Search

A study of $B_c^{+}\to K^{+}{K}^{-}{\pi }^{+}$ decays is performed for the first time using data corresponding to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$ collected by the LHCb experiment in $pp$ collisions at center-of-mass energies of 7 and 8 TeV. Evidence for the decay $B_c^{+}\to {\chi }_{c0}(\to K^{+}{K}^{-}){\pi }^{+}$ is reported with a significance of 4.0 standard deviations, giving $\frac{\sigma (B_c^{+})}{\sigma (B^{+})}\times \mathcal{B}(B_c^{+}\to {\chi }_{c0}{\pi }^{+})=(9.8_{-3.0}^{+3.4}(\mathrm{stat})\pm 0.8(\mathrm{syst}))\times {10}^{-6}$. Here $\mathcal{B}$ denotes a branching fraction while $\sigma (B_c^{+})$ and $\sigma (B^{+})$ are the production cross sections for $B_c^{+}$ and $B^{+}$ mesons. An indication of $\overline{b}c$ weak annihilation is found for the region $m(K^{-}{\pi }^{+})<1.834\mathrm{GeV}/c^2$, with a significance of 2.4 standard deviations.

The relative abundance of the three decay modes $B^0\to D^{-}{K}^{+}$, $B^0\to D^{-}{\pi }^{+}$, and $B_s^0\to D_s^{-}{\pi }^{+}$ produced in 7 TeV $pp$ collisions at the LHC is determined from data corresponding to an integrated luminosity of $35{\mathrm{pb}}^{-1}$. The branching fraction of $B^0\to D^{-}{K}^{+}$ is found to be $\mathcal{B}(B^0\to D^{-}{K}^{+})=(2.01\pm {0.18}^{\mathrm{stat}}\pm {0.14}^{\mathrm{syst}})\times {10}^{-4}$. The ratio of fragmentation fractions $f_s/f_d$ is determined through the relative abundance of $B_s^0\to D_s^{-}{\pi }^{+}$ to $B^0\to D^{-}{K}^{+}$ and $B^0\to D^{-}{\pi }^{+}$, leading to $f_s/f_d=0.253\pm 0.017\pm 0.017\pm 0.020$, where the uncertainties are statistical, systematic, and theoretical, respectively.

First observations and measurements of the branching fractions of the ${\overline{B}}_s^0\to D^{+}{D}^{-}$, ${\overline{B}}_s^0\to D_s^{+}{D}^{-}$ and ${\overline{B}}_s^0\to D^0{\overline{D}}^0$ decays are presented using $1.0{\mathrm{fb}}^{-1}$ of data collected by the LHCb experiment. These branching fractions are normalized to those of ${\overline{B}}^0\to D^{+}{D}^{-}$, $B^0\to D^{-}{D}_s^{+}$ and $B^{-}\to D^0{D}_s^{-}$, respectively. An excess of events consistent with the decay ${\overline{B}}^0\to D^0{\overline{D}}^0$ is also seen, and its branching fraction is measured relative to that of $B^{-}\to D^0{D}_s^{-}$. Improved measurements of the branching fractions $\mathcal{B}({\overline{B}}_s^0\to D_s^{+}{D}_s^{-})$ and $\mathcal{B}(B^{-}\to D^0{D}_s^{-})$ are reported, each relative to $\mathcal{B}(B^0\to D^{-}{D}_s^{+})$. The ratios of branching fractions are $\frac{\mathcal{B}({\overline{B}}_s^0\to D^{+}{D}^{-})}{\mathcal{B}({\overline{B}}^0\to D^{+}{D}^{-})}=1.08\pm 0.20\pm 0.10$, $\frac{\mathcal{B}({\overline{B}}_s^0\to D_s^{+}{D}^{-})}{\mathcal{B}(B^0\to D^{-}{D}_s^{+})}=0.050\pm 0.008\pm 0.004$, $\frac{\mathcal{B}({\overline{B}}_s^0\to D^0{\overline{D}}^0)}{\mathcal{B}(B^{-}\to D^0{D}_s^{-})}=0.019\pm 0.003\pm 0.003$, $\frac{\mathcal{B}({\overline{B}}^0\to D^0{\overline{D}}^0)}{\mathcal{B}(B^{-}\to D^0{D}_s^{-})}<0.0024$ at 90% CL, $\frac{\mathcal{B}({\overline{B}}_s^0\to D_s^{+}{D}_s^{-})}{\mathcal{B}(B^0\to D^{-}{D}_s^{+})}=0.56\pm 0.03\pm 0.04$, $\frac{\mathcal{B}(B^{-}\to D^0{D}_s^{-})}{\mathcal{B}(B^0\to D^{-}{D}_s^{+})}=1.22\pm 0.02\pm 0.07$, where the uncertainties are statistical and systematic, respectively.

