arXiv subjects

Bernd A. Kniehl

Publications and source records attributed to Bernd A. Kniehl.

At least 19 recordsLinked to original sources

arXiv2026

RI/SMOM renormalization for lattice QCD: bilinear and three-quark operators

We review perturbative matching between the regularization-invariant symmetric MOM (RI/SMOM) and MS schemes at the symmetric subtraction point, which is relevant for lattice QCD simulations. For bilinear operators we summarize three-loop conversion factors for local quark currents and for the n=2,3 twist-two moments of structure functions. For three-quark operators we summarize two-loop RI/SMOM matching for N=0 baryonic operators and three-loop anomalous dimensions together with two-loop matching for the N=1 Mellin moment, enabling improved lattice studies of baryon distribution amplitudes. All numerical results quoted here are given in Landau gauge.

hep-lat↗

arXiv2026

Probing Heavy-Quark Spin Symmetry in Double $J/ψ$ Hadroproduction

We perform the first complete $\mathcal{O}(α_s^5)$ analysis of the prompt hadroproduction of $J/ψ$ pairs with large transverse momenta $p_T^{ψψ}$ in the nonrelativistic-QCD factorization framework, including all possible Fock state combinations $c\bar{c}(m)+c\bar{c}(n)$, with $m,n={}^3S_1^{[1,8]},{}^1S_0^{[8]},{}^3P_J^{[1,8]}$. We observe that CMS and ATLAS data constrain a specific linear combination of the long-distance matrix elements (LDMEs) $\langle\mathcal{O}^{J/ψ}({}^1S_0^{[8]})\rangle$ and $\langle\mathcal{O}^{J/ψ}({}^3P_0^{[8]})\rangle$. In conjunction with two other combinations fixed by single prompt $J/ψ$ hadroproduction, we gain a new LDME set, which turns out to be largely compatible with the world data of prompt $J/ψ$ yield and polarization and to probe heavy-quark spin symmetry, by which agreement is established with LHCb data of prompt $η_c$ yield. Our $\mathcal{O}(α_s^5)$ predictions also nicely agree with CMS and ATLAS data in the lowest bins of $J/ψ$ pair invariant mass $m^{ψψ}$, beyond leading-order kinematics.

hep-ph↗

arXiv2026

Relativistic corrections to gluon fragmentation into the $^3P_{J}^{[1,8]}$ states

We compute relativistic corrections to the gluon fragmentation functions to ${}^3P_J^{[1,8]}$ Fock states of heavy quarkonium within non-relativistic QCD factorization framework. We find that, at $\mathcal{O}(v^2)$ sub-leading order, the $S$-$D$ mixing effect must be taken into account to absorb the infrared divergence of spin-triplet $P$-wave production within full QCD into the NRQCD long-distance matrix elements. Unlike the $S$-wave case, we find that the short-distance coefficients of the fragmentation functions at leading and sub-leading order are no longer proportional to each other. However, upon convolution with the gluon production cross section, their ratios are almost constant across the whole $p_T$ region. We find the relativistic corrections to be negative and substantial, which makes them a non-negligible ingredient in the study of $J/ψ$ production at the LHC.

hep-ph↗

arXiv2025

Next-to-leading-order QCD corrections to double prompt $J/ψ$ hadroproduction

Within the framework of nonrelativistic-QCD (NRQCD) factorization, we perform a comprehensive investigation of the color singlet (CS) contribution to prompt $J/ψ$ pair production at the CERN Large Hadron Collider at next-to-leading order (NLO) in $α_s$. Specifically, we compare our NLO predictions with measurements from the LHCb, CMS, and ATLAS Collaborations. We find that the CS contribution itself can well describe the LHCb data in most of the experimental bins, except in the regions where the fixed-order calculation is spoiled by the emission of soft or hard-collinear gluons. In the CMS and ATLAS cases, however, the CS predictions greatly undershoot both the measured total and differential cross sections, despite sizable $K$ factors, of 2--3, for the total cross sections.

hep-ph↗

arXiv2024

Next-to-leading-order relativistic and QCD corrections to prompt $\boldsymbol{J/ψ}$ pair photoproduction at future $\boldsymbol{e^+e^-}$ colliders

