Constraints on Nonrelativistic-QCD Long-Distance Matrix Elements from J/ψ Plus W/Z Production at the LHC.

We study the associated production of prompt J/ψ mesons and W or Z bosons within the factorization approach of nonrelativistic QCD (NRQCD) at next-to-leading order in α_{s}, via intermediate color singlet ^{3}S_{1}^{[1]} and ^{3}P_{J}^{[1]} and color octet ^{1}S_{0}^{[8]}, ^{3}S_{1}^{[8]}, and ^{3}P_{J}^{[8]} states. Requiring for our predictions to be compatible with recent ATLAS measurements yields stringent new constraints on charmonium long-distance matrix elements (LDMEs) being nonperturbative, process-independent input parameters. Considering four popular LDME sets fitted to data of single J/ψ inclusive production, we find that one is marginally compatible with the data, with central predictions typically falling short by a factor of 3, one is unfavored, the factor of shortfall being about 1 order of magnitude, and two violate cross section positivity for direct J/ψ+W/Z production. The large rate of prompt J/ψ plus W production observed by ATLAS provides strong evidence for the color octet mechanism inherent to NRQCD factorization, the leading color singlet contribution entering only at O(G_{F}α_{s}^{4}), beyond the order considered here.

Deciphering the X(3872) via its Polarization in Prompt Production at the CERN LHC.

Based on the hypothesis that the X(3872) exotic hadron is a mixture of χ_{c1}(2P) and other states and that its prompt hadroproduction predominately proceeds via its χ_{c1}(2P) component, we calculate the prompt-X(3872) polarization at the CERN LHC through next-to-leading order in α_{s} within the factorization formalism of nonrelativistic QCD, including both the color-singlet ^{3}P_{1}^{[1]} and color-octet ^{3}S_{1}^{[8]} cc[over ¯] Fock states. We also consider the polarization of the J/ψ produced by the subsequent X(3872) decay. We predict that, under ATLAS, CMS, and LHCb experimental conditions, the X(3872) is largely longitudinally polarized, while the J/ψ is largely transversely polarized. We propose that the LHC experiments perform such polarization measurements to pin down the nature of the X(3872) and other X, Y, Z exotic states with nonzero spin.

Double Prompt J/ψ Hadroproduction in the Parton Reggeization Approach with High-Energy Resummation.

We study double prompt J/ψ hadroproduction within the nonrelativistic-QCD factorization formalism adopting the parton Reggeization approach to treat initial-state radiation in a gauge invariant and infrared-safe way. We present first predictions for the cross section distributions in the transverse momenta of the subleading J/ψ meson and the J/ψ pair. Already at leading order in α_{s}, these predictions as well as those for the total cross section and its distributions in the invariant mass m_{ψψ} and the rapidity separation |Y| of the J/ψ pair nicely agree with recent ATLAS and CMS Collaboration measurements, except for the large-m_{ψψ} and large-|Y| regions, where the predictions substantially undershoot the data. In the latter regions, Balitsky-Fadin-Kuraev-Lipatov resummation is shown to enhance the cross sections by up to a factor of 2 and so to improve the description of the data.

Breakdown of Nonrelativistic QCD Factorization in Processes Involving Two Quarkonia and its Cure.

We study inclusive processes involving two heavy quarkonia in nonrelativistic QCD (NRQCD) and demonstrate that, in the presence of two P-wave Fock states, NRQCD factorization breaks down, leaving uncanceled infrared singularities. As phenomenologically important examples, we consider the decay ϒ→χ_{cJ}+X via bb[over ¯](^{3}P_{J_{b}}^{[8]})→cc[over ¯](^{3}P_{J}^{[1]})+gg and the production process e^{+}e^{-}→J/ψ+χ_{cJ}+X via e^{+}e^{-}→cc[over ¯](^{3}P_{J_{1}}^{[8]})+cc[over ¯](^{3}P_{J}^{[1]})+g. We infer that such singularities will appear for double quarkonium hadroproduction at next-to-leading order. As a solution to this problem, we introduce to NRQCD effective field theory new types of operators whose quantum corrections absorb these singularities.

