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1. Interpolation for Curves in Projective Space with Bounded Error

   https://doi.org/10.1093/imrn/rnz136  

   Larson, Eric (July 2019, International Mathematics Research Notices)

   Abstract Given $$n$$ general points $$p_1, p_2, \ldots , p_n \in{\mathbb{P}}^r$$ it is natural to ask whether there is a curve of given degree $$d$$ and genus $$g$$ passing through them; by counting dimensions a natural conjecture is that such a curve exists if and only if $$\begin{equation*}n \leq \left\lfloor \frac{(r + 1)d - (r - 3)(g - 1)}{r - 1}\right\rfloor.\end{equation*}$$The case of curves with nonspecial hyperplane section was recently studied in [2], where the above conjecture was shown to hold with exactly three exceptions. In this paper, we prove a “bounded-error analog” for special linear series on general curves; more precisely we show that existence of such a curve subject to the stronger inequality $$\begin{equation*}n \leq \left\lfloor \frac{(r + 1)d - (r - 3)(g - 1)}{r - 1}\right\rfloor - 3.\end{equation*}$$Note that the $-3$ cannot be replaced with $-2$ without introducing exceptions (as a canonical curve in $${\mathbb{P}}^3$$ can only pass through nine general points, while a naive dimension count predicts twelve). We also use the same technique to prove that the twist of the normal bundle $$N_C(-1)$$ satisfies interpolation for curves whose degree is sufficiently large relative to their genus, and deduce from this that the number of general points contained in the hyperplane section of a general curve is at least $$\begin{equation*}\min\left(d, \frac{(r - 1)^2 d - (r - 2)^2 g - (2r^2 - 5r + 12)}{(r - 2)^2}\right).\end{equation*}$$ As explained in [7], these results play a key role in the author’s proof of the maximal rank conjecture [9]. 

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2. Observation of $$ {\Lambda}_b^0 $$ → D+pπ−π− and $$ {\Lambda}_b^0 $$ → D*+pπ−π− decays

   https://doi.org/10.1007/JHEP03(2022)153  

   Aaij, R.; Abdelmotteleb, A. S.; Abellán Beteta, C.; Abudinén, F.; Ackernley, T.; Adeva, B.; Adinolfi, M.; Afsharnia, H.; Agapopoulou, C.; Aidala, C. A.; et al (March 2022, Journal of High Energy Physics)

   Abstract The multihadron decays $$ {\Lambda}_b^0 $$ Λ b 0 → D + pπ−π− and $$ {\Lambda}_b^0 $$ Λ b 0 → D * + pπ−π− are observed in data corresponding to an integrated luminosity of 3 fb − 1 , collected in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV by the LHCb detector. Using the decay $$ {\Lambda}_b^0 $$ Λ b 0 → $$ {\Lambda}_c^{+} $$ Λ c + π + π − π − as a normalisation channel, the ratio of branching fractions is measured to be $$ \frac{\mathcal{B}\left({\Lambda}_b^0\to {D}^{+}p{\pi}^{-}{\pi}^{-}\right)}{\mathcal{B}\left({\Lambda}_b^0\to {\Lambda}_c^0{\pi}^{+}{\pi}^{-}{\pi}^{-}\right)}\times \frac{\mathcal{B}\left({D}^{+}\to {K}^{-}{\pi}^{+}{\pi}^{+}\right)}{\mathcal{B}\left({\Lambda}_c^0\to {pK}^{-}{\pi}^{-}\right)}=\left(5.35\pm 0.21\pm 0.16\right)\%, $$ B Λ b 0 → D + p π − π − B Λ b 0 → Λ c 0 π + π − π − × B D + → K − π + π + B Λ c 0 → pK − π − = 5.35 ± 0.21 ± 0.16 % , where the first uncertainty is statistical and the second systematic. The ratio of branching fractions for the $$ {\Lambda}_b^0 $$ Λ b 0 → D *+ pπ − π − and $$ {\Lambda}_b^0 $$ Λ b 0 → D + pπ − π − decays is found to be $$ \frac{\mathcal{B}\left({\Lambda}_b^0\to {D}^{\ast +}p{\pi}^{-}{\pi}^{-}\right)}{\mathcal{B}\left({\Lambda}_b^0\to {D}^{+}p{\pi}^{-}{\pi}^{-}\right)}\times \left(\mathcal{B}\left({D}^{\ast +}\to {D}^{+}{\pi}^0\right)+\mathcal{B}\left({D}^{\ast +}\to {D}^{+}\gamma \right)\right)=\left(61.3\pm 4.3\pm 4.0\right)\%. $$ B Λ b 0 → D ∗ + p π − π − B Λ b 0 → D + p π − π − × B D ∗ + → D + π 0 + B D ∗ + → D + γ = 61.3 ± 4.3 ± 4.0 % . 

