M. Yu. Azarkin, I. M. Dremin, A. V. Leonidov
It is shown that the soft mechanism of multiparticle production by Lund hadronic strings formed by colliding constituent degrees of freedom generates a shape of angular correlations similar to the ridge structure observed in the pp collisions at 7 TeV at the LHC.
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One of the most important experimental results for proton-proton scattering at the LHC is the observation of a so-called "ridge" structure in the two particle correlation function versus the pseudorapidity difference $Δη$ and the azimuthal angle difference $Δϕ$. One finds a strong correlation around $Δϕ=0$, extended over many units in $Δη$. We show that a hydrodynamical expansion based on flux tube initial conditions leads in a natural way to the observed structure. To get this result, we have to perform an event-by-event calculation, because the effect is due to statistical fluctuations of th…
We show that the key features of the CMS result on the ridge correlation seen for high multiplicity events in sqrt(s)=7TeV proton-proton collisions at the LHC can be understood in the Color Glass Condensate framework of high energy QCD. The same formalism underlies the explanation of the ridge events seen in A+A collisions at RHIC, albeit it is likely that flow effects may enhance the magnitude of the signal in the latter.
We discuss the physics of the ridge -- azimuthally collimated long range rapidity correlations -- in high multiplicity proton-proton and proton-nucleus collisions. We outline some of the theoretical discussions in the literature that address the systematics of these ridge correlations.
We demonstrate that the recent measurement of azimuthally collimated, long range rapidity ("ridge") correlations in $\sqrt{s}=13$ TeV proton-proton (p+p) collisions by the ATLAS collaboration at the LHC are in agreement with expectations from the color glass condensate effective theory of high energy QCD. The observation that the integrated near side yield as a function of multiplicity is independent of collision energy is a natural consequence of the fact that multiparticle production is driven by a single semi-hard saturation scale in the color glass condensate framework. We argue further th…
An unexpected result at the RHIC and the LHC is the observation that high-multiplicity hadronic events in heavy-ion and proton-proton collisions are distributed as two "ridges", approximately flat in rapidity and opposite in azimuthal angle. We propose that the origin of these events is due to the inelastic collisions of aligned gluonic flux tubes that underly the color confinement of the quarks in each proton. We predict that high-multiplicity hadronic ridges will also be produced in the high energy photon-photon collisions accessible at the LHC in ultra-peripheral proton-proton collisions or…
The Dynamics of Particle-Particle Correlations and the Ridge Effect in Proton-Proton Collisions
本研究首次利用动量空间蒙特卡洛代码中的BFKL动力学计算质子-质子碰撞的末态关联，探究高能QCD动力学对长程快度关联和脊效应的贡献。
An $η$-elongated same-side 2D peak ("soft ridge") in minimum-bias angular correlations from heavy ion collisions has been attributed both to jet formation and to initial-state geometry structure coupled to radial flow. We consider evidence for both interpretations.
The CMS collaboration at the LHC has reported a remarkable and unexpected phenomenon in very high-multiplicity high energy proton-proton collisions: a positive correlation between two particles produced at similar azimuthal angles, spanning a large range in rapidity. We suggest that this "ridge"-like correlation may be a reflection of the rare events generated by the collision of aligned flux tubes connecting the valence quarks in the wave functions of the colliding protons. The "spray" of particles resulting from the approximate line source produced in such inelastic collisions then gives ris…
The ridge signal, which is long-ranged in rapidity, in the di-hadron correlations in high-multiplicity p-p and p-A collisions opened up a whole new research area in high-energy QCD. Although the ridge had been observed in A-A collisions and interpreted as a result of the radial flow of quark-gluon plasma, it had not appeared until recently in the data of small collision systems such as p-p and p-A, nor had it been predicted theoretically or seen in the event generators. There are two competing approaches that attempt to explain the systematics of the di-hadron ridge signal; hydrodynamics and g…
We study untriggered di-hadron correlations in Pb+Pb at 2.76 TeV, based on an event-by-event simulation of a hydrodynamic expansion starting from flux tube initial conditions. The correlation function shows interesting structures as a function of the pseudorapidity difference $Δη$ and the azimuthal angle difference $Δϕ$, in particular comparing different centralities. We can clearly identify a peak-like nearside structure associated with very low momentum components of jets for peripheral collisions, which disappears towards central collisions. On the other hand, a very broad ridge structure f…
