Bing An Li
A new limit of pion form factor at very large $Q^2$ is obtained by using a pion wave function determined from an effective chiral field theory of mesons. It shows that when $Q^2>>(1.8GeV)^2$ the pion form factor reaches the asymptotic limit ${α_s(Q^2)\over Q^2}$.
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New precise data on the low energy electron-positron annihilation into hadrons from Novosibirsk are used to obtain bounds on the elasticity parameter and the difference between the phase of the pion form factor and that of pion pion scattering
The pion form factor at very large $Q^2$ is obtained by using a new pion wave function. It shows that when $Q^2>>(1.8GeV)^2$ the pion form factor reaches the asymptotic limit ${α_s(Q^2)\over Q^2}$
The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pionic strong interactions is used to compute the rho-meson propagator at the two-loop level.
An addtional intrinsic form factors of pion and kaons have been studied.
We investigate restrictions on the hadronic contribution to the muon $(g-2)$ factor and to the pion electromagnetic formfactor from the analytical properties of the pion formfactor and the experimental data of the pion formfactor in the space-like [1] region. The values of the pion formfactor of [1] have been improved (see Table 1) and the values of the pion formfactor have been calculated at 20 additional points (see Table 2).
The claim by Haberzettl (Phys.Rev.Lett.85 (2000) 3576) that the axial form factor of the nucleon cannot be accessed through threshold pion electroproduction is unfounded.
We review the determination of the NLO Brodsky-Lepage-Mackenzie (BLM) renormalization scale for the pion transition form factor. We argue that the prediction for the pion transition form factor is independent of the factorization scale at every order in the strong coupling constant.
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 pion wave function is discussed in the light of the recent CLEO data on the pion gamma transition form factor. It turns out that the wave function is close to the asymptotic form whereas wave functions strongly concentrated in the end-point regions are disfavoured. Consequences for other exclusive quantities, as for instance the pion's electromagnetic form factor, are also discussed.
We propose a perturbative evaluation for the next-to-leading-order (NLO) $O(1/Q^4)$ power correction to the photon-pion transition form factor. The effects of the NLO power correction are analyzed.
We develop a formalism to calculate form factor and charge density distribution of pion in the chiral limit using the holographic dual model of QCD with hard-wall cutoff. We introduce two conjugate pion wave functions and present analytic expressions for these functions and for the pion form factor. They allow to relate such observables as the pion decay constant and the pion charge electric radius to the values of chiral condensate and hard-wall cutoff scale. The evolution of the pion form factor to large values of the momentum transfer is discussed, and results are compared to existing exper…
We calculate electromagnetic pion form factors with an analytic model for $α_{\rm s}(Q^2)$ which is infrared (IR) finite without invoking a ``freezing'' hypothesis. We show that for the asymptotic pion distribution amplitude, $F_{π^{0}γ^{*}γ}$ agrees well with the data, whereas the IR-enhanced hard contribution to $F_π$ and the soft (nonfactorizing) part can jointly account for the data.
The light-front approach is applied to calculate the electromagnetic current for quark-antiquark bound states for the pion. The pion electromagnetic form factor is obtnaide from the "+" and "-" components of the electromagnetic current in the Drell-Yan frame, with different models of the pi-q\bar{q} vertex and the results for the pion electromagnetic form factor are compared with the experimental data up to 10 [GeV/c]^2 and anothers hadronic models. The rotational symmetry propreties of the pion electromagnetic current related with the zero-modes in the light-front are investigate.
We study the pion Distribution Amplitude (πDA) in the context of a nonlocal chiral quark model. The corresponding Lagrangian reproduces the phenomenological values of the pion mass and decay constant, as well as the momentum dependence of the quark propagator obtained in lattice calculations. It is found that the obtained πDA has two symmetric maxima, which arise from the new contributions generated by the nonlocal character of the interactions. This πDA is applied to leading order and next-to-leading order calculations of the pion-photon transition form factor. Implications of the results are…
We review a nonlocal-condensate approach and its application in QCD sum rules for the spacelike electromagnetic pion form factor. It is shown that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor.
An overview on chiral perturbation theory calculations of form factors is presented. The main focus is given on the form factors related to the lightest meson, pion, namely: pion decay constant, pion vector and scalar form factor, radiative pion decay and transition form factor. A pure calculation within the effective theory can be extended using further methods, as resonance chiral theory and leading logarithm calculations.
