A. Radyushkin
I discuss the subject of powerlike asymptotic behavior of hadronic form factors in pre-QCD analyses of soft (Feynman/Drell-Yan) and hard (West) mechanisms, and also recent derivation of $1/Q^2$ asymptotics of meson form factors in AdS/QCD. At the end, I briefly comment on "light-front holography" ansatz.
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Using global fits of valence u and d quark parton distributions and data on quark and nucleon form factors in the Euclidean region, we derive a light-front quark model for the nucleon structure consistent with quark counting rules.
We derive the general counting rules for a quantum effective field theory (EFT) in $\mathsf{d}$ dimensions. The rules are valid for strongly and weakly coupled theories, and predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of cross sections is controlled by the $Λ$ power counting of EFT, not by chiral counting, even for chiral perturbation theory ($χ$PT). The relation between $Λ$ and $f$ is generalized to $\mathsf{d}$ dimensions. We show that t…
Instead of using a simple reggeon-exchange model, we provide a model-independent estimate of high-energy contribution to the Adler-Weisberger sum-rule. Results and conclusions of the paper remain unchanged.
We propose a phenomenological light-front wave function for hadrons with arbitrary twist-dimension (mesons, baryons and multiquark states), which gives the correct scaling behavior of structure functions (parton distributions) and form factors for pions and nucleons. For other hadronic states the proposed wave function produces form factors consistent with quark counting rules, and gives predictions for structure functions (parton distributions). As an application we build a light-front quark model for nucleons based on the proposed wave function.
By studying $ππ$ scattering amplitudes in the large $N_c$ limit, we clarify the $N_c$ dependence of the $S$ matrix pole position. It is demonstrated that analyticity and the $N_c$ counting rule exclude the existence of $S$ matrix poles with ${\cal M}, Γ\sim O(1)$. Especially the properties of $σ$ and $f_0(980)$ with respect to the $1/N_c$ expansion are discussed. We point out that in general tetra-quark resonances do not exist.
In a recent paper [1] a master formula has been presented for the power counting of a general effective field theory. We first show that this master formula follows immediately from the concept of chiral dimensions (loop counting), together with standard dimensional analysis. Subsequently, [1] has disputed the relevance of chiral counting for chiral Lagrangians, and in particular for the electroweak chiral Lagrangian including a light Higgs boson. As an alternative, a power counting based on `primary dimensions' has been proposed. The difficulties encountered with this scheme led the authors t…
In models with extra dimensions, branes have been usually treated as solid bodies though they are prohibited by the relativity. In the previous letter, we proposed a method of taking account of brane fluctuation by introducing Nambu-Goldstone bosons, and prove that when a tension of the brane is small, the interaction between boundary fields and Kaluza-Klein modes is suppressed exponentially. In this letter, we further investigate this suppression in more generic configuration, and obtain three counting rules, ``AND'', ``OR'' and ``STACK'' rules, depending on the softness of branes and the cha…
The constituent counting rules, i.e., the scaling behavior of amplitudes (in terms of the number of fundamental constituents) for exclusive processes when high energy scales are present, have been known for decades, and have been borne out in a number of experiments. Such scaling would be sensitive, in particular, to possible exotic multiquark content. Here we examine how one may use the rules to test for pentaquarks in electroproduction, or for tetraquarks in e^+ e^- annihilation. An interesting new type of scaling (separate Mandelstam s and t behavior) arises in the forward scattering direct…
QCD constituent counting rules define the scaling behavior of exclusive hadronic scattering and electromagnetic scattering amplitudes at high momentum transfer in terms of the total number of fundamental constituents in the initial and final states participating in the hard subprocess. The scaling laws reflect the twist of the leading Fock state for each hadron and hence the leading operator that creates the composite state from the vacuum. Thus, the constituent counting scaling laws can be used to identify the twist of exotic hadronic candidates such as tetraquarks and pentaquarks. Effective …
