One possible extension of the Standard Model scalar sector includes SU(2)_L doublet scalars that are color octets rather than singlets. We focus on models in which the couplings to fermions are consistent with the principle of minimal flavor violation (MFV), in which case these color octet scalars couple most strongly to the third generation of quarks. When the Yukawa coupling of color octet scalars to Standard Model fermions is less than unity, these states can live long enough to bind into color-singlet spin-0 hadrons, which we call octetonia. In this paper, we consider the phenomenology of octetonia at the Large Hadron Collider (LHC). Predictions for their production via gluon-gluon fusion and their two-body decays into Standard Model gauge bosons, Higgs bosons, and \bar{t}t are presented.
Color scalars are salient features of non-minimal SU(5) model, where Higgs sector is extended by 45-dimensional multiplet. We show that gauge coupling unification can be realized in this model with TeV octet scalar and intermediate (~10^6 GeV) color-triplet scalar at scale larger than 10^{15} GeV. We analyze the possible LHC signatures of these TeV octet scalars. We emphasize that multi-(b)-jet final states provide significant signal for direct probe of octet scalars at the LHC.
We study the effect of color octet scalars on the high transverse momenta four-jet cross section at the LHC. We consider both weak singlet and doublet scalars, concentrating on the case of small couplings to quarks. We find that a relatively early discovery at the LHC is possible for a range of scalar masses.
Color octet (pseudo)scalars, if they exist, will be copiously produced at the CERN Large Hadron Collider (LHC). However, their detection can become a very challenging task. In particular, if their decay into a pair of top quarks is kinematically forbidden, the main decay channel would be into two jets, with a very large background. In this Brief Report we explore the possibility of using anomaly-induced decays of the color octet pseudoscalars into gauge bosons to find them at the LHC.
In this work, we investigated resonant production of spin-3/2 color octet electron at the Large Hadron electron Collider (LHeC). Signal and background analysis have been performed and discovery, observation and exclusion limits are determined for spin 3/2 color octet electron masses. Reachable values of the compositeness scale are presented as a function of the spin-3/2 color octet electron masses.
We study contributions from color-octet quarkonium formation mechanisms to $p_\perp$-integrated $ψ'$ production cross sections in pion-nucleon reactions. The observed polarization of the $ψ'$ is not reproduced by the lowest-order leading-twist color-singlet and color-octet mechanisms. This suggests that there are important quarkonium production mechanisms beyond leading twist.
We have calculated the leading color-octet contributions to the production of $J/ψ$ particles in photon-proton collisions. Using the values for the color-octet matrix elements extracted from fits to prompt $J/ψ$ data at the Tevatron, we demonstrate that distinctive color-octet signatures should be visible in $J/ψ$ photoproduction. However, these predictions appear at variance with recent experimental data obtained at HERA, indicating that the phenomenological importance of the color-octet contributions is smaller than expected from theoretical considerations and suggested by the Tevatron fits.
We study the initial state radiation process $e^+ e^-\to{J/ψ}+X+γ$ for $J/ψ$ production at B factory, and find the cross section is 61% larger than it's Born one for color octet part and is about half as it's Born one for color singlet part. Furthermore, the color singlet and color octet signal are very clearly separated in it's $E_γ$ spectra due to kinematics difference. We suggest to measure this $E_γ$ spectra at B factory to determine the color octet effect.
Elements of the phenomenology of color-octet scalars (sgluons), as predicted in the hybrid N=1/N=2 supersymmetric model, are discussed in the light of forthcoming experiments at the CERN Large Hadron Collider.
Calculations for inclusive J/psi production in Upsilon decay through the color-octet mechanisms b\bar b[^3S_1, 1] -> c \bar c[^{2s+1}L_J, 8] + g are presented. It is shown that these O(alpha^5_sv^4_c) contributions compete with other color-octet mechanisms considered in the literature. A critical numerical analysis of the color-octet contributions to Upsilon -> J/psi + X shows that further work in this channel, both theoretical and experimental, is necessary in order to clearly understand the significance of the color-octet component of the c \bar c component inside the J/psi system.
We calculated the polarization of ψ' due to gg \to Q\bar{Q}[^3P_J^(8)]g \to ψ^λcolor-octet quarkonia production. We find that at low transverse momenta the ψ' is unpolarized due to the contributions proportional to the L=S=0 and L=S=1 color-octet matrix elements. As p_\perp increases, the ψ' mesons become 100% polarized, as predicted by fragmentation calculations. Polarization due to lowest order color-singlet production is also considered, which qualitatively has a similar shape to the color-octet production.
