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 invariant masses. The cross section and the distributions depend on the value of the cut-off parameter of a form factor correcting amplitudes for off-shellness of $t$-channel pions. Rather large cross section is found for the whole phase space ($σ\sim$ 1-5 $μ$b, including absorption corrections). Relatively large four-pion invariant masses are populated in the considered diffractive mechanism compared to other mechanisms discussed so far in the context of four-pion production. We investigate whether the triple Regge exchange processes could be identified with the existing LHC detectors. We consider the case of ATLAS and ALICE cuts. The ATLAS (or CMS) has better chances to identify the process in the region of large invariant masses $M_{4 π} > 10$ GeV. In the case of the ALICE experiment the considered mechanism competes with other mechanisms (production of $σσ$, $ρρ$ pairs or single resonances) and cannot be unambiguously identified.
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…
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.
High-mass diffractive production of protons on the deuteron target is studied in the next-to-leading order (NLO) of the perturbative QCD in the BFKL approach. The non-trivial part of the NLO contributions coming from the triple interactions of the exchanged reggeons is considered. Analytic formulas are presented and shown to be infrared free and so ready for practical calculation.
In this note we analyse the relation between the triple-pomeron and Good-Walker formalisms for diffractive excitation in DIS and hadronic collisions. In both approaches gap events are interpreted as the shadow of absorption into inelastic channels. We here argue that the two formalisms are just different views of the same phenomenon. We first demonstrate how this relation works in a simple toy model, and then show how the relevant features of the toy model are also realized in real perturbative QCD.
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…
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.
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 …
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 study integrations over light-cone momenta in the high energy effective action of QCD. After a review of the effective action, we arrive on a regularization mechanism from matching with QCD diagrams, which we apply to a re-derivation of the reggeized gluon and of the BFKL-equation. We study consequences of the proposed regularization on the analytic structure of 2->3 and 2->4 production amplitudes in the Multi-Regge-Kinematics. We derive a certain part of the 1-loop corrections to the production vertex and demonstrate that they yield the on-set of corrections demanded by the Steinmann-relat…
The structure constants of twist-two operators with spin $j$ in the BFKL limit $g^2\rightarrow 0, j\rightarrow 1$ but ${g^2\over j-1}\sim 1$ are determined from the calculation of the three-point correlator of twist-two light-ray operators in the triple Regge limit. It is well known that the anomalous dimensions of twist-two operators in this limit are determined by the BFKL intercept. Similarly, the obtained structure constants are determined by an analytic function of three BFKL intercepts.
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 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 …
In this work, the pion-induced $f_1(1285)$ production off a nucleon target is investigated in an effective Lagrangian approach with an interpolating Reggeized treatment in a large range of the pion-beam momentum from threshold up to several tens of GeV. The $s$-channel, $u$-channel, and $t $-channel Born terms are included to calculate production cross sections. An interpolating Reggeized treatment is applied to the $t$ channel, which is found to be important to reproduce the behavior of the existent experimental total cross sections at both low ($\lesssim$ 8 GeV) and high pion-beam momenta ($…
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 revisit the evaluation of the pionic mechanism of the $\bar{u}-\bar{d}$-asymmetry in the proton structure function. Our analysis is based on the extended AGK unitarity relation between contributions of different mechanisms to the inclusive particle production and the total photoabsorption cross-section (i.e. the proton structure function). We reanalyze the role of isovector reggeons in inclusive production of nucleons and Delta isobars in hadronic reactions. We find rather large contribution of reggeon-exchange induced production of Delta isobars. This leaves much less room for the pion-exc…