First observations of the Cabibbo-suppressed decays ${\overline{B}}^0\to D^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to D^0{K}^{-}{\pi }^{+}{\pi }^{-}$ are reported using $35{\mathrm{pb}}^{-1}$ of data collected with the LHCb detector. Their branching fractions are measured with respect to the corresponding Cabibbo-favored decays, from which we obtain $\mathcal{B}({\overline{B}}^0\to D^{+}{K}^{-}{\pi }^{+}{\pi }^{-})/\mathcal{B}({\overline{B}}^0\to D^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-})=(5.9\pm 1.1\pm 0.5)\times {10}^{-2}$ and $\mathcal{B}(B^{-}\to D^0{K}^{-}{\pi }^{+}{\pi }^{-})/\mathcal{B}(B^{-}\to D^0{\pi }^{-}{\pi }^{+}{\pi }^{-})=(9.4\pm 1.3\pm 0.9)\times {10}^{-2}$, where the uncertainties are statistical and systematic, respectively. The $B^{-}\to D^0{K}^{-}{\pi }^{+}{\pi }^{-}$ decay is particularly interesting, as it can be used in a similar way to $B^{-}\to D^0{K}^{-}$ to measure the Cabibbo-Kobayashi-Maskawa phase $\gamma$.

We report a measurement of the $CP$-violation parameter $\sin 2{\varphi }_1$ at the ${\rm Y}(5S)$ resonance using a new tagging method, called “$B\mathrm{\text{−}}\pi$ tagging.” In ${\rm Y}(5S)$ decays containing a neutral $B$ meson, a charged $B$, and a charged pion, the neutral $B$ is reconstructed in the $J/\psi K_S^0$ $CP$-eigenstate decay channel. The initial flavor of the neutral $B$ meson at the moment of the ${\rm Y}(5S)$ decay is opposite to that of the charged $B$ and may thus be inferred from the charge of the pion without reconstructing the charged $B$. From the asymmetry between $B\mathrm{\text{−}}{\pi }^{+}$ and $B\mathrm{\text{−}}{\pi }^{-}$ tagged $J/\psi K_S^0$ yields, we determine $\sin 2{\varphi }_1=0.57\pm 0.58(\mathrm{stat})\pm 0.06(\mathrm{syst})$. The results are based on $121{\mathrm{fb}}^{-1}$ of data recorded by the Belle detector at the KEKB $e^{+}{e}^{-}$ collider.

Decays of $B^0$ and $B_s^0$ mesons to the charmless baryonic final states $p\overline{p}{h}^{+}{h}^{\prime -}$, where $h$ and $h^{\prime }$ each denote a kaon or a pion, are searched for using the LHCb detector. The analysis is based on a sample of proton-proton collision data collected at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of $3{\mathrm{fb}}^{-1}$. Four-body charmless baryonic $B_s^0$ decays are observed for the first time. The decays $B_s^0\to p\overline{p}{K}^{+}{K}^{-}$, $B_s^0\to p\overline{p}{K}^{\pm }{\pi }^{\mp }$, $B^0\to p\overline{p}{K}^{\pm }{\pi }^{\mp }$ and $B^0\to p\overline{p}{\pi }^{+}{\pi }^{-}$ are observed with a significance greater than 5 standard deviations; evidence at 4.1 standard deviations is found for the $B^0\to p\overline{p}{K}^{+}{K}^{-}$ decay and an upper limit is set on the branching fraction for $B_s^0\to p\overline{p}{\pi }^{+}{\pi }^{-}$. Branching fractions in the kinematic region $m(p\overline{p})<2850\mathrm{MeV}/c^2$ are measured relative to the $B^0\to J/\psi (\to p\overline{p})K^{*}(892{)}^0$ channel.

