It is argued that $W/Z$ boson production in ultra-relativistic $pp$ collisions in the fragmentation region, subject to a kinematic cut on the boson transverse momentum $Q_\perp>Q_{\perp\min}$, with 1 GeV/c$\ll Q_{\perp\min}\ll M_{W/Z}$, must be dominated by the Compton mechanism $qg\to q'W/Z$. We propose applications for boson hadroproduction in this kinematics and formulate the factorization theorem. The analysis of QCD enhancements indicates that Regge behavior should manifest itself not only in the $s$ but also in $Q_\perp$-dependence of the boson production differential cross-section.
We compare the numerical predictions of the k_T-factorization approach (semihard theory) for heavy quark production in high energy nucleon-nucleon and photon-nucleon collisions with the experimental data from Tevatron-collider and HERA. Predictions for heavy quark production at Tevatron, LHC and HERA are also presented.
The p_T-spectra for direct J/psi and psi' in hadroproduction at Tevatron energy have been calculated based on NRQCD formalism and fragmentation approximation in the collinear parton model and k_T-factorization approach. We have described the CDF data and obtained a good agreement between the predictions obtained in the parton model and k_T-factorization approach. We performed the calculations using the relevant leading order in alpha_s hard amplitudes and the equal values of the color-octet long-distance matrix elements for the both models.
The hadroproduction of direct J/Psi in the framework of the k_\perp-factorization approach is studied. The color-singlet contribution is essentially larger than in the collinear approach but is still an order of magnitude below the data. The deficit may be well described by the color octet contribution with the value of the matrix element <0|O^{J/Ψ}_8(^3S_1)|0> substantially decreased in comparison with the fits in the collinear factorization. This should lead to a reduction of the large transverse polarization, predicted in the collinear approach.
We study the production of prompt photons at high energy in the framework of the k_T-factorization approach. The amplitude for production of a single photon associated with quark pair in the fusion of two off-shell gluons is calculated. Theoretical results are compared with the Tevatron data.
We consider the processes of compare the heavy quark production using the unintegrated gluon distributions. The numerical predictions for high energy nucleon-nucleon and photon-nucleon collisions of the $k_T$-factorization approach (semihard theory) are compared with the experimental data from Tevatron-collider and HERA. The total production cross sections and $p_T$ distributions are considered and they are in reasonable agreement with the data for rather value of QCD scale.
We compare the numerical predictions for heavy quark production in high energy hadron collisions of the conventional QCD parton model and the $k_T$-factorization approach (semihard theory). The total production cross sections, one-particle rapidity and $p_T$ distributions as well as two-particle correlations are considered. The difference in the predictions of the two approaches is not very large, while the shapes of the distributions are slightly different.
We present a new approach for the prompt production of quarkonia which is based on the $k_T$-factorization method. The production of even C-parity quarkonia proceeds via the fusion of two (off-shell) gluons. Especially in the kinematics of the LHCb experiment these processes are thus expected to be a sensitive probe of the small-$x$ gluon distribution. We calculate the relevant off-shell matrix elements in terms of the light-front wave functions of the quarkonium states. We present our results for scalar and pseudoscalar charmonia and discuss photon transition form factors as well as cross sec…
We study the resummation of singular distributions for electroweak-boson production at large transverse momentum in hadronic collisions. We describe the factorization properties of the cross section near partonic threshold and construct the resummed cross section at next-to-leading logarithmic accuracy in moment space in terms of soft gluon anomalous dimensions. We present full analytical results for the expansion of the resummed cross section up to next-to-next-to-leading order. Our results can be applied to W, Z, and virtual gamma production at hadron colliders.
We compare the theoretical status and the numerical predictions of two approaches for heavy quark production in the high energy hadron collisions, namely the conventional LO parton model with collinear approximation and $k_T$-factorization approach. The main assumptions used in the calculations are discussed. To extract the differences coming from the matrix elements we use very simple gluon structure function and fixed coupling. It is shown that the $k_T$-factorization approach calculated formally in LO and with Sudakov form factor accounts for many contributions related usually to NLO (and e…
We discuss the applicability of the $k_T$ factorization theorem to low-$p_T$ hadron production in hadron-hadron collision in a simple toy model, which involves only scalar particles and gluons. It has been shown that the $k_T$ factorization for high-$p_T$ hadron hadroproduction is broken by soft gluons in the Glauber region, which are exchanged among a transverse-momentum-dependent (TMD) parton density and other subprocesses of the collision. We explain that the contour of a loop momentum can be deformed away from the Glauber region at low $p_T$, so the above residual infrared divergence is fa…
By combining NRQCD factorization and collinear factorization, we compute a series of relativistic corrections for $J/ψ$ hadroproduction to all orders in $v^2$ at large $p_T$ limit. The $v^2$ expansion converges well for all channels. We find that the ratio of relativistic correction term to the corresponding leading term is independent of kinematic variables for any channel, which generalizes the proportional relations found in previous works to all orders.