The pole counting rule is a powerful and model-independent method to distinguish a confining state from a hadronic molecule. It has been applied to the explorations of $X(6900)$, $X_1(2900)$ as well as $Z_c(3900)$, $X(3872)$, $X(4660)$, etc.. For $X(6900)$, both a confining state and a molecular state are not excluded, because lacking of enough data. For $X_1(2900)$, the analysis shows that it should be a $\bar{D}_1 K$ molecule, with $J^P=1^-$ and an iso-singlet interpretation is much more favorable. Finally, it is noted that almost all XYZ particles with exotic quantum numbers can be interpre…
We introduce a systematic way to write down the Fock components of a hadronic light-cone wave function with $n$ partons and orbital angular momentum projection $l_z$. We show that the wave function amplitude $ψ_n(x_i,k_{i\perp},l_{zi})$ has a leading behavior $1/(k^2_\perp)^{[n+|l_z|+{\rm min}(n'+|l_z'|)]/2-1}$ when all parton transverse momenta are uniformly large, where $n'$ and $l_z'$ are the number of partons and orbital angular momentum projection, respectively, of an amplitude that mixes under renormalization. The result can be used as a constraint in modeling the hadronic light-cone wav…
We present rules for determining the number of physical parameters in models with exact flavor symmetries. In such models the total number of parameters (physical and unphysical) needed to described a matrix is less than in a model without the symmetries. Several toy examples are studied in order to demonstrate the rules. The use of global symmetries in studying the minimally supersymmetric standard model (MSSM) is examined.
At high energies, the cross section of a hard exclusive process at finite scattering angle falls off as a negative power of the center-of-mass energy $\sqrt{s}$. If all involved quark-gluon compositions undergo hard momentum transfers, the scaling of the fall-off is determined by the underlying valence structures of the initial and final states, known as the constituent counting rules. It was argued in the literature that the counting rules are a powerful tool to determine the valence degrees of freedom inside multiquark states when applied to exclusive production processes. However, we demons…
The counting rule for Nambu-Goldstone modes is discussed using Mori's projection operator method in nonrelativistic systems at zero and finite temperatures. We show that the number of Nambu-Goldstone modes is equal to the number of broken charges, Q_a, minus half the rank of the expectation value of [Q_a,Q_b].
The exclusive processes are considered, where a point-like source of heavy quark-antiquark pairs $Q \bar Q$, e.g. their electromagnetic current, produces a pair consisting of a heavy quarkoniumlike exotic meson (tetraquark) or baryon (pentaquark) and a light meson or an antibaryon. For a sufficiently large mass of the heavy quark $m_Q$ there is a range of the energy $E$ above the $Q \bar Q$ threshold, where $E \ll m_Q$ and still the energy is large compared to the strong interaction scale, $E \gg Λ_{QCD}$. It is shown that in this energy range, where the heavy quarks are nonrelelativistic, a s…
We study the large-Q^2 behavior of the meson form factor F_M (Q^2) constructed using the holographic light-front wave functions proposed recently by Brodsky and de Teramond. We show that this model can be also obtained within the Migdal's regularization approach (``meromorphization''), if one applies it to 3-point function for scalar currents made of scalar quarks. We found that the asymptotic 1/Q^2 behavior of F_M (Q^2) is generated by soft Feynman mechanism rather than by short distance dynamics, which causes very late onset of the 1/Q^2 asymptotic behavior. Using meromorphization for spin-1…
We have studied the energy dependence of the $pp$ elastic scattering data and the pion-photoproduction data at 90$^\circ$ c.m. angle in light of the new generalized counting rule derived for exclusive processes. We show that by including the helicity flipping amplitudes (with energy dependence given by the generalized counting rule) and their interference with the Landshoff amplitude, we are able to reproduce the energy dependence of all cross-section and spin-correlation (A$_{NN}$) data available above the resonance region. The pion-photoproduction data can also be described by this approach,…