The first observation of the decay $B^0\to D^0{\overline{D}}^0{K}^{+}{\pi }^{-}$ is reported using proton-proton collision data corresponding to an integrated luminosity of $4.7{\mathrm{fb}}^{-1}$ collected by the LHCb experiment in 2011, 2012 and 2016. The measurement is performed in the full kinematically allowed range of the decay outside of the $D^{*-}$ region. The ratio of the branching fraction relative to that of the control channel $B^0\to D^{*-}{D}^0{K}^{+}$ is measured to be $\mathcal{R}=(14.2\pm 1.1\pm 1.0)\%$, where the first uncertainty is statistical and the second is systematic. The absolute branching fraction of $B^0\to D^0{\overline{D}}^0{K}^{+}{\pi }^{-}$ decays is thus determined to be $\mathcal{B}(B^0\to D^0{\overline{D}}^0{K}^{+}{\pi }^{-})=(3.50\pm 0.27\pm 0.26\pm 0.30)\times {10}^{-4}$, where the third uncertainty is due to the branching fraction of the control channel. This decay mode is expected to provide insights to spectroscopy and the charm-loop contributions in rare semileptonic decays.

We report the results of searches for $B^{+}\to J/\psi {\eta }^{\prime }{K}^{+}$ and $B^0\to J/\psi {\eta }^{\prime }{K}_S^0$ decays, using a sample of $388\times {10}^6$ $B\overline{B}$ pairs collected with the Belle detector at the ${\rm Y}(4S)$ resonance. No statistically significant signal is found for either of the two decay modes and upper limits for the branching fractions are determined to be $\mathcal{B}(B^{+}\to J/\psi {\eta }^{\prime }{K}^{+})<8.8\times {10}^{-5}$ and $\mathcal{B}(B^0\to J/\psi {\eta }^{\prime }{K}_S^0)<2.5\times {10}^{-5}$ at 90% confidence level.

We have searched for the lepton flavor violating decay ${\tau }^{-}\to {\mu }^{-}\eta$ using a data sample of $84.3{\mathrm{f}\mathrm{b}}^{-1}$ accumulated with the Belle detector at KEK. The $\eta$ meson was detected through the decay modes: $\eta \to \gamma \gamma$ and ${\pi }^{+}{\pi }^{-}{\pi }^0$. No signal candidates are found, and we obtain an upper limit for the branching fraction $\mathcal{B}({\tau }^{-}\to {\mu }^{-}\eta )<3.4\times {10}^{-7}$ at the 90% confidence level.

The ratio of the ${\Lambda }_b^0$ baryon lifetime to that of the ${\overline{B}}^0$ meson is measured using $1.0{\mathrm{fb}}^{-1}$ of integrated luminosity in 7 TeV center-of-mass energy $pp$ collisions at the LHC. The ${\Lambda }_b^0$ baryon is observed for the first time in the decay mode ${\Lambda }_b^0\to J/\psi p{K}^{-}$, while the ${\overline{B}}^0$ meson decay used is the well known ${\overline{B}}^0\to J/\psi {\pi }^{+}{K}^{-}$ mode, where the ${\pi }^{+}{K}^{-}$ mass is consistent with that of the ${\overline{K}}^{*0}(892)$ meson. The ratio of lifetimes is measured to be $0.976\pm 0.012\pm 0.006$, in agreement with theoretical expectations based on the heavy quark expansion. Using previous determinations of the ${\overline{B}}^0$ meson lifetime, the ${\Lambda }_b^0$ lifetime is found to be $1.482\pm 0.018\pm 0.012\mathrm{ps}$. In both cases, the first uncertainty is statistical and the second systematic.