The behavior of the transition pion form factor for processes γ^*γ-> π^0 and γ^* γ^* -> π^0 at large values of space-like photon momenta is estimated within the nonlocal covariant quark-pion model. It is shown that, in general, the coefficient of the leading asymptotic term depends dynamically on the ratio of the constituent quark mass and the average virtuality of quarks in the vacuum and kinematically on the ratio of photon virtualities. The kinematic dependence of the transition form factor allows us to obtain the relation between the pion light-cone distribution amplitude and the quark-pio…
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 discuss how a charged Higgs propagator would modify the form factor in tau- -> pi- pi0 nu_tau decays.
We study the pion form factor in a broad range of spacelike momentum transfers within the local-duality version of QCD sum rules. We make use of the recently calculated two-loop double spectral density of the $<AVA>$ correlator including O(1) and $O(α_s)$ terms, which allows us to give predictions for the pion form factor and to study the interplay between the nonperturbative and perturbative contributions to the pion form factor without any reference to the pion distribution amplitude. Our results demonstrate the dominance of the nonperturbative contribution to the form factor up to relativel…
The holographic QCD prediction for the pion distribution amplitude (DA) $ϕ_{hol}(u)$ is used to compute the pion spacelike electromagnetic form factor $F_π(Q^2)$ within the QCD light-cone sum rule method. In calculations the pion's renormalon-based model twist-4 DA, as well as the asymptotic twist-4 DA are employed. Obtained theoretical predictions are compared with experimental data and with results of the holographic QCD.
We present main ideas and obtained results of our recent calculations of Coulomb and QCD contribution to the pion diffractive dissociation into two jets.
We study the form factors of the low energy anomalous pion-2-photon and photon-3-pion processes in the nonlocal chiral quark model which incorporates the momentum dependence of the dynamical quark mass and realizes correctly the chiral symmetries. The obtained slope parameter for pion-2-photon is in reasonable agreement with the direct experimental results but smaller than the ones invoking vector meson dominance. Our result for the photon-3-pion form factor interpolates between the two extremes of theoretical approaches, with the largest one provided by the vector meson dominance and the smal…
We provide a novel approach to calculate the gravitational form factor of pion under the ladder approximation of the Bethe-Salpeter equation, with contact interactions. Central to this approach is a symmetry-preserving treatment of the dressed $ππ$ amplitude, which shows explicitly the contributions from intrinsic quarks and bound states, the latter being necessary to produce the $D$-term of pion in the soft-pion limit. The approach we provide in this work can be applied to many processes of physical significance.
We derive the lowest-order $q\bar q$ valence light-front wave function for the pion with Lz=0 and |Lz|=1, which reproduces its valence parton distribution and the electromagnetic form factor consistent with data.
This work presents the results of our analysis of the accuracy of the pion form factor derived from the local-duality version of QCD sum rules.
The pion electromagnetic form factor is calculated within the QCD light-cone sum rule method and using a renormalon model for the higher twist distribution amplitudes (DAs). The theoretical predictions are compared with the experimental data and constraints on the pion leading and twist-4 DAs are extracted. An upper bound on the twist-4 contribution to the form factor and estimates of effects due to higher conformal spins in the pion twist-4 DAs are obtained.
