Relativistic corrections to prompt J/ψJ/\psi photo- and hadroproduction

We systematically calculate the relativistic corrections to prompt $J/\psi$ photoproduction and hadroproduction using the factorization formalism of nonrelativistic QCD. Specifically, we include the ${}^3\!S_1^{[1]}$ and ${}^3\!P_{J}^{[1]}$ color-singlet and the ${}^3\!S_1^{[8]}$, ${}^1\!S_{0}^{[8]}$, and ${}^3\!P_{J}^{[8]}$ color-octet channels as well as the effects due to the mixing between the ${}^3\!S_1^{[8]}$ and ${}^3\!D_1^{[8]}$ channels. We provide all the squared hard-scattering amplitudes in analytic form. Assuming the nonrelativistic-QCD long-distance matrix elements to satisfy the velocity scaling rules, we find the relativistic corrections to be appreciable, except in the ${}^3\!S_1^{[1]}$ color-singlet channel of hadroproduction. We also observe significant differences in the line shapes of the relativistic corrections between photoproduction and hadroproduction.Comment: 26 pages, 3 figures, matches journal versio

Relativistic corrections to J/ψJ/\psi polarization in photo- and hadroproduction

We systematically calculate the relativistic corrections to the polarization variables of prompt $J/\psi$ photoproduction and hadroproduction using the factorization formalism of nonrelativistic QCD. Specifically, we include the ${}^3\!S_1^{[1]}$ and ${}^3\!P_{J}^{[1]}$ color-singlet and the ${}^3\!S_1^{[8]}$, ${}^1\!S_{0}^{[8]}$, and ${}^3\!P_{J}^{[8]}$ color-octet channels as well as the effects due to the mixing between the ${}^3\!S_1^{[8]}$ and ${}^3\!D_1^{[8]}$ channels. We provide all the squared hard-scattering amplitudes in analytic form. Assuming the nonrelativistic-QCD long-distance matrix elements to satisfy the velocity scaling rules, we find the relativistic corrections to be appreciable, especially at small transverse momentum $p_T$ and large inelasticity $z$. The results obtained here and in our previous work on the unpolarized yield [Phys. Rev. D 90, 014045 (2014)] will help to render global analyses of prompt $J/\psi$ production data more complete and hopefully to shed light on the $J/\psi$ polarization puzzle.Comment: 42 pages, 4 figures, matches journal version, PRD Editors' Suggestio

Complete Nonrelativistic-QCD Prediction for Prompt Double J/ψJ/\psi Hadroproduction

We perform a complete study of prompt double $J/\psi$ hadroproduction at leading order in the nonrelativistic-QCD factorization framework by including all possible pairings of the $c\bar{c}$ Fock states ${}^1\!S_0^{[8]}$, ${}^3\!S_1^{[1,8]}$, and ${}^3\!P_J^{[1,8]}$ with $J=0,1,2$. We find that the ${}^1\!S_0^{[8]}$ and ${}^3\!P_J^{[8]}$ channels of $J/\psi$ and $\psi^\prime$ production and the ${}^3\!P_J^{[1]}$ and ${}^3\!S_1^{[8]}$ channels of $\chi_{cJ}$ production, which have been overlooked so far, greatly dominate at large invariant masses and rapidity separations of the $J/\psi$ pair, and that their inclusion nearly fills the large gap between previous incomplete predictions within the color-singlet model and the recent measurement by the CMS Collaboration at the CERN LHC, leaving room for next-to-leading-order corrections of typical size.Comment: 5 pages, 4 figures, matches journal versio

Environmental factors controlling the distributions of Botryococcus braunii (A, B and L) biomarkers in a subtropical freshwater wetland