We report a study of the suppressed decays $B^{-}\to [K^{+}{\pi }^{-}{]}_D{K}^{-}$ and $B^{-}\to [K^{+}{\pi }^{-}{]}_D{\pi }^{-}$, where $[K^{+}{\pi }^{-}{]}_D$ indicates that the $K^{+}{\pi }^{-}$ pair originates from a neutral $D$ meson. These decay modes are sensitive to the unitarity triangle angle ${\varphi }_3$. We use a data sample containing $275\times {10}^6$ $B\overline{B}$ pairs recorded at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric $e^{+}{e}^{-}$ storage ring. The signal for $B^{-}\to [K^{+}{\pi }^{-}{]}_D{K}^{-}$ is not statistically significant, and we set a limit $r_B<0.27$ at $90\%$ confidence level, where $r_B$ is the magnitude of the ratio of amplitudes $|A(B^{-}\to {\overline{D}}^0{K}^{-})/A(B^{-}\to D^0{K}^{-})|$. We observe a signal with $6.4\sigma$ statistical significance in the related mode, $B^{-}\to [K^{+}{\pi }^{-}{]}_D{\pi }^{-}$.

A baryonic decay of the $B_c^{+}$ meson, $B_c^{+}\to J/\psi p\overline{p}{\pi }^{+}$, is observed for the first time, with a significance of 7.3 standard deviations, in $pp$ collision data collected with the LHCb detector and corresponding to an integrated luminosity of $3.0{\text{fb}}^{-1}$ taken at center-of-mass energies of 7 and 8 TeV. With the $B_c^{+}\to J/\psi {\pi }^{+}$ decay as the normalization channel, the ratio of branching fractions is measured to be $\mathcal{B}(B_c^{+}\to J/\psi p\overline{p}{\pi }^{+})/\mathcal{B}(B_c^{+}\to J/\psi {\pi }^{+})=0.143_{-0.034}^{+0.039}(\text{stat})\pm 0.013(\text{syst})$. The mass of the $B_c^{+}$ meson is determined as $M(B_c^{+})=6274.0\pm 1.8(\text{stat})\pm 0.4(\text{syst})\mathrm{MeV}/c^2$, using the $B_c^{+}\to J/\psi p\overline{p}{\pi }^{+}$ channel.

We present a measurement of the time-dependent $CP$-violating asymmetry in $B_s^0\to J/\psi \varphi$ decays, using data collected with the LHCb detector at the LHC. The decay time distribution of $B_s^0\to J/\psi \varphi$ is characterized by the decay widths ${\Gamma }_H$ and ${\Gamma }_L$ of the heavy and light mass eigenstates, respectively, of the $B_s^0-{\overline{B}}_s^0$ system and by a $CP$-violating phase ${\varphi }_s$. In a sample of about 8500 $B_s^0\to J/\psi \varphi$ events isolated from $0.37{\mathrm{fb}}^{-1}$ of $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$, we measure ${\varphi }_s=0.15\pm 0.18(\mathrm{stat})\pm 0.06(\mathrm{syst})\mathrm{rad}$. We also find an average $B_s^0$ decay width ${\Gamma }_s\equiv ({\Gamma }_L+{\Gamma }_H)/2=0.657\pm 0.009(\mathrm{stat})\pm 0.008(\mathrm{syst}){\mathrm{ps}}^{-1}$ and a decay width difference $\Delta {\Gamma }_s\equiv {\Gamma }_L-{\Gamma }_H=0.123\pm 0.029(\mathrm{stat})\pm 0.011(\mathrm{syst}){\mathrm{ps}}^{-1}$. Our measurement is insensitive to the transformation $({\varphi }_s,\Delta {\Gamma }_s)\mapsto (\pi -{\varphi }_s,-\Delta {\Gamma }_s)$.

A search for $B_s^0\to {\mu }^{+}{\mu }^{-}$ and $B^0\to {\mu }^{+}{\mu }^{-}$ decays is performed using $1.0{\mathrm{fb}}^{-1}$ of $pp$ collision data collected at $\sqrt{s}=7\mathrm{TeV}$ with the LHCb experiment at the Large Hadron Collider. For both decays, the number of observed events is consistent with expectation from background and standard model signal predictions. Upper limits on the branching fractions are determined to be $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-})<4.5(3.8)\times {10}^{-9}$ and $\mathcal{B}(B^0\to {\mu }^{+}{\mu }^{-})<1.0(0.81)\times {10}^{-9}$ at 95% (90%) confidence level.

