We present a construction of the pion electromagnetic form factor where the transition from large-Nc Regge vector meson dominance models with infinitely many resonances to perturbative QCD is built in explicitly. The construction is based on an appropriate assignment of residues to the Regge poles, which fulfills the constraints of the parton-hadron duality and perturbative QCD. The model contains a slowly falling off non-perturbative contribution which dominates over the perturbative QCD radiative corrections for the experimentally accessible momenta. The leading order and next-to-leading order calculations show a converging pattern which describes the available data within uncertainties, while the onset of asymptotic QCD takes place at extremely high momenta, Q ~ 10^3-10^4 GeV. The method can be straightforwardly extended to study other form factors where the perturbative QCD result is available.
We have recently presented a Regge description of pion-pion total cross sections valid above 1.4 GeV, consistent with the few existing experiments, factorization and crossing symmetry. In this note we show how it also describes a further large data sample obtained from an analysis of experiments on $π^\pm p\to XΔ^{++}$ and $π^\pm n\to Xp$.
We propose a model-independent ansatz $M={β_x}\left(x+c_0\right)^ν+c_1$ ($x=l,\,n_r$) and then use it to fit the orbital and radial pion Regge trajectories without the preset values. It is shown that nonzero $c_1$ is reasonable and acceptable. Nonzero $c_1$ gives an explanation for the nonlinearity of the pion Regge trajectories in the usually employed $(M^2,\,x)$ plane. As $m_R$ or $c_1$ is chosen appropriately, both the orbital and radial pion Regge trajectories are linear in the $((M-m_R)^2,\,x)$ plane whether the $π^0$ is included or not on the Regge trajectories. The fitted pion Regge tra…
Some results on the perturbative Regge asymptotics are reviewed. The concepts of the reggeon interaction approach and the double logarithmic approximation are outlined. Contribution to the Zeuthen Workshop on QCD and QED at higher order, Rheinsberg, April 1996.
We discuss a possibility that linear Regge trajectories originate not from gluonic strings connecting quarks, as it is usually assumed, but from pion excitations of light hadrons. From this point of view, at large angular momenta both baryons and mesons lying on linear Regge trajectories are slowly rotating thick strings of pion field, giving rise to a universal slope computable from the pion decay constant. The finite resonance widths are mainly due to the semiclassical radiation of pion fields by the rotating elongated chiral solitons. Quantum fluctuations about the soliton determine a strin…
Using the Kirschner-Lipatov equation as a basis, we study high energy elastic quark-quark amplitudes, which correspond to secondary Reggeons and pion exchange in the double-logarithmic approximation of perturbative QCD.
We analyze the pi -> gamma* gamma* amplitude in the framework of radial Regge models in the large-Nc limit. With the assumption of similarity of the asymptotic Regge rho and omega meson spectra we find that the pion distribution amplitude is constant in the large-$N_c$ limit at the scale Q0 where the QCD radiative corrections are absent -- a result found earlier in a class of chiral quark models. We discuss the constraints on the couplings from the anomaly and from the limit of large photon virtualities, and find that the coupling of the pion to excited rho and omega mesons must be asymptotica…
Integral kernels describing the pair interaction of reggeized gluons and quarks are reconstructed in terms of conformal symmetric 4-point functions in the transverse plane of impact parameters.
The reaction $γp \to π^0 p$ is investigated in the energy range above the resonance region. The amplitudes include the leading Regge singularities in the cross-channel and correctly describe the differential cross section for beam energies above 4 GeV and for the $s-$channel scattering angle $\cosθ_s\ge 0.6$. The energy dependence of the beam asymmetry and the reaction $γn \to π^0 n$ seem is quantitative consistent with the Regge-pole dominance.
After recalling the theoretical and experimental status of QCD in the Regge limit and the requirement of high energy scattering process of onium-onium type for testing this limit, we show that the International Linear Collider would be a major step in this field.
We review our recent description of high energy forward hadronic cross sections and in particular of pion scattering data by means of Regge theory. We obtain a prediction for the total proton-proton cross section at LHC. In addition, and contrary to some suggestions in the literature we show that standard Regge behavior can accommodate both crossing symmetry and factorization. Some consequences for low energy pion-pion scattering are briefly discussed.