A mechanism of the power-counting breaking in chiral perturbation theory
本文针对πK散射𝒪(p⁶)阶修正异常大的手征展开收敛性问题，分析发现双圈等低对称性图违反幂次计数规则，大K介子质量有次要贡献，未来需重视这类多圈低对称图。
Verifying the existence of bound states of gluons and distinguishing them from conventional quark-antiquark, hybrid or tetraquark states has remained a key problem in QCD. We show that QCD counting rules for the power-law fall-off of production cross sections at high momentum transfer can be used to distinguish gluonium states from conventional hadrons. The valence two-gluon contribution to a 0^+ gluonium bound state has L=0 and thus twist (dimension minus spin of their minimum interpolating operators) tau=2. The competing twist assignments for scalar f_0 mesons have twist tau = 3 for the vale…
The large-$N_c$ consistency conditions for axial vector and isovector magnetic couplings of pions to baryons are discussed from the point of view of low-energy current-algebra sum rules (Adler-Weisberger, Cabibbo-Radicati). In particular, we show how the result that ratios of axial vector and isovector magnetic coupling constants get corrections only at the order $1/N_c^2$ follows from the $N_c$-counting of appropriate cross sections. This counting is performed using various approaches at the quark and hadronic level. Other implications of our method are also presented.
High-Energy Fixed-Angle Meson Scattering and the Constituent Counting Rule in Holographic QCD
本文在自底向上全息QCD模型中推广Polchinski-Strassler方法，构造π介子和ρ介子高能固定角散射振幅，结果符合QCD组分计数规则，并给出计算散射角依赖性的新途径。
The empirical identification of bound states of gluons has remained a central goal of hadron spectroscopy. We suggest an experimentally challenging, but model--independent way to assess which zero charge, isospin-zero mesons have a large gluonium light-front wavefunction component in the quark and gluon Fock space of QCD. Our method exploits QCD counting rules which relate the power-law fall-off of production amplitudes at high momentum transfer to the meson's twist (dimension minus spin of its minimum interpolating operators). Scalar $0^+$ glueballs composed of two valence gluons with zero in…
We show how deviations from the dimensional scaling laws for exclusive processes may be related to a breakdown in the locality of quark-hadron duality. The essential principles are illustrated in a pedagogic model of a composite system with two spinless charged constituents, for which a dual picture for the low-energy resonance phenomena and high-energy scaling behavior can be established. We introduce the concept of "restricted locality" of quark-hadron duality and show how this results in deviations from the pQCD quark counting rules above the resonance region. In particular it can be a poss…
I briefly review how nonrelativistic effective field theories solve old puzzles and open problems in heavy quarkonium physics.
In nuclear chiral perturbation theory (ChPT), an operator is defined in a space with a cutoff which may be varied within a certain range. The operator runs as a result of the variation of the cutoff [renormalization group (RG) running]. In order for ChPT to be useful, the operator should run in a way consistent with the counting rule; that is, the running of chiral counter terms have to be of natural size. We vary the cutoff using the Wilsonian renormalization group (WRG) equation, and examine this consistency. As an example, we study the s-wave pion production operator for NN\to d pi, derived…
The 1/Nc expansion is one of the very few methods we have for generating a systematic expansion of QCD at the energy scale relevant to hadron structure. The present formulation of this theory relies on the double-line notation for calculating the leading order of a diagram in the 1/Nc expansion, where the local SU(Nc) gauge symmetry is substituted by a U(Nc) symmetry and the associated U(1) ghost field is ignored. In the current work we demonstrate the insufficiency of this formulation for describing certain non-planar diagrams. We derive a more complete set of Feynman rules that include the U…
We clarify the origin and cancellation of contact terms in the weak annihilation amplitudes contributing to $B\to V γ$. It is demonstrated that the photon emission from the final-state quarks vanishes in the chiral limit of massless quarks. The contact terms in the QCD light-cone sum rule evaluation of the weak annihilation amplitudes are also discussed.
