Resummation and renormalization of kinematical effects in inclusive PP-wave quarkonium production

We investigate the renormalization properties of the shape function formalism for inclusive production of $P$-wave heavy quarkonia, which arises from resumming a class of corrections coming from kinematical effects associated with the motion of the heavy quark and antiquark pair relative to the quarkonium. Such kinematical effects are encoded in the nonperturbative shape functions, which are normalized to the corresponding nonrelativistic QCD long-distance matrix elements. By using the known ultraviolet divergences in the matrix elements, we derive the large-momentum asymptotic behavior of the shape functions. This strongly constrains the form of the shape functions and significantly reduces the dependence on the nonperturbative model. Based on these results we show that the shape function formalism at loop level can be useful in taming the threshold logarithms at large transverse momentum, and at small transverse momentum the kinematical corrections reduce the sizes of $\chi_c$ and $\chi_b$ cross sections which may improve agreement with measurements.Comment: 51 pages, 11 figures, minor revisions, version published in JHE

Mesonic decay constant and mass ratios and the conformal window

Two particular ratios related to mesons are proposed for the study of the conformal window in $SU(3)$ gauge theory and fundamental fermions. Lattice and other studies indicate that the lower end, $N_f^*$, is at around 7 - 13 flavors which is a wide range without a clear consensus. Here we propose the decay constant to mass ratios of mesons, $f_{PS,V} / m_V$, as a proxy since below the conformal window lattice studies have shown that they are largely $N_f$-independent while at the upper end of the conformal window they are vanishing. The drop from the non-zero constant value to zero at $N_f = 16.5$ might be indicative of $N_f^*$. We compute $f_V / m_V$ to N$^3$LO and $f_{PS} / m_V$ to NNLO order in (p)NRQCD. The results are unambiguously reliable just below $N_f = 16.5$, hence the results are expanded \'a la Banks-Zaks in $\varepsilon = 16.5 - N_f$. The convergence properties of the series and matching with the non-perturbative infinite volume, continuum and chiral extrapolated lattice results at $N_f = 10$ suggest that the perturbative results might be reliable down to $N_f = 12$. A sudden drop is observed at $N_f = 12$ and $N_f = 13$ in $f_V / m_V$ and $f_{PS} / m_V$, respectively.Comment: The 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermi National Accelerator Laborator

Quarkonium production and polarization: where do we stand?

We review the current status of heavy quarkonium production phenomenology based on nonrelativistic effective field theories, focusing on spintriplet S -wave states such as J/ψ, ψ(2S ), and ϒ. We present some representative examples for heavy quarkonium production mechanisms proposed in the literature, which vary significantly depending on the choice of data employed in analyses. We then discuss the rôle of polarization in discriminating between the different possible scenarios for quarkonium production. Other observables that may be useful in pinpointing the production mechanism are also introduced, such as the ηc production, associated production of J/ψ plus a gauge boson, and J/ψ production at the Electron-Ion Collider

Higgs-Stoponium Mixing Near the Stop-Antistop Threshold

Supersymmetric extensions of the standard model contain additional heavy neutral Higgs bosons that are coupled to heavy scalar top quarks (stops). This system exhibits interesting field theoretic phenomena when the Higgs mass is close to the stop-antistop production threshold. Existing work in the literature has examined the digluon-to-diphoton cross section near threshold and has focused on enhancements in the cross section that might arise either from the perturbative contributions to the Higgs-to-digluon and Higgs-to-diphoton form factors or from mixing of the Higgs boson with stoponium states. Near threshold, enhancements in the relevant amplitudes that go as inverse powers of the stop-antistop relative velocity require resummations of perturbation theory and/or nonperturbative treatments. We present a complete formulation of threshold effects at leading order in the stop-antistop relative velocity in terms of nonrelativistic effective field theory. We give detailed numerical calculations for the case in which the stop-antistop Green's function is modeled with a Coulomb-Schr\"odinger Green's function. We find several general effects that do not appear in a purely perturbative treatment. Higgs-stop-antistop mixing effects displace physical masses from the threshold region, thereby rendering the perturbative threshold enhancements inoperative. In the case of large Higgs-stop-antistop couplings, the displacement of a physical state above threshold substantially increases its width, owing to its decay width to a stop-antistop pair, and greatly reduces its contribution to the cross section.Comment: 45 pages, 13 figures, minor corrections, references added, figures 2--5 updated, version published in Phys. Rev.

Addendum: New approach to the resummation of logarithms in Higgs-boson decays to a vector quarkonium plus a photon [Phys. Rev. D 95, 054018 (2017)]

In this addendum to Phys.\ Rev.\ D {\bf 95}, 054018 (2017) we recompute the rates for the decays of the Higgs boson to a vector quarkonium plus a photon, where the vector quarkonium is $J/\psi$, $\Upsilon(1S)$, $\Upsilon(2S)$, or $\Upsilon(3S)$. We correct an error in the Abel-Pad\'e summation formula that was used to carry out the evolution of the quarkonium light-cone distribution amplitude in Phys.\ Rev.\ D {\bf 95}, 054018 (2017). We also correct an error in the scale of quarkonium wave function at the origin in Phys.\ Rev.\ D {\bf 95}, 054018 (2017) and introduce several additional refinements in the calculation.Comment: 7 pages, [v2] Abel-Pade summation formula corrected, [v3] PRD versio