Complete Nonrelativistic-QCD Prediction for Prompt Double J/ψ Hadroproduction.

We perform a complete study of prompt double J/ψ hadroproduction at leading order in the nonrelativistic-QCD factorization framework by including all possible pairings of the cc̅ 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/ψ and ψ'} production and the (3)P(J)([1]) and (3)S(1)([8]) channels of χ(cJ) production, which have been overlooked so far, greatly dominate at large invariant masses and rapidity separations of the J/ψ 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.

η(c) production at the LHC challenges nonrelativistic QCD factorization.

We analyze the first measurement of η_{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 α_{s} and the relative velocity v of the bound quarks including the feeddown from h_{c} mesons. Converting the long-distance matrix elements extracted by various groups from J/ψ yield and polarization data to the η_{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.

All-order renormalization of the propagator matrix for fermionic systems with flavor mixing.

We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions and their expansions through two loops for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions. We identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exhaust them. We then explain how our results may be generalized to the case of unstable fermions, in which we encounter the phenomenon of WFR bifurcation. In the special case of a solitary unstable fermion, the all-order-renormalized propagator is presented in a particularly compact form.

J/ψ polarization at the Tevatron and the LHC: nonrelativistic-QCD factorization at the crossroads.

We study the polarization observables of J/ψ hadroproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics. We complete the present knowledge of the relativistic corrections by also providing the contribution due to the intermediate (3)P(J)([8]) color-octet states at this order, which turns out to be quite significant. Exploiting the color-octet long-distance matrix elements previously extracted through a global fit to experimental data of unpolarized J/ψ production, we provide theoretical predictions in the helicity and Collins-Soper frames and compare them with data taken by CDF at Fermilab Tevatron I and II and by ALICE at CERN LHC. The notorious CDF J/ψ polarization anomaly familiar from leading-order analyses persists at the quantum level, while the situation looks promising for the LHC, which is bound to bring final clarification.

Probing nonrelativistic QCD factorization in polarized J/ψ photoproduction at next-to-leading order.

We analyze the polarization observables of J/ψ photoproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD). This is a complete next-to-leading-order study of heavy-quarkonium polarization including the full relativistic corrections due to the intermediate (1)S(0)([8]), (3)S(1)([8]), and (3)P(J)([8]) color-octet states closing a gap in the worldwide endeavor to test NRQCD factorization at the quantum level. We present theoretical predictions in the helicity, target, and Collins-Soper frames of DESY HERA, evaluated using the color-octet long-distance matrix elements previously extracted through a global fit to experimental data of unpolarized J/ψ production, and confront them with recent measurements by the H1 and ZEUS Collaborations. We find the overall agreement to be satisfactory but the case for NRQCD to be not as strong as for the J/ψ yield.

Reconciling J/ψ production at HERA, RHIC, Tevatron, and LHC with nonrelativistic QCD factorization at next-to-leading order.

We calculate the cross section of inclusive direct J/ψ hadroproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics, including the full relativistic corrections due to the intermediate 1S(0)[8], 3S(1)[8], and 3P(J)[8] color-octet states. We perform a combined fit of the color-octet long-distance matrix elements to the transverse-momentum (p(T)) distributions measured by CDF at the Fermilab Tevatron and H1 at DESY HERA and demonstrate that they also successfully describe the p(T) distributions from PHENIX at BNL RHIC and CMS at the CERN LHC as well as the photon-proton c.m. energy and (with worse agreement) the inelasticity distributions from H1. This provides a first rigorous test of nonrelativistic QCD factorization at next-to-leading order. In all experiments, the color-octet processes are shown to be indispensable.

Ultrahigh-energy neutrino-nucleon deep-inelastic scattering and the Froissart bound.