I discuss the impact of color-octet contributions and higher-order QCD corrections on the cross section for inelastic $J/ψ$ photoproduction. The theoretical predictions are compared with recent experimental data obtained at HERA.
New physics at the weak scale that can couple to quarks typically gives rise to unacceptably large flavor changing neutral currents. An attractive way to avoid this problem is to impose the principal of minimal flavor violation (MFV). Recently it was noted that in MFV only scalars with the same gauge quantum numbers as the standard model Higgs doublet or color octet scalars with the same weak quantum numbers as the Higgs doublet can couple to quarks. In this paper we compute the one-loop rate for production of a single color octet scalar through gluon fusion at the LHC, which can become greate…
We discuss neutrinoless double beta decay and lepton flavor violating decays such as $μ-> eγ$ in the colored seesaw scenario. In this mechanism, neutrino masses are generated at one-loop via the exchange of TeV-scale fermionic and scalar color octets. The same particles mediate lepton number and flavor violating processes. We show that within this framework a dominant color octet contribution to neutrinoless double beta decay is possible without being in conflict with constraints from lepton flavor violating processes. We furthermore compare the "direct" color octet contribution to neutrinoles…
Several models of new physics, such as grand unified theories, Pati-Salam models, chiral color models, etc., predict the existence of an $SU(2)_L$ doublet of color-octet scalars (COS). In the Manohar-Wise model, the Yukawa couplings of the COS are assumed to be consistent with Minimal Flavor Violation ensuring constraints from flavor physics are satisfied even for relatively light scalars. In this simple model we consider the production of color singlet bound states of COS that we call octetonium. Octetonium are mainly produced via gluon-gluon fusion and have significant production cross secti…
The inclusive cross section for the production of $J/ψ$ in $e^+ e^-$ annihilation is studied using a recently developed factorization formalism. In addition to the conventional color-singlet contribution, we include contributions from $c \bar c$ pairs that are produced at short distances in color-octet states. The color-octet contributions are suppressed by the smaller probability for the color-octet $c \bar c$ pair to evolve into a state that includes a $ψ$, but they may dominate near the upper endpoint of the $ψ$ energy spectrum. The signature for the color-octet contribution is a dramatic c…
I review recent developments in theoretical understandings of J/psi productions in various processes at Tevatron, B decay and J/psi photoproduction including the color-octet mechanism.
Recently has been shown that the physical (mass eigenstate) color-octet technirho does not couple to two gluons. In this letter we study how this result affects the presently accepted limits for the color-octet technirho mass obtained from the study of dijets production at the Tevatron. First we show that data from Tevatron Run 1b can not exclude any mass range. Finally, we obtain limits for the Tevatron Run II.
We study radiative decays of $Υ$ to light quark jets in nonrelativistic QCD by taking both the color singlet and color octet $b\bar b$ operators into consideration. The cut for quark jet energy and cut for the angle between two quark jets are introduced. The sensitivity to the soft and collinear singularities in the loop integrals are greatly reduced by these cuts. With the jet energy cut of about 1 GeV, and the jet angle cut of about $36^\circ$, the branching ratio for $Υ\toγq\bar q$ is found to be $8.2\times 10^{-4}$ from color singlet contributions. The color octet contributions could be mu…
We consider the energy and the polar angle distributions of J/ψ's produced via the color-singlet and the color-octet (^3S_1^{(8)}) mechanisms in Z^0 \to J/ψ+X at LEP. Since both distributions of the J/ψproduced via color-octet mechanism are significantly different from those via color-singlet mechanism, these observables can be used as tests of color-octet production mechanism for heavy quarkonia. We also discuss Z^0 \rightarrow Υ+ X and W \to J/ψ( or Υ) + X in brief.
In this study we investigated indirect manifestations of color octet electron at the next generation linear colliders: International Linear Collider (ILC) and Compact Linear Collider (CLIC). Namely, production of two gluons via color octet electron exchange is considered. Signal and background analysis have been performed taking into account initial state radiation and beamstrahlung. We show that color octet electron (e_(8)) manifestation will be seen upto M(e_(8))=1.75 TeV and 1.70 TeV at ILC and CLIC with sqrt(s)=0.5 TeV, respectively. CLIC with sqrt(s)=3 TeV will be sensitive upto M(e_(8))=…
To test the color-octet model of heavy quarkonium productions, we propose $ψ'$-productions at small-$p_T$ regions in polarized $pp$ collisions for the forthcoming RHIC polarized experiments, whose experimental test at $\sqrt s=50$ GeV might be very promising.