We obtain prompt di-photon cross-section in proton-nucleus collisions in Hamiltonian light-cone approach within a hybrid approximation, treating the projectile proton in the parton model and the target nucleus in the Color-Glass-Condensate approach. We study in details the di-photon correlations in quark-nucleus and proton-nucleus collisions at RHIC and the LHC. We show that the single fragmentation di-photon produces the away side correlations peak, and the double fragmentation component of prompt di-photon is responsible for the near-side peak, and the long-range in rapidity near-side azimut…
Analysis of the near-side ridge structure in pp collisions via Momentum-Kick Model
本研究利用动量踢模型(MKM)解释LHC高多重数pp碰撞中的近侧脊状结构，通过引入多重数依赖性成功拟合13 TeV和7 TeV数据，并对14 TeV碰撞结果作出预测。
One of the remarkable features of high-multiplicity hadronic events in proton-proton collisions at the LHC is the fact that the produced particles appear as two "ridges", opposite in azimuthal angle $ϕ$, with approximately flat rapidity distributions. This phenomena can be identified with the inelastic collision of gluonic flux tubes associated with the QCD interactions responsible for quark confinement in hadrons. In this paper we analyze the ridge phenomena when the collision involves a flux tube connecting the quark and antiquark of a high energy real or virtual photon. We discuss gluonic t…
A phenomenological analysis is presented of recent two-particle angular correlation data on relative pseudorapidity ($η$) and azimuth reported by the Compact Muon Solenoid (CMS) Collaboration for $\sqrt{s}$ = 7 TeV proton-proton collisions. The data are described with an empirical jet-like model developed for similar angular correlation measurements obtained from heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC). The same-side (small relative azimuth), $η$-extended correlation structure, referred to as the {\em ridge}, is compared with three phenomenological correlation struct…
Pseudorapidity and azimuthal three-particle correlations are studied based on a correlated-cluster model of multiparticle production. The model provides a common framework for correlations in proton-proton and heavy-ion collisions allowing easy comparison with the measurements. It is shown that azimuthal cluster correlations are definitely required in order to understand three-particle correlations in the near-side ridge effect. This is similar to the explanation of the ridge phenomenon found in our previous analysis of two-particle correlations and generalizes the model to higher-order correl…
We look at the new two-particle Bose-Einstein correlation (BEC) function accompanied by the color-electric flux model which can explain the "ridge" behavior in enhanced angular correlation between two identical pions at very broad rapidity with high multiplicity. We argue that such an investigation could probe both the size and the temperature of the source of two pions emitted into a narrow range of azimuthal angles. We can confirm the ev- idence for quark-gluon phase due to interaction of outgoing pions (having high transverse momenta) with the medium in thermal bath in proton-proton collisi…
We show that the long-range rapidity correlations between the produced charged-hadron pairs from two BFKL parton showers generate considerable azimuthal angle correlations. These correlations have no 1/N_c suppression. The effect of gluon saturation on these correlations are discussed and we show that it is important. We show that a pronounced ridge-like structure emerges by going from the BFKL to the saturation region. We show that the ridge structure at high-energy proton-proton and nucleus-nucleus collisions has the same origin and its main feature can be understood due to initial-state eff…
A few-body proton image, expected to be derivable from QCD in the renormalization group procedure for effective particles, is used within the Monte Carlo Glauber model to calculate the anisotropy coefficients in the initial collision-state of matter in high-energy high-multiplicity proton-proton interaction events. We estimate the ridge-like correlations in the final hadronic state by assuming their proportionality to the initial collision-state anisotropy. In our estimates, some distinct few-body proton structures appear capable of accounting for the magnitude of p-p ridge effect, with potent…
We investigate long range rapidity correlations of pairs of prompt photon and jet in the Color Glass Condensate (CGC) framework in proton-proton and proton-nucleus collisions at RHIC and the LHC. We show that photon-jet correlations exhibit long-range azimuthal collimation at near-side for low transverse momenta of the produced photon and jet in high-multiplicity events. These ridge-like features are strikingly similar to the observed ridge effect for di-hadron correlations at RHIC and the LHC. We show that correlations in the relative rapidity and the relative azimuthal angle between pairs of…
