Real Gluon Research Articles

Gluon polarization tensor and dispersion relation in a weakly magnetized medium

We study the polarization and dispersion properties of gluons moving within a weakly magnetized background at one-loop order. To this end, we show two alternative derivations of the charged fermion propagator in the weak field expansion and use this expression to compute the lowest order magnetic field correction to the gluon polarization tensor. We explicitly show that, in spite of its cumbersome appearance, the gluon polarization tensor is transverse as required by gauge invariance. We also show that none of the three polarization modes develops a magnetic mass and that gluons propagate along the light cone, non withstanding that Lorentz invariance is lost due to the presence of the magnetic field. By comparing with the expression for the gluon polarization tensor valid to all orders in the magnetic field, the existence of a second solution, corresponding to a finite gluon mass, is shown to be spurious and an artifact of the lowest order approximation in the field strength. We also study the strength of the polarization modes for real gluons. We conclude that, provided the spurious solutions are discarded, the lowest order approximation to the gluon polarization and dispersion properties is good as long as the field strength is small compared to the loop fermion mass.

Production of χc meson pairs with additional emission

We discus mechanism of double χc production with large rapidity separation. The first order pertubative correction to gg→χcχc process includes additional emission of gluon among χc pair. We have considered real gluon distribution as well as virtual correction to the production process of χc pairs. Results for two scalar χc0χc0 and two axial mesons χc1χc1 are shown.

Mass dependence of Higgs boson production at large transverse momentum through a bottom-quark loop

In the production of the Higgs through a bottom-quark loop, the transverse momentum distribution of the Higgs at large $P_T$ is complicated by its dependence on two other important scales: the bottom quark mass $m_b$ and the Higgs mass $m_H$. A strategy for simplifying the calculation of the cross section at large $P_T$ is to calculate only the leading terms in its expansion in $m_b^2/P_T^2$. In this paper, we consider the bottom-quark-loop contribution to the parton process $q\bar{q}\to H+g$ at leading order in $\alpha_s$. We show that the leading power of $1/P_T^2$ can be expressed in the form of a factorization formula that separates the large scale $P_T$ from the scale of the masses. All the dependence on $m_b$ and $m_H$ can be factorized into a distribution amplitude for $b \bar b$ in the Higgs, a distribution amplitude for $b \bar b$ in a real gluon, and an endpoint contribution. The factorization formula can be used to organize the calculation of the leading terms in the expansion in $m_b^2/P_T^2$ so that every calculation involves at most two scales.

Dynamical gluon mass in the instanton vacuum model

We consider the modifications of gluon properties in the instanton liquid model (ILM) for the QCD vacuum. Rescattering of gluons on instantons generates the dynamical momentum-dependent gluon mass Mg(q). First, we consider the case of a scalar gluon, no zero-mode problem occurs and its dynamical mass Ms(q) can be found. Using the typical phenomenological values of the average instanton size ρ=1/3 fm and average inter-instanton distance R=1 fm we get Ms(0)=256 MeV. We then extend this approach to the real vector gluon with zero-modes carefully considered. We obtain the following expression Mg2(q)=2Ms2(q). This modification of the gluon in the instanton media will shed light on nonperturbative aspect on heavy quarkonium physics.

Mass dependence of Higgs production at large transverse momentum

The transverse momentum distribution of the Higgs at large PT is complicated by its dependence on three important energy scales: PT, the top quark mass mt, and the Higgs mass mH. A strategy for simplifying the calculation of the cross section at large PT is to calculate only the leading terms in its expansion in mt2/PT2 and/or mH2/PT2. The expansion of the cross section in inverse powers of PT is complicated by logarithms of PT and by mass singularities. In this paper, we consider the top-quark loop contribution to the subprocess qoverline{q}to H+g at leading order in αs. We show that the leading power of 1/PT2 can be expressed in the form of a factorization formula that separates the large scale PT from the scale of the masses. All the dependence on mt and mH can be factorized into a distribution amplitude for toverline{t} in the Higgs, a distribution amplitude for toverline{t} in a real gluon, and an endpoint contribution. The factorization formula can be used to simplify calculations of the PT distribution at large PT to next-to-leading order in αs. The results are readily applied to the qg process via a straightforward analytical continuation.

Correct definition of color singlet P-wave non-perturbative matrix element of heavy quarkonium production

Recently we have proved factorization of infrared divergences in NRQCD S-wave heavy quarkonium production at high energy colliders at all orders in coupling constant. One of the problem which still exists in the higher order pQCD calculation of color singlet P-wave heavy quarkonium production/anihillation is the appearance of noncanceling infrared divergences due to real soft gluons exchange, although no such infrared divergences are present in the color singlet S-wave heavy quarkonium. In this paper we find that since the non-perturbative matrix element of the color singlet P-wave heavy quarkonium production contains derivative operators, the gauge links are necessary to make it gauge invariant and be consistent with the factorization of such non-canceling infrared divergences at all orders in coupling constant.