We construct the two- and three-nucleon potential based on the most general chiral effective pion-nucleon Lagrangian using the method of unitary transformations. For that, we develop a power counting scheme consistent with this projection formalism. In contrast to previous results obtained in old-fashioned time-ordered perturbation theory, the method employed leads to energy-independent potentials. We discuss in detail the similarities and differences to the existing chiral nucleon-nucleon potentials. We also show that to leading order in the power counting, the three-nucleon forces vanish len…
We hypothesize that the correct power counting for charmonia is in the parameter Lambda_QCD/m_c, but is not based purely on dimensional analysis (as is HQET). This power counting leads to predictions which differ from those resulting from the usual velocity power counting rules of NRQCD. In particular, we show that while Lambda_QCD/m_c power counting preserves the empirically verified predictions of spin symmetry in decays, it also leads to new predictions which include: A hierarchy between spin singlet and triplet octet matrix elements in the J/psi system. A quenching of the net polarization …
We analyze the CLAS data on the photoproduction of hyperon resonances, as well as the available data for the ground state $Λ$ and $Σ^{0}$ of the CLAS and SLAC-E84 collaborations, by considering constituent-counting rule suggested by perturbative QCD. The counting rule emerges as a scaling behavior of cross sections in hard exclusive reactions with large scattering angles, and it enables us to determine the number of elementary constituents inside hadrons. Therefore, it could be used as a new method for identifying internal constituents of exotic-hadron candidates. From the analyses of the $γ\,…
A comprehensive study on the nature of the $Z_c(3900)$ resonant structure is carried out in this work. By constructing the pertinent effective Lagrangians and considering the important final-state-interaction effects, we first give a unified description to all the relevant experimental data available, including the $J/ψπ$ and $ππ$ invariant mass distributions from the $e^+e^-\to J/ψππ$ process, the $h_cπ$ distribution from $e^+e^-\to h_cππ$ and also the $D\bar D^{*}$ spectrum in the $e^+e^-\to D\bar D^{*}π$ process. After fitting the unknown parameters to the previous data, we search the pole …
The constituent counting ruling (CCR) has been found to hold for numerous hard, exclusive processes. It predicts the differential cross section at high energies and fixed $\cos θ_{c.m.}$ should follow $\frac{d σ}{dt} \sim \frac{1}{s^{n-2}}$, where $n$ is the minimal number of constituents involved in the reaction. Here we provide an in-depth analysis of the reaction $γp \rightarrow ωp$ at $θ_{c.m.}\sim 90^\circ$ using CLAS data with an energy range of $s = 5 - 8$ GeV$^2$, where the CCR has been shown to work in other reactions. We argue for a stringent method to select data to test the CCR and…
We propose to use hard exclusive production of an exotic hadron for finding its internal quark-gluon configuration by the constituent-counting rule in perturbative QCD. In particular, the cross section for the exclusive process $π^- + p \to K^0 + Λ(1405)$ is estimated at the scattering angle $θ=90^\circ$ in the center-of-mass frame by using current experimental data. In comparison, the cross section for the ground-state $Λ$ production $π^- + p \to K^0 + Λ$ is also shown. We suggest that the internal quark configuration of $Λ(1405)$ should be determined by the asymptotic scaling behavior of the…
We explain a method to find internal quark configurations of exotic hadron candidates by using the constituent counting rule. The counting rule was theoretically predicted in perturbative QCD for hard exclusive hadron reactions, and it has been tested in experiments for stable hadrons including compound systems of hadrons such as the deuteron, $^3$H, and $^3$He. It indicates that the cross section scales as $dσ/dt \sim 1/s^{n-2}$, where $s$ is the center-of-mass energy squared and $n$ is the total number of constituents. We apply this method for finding internal configurations of exotic hadron…
A recently proposed scheme is used to saturate the spectral side of the QCD sum rules derived from the thermal, two-point correlation functions of the vector and the axial-vector currents. At low temperature, it constructs the spectral representation from all the one-loop Feynman diagrams for the two-point functions. The old saturation scheme treats incorrectly some of these contributions. We end up with the familiar QCD sum rules obtained from the difference of the two corresponding vacuum correlation functions. The possibility of obtaining new sum rules in other media is discussed.
