In this paper we perform a numerical study of the tranverse expansion of hadronic scattering amplitudes in the dipole picture of high energy QCD. We go beyond the mean field approximation by including fluctuations and also wave function saturation effects, and the evolution with both a fixed and a running coupling is investigated. We also study the nonperturbative aspects, and as has been predicted earlier, our results indicate that the Froissart-Martin bound is saturated once confinement effects are included in the evolution. Thus the total cross section increases proportional to the square of the logarithm of the cms energy. Furthermore it is seen that we obtain a reasonable value for the proportionality coefficient. The impact of saturation and non-leading effects on this coefficient is also studied.
Using the QCD dipole picture of BFKL dynamics, the quasi elastic component of the diffractive gamma*-dipole cross-section, dominating at small M^2/Q^2, is calculated.
Forward differential cross-section for diffraction dissociation of virtual photons on nucleon target is calculated in the QCD dipole picture. The numerical estimates are presented and discussed.
The initial-state radiation of soft colour dipoles produced together with a single QCD Pomeron exchange (BFKL) in onium-onium scattering is calculated in the framework of Mueller's approach. The resulting dipole production grows with increasing energy and reveals an unexpected feature of a power-law tail at appreciably large transverse distances from the collision axis, this phenomenon being related to the scale-invariant structure of dipole-dipole correlations.
We derive two coupled non-linear evolution equations corresponding to the truncation of the Balitsky infinite hierarchy of saturation equations after inclusion of dipole-dipole correlations, i.e. one step beyond the Balitsky-Kovchegov (BK) equation. We exhibit an exact solution for maximal correlation which still satisfies the same asymptotic geometric scaling as BK but with the S-matrix going to 1/2 (instead of 0) in the full saturation region.
We pose the question: how far can we push the QCD dipole model and the idea of QCD saturation to the kinematical regions traditionally associated with soft nonperturbative physics? The answer is that it works sufficiently well allowing a smooth transition from hard (BFKL) pomeron to the soft one.
Compact and well defined formulae for the shadow of the virtual photon interacting with a large nucleus at small $x_{Bj}$ are given in the QCD dipole picture. Two classes of contributions are considered: (a) quasi-elastic interaction of the $q\bar{q}$ dipole and (b) multi-pomeron coupling.
Fourier-positivity, i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position (r) space. They are Bessel transforms of positive transverse momentum dependent gluon distributions. Using mathematical Fourier-positivity constraints on the limit r -> 0 behavior of the dipole amplitudes, we identify the common origin of the violation of Fourier-positivity for various, however phenomenologically convenient, dipole models. It is due to the beh…
The Good-Walker mechanism for diffraction is shown to provide a link between total and diffractive structure functions and to be relevant for QCD calculations at small x_{Bj}. For Deep-Inelastic scattering on a small-size target (cf. an onium) the r\^ ole of Good-Walker ``diffractive eigenstates'' is played by the QCD dipoles appearing in the $1/N_C$ limit of QCD. Hard diffraction is thus related to the QCD tripe-dipole vertex which has been recently identified (and calculated) as being a conformal invariant correlator and/or a closed-string amplitude. An extension to hard diffraction at HERA …
Evolution equations for multiplicities in QCD cascades can, both in the parton and dipole picture, be used to estimate corrections beyond the formal accuracy of the modified leading log approximation (MLLA). The differences between the two pictures, and other uncertainties beyond first order MLLA corrections, are here investigated in some detail. For example, I discuss how some colour suppressed corrections, which cannot be determined without better knowledge of non-perturbative QCD, are related to the question of colour reconnection. A generalized evolution equation for the dipole cascade is …
The QCD dipole picture of BFKL dynamics provides an attractive theoretical approach to the study of the QCD (resummed) perturbative expansion of small-x physics and more generally to hard high-energy processes. We discuss applications to the phenomenology of proton structure functions in the HERA range and to the longstanding problem of unitarity corrections, and outline some specific predictions of the dipole picture.
