Iterative forcing and hyperimmunity in reverse mathematics

The separation between two theorems in reverse mathematics is usually done by constructing a Turing ideal satisfying a theorem P and avoiding the solutions to a fixed instance of a theorem Q. Lerman, Solomon and Towsner introduced a forcing technique for iterating a computable non-reducibility in order to separate theorems over omega-models. In this paper, we present a modularized version of their framework in terms of preservation of hyperimmunity and show that it is powerful enough to obtain the same separations results as Wang did with his notion of preservation of definitions.Comment: 15 page

Effectiveness of Hindman's theorem for bounded sums

We consider the strength and effective content of restricted versions of Hindman's Theorem in which the number of colors is specified and the length of the sums has a specified finite bound. Let $\mathsf{HT}^{\leq n}_k$ denote the assertion that for each $k$-coloring $c$ of $\mathbb{N}$ there is an infinite set $X \subseteq \mathbb{N}$ such that all sums $\sum_{x \in F} x$ for $F \subseteq X$ and $0 < |F| \leq n$ have the same color. We prove that there is a computable $2$-coloring $c$ of $\mathbb{N}$ such that there is no infinite computable set $X$ such that all nonempty sums of at most $2$ elements of $X$ have the same color. It follows that $\mathsf{HT}^{\leq 2}_2$ is not provable in $\mathsf{RCA}_0$ and in fact we show that it implies $\mathsf{SRT}^2_2$ in $\mathsf{RCA}_0$. We also show that there is a computable instance of $\mathsf{HT}^{\leq 3}_3$ with all solutions computing $0'$. The proof of this result shows that $\mathsf{HT}^{\leq 3}_3$ implies $\mathsf{ACA}_0$ in $\mathsf{RCA}_0$

Test of lepton universality in b→sℓ+ℓ−b \rightarrow s \ell^+ \ell^- decays

The first simultaneous test of muon-electron universality using $B^{+}\rightarrow K^{+}\ell^{+}\ell^{-}$ and $B^{0}\rightarrow K^{*0}\ell^{+}\ell^{-}$ decays is performed, in two ranges of the dilepton invariant-mass squared, $q^{2}$. The analysis uses beauty mesons produced in proton-proton collisions collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 $\mathrm{fb}^{-1}$. Each of the four lepton universality measurements reported is either the first in the given $q^{2}$ interval or supersedes previous LHCb measurements. The results are compatible with the predictions of the Standard Model.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-046.html (LHCb public pages

Precision measurement of CP\it{CP} violation in the penguin-mediated decay Bs0→ϕϕB_s^{0}\rightarrow\phi\phi

A flavor-tagged time-dependent angular analysis of the decay $B_s^{0}\rightarrow\phi\phi$ is performed using $pp$ collision data collected by the LHCb experiment at % at $\sqrt{s}=13$ TeV, the center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6 fb^{-1}. The $\it{CP}$-violating phase and direct $\it{CP}$-violation parameter are measured to be $\phi_{s\bar{s}s} = -0.042 \pm 0.075 \pm 0.009$ rad and $|\lambda|=1.004\pm 0.030 \pm 0.009$, respectively, assuming the same values for all polarization states of the $\phi\phi$ system. In these results, the first uncertainties are statistical and the second systematic. These parameters are also determined separately for each polarization state, showing no evidence for polarization dependence. The results are combined with previous LHCb measurements using $pp$ collisions at center-of-mass energies of 7 and 8 TeV, yielding $\phi_{s\bar{s}s} = -0.074 \pm 0.069$ rad and $|lambda|=1.009 \pm 0.030$. This is the most precise study of time-dependent $\it{CP}$ violation in a penguin-dominated $B$ meson decay. The results are consistent with $\it{CP}$ symmetry and with the Standard Model predictions.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2023-001.html (LHCb public pages

First observation of a doubly charged tetraquark and its neutral partner

A combined amplitude analysis is performed for the decays $B^0 \rightarrow \overline{D}^0 D^+_s\pi^-$ and $B^+\rightarrow D^- D^+_s\pi^+$, which are related by isospin symmetry. The analysis is based on data collected by the LHCb detector in proton-proton collisions at center-of-mass energies of 7, 8 and 13$\,\rm{TeV}$. The full data sample corresponds to an integrated luminosity of 9$\,\rm{fb^{-1}}$. Two new resonant states with masses of $2.908\pm0.011\pm0.020\,\rm{GeV}$ and widths of $0.136\pm0.023\pm0.011\,\rm{GeV}$ are observed, which decay to $D^+_s\pi^+$ and $D^+_s\pi^-$ respectively. The former state indicates the first observation of a doubly charged open-charm tetraquark state with minimal quark content $[c\bar{s}u\bar{d}]$, and the latter state is a neutral tetraquark composed of $[c\bar{s}\bar{u}d]$ quarks. Both states are found to have spin-parity $0^+$, and their resonant parameters are consistent with each other, which suggests that they belong to an isospin triplet.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-026.html (LHCb public pages

Observation of a resonant structure near the Ds+Ds−D_s^+ D_s^- threshold in the B+→Ds+Ds−K+B^+\to D_s^+ D_s^- K^+ decay

