Light-cone Expansion Research Articles

An improved calculation of the D(s)∗D(s)V\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{(s)}^*D_{(s)}V$$\\end{document} and B(s)∗B(s)V\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)}^*B_{(s)}V$$\\end{document} couplings from light-cone sum rules

We present an improved calculation of the D(s)∗D(s)V\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{(s)}^*D_{(s)}V$$\\end{document} and B(s)∗B(s)V\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)}^*B_{(s)}V$$\\end{document} coupling constants, where V denotes ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document}, K∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K^*$$\\end{document}, ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}, and ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons. These couplings govern the long-distance quantum chromodynamics (QCD) in interactions between heavy pseudo-scalar/vector mesons and light vector mesons. Our analysis is conducted within the framework of QCD light-cone sum rules (LCSRs) by utilizing the light-cone distribution amplitudes (LCDAs) of light vector mesons. By systematically incorporating the subleading power corrections and higher-twist contributions at the leading order (LO) and including the next-to-leading order (NLO) corrections at leading power, we achieve enhanced accuracy in the light-cone operator product expansion (OPE) for the underlying correlation function. In assessing the reliability of the established LCSRs, we consider uncertainties arising from the choice of the quark–hadron duality region in the double dispersion relation. Building upon these improvements, we accomplish an optimized computation and analysis for the strong coupling constants gH∗HV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{H^*HV}$$\\end{document} which are used to extract the effective coupling λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} in the heavy meson chiral perturbation theory (HMχ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}PT). Furthermore, we investigate the SU(3) flavor symmetry-breaking effects in detail and compare our sum rule calculations with previous studies in an exploratory way.

Non-factorisable effects in the decays {overline{B}}_s^0to {D}_s^{+}{pi}^{-} and {overline{B}}^0to {D}^{+}{K}^{-} from LCSR

In light of the current discrepancies between the recent predictions based on QCD factorisation (QCDF) and the experimental data for several non-leptonic colour-allowed two-body B-meson decays, we obtain new determinations of the non-factorisable soft-gluon contribution to the decays {overline{B}}_s^0to {D}_s^{+}{pi}^{-} and {overline{B}}^0to {D}^{+}{K}^{-} , using the framework of light-cone sum rule (LCSR), with a suitable three-point correlation function and B-meson light-cone distribution amplitudes. In particular, we discuss the problem associated with a double light-cone (LC) expansion of the correlator, and motivate future determinations of the three-particle B-meson matrix element with the gluon and the spectator quark aligned along different light-cone directions. Performing a LC-local operator product expansion of the correlation function, we find, for both modes considered, the non-factorisable part of the amplitude to be sizeable and positive, however, with very large systematic uncertainties. Furthermore, we also determine for the first time, using LCSR, the factorisable amplitudes at LO-QCD, and thus the corresponding branching fractions. Our predictions are in agreement with the experimental data and consistent with the results based on QCDF, although again within very large uncertainties. In this respect, we provide a rich outlook for future improvements and investigations.

Axial-vector transition form factors and e+e− → f1π+π−

We study the transition form factors (TFFs) of axial-vector mesons in the context of currently available experimental data, including new constraints from e+e− → f1(1285)π+π− that imply stringent limits on the high-energy behavior and, for the first time, allow us to provide an unambiguous determination of the couplings corresponding to the two antisymmetric TFFs. We discuss how these constraints can be implemented in a vector-meson-dominance picture, and, in combination with contributions from the light-cone expansion, construct TFFs as input for the evaluation of axial-vector contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

Factorized lightcone expansion of conformal blocks

We present a factorized decomposition of 4-point scalar conformal blocks near the lightcone, which applies to arbitrary intermediate spin and general spacetime dimensions. Then we discuss the systematic expansion in large intermediate spin and the resummations of the large-spin tails of Regge trajectories. The basic integrals for the Lorentzian inversion are given by Wilson functions.

Charmonia production in W → (cc̄)Ds(∗) decays

In this paper, production of charmonium state [Formula: see text] in exclusive [Formula: see text] decays is analyzed in the framework of both leading order Non-relativistic Quantum Chromodynamics (NRQCD) and light-cone (LC) expansion models. Analytical and numerical predictions for the branching fractions of these decays in both the approaches are given. The typical value of the branching fractions is [Formula: see text][Formula: see text][Formula: see text] and it turns out that the LC results are significantly larger than NRQCD ones (approximately two or four times increase depending on the quantum numbers of the final particles), so the effect of internal quark motion should be taken into account. Some rough estimates of color-octet contributions are presented and it is shown that these contributions could be comparable with color-singlet results.

Lightcone expansions of conformal blocks in closed form

We present new closed-form expressions for 4-point scalar conformal blocks in the s- and t-channel lightcone expansions. Our formulae apply to intermediate operators of arbitrary spin in general dimensions. For physical spin ℓ, they are composed of at most (ℓ + 1) Gaussian hypergeometric functions at each order.