In this paper, we investigate the influence of coherent pion emission on long-range azimuthal correlations in relativistic proton-proton collisions. We study the pion momentum distribution for a coherent source with both transverse and Bjorken longitudinal expansions, and calculate the two-particle correlation function $C(Δη,Δϕ)$. A "ridge" structure is observed in the correlation function $C(Δη,Δϕ)$ of the coherent pion emission, whether the coherent source is expanding or static. The onset of this long-range azimuthal correlation can be traced back to the asymmetric initial transverse profil…
We show that the "ridge" phenomenon in the two-particle angular correlation function, as observed by the CMS experiment, can be reproduced by implementing an impact parameter dependent azimuthal correlation of the scattering planes of individual partonic interactions. Such an approach is motivated by the observation that even for moderate impact parameters a substantial number of partonic interactions may be produced, while at the same time the protons are sufficiently far apart to create a preferential direction in azimuth. A re-tune of the Pythia6 Z2 tune based on underlying event and minimu…
Ridge-like correlations in high-energy proton-proton collisions reported by the CMS collaboration suggest a collective flow that resembles the one in heavy-ion collisions. If the hydrodynamic description is valid then the effect results from the initial anisotropy of the colliding matter which depends on the structure of protons. Following recent theoretical developments, we propose several phenomenological models of the proton structure and calculate the anisotropy coefficients using the Monte Carlo Glauber model. Our estimates suggest that the event multiplicity dependence allows one to disc…
The 2D azimuth & rapidity structure of the two-particle correlations in relativistic A+A collisions is altered significantly by the presence of sharp inhomogeneities in superdense matter formed in such processes. The causality constraints enforce one to associate the long-range longitudinal correlations observed in a narrow angular interval, the so-called (soft) ridge, with peculiarities of the initial conditions of collision process. This study's objective is to analyze whether multiform initial tubular structures, undergoing the subsequent hydrodynamic evolution and gradual decoupling, can f…
In this study, the momentum-kick model is used to understand the ridge behaviours in dihadron $Δη$--$Δφ$ correlations recently reported by the LHC in high-multiplicity proton-proton (pp) collisions. The kick stand model is based on a momentum kick by leading jets to partons in the medium close to the leading jets. The medium where partons move freely is assumed in the model regardless of collision systems. This helps us apply the method to small systems like pp collisions in a simple way. Also, the momentum transfer is purely kinematic and this provides us a strong way to approach the ridge be…
We present a microscopic model for collective effects in high multiplicity proton--proton collisions, where multiple partonic subcollisions give rise to a dense system of strings. From lattice calculations we know that QCD strings are transversely extended, and we argue that this should result in a transverse pressure and expansion, similar to the flow in a deconfined plasma. The model is implemented in the PYTHIA8 Monte Carlo event generator, and we find that it can qualitatively reproduce the long range azimuthal correlations forming a near-side ridge in high multiplicity proton--proton even…
A same-side (SS, on azimuth $ϕ$) 2D peak in measured angular correlations from 200 GeV \pp collisions exhibits properties expected for jet formation. In more-central \auau collisions the SS peak becomes elongated on pseudorapidity $η$ and the transverse momentum $p_t$ structure is modified. In the latter case the SS 2D peak has been referred to as a "Soft Ridge", and arguments have been presented that the elongated peak represents flow phenomena ("triangular" and "higher harmonic" flows), possibly related to the initial-state ågeometry. In this presentation I demonstrate that "higher harmonic …
We consider two-gluon production in dilute-dense collisions within the Color Glass Condensate framework, applicable to both proton-nucleus and heavy-light ion collisions. We go beyond the glasma graph approximation which is valid in the dilute-dilute limit and show the correspondence between the glasma graphs and the $k_T$-factorized approach that we use in our calculation. We then identify the classical uncorrelated, and the Hanbury-Brown-Twiss (HBT) and Bose enhancement correlated contributions, with the Bose enhancement contribution being suppressed by the number of degrees of freedom with …
The angular correlations measured in proton-proton collisions at 7 TeV are decomposed into contributions from back to back emission and elliptic flow. Modeling the dominant term in the correlation functions as a momentum conservation effect or as an effect of the initial transverse velocity of the source, the remaining elliptic flow component can be estimated. The elliptic flow coefficient extracted from the CMS Collaboration data is 0.04-0.08. No additional small-angle, ridge-like correlations are needed to explain the experimental data.
