Differential Branching Fraction Research Articles

UsingΛb→Λμ+μ−data within a Bayesian analysis of|ΔB|=|ΔS|=1decays

We study the impact of including the baryonic decay $\Lambda_b\to \Lambda(\to p \pi^-)\mu^+\mu^-$ in a Bayesian analysis of $|\Delta B | = |\Delta S| = 1$ transitions. We perform fits of the Wilson coefficients $C_{9}$, $C_{9'}$, $C_{10}$ and $C_{10'}$, in addition to the relevant nuisance parameters. Our analysis combines data for the differential branching fraction and three angular observables of $\Lambda_b\to \Lambda(\to p \pi^-)\mu^+\mu^-$ with data for the branching ratios of $B_s \to \mu^+\mu^-$ and inclusive $b \to s\ell^+\ell^-$ decays. Newly available precise lattice QCD results for the full set of $\Lambda_b \to \Lambda$ form factors are used to evaluate the observables of the baryonic decay. Our fits prefer shifts to $C_{9}$ that are opposite in sign compared to those found in global fits of only mesonic decays, and the posterior odds show no evidence of physics beyond the Standard Model. We investigate a possible hadronic origin of the observed tensions between theory and experiment.

Angular analysis and differential branching fraction of the decay: B → K⁎μ+μ−

Measurements of rare B meson decay properties provide an alternative approach to direct searches for physics beyond the Standard Model. These decays, which proceed through flavor-changing neutral currents, can have interferences from new physics through loop diagrams and hence an excellent probe. In particular, the angular distribution of the decay B→K⁎μ+μ− can be measured to estimate the forward-backward asymmetries of the muons, the longitudinal polarization fractions of K⁎ and the differential branching fractions, as a function of the dimuon invariant mass. Results based on data recorded by the CMS experiment at centre-of-mass energy of 7 TeV are presented.

Λb→Λℓ+ℓ−form factors, differential branching fraction, and angular observables from lattice QCD with relativisticbquarks

Using $(2+1)$-flavor lattice QCD, we compute the 10 form factors describing the $\Lambda_b \to \Lambda$ matrix elements of the $b \to s$ vector, axial vector, and tensor currents. The calculation is based on gauge field ensembles generated by the RBC and UKQCD Collaborations with a domain-wall action for the $u$, $d$, and $s$ quarks and the Iwasaki gauge action. The $b$ quark is implemented using an anisotropic clover action, tuned nonperturbatively to the physical point, and the currents are renormalized with a mostly nonperturbative method. We perform simultaneous chiral, continuum, and kinematic extrapolations of the form factors through modified $z$ expansions. Using our form factor results, we obtain precise predictions for the $\Lambda_b \to \Lambda(\to p^+ \pi^-) \mu^+ \mu^-$ differential branching fraction and angular observables in the Standard Model.

Optimal-observable analysis of possible new physics inB→D(*)τντ

We study all possible observables in $B\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\tau}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ with new physics (NP), including new vector, scalar and tensor interactions, and investigate the prospects of extracting NP Wilson coefficients with optimal observables. The analysis shows that, overall, the full ${q}^{2}$ integrated observables in $B\ensuremath{\rightarrow}D\ensuremath{\tau}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ are more sensitive towards the scalar current, whereas the bin-by-bin analysis of ${q}^{2}$ distribution of the differential branching fraction points to regions of ${q}^{2}$ sensitive to tensor interactions. Interestingly, the observables in $B\ensuremath{\rightarrow}{D}^{*}\ensuremath{\tau}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ are more sensitive to tensor interactions, and bin-by-bin analysis of this mode shows the distinct regions of ${q}^{2}$ sensitive to vector or scalar interactions. In addition to that, the $\ensuremath{\tau}$ polarization asymmetry is found to be more sensitive to NP compared to the other observables, in both decay modes.

Angular analysis of the decay B0 → K⁎0μ+μ− from pp collisions at [formula omitted

The angular distributions and the differential branching fraction of the decay B0→K⁎(892)0μ+μ− are studied using data corresponding to an integrated luminosity of 20.5 fb−1 collected with the CMS detector at the LHC in pp collisions at s=8 TeV. From 1430 signal decays, the forward–backward asymmetry of the muons, the K⁎(892)0 longitudinal polarization fraction, and the differential branching fraction are determined as a function of the dimuon invariant mass squared. The measurements are among the most precise to date and are in good agreement with standard model predictions.