Using a proton-proton collision data sample corresponding to an integrated luminosity of $3{\mathrm{fb}}^{-1}$ collected by LHCb at center-of-mass energies of 7 and 8 TeV, about 3800 ${\mathrm{\Xi }}_b^0\to {\mathrm{\Xi }}_c^{+}{\pi }^{-}$, ${\mathrm{\Xi }}_c^{+}\to p{K}^{-}{\pi }^{+}$ signal decays are reconstructed. From this sample, the first measurement of the ${\mathrm{\Xi }}_b^0$ baryon lifetime is made, relative to that of the ${\mathrm{\Lambda }}_b^0$ baryon. The mass differences $M({\mathrm{\Xi }}_b^0)-M({\mathrm{\Lambda }}_b^0)$ and $M({\mathrm{\Xi }}_c^{+})-M({\mathrm{\Lambda }}_c^{+})$ are also measured with precision more than 4 times better than the current world averages. The resulting values are $$\begin{gathered} \frac{{\tau }_{{\mathrm{\Xi }}_b^0}}{{\tau }_{{\mathrm{\Lambda }}_b^0}}=1.006\pm 0.018\pm 0.010, \\ M({\mathrm{\Xi }}_b^0)-M({\mathrm{\Lambda }}_b^0)=172.44\pm 0.39\pm 0.17\mathrm{MeV}/c^2, \\ M({\mathrm{\Xi }}_c^{+})-M({\mathrm{\Lambda }}_c^{+})=181.51\pm 0.14\pm 0.10\mathrm{MeV}/c^2, \end{gathered}$$where the first uncertainty is statistical and the second is systematic. The relative rate of ${\mathrm{\Xi }}_b^0$ to ${\mathrm{\Lambda }}_b^0$ baryon production is measured to be $$\frac{f_{{\mathrm{\Xi }}_b^0}}{f_{{\mathrm{\Lambda }}_b^0}}\frac{\mathcal{B}({\mathrm{\Xi }}_b^0\to {\mathrm{\Xi }}_c^{+}{\pi }^{-})}{\mathcal{B}({\mathrm{\Lambda }}_b^0\to {\mathrm{\Lambda }}_c^{+}{\pi }^{-})}\frac{\mathcal{B}({\mathrm{\Xi }}_c^{+}\to p{K}^{-}{\pi }^{+})}{\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to p{K}^{-}{\pi }^{+})}=(1.88\pm 0.04\pm 0.03)\times 10^{-2},$$where the first factor is the ratio of fragmentation fractions, $b\to {\mathrm{\Xi }}_b^0$ relative to $b\to {\mathrm{\Lambda }}_b^0$. Relative production rates as functions of transverse momentum and pseudorapidity are also presented.

A search for charge-parity ($CP$) violation in Cabibbo-suppressed $D_s^{+}\to K_{\mathrm{S}}^0{\pi }^{+}$, $D^{+}\to K_{\mathrm{S}}^0{K}^{+}$, and $D^{+}\to \varphi {\pi }^{+}$ decays is reported using proton-proton collision data, corresponding to an integrated luminosity of $3.8{\mathrm{fb}}^{-1}$, collected at a center-of-mass energy of 13 TeV with the LHCb detector. High-yield samples of kinematically and topologically similar Cabibbo-favored $D_{(s)}^{+}$ decays are analyzed to subtract nuisance asymmetries due to production and detection effects, including those induced by $CP$ violation in the neutral kaon system. The results are $$\begin{gathered} {\mathcal{A}}_{CP}(D_s^{+}\to K_{\mathrm{S}}^0{\pi }^{+})=(1.3\pm 1.9\pm 0.5)\times {10}^{-3}, \\ {\mathcal{A}}_{CP}(D^{+}\to K_{\mathrm{S}}^0{K}^{+})=(-0.09\pm 0.65\pm 0.48)\times {10}^{-3}, \\ {\mathcal{A}}_{CP}(D^{+}\to \varphi {\pi }^{+})=(0.05\pm 0.42\pm 0.29)\times {10}^{-3}, \end{gathered}$$where the first uncertainties are statistical and the second systematic. They are the most precise measurements of these quantities to date, and are consistent with $CP$ symmetry. A combination with previous LHCb measurements, based on data collected at 7 and 8 TeV, is also reported.

