Strict Finitism's Unrequited Love for Computational Complexity

As a philosophy of mathematics, strict finitism has been traditionally concerned with the notion of feasibility, defended mostly by appealing to the physicality of mathematical practice. This has led the strict finitists to influence and be influenced by the field of computational complexity theory, under the widely held belief that this branch of mathematics is concerned with the study of what is “feasible in practice”. In this paper, I survey these ideas and contend that, contrary to popular belief, complexity theory is not what the ultrafinitists think it is, and that it does not provide a theoretical framework in which to formalize their ideas —at least not while defending the material grounds for feasibility. I conclude that the subject matter of complexity theory is not proving physical resource bounds in computation, but rather proving the absence of exploitable properties in a search space

Multiplicity dependence of light (anti-)nuclei production in p–Pb collisions at sNN=5.02 TeV

The measurement of the deuteron and anti-deuteron production in the rapidity range −1 < y < 0 as a function of transverse momentum and event multiplicity in p–Pb collisions at √sNN = 5.02 TeV is presented. (Anti-)deuterons are identified via their specific energy loss dE/dx and via their time-of- flight. Their production in p–Pb collisions is compared to pp and Pb–Pb collisions and is discussed within the context of thermal and coalescence models. The ratio of integrated yields of deuterons to protons (d/p) shows a significant increase as a function of the charged-particle multiplicity of the event starting from values similar to those observed in pp collisions at low multiplicities and approaching those observed in Pb–Pb collisions at high multiplicities. The mean transverse particle momenta are extracted from the deuteron spectra and the values are similar to those obtained for p and particles. Thus, deuteron spectra do not follow mass ordering. This behaviour is in contrast to the trend observed for non-composite particles in p–Pb collisions. In addition, the production of the rare 3He and 3He nuclei has been studied. The spectrum corresponding to all non-single diffractive p-Pb collisions is obtained in the rapidity window −1 < y < 0 and the pT-integrated yield dN/dy is extracted. It is found that the yields of protons, deuterons, and 3He, normalised by the spin degeneracy factor, follow an exponential decrease with mass number

Measurement of electrons from semileptonic heavy-flavour hadron decays at midrapidity in pp and Pb–Pb collisions at √sNN = 5.02 TeV

The differential invariant yield as a function of transverse momentum (pT) of electrons from semileptonic heavy-flavour hadron decays was measured at midrapidity in central (0–10%), semi-central (30–50%) and peripheral (60–80%) lead–lead (Pb–Pb) collisions at √sNN = 5.02 TeV in the pT intervals 0.5–26 GeV/c (0–10% and 30–50%) and 0.5–10 GeV/c (60–80%). The production cross section in proton–proton (pp) collisions at √s = 5.02 TeV was measured as well in 0.5 < pT < 10 GeV/c and it lies close to the upper band of perturbative QCD calculation uncertainties up to pT = 5 GeV/c and close to the mean value for larger pT. The modification of the electron yield with respect to what is expected for an incoherent superposition of nucleon–nucleon collisions is evaluated by measuring the nuclear modification factor RAA. The measurement of the RAA in different centrality classes allows in-medium energy loss of charm and beauty quarks to be investigated. The RAA shows a suppression with respect to unity at intermediate pT, which increases while moving towards more central collisions. Moreover, the measured RAA is sensitive to the modification of the parton distribution functions (PDF) in nuclei, like nuclear shadowing, which causes a suppression of the heavy-quark production at low pT in heavy-ion collisions at LHC

Nuclear modification factor of light neutral-meson spectra up to high transverse momentum in p–Pb collisions at sNN=8.16 TeV

International audienceNeutral pion (π0) and η meson production cross sections were measured up to unprecedentedly high transverse momenta (pT) in p–Pb collisions at sNN=8.16TeV. The mesons were reconstructed via their two-photon decay channel in the rapidity interval −1.3&lt;y&lt;0.3 in the ranges of 0.4&lt;pT&lt;200 GeV/c and 1.0&lt;pT&lt;50 GeV/c, respectively. The respective nuclear modification factor (RpPb) is presented for pT up to of 200 and 30 GeV/c, where the former was achieved by extending the π0 measurement in pp collisions at s=8TeV using the merged cluster technique. The values of RpPb are below unity for pT&lt;10 GeV/c, while they are consistent with unity for pT&gt;10 GeV/c, leaving essentially no room for final state energy loss. The new data provide strong constraints for nuclear parton distribution and fragmentation functions over a broad kinematic range and are compared to model predictions as well as previous results at sNN=5.02TeV