The B → K* transition form factors within the QCD light-cone sum rules and their application to the semi-leptonic decay B → K* μ+μ−

We present a detailed calculation on the transition form factors (TFFs), V and within the QCD light-cone sum rules (LCSRs). To suppress the contributions from high-twist light-cone distribution amplitudes, we adopt a right-handed chiral correlator to do the LCSR calculation. In the resultant LCSRs for the TFFs, the transverse leading-twist distribution amplitude provides over 90% contribution, thus those TFFs provide good platforms for testing the property of We suggest a model for in which two parameters and dominantly control its longitudinal distribution. With a proper choice of and our predictions on TFFs are consistent with those of lattice QCD predictions. As an application, we also calculate the branching fraction of the B-meson rare decay The predicted differential branching fraction is consistent with the LHCb and Belle measurements within errors. After integrating over the allowable q2-region, we get the branching fraction, where the errors are squared average of the mentioned error sources. When the precision of experimental measurements or the other source of theoretical uncertainties for this process have been further improved in the future, we may get a definite conclusion on the behavior of

First measurement of the differential branching fraction and CP asymmetry of the B ± → π ± μ + μ − decay

The differential branching fraction with respect to the dimuon invariant mass squared, and the $C\!P$ asymmetry of the $B^\pm\to\pi^\pm\mu^+\mu^-$ decay are measured for the first time. The CKM matrix elements $|V_{td}|$ and $|V_{ts}|$, and the ratio $|V_{td}/V_{ts}|$ are determined. The analysis is performed using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb$^{-1}$, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The total branching fraction and $C\!P$ asymmetry of $B^\pm\to\pi^\pm\mu^+\mu^-$ decays are measured to be \begin{eqnarray} \mathcal{B}(B^\pm\to\pi^\pm\mu^+\mu^-) &=& (1.83 \pm 0.24 \pm 0.05) \times 10^{-8}\,\,\,\mathrm{and} \nonumber\\ \mathcal{A}_{C\!P}(B^\pm\to\pi^\pm\mu^+\mu^-) &=& -0.11 \pm 0.12 \pm 0.01\,, \nonumber \end{eqnarray} where the first uncertainties are statistical and the second are systematic. These are the most precise measurements of these observables to date, and they are compatible with the predictions of the Standard Model.

Angular analysis and differential branching fraction of the decay B s 0 → ϕμ + μ −

An angular analysis and a measurement of the differential branching fraction of the decay $B^0_s\to\phi\mu^+\mu^-$ are presented, using data corresponding to an integrated luminosity of $3.0\, {\rm fb^{-1}}$ of $pp$ collisions recorded by the LHCb experiment at $\sqrt{s} = 7$ and $8\, {\rm TeV}$. Measurements are reported as a function of $q^{2}$, the square of the dimuon invariant mass and results of the angular analysis are found to be consistent with the Standard Model. In the range $1<q^2<6\, {\rm GeV}^{2}/c^{4}$, where precise theoretical calculations are available, the differential branching fraction is found to be more than $3\,\sigma$ below the Standard Model predictions.

Ward identities, B → V transition form factors and applications

Long distance effects are studied in the rare exclusive semileptonic B(d,s) → Vℓ+ℓ− decays, where V denotes a K* or ϕ meson. The form factors, which describe the meson transition amplitudes in the effective Hamiltonian approach, are calculated by means of Ward identities, experimental constraints and extrapolated within a general vector meson dominance framework. These form factors are then compared to the ones obtained in Lattice QCD simulations, with Light Cone Sum Rules and a Dyson-Schwinger equation approach. Additionally, the Bd → K*ℓ+ℓ− and Bs → ϕℓ+ℓ− branching ratios are computed and the differential branching fractions are given as a function of the squared-momentum transfer.