Asymptotic behavior of meson transition form factors

One of the open issues in evaluations of the contribution from hadronic light- by-light scattering to the anomalous magnetic moment of the muon (g − 2)μ concerns the role of heavier scalar, axial-vector, and tensor-meson intermediate states. The coupling of axial vectors to virtual photons is suppressed for small virtualities by the Landau-Yang theorem, but otherwise there are few rigorous constraints on the corresponding form factors. In this paper, we first derive the Lorentz decomposition of the two-photon matrix elements into scalar functions following the general recipe by Bardeen, Tung, and Tarrach. Based on this decomposition, we then calculate the asymptotic behavior of the meson transition form factors from a light-cone expansion in analogy to the asymptotic limits for the pseudoscalar transition form factor derived by Brodsky and Lepage. Finally, we compare our results to existing data as well as previous models employed in the literature.

Closed-form expression for cross-channel conformal blocks near the lightcone

In the study of conformal field theories, conformal blocks in the lightcone limit are fundamental to the analytic conformal bootstrap method. Here we consider the lightcone limit of 4-point functions of generic scalar primaries. Based on the nonperturbative pole structure in spin of Lorentzian inversion, we propose the natural basis functions for cross-channel conformal blocks. In this new basis, we find a closed-form expression for crossed conformal blocks in terms of the Kampé de Fériet function, which applies to intermediate operators of arbitrary spin in general dimensions. We derive the general Lorentzian inversion for the case of identical external scaling dimensions. Our results for the lightcone limit also shed light on the complete analytic structure of conformal blocks in the lightcone expansion.

Collinear matching for Sivers function at next-to-leading order

We evaluate the light-cone operator product expansion for unpolarized transverse momentum dependent (TMD) operator in the background-field technique up twist-3 inclusively. The next-to-leading order (NLO) matching coefficient for the Sivers function is derived. The method, as well as many details of the calculation are presented.

Bootstrap and collider physics of parity violating conformal field theories in d = 3

We study the crossing equations in d = 3 for the four point function of two U(1) currents and two scalars including the presence of a parity violating term for the s-channel stress tensor exchange. We show the existence of a new tower of double trace operators in the t-channel whose presence is necessary for the crossing equation to be satisfied and determine the corresponding large spin parity violating OPE coefficients. Contrary to the parity even situation, we find that the parity odd s-channel light cone stress tensor block do not have logarithmic singularities. This implies that the parity odd term does not contribute to anomalous dimensions in the crossed channel at this order light cone expansion. We then study the constraints imposed by reflection positivity and crossing symmetry on such a four point function. We reproduce the previously known parity odd collider bounds through this analysis. The contribution of the parity violating term in the collider bound results from a square root branch cut present in the light cone block as opposed to a logarithmic cut in the parity even case, together with the application of the Cauchy-Schwarz inequality.

Matching of transverse momentum dependent distributions at twist-3

We derive the leading order matching of the quark generated polarized transverse momentum dependent (TMD) distributions onto the collinear functions at small values of the transverse distance. Starting from the very definition of the TMD operator and performing the light-cone operator product expansion up to twist-3 order, we evaluate each distribution directly in position space. We primarily consider the cases of Sivers, Boer-Mulders and worm-gear functions. The effects of the TMD process dependence on the matching are explicitly shown. We also discuss the moments of TMD distributions which can be relevant for lattice calculations.

The Mass and Decay Properties of the 1−+ Light Hybrid Meson

We calculate the complete form of the dimension-8 condensate contributions in the two-point correlator of the (1−+,0++) light hybrid current considering the operator mixing under renormalization. We find the inclusion these higher power corrections as well as the update of 〈g3G3〉 increase the QCD sum rule mass prediction for the 1−+ light hybrid. The obtained conservative mass range 1.72–2.60 GeV does not favor the π1(1400) and the π1(1600) to be pure hybrid states and suggests the π1(2015) observed by E852 is more likely to have much of a hybrid constituent. We also study the b1π and ρπ decay patterns of the 1−+ light hybrid with light-cone QCD sum rules. We obtain a relatively large partial decay width of the b1π mode, which is consistent with the predictions from the flux tube models and lattice QCD. More interestingly, using the tensor interpolating current we find the partial decay width of the ρπ mode is very small due to the lack of the leading twist contribution in the light-cone expansion of the correlation function.