The discovery of collectivity in proton-proton collisions, is one of the most puzzling outcomes from the two first runs at LHC, as it points to the possibility of creation of a Quark-Gluon Plasma, earlier believed to only be created in heavy ion collisions. One key observation from heavy ion collisions is still not observed in proton-proton, namely jet-quenching. In this letter it is shown how a model capable of describing soft collective features of proton-proton collisions, also predicts modifications to jet fragmentation properties. With this starting point, several new observables suited f…
An interpretation of the ridge phenomenon found in pp collisions at 7 TeV is given in terms of enhancement of soft partons due to energy loss of semihard jets. A description of ridge formation in nuclear collisions can directly be extended to pp collisions, since hydrodynamics is not used, and azimuthal anisotropy is generated by semihard scattering. Both the p_T and multiplicity dependencies are well reproduced. Some suggestions are made about other observables.
I present an overview of the ridge phenomenon in proton-proton and proton-lead collisions. This novel collimation between rapidity separated hadron pairs is a consequence of non-linear gluon dynamics within the small-x wave-function of the colliding hadrons.
The annihilation of a lepton pair into a proton-antiproton pair, and the reverse process, allow for a measurement of the timelike proton form factors. This work aims at studying the corrections due to direct soft interactions between the proton and the antiproton before their annihilation or after their creation. The analysis is carried on in the spacetime formalism used by us in a series of recent works on timelike FFs. In particular the effect of $\bar{p}p$ annihilation into many-meson states is considered. We expect it to determine similar real and imaginary parts for the form factor near t…
We calculate the cross section for production of a soft photon and two hard jets in the forward rapidity region in proton-nucleus collisions at high energies. The calculation is performed within the hybrid formalism. The hardness of the final particles is defined with respect to the saturation scale of the nucleus. We consider both the correlation limit of small momentum imbalance and the dilute target limit where the momentum imbalance is of the order of the hardness of the jets. The results depend on the first two transverse-momentum-dependent (TMD) gluon distributions of the nucleus.
It is shown that protons become more active at the periphery with increase of their collision energy. By computing the impact parameter distribution of the proton-proton overlap function at LHC energies and comparing it with ISR (and S$p\bar p$S for $p\bar p$) data, we conclude that the peripheral region of protons plays an increasing role in the rise of total cross sections through multiparticle dynamics. The size of the proton as well as its blackness increase with energy. The protons become more black both in the central region and, especially, at the periphery. This effect can be related t…
Chiral enhancement in soft-photon bremsstrahlung and charge asymmetry in low-energy lepton-proton scattering
基于重子重手征有效场理论，本文计算了低能轻子-质子散射中软光子轫致辐射的次领头阶辐射校正，发现末态质子辐射费曼图引发手征增强，结合双光子交换结果给出了完整的电荷不对称性预测，可与即将公布的 MUSE 数据比较。
CGC-induced longitudinal ridge in p-Pb collisions
本研究在CGC有效场论框架下，探讨了p-Pb碰撞中CGC诱导的纵向脊柱形成机制，发现快速性相关性在特定动量条件下出现反弹现象，并揭示了碰撞能量与动量分布对脊柱形成的影响。
Lepton-proton two-photon exchange with improved soft-photon approximation including proton's structure effects in HB$χ$PT
本文在重子手征微扰理论框架下，采用改进的软光子近似和稳健的解析方法，计算了MUSE实验相关低能轻子-质子弹性散射的双光子交换修正，并纳入质子结构效应，实现了对轻子电荷不对称性的模型无关估计。
We provide a detailed study of prompt double $J/ψ$ production within the non-relativistic QCD (NRQCD) framework in proton-proton collisions at the LHC. We confront the recent LHC data with the results obtained at leading-order (LO) in the NRQCD framework within two approaches of the collinear factorization and the $k_T$-factorization. We show that the LHCb data are consistent with the $k_T$-factorized LO NRQCD results. We show that the full LO NRQCD formalism cannot describe the recent CMS data, with about one order of magnitude discrepancy. If the CMS data are confirmed, this indicates rather…
Proton-proton (pp) collisions have been traditionally used as a baseline measurement in the search for a deconfined state of matter in heavy-ion collisions at ultrarelativistic energies. The unprecedented collision energies that are available at the Large Hadron Collider (LHC) at the European Laboratory for Nuclear Research (CERN) have illuminated new challenges in understanding the possible formation of droplets of this deconfined matter of partonic degrees of freedom in hadronic collisions, especially in high-multiplicity events. Enhancement of multi-strange particles compared to pions, degr…
We show that in supersymmetric grand unified theories new effective D=4 and D=5 operators for proton decay are induced by soft SUSY-breaking terms, when heavy GUT gauge bosons are integrated out, in addition to the standard D=6 ones. As a result, the proton lifetime in gauge mediated channels can be enhanced or even suppressed depending on the size of the heavy Higgses soft terms.