We present a simple formula for the total cross section σ(νN) of neutral- and charged-current deep-inelastic scattering of ultrahigh-energy neutrinos on isoscalar nuclear targets, which is proportional to the structure function F(2)(νN)(M(V)(2)/s,M(V)(2)), where M(V) is the intermediate-boson mass and s is the square of the center-of-mass energy. The coefficient in front of F(2)(νN)(x,Q(2)) depends on the asymptotic low-x behavior of F(2)(νN). It contains an additional lns term if F(2)(νN) scales with a power of ln(1/x). Hence, an asymptotic low-x behavior F(2)(νN)∝ln(2)(1/x), which is frequently assumed in the literature, already leads to a violation of the Froissart bound on σ(νN).

Complete next-to-leading-order corrections to J/psi photoproduction in nonrelativistic quantum chromodynamics.

We calculate the cross section of inclusive direct J/psi photoproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics for the first time including the full relativistic corrections due to the intermediate {1}S{0}{[8]}, {3}S{1}{[8]}, and {3}P{J}{[8]} color-octet states. A comparison of our results to recent H1 data suggests that the color-octet mechanism is indeed realized in J/psi photoproduction, although the predictivity of our results still suffers from uncertainties in the color-octet long-distance matrix elements.

Orthopositronium lifetime: analytic results in O(alpha) and O(alpha3lnalpha).

We present the O(alpha) and O(alpha3lnalpha) corrections to the total decay width of orthopositronium in closed analytic form, in terms of basic irrational numbers, which can be evaluated numerically to arbitrary precision.

Two-loop virtual top-quark effect on Higgs-boson decay to bottom quarks.

In most of the mass range encompassed by the limits from the direct search and the electroweak precision tests, the Higgs boson of the standard model preferably decays to bottom quarks. We present, in analytic form, the dominant two-loop electroweak correction, of O(GF2mt4), to the partial width of this decay. It amplifies the familiar enhancement due to the O(GFmt2) one-loop correction by about +16% and thus more than compensates the screening by about -8% through strong-interaction effects of order O(alphasGFmt2).

Simple approach to renormalize the Cabibbo-Kobayashi-Maskawa matrix.

We present an on-shell scheme to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) matrix. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass and gauge-dependent wave function renormalization contributions, and to implement the on-shell renormalization of the former with nondiagonal mass counterterm matrices. Diagonalization of the complete mass matrix leads to an explicit CKM counterterm matrix, which automatically satisfies all the following important properties: it is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are nonsingular in the limit in which any two fermions become mass degenerate.

Heavy-quarkonium creation and annihilation with O(alpha(3)(s)ln(alpha(s)) accuracy.

We calculate the O(alpha(3)(s)ln(alpha(s)) contributions to the heavy-quarkonium production and annihilation rates. Our result sheds new light on the structure of the high-order perturbative corrections and opens a new perspective for a high-precision theoretical analysis. We also determine the three-loop anomalous dimensions of the nonrelativistic vector and pseudoscalar currents.

Evidence for the color-octet mechanism from CERN LEP2 gamma gamma --> J/psi + X Data.

We present theoretical predictions for the transverse-momentum distribution of J/psi mesons promptly produced in gammagamma collisions within the factorization formalism of nonrelativistic quantum chromodynamics, including the contributions from both direct and resolved photons, and we perform a conservative error analysis. The fraction of J/psi mesons from decays of bottom-flavored hadrons is estimated to be negligibly small. New data taken by the DELPHI Collaboration at LEP2 nicely confirm these predictions, while they disfavor those obtained within the traditional color-singlet model.

Mass of the eta b and alpha s from the nonrelativistic renormalization group.

We sum up the next-to-leading logarithmic corrections to the heavy-quarkonium hyperfine splitting, using the nonrelativistic renormalization group. On the basis of this result, we predict the mass of the eta(b) meson to be M(eta(b))=9421+/-11(th)+9-8(delta alpha(s)) MeV. The experimental measurement of M(eta(b)) with a few MeV error would be sufficient to determine alpha(s)(M(Z)) with an accuracy of +/-0.003. For the hyperfine splitting in charmonium, the use of the nonrelativistic renormalization group brings the perturbative prediction significantly closer to the experimental figure.