Differential branching fraction and angular analysis of Λ0 b → Λμ+μ− decays

AbstractThe differential branching fraction of the rare decayΛb0 → Λμ+μ−is measured as a function ofq2, the square of the dimuon invariant mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb−1, collected by the LHCb experiment. Evidence of signal is observed in theq2region below the square of theJ/ψmass. Integrating over 15&lt; q2&lt;20 GeV2/c4the differential branching fraction is measured as$$ \mathrm{d}\mathrm{\mathcal{B}}\left({\varLambda}_b^0\to \varLambda {\mu}^{+}{\mu}^{-}\right)/d{q}^2=\left({1.18}_{-0.08}^{+0.09}\pm 0.03\pm 0.27\right)\times {10}^{-7}{\left({\mathrm{GeV}}^2/{c}^4\right)}^{-1}, $$dℬΛb0→Λμ+μ−/dq2=1.18−0.08+0.09±0.03±0.27×10−7GeV2/c4−1,where the uncertainties are statistical, systematic and due to the normalisation mode,Λb0 → J/ψΛ, respectively. In theq2intervals where the signal is observed, angular distributions are studied and the forward-backward asymmetries in the dimuon (AFBℓ) and hadron (AFBh) systems are measured for the first time. In the range 15&lt; q2&lt;20 GeV2/c4they are found to be$$ \begin{array}{l}{A}_{\mathrm{FB}}^{\ell }=-0.05\pm 0.09\left(\mathrm{stat}\right)\pm 0.03\left(\mathrm{syst}\right)\;\mathrm{and}\hfill \\ {}{A}_{\mathrm{FB}}^h=-0.29\pm 0.07\left(\mathrm{stat}\right)\pm 0.03\left(\mathrm{syst}\right).\hfill \end{array} $$AFBℓ=−0.05±0.09stat±0.03systandAFBh=−0.29±0.07stat±0.03syst.

S-wave resonance contributions to theB(s)0→J/ψπ+π−andBs→π+π−μ+μ−decays

We study $S$-wave resonance contributions to the ${B}_{(s)}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decays in the perturbative QCD framework by introducing two-hadron distribution amplitudes for final states. The Breit--Wigner formula for the ${f}_{0}(500)$, ${f}_{0}(1500)$, and ${f}_{0}(1790)$ resonances and the Flatt\'e model for the ${f}_{0}(980)$ resonance are adopted to parametrize the timelike scalar form factors in the two-pion distribution amplitudes, which include both resonant and nonresonant contributions. The resultant branching fraction and differential branching fraction in the pion-pair invariant mass for each resonance channel are consistent with experimental data. The determined $S$-wave two-pion distribution amplitudes, containing the information of both resonant and nonresonant rescattering phases, can be employed to predict direct $CP$ asymmetries of other three-body hadronic $B$ meson decays in various localized regions of two-pion phase space.

B→πℓνandBs→Kℓνform factors and|Vub|from2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks

We calculate the $B \to\pi\ell\nu$ and $B_s \to K \ell\nu$ form factors in dynamical lattice QCD. We use the (2+1)-flavor RBC-UKQCD gauge-field ensembles generated with the domain-wall fermion and Iwasaki gauge actions. For the $b$ quarks we use the anisotropic clover action with a relativistic heavy-quark interpretation. We analyze two lattice spacings $a \approx 0.11, 0.086$ fm and unitary pion masses as light as $M_\pi \approx 290$ MeV. We simultaneously extrapolate our numerical results to the physical light-quark masses and to the continuum and interpolate in the pion/kaon energy using SU(2) "hard-pion" chiral perturbation theory. We provide complete error budgets for the form factors $f_+(q^2)$ and $f_0(q^2)$ at three momenta that span the $q^2$ range accessible in our numerical simulations. We extrapolate these results to $q^2 = 0$ using a model-independent $z$-parametrization and present our final form factors as the $z$-coefficients and the matrix of correlations between them. Our results agree with other lattice determinations using staggered light quarks and provide important independent cross-checks. Both $B \to\pi\ell\nu$ and $B_s \to K \ell\nu$ decays enable a determination of the CKM matrix element $|V_{ub}|$. To illustrate this, we perform a combined $z$-fit of our numerical $B\to\pi\ell\nu$ form-factor data with the experimental branching-fraction measurements leaving the relative normalization as a free parameter; we obtain $|V_{ub}| = 3.61(32) \times 10^{-3}$, where the error includes statistical and systematic uncertainties. This approach can be applied to $B_s\to K \ell\nu$ decay to determine $|V_{ub}|$ once the process has been measured experimentally. Finally, in anticipation of future measurements, we make predictions for $B \to \pi\ell\nu$ and $B_s\to K \ell\nu$ Standard-Model differential branching fractions and forward-backward asymmetries.