We consider exclusive multi-peripheral production of four charged pions in proton-proton collisions at high energies with simultaneous exchange of three pomerons/reggeons. The amplitude(s) for the genuine $2 \to 6$ process are written in the Regge approach. The calculation is performed with the help of the GenEx Monte Carlo code. Some corrections at low invariant masses in the two-body subsystems are necessary for application of the Regge formalism. We estimate the corresponding cross section and present differential distributions in rapidity, transverse momenta and two- and four-pion invarian…
The known analytic properties of the Compton amplitude at small $Q^2$ place significant constraints on its behaviour at large $Q^2$. This calls for a re-evaluation of the role of perturbative evolution in past fits to data.
As noticed by Fadin, Kuraev and Lipatov in 1975 incorporation of asymptotic freedom into the BFKL equation splits the QCD pomeron into a series of isolated poles in complex angular momentum plane. Following our earlier work on the proton structure function we explore the phenomenological consequences of the emerging BFKL-Regge factorized expansion for the small-$x$ structure function of the pion $F_{2π}(x,Q^2)$. We calculate $F_{2π}$ in a small-$x$ region and find good agreement with the recent H1 determination of $F_{2π}(x,Q^2)$. We also present the BFKL-Regge factorization based evaluation o…
Deep-inelastic scattering at small x is a new field of QCD phenomenology which HERA experiments started to explore. The data show the feature expected by the perturbative Regge asymptotics. We describe the parton picture of structure function evolution both for increasing $Q^2$ and for decreasing $x$ and discuss the leading logarithmic approximation of QCD on which this picture is based. The steep rise of the parton density towards smaller $x$ gets saturated by parton recombination. An essential improvement of the leading logarithmic approximation has to be worked out in order to satisfy the u…
Central diffractive event topologies at the LHC energies can be identified by two different approaches. First, the forward scattered protons can be measured in Roman pots. Second, a veto on hadronic activity away from midrapidity can be imposed to define a double-gap topology. Such a double-gap topology trigger has been implemented by the ALICE collaboration in Run 1 and Run 2 of the LHC. The analysis of these events allows to determine the charged-particle multiplicity within the acceptance. The excellent particle identification capabilities of ALICE allows to study two-track events both in t…
Two key issues in the application of perturbative QCD and Regge predictions to high energy processes are whether the hard and soft pomerons should be considered as two separate distinct exchanges and whether the Regge intercepts are Q^2 independent or not. Models involving a distinct hard pomeron exchange predict much larger values for the LHC total cross-section. Here we argue that there is a polarized analogue of this issue in the isovector part of the spin structure function g_1 and that the spin data appear to favour a distinct hard exchange.
Calculations of central exclusive diffractive production (CEDP) of two pions via continuum and resonance mechanism are presented in the Regge-eikonal approach. Data from STAR, ISR, CDF and CMS were analysed and compared with theoretical description. Preliminary extraction of $f_0(500)$, $f_0(980)$ and $f_2(1270)$ couplings to Pomeron, and also $ρ$ meson contribution from photoproduction mechanism to the CEDP cross-section are considered. We show possible nuances and problems of calculations and prospects of investigations at present and future hadron colliders.
Compatibility of the Reggeized form of QCD multi-particle amplitudes with the s-channel unitarity requires fulfilment of an infinite number of the "bootstrap" relations. On the other hand, it turns out that fulfillment of all these relations ensures the Reggeized form of energy dependent radiative corrections order by order in perturbation theory. It is extremely nontrivial, that all these relations are fulfilled if the Reggeon vertices and trajectory satisfy several bootstrap conditions. The full set of these conditions in the next-to-leading order was derived in the last year and the ultimat…
The concept of incomplete vector-meson dominance and Regge models is applied to the transition form factor of the pion. First, we argue that variants of the chiral quark model fulfilling the chiral anomaly may violate the Terazawa-West unitarity bounds, as these bounds are based on unverified assumptions for the real parts of the amplitudes, precluding a possible presence of polynomial terms. A direct consequence is that the transition form factor need not necessarily vanish at large values of the photon virtuality. Moreover, in the range of the BaBar experiment, the Terazawa-West bound is an …
The exciting feature of recent times is the inflow of new experimental data. Fits to the $π, \r$ and f meson resonances found by the VES collaboration, along with those of the PDG 1998 compilation are reported using a non-linear model for Regge trajectories. There are only five parameters including the pion mass and the states come out as Regge -type excitations of the pion. Total number of mesons fitted are 23 and the fit is good to $\sim$ 3% for 18 of them and $\sim$ 9% for others.