In this paper we study the description of saturation in Balitsky, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (B-JIMWLK) picture when restricted to observables made up only from dipole operators. We derive a functional form of the evolution equation for the dipole probability distribution and find a one-parameter family of exact solutions to the dipole evolution equations.
The magnetic dipole moments of the ${\cal D}_2$, and ${\cal D}_{S_2}$, ${\cal B}_2$, and ${\cal B}_{S_2}$ heavy tensor mesons are estimated in framework of the light cone QCD sum rules. It is observed that the magnetic dipole moments for the charged mesons are larger than that of its neutral counterpart. It is found that the $SU(3)$ flavor symmetry violation is about 10\% in both $b$ and $c$ sectors.
In this publication the construction of an automatic algorithm to subtract infrared divergences in real QCD corrections through the Catani-Seymour dipole subtraction method [arXiv:hep-ph/9605323] is reported. The resulting computer code has been implemented in the matrix element generator AMEGIC++ [arXiv:hep-ph/0109036]. This will allow for the automatic generation of dipole subtraction terms and their integrals over the one-parton emission phase space for any given process. If the virtual matrix element is provided as well, this then directly leads to an NLO QCD parton level event generator.
Magnetic dipole moments of the negative parity light and heavy tensor mesons are calculated within the light cone QCD sum rules method. The results are compared with the positive parity counterparts of the corresponding tensor mesons. The results of the analysis show that the magnetic dipole moments of the negative parity light mesons are smaller compared to those of the positive parity mesons. Contrary to the light meson case, magnetic dipole moments of the negative parity heavy mesons are larger than the ones for the positive parity mesons.
This is the talk given at ``Gribov-75 Memorial Workshop on Quarks, Hadrons, and Strong Interactions", May 22-24, 2005, Budapest. Hungary. In this talk we discuss the BFKL Pomeron Calculus and its interrelation with thecolour dipole approach. The two key problems we consider are the probabilistic interpretation of the BFKL Pomeron Calculus and the possiblescenario for the asymptotic behaviour of the scattering amplitude at high energyin QCD.
The soft gluon part of a proton wave function is investigated and compared with an onium case. It is argued that at every step of the gluon cascade new color structures appear. Dipole equation kernel emerges when a diquark limit is assumed.
Using the QCD sum rule approach, we calculate the electric dipole moment of the neutron induced by a vacuum theta--angle to approximately 40-50% precision, d_n = 2.4 x 10^{-16} θe.cm. Combined with the new experimental bound, this translates into the limit |θ|< 3 x 10^{-10}.
In this contribution, we present a study of the coherent and incoherent nuclear DVCS process in the small-$x$ regime within the color dipole formalism. Predictions for the nuclear DVCS cross section at photon level in the collider kinematics are presented.
In this contribution we present an exploratory QCD analysis of the neutrino structure functions in charged current DIS using the color dipole formalism. The corresponding dipole cross sections are taken from recent phenomenological and theoretical studies in deep inelastic inclusive production, including nuclear shadowing corrections. The theoretical predictions are compared to the available experimental results in the small-x region.
We show the role played by QCD evolution and skewedness effects in the DVCS cross section at large $Q^2$ within the color dipole description of the process at photon level. The dipole cross section is given by the saturation model, which can be improved by DGLAP evolution at high photon virtualities. We investigate both possibilities as well as the off-forward effect through a simple phenomenological parametrisation. The results are compared to the recent ZEUS DVCS data.
A gluon forward jet playing the role of a deep probe in high energy scattering, we analyze its infinite momentum QCD wave function in terms of dipole (color-singlet quark-antiquark) configurations using k_T-factorization properties. The comparison is made with virtual photon quark-antiquark configurations. Some implications for hard processes with forward jets at Hera and Tevatron are suggested.