We present an analysis of QCD sum rules for pion form factor in next-to-leading order of perturbation theory for the case of pseudoscalar pion currents. The essential instanton contribution is reanalysed with account for present more accurate values of parameters entering Single Instanton Approximation (SIA). The theoretical curve obtained for Q^2 dependence of pion form factor is in a good agreement with existing experimental data. To calculate NLO corrections for double spectral densities we developed an effective computational technic. The details of the method together with the results for…
The Non-perturbative term for the Axial-vector Form Factor of Pion Decay
利用赝矢量耦合π-核子相互作用的非微扰项计算π⁺→γ+e⁺+ν_e衰变的轴矢量形状因子，自能近似为最低阶常数，该参数对改善形状因子值及先前研究中的矢量形状因子有重要意义。
Re-examination of the Perturbative Pion Form Factor with Sudakov Suppression
重新研究了具有Sudakov抑制的微扰π介子形状因子。考虑到规则$Q^2$区域中的多胶子交换，我们建议将运行耦合常数冻结在$α_s(t=\sqrt{<{\bf k}_{T}^{2}>})$，而$\sqrt{<{\bf k}_{T}^{2}>}$是平均横动量，它可以由π介子波函数确定。此外，我们还修正了以前关于Sudakov抑制因子的计算，该因子在微扰预言π介子形状因子中起着重要作用。
Electromagnetic pion form factor at finite temperature
利用量子色动力学有限能量求和规则，得到了π介子在类空区和有限温度下的电磁形状因子$F_π(Q^{2},T)$.形状因子随T的增加而减小，并在某一临界温度消失，此时π介子半径发散。这种发散可以解释为夸克解除禁闭的信号。
The electromagnetic pion form-factor is calculated in a Bethe-Salpeter approach which accounts for pion rescattering. In the scattering kernel the pion-pion contact interaction from lowest-order chiral perturbation theory is considered together with an optional vector meson in the s-channel. Correspondingly the virtual photon couples to a two-pion state and optionally to the vector meson. It is shown that for reasonable ranges of input parameters the experimentally observed pion form-factor cannot be described by the iterated pion-pion contact interaction alone, i.e. without an elementary vect…
We calculate the time-like pion electromagnetic form factor in the $k_T$ factorization formalism with the inclusion of the next-to-leading-order(NLO) corrections to the leading-twist and sub-leading-twist contributions. It's found that the total NLO correction can enhance (reduce) the magnitude (strong phase) of the leading order form factor by $20\% - 30\%$ ( $< 15^o$) in the considered invariant mass squared $q^2 > 5$ GeV$^2$, and the NLO twist-3 correction play the key role to narrow the gap between the pQCD predictions and the measured values for the time-like pion electromagnetic form fac…
The asymptotics of pion charge form factor is obtained in the framework of relativistic Hamiltonian dynamics for the infinite value limit of momentum transfer and zero value limit of constituent--quark mass. It is shown that this asymptotics is the same as given by the perturbative QCD and is determined by relativistic kinematics only, being independent on the constituent quarks interaction in pion.
Recent BaBaR data on the pion transition form factor, whose Q^2 dependence is much steeper then predicted by asymptotic Quantum Chromodynamics (QCD), have caused a renewed interest in its theoretical description. We present here a formalism based on a model independent low energy description and a high energy description based on QCD, which match at a scale Q_0. The high energy description incorporates a flat pion distribution amplitude, phi(x)=1, at the matching scale Q_0 and QCD evolution from Q_0 to Q>Q_0. The flat pion distribution is connected, through soft pion theorems and chiral symmet…
Consequence of the Wigner Rotation: Perturbative QCD Analysis of the Pion Form Factor
在QCD计算π介子形状因子时，我们分析了由于维格纳旋转而自然包含在π介子光锥波函数中的高螺旋度（$λ_{1}+λ_{1}=\pm 1$）分量的微扰贡献.指出这些贡献除了利用具有分布振幅渐近形式的因子分解公式计算出的普通螺旋度分量的微扰贡献外，还可以提供拟合π形状因子数据所需的另一部分贡献.我们提出了一种方法来测试更高的螺旋状态的贡献。
We show that a recent claim (H.Haberzettl, Phys. Rev. Lett. 85 (2000) 3576) that one cannot extract the nucleon weak axial form factor G_A (t) from charged pion threshold electroproduction is incorrect. Thus previous calculations remain valid and threshold charged pion electroproduction experiments can indeed be used to determine G_A (t), and they should certainly be pursued.
The role of the reaction e+e- --> e+ e-pi+pi- in the pion form factor measurements via radiative return method without photon tagging is studied in detail. The analysis is based on the developed Monte Carlo program EKHARA, which ingredients are also presented.
The Vector Pion form factor below 1 GeV is analyzed using experimental data on its modulus, the P-wave pion pion phase shifts and dispersion relation. It is found that causality is satisfied. Using dispersion relation, terms proportional to s squared and s cubed are calculated using the experimental data, where s is the momentum transfer. They are much larger than the one-loop and two-loop Chiral Perturbation Theory calculations. Unitarized model calculations agree very well with dispersion relation results.