1. Introduction 2. The Gross-Neveu Model 3. QCD 3.1 N-Counting Rules for Diagrams 3.1.1 U(1) Ghosts 3.2 The 't Hooft Model 3.3 $N$-Counting Rules for Correlation Functions 3.4 The Master Field 4. Meson Phenomenology 4.1 Zweig's Rule 4.2 Exotics 4.3 Chiral Perturbation Theory 4.4 Non-leptonic K Decay 4.5 $K-\bar K$ mixing 4.6 Axial U(1) and the eta' Mass 4.7 Resonances and 1/N 5 Baryons 5.1 N-Counting Rules for Baryons 5.2 The Non-Relativistic Quark Model 6 Spin-Flavor Symmetry for Baryons 6.1 Consistency Conditions 6.2 1/N Corrections 6.3 Solution of Consistency Conditions 7 Masses with SU(3) …
Analysis of the hidden-charm-hidden-strange tetraquark mass spectrum via the QCD sum rules
本文构造双夸克-反双夸克四夸克流，用传统QCD求和规则并计入轻味SU(3)破缺，系统计算隐粲隐奇异四夸克质量谱，重新辨认多个X态及LHCb新态。
In the conventional approach to the $1/N_c$ expansion, electroweak interactions are switched off and large $N_c$ QCD is treated in isolation. We study the self-consistency of taking the large $N_c$ limit in the presence of electroweak interaction. If the electroweak coupling constants are held constant, the large $N_c$ counting rules are violated by processes involving internal photon or weak boson lines. Anomaly cancellations, however, fix the ratio of electric charges of different fermions. This allows a self-consistent way to scale down the electronic charge $e$ in the large $N_c$ limit and…
When global continuous symmetries are spontaneously broken, there appear gapless collective excitations called Nambu-Goldstone modes (NGMs) that govern the low-energy property of the system. The application of this famous theorem ranges from high-energy, particle physics to condensed matter and atomic physics. When a symmetry breaking occurs in systems that lack the Lorentz invariance to start with, as is usually the case in condensed matter systems, the number of resulting NGMs can be fewer than that of broken symmetry generators, and the dispersion of NGMs is not necessarily linear. In this …
We revisit the formulation of the principle of minimal flavor violation (MFV) in the minimal supersymmetric extension of the standard model, both at moderate and large tan(beta), and with or without new CP-violating phases. We introduce a counting rule which keeps track of the highly hierarchical structure of the Yukawa matrices. In this manner, we are able to control systematically which terms can be discarded in the soft SUSY breaking part of the Lagrangian. We argue that for the implementation of this counting rule, it is convenient to introduce a new basis of matrices in which both the squ…
We present a simple method to count the number of hadronic form factors based on the partial wave formalism and crossing symmetry. In particular, we show that the number of independent nucleon form factors of spin-n, twist-2 operators (the vector current and energy-momentum tensor being special examples) is n+1. These generalized form factors define the generalized (off-forward) parton distributions that have been studied extensively in the recent literature. In proving this result, we also show how the J^{PC} rules for onium states arise in the helicity formalism.
An explicit expression of the generating functional of two-flavor low-energy QCD with external sources in the presence of non-vanishing nucleon densities has been derived recently [1]. Within this approach we derive power counting rules for the calculation of in-medium pion properties. We develop the so-called standard rules for residual nucleon energies of the order of the pion mass and a modified scheme (non-standard counting) for vanishing residual nucleon energies. We also establish the different scales for the range of applicability of this perturbative expansion, which are \sqrt{6}πf_π\s…
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