels, the pseudoscalar channel plays a more prominent role. The final result is in satisfactory agreement with experimental data. A prediction for the differential decay width is presented.

Next-to-leading order QCD corrections to the production of Bc and Bc* through W+ -boson decays

In this paper, we calculate the total decay widths for the $W^+$-boson decays, $W^+ \to B_c+b+\bar{s}+X$ and $W^+ \to B^*_c+b+\bar{s}+X$, up to next-to-leading order (NLO) accuracy within the framework of the nonrelativistic QCD theory. Both the fixed-order and the fragmentation approaches are adopted to do the calculation. Differential decay widths $d\Gamma/dz$ and $d\Gamma/ds_1$ are also given. We find that the NLO corrections are significant in those two $W^+$ decay channels. Our numerical results show that at the LHC, there are about $7.03\times 10^4$ $B_c$-meson events and $5.10\times 10^4$ $B^*_c$-meson events to be produced via the $W^+$-boson decays per operation year.

Polarization in (quasi-)two-body decays and new physics

We consider two-body and quasi-two-body decays of the type f_1 rightarrow f_2 B, where f_1 and f_2 are spin-1/2 fermions and B a spin-0 or spin-1 boson. After recalling the non-covariant formalism for decay amplitudes, we derive the expression of the differential decay width and of the polarizations of the final spinning particles, both on- and off-shell. We find an intriguing geometrical interpretation of the results about the polarization. We also illustrate some methods for measuring the polarizations of the resonances and for optimizing data analysis. Then we propose applications to semi-leptonic weak decays, with a major attention to the T-odd component of the polarization; this may help to find, simultaneously, possible time-reversal violations and hints to physics beyond the standard model. We suggest also a CPT test. Last, we discuss some T-odd observables for the production process of f_1 and for the study of the strong final state interactions of non-leptonic decays.

Updated measurement of time-dependent CP-violating observables in {{B} ^0_{s}} rightarrow J/psi K^+ K^- decays

The decay-time-dependent CP asymmetry in {{B} ^0_{s}} rightarrow J/psi {{K} ^+} {{K} ^-} decays is measured using proton–proton collision data, corresponding to an integrated luminosity of 1.9,mathrm{fb}^{-1} , collected with the LHCb detector at a centre-of-mass energy of 13,mathrm {TeV} in 2015 and 2016. Using a sample of approximately 117 000 signal decays with an invariant {{K} ^+} {{K} ^-} mass in the vicinity of the phi (1020) resonance, the CP-violating phase phi _s is measured, along with the difference in decay widths of the light and heavy mass eigenstates of the {{B} ^0_{s}} -{{overline{B}{}} {}^0_{s}} system, Delta Gamma _s. The difference of the average {{B} ^0_{s}} and {{B} ^0} meson decay widths, Gamma _s-Gamma _d, is determined using in addition a sample of {{B} ^0} rightarrow J/psi {{K} ^+} {{pi } ^-} decays. The values obtained are phi _s = -0.083pm 0.041pm 0.006mathrm { ,rad} , Delta Gamma _s = 0.077 pm 0.008 pm 0.003 {mathrm { ,ps^{-1}}} and Gamma _s-Gamma _d = -0.0041 pm 0.0024 pm 0.0015{mathrm { ,ps^{-1}}} , where the first uncertainty is statistical and the second systematic. These are the most precise single measurements of these quantities to date and are consistent with expectations based on the Standard Model and with a previous LHCb analysis of this decay using data recorded at centre-of-mass energies 7 and 8 TeV. Finally, the results are combined with recent results from {{B} ^0_{s}} rightarrow J/psi {{pi } ^+} {{pi } ^-} decays obtained using the same dataset as this analysis, and with previous independent LHCb results.

Measurement of the CP-violating phase ϕs from [formula omitted] decays in 13 TeV pp collisions

Decays of Bs0 and B‾0s mesons into J/ψπ+π− final states are studied in a data sample corresponding to 1.9 fb−1 of integrated luminosity collected with the LHCb detector in 13 TeV pp collisions. A time-dependent amplitude analysis is used to determine the final-state resonance contributions, the CP-violating phase ϕs=−0.057±0.060±0.011 rad, the decay-width difference between the heavier mass Bs0 eigenstate and the B0 meson of −0.050±0.004±0.004 ps−1, and the CP-violating parameter |λ|=1.01−0.06+0.08±0.03, where the first uncertainty is statistical and the second systematic. These results are combined with previous LHCb measurements in the same decay channel using 7 TeV and 8 TeV pp collisions obtaining ϕs=0.002±0.044±0.012 rad, and |λ|=0.949±0.036±0.019.

Signals of New Physics in B-Mesons Mixing Mass and Decay Width Differences

The measurement of $$ {B}_q^0-\overline{B_q^0} $$ (q = d, s) mixing mass difference and decay width differences is an important ingredient for searching physics beyond the standard model. In this paper, we investigate $$ {B}_q^0-\overline{B_q^0} $$ mixing mass and decay width differences in the Z′ model. It is found that these differences are enhanced relative to the standard model prediction and give signals for new physics. Depending upon the mass of Z′ boson, the Z′-mediated flavour-changing neutral current gives a contribution to mass and decay width differences in $$ {B}_q^0-\overline{B_q^0} $$ mixing.

Distribution amplitudes of heavy-light mesons

A symmetry-preserving approach to the continuum bound-state problem in quantum field theory is used to calculate the masses, leptonic decay constants and light-front distribution amplitudes of empirically accessible heavy-light mesons. The inverse moment of the B-meson distribution is particularly important in treatments of exclusive B-decays using effective field theory and the factorisation formalism; and its value is therefore computed: λB(ζ=2GeV)=0.54(3)GeV. As an example and in anticipation of precision measurements at new-generation B-factories, the branching fraction for the rare B→γ(Eγ)ℓνℓ radiative decay is also calculated, retaining 1/mB2 and 1/Eγ2 corrections to the differential decay width, with the result ΓB→γℓνℓ/ΓB=0.47(15) on Eγ>1.5GeV.