Off-shell gluon production in interaction of a projectile with 2 or 3 targets

Within the effective QCD action for the Regge kinematics, the amplitudes for virtual gluon emission are studied in collision of a projectile with two and three targets. It is demonstrated that all non-Feynman singularities cancel between induced vertices and rescattering contributions. Formulas simplify considerably in a special gauge, which is a straightforward generalization of the light-cone gauge for emission of real gluons.

Double Charmonia Production at LHCb

In this note next-to-leading order corrections to double charmonium production at LHCb are considered. It is shown that real gluon emission leads to significant change of the cross sections of considered processes. For example, forbidden at leading order production of C-odd state XcJ/Ψ is possible at NLO. Distributions over various kinematical variables are analyzed and the question of separating contributions of different mechanisms (direct J/ΨJ/Ψ production, radiative feed-down from XcJ/Ψ, double parton scattering) is considered.

The LPM effect in sequential bremsstrahlung: 4-gluon vertices

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. In this paper, we continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-gluon approximations. In particular, this paper completes the calculation of the rate for real double gluon bremsstrahlung from an initial gluon with various simplifying assumptions (thick media; $\hat q$ approximation; and large $N_c$) by now including processes involving 4-gluon vertices.

Production ofJ/ψ+χcandJ/ψ+J/ψwith real gluon emission at the LHC

In the present work we study production of $J/\psi + \chi_c$ and $J/\psi + J/\psi$ in LHC. The first process is forbidden at the leading order in gluon fusion due to the $C$-parity conservation, and the first non-vanishing contribution is given by the process with additional emission of real gluon. Considering the direct production of $J/\psi + J/\psi$, where the leading order is allowed, we have found that the contribution from the higher order process with real gluon emission is comparable and even more significant than the leading order. Moreover, account of this higher order effect dramatically changes kinematical distributions. Through the present paper we study in details different channels of paired $J/\psi + J/\psi$ production: direct $J/\psi + J/\psi$ production, feed-down from $J/\psi + \chi_c$ channel, double parton scattering. We also try to find kinematical distributions that are most suitable to separate these different channels.

The LPM effect in sequential bremsstrahlung 2: factorization

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. In this paper, we continue analysis of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-gluon approximations. In particular, this paper analyzes the subtle problem of how to precisely separate overlapping double splitting (e.g.\ overlapping double bremsstrahlung) from the case of consecutive, independent bremsstrahlung (which is the case that would be implemented in a Monte Carlo simulation based solely on single splitting rates). As an example of the method, we consider the rate of real double gluon bremsstrahlung from an initial gluon with various simplifying assumptions (thick media; $\hat q$ approximation; large $N_c$; and neglect for the moment of processes involving 4-gluon vertices) and explicitly compute the correction $\Delta\,d\Gamma/dx\,dy$ due to overlapping formation times.

BFKL equation for an integrated gluon density

We show how it is possible to rewrite the BFKL equation for the unintegrated gluon distribution, in terms of integrated gluons, similar to that used in DGLAP. We add to our equation the next-to-leading log terms which provide exact energy-momentum conservation and account for the kinematic constraint in real gluon emission. In this way the equation includes the major part of the higher-order corrections to BFKL evolution. We discuss the possibility to obtain a unified BFKL-DGLAP evolution equation relevant to processes at the LHC where both log(1/x) and logQ^2 are large simultaneously.

The role of Glauber exchange in soft collinear effective theory and the Balitsky–Fadin–Kuraev–Lipatov Equation

In soft collinear effective theory (SCET) the interaction between high energy quarks moving in opposite directions involving momentum transfer much smaller than the center-of-mass energy is described by the Glauber interaction operator which has two-dimensional Coulomb-like behavior. Here, we determine this n–n¯ collinear Glauber interaction operator and consider its renormalization properties at one loop. At this order a rapidity divergence appears which gives rise to an infrared divergent (IR) rapidity anomalous dimension commonly called the gluon Regge trajectory. We then go on to consider the forward quark scattering cross section in SCET. The emission of real soft gluons from the Glauber interaction gives rise to the Lipatov vertex. Squaring and adding the real and virtual amplitudes results in a cancelation of IR divergences, however the rapidity divergence remains. We introduce a rapidity counter-term to cancel the rapidity divergence, and derive a rapidity renormalization group equation which is the Balitsky–Fadin–Kuraev–Lipatov Equation. This connects Glauber interactions with the emergence of Regge behavior in SCET.

Minimal physical constraints on the angular distributions of two-body boson decays

The angular distribution of the two-body decay of a boson of unknown properties is strongly constrained by angular momentum conservation and rotation invariance, as well as by the nature of the detected decay particles and of the colliding ones. Knowing the border between the "physical" and "unphysical" parameter domains defined by these "minimal constraints" (excluding specific hypotheses on what is still subject of measurement) is a useful ingredient in the experimental determinations of angular distributions and can provide model-independent criteria for spin characterizations. In particular, analysing the angular decay distribution with the general parametrization for the J = 2 case can provide a model-independent discrimination between the J = 0 and J = 2 hypotheses for a particle produced by two real gluons and decaying into two real photons.