The properties of the orbitally excited ($L=1$) $B_s^0$ states are studied by using $1.0{\mathrm{fb}}^{-1}$ of $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$ collected with the LHCb detector. The first observation of the $B_{s2}^{*}(5840{)}^0$ meson decaying to $B^{*+}{K}^{-}$ is reported, and the corresponding branching fraction measured relative to the $B^{+}{K}^{-}$ decay mode. The $B_{s1}(5830{)}^0\to B^{*+}{K}^{-}$ decay is observed as well. The width of the $B_{s2}^{*}(5840{)}^0$ state is measured for the first time, and the masses of the two states are determined with the highest precision to date. The observation of the $B_{s2}^{*}(5840{)}^0\to B^{*+}{K}^{-}$ decay favors the spin-parity assignment $J^P=2^{+}$ for the $B_{s2}^{*}(5840{)}^0$ meson. In addition, the most precise measurement of the mass difference $m(B^{*+})-m(B^{+})=45.01\pm 0.30(\mathrm{stat})\pm 0.23(\mathrm{syst})\mathrm{MeV}/c^2$ is obtained.

Dynamics and direct $CP$ violation in three-body charmless decays of charged $B$ mesons to a proton, an antiproton and a light meson (pion or kaon) are studied using data, corresponding to an integrated luminosity of $1.0{\mathrm{fb}}^{-1}$, collected by the LHCb experiment in $pp$ collisions at a center-of-mass energy of 7 TeV. Production spectra are determined as a function of Dalitz-plot and helicity variables. The forward-backward asymmetry of the light meson in the $p\overline{p}$ rest frame is measured. No significant $CP$ asymmetry in $B^{+}\to p\overline{p}{K}^{+}$ decay is found in any region of the Dalitz plane. We present the first observation of the decay $B^{+}\to \overline{\Lambda }(1520)(\to K^{+}\overline{p})p$ near the $K^{+}\overline{p}$ threshold and measure $\mathcal{B}(B^{+}\to \overline{\Lambda }(1520)p)=({3.9}_{-0.9}^{+1.0}(\mathrm{stat})\pm 0.1(\mathrm{syst})\pm 0.3(\mathrm{BF}))\times {10}^{-7}$, where BF denotes the uncertainty on secondary branching fractions.

The decay ${\overline{B}}_s^0\to J/\psi {\pi }^{+}{\pi }^{-}$ can be exploited to study $CP$ violation. A detailed understanding of its structure is imperative in order to optimize its usefulness. An analysis of this three-body final state is performed using a $1.0{\mathrm{fb}}^{-1}$ sample of data produced in 7 TeV $pp$ collisions at the LHC and collected by the LHCb experiment. A modified Dalitz plot analysis of the final state is performed using both the invariant mass spectra and the decay angular distributions. The ${\pi }^{+}{\pi }^{-}$ system is shown to be dominantly in an $S$-wave state, and the $CP$-odd fraction in this ${\overline{B}}_s^0$ decay is shown to be greater than 0.977 at 95% confidence level. In addition, we report the first measurement of the $J/\psi {\pi }^{+}{\pi }^{-}$ branching fraction relative to $J/\psi \varphi$ of $(19.79\pm 0.47\pm 0.52)\%$.

Using $pp$ collision data collected by LHCb at center-of-mass energies $\sqrt{s}=7\mathrm{TeV}$ and 8 TeV, corresponding to an integrated luminosity of $3{\mathrm{fb}}^{-1}$, the ratio of the branching fraction of the $B_c^{+}\to \psi (2S){\pi }^{+}$ decay relative to that of the $B_c^{+}\to J/\psi {\pi }^{+}$ decay is measured to be $0.268\pm 0.032(\mathrm{stat})\pm 0.007(\mathrm{syst})\pm 0.006(\mathrm{BF})$. The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainties on the branching fractions of the $J/\psi \to {\mu }^{+}{\mu }^{-}$ and $\psi (2S)\to {\mu }^{+}{\mu }^{-}$ decays. This measurement is consistent with the previous LHCb result, and the statistical uncertainty is halved.