In composite models with colored preons leptogluons (l_(8)) has a same status with leptoquarks, excited leptons and quarks etc. We analyze resonant production of color octet electron (e_(8)) at QCD Explorer stage of the Large Hadron electron Collider (LHeC). It is shown that the e_(8) discovery at the LHeC will simultaneously determine the compositeness scale.
We compute the one-loop contributions from a color octet scalar to the tensor anomalous couplings of top and bottom quarks to gluons, photons and W bosons. We use known constraints on the parameters of the model to compare the predicted size of these couplings with existing phenomenological constraints.
The importance of the color octet component in P-wave charmonia is discussed in the context of exclusive decay processes. It is vital to include this contribution already at the level of the two-body decay channels. The ππand proton-antiproton channels are used as examples.
Gluon fragmentation represents the dominant source of high energy prompt quarkonia at hadron colliders. Fragmentation approximations break down, however, when a quarkonium's transverse momentum becomes comparable to its mass. In this paper, we identify a large class of color-octet diagrams that mediate quarkonia production at all energies and reduce to the dominant set of gluon fragmentation graphs in the high $p_\perp$ limit. They contribute to quarkonia differential cross sections at the same order as color-singlet diagrams and bring theoretical predictions for Upsilon and Psi production at …
We show that the usual vector meson dominance method does not apply directly to the mixing of a color-octet vector boson (color-octet technirho) with the gluon because of gauge invariance. We propose a gauge invariant method where one works in a physical basis with mass eigenstate fields. As a result, we show that the physical technirho does not couple to two gluons, contrary to the general belief. Consequences for the production of a pair of color-octet, isosinglet technipions (technietas) at Fermilab is analysed by means of a simulation of the signal and background, including kinematical cut…
Di-jet resonance searches are simple, yet powerful and model-independent, probes for discovering new particles at hadron colliders. Once such a resonance has been discovered it is important to determine the mass, spin, couplings, chiral behavior and color properties to determine the underlying theoretical structure. We propose a new variable which, in the absence of decays of the resonance into new non-standard states, distinguishes between color-octet and color-singlet resonances. To keep our study widely applicable we study phenomenological models of color-octet and color-singlet resonances …
We extract constraints on the parameter space of the MW model by comparing the cross-sections for dijet, top-pair, dijet-pair, $t\bar t t \bar t$ and $b\bar b b \bar b$ productions at the LHC with the strongest available experimental limits from ATLAS or CMS at 8 or 13 TeV. Overall we find that masses below 1 TeV have not been excluded for color octet scalars as it is often claimed in the literature. The constraints that can be placed on coupling constants are typically weaker than those from existing theoretical considerations, with the exception of the parameter $η_D$.
J/psi production in top quark rare decays is investigated under the framework of NRQCD factorization formalism. Various production channels are studied, and we find that the contributions from the color-singlet quark fragmentation and the color-octet gluon fragmentation are both over 3 orders larger than that from the leading order color-singlet process. The numerical results show that the branching ratio B(t -> c + J/psi + X) is about 10^{-14} in the SM, and 10^{-10} in the MSSM.
The scalar color octet contribution to the resonance $t\bar{t}$-pair production at the LHC is calculated and analysed with account of the one loop effective two gluon vertex. It is shown that this contribution from the scalar color octet $F_2$ predicted by the minimal model with the four color quark-lepton symmetry is for $\sqrt{s}=13$ TeV of about a few percents for $750 < m_{F_2} < 1800$ GeV and can exceed 10% for $400 < m_{F_2} < 750$ GeV. It is also pointed out that the search for the scalar octet $F_2$ as the resonance in the dijet mass spectra seems to be difficult because of the smallne…
An appended sector of two octet-colored scalars, each an electroweak doublet, is an interesting extension of the simple two Higgs doublet model motivated by the minimal flavor violation. Their rich CP violating interaction gives rise to a sizable electron electric dipole moment, besides the quark electric dipole moment via the two-loop contribution of Barr-Zee mechanism.
We study $J/Ψ$ production at photon-photon colliders, which can be realised with Compton scaterring of laser photons at $e^+e^-$ colliders. We find that the production rate through the color-octet channel is comparable to that through the color-singlet channel. Experimentally the two mechanisms can be studied separately because the processes have different signals.