It is shown that the colour dipole approach to hard scattering at high energy is fully compatible with k_T factorization at the leading logarithm approximation (in -log x_Bj). The relations between the dipole amplitudes and unintegrated diagonal and non-diagonal gluon distributions are given. It is also shown that including the exact gluon kinematics in the k_T factorization formula destroys the conservation of transverse position vectors and thus is incompatible with the dipole model for both elastic and diffractive amplitudes.
We use the method of thermal QCD sum rules to investigate the effects of temperature on the neutron electric dipole moment d_n induced by the vacuum \barθ-angle. Then, we analyze and discuss the thermal behaviour of the ratio {d_n \over \barθ} in connection with the restoration of the strong CP symmetry breaking.
We demonstrate that the QCD sum rule method can be successfully applied to the calculation of CP-odd electromagnetic observables induced by a vacuum theta--angle. We implement the approach in calculating the electric dipole moment of the rho meson to ~30% precision, and find that the result can also be explicitly related to the vacuum topological susceptibility.
The magnetic dipole moments of the light tensor mesons $f_2$, $a_2$ and strange $K_2^{\ast 0} (1430)$ tensor meson are calculated in the framework of the light cone QCD sum rules. It is observed that the values of the magnetic dipole moment for the charged tensor particles are considerably different from zero. These values are very close to zero for the light neutral $f_2$ and $a_2$ tensor mesons, while it has a small nonzero value for the neutral strange $K_2^{\ast 0} (1430)$ tensor meson.
the forward jet playing the role of a hard probe is analyzed in terms of QCD dipole (color-singlet q\bar q) configurations in the transverse position space. There are sizable differences with the analogous q\bar q configurations of a hard photon which may lead to significant phenomenological consequences on the analysis of hard processes using a forward jet probe, e.g. at the Tevatron. A geometrical interpretation of the resulting distribution in terms of black disk diffraction is proposed.
Using the QCD dipole picture of the BFKL pomeron, the cross-section of single diffractive dissociation of virtual photons at high energy and large diffractively excited masses is calculated. The calculation takes into account the full impact-parameter phase-space and thus allows to obtain an exact value of the triple BFKL Pomeron vertex. It appears large enough to compensate the perturbative 6-gluon coupling factor (alpha/pi)^3 thus suggesting a rather appreciable diffractive cross-section.
We show that the recently developed Hamiltonian theory for high energy evolution in QCD in the dilute regime and in the presence of Bremsstrahlung is consistent with the color dipole picture in the limit where the number of colors N_c is large. The color dipoles are quark-antiquark pairs which can radiate arbitrarily many soft gluons, and the evolution consists in the splitting of any such a dipole into two. We construct the color glass weight function of an onium as a superposition of color dipoles, each represented by a pair of Wilson lines. We show that the action of the Bremsstrahlung Hami…
We present predictions at NLO accuracy in QCD for top-quark pair production induced by an anomalous chromomagnetic dipole moment of the top quark. Our results are obtained for total as well as fully differential cross sections, including matching to parton shower simulations. This process is expected to provide the most stringent direct limits on top-quark chromomagnetic dipole moment. We find that NLO corrections increase the contribution from the dipole moment by about 50\% at the LHC, and significantly reduce the renormalization and factorization scale dependence. Using the NLO prediction, …
Due to the very short life time of the $Δ$ baryons, a direct measurement on the electromagnetic moments of these systems is almost impossible in the experiment and can only be done indirectly. Although only for the magnetic dipole moments of $Δ^{++}$ and $Δ^{+}$ systems there are some experimental data, the theoretical, phenomenological and lattice calculations could play crucial role. In present work, the magnetic dipole ($μ_Δ$) , electric quadrupole ($Q_Δ$) and magnetic octupole ($O_Δ$) moments of these baryons are computed within the light cone QCD sum rules. The results are compared with t…
The electric dipole moments of nucleons (NEDM, d_N) are calculated using the method of QCD sum rules. Our calculations are based on the parity and time reversal violating parameter $\thetabar$ in QCD and establish a functional dependence of the NEDM on $\thetabar$, without assuming a perturbative expansion of this symmetry breaking parameter. The results obtained from the QCD sum rules approach are shown to be consistent with the general symmetry constraints on CP violations in QCD, including the necessity of: (1) finite quark masses, (2) spontaneous chiral symmetry breaking, and (3) the U_A(1…
We perform an adjust to the most recent structure function data, considering the QCD dipole picture applied to ep scattering. The structure function F2 at small x and intermediate Q2 can be described by the model containing an economical number of free-parameters, which encodes the hard Pomeron physics. The longitudinal structure function and the gluon distribution are predicted without further adjustments. The data description is effective, whereas a resummed next-to-leading level analysis is deserved.