Elliptic Flow of Electrons from Beauty-Hadron Decays in Pb-Pb Collisions at sNN\sqrt {s_{NN}} = 5.02 TeV

The elliptic flow of electrons from beauty hadron decays at midrapidity (|y|<0.8) is measured in Pb-Pb collisions at $\sqrt {s_{NN}}$ = 5.02 TeV with the ALICE detector at the LHC. The azimuthal distribution of the particles produced in the collisions can be parametrized with a Fourier expansion, in which the second harmonic coefficient represents the elliptic flow, $v_2$. The $v_2$ coefficient of electrons from beauty hadron decays is measured for the first time in the transverse momentum ($p_T$) range 1.3–6 GeV/c in the centrality class 30%–50%. The measurement of electrons from beauty-hadron decays exploits their larger mean proper decay length cτ ≈ 500 μm compared to that of charm hadrons and most of the other background sources. The $v_2$ of electrons from beauty hadron decays at midrapidity is found to be positive with a significance of 3.75 σ. The results provide insights into the degree of thermalization of beauty quarks in the medium. A model assuming full thermalization of beauty quarks is strongly disfavored by the measurement at high $p_T$, but is in agreement with the results at low $p_T$. Transport models including substantial interactions of beauty quarks with an expanding strongly interacting medium describe the measurement within uncertainties

Production of pions, kaons, (anti-)protons and ϕ\phi mesons in Xe–Xe collisions at sNN\sqrt{s_{\mathrm{NN}}} = 5.44 TeV

The first measurement of the production of pions, kaons, (anti-)protons and $\phi$ mesons at midrapidity in Xe–Xe collisions at $\sqrt{s_{\mathrm{NN}}} = 5.44~\text {TeV}$ is presented. Transverse momentum ($p_{\mathrm{T}}$) spectra and $p_{\mathrm{T}}$-integrated yields are extracted in several centrality intervals bridging from p–Pb to mid-central Pb–Pb collisions in terms of final-state multiplicity. The study of Xe–Xe and Pb–Pb collisions allows systems at similar charged-particle multiplicities but with different initial geometrical eccentricities to be investigated. A detailed comparison of the spectral shapes in the two systems reveals an opposite behaviour for radial and elliptic flow. In particular, this study shows that the radial flow does not depend on the colliding system when compared at similar charged-particle multiplicity. In terms of hadron chemistry, the previously observed smooth evolution of particle ratios with multiplicity from small to large collision systems is also found to hold in Xe–Xe. In addition, our results confirm that two remarkable features of particle production at LHC energies are also valid in the collision of medium-sized nuclei: the lower proton-to-pion ratio with respect to the thermal model expectations and the increase of the $\phi$-to-pion ratio with increasing final-state multiplicity

J/ψ\psi production as a function of charged-particle multiplicity in p-Pb collisions at sNN = 8.16\sqrt{\textit{s}_{\rm NN}}~=~8.16 TeV

Inclusive J/ψ yields and average transverse momenta in p-Pb collisions at a center-of-mass energy per nucleon pair $\sqrt{s_{\mathrm{NN}}}$ = 8.16 TeV are measured as a function of the charged-particle pseudorapidity density with ALICE. The J/ψ mesons are reconstructed at forward (2.03 < y$_{cms}$< 3.53) and backward (−4.46 < y$_{cms}$< −2.96) center-of-mass rapidity in their dimuon decay channel while the charged-particle pseudorapidity density is measured around midrapidity. The J/ψ yields at forward and backward rapidity normalized to their respective average values increase with the normalized charged-particle pseudorapidity density, the former showing a weaker increase than the latter. The normalized average transverse momenta at forward and backward rapidity manifest a steady increase from low to high charged-particle pseudorapidity density with a saturation beyond the average value

