arXiv subjects

G. P. Korchemsky

Publications and source records attributed to G. P. Korchemsky.

At least 73 records · Page 4Linked to original sources

arXiv2003

Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain

We construct the Baxter Q-operator and the representation of the Separated Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the diagrammatical approach, we calculate Sklyanin's integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the Q-operator. We show that the transition kernel to the SoV representation is factorized into the product of certain operators each depending on a single separated variable. As a consequence, it has a universal pyramid-like form that has been already observed for various quantum integrable models such as periodic Toda chain, closed SL(2,R) and SL(2,C) spin chains.

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arXiv2003