In this work, we present a thorough analysis of $η_c(1S,2S)$ quarkonia hadroproduction in $k_\perp$-factorisation in the framework of the light-front potential approach for the quarkonium wave function. The off-shell matrix elements for the $g^* g^* η_c(1S,2S)$ vertices are derived. We discuss the importance of taking into account the gluon virtualities. %We discuss the role of relativistic corrections, the Melosh spin-rotation and theoretical uncertainties by comparing our results with the standard NRQCD approach. We present the transverse momentum distributions of $η_c$ for several models of…
We present a calculation for the polarizations of $J/ψ$ and $ψ'$ produced in the hadron collisions at the Fermilab Tevatron. Various color octet channels including ${}^1S_0^{(8)}$, ${}^3P_J^{(8)}$, and ${}^3S_1^{(8)}$ as well as contributions from $χ_{cJ}$ decays are considered in the $k_t$ factorization approach. We find that in a rather wide range of the transverse momenta of $J/ψ$ and $ψ'$, the production rates could be dominated by the ${}^1S_0^{(8)}$ channel, and the predicted polarizations from the ${}^1S_0^{(8)}$ channel and $χ_{cJ}$ feeddown contributions are roughly compatible with th…
In this work, we present a thorough analysis of scalar $P$-wave $χ_{Q0}$, $Q=c,b$ quarkonia electromagnetic form factors for the $γ^* γ^* \to χ_{Q0}$ couplings, as well as their hadroproduction observables in $k_\perp$-factorisation using the light-front potential approach for the quarkonium wave function. The electromagnetic form factors are presented as functions of photon virtualities. We discuss the role of the Melosh spin-rotation and relativistic corrections estimated by comparing our results with those in the standard nonrelativistic QCD (NRQCD) approach. Theoretical uncertainties of ou…
We consider the prompt photon production at high energy hadron colliders in the framework of k_T-factorization approach. The unintegrated quark and gluon distributions in a proton are determined using the Kimber-Martin-Ryskin prescription. The conservative error analisys is performed. We investigate both inclusive prompt photon and prompt photon and associated muon production rates. In Standard Model such events come mainly due to Compton scattering process where the final heavy (charm or bottom) quark produces a muon. The theoretical results are compared with recent experimental data taken by…
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…
We present some results on renormalization and factorization scale dependence of soft-gluon resummation, at the next-to-leading-logarithmic level, in the fixed-target hadro-production cross-section for prompt photons.
We demonstrate the violation of kT-factorization for quark production in high energy hadronic collisions. This violation is quantified in the Color Glass Condensate framework and studied as a function of the quark mass, the quark transverse momentum, and the saturation scale Qsat, which is a measure of large parton densities. At x values where parton densities are large but leading twist shadowing effects are still small, violations of kT-factorization can be significant - especially for lighter quarks. At very small x, where leading twist shadowing is large, we show that violations of kT-fact…
We study pp and p\bar p collisions which lead to the exclusive production of J/psi or Upsilon from the pomeron-odderon and the pomeron-photon fusion. We calculate scattering amplitudes of these processes in the lowest order approximation and in the framework of k_T factorization. We present estimates of cross sections for the kinematic conditions of the Tevatron and of the LHC.