Azimuthal correlation among jets produced in association with a bottom or top quark pair at the LHC

Angular correlation of jets produced in association with a massive scalar, vector or tensor boson is crucial in the determination of their spin and CP properties. We study jet angular correlations in events with a high mass bottom quark pair or a top quark pair and two jets at the LHC, whose cross-section is dominated by the virtual gluon fusion sub-processes when appropriate kinematic selection cuts (vector-boson fusion cuts) are applied. We evaluate helicity amplitudes for sub-processes initiated by qq, qg and gg collisions in the limit where the intermediate gluons are collinear to the initial partons. We first obtain a general expression for the azimuthal angle correlations among the dijets and t t-bar or b b-bar, in terms of the gg to t t-bar or b b-bar helicity amplitudes in the real gluon approximation of the full matrix elements, and find simple analytic expressions in the two kinematic limits, the production of a heavy quark pair near the threshold, and in the relativistic limit where the invariant mass of the heavy quark pair is much larger than the quark mass. For b b-bar + 2 jets we find strong azimuthal angle correlations which are distinct from those expected for events with a CP-even or odd scalar boson which may decay into a b b-bar pair. For t t-bar + 2 jets we find that the angular correlations are similar to that of a CP-odd scalar+2 jets near the threshold M_(t t-bar) ~ 2 m_t, while in the relativistic limit they resemble the distribution for b b-bar + 2 jets. These correlations in the standard QCD processes will help establish the experimental technique to measure the spin and CP properties of new particles produced via gluon fusion at the LHC.

One-Loop Factorization for Inclusive Hadron Production inp−ACollisions in the Saturation Formalism

We demonstrate the QCD factorization for inclusive hadron production in p-A collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. In particular, we find that the cross section can be written into a factorization form in the coordinate space at the next-to-leading order, while the naive form of the convolution in the transverse momentum space does not hold. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final-state hadron, as well as the rapidity divergence with small-x dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole gluon distribution function. The hard coefficient function is evaluated at one-loop order, and contains no divergence.

Four-point vector correlators and AdS/QCD correspondence

We derive the four-point vector correlators in QCD from AdS/QCD correspondence. It is shown that meson poles are correctly reproduced. The final expression also suggests a nonzero amplitude in the limit of zero virtuality of two longitudinal gluons. This fact does not mean that one can produce, absorb or scatter real longitudinal gluons.

Production of two gluons in the Lipatov effective action formalism

The one-loop diffractive amplitude for emission of two real gluons with widely different rapidities is studied in the Lipatov effective action formalism. It is shown that after integration over longitudinal momenta in the loop the resulting expression coincides with the one obtained by the Lipatov-Bartels formalism in transversal space provided the same prescription is used to exclude divergent contributions as previously proposed for emission of a single real gluon.

Testing the RRPP vertex of effective Regge action

We discuss the possibility of checking the vertex with creation of two real gluons in collision of two reggeized ones (RRPP) which can reveal themselves in process of scalar meson production in high energy peripheral nucleon collisions. Numerical estimations of the cross section of a pair of charged pion production for the LHC facility give the value of an order of 10 mb. We also estimate the excess of production of positively charged muons (as a decay of pions) created by cosmic ray proton collisions with the atmosphere gas nuclei to be in reasonable agreement with modern data. The effects of higher orders which reveal themselves as a screening factor are considered in terms of impact parameter representation. We estimate the cross section of pion pair production in central region to fall faster than factorial σn∼1/(n2n!).

On the equivalence of soft and zero-bin subtractions

Zero-bin subtractions are required to avoid double counting soft contributions in collinear loop integrals in soft-collinear effective theory (SCET). In traditional approaches to factorization, double counting is avoided by dividing jet functions by matrix elements of soft Wilson lines. In this paper, we compare the two approaches to double counting, studying the quark form factor and deep inelastic scattering (DIS) as ${x}_{B}\ensuremath{\rightarrow}1$ as examples. We explain how the zero-bin subtractions in SCET are required to reproduce the well-established factorization theorem for DIS as ${x}_{B}\ensuremath{\rightarrow}1$. We study one-loop virtual contributions to the quark form factor and real gluon emission diagrams in DIS. The two approaches to double counting are equivalent if dimensional regularization (DR) is used to regulate infrared (IR) divergences. We discuss in detail ambiguities in the calculation of one-loop scaleless integrals in DR in SCET and perturbative QCD. We also demonstrate a nontrivial check of the equivalence of the zero-bin subtraction and the soft Wilson line subtraction in the virtual two-loop Abelian contributions to the quark form factor.