New precise experimental information on $σ_{tot}(e^+e^- \to π^+ π^-)$ is transferred into the space-like region, by taking advantage of the analyticity. As a result a rigorous pion electromagnetic form factor behavior is obtained. The latter with some existing model predictions is compared.
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.
The pion-photon transition form factor is studied by employing two types of Sum Rules: Light Cone Sum Rules (LCSR) and Anomaly Sum Rules (ASR). By comparing the predictions for the pion-photon transition form factor, obtained from these two approaches, the applicability limit of the LCSRs at low momenta is determined. Reciprocally, the ASR threshold dependence on the momentum was extracted using our LCSR-based method in combination with two different types of pion distribution amplitudes and found that at higher Q2 it approaches a constant.
The analysis of the $πγ$ transition form factor provides severe constraints on the pion's wave function. This information is used to examine charmonium decays into two pions critically. It will be argued that the standard perturbative QCD analysis of these reactions fails, i.e. the need for additional contributions can convincingly be demonstrated. Colour-octet admixtures to the charmonium states are proposed as a possible dynamical mechanisms to solve the puzzle. Consequences of the $πγ$ analysis for the electromagnetic form factor of the pion are also discussed.
Light-cone sum rules have proved to be very useful in calculating hadronic matrix elements for exclusive processes. I present recent applications of this method to the pion electromagnetic form factor and to the form factors of $γ^* ρ\to π$ and $γ^*γ\to π^0$ transitions.
This letter is an investigation of the pion form factor utilizing recently developed effective field theory techniques. The primary results reported are: Both the transition and electromagnetic form factors are corrected at order $Λ/Q$. However, these corrections only arise due to time ordered products which are sensitive to soft components of the pion. The usual higher twist wave function corrections contribute only at order $Λ^2/Q^2$, when the quark mass vanishes. In the case of the electromagnetic form factor the $Λ/Q$ power correction is enhanced by a power of $1/α_s(Q)$ relative to the le…
Gravitational form factors of pion in a nonlocal quark model
该研究通过等效原理在非定域夸克模型中引入引力场，计算了π介子的引力形状因子，发现气泡图贡献显著。
We discuss the soft contribution to the elastic pion form factor with the mass evolution from current to constituent quark being taken into account in a light-front quark model(LFQM).
From the properties of analyticity and unitarity it has been recently obtained an exponentiated expression for the pion form factor. In this work I show the validity of this expression comparing its order p^6 term with the one exactly calculated in ChPT.
We study a model-independent parameterization of the vector pion form factor that arises from the constraints of analyticity and unitarity. Our description should be suitable up to s^(1/2) ~ 1.2 GeV and allows a model-independent determination of the mass of the rho(770) resonance. We analyse the experimental data on tau^- -> pion^- pion^0 nu_tau and e^+ e^- -> pion^+ pion^- in this framework, and its consequences on the low-energy observables worked out by chiral perturbation theory. An evaluation of the two pion contribution to the anomalous magnetic moment of the muon, a_{mu}, and to the fi…
Neutral and charged pion Form Factors in the intermediate-energy region from double-dilaton HQCD model
基于双稀顿Holographic QCD模型计算中性与带电π介子形式因子，揭示中等能量区域非微扰强相互作用的影响，探讨等旋破缺效应。
Light constituent quark masses and the corresponding dynamical quark masses are determined by data, the quark-level linear sigma model, and infrared QCD. This allows to define effective nonstrange and strange current quark masses, which reproduce the experimental pion and kaon masses very accurately, by simple additivity. In contrast, the usual nonstrange and strange current quarks employed by the Particle Data Group and Chiral Perturbation Theory do not allow a straightforward quantitative explanation of the pion and kaon masses.