Jet-associated deuteron production in pp collisions at s=13 TeV

International audienceDeuteron production in high-energy collisions is sensitive to the space–time evolution of the collision system, and is typically described by a coalescence mechanism. For the first time, we present results on jet-associated deuteron production in pp collisions at s=13 TeV, providing an opportunity to test the established picture for deuteron production in events with a hard scattering. Using a trigger particle with high transverse-momentum (pT&gt;5 GeV/c) as a proxy for the presence of a jet at midrapidity, we observe a measurable population of deuterons being produced around the jet proxy. The associated deuteron yield measured in a narrow angular range around the trigger particle differs by 2.4–4.8 standard deviations from the uncorrelated background. The data are described by PYTHIA model calculations featuring baryon coalescence

Measurement of beauty-strange meson production in Pb–Pb collisions at <math altimg="si1.svg"><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">NN</mi></mrow></msub></mrow></msqrt><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mn>5.02</mn><mspace width="0.25em"/><mrow><mi mathvariant="normal">TeV</mi></mrow></math> via non-prompt <math altimg="si2.svg"><msubsup><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msubsup></math> mesons

International audienceThe production yields of non-prompt Ds+ mesons, namely Ds+ mesons from beauty-hadron decays, were measured for the first time as a function of the transverse momentum (pT) at midrapidity (|y|&lt;0.5) in central and semi-central Pb–Pb collisions at a centre-of-mass energy per nucleon pair sNN=5.02TeV with the ALICE experiment at the LHC. The Ds+ mesons and their charge conjugates were reconstructed from the hadronic decay channel Ds+→ϕπ+, with ϕ→K−K+, in the 4&lt;pT&lt;36GeV/c and 2&lt;pT&lt;24GeV/c intervals for the 0–10% and 30–50% centrality classes, respectively. The measured yields of non-prompt Ds+ mesons are compared to those of prompt Ds+ and non-prompt D0 mesons by calculating the ratios of the production yields in Pb–Pb collisions and the nuclear modification factor RAA. The ratio between the RAA of non-prompt Ds+ and prompt Ds+ mesons, and that between the RAA of non-prompt Ds+ and non-prompt D0 mesons in central Pb–Pb collisions are found to be on average higher than unity in the 4&lt;pT&lt;12GeV/c interval with a statistical significance of about 1.6σ and 1.7σ, respectively. The measured RAA ratios are compared with the predictions of theoretical models of heavy-quark transport in a hydrodynamically expanding QGP that incorporate hadronisation via quark recombination

Measurement of the Cross Sections of Ξc0\Xi^0_{c} and Ξc+\Xi^+_{c} Baryons and of the Branching-Fraction Ratio BR(Ξc0→Ξ−e+νe\Xi^0_{c} \rightarrow \Xi^-{e}^+\nu_{ e})/BR(Ξc0→Ξ−π+\Xi^0_{c} \rightarrow \Xi^-\pi^+) in pp collisions at 13 TeV

The $p_T$-differential cross sections of prompt charm-strange baryons Ξ$_c^0$ and Ξ$_c^+$ were measured at midrapidity (|y|<0.5) in proton-proton (pp) collisions at a center-of-mass energy $\sqrt{s}$ = 13 TeV with the ALICE detector at the LHC. The Ξ$_c^0$ baryon was reconstructed via both the semileptonic decay (Ξ$^-$e$^+$ν$_e$) and the hadronic decay (Ξ$^-$π$^+$) channels. The Ξ$_c^+$ baryon was reconstructed via the hadronic decay (Ξ$^-$π$^+$π$^+$) channel. The branching-fraction ratio BR(Ξ$_c^0$→Ξ$^-$e$^+$ν$_e$)/BR(Ξ$_c^0$→Ξ$^-$π$^+$) = 1.38±0.14(stat)±0.22(syst) was measured with a total uncertainty reduced by a factor of about 3 with respect to the current world average reported by the Particle Data Group. The transverse momentum ($p_T$) dependence of the Ξ$_c^0-$ and Ξ$_c^+$-baryon production relative to the D$^0$ meson and to the Σ$_c^{0,+,++}$- and Λ$_c^+$-baryon production are reported. The baryon-to-meson ratio increases toward low $p_T$ up to a value of approximately 0.3. The measurements are compared with various models that take different hadronization mechanisms into consideration. The results provide stringent constraints to these theoretical calculations and additional evidence that different processes are involved in charm hadronization in electron-positron (e$^+$e$^-$) and hadronic collisions