The magnetic dipole moment of the exotic $Z_b(10610)$ state is calculated within the light cone QCD sum rule method using the diquark-antidiquark and molecule interpolating currents. The magnetic dipole moment is obtained as $μ_{Z_b}=1.73\pm 0.63~μ_N$ in diquark-antidiquark picture and $μ_{Z_b}=1.59\pm 0.58~μ_N$ in the molecular case. The obtained results in both pictures together with the results of other theoretical studies on the spectroscopic parameters of the $Z_b(10610)$ state may be useful in determination of the nature and quark organization of this state.
It is argued that the QCD dipole picture allows to build an unified theoretical description -based on BFKL dynamics- of the total and diffractive nucleon structure functions. This description is in qualitative agreement with the present collection of data obtained by the H1 collaboration. More precise theoretical estimates, in particular the determination of the normalizations and proton transverse momentum behaviour of the diffractive components, are shown to be required in order to reach definite conclusions.
By using thermal QCD sum rules to investigate the $\barθ$ induced neutron electric dipole moment $d_n$, we have examined the behaviour of broken CP symmetry at finite temperature. We find that, below the critical temperature, the ratio $\mid {d_n \over \barθ}\mid$ slightly decreases but survives at temperature effects, implying T nonrestoration of CP-invariance \cite{Chabab}.
We derive inclusive and diffractive forward-gluon production in the scattering of a $q\bar{q}$ dipole off an arbitrary target in the high-energy eikonal approximation, suitable to study the saturation regime. We show how the inclusive cross-section is related to the total cross-section for the scattering of a colorless pair of gluons on the target: the gluon-production cross-section can be expressed as a convolution between this $gg$ dipole total cross-section and a dipole distribution. We then consider as an application the forward-jet production from an incident hadron and describe forward-j…
We study the neutron electric dipole moment in the presence of the CP-violating operators up to the dimension five in terms of the QCD sum rules. It is found that the OPE calculation is robust when exploiting a particular interpolating field for neutron, while there exist some uncertainties on the phenomenological side. By using input parameters obtained from the lattice calculation, we derive a conservative limit for the contributions of the CP violating operators. We also show the detail of the derivation of the sum rules.
In this paper, the renormalization-group equations for the (flavor-conserving) CP-violating interaction are derived up to the dimension six, including all the four-quark operators, at one-loop level. We apply them to the models with the neutral scalar boson or the color-octet scalar boson which have CP-violating Yukawa interactions with quarks, and discuss the neutron electric dipole moment in these models.
A parton-shower model for hadronic collisions based on the emission properties of QCD dipoles is proposed. This proposal therefore extends the well-known radiation pattern of pure final-state colour dipoles to QCD initial-state radiation, both of which are treated perturbatively. Corresponding dipole splitting functions are derived and the kinematics of all dipole splittings is discussed. Application to hadron production in electron-positron annihilation, to Drell-Yan lepton-pair and QCD jet production yields encouraging results.