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3. Measurement of branching fractions and search for CP violation in D0 → π+π−η, D0 → K+K−η, and D0 → ϕη at Belle

   https://doi.org/10.1007/JHEP09(2021)075  

   Li, L. K.; Schwartz, A. J.; Kinoshita, K.; Adachi, I.; Aihara, H.; Al Said, S.; Asner, D. M.; Atmacan, H.; Aulchenko, V.; Aushev, T.; et al (September 2021, Journal of High Energy Physics)

   A bstract We measure the branching fractions and CP asymmetries for the singly Cabibbo-suppressed decays D 0 → π + π − η , D 0 → K + K − η , and D 0 → ϕη , using 980 fb − 1 of data from the Belle experiment at the KEKB e + e − collider. We obtain $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({D}^0\to {\pi}^{+}{\pi}^{-}\eta \right)=\left[1.22\pm 0.02\left(\mathrm{stat}\right)\pm 0.02\left(\mathrm{syst}\right)\pm 0.03\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-3},\\ {}\mathcal{B}\left({D}^0\to {K}^{+}{K}^{-}\eta \right)=\left[{1.80}_{-0.06}^{+0.07}\left(\mathrm{stat}\right)\pm 0.04\left(\mathrm{syst}\right)\pm 0.05\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-4},\\ {}\mathcal{B}\left({D}^0\to \phi \eta \right)=\left[1.84\pm 0.09\left(\mathrm{stat}\right)\pm 0.06\left(\mathrm{syst}\right)\pm 0.05\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-4},\end{array}} $$ B D 0 → π + π − η = 1.22 ± 0.02 stat ± 0.02 syst ± 0.03 B ref × 10 − 3 , B D 0 → K + K − η = 1.80 − 0.06 + 0.07 stat ± 0.04 syst ± 0.05 B ref × 10 − 4 , B D 0 → ϕη = 1.84 ± 0.09 stat ± 0.06 syst ± 0.05 B ref × 10 − 4 , where the third uncertainty ( $$ \mathcal{B} $$ B ref ) is from the uncertainty in the branching fraction of the reference mode D 0 → K − π + η . The color-suppressed decay D 0 → ϕη is observed for the first time, with very high significance. The results for the CP asymmetries are $$ {\displaystyle \begin{array}{c}{A}_{CP}\left({D}^0\ {\pi}^{+}{\pi}^{-}\eta \right)=\left[0.9\pm 1.2\left(\mathrm{stat}\right)\pm 0.5\left(\mathrm{syst}\right)\right]\%,\\ {}{A}_{CP}\left({D}^0\to {K}^{+}{K}^{-}\eta \right)=\left[-1.4\pm 3.3\left(\mathrm{stat}\right)\pm 1.1\left(\mathrm{syst}\right)\right]\%,\\ {} ACP\ \left({D}^0\to \phi \eta \right)=\left[-1.9\pm 4.4\left(\mathrm{stat}\right)\pm 0.6\left(\mathrm{syst}\right)\right]\%.\end{array}} $$ A CP D 0 π + π − η = 0.9 ± 1.2 stat ± 0.5 syst % , A CP D 0 → K + K − η = − 1.4 ± 3.3 stat ± 1.1 syst % , ACP D 0 → ϕη = − 1.9 ± 4.4 stat ± 0.6 syst % . The results for D 0 → π + π − η are a significant improvement over previous results. The branching fraction and A CP results for D 0 → K + K − η , and the ACP result for D 0 → ϕη , are the first such measurements. No evidence for CP violation is found in any of these decays. 