Applying the nonrelativistic quantum chromodynamics factorization formalism to the $Υ(1S,2S,3S)$ hadroproduction, a complete analysis on the polarization parameters $λ_θ$, $λ_{θϕ}$, $λ_ϕ$ for the production are presented at QCD next-to-leading order. With the long-distance matrix elements extracted from experimental data for the production rate and polarization parameter $λ_θ$ of $Υ$ hadroproduction, our results provide a good description for the measured parameters $λ_{θϕ}$ and $λ_ϕ$ in both the helicity and the Collins-Soper frames. In our calculations the frame invariant parameter $\tildeλ$…
Results from a phenomenological analysis of $W$ and $Z$ hard diffractive hadroproduction at high energies are reported. Using the Regge factorization approach, we consider the recent diffractive parton density functions extracted by the H1 Collaboration at DESY-HERA. In addition, we take into account multiple Pomeron exchange corrections considering a gap survival probability factor. It is find that the ratio of diffractive to non-diffractive boson production is in good agreement with the CDF and D0 data. We make predictions which could be compared to future measurements at the LHC.
We present the complete next-to-leading order QCD corrections to the polarized hadroproduction of heavy flavors which soon will be studied experimentally in polarized pp collisions at the BNL RHIC in order to constrain the polarized gluon density Delta g. It is demonstrated that the dependence on unphysical renormalization and factorization scales is strongly reduced beyond the leading order. The sensitivity of the heavy quark spin asymmetry to Delta g is studied, including the limited detector acceptance for experimentally observable leptons from heavy quark decays at the BNL RHIC. As a furth…
The amplitude for production of a single photon associated with quark pair in the fusion of two off-shell gluons is calculated. The matrix element found is applied to the inclusive prompt photon hadroproduction at high energies in the framework of kt-factorization QCD approach. The total and differential cross sections are calculated in both central and forward pseudo-rapidity regions. The conservative error analisys is performed. We used the unintegrated gluon distributions in a proton which were obtained from the full CCFM evolution equation as well as from the Kimber-Martin-Ryskin prescript…
The production of heavy quarks at large $\pt$ ($\pt\gg m$) in hadronic collisions is considered. The analysis is carried out in the framework of perturbative fragmentation functions, thereby allowing a resummation at the NLO level of final state large mass logarithms of the kind $\log(\pt/m)$. The case of $b$-quark production is considered in detail. The resulting theoretical uncertainty from factorization/renormalization scales at large $\pt$ is found to be much smaller than that shown by the full $O(\as^3)$ perturbative calculation.
A contribution to $J/ψ$ hadroproduction is analyzed in which the meson production is mediated by three-gluon partonic state, with two gluons coming from the target and one gluon from the projectile. This mechanism involves double gluon density in one of the protons, hence this contribution enters at a non-leading twist. It is, however, relevant due to an enhancement factor coming from large double gluon density at small~$x$. We calculate the three-gluon contribution to $J/ψ$ hadroproduction within perturbative QCD in the $k_T$-factorization framework. Results are obtained for differential $p_T…
If studies of electroweak gauge boson final states at the Large Hadron Collider, for Standard Model physics and beyond, are sensitive to effects of the initial state's transverse momentum distribution, appropriate generalizations of QCD shower evolution are required. We propose a method to do this based on QCD transverse momentum dependent (TMD) factorization at high energy. The method incorporates experimental information from the high-precision deep inelastic scattering (DIS) measurements, and includes experimental and theoretical uncertainties on TMD parton density functions. We illustrate …
The quarkonium hadroproduction in association with a photon at high energies provides a probe of the dynamics of the strong interactions as it is dependent on the nuclear gluon distribution. Therefore, it could be used to constrain the behavior of the nuclear gluon distribution in proton-nucleus and nucleus-nucleus collisions. Such processes are useful to single out the magnitude of the shadowing/antishadowing effects in the nuclear parton densities. In this work we investigate the influence of nuclear effects in the production of JPsi + photon and Upsilon + photon and estimate the transverse …
Gravitational Compton scattering process with a massive fermion is studied in the context of the linearized gravity. Gravitational gauge invariance and graviton transversality cause the transition amplitude to be factorized into that of scalar QED Compton scattering and that of fermion QED Compton scattering with an overall kinematical factor. The factorization is shown explicitly and its physical implications are discussed.
We show that factorization holds for the deeply virtual Compton scattering amplitude in QCD, up to power suppressed terms, to all orders in perturbation theory. Furthermore, we show that the virtuality of the produced photon does not influence the general theorem.
Asymmetries in the hadroproduction of charm particles directly probe power corrections to the QCD factorization theorems. In this paper, the heavy-quark recombination mechanism, a power correction that explains charm meson asymmetries, is extended to charm baryons. In this mechanism, a light quark participates in the hard scattering that creates a charm quark and they hadronize together into a charm baryon. This provides a natural and economical explanation for the Λ_c^+/Λ_c^- asymmetries measured in πN and p N collisions.