The $F_{2}$, $F_{G}$, $R=F_{L}/F_{T}$ proton structure functions are derived in the QCD dipole picture of BFKL dynamics. We get a three parameter fit describing the 1994 H1 proton structure function $F_{2}$ data in the low $x$, moderate $Q^{2}$ range. Without any additional parameter, the gluon density and the longitudinal structure functions are predicted.The diffractive dissociation processes are also discussed, and a new prediction for the proton diffractive structure function is obtained.
Perturbative QCD Prediction of the Hyperon EDM from CP-violating Dipole Interactions
Shandong Jianzhu University（山东建筑大学）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大李政道研究所）；Shanghai Jiao Tong University（上海交通大学）；Henan Normal University（河南师范大学）；Chinese Academy of Sciences（中国科学院）；University of Jyväskylä（于韦斯屈莱大学）；Helsinki Institute of Physics（赫尔辛基物理研究所）
Here, we discuss QCD predictions on multiplicities in parton and dipole approaches. The most general treatment is based on the notion of the generating functions. The generating function G is defined as $G(u,y)=\sum_nu^nP_n(y)$, where $P_n$ is the probability of the n-particle production at energy denoted by y, u is an auxiliary variable. The mean multiplicity and higher moments of the multiplicity distribution $P_n$ are given by the u-derivatives of G at u=1.
We describe an implementation of a subtraction scheme in the nonrelativistic-QCD treatment of heavy-quarkonium production at next-to-leading-order in the strong-coupling constant, covering $S$- and $P$-wave bound states. It is based on the dipole subtraction in the massless version by Catani and Seymour and its extension to massive quarks by Phaf and Weinzierl. Important additions include the treatment of heavy-quark bound states, in particular due to the more complicated infrared-divergence structure in the case of $P$-wave states.
We consider the effect of an energy-dependent dipole form factor in the high-energy behavior of the forward amplitude. The connection between the semihard parton-level dynamics and the hadron-hadron scattering is established by an eikonal QCD-based model. Our results for the proton-proton ($pp$) and antiproton-proton ($\bar{p}p$) total cross sections, $σ_{tot}^{pp,\bar{p}p}(s)$, obtained using the CTEQ6L1 parton distribution function, are consistent with the recent data from the TOTEM experiment.
We evaluate a number of new instanton-induced phenomena in QCD, starting with static dipole-dipole potentials, and proceeding to quark-quark and dipole-dipole scattering at high energy. We use a non-perturbative formulation of the scattering amplitude in terms of a correlator of two Wilson-lines (quarks) or Wilson-loops (dipoles) and analyze the Euclidean amplitudes with both perturbative gluons and instantons. The results are analytically continued to Minkowski geometry, by interpreting the angle between the Wilson lines as rapidity. We discuss the relevance of our results for the phenomenolo…
I discuss elastic dipole-dipole scattering in QCD at high energies, with emphasis on the relation between Mueller's dipole picture and the Color Glass Condensate, and on the importance of rare fluctuations for the high-energy limit of the S-matrix.
We present a complete analysis of the electric dipole moment (EDM) of the ρ-meson induced by CP violating operators of dimension 4 and 5 within the QCD sum rules approach. The set of CP-odd operators includes the theta term and the electric and chromoelectric dipole moments of the three light quarks. We find that the ρ-meson EDM induced purely by the EDMs of quarks is smaller, but still in reasonable agreement, with the predictions of a naive constituent quark model. However, the chromoelectric dipole moments, including that of the strange quark, give comparable and sometimes larger contributi…
In this work we consider the QCD parton saturation models to describe soft interactions at the high energy limit. The total and elastic cross sections as well as the elastic slope parameter are obtained for proton-proton and pion-proton collisions and compared to recent experimental results. The analyses are done within the color dipole formalism taking into account saturation models which have been tested against DIS data. The main point is that the match between soft and hard interaction occurs in the saturation region which can be described by high density QCD approaches. Discussion is perf…
In this work, we briefly report on the current status of an alternative subtraction scheme which is based on the splitting kernels of an improved parton shower prescription. Our focus is here on more recent developments as well as generic arguments on the scaling behaviour.