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4. Measurement of beauty and charm production in pp collisions at $$ \sqrt{s} $$ = 5.02 TeV via non-prompt and prompt D mesons

   https://doi.org/10.1007/JHEP05(2021)220  

   Acharya, S.; Adamová, D.; Adler, A.; Adolfsson, J.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; Ahn, S. U.; et al (May 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract The p T -differential production cross sections of prompt and non-prompt (produced in beauty-hadron decays) D mesons were measured by the ALICE experiment at midrapidity ( | y | < 0 . 5) in proton-proton collisions at $$ \sqrt{s} $$ s = 5 . 02 TeV. The data sample used in the analysis corresponds to an integrated luminosity of (19 . 3 ± 0 . 4) nb − 1 . D mesons were reconstructed from their decays D 0 → K − π + , D + → K − π + π + , and $$ {\mathrm{D}}_{\mathrm{s}}^{+}\to \upphi {\uppi}^{+}\to {\mathrm{K}}^{-}{\mathrm{K}}^{+}{\uppi}^{+} $$ D s + → ϕ π + → K − K + π + and their charge conjugates. Compared to previous measurements in the same rapidity region, the cross sections of prompt D + and $$ {\mathrm{D}}_{\mathrm{s}}^{+} $$ D s + mesons have an extended p T coverage and total uncertainties reduced by a factor ranging from 1.05 to 1.6, depending on p T , allowing for a more precise determination of their p T -integrated cross sections. The results are well described by perturbative QCD calculations. The fragmentation fraction of heavy quarks to strange mesons divided by the one to non-strange mesons, f s / ( f u + f d ), is compatible for charm and beauty quarks and with previous measurements at different centre-of-mass energies and collision systems. The $$ \mathrm{b}\overline{\mathrm{b}} $$ b b ¯ production cross section per rapidity unit at midrapidity, estimated from non-prompt D-meson measurements, is $$ \mathrm{d}{\sigma}_{\mathrm{b}\overline{\mathrm{b}}}/\mathrm{d}y\left|{}_{\left|\mathrm{y}\right|<0.5}=34.5\pm 2.4{\left(\mathrm{stat}\right)}_{-2.9}^{+4.7}\left(\mathrm{tot}.\mathrm{syst}\right)\right. $$ d σ b b ¯ / d y y < 0.5 = 34.5 ± 2.4 stat − 2.9 + 4.7 tot . syst μb. It is compatible with previous measurements at the same centre-of-mass energy and with the cross section pre- dicted by perturbative QCD calculations. 

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5. Measurement of the inclusive branching fractions for $${B}_{s}^{0}$$ decays into D mesons via hadronic tagging

   https://doi.org/10.1007/JHEP04(2025)114  

   Adachi, I; Aggarwal, L; Ahmed, H; Aihara, H; Akopov, N; Aloisio, A; Al_Said, S; Althubiti, N; Anh_Ky, N; Asner, D M; et al (April 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We report measurements of the absolute branching fractions$$\mathcal{B}\left({B}_{s}^{0}\to {D}_{s}^{\pm }X\right)$$,$$\mathcal{B}\left({B}_{s}^{0}\to {D}^{0}/{\overline{D} }^{0}X\right)$$, and$$\mathcal{B}\left({B}_{s}^{0}\to {D}^{\pm }X\right)$$, where the latter is measured for the first time. The results are based on a 121.4 fb⁻¹data sample collected at the Υ(10860) resonance by the Belle detector at the KEKB asymmetric-energye⁺e⁻collider. We reconstruct one$${B}_{s}^{0}$$meson in$${e}^{+}{e}^{-}\to \Upsilon\left(10860\right)\to {B}_{s}^{*}{\overline{B} }_{s}^{*}$$events and measure yields of$${D}_{s}^{+}$$,D⁰, andD⁺mesons in the rest of the event. We obtain$$\mathcal{B}\left({B}_{s}^{0}\to {D}_{s}^{\pm }X\right)=\left(68.6\pm 7.2\pm 4.0\right)\%$$,$$\mathcal{B}\left({B}_{s}^{0}\to {D}^{0}/{\overline{D} }^{0}X\right)=\left(21.5\pm 6.1\pm 1.8\right)\%$$, and$$\mathcal{B}\left({B}_{s}^{0}\to {D}^{\pm }X\right)=\left(12.6\pm 4.6\pm 1.3\right)\%$$, where the first uncertainty is statistical and the second is systematic. Averaging with previous Belle measurements gives$$\mathcal{B}\left({B}_{s}^{0}\to {D}_{s}^{\pm }X\right)=\left(63.4\pm 4.5\pm 2.2\right)\%$$and$$\mathcal{B}\left({B}_{s}^{0}\to {D}^{0}/{\overline{D} }^{0}X\right)=\left(23.9\pm 4.1\pm 1.8\right)\%$$. For the$${B}_{s}^{0}$$production fraction at the Υ(10860), we find$${f}_{s}=\left({21.4}_{-1.7}^{+1.5}\right)\%$$. 

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