We extract constraints on the pion distribution amplitude from available data on the pion-photon transition form factor in the framework of light-cone sum rules. A pronounced discrepancy $(2.7-3)σ$ between the Gegenbauer expansion coefficients extracted from the CELLO, CLEO, and Belle experimental data relative to those from BaBar is found. Predictions for the pion-photon transition form factor are presented by employing a pion distribution amplitude obtained long ago from QCD sum rules with nonlocal condensates. These predictions comply with the Belle data but disagree with those of BaBar bey…
Quark structure of the pion and pion form factor
我们考虑在低和中等高动量转移区域的π介子结构：在低$Q^2$，π介子被视为一个组成夸克的复合系统;在中等高动量转移，$Q^2=10\div25\;GeV^2$，π介子\ff内计算微扰QCD考虑单胶子硬交换。利用π介子\ff在$Q^2<3\;GeV^2$的数据和π介子轴向矢量衰变常数，我们重建了软区和中间区的π介子\wf。这个波函数与一个胶子硬散射振幅相结合，允许在硬区$Q^2=10\div25\;GeV^2$的π \ff的计算。重建的π介子\wf的一个具体特点是准区字符的$q\bar q$ -激发。根据得到的π介子\wf和π介子的深度非弹性散射数据，确定了组分夸克中的价夸克分布。
It has been pointed out that the recent BaBar data on the pi gamma^* -> gamma transition form factor F_{pi gamma}(Q^2) at low (high) momentum transfer squared Q^2 indicate an asymptotic (flat) pion distribution amplitude. These seemingly contradictory observations can be reconciled in the k_T factorization theorem: the increase of the measured Q^2F_{pi gamma}(Q^2) for Q^2 > 10 GeV^2 is explained by convoluting a k_T dependent hard kernel with a flat pion distribution amplitude, k_T being a parton transverse momentum. The low Q^2 data are accommodated by including the resummation of alpha_s ln^…
We discuss a constraint of conformal symmetry in the analysis of the pion form factor. The usual power-law behavior of the form factor obtained in the perturbative QCD analysis can also be attained by taking negligible quark masses in the nonperturbative quark model analysis, confirming the recent AdS/CFT correspondence. We analyze the transition from soft to hard contributions in the pion form factor considering a momentum-dependent dynamical quark mass from a nonnegligible constituent quark mass at low momentum region to a negligible current quark mass at high momentum region. We find a corr…
We calculate the transition form factor of the neutral pion where one photon is virtual and another photon is real in the model where the light constituent quark mass and the quark-pion vertex are taken to be momentum independent. Radiative corrections to the lowest order triangle quark Feynman amplitude are calculated. The resummation of the lowest radiative corrections to the virtual photon vertex is done by applying the Sudakov exponential hypothesis. Using fitting parameters, the quark mass and the strong coupling constant, the results on the pion transition form factor are compared with e…
In this paper we calculate the power corrections to the pion transition form factor within the framework of perturbative QCD approach on the basis of $k_T$ factorization. The power suppressed contributions from higher twist pion wave functions and the hadronic structure of photon are investigated. We find that there exists strong cancellation between the two kinds contributions, thus the total power corrections considered currently are very small, and the prediction of the leading power contribution with joint resummation improved perturbative QCD approach is almost unchanged. This result conf…
It is shown that the data on the pion charge form factor admit the possibility for a substantial sea-quark components in the pion wave function. If the charge form factor is calculated with instant form kinematics in a constituent quark model that is extended to include explicit $(q\bar q)^2$ components in the pion wave function, that component will give the dominant contribution to the calculated $π^+$ charge form factor at large values of momentum transfer. The present experimental values $Q^2$ can be described well with $(q\bar q)^2$ component admixtures of up to 50%. The sensitivity of the…
We consider a model with $ρππ$, $ρKK$, and gauge-invariant $ργ$ couplings and obtain the pion form factor $F_π$ at timelike momentum transfers by resummation of pion and kaon loops. We use a dispersion representation for the loop diagrams and analyse ambiguities related to subtraction constants. The resulting representation for $F_π$ is shown to have the form of the conventional vector meson dominance formula with one important distinction - the effective $ρ$-meson decay constant $f^{\rm eff}_ρ$ turns out to depend on the momentum transfer. For the electromagnetic pion form factor we include i…
We suggest to probe the pion light-cone distribution amplitude, applying a dispersion relation for the pion electromagnetic form factor. Instead of the standard dispersion relation, we use the equation between the spacelike form factor $F_π(Q^2)$ and the integrated modulus of the timelike form factor. For $F_π(Q^2)$, the QCD light-cone sum rule with a dominant twist-2 term is used. Adopting for the pion twist-2 distribution amplitude a certain combination of the first few Gegenbauer polynomials, it is possible to fit their coefficients $a_{2,4,6,...}$ (Gegenbauer moments) from this equation, e…
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