We show that Pomeron interactions generate important corrections to the Gribov-Glauber formula, which is used to extract proton-proton cross sections from proton-air collisions at high energy. We show that these corrections are larger than the errors for proton-air cross sections measured at ultra high energies in cosmic ray experiments. We present a description of these data in our model for soft interactions at high energies, which describes all available accelerator data including that from the LHC.
The leading order single inclusive soft gluon production in high energy proton-nucleus (pA) collisions has been studied by various approaches for more than two decades. The first correction due to the gluon saturation in proton was analytically attempted recently through a diagrammatic approach in which only partial results were obtained. An important feature of the first saturation correction is that it includes both initial state and final state interactions. In this paper, we present the complete result derived from the Color Glass Condensate framework. Our approach is to analytically solve…
In this paper we continue our program to construct a model for high energy soft interactions, based on the CGC/saturation approach. We demonstrate that in our model which describes diffractive physics as well as multi-particle production at high energy, the density variation mechanism leads to the value of $v_2$ which is about $60\% ÷70\%$ of the measured $v_2$. Bearing in mind that in CGC/saturation approach there are two other mechanisms present: Bose enhancement in the wave function and local anisotropy, we believe that the azimuthal long range rapidity correlations in proton-proton collisi…
It is suggested that the colorless systems of interacting soft-gluons in large-rapidity-gap events are open dynamical complex systems in which self-organized criticality and BTW-clusters play an important role. Theoretical arguments and experimental evidences supporting such a statistical approach to deep-inelastic scattering are presented.
The hadron inclusive spectra in pp collisions at high energies are analyzed within a soft QCD model, namely the quark-gluon string model. In addition to the sea quark distribution in the incoming proton we consider also the unintegrated gluon distribution that has an increasing behaviour when the gluon transverse momentum grows. It leads to an increase of the inclusive spectra of hadrons and their multiplicity in the central rapidity region of pp collision at LHC energies.
The jet fragmentation function describes the longitudinal momentum distribution of hadrons inside a reconstructed jet. We study the jet fragmentation function in proton-proton collisions in the framework of soft-collinear effective theory (SCET). We find that, up to power corrections, the jet fragmentation function can be expressed as the ratio of the fragmenting jet function and the unmeasured jet function. Using renormalization group techniques, we are able to resum large logarithms of jet radii R in the perturbative expansion of the cross section. We use our theoretical formalism to describ…
Hadron spectra measured in high-energy collisions present distributions which can be derived from the non-extensive statistical and thermodynamical phenomena. Based on earlier theoretical developments, it seems, the methods are very applicable for jets hadronization processes in electron-positron, proton-proton, and even in heavy-ion collisions. Here, we present what can was learnt from the recent theoretical and phenomenological developments: transverse momentum spectra and azimuthal anisotropy ($v_2$) of charge averaged pions, kaons and protons stemming from central Pb+Pb collisions at $\sqr…
We analyze the inclusive spectra of hadrons produced in $pp$ collisions at high energies in the mid-rapidity region within the soft QCD and perturbative QCD assuming the possible creation of the soft gluons at low intrinsic transverse momenta $k_t$. From the best description of the LHC data we found the parametrization of the unintegrated gluon distribution which at low $k_t$ is different from the one obtained within the perturbative QCD.
Regge models for proton structure function with and without a hard Pomeron contribution are compared with all available data in the region $W>3$ GeV, $Q^{2}\leq 3000$ GeV$^{2}$ and $x<0.75$. It is shown that the data do not support a hard Pomeron term in $γ^{*} p$ amplitude. Moreover, the data support the idea that the soft Pomeron, either is a double pole with $α_{P}(0)=1$ in the angular momentum $j$-plane, or is a simple pole with $α_{P}(0)=1+ε$ where $ε\ll 1$.