In this paper, we investigate the inclusive diffractive hadroproduction for $\rm η_{c}$ and $\rm η_{b}$ at the LHC energies. Based on the NRQCD factorization formalism and the resolved-Pomeron model for the quarkonium production mechanism, we estimate the rapidity, momentum fraction loss dependence of the cross section. We give prediction ratios for single and central diffractive processes with respect to non diffractive process. These inclusive processes are sensitive to gluon content of Pomeron for small-$x$ and Reggeon for large-$x$, useful to study small and large-$x$ physics and good to t…
We systematically calculate the relativistic corrections to prompt $J/ψ$ 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 ve…
We calculate the one-loop corrections to a general off-forward deeply-virtual Compton process at leading twist for both parton helicity-dependent and independent cases. We show that the infrared divergences can be factorized entirely into off-forward parton distributions, even when one of the two photons is onshell. We argue that this property persists to all orders in perturbation theory. We obtain the next-to-leading order Wilson coefficients for the general leading-twist expansion of the product of two electromagnetic currents in the \overline{\rm MS} scheme.
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.
We calculate the cross sections of inclusive J/psi production in photoproduction and two-photon scattering, involving both direct and resolved photons, and in e^+e^- annihilation at next-to-leading order (NLO) within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD), including the full relativistic corrections due to the intermediate ^1S_0^{[8]}, ^3S_1^{[8]}, and ^3P_J^{[8]} color-octet (CO) states. Exploiting also our previous results on hadroproduction, we perform a combined fit of the respective CO long-distance matrix elements (LDMEs) to all available high-quali…
We describe a light-cone wave function formalism for hadroproduction of heavy-flavors via gluon-gluon fusion. The developed approach is well suited to address coherence effects in heavy-quark production on nuclei at small $x_{2} \lsim 0.1\cdot A^{-1/3}$. Nuclear attenuation in hadroproduction of heavy-flavors is found to be similar to shadowing effects for heavy-flavor structure functions in deep-inelastic scattering from nuclei. Nevertheless, remaining differences in the theoretical formulation of both processes imply corrections to factorization theorems.
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 $c\bar{c}$ 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 $J/ψ$ and $ψ^\prime$ 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 i…
We propose the inclusive hadroproduction of a heavy-light dijet system, as a new channel for the investigation of high energy QCD. We build up a hybrid factorization that incorporates a partial next-to-leading BFKL resummation inside the standard collinear description of observables. We present a detailed analysis of different observables: cross-section summed over azimuthal angles and differential in rapidity and azimuthal distribution. The stability that these distributions show under higher-order corrections motivates our interest in future studies, doable at new generation colliding machin…
We show that hard-scattering factorization is violated in the production of high-p_T hadrons in hadron-hadron collisions, in the case that the hadrons are back-to-back, so that k_T factorization is to be used. The explicit counterexample that we construct is for the single-spin asymmetry with one beam transversely polarized. The Sivers function needed here has particular sensitivity to the Wilson lines in the parton densities. We use a greatly simplified model theory to make the breakdown of factorization easy to check explicitly. But the counterexample implies that standard arguments for fact…
Based on the non-relativistic quantum chromodynamics factorization formalism, the polarization parameters $λ_{θϕ}$ and $λ_ϕ$ of $J/ψ$ hadroproduction are analyzed in helicity frame and calculated at QCD next-to-leading order for the first time. For prompt $J/ψ$ production, we take into account the feeddown contributions from $χ_{cJ}$ and $ψ(2S)$ decays. The theoretical predictions for the polarization parameters $λ_{θϕ}$ and $λ_ϕ$ of $J/ψ$ are presented. With the theoretical results we have done the fit to the experimental measurements on yield and polarization for $J/ψ$ hadroproduction simult…
We systematically calculate the relativistic corrections to the polarization variables of prompt $J/ψ$ 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 mat…
Based on the non-relativistic QCD factorization scheme, we study the hadroproduction of the bottomonium states $Υ(5S)$ and $Υ(6S)$. We argue to search for them in the final states $Υ(1S,2S,3S)π^+π^-$, which are found to have anomalously large production rates at $Υ(5S)$. The enhanced rates for the dipionic transitions in the $Υ(5S)$-energy region could, besides $Υ(5S)$, be ascribed to $Y_b(10890)$, a state reported by the Belle collaboration, which may be interpreted as a tetraquark. The LHC/Tevatron measurements are capable of making a case in favor of or against the existence of $Y_b(10890)$…
Inclusive hadroproduction of $χ_{c1}(3872)$, $X_b$ and pentaquarks
Technical University of Munich（慕尼黑工业大学）；II. Institut für Theoretische Physik, Universität Hamburg（汉堡大学理论物理第二研究所）；Central China Normal University（华中师范大学）
I discuss recent progress in the theory of exclusive meson production and Compton scattering, focusing on hard-scattering factorization and on the dipole formalism.