We present a comparative study of the pion induced production of $K^0 Λ$ and $D^- Λ_c^+$ off the nucleon. A hybrid framework is utilized by combining an effective Lagrangian method with a Regge approach. We consider the $t$-channel process in a plannar diagram by vector-meson Reggeon exchanges and the $u$-channel one in a non-planar diagram by baryon Reggeon exchanges. The present model reproduces the $K^0 Λ$ production data well with a few parameters. Having fixed them, we predict the $D^- Λ_c^+$ production, which turns out to be about $10^4-10^6$ times smaller than the strangeness one, depen…
We evaluate differential distributions for the four-body $p p \to p p π^+ π^-$ reaction which constitutes a irreducible background to three-body processes $p p \to p p M$, where $M$ are a broad resonances in the $π^+ π^-$ channel, e.g. $M=σ, ρ^{0}, f_{0}(980), f_{2}(1275), f_{0}(1500)$. We include both double-diffractive contribution (both pomeron and reggeon exchanges) as well as the pion-pion rescattering contribution. The first process dominates at higher energies and small pion-pion invariant masses while the second becomes important at lower energies and higher pion-pion invariant masses.…
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…
Charge exchange process $π^-p\toπ^0n$ and elastic scatterings $π^\pm p\to π^\pm p$ are investigated within the Regge framework where the relativistic Born amplitude is reggeized for the $t$-channel meson exchange. Charge exchange cross section is featured by the single $ρ$ exchange. Additional correction by Regge cuts, $ρ$-$f_2$ and $ρ$-Pomeron, agree with differential cross sections and new trajectory for the $ρ'(1450)$ exchange is attempted to reproduce polarization data. For the description of elastic scattering data up to pion momentum $P_{\rm Lab}\approx 250$ GeV/c, Pomeron exchange of th…
Calculations of central exclusive diffractive di-pion continuum production are presented in the Regge-eikonal approach. Data from ISR, STAR, CDF and CMS were analyzed and compared with theoretical description. We also consider theoretical predictions for LHC, possible nuances and problems of calculations and prospects of investigations at present and future hadron colliders.
From soft to hard regime in elastic pion-pion scattering above resonances
本文讨论了在中等能量下，pQCD硬双胶子（2G）交换对硬弹性$ππ$散射的贡献中Glauber-Gribov-Landshoff（GGL）分量占主导地位的开始.这种硬$ππ$散射可能是通过$γγ\to π^+ π^-$反应上的终态相互作用产生的，在该反应中，pQCD夸克交换贡献已知是强度不足的。虽然在非相对论近似的GGL振幅被称为是免费的抑制的π形状因子，我们表明，在相对论光锥的方法，它获得了一个残余的，虽然很弱，抑制。此外，z是相同的机制，它没有端点贡献。我们评估的GGL振幅与模型光锥波函数与π电荷形状因子数据一致。基于$NN$和$πN$总截面数据和Regge因子分解估计了弹性$ππ$散射的软贡献，这给出了与先前从$πN \to X N, X Δ$数据的吸收模型分析中推导出的$ππ$总截面一致的$ππ$总截面。我们评估了Regge吸收模型中软振幅的大$|t|$尾。我们发现，当同号$π^\pmπ^\pm$散射时，硬GGL机制在$|t|\gsim$ 3 GeV $^{-2}$处占据主导地位，而在反号$π^\pmπ^\mp$散射时，硬GGL机制在$|t|\lsim$ 4 GeV $^{-2}$处占据主导地位.
In this work, we perform a detailed study of the $τ^-\toπ^-π^0γν$ decay process within the resonance chiral theory. We pay special attention to the triple-product asymmetry in the $τ^-\toπ^-π^0γν$ process. The minimal resonance chiral Lagrangian and the odd-intrinsic parity resonance operators are simultaneously included to calculate the decay amplitudes. Various invariant-mass distributions in the $π^-π^0$, $π^-γ$ and $π^0γ$ systems are studied and they reveal different resonance dynamics. We further predict the intriguing nonzero triple-product asymmetry distributions, which may provide usef…
We investigate, within N=4 SYM, the high energy behavior in the triple Regge limit of a six point correlator of R-currents. Using the leading logarithmic approximation, we sum all diagrams whose color lines fit onto the surface of a sphere. We find three distinct classes of graphs, and one of them contains the triple Pomeron vertex known from QCD. We present results which, within the AdS/CFT correspondence, can be compared with scattering amplitudes in the dual string theory.
The processes of dielectron production in deuteron-proton collisions at intermediate incident deuteron beam energies are analyzed in the spectator model within the one-pion exchange reggeized approach. We focus mainly on the momentum and angle distributions of the proton-spectator and the proton emitted in quasi-free $NN$ processes at small angles in the laboratory frame. It is shown that the inclusion of many channels in quasi-free $NN$ interaction allows us to describe the HADES data quite satisfactorily at incident deuteron kinetic energies of about 2.5 GeV.