We present a general framework for the calculation of soft functions for SCET_I observables through next-to-next-to-leading order (NNLO) in the strong coupling constant. As an example of our formalism we show how it can be used to obtain the complete NNLO soft function for the $N$-jettiness event shape variable. We present numerical results for two examples with phenomenological impact: the one-jettiness soft function for both electron-proton and proton-proton collisions.
We compare the high energy behaviour of hadronic photon-photon cross-sections in different models. We find that the photon-photon cross-section appears to rise faster than the purely hadronic ones (proton-proton and proton-antiproton).
We investigate the transverse polarization of a hyperon produced in the high-energy unpolarized proton-proton collision, $pp\toΛ^\uparrow X$, based on the collinear twist-3 factorization formalism. We focus on the contribution from the twist-3 distribution in one of the unpolarized proton and the transversity fragmentation function for the final hyperon. Utilizing the "master formula" for the soft-gluon-pole cross section, we clarify the reason for why it receives only the derivative term of the twist-3 distribution. We also present the first computation of the soft-fermion-pole cross section …
We investigate the role of nonperturbative quark-gluon dynamics in soft high energy processes. In order to reproduce differential and total cross sections for elastic proton-proton and proton-antiproton-scattering at high energy and small momentum transfer it turns out that we need two scales, the gluonic correlation length and a confinement scale. We find a small gluonic correlation length, a = 0.2 fm, in accordance with recent lattice QCD results.
Proton Structure from a Soft-Wall Holographic QCD Model: Mass Spectrum, Form Factors, and Mechanical Properties
采用软墙全息模型，通过胶子凝聚和线性禁闭同时计算质子的质量谱、电磁形状因子和引力形状因子，结果与实验和格点QCD吻合。
We discuss correlations in the hadron production in the $pp$-collision with emphasize on the ridge-like structure origin in the two-particle correlation function. We suggest that this structure can appear due to a rotating nature of the transient state of matter generated in the intermidiate stage of proton collison.
The use of the differential gluon structure function of the proton ${\cal F}(x,Q^{2})$ introduced by Fadin, Kuraev and Lipatov in 1975 is called upon in many applications of small-x QCD. We report here the first determination of ${\cal F}(x,Q^{2})$ from the experimental data on the small-x proton structure function $F_{2p}(x,Q^{2})$. We give convenient parameterizations for ${\cal F}(x,Q^{2})$ based partly on the available DGLAP evolution fits (GRV, CTEQ & MRS) to parton distribution functions and on realistic extrapolations into soft region. We discuss an impact of soft gluons on various obse…
Unveiling the origin of XMM-Newton soft proton flares II. Systematics in the proton spectral analysis
本文研究了XMM-Newton望远镜的软质子耀斑，通过55次MOS和PN观测数据测试转换矩阵，发现望远镜输入端质子能谱的物理模型为幂律谱，并需引入现象学成分以修正低能区矩阵的不精确性。
The Bloch-Nordsieck model for the parton distribution of hadrons in impact parameter space, constructed using soft gluon summation, is investigated in detail. Its dependence upon the infrared structure of the strong coupling constant $α_s$ is discussed, both for finite as well as singular, but integrable, $α_s$. The formalism is applied to the prediction of total proton-proton and proton-antiproton cross-sections, where screening, due to soft gluon emission from the initial valence quarks, becomes evident.
A recently published soft Regge Dipole Pomeron model intended for all $x$ and $Q^2$ is proved to give a good agreement with (non fitted) recent HERA data from ZEUS (SVX95) on the protonstructure function $F_2^p(x,Q^2)$ at low $Q^2$ and low $x$. The model also reproduces (without fit) the recently estimated experimental derivatives ${\partial F_2^p\over\partial\ell n Q^2}$ and ${\partial \ell n F_2^p\over\partial\ell n (1/x)}$ in a wide $x$ and $Q^2$-region.
A new version of a Monte Carlo Program for hadronic multi-particle production is presented. It is based on the two-component Dual Parton Model which includes the dual topological unitarization of soft and hard cross sections. The model treats both soft (low $p_{\perp}$) and hard (minijet, large $p_{\perp}$) processes in a unified and consistent way. The unified description is important at TeV-energies of hadron colliders, where the hard perturbative cross sections of QCD become large and comparable to the total cross sections.
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