In order to make quantitative predictions for jet cross sections in perturbative QCD, it is essential to calculate them to next-to-leading accuracy. This has traditionally been an extremely laborious process. Using a new formalism, imaginatively called the dipole formalism, we are able to construct a completely general algorithm for next-to-leading order calculations of arbitrary jet quantities in arbitrary processes. In this paper we present the basic ideas behind the algorithm and illustrate them with a simple example.
We briefly describe a new general algorithm for carrying out QCD calculations to next-to-leading order in perturbation theory. The algorithm can be used for computing arbitrary jet cross sections in arbitrary processes and can be straightforwardly implemented in general-purpose Monte Carlo programs. We show numerical results for the specific case of jet cross sections in deep inelastic scattering at HERA energies.
We present a detailed study of the electric dipole moment of the neutron induced by a vacuum theta angle within the framework of QCD sum rules. At next-to-next-to leading order in the operator product expansion, we find the result d_n(θ) = 2.4 x 10^{-16} θe cm, to approximately 40% precision. With the current experimental bound this translates into a limit on the theta parameter of |θ| < 3 x 10^{-10}. We compare this result with the long-standing estimates obtained within chiral perturbation theory, and observe a numerical similarity, but also significant differences in the source of the domin…
We present an independent calculation of that part of the O(α_s^2) contribution to the decay width Γ(\bar B -> X_s γ) which arises from the self-interference term of the electromagnetic dipole operator O_7. Using a different method, we find complete agreement with a previous calculation. This NNLL contribution is an important ingredient for the complete NNLL prediction of Γ(\bar B -> X_s γ) which will resolve the charm quark mass ambiguity appearing at NLL accuracy.
We briefly describe a new general algorithm for carrying out QCD calculations to next-to-leading order in perturbation theory. The algorithm can be used for computing arbitrary jet cross sections in arbitrary processes and can be straightforwardly implemented in general purpose Monte Carlo programs. We show numerical results for the specific case of jet cross sections in deep inelastic scattering.
We compute the next-to-leading order corrections to soft-gluon radiation differentially in the one-emission phase space. We show that their contribution to the evolution of color dipoles can be obtained in a modified subtraction scheme, such that both one- and two-emission terms are amenable to Monte-Carlo integration. The two-loop cusp anomalous dimension is recovered naturally upon integration over the full phase space. We present two independent implementations of the new algorithm in the two event generators Pythia and Sherpa, and we compare the resulting fully differential simulation to t…
The dipole subtraction method for calculating next-to-leading order corrections in QCD was originally only formulated for massless partons. In this paper we extend its definition to include massive partons, namely quarks, squarks and gluinos. We pay particular attention to the quasi-collinear region, which gives rise to terms that are enhanced by logarithms of the parton masses, M. By ensuring that our subtraction cross section matches the exact real cross section in all quasi-collinear regions we achieve uniform convergence both for hard scales Q ~= M and Q >> M. Moreover, taking the masses t…
In this contribution we apply the QCD dipole picture combined with $k_T$-factorization to get predictions for deep-inelastic scattering on an onium. Assuming renormalization-group factorization, we get predictions for the $F_2, F_G$ and $R= F_L/F_T$ proton structure functions. We obtain a three-parameter fit of the 1994 H1 data in the low-$x_{bj}$, moderate-$Q^2$ range. $F_G/F_2$ and $R$ are then predicted without any additionnal parameter. The BFKL dynamics contained in the dipole model is shown to provide a relevant model in describing the HERA data. The prediction for $F_2$ and $F_G$ are co…
Using the QCD dipole picture of BFKL dynamics and the conformal invariance properties of the BFKL kernel in transverse coordinate space, we show that the 1--to--p dipole densities can be expressed in terms of dual Shapiro- Virasoro amplitudes B{2p+2} and their generalization including non-zero conformal spins. We discuss the possibility of an effective closed string theory of interacting QCD dipoles.