Higher-twist effects in light-cone sum rule for the Brightarrow pi form factor

We calculate the higher-twist corrections to the QCD light-cone sum rule for the B rightarrow pi transition form factor. The light-cone expansion of the massive quark propagator in the external gluonic field is extended to include new terms containing the derivatives of the gluon-field strength. The resulting analytical expressions for the twist-5 and twist-6 contributions to the correlation function are obtained in a factorized approximation, expressed via the product of the lower-twist pion distribution amplitudes and the quark-condensate density. The numerical analysis reveals that new higher-twist effects for the B rightarrow pi form factor are strongly suppressed. This result justifies the conventional truncation of the operator product expansion in the light-cone sum rules up to twist-4 terms.

A Mellin space approach to the conformal bootstrap

We describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of CFTd four point functions and expands them in terms of crossing symmetric combinations of AdSd+1 Witten exchange functions. We consider arbitrary external scalar operators and set up the conditions for consistency with the operator product expansion. Namely, we demand cancellation of spurious powers (of the cross ratios, in position space) which translate into spurious poles in Mellin space. We discuss two contexts in which we can immediately apply this method by imposing the simplest set of constraint equations. The first is the epsilon expansion. We mostly focus on the Wilson-Fisher fixed point as studied in an epsilon expansion about d = 4. We reproduce Feynman diagram results for operator dimensions to O(ϵ3) rather straightforwardly. This approach also yields new analytic predictions for OPE coefficients to the same order which fit nicely with recent numerical estimates for the Ising model (at ϵ = 1). We will also mention some leading order results for scalar theories near three and six dimensions. The second context is a large spin expansion, in any dimension, where we are able to reproduce and go a bit beyond some of the results recently obtained using the (double) light cone expansion. We also have a preliminary discussion about numerical implementation of the above bootstrap scheme in the absence of a small parameter.

The (2, 0) superconformal bootstrap

We develop the conformal bootstrap program for six-dimensional conformal field theories with $(2,0)$ supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on OPE coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the lightcone expansion of the crossing equation. Our principal result is strong evidence that the $A_1$ theory realizes the minimal allowed central charge $(c=25)$ for any interacting $(2,0)$ theory. This implies that the full stress tensor four-point function of the $A_1$ theory is the unique unitary solution to the crossing symmetry equation at $c=25$. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting $(2,0)$ theory of central charge $c$. For large $c$, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.

Perturbative description of the fermionic projector: Normalization, causality, and Furry's theorem

The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that they only involve bounded line integrals. For the resulting loop diagrams we prove a generalized Furry theorem.

NLO BFKL AND ANOMALOUS DIMENSIONS OF LIGHT-RAY OPERATORS

The anomalous dimensions of light-ray operators of twist two are obtained by analytical continuation of the anomalous dimensions of corresponding local operators. I demonstrate that the asymptotics of these anomalous dimensions at the "BFKL point" j → 1 can be obtained by comparing the light-cone operator expansion with the high-energy expansion in Wilson lines.

Form factors $ f_{ + }^{{B \to \pi }}(0) $ and $ f_{ + }^{{D \to \pi }}(0) $ in QCD and determination of |V ub | and |V cd |

We present a QCD study on B, D → π semileptonic transitions at zero momentum transfer and an estimate of magnitudes of the associated CKM matrix elements. Light cone sum rules (LCSRs) with chiral correlator are applied to calculate the form factors $ f_{ + }^{{B \to \pi }}(0) $ and $ f_{ + }^{{D \to \pi }}(0) $ . We show that there is no twist-3 and-5 component involved in the light-cone expansions such that the resulting sum rules have a good convergence and offer an understanding of these form factors at twist-5 level. A detailed $ \mathcal{O}\left( {{\alpha_s}} \right) $ computation is carried out in leading twist-2 approximation and the $ \overline {MS} $ masses are employed for the underlying heavy quarks. With the updated inputs and experimental data, we have $ f_{ + }^{{B \to \pi }}(0) = 0.28_{{ - 0.02}}^{{ + 0.05}} $ and $ \left| {{V_{{ub}}}} \right| = \left( {3.4_{{ - 0.6}}^{{ + 0.2}}\pm 0.1\pm 0.1} \right) \times {10^{{ - 3}}};f_{ + }^{{D \to \pi }}(0) = 0.62\pm 0.03 $ and $ \left| {{V_{{cd}}}} \right| = 0.244\pm 0.005\pm 0.003\pm 0.008 $ . As a by-product, a numerical estimate for the decay constant f D is yielded as $ {f_D} = 190_{{ - 11}}^{{ + 15}}{\text{MeV}} $ .

The causal perturbation expansion revisited: Rescaling the interacting Dirac sea

The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.

Electroproduction of theN*(1535)Resonance at Large Momentum Transfer

We report on the first lattice calculation of light-cone distribution amplitudes of the N*(1535) resonance, which are used to calculate the transition form factors at large momentum transfers using light-cone sum rules. In the region Q2>2 GeV2, where the light-cone expansion is expected to converge, the results appear to be in good agreement with the experimental data.