We propose the study of the inclusive hadroproduction of a heavy-flavored jet in association with a light jet, as a probe channel of strong interactions at high energies. We build up a hybrid factorization that encodes genuine high-energy effects, provided by a partial next-to-leading BFKL resummation, inside the standard collinear structure of the cross section. We present a detailed analysis of different distributions, shaped on kinematic ranges typical of experimental analyses at the Large Hadron Collider, and differential in rapidity, azimuthal angle and transverse momentum. The fair stabi…
In this work we consider the dilepton production via timelike Compton scattering (TCS) in electron-proton and proton-proton collisions. In particular, the differential cross section in terms of the dilepton invariant mass and rapidity is computed within the $k_T$-factorization approach. Besides, we utilize distinct unintegrated gluon distributions (UGD) in order to compare their impact on the differential cross section of TCS in $pp$ ($ep$) collisions evaluated at the LHC (LHeC), HL-LHC (LHeC), HE-LHC (LHeC) and FCC-hh (eh) center-of-mass energies.
We investigate the inclusive hadroproduction of a heavy quarkonium ($J/ψ$ or $Υ$), in association with a light-flavored jet, as a testing ground for the semi-hard regime of QCD. Our theoretical setup is the hybrid high-energy and collinear factorization, where the standard collinear approach is supplemented by the $t$-channel resummation of leading and next-to-leading energy logarithms à la BFKL. We present predictions for rapidity and azimuthal-angle differential distributions, hunting for stabilizing effects of the high-energy series under higher-order corrections. Our reaction represents an…
We derive the complete factorization formula for the leading power contribution in wide angle Compton scattering. It consists of the soft- and hard-spectator contributions. The hard-spectator contribution is well known and defined in the form of the convolution of a hard kernel with the nucleon distribution amplitudes. The soft-spectator contribution describes the scattering which involves the soft modes. We use the soft collinear effective theory in order to define this term in a field theoretical approach. Using the SCET framework we provide the proof of the factorization formula. We also co…
We study analytical properties of the hard exclusive process amplitudes. We found that QCD factorization for deeply virtual Compton scattering and hard exclusive vector meson production results in the subtracted dispersion relation with the subtraction constant determined by the Polyakov-Weiss $D$-term.
We study the prompt photon hadroproduction at the LHC with the $k_T$-factorization approach and the $qg^* \to qγ$ and $g^*g^* \to q\bar qγ$ partonic channels, using three unintegrated gluon distributions which depend on gluon transverse momentum. They represent three different theoretical schemes which are usually considered in the $k_T$-factorization approach, known under the acronyms: KMR, CCFM and GBW gluon distributions. We find sensitivity of the calculated prompt photon transverse momentum distribution to the gluon transverse momentum distribution. The predictions obtained with the three…
In this paper we present a new derivation of the QCD factorization. We deduce the k_T- and collinear factorizations for the DIS structure functions by consecutive reductions of a more general theoretical construction. We begin by studying the amplitude of the forward Compton scattering off a hadron target, representing this amplitude as a set of convolutions of two blobs connected by the simplest, two-parton intermediate states. Each blob in the convolutions can contain both the perturbative and non-perturbative contributions. We formulate conditions for separating the perturbative and non-per…
At the Large Hadron Collider (LHC) it will become possible for the first time to investigate experimentally the forward region in hadron-hadron collisions via high-$p_T$ processes. In the LHC forward kinematics QCD logarithmic corrections in the hard transverse momentum and in the large rapidity interval may both be quantitatively significant. We analyze the hadroproduction of forward jets in the framework of QCD high-energy factorization, which allows one to resum consistently both kinds of corrections to higher orders in QCD perturbation theory. We compute the short-distance matrix elements …