Within the framework of nonrelativistic-QCD factorization, we calculate both the next-to-leading-order relativistic and QCD corrections to prompt $J/ψ$ pair production, with feeddown from $ψ(2S)$ mesons, via photon-photon collisions at future $e^+e^-$ colliders including the Future Circular Lepton Collider (FCC-ee), the Circular Electron Positron Collider (CEPC), and the Compact Linear Collider (CLIC). We present total cross sections and distributions in single $J/ψ$ transverse momentum and rapidity, and in $J/ψ$ pair invariant mass. The relativistic and QCD corrections both turn out to be large and negative. Yet, the production rates are large enough for useful experimental studies.

hep-ph↗

arXiv2024

Relativistic corrections to prompt double charmonium hadroproduction near threshold

We calculate the relativistic corrections to prompt $J/ψ$ pair and $J/ψ+ψ(2S)$ hadroproduction through the color-singlet channel within the framework of nonrelativistic QCD (NRQCD) factorization. The short-distance coefficients are obtained by matching full-QCD and NRQCD calculations at the partonic level, in which both squared amplitude and phase space are expanded in $v^2$. We find that such an expansion of the phase space spoils the convergence of NRQCD factorization near the production threshold. To fix this problem, we propose to modify the matching between full QCD and NRQCD by adopting the physical phase space. In this modified approach, the theoretical uncertainties due to the choice of charm quark mass $m_c$ are largely reduced and the overall agreement of our predictions with LHC data is significantly improved, both as for total and differential cross sections.

hep-ph↗

arXiv2023

Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling

We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be ${\cal N} =4$ supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of momentum transfer and of Bjorken $x$. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point $x=0$ and a smooth behaviour in the vicinity of the point

hep-ph↗

arXiv2023

Global analysis of $ψ(2S)$ inclusive hadroproduction at next-to-leading order in nonrelativistic-QCD factorization

Working in the nonrelativistic-QCD factorization framework at next-to-leading order in $α_s$, we fit the relevant color octet (CO) long-distance matrix elements (LDMEs) of the $ψ(2S)$ meson, $\langle {\cal O}^{ψ(2S)}({^1S}_0^{[8]})\rangle$, $\langle {\cal O}^{ψ(2S)}({^3S}_1^{[8]})\rangle$, and $\langle {\cal O}^{ψ(2S)}({^3P}_0^{[8]})\rangle$, to 1001 data points of upolarized and polarized $ψ(2S)$ inclusive hadroproduction. We do four different fits, with filters on polarization and low to middle transverse momentum $p_T$. We find that a successful description of the data is only possible with a large low-$p_T$ cut. Our results are one order of magnitude more precise than previous determinations of these color octet long-distance matrix elements.

hep-ph↗

arXiv2023

Dipole Subtraction vs. Phase Space Slicing in NLO NRQCD Heavy-Quarkonium Production Calculations

We compare two approaches to evaluate cross sections of heavy-quarkonium production at next-to-leading order in nonrelativistic QCD involving $S$- and $P$-wave Fock states: the customary approach based on phase space slicing and the approach based on dipole subtraction recently elaborated by us. We find reasonable agreement between the numerical results of the two implementations, but the dipole subtraction implementation outperforms the phase space slicing one both with regard to accuracy and speed.

hep-ph↗

arXiv2023

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 ${^1S}_0^{[8]}$, ${^3S}_1^{[8]}$ and ${^3P}_J^{[8]}$ 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 three, one is unfavored, the factor of shortfall being about one 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 $\mathcal{O}(G_Fα_s^4)$, beyond the order considered here.

hep-ph↗

arXiv2023

Specializations of partial differential equations for Feynman integrals

Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the differentiable constraints $z_i=y_i(x_j)$. In our algorithm, the powers of propagators can be considered as arbitrary parameters. Our algorithm can also be used for the reduction of multiple hypergeometric sums to sums of lower dimension, finding special values and reduction equations of hypergeometric functions in a singular locus of continuous variables, or finding systems of partial differential equations for master integrals with arbitrary powers of propagators. As an illustration, we produce a differential equation of fourth order in one variable for the one-loop two-point Feynman diagram with two different masses and arbitrary propagator powers.