Measurement of theD0→π−e+νedifferential decay branching fraction as a function ofq2and study of form factor parametrizations

Based on a sample of 500 million $e^+e^- \to c\bar c$ events recorded by the BaBar detector at c.m. energies of close to 10.6 GeV, we report on a study of the decay $D^0 \to \pi^- e^+ \nu_e$. We measure the ratio of branching fractions $R_D = {\cal B}(D^0 \to \pi^- e^+ \nu_e)/{\cal B}(D^0 \to K^- \pi^+) = 0.0713 \pm 0.0017_{stat.} \pm 0.0024_{syst.}$, and use the present world average for ${\cal B}(D^0 \to K^- \pi^+)$ to obtain ${\cal B}(D^0 \to \pi^- e^+ \nu_e) = (2.770 \pm 0.068_{{\rm stat.}} \pm 0.092_{{\rm syst.}} \pm 0.037_{{\rm ext.}})\times 10^{-3}$ where the third error accounts for the uncertainty on the branching fraction for the reference channel. The measured dependence of the differential branching fraction on $q^2$, the four-momentum transfer squared between the $D$ and the $\pi$ meson, is compared to various theoretical predictions for the hadronic form factor, $f_{+,D}^{\pi}(q^2)$, and the normalization $|V_{cd}| \times f_{+,D}^{\pi}(q^2=0)=0.1374\pm0.0038_{{\rm stat.}} \pm0.0022_{{\rm syst.}} \pm0.0009_{{\rm ext.}}$ is extracted from a fit to data. Using the most recent LQCD prediction of $f_{+,D}^{\pi}(q^2=0)=0.666 \pm 0.029$, we obtain $|V_{cd}|=0.206 \pm 0.007_{\rm exp.} \pm 0.009_{\rm LQCD}$. Assuming instead, $|V_{cd}|=|V_{us}|=0.2252 \pm 0.0009$, we obtain $f_{+,D}^{\pi}(q^2=0)=0.610 \pm 0.020_{\rm exp.} \pm 0.005_{\rm ext.}$. The $q^2$ dependence of $f_{+,D}^{\pi}(q^2)$ is compared to a variety of multi-pole parameterizations. This information is applied to $B^0 \to \pi^- e^+ \nu_e$ decays and, combined with an earlier $B^0 \to \pi^- e^+ \nu_e$ measurement by BaBar, is used to derive estimates of $|V_{ub}|$.

First observations of the rare decays B + → K + π + π − μ + μ − and B +→ ϕK + μ + μ −

First observations of the rare decays $B^+\rightarrow K^+\pi^+\pi^-\mu^+\mu^-$ and $B^+\rightarrow \phi K^+\mu^+\mu^-$ are presented using data corresponding to an integrated luminosity of $3.0\,{fb}^{-1}$, collected by the LHCb experiment at centre-of-mass energies of $7$ and $8\mathrm{\,TeV}$. The branching fractions of the decays are \begin{eqnarray*} \mathcal{B}(B^+\rightarrow K^+\pi^+\pi^-\mu^+\mu^-) &=& (4.36\,^{+0.29}_{-0.27}\,\mathrm{(stat)}\pm 0.21\,\mathrm{(syst)}\pm0.18\,\mathrm{(norm)})\times10^{-7},\\ \mathcal{B}(B^+\rightarrow\phi K^+\mu^+\mu^-) &=& (0.82 \,^{+0.19}_{-0.17}\,\mathrm{(stat)}\,^{+0.10}_{-0.04}\,\mathrm{(syst)}\pm0.27\,\mathrm{(norm)}) \times10^{-7},\end{eqnarray*} where the uncertainties are statistical, systematic, and due to the uncertainty on the branching fractions of the normalisation modes. A measurement of the differential branching fraction in bins of the invariant mass squared of the dimuon system is also presented for the decay $B^+\rightarrow K^+\pi^+\pi^-\mu^{+}\mu^{-}$.

Bs→Kℓνform factors from lattice QCD

We report the first lattice QCD calculation of the form factors for the standard model tree-level decay $B_s\to K \ell\nu$. In combination with future measurement, this calculation will provide an alternative exclusive semileptonic determination of $|V_{ub}|$. We compare our results with previous model calculations, make predictions for differential decay rates and branching fractions, and predict the ratio of differential branching fractions between $B_s\to K\tau\nu$ and $B_s\to K\mu\nu$. We also present standard model predictions for differential decay rate forward-backward asymmetries, polarization fractions, and calculate potentially useful ratios of $B_s\to K$ form factors with those of the fictitious $B_s\to\eta_s$ decay. Our lattice simulations utilize NRQCD $b$ and HISQ light quarks on a subset of the MILC Collaboration's $2+1$ asqtad gauge configurations, including two lattice spacings and a range of light quark masses.