Employing the Worldline casting of the Dosch-Simonov Stochastic Vacuum Model(SVM) for QCD, a simulated meson-meson scattering is studied in the Regge kinematical regime. The process is modelled in terms of the "helicoidal" Wilson contour first introduced by Janic and Peschanski in a related study based on an AdS/CFT-type approach. Using lattice supported estimations for the behavior of a two-point, field strength correlation function, as defined in the framework of the SVM, the reggeon slope and intercept are calculated in a semiclassical approximation. The resulting values are in good agreeme…
The procedure to improve the convergence in transverse momentum space of the NLL BFKL kernel using a w-shift is revisited. An accurate approximation to this shift only depending on transverse momenta is presented. This approximation is based on a Bessel function of the first kind with argument depending on the strong coupling and a double logarithm of the ratio of transverse scales. A comparison between different renormalization schemes is also included.
We perform a detailed Regge analysis of NN, pion-N and pion-pion scattering. From it, we find expressions that represent the pion-pion scattering amplitudes with an accuracy of a few percent, for exchange of isospin zero, and $\sim15%$ for exchange of isospin 1, and this for energies s^{1/2}> 1.4 GeV and for momentum transfers |t|^{1/2}< 0.4 GeV. These Regge formulas are perfectly compatible with the low energy (s^{1/2}< 1.4 GeV) scattering amplitudes deduced from pion-pion phase shift analyses as well as with higher energy (s^{1/2}>1.4 GeV) experimental pion-pion cross sections. They are also…
Proton-proton differential and total cross sections provide information on the energy dependence of proton shape and size. We show that the deviation from exponential behavior of the diffraction cone observed near $t=-0.1$ GeV$^2$, (so-called break), both at the ISR and the LHC follows from the $t$-channel two-pion loop contributions, imposed by unitarity. By using a simple Regge-pole model, we extrapolate the "break" from the ISR energy region to that of the LHC. This allows us to answer two important questions: 1) To what extent is the "break" observed recently at the LHC a "recurrence" of t…
Recently, the RHICf Collaboration measured the transverse single-spin asymmetries of the very forward neutral pion in polarized $p+p$ collisions at $\sqrt{s}=510$ GeV, produced at large pseudorapidity ($η\gtrsim 6$). The data show large asymmetries both in longitudinal momentum fraction $x_F$ and transverse momentum $p_T$ at $p_T<1\,\mathrm{GeV}/c$. Employing baryonic triple Regge exchanges, we describe the complete RHICf data for the first time and show that the neutral pion production at low $p_T$ can be interpreted as a diffractive one.
Electroproduction of $π^+$ above the resonance region is analyzed in the Regge model for $π+ρ$ exchanges. Importance of the roles of pion and proton form factors in the process is discussed in comparison with existing models of Kaskulov and Mosel, and of Vrancx and Rychebusch. It is shown that the present model with proton form factor of a simple dipole-type yields a better description of DESY and JLab data over those models for high $Q^2$ and $-t$ region up to 5 GeV$^2$.
We estimate final state interactions in the B-meson decays into two pions by the Regge model. We consider Pomeron exchange and the leading Regge trajectories that can relate intermediate particles to the final state. In some cases, most notably B => pi^0 pi^0 and B => pi^+ pi^-, the effect is relevant and produces a better agreement between theory and experiment.
We consider the Olsson sum rule, i.e., the forward dispersion relation for pion-pion scattering with exchange of isospin unity at threshold. We show that, if using the S0, S2 and P wave expressions of Colangelo, Gasser and Leutwyler, then either the sum rule is not satisfied or, if adjusting the residue of the rho exchange Regge amplitude to have the sum rule satisfied (as recently proposed by Caprini, Colangelo and Leutwyler) then the subsequent high energy amplitude is in disagreement with experimental pi-pi cross sections.