An amplitude analysis of the $B^+\to D_s^+ D_s^- K^+$ decay is carried out to study for the first time its intermediate resonant contributions, using proton-proton collision data collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV. A near-threshold peaking structure, referred to as $X(3960)$, is observed in the $D_s^+ D_s^-$ invariant-mass spectrum with significance greater than 12 standard deviations. The mass, width and the quantum numbers of the structure are measured to be $3956\pm5\pm10$ MeV, $43\pm13\pm8$ MeV and $J^{PC}=0^{++}$, respectively, where the first uncertainties are statistical and the second systematic. The properties of the new structure are consistent with recent theoretical predictions for a state composed of $c\bar{c}s\bar{s}$ quarks. Evidence for an additional structure is found around 4140 MeV in the $D_s^+ D_s^-$ invariant mass, which might be caused either by a new resonance with the $0^{++}$ assignment or by a $J/\psi \phi\leftrightarrow D_s^+ D_s^-$ coupled-channel effect.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-018.html (LHCb public pages

Measurement of the Λb0→Λ(1520)μ+μ−\Lambda_{b}^{0}\to \Lambda(1520) \mu^{+}\mu^{-} differential branching fraction

The branching fraction of the rare decay $\Lambda_{b}^{0}\to \Lambda(1520) \mu^{+}\mu^{-}$ is measured for the first time, in the squared dimuon mass intervals, $q^2$, excluding the $J/\psi$ and $\psi(2S)$ regions. The data sample analyzed was collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of $9\ \mathrm{fb}^{-1}$. The result in the highest$q^{2}$interval,$q^{2} >15.0\ \mathrm{GeV}^2/c^4$, where theoretical predictions have the smallest model dependence, agrees with the predictions.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-050.html (LHCb public pages

Angular Analysis of the B+ -> K*(+)mu(+) mu(-) Decay

We present an angular analysis of the B + → K * + ( → K 0 S π + ) μ + μ − decay using 9     fb − 1 of p p collision data collected with the LHCb experiment. For the first time, the full set of C P -averaged angular observables is measured in intervals of the dimuon invariant mass squared. Local deviations from standard model predictions are observed, similar to those in previous LHCb analyses of the isospin-partner B 0 → K * 0 μ + μ − decay. The global tension is dependent on which effective couplings are considered and on the choice of theory nuisance parameters

Study of coherent J/ψJ/ψ production in lead-lead collisions at sNN=5TeV\sqrt{s_{NN}} = 5 TeV

Coherent production of $J/\psi$ mesons is studied in ultraperipheral lead-lead collisions at a nucleon-nucleon centre-of-mass energy of 5 TeV, using a data sample collected by the LHCb experiment corresponding to an integrated luminosity of about $10 \mu b^{-1}$. The $J/\psi$ mesons are reconstructed in the dimuon final state and are required to have transverse momentum below 1 GeV. The cross-section within the rapidity range of $2.0 < y < 4.5$ is measured to be $4.45\pm0.24\pm0.18\pm0.58$ mb, where the first uncertainty is statistical, the second systematic and the third originates from the luminosity determination. The cross-section is also measured in $J/\psi$ rapidity intervals. The results are compared to predictions from phenomenological models

Study of the ψ2(3823)ψ_2(3823) and χc1(3872)χ_{c1}(3872) states in B+→(Jψπ+π−)K+B^+ \rightarrow \left( Jψπ^+π^-\right)K^+ decays

The decays $B^+\rightarrow J/\psi \pi^+ \pi^- K^+$ are studied using a data set corresponding to an integrated luminosity of 9fb$^{-1}$ collected with the LHCb detector in proton-proton collisions between 2011 and 2018. Precise measurements of the ratios of branching fractions with the intermediate $\psi_2(3823)$, $\chi_{c1}(3872)$ and $\psi(2S)$ states are reported. The decay of $B^+\rightarrow \psi_2(3823)K^+$ with $\psi_2(3823)\rightarrow J\psi\pi^+\pi^-$ is observed for the first time with a significance of 5.1 standard deviations. The mass differences between the $\psi_2(3823)$, $\chi_{c1}(3872)$ and $\psi(2S)$ states are measured to be $$\begin{array}{rcl} m_{\chi_{c1(3872)}} - m_{\psi_2(3823)} &= & 47.50 \pm 0.53 \pm 0.13\,\mathrm{MeV/}c^2\,, \\ m_{\psi_2(3823)} - m_{\psi(2S)} &= & 137.98 \pm 0.53 \pm 0.14\,\mathrm{MeV/}c^2\,, \\ m_{\chi_{c1}(3872)} - m_{\psi(2S)} &= & 185.49 \pm 0.06 \pm 0.03\,\mathrm{MeV/}c^2\,, \end{array}$$ resulting in the most precise determination of the $\chi_{c1}(3782)$ mass. The width of the $\psi_2(3823)$ state is found to be below 5.2MeV at 90\% confidence level. The Breit-Wigner width of the $\chi_{c1}(3872)$ state is measured to be $$\Gamma^{\mathrm{BW}}_{\chi_{c1}(3872)} = 0.96^{+0.19}_{-0.18}\pm0.21 \mathrm{MeV},$$ which is inconsistent with zero by 5.5 standard deviations