The cross section of χ_{cJ} hadroproduction is calculated in the k_t-factorization approach. We find a significant contribution of the χ_{c1} state due to non-applicability of the Landau-Yang theorem because of off-shell gluons. The results are in agreement with data and, in contrast to the collinear factorization, show a dominance of the color singlet part and a strong suppression of the color octet contribution. Our results could therefore lead to a solution of the longstanding controversy between the color singlet model and the color octet mechanism.
This paper completes the study of the next-to-leading order (NLO) QCD corrections to massive color-octet vector boson production at the LHC and Tevatron. The massive color-octet vector bosons are generically referred to as colorons. Building on our previous calculation of quark-initiated coloron production at NLO, we use the pinch technique to investigate coloron production via gluon fusion. We demonstrate that this one-loop production amplitude is finite, and find that its numerical contribution to coloron production is typically four orders of magnitude smaller than the contribution from qua…
A factorization theorem for $P$-wave quarkonium production, recently derived by Bodwin, Braaten, Yuan and Lepage, is applied to $Υ\to χ_{cJ} + X$, where $χ_{cJ}$ labels the ${}^3 P_J$ charmonium states. The widths for $χ_{cJ}$ production through color-singlet $P$-wave and color-octet $S$-wave $c \bar c$ subprocesses are computed each to leading order in $α_s$. Experimental data on $Υ\to J / ψ+ X$ is used to obtain an upper bound on a nonperturbative parameter (related to the probability for color-octet $S$-wave $c \bar c$ hadronization into $P$-wave charmonium) that enters into the factorizati…
The cross section between a $c \bar c$ pair and a nucleon is small and sensitive to the $c - \bar c$ separation if the pair is in a color-singlet state, but very large and insensitive to the separation if it is in a color-octet state. We use this property in an absorption model involving both color components to deduce the color structure of $c \bar c$ pairs produced in $p(B)A \to ψX$ reactions. Our analysis shows that the NA3, NA38 and E772 data are not inconsistent with the theoretical picture that color-octet and color-singlet precursors are produced in roughly equal proportions if the prod…
We calculated the color-octet contribution to the $\ps$ hadroproduction at fixed target energies $\sqrt(s)\simeq40$ GeV. We consider the $\ps$ production with transverse momenta which can not be explained by primordial motion of partons, $p_T>1.5$ GeV. It is shown that color octet contribution is dominant at these energies and reduces large dicrepancies between experimental data and color singlet model predictions. Having taken into account both contribution one needs a K-factor about 2-3 to explain the experimental data.
Color-octet mechanism for the decay B\to η^\prime X is proposed to explain the large branching ratio of Br(B\to η^\prime X)\sim 1\times 10^{-3} recently announced by CLEO. We argue that the inclusive η^\prime production in B decays may dominantly come from the Cabbibo favored b\to (\bar c c)_8s process where \bar c c pair is in a color-octet configuration, and followed by the nonperturbative transition (\bar c c)_8\to η^\prime X. The color-octet intrinsic charm component in the higher Fock states of η^\prime is crucial and is induced by the strong coupling of η^\prime to gluons via QCD axial a…
We propose that the possible 750 GeV diphoton excess can be explained in the color-octet neutrino mass model extended with a scalar singlet $Φ$. The model generally contains $N_s$ species of color-octet, electroweak doublet scalars $S$ and $N_f$ species of color-octet, electroweak triplet $χ$ or singlet $ρ$ fermions. While both scalars and fermions contribute to the production of $Φ$ through gluon fusion, only the charged members induce the diphoton decay of $Φ$. The diphoton rate can be significantly enhanced due to interference between the scalar and fermion loops. We show that the diphoton …
An unresolved problem in J/psi phenomenology is a systematic understanding of the differential photoproduction cross section, dsigma/dz [gamma + p -> J/psi + X], where z= E_psi/E_gamma in the proton rest frame. In the non-relativistic QCD (NRQCD) factorization formalism, fixed-order perturbative calculations of color-octet mechanisms suffer from large perturbative and nonperturbative corrections that grow rapidly in the endpoint region, z -> 1. In this paper, NRQCD and soft collinear effective theory are combined to resum these large corrections to the color-octet photoproduction cross section…
We consider new physics contributions to the top-quark forward-backward asymmetry from a neutral $V^0_8$ or charged $V^+_8$ color-octet vector exchanged in the $t$-channel. We study the phenomenological constraints on these particles arising from the Tevatron and LHC7 measurements and compare them with those on their color singlet counterparts $Z^\prime$ and $W^\prime$. We find that the color octets fare better than the singlets in that they generate a lower $A_C$, a lower high-invariant mass cross-section at LHC7 and a lower same sign top-pair cross-section. However, they also generate a lowe…
Many new-physics models, especially those with a color-triplet top-quark partner, contain a heavy color-octet state. The "naturalness" argument for a light Higgs boson requires that the color-octet state be not much heavier than a TeV, and thus it can be pair-produced with large cross sections at high-energy hadron colliders. It may decay preferentially to a top quark plus a top-partner, which subsequently decays to a top quark plus a color-singlet state. This singlet can serve as a WIMP dark-matter candidate. Such decay chains lead to a spectacular signal of four top quarks plus missing energ…
We report the recent progress in the studies of D-wave heavy quarkonia production from gluon fragmentation at the Tevatron and in Z^0 decays, and the D-wave charmonia production in B decays. We show that the color-octet contributions are of crucial importance to the production of D-wave quarkonia. Signals, as strong as that for J/ψand ψ^\prime, should be seen for the D-wave charmonium in the processes. These will provide a test of the color-octet production mechanism.