Here we report the molecular biomarker co-occurrence of three different races of Botryococcus braunii (B. braunii) in the freshwater wetland ecosystem of the Florida Everglades, USA. Thespecific biomarkers include C32–C34 botryococcenes for race B, C27–C32 n-alkadienes and n-alkatrienes for race A, and lycopadiene for race L. The n-alkadienes and n-alkatrienes were present up to 3.1 and 69.5 µg/g dry weight (dw), while lycopadiene was detected in lower amounts up to 3.0 and 1.5 µg/g dw in periphyton and floc samples, respectively. Nutrient concentrations (P and N) did not significantly correlate with the abundances of these compounds. In contrast, n-alkadienes and n-alkatrienes were present in wider diversity and higher abundance in the floc from slough (deeper water and longer hydroperiod) than ridge (shallower water and shorter hydroperiod) locations. n-Alkadienes, n-alkatrienes, and lycopadiene, showed lower δ13C values from −40.0 to −35.5‰, suggesting that the source organisms B. braunii at least partially utilize recycled CO2 (13C depleted) produced from OM respiration rather than atmospheric CO2 (13C enriched) as the major carbon sources

ηc\eta_c production at the LHC challenges nonrelativistic-QCD factorization

We analyze the first measurement of $\eta_c$ production, performed by the LHCb Collaboration, in the nonrelativistic-QCD (NRQCD) factorization framework at next-to-leading order (NLO) in the strong-coupling constant $\alpha_s$ and the relative velocity $v$ of the bound quarks including the feeddown from $h_c$ mesons. Converting the long-distance matrix elements (LDMEs) extracted by various groups from $J/\psi$ yield and polarization data to the $\eta_c$ case using heavy-quark spin symmetry, we find that the resulting NLO NRQCD predictions greatly overshoot the LHCb data, while the color-singlet model provides an excellent description.Comment: 5 pages, 2 figures, minor changes, note regarding arXiv:1411.7350 [hep-ph] added, accepted for publication in Physical Review Letter

Inclusive χcJ\chi_{cJ} production in Υ\Upsilon decay at O(αs5)\mathcal{O}(\alpha_s^5) in NRQCD factorization

Inclusive $\chi_{cJ}$ $(J=0,1,2)$ production from $\Upsilon(1S)$ decay is studied within the framework of nonrelativistic QCD (NRQCD) factorization at leading order in $v_Q^2$, which includes the contributions of $b\bar{b}({}^3S_1^{[1]})\to c\bar{c}(^3P_J^{[1]})+X$ and $b\bar{b}({}^3S_1^{[1]})\to c\bar{c}(^3S_1^{[8]})+X$. For both channels, the short-distance coefficients are calculated through ${\cal O}(\alpha_s^5)$, which is next-to-leading order for the second one. By fitting to the measured $\Upsilon(1S)$ branching fractions to $\chi_{c1}$ and $\chi_{c2}$, we obtain the color-octet long-distance matrix element (LDME) $\langle\mathcal{O}^{\chi_{c0}}({}^3S_1^{[8]})\rangle =(4.04\pm0.47_{-0.34}^{+0.67})\times10^{-3}$ GeV$^3$, where the first error is experimental and the second one due to the renormalization scale dependence, if we use as input $\langle\mathcal{O}^{\chi_{c0}}({}^3P_0^{[1]})\rangle=0.107$ GeV$^5$ as obtained via potential-model analysis. Previous LDME sets, extracted from data of prompt $\chi_{cJ}$ hadroproduction, yield theoretical predictions that systematically undershoot or mildly overshoot the experimental values of $\mathcal{B}(\Upsilon\to \chi_{cJ}+X)$.Comment: 10 pages, 8 figures, minor changes, matches journal versio

Positive del Pezzo Geometry

Real, complex, and tropical algebraic geometry join forces in a new branch of mathematical physics called positive geometry. We develop the positive geometry of del Pezzo surfaces and their moduli spaces, viewed as very affine varieties. Their connected components are derived from polyhedral spaces with Weyl group symmetries. We study their canonical forms and scattering amplitudes, and we solve the likelihood equations.Comment: 34 pages, 4 figure