Calculation ofB0→K*0μ+μ−andBs0→ϕμ+μ−Observables Using Form Factors from Lattice QCD

We calculate the differential branching fractions and angular distributions of the rare decays $B^0 \to K^{*0} \mu^+ \mu^-$ and $B_s^0 \to \phi \mu^+ \mu^-$, using for the first time form factors from unquenched lattice QCD. We focus on the kinematic region where the $K^*$ or $\phi$ recoils softly; there the newly available form factors are most precise and the nonlocal matrix elements can be included via an operator product expansion. Our results for the differential branching fractions calculated in the Standard Model are higher than the experimental data. We consider the possibility that the deviations are caused by new physics, and perform a fit of the Wilson coefficients $C_9$ and $C_9^\prime$ to the experimental data for multiple $B^0 \to K^{*0} \mu^+ \mu^-$ and $B_s^0 \to \phi \mu^+ \mu^-$ observables. In agreement with recent results from complementary studies, we obtain $C_9-C_9^{SM} = -1.0 \pm 0.6$ and $C_9^\prime = 1.2 \pm 1.0$, whose deviations from zero would indicate the presence of non-standard fundamental interactions.

Predicting theB→K*form factors in light-cone QCD

We use QCD light-cone sum rules with holographic anti de Sitter/Chromodynamics (AdS/QCD) Distribution Amplitudes (DAs) for the $K^*$ meson in order to predict the full set of seven $B \to K^*$ transition form factors for intermediate-to-high recoil of the vector meson. We provide simple parametrizations for the form factors that fit our AdS/QCD predictions. We also provide parametrizations that fit both our AdS/QCD predictions and the most recent lattice data for low recoil. We use our form factors to predict the differential and total branching fraction of the rare dileptonic decay $B \to K^* \mu^+ \mu^-$ which we compare to the recent LHCb data.

The study of rare $ {B_c}\to D_{s,d}^{{\left( * \right)}}l\overline{l} $ decays

In this paper, we study rare decays $B_c\rightarrow D^{(*)}_{s,d}l\bar{l}$ within the Standard Model. The penguin, box, annihilation, color-favored cascade and color-suppressed cascade contributions are included. Based on our calculation, the annihilation and color-favored cascade diagrams play important roles in the differential branching fractions, forward-backward asymmetries, longitudinal polarizations of the final vector mesons and leptonic longitudinal polarization asymmetries. More importantly, color-favored cascade decays largely enhance the resonance cascade contributions. To avoid the resonance cascade contribution pollution, new cutting regions are put forward.

Measurement of $${\Upsilon } $$ Υ production in $${{\mathrm {p}}} {{\mathrm {p}}} $$ p p collisions at $${\sqrt{s}} =2.76{\mathrm {\,TeV}} $$ s = 2.76 TeV

The production of Upsilon(1S), Upsilon(2S) and Upsilon(3S) mesons decaying into the dimuon final state is studied with the LHCb detector using a data sample corresponding to an integrated luminosity of 3.3 pb^{-1} collected in proton-proton collisions at a centre-of-mass energy of sqrt{s}=2.76 TeV. The differential production cross-sections times dimuon branching fractions are measured as functions of the Upsilon transverse momentum and rapidity, over the ranges p_T<15 GeV/c and 2.0<y<4.5. The total cross-sections in this kinematic region, assuming unpolarised production, are measured to be sigma(pp -> Upsilon(1S) X) x B(Upsilon(1S) -> mu+mu-) = 1.111 +/- 0.043 +/- 0.044 nb, sigma(pp -> Upsilon(2S) X) x B(Upsilon(2S) -> mu+mu-) = 0.264 +/- 0.023 +/- 0.011 nb, sigma(pp -> Upsilon(3S) X) x B(Upsilon(3S) -> mu+mu-) = 0.159 +/- 0.020 +/- 0.007 nb, where the first uncertainty is statistical and the second systematic.

Angular analysis and branching fraction measurement of the decay [formula omitted

The angular distributions and the differential branching fraction of the decay B0→K⁎(892)0μ+μ− are studied using a data sample corresponding to an integrated luminosity of 5.2 fb−1 collected with the CMS detector at the LHC in pp collisions at s=7 TeV. From more than 400 signal decays, the forward–backward asymmetry of the muons, the K⁎(892)0 longitudinal polarization fraction, and the differential branching fraction are determined as a function of the square of the dimuon invariant mass. The measurements are in good agreement with standard model predictions.