hep-th↗

arXiv2022

Renormalization of three-quark operators at two loops in the RI${}'$/SMOM scheme

We consider the renormalization of the three-quark operators without derivatives at next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the $\bar{\rm MS}$ scheme and the regularization invariant symmetric MOM (RI/SMOM, RI${}'$/SMOM) schemes. The results are presented both analytically in $R_ξ$ gauge in terms of a set of master integrals and numerically in Landau gauge. They can be used to reduce the errors in determinations of baryonic distribution amplitudes in lattice QCD simulations.

hep-ph↗

arXiv2021

Angular analysis of bottom-flavored hadron production in semileptonic decays of polarized top quarks

We study the inclusive production of bottom-flavored hadrons from semileptonic decays of polarized top quarks at next-to-leading order in QCD using fragmentation functions recently determined from a global fit to $e^+e^-$ data. We provide the relevant differential decay widths at parton level in analytic form. These results fill an important gap in the theoretical interpretation of recent measurements of the top-quark polarization and the $t\bar{t}$ spin correlations using dilepton final states in proton-proton collisions at the CERN Large Hadron Collider. As an illustration, we study the distributions in the scaled bottom-hadron energy of the polarized-top-quark decay widths for different $W$-boson helicities.

hep-ph↗

arXiv2020

Moments $n=2$ and $n=3$ of the Wilson twist-two operators at three loops in the RI${}'$/SMOM scheme

We study the renormalization of the matrix elements of the twist-two non-singlet bilinear quark operators, contributing to the $n=2$ and $n=3$ moments of the structure functions, at next-to-next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the $\overline{\rm MS}$ scheme and the regularization-invariant symmetric momentum subtraction (RI/SMOM, RI${}'$/SMOM) schemes. The obtained results can be used to reduce errors in determinations of moments of structure functions from lattice QCD simulations. The results are given in Landau gauge.

hep-ph↗

arXiv2020

Inclusive $J/ψ$ and $η_c$ production in $Υ$ decay at $\mathcal{O}(α_s^5)$ in nonrelativistic QCD factorization

We study $J/ψ$ and $η_c$ inclusive production in $Υ$ decay within the framework of nonrelativistic-QCD (NRQCD) factorization. In the latter case, for which no experimental data exist so far, we also include the $h_c$ feed-down contribution. We calculate the short distance coefficients completely through $\mathcal{O}(α_s^5)$. The NRQCD predictions for the branching fraction $\mathcal{B}(Υ\to J/ψ+X)$ via direct production, evaluated with different sets of long-distance matrix elements (LDMEs), all agree with the experimental data in a reasonable range of renormalization scale. Using $η_c$ and $h_c$ LDMEs obtained from $J/ψ$ and $χ_c$ ones via heavy-quark spin symmetry, we find that the bulk of $\mathcal{B}(Υ\toη_c+X)$ via prompt production arises from the $c\bar{c}({}^3\!S_1^{[8]})$ Fock state. The experimental study of this decay process would, therefore, provide a particularly clean probe of the color octet mechanism of heavy-quarkonium production.

hep-ph↗

arXiv2020

Bilinear quark operators in the RI/SMOM scheme at three loops

We consider the renormalization of the matrix elements of the bilinear quark operators $\barψψ$, $\barψγ_μψ$, and $\barψσ_{μν}ψ$ at next-to-next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the $\overline{\rm MS}$ scheme and the regularization invariant symmetric momentum subtraction (RI/SMOM) scheme. The obtained results can be used to reduce the errors in determinations of quark masses from lattice QCD simulations. The results are given in Landau gauge.

hep-ph↗

arXiv2019

Dipole subtraction at next-to-leading order in nonrelativistic-QCD factorization

We describe an implementation of a subtraction scheme in the nonrelativistic-QCD treatment of heavy-quarkonium production at next-to-leading-order in the strong-coupling constant, covering $S$- and $P$-wave bound states. It is based on the dipole subtraction in the massless version by Catani and Seymour and its extension to massive quarks by Phaf and Weinzierl. Important additions include the treatment of heavy-quark bound states, in particular due to the more complicated infrared-divergence structure in the case of $P$-wave states.

hep-ph↗

arXiv2019

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 measurements, except for the large-$m_{ψψ}$ and large-$|Y|$ regions, where the predictions substantially undershoot the data. In the latter regions, BFKL resummation is shown to enhance the cross sections by up to a factor of two and so to improve the description of the data.

hep-ph↗