We review the parton model and the Regge approach to the QCD description of the deep-inelastic $ep$ scattering at the small Bjorken variable $x$ and demonstrate their relation with the DGLAP and BFKL evolution equations. It is shown, that in the leading logarithmic approximation the gluon is reggeized and the pomeron is a compound state of two reggeized gluons. The conformal invariance of the BFKL pomeron in the impact parameter space is used to investigate the scattering amplitudes at high energies and fixed momentum transfers. The remarkable properties of the Schrödinger equation for compoun…
The high-energy limit of gauge-theory amplitudes features both a Regge pole and Regge cuts. We show how to disentangle these, and hence how to determine the Regge trajectory beyond two loops. While the nonplanar part of multiple Reggeon $t$-channel exchange forms a Regge cut, the planar part contributes to the pole along with the single Reggeon. With this, we find that the infrared singularities of the trajectory are given by the cusp anomalous dimension. By matching to recent QCD results, we determine the quark and gluon impact factors to two loops and the Regge trajectory to three loops.
We study pion induced reactions for charmed baryons $B$, $π$ + N $\rightarrow$ $D^*$ + $B$. First we estimate charm production rates in comparison with strangeness production using a Regge model which is dominated by vector ($D^*$ or $K^*$ ) Reggeon exchange. Then we examine the production rates of various charmed baryons $B$ in a quark-diquark model. We find that the production of excited states are not necessarily suppressed, a sharp contrast to strangeness production, which is a unique feature of the charm production with a large momentum transfer.
We explain how Regge theory and perturbative evolution may be made compatible at small x. The result not only gives striking support to the two-pomeron description of small-x behaviour, but gives a rather clean test of perturbative QCD itself. When x is very small, or Q^2 is very large, the proton's gluon distribution function is significantly larger than is commonly believed. Perturbative evolution is invalid below Q^2\approx 5 GeV^2.
We present a systematic analysis of backward pion photoproduction for the reactions gamma p -> pi0 p and gamma p -> pi+ n. Regge phenomenology is applied at invariant collision energies above 3 GeV in order to fix the reaction amplitude. A comparision with older data on pi0- and pi+ photoproduction at theta = 180 degrees indicates that the high-energy limit as given by the Regge calculation could be reached possibly at energies of around sqrt{s} = 3 GeV. In the energy region of sqrt{s} < 2.5 GeV, covered by the new measurements of gamma p -> pi0 p differential cross sections at large angles at…
We show how the Regge trajectory of a resonance can be obtained from its pole in a scattering process and analytic constraints in the complex angular momentum plane. The method is suited for resonances that dominate an elastic scattering amplitude. In particular, from the rho(770) resonance pole in pion-pion scattering, we obtain its linear Regge trajectory, characteristic of ordinary quark-antiquark states. In contrast, the f0(500) pole -the sigma meson- which dominates scalar isoscalar pion-pion scattering, yields a non-linear trajectory with a much smaller slope at the f0(500) mass. Convers…
We explore the BaBar puzzle within the Regge approach. After reviewing the chiral quark models in applications to PDF and PDA of the pion, we argue that variants of these models, fulfilling the chiral anomaly, may in fact violate the second Terazawa-West unitarity bound, which is based on unverified assumptions for the real part of the amplitude. Consequently, the transition form factor need not vanish at large values of the photon virtuality. Then we show that the experimental data may be properly explained with incomplete vector-meson dominance in a simple model with one state, as well as in…
Around $θ_π= 90^\circ$, the coupling to the $ρ^\circ N$ channel leads to a good accounting of the charged pion exclusive photoproduction cross section in the energy range 3 $<E_γ<$ 10 GeV, where experimental data exist. Starting from a Regge Pole approach that successfully describes vector meson production, the singular part of the corresponding box diagrams (where the intermediate vector meson-baryon pair propagates on-shell) is evaluated without any further assumptions (unitarity). Such a treatment provides an explanation of the $s^{-7}$ scaling of the cross section. Elastic rescattering of …