We calculate the direct production rate of $J/ψ$ in top quark decays. The color-octet $J/ψ$ production via $t\rightarrow W^+ b J/ψ$ is shown to have a large branching ratio of order $1.5\times 10^{-4}$, which is over an order of magnitude higher than that of the color-singlet $J/ψ$ production via $t\rightarrow W^+ b J/ψ~g~g $ or $t\rightarrow W^+ b~χ_{cJ}~g$ followed by $χ_{cJ}\rightarrow J/ψ~γ$. This result can be used as a powerful tool to test the importance of the color-octet mechanism in heavy quarkonium production.
We analyze the relation between the present (and foreseen) bounds on matter stability and the presence of TeV-scale color octet scalar states in nonsupersymmetric SO(10) grand unification with one adjoint Higgs representation triggering the symmetry breaking. This scenario, discarded long ago due to tree-level tachyonic instabilities appearing in all phenomenologically viable breaking patterns, has been recently revived at the quantum level. By including the relevant two-loop corrections we find a tight correlation between the octet mass and the unification scale which either requires a light …
Photoproduction of $J/ψ$ is considered including the color-octet contributions from the various partial wave states, $^{2S+1}L_J$ = $^1S_0$, $^3S_1$ and $^3P_J$. The production cross section depends on three new nonperturbative parameters defined in NRQCD, called the color-octet matrix elements. Using the color-octet matrix elements determined by fitting the $J/ψ$ production at the Tevatron, we find that the color-octet($c\bar{c}) _{8}({^1S_0}~{\rm and~}~{^3P_J})$ contributions to the $J/ψ$ photoproductions at the fixed target experiments and HERA are too large compared to the data on $σ(γ+ p …
We consider a color octet scalar particle and its exotic decay in the channel gluon-$γ$ using an effective Lagrangian description for its strong and electromagnetic interactions. Such a state is present in many extensions of the Standard Model, and in particular in composite Higgs models with top partial compositeness, where couplings to photons arise via the Wess-Zumino-Witten term. We find that final states with one or two photons allow for a better reach at the LHC, even for small branching ratios. Masses up to $1.2$ TeV can be probed at the HL-LHC by use of all final states. Finally, we es…
We study contributions from color-octet quarkonium formation mechanisms to $J/ψ$ hadroproduction at low $p_\perp$. We include transitions of color-octet $c\bar{c}$ states into ``direct'' $J/ψ$ and into $χ_{1,2}$ which decay radiatively into a $J/ψ$. Together with earlier work, this calculation constitutes a complete analysis of $p_\perp$-integrated $J/ψ$ production at leading twist. We find that the leading-twist contribution is not sufficient to reproduce the observed production rates and polarization of the $J/ψ$ and $χ_{1,2}$. Hence there must exist other important quarkonium production mec…
We study the possibility to probe the unpolarized and linearly polarized transverse momentum- dependent gluon distributions in unpolarized pp collision in charmonium and bottomonium produc- tion, employing non-relativistic QCD (NRQCD) based color octet model within transverse momentum dependent (TMD) factorization framework. The transverse momentum (p T ) and rapidity distributions of J/ψ and Υ(1S) at LHCb, RHIC and AFTER energies are estimated. Significant modulations in transverse momentum spectrum of quarkonium in the low p T region is obtained when contributions of linearly polarized gluon…
We study the properties and production mechanisms of color-octet scalars at the LHC. We focus on the single production of both charged and neutral members of an (8,2)_1/2 doublet through bottom quark initial states. These channels provide a window to the underlying Yukawa structure of the scalar sector. Color-octet scalars naturally appear in grand unified theories based on the SU(5) gauge symmetry. In the context of adjoint SU(5) these fields are expected to be light to satisfy constraints coming from unification and proton decay, and may have TeV-scale masses. One combination of their coupli…