The couplings $g_{ρHH}$ of the $ρ$ meson with any hadron H are calculated in a holographic dual of QCD where the Regge trajectories for mesons are manifest. The resulting couplings grow linearly with the exciting number of H, thus are far from universal. A simple argument has been given for this behavior based on quasi-classical picture of excited hadrons. It seems that in holographic duals with exact Regge trajectories the $g_{ρHH}$ universality should be violated. The $ρ$-dominance for the electromagnetic form factors of H are also strongly violated, except for the lowest state, the pion. Qu…
This paper is a brief survey of the Balitskii-Fadin-Kuraev-Lipatov (BFKL) approach for the description of hard or semi-hard processes in the so-called Regge limit of perturbative QCD. The starting point is a fundamental property of perturbative QCD, the gluon Reggeization. This property, combined with s-channel unitarity, allows to predict the growth in energy of the amplitude of hard or semi-hard processes with exchange of vacuum quantum numbers in the $t$-channel. When also the so-called impact factors of the colliding particles are known, then not only the behavior with the energy, but the …
We derive and apply the finite energy sum rules to pion photoproduction. We evaluate the low energy part of the sum rules using several state-of-the-art models. We show how the differences in the low energy side of the sum rules might originate from different quantum number assignments of baryon resonances. We interpret the observed features in the low energy side of the sum rules with the expectation from Regge theory. Finally, we present a model, in terms of a Regge-pole expansion, that matches the sum rules and the high-energy observables.
We propose a QCD-inspired two-component Pomeron form which gives an excellent description of the proton-proton, pi-proton, kaon-proton, gamma-proton and gamma-gamma total cross sections. Our fit has a better CHI2/dof for a smaller number of parameters as compared with the PDG fit. Our 2-Pomeron form is fully compatible with weak Regge exchange-degeneracy, universality, Regge factorization and the generalized vector dominance model.
It is shown that subdominant terms found in the reggeized gluon diagram technique, to be added to Pomeron fan diagrams with the 3P interaction, can be exactly taken into account by taking the initial condition for evolution in the Glauber form. This demonstrates complete equivalence of the dipole picture and the reggeized gluon approach not only on the leading level but also on the subleading level.
In frames of effective Regge action the vertices describing conversion of two reggeized gluons to one two and three ordinary gluons was constructed. The self-consistency: Bose symmetry and gauge invariance properties checks was shown to be fulfilled. The simplest one with creation of a single gluon was intensively verified in programs of experimental and theoretical treatment since it determine the kernel of of the known BFKL equation. Here we discuss the possibility to check the vertex with creation of two real gluons, which can reveal itself in process of scalar mesons production in high ene…
Starting from the multi-Regge effective action for high-energy scattering in QCD a $t$-channel approach can be developed which is similar to the approach by White based on general Regge arguments. The BFKL kernel of reggeized gluon interaction, contributions to the $2 \rightarrow 4 $ reggeized gluon vertex function and the one-loop correction to the BFKL kernel are considered. The conditions are discussed under which this approach can provide a simple estimante of the next-to-leading logarithmic corrections to the BFKL perturbative pomeron intercept.
We discuss some problems concerning the application of perturbative QCD to high energy soft processes. We show that summing the contributions of the lowest twist operators for non-singlet $t$-channel leads to a Regge-like amplitude. Singlet case is also discussed.
The rates of inclusive photo- and electroproduction of the eta_c meson: gamma* + p -> eta_c + X are calculated in the triple Regge region, integrated over the diffractive mass X. For the Regge exchanges we use the hard Pomeron and Odderon, both being calculated in the framework of perturbative QCD. The integrated cross-section depends upon the coupling of the BFKL pomeron to two $C=-1$ odderons, and it is found to be of the order 60 pb for photoproduction and 1.5 pb at Q^2=25 GeV^2.
Pion Compton scattering is studied in perturbative QCD for real and space--like initial photons. Different methods for the convolution of the hard amplitude with the pion wave--functions, which have in the past led to conflicting results, are compared.
The first three coefficients of the Taylor's series expansion of the vector pion form factor as a function of the momentum transfer are evaluated using experimental data on the pion form factor and the P-wave pi pi phase shifts. The real part of the form factor as a function of energy is also calculated by dispersion relation. Comparisons these results with Chiral Perturbation Theory and unitarized models are given.
We recalculate the pion electromagnetic form factor based on the perturbative QCD formalism that includes the Sudakov resummation. We take into account the evolution of the pion wave function in $b$, which represents the transverse extent of the pion. An infrared enhancement is observed when $1/b$ approaches $Λ_{QCD}$. We propose to freeze the evolution of the wave function at some scale above $Λ_{QCD}$, such that perturbative contributions are stablized. Our predictions are consistent with experimental data, and insensitive to the variation of relevant parameters.
We investigate the charged pion photoproduction off the proton target with the Delta(1232) baryon in the final state, i.e. gamma p -> pi^- Delta^++(1232) and gamma p -> pi^+ Delta^0(1232), based on the effective Lagrangian method, beyond the resonance region, E_cm >~ GeV. We employ the pi- and rho-meson Regge trajectories in the t-channel, in addition to the proton- and Delta-pole, in the s- and u-channels respectively, and the contact-interaction contributions. A specific scheme for the form factor which satisfies the Ward-Takahashi identity, crossing symmetry, and on-shell condition, is take…
Single and double inclusive cross-sections for gluon jet production from within the triple pomeron vertex are studied in the reggeized gluon technique. It is shown that to satisfy the AGK rules the vertex has to be fully symmetric in all four reggeized gluons which form the two final pomerons. The single inclusive cross-sections are found for different cuttings of the triple pomeron vertex. They sum into the expression obtained by Yu.Kovchegov and K.Tuchin in the colour dipole picture. The found double inclusive cross-sections satisfy the AGK rules.
By reanalysing transverse momentum dependence in the perturbative calculation of pion form factor an improved expression of pion form factor which takes into account the transverse momentum dependenc in hard scattering amplitude and intrinsic transverse momentum dependence associated with pion wave functions is given to leading order, which is available for momentum transfers of the order of a few GeV as well as for $Q \to \infty$. Our scheme can be extended to evaluate the contributions to the pion form factor beyond leading order.
The perturbative pion form factor with Sudakov suppression is re-examined. Taking into account the multi-gluon exchange in the law $Q^2$ regions, we suggest that the running coupling constant should be frozen at $α_s(t=\sqrt{<{\bf k}_{T}^{2}>})$ and $\sqrt{<{\bf k}_{T}^{2}>}$ is the average transverse momentum which can be determined by the pionic wave function. In addition, we correct the previous calculations about the Sudakov suppression factor which plays an important role in the perturbative predictions for the pion form factor.
We analyse the perturbative contributions from the higher helicity ($λ_{1}+λ_{1}=\pm 1$) components, which should be naturally contained in the light-cone wave function for the pion as a consequence of the Wigner rotation, in the QCD calculation of the pion form factor. It is pointed out that the contributions may provide the other fraction needed to fit the pion form factor data besides the perturbative contributions from the ordinary helicity components evaluated using the factorization formula with the asymptotic form of the distribution amplitude. We suggest a way to test the higher helici…
We use the transverse-momentum dependence of the cross section for diffractive dissociation of high energy pions to two jets to study some non-perturbative Light-Cone wave functions of the pion. We compare the predictions for this distribution by Gaussian and Coulomb wave functions as well as the wave function derived from solution of the Light-Cone Hamiltonian in the Singlet Model. We conclude that this experimentally measured information provides a powerful tool for these studies.
In this paper we present a combined analysis of the H1 data on leading baryon and diffractive structure functions from DIS, which are handled as two components of the same semi-inclusive process. The available structure function data are analyzed in a series of fits in which three main exchanges are taking into account: pomeron, reggeon and pion. For each of these contributions, Regge factorization of the correspondent structure function is assumed. By this procedure, we extract information about the interface between the diffractive, pomeron-dominated, region and the leading proton spectrum, …
We study bottomonium hadroproduction in proton-antiproton collisions at the Fermilab Tevatron in the framework of the quasi-multi-Regge kinematics approach and the factorization formalism of non-relativistic QCD at leading order in the strong-coupling constant alpha_s and the relative velocity v of the bound quarks. The transverse-momentum distributions of prompt Upsilon(nS)-meson production measured at the Tevatron are fitted to obtain the non-perturbative long-distance matrix elements for different choices of un-integrated gluon distribution functions of the proton.