Polarized heavy quarkonium productions in $Z^0$ decays are considered. We find that polarizations of the produced quarkonia are independent of that of the parent Z^0 provided that one considers the energy distribution or the total production rate. Produced J/psi's via the color-octet and the color- singlet mechanisms are expected to be 19% and 29% longitudinally polarized, respectively. The energy dependence of eta_{1,8}(x)=\frac{dGamma_{1,8}^L}{dx} /\frac{dGamma_{1,8}}{d x} is very sensitive to the production mechanism, and therefore the measurement of η(x)_exp will be an independent probe of…
We report the first complete calculation of QCD corrections to the production of a massive color-octet vector boson. Our next-to-leading-order (NLO) calculation includes both virtual corrections as well as corrections arising from the emission of gluons and light quarks, and we demonstrate the reduction in factorization-scale dependence relative to the leading-order approximation used in previous hadron collider studies. We show that the QCD NLO corrections to coloron production are as large as 30%, and that the residual factorization scale-dependence is reduced to of order 2%. We also calcula…
We investigate $J/ψ$ photoproduction asymmetries in the framework of the NRQCD factorization approach. It is shown that the color octet contribution leads to large uncertainties in the predicted asymmetries which rules out the possibility to precisely measure the gluon polarization in the nucleon through this final state. For small values of the color octet parameters being compatible with $J/ψ$ photoproduction data it appears possible that a measurement of $J/ψ$ asymmetries could provide a new test for the NRQCD factorization approach, on one hand, or a measurement of the polarized gluon dist…
In an extension of the Standard Model with a scalar color octet, the possibility of the strongly first-order electroweak phase transition is studied, by examining the finite-temperature effective Higgs potential at the one-loop level. It is found that there are wide regions in the parameter space that allow the strongly first-order electroweak phase transition, where the Higgs boson mass is larger than the experimental lower bound of 115 GeV, and the masses of the scalar color octet is around 200 GeV. The parameter regions may be explored at the LHC with respect to the electroweak phase transi…
We investigate $J/ψ$ photoproduction asymmetries in the framework of the NRQCD factorization approach. It is shown that the color octet contribution leads to large uncertainties in the predicted asymmetries which rules out the possibility to precisely measure the gluon polarization in the nucleon through this final state. For small values of the color octet parameters being compatible with $J/ψ$ photoproduction data it appears possible that a measurement of $J/ψ$ asymmetries could provide a new test for the NRQCD factorization approach, on one hand, or a measurement of the polarized gluon dist…
In this paper, we study how the interaction of the axigluon with quarks is modified when we introduce new color-octet spin-one fields in a chiral color model. We show that in this case the strength of this interaction is not completely determined by the gauge symmetry any more and can be significantly weaker than the one predicted in the original chiral color model. In this way, we reinterpret the non-observability of the axigluon at the Tevatron, not as a limit on the axigluon mass, but as a limit on the strength of the axigluon coupling to quarks.
A factorization theorem for $P$-wave quarkonium production, recently derived by Bodwin, Braaten, Yuan and Lepage, is applied to $Υ\to χ_{cJ} + X$, where $χ_{cJ}$ labels the ${}^3 P_J$ charmonium states. The widths for $χ_{cJ}$ production through color-singlet $P$-wave and color-octet $S$-wave $c \bar c$ subprocesses are computed each to leading order in $α_s$. Experimental data on $Υ\to J / ψ+ X$ is used to obtain an upper bound on a nonperturbative parameter (related to the probability for color-octet $S$-wave $c \bar c$ hadronization into $P$-wave charmonium) that enters into the factorizati…
We evaluate the next-to-next-to-leading order soft function for the production of a massive color octet state at rest in the collision of two massless colored partons in either the fundamental or the adjoint representation. The main application of our result is the determination of the threshold expansion of the heavy-quark pair-production cross sections in the quark annihilation and gluon fusion channels. We discuss the factorization necessary for this purpose and explain the relationship between hard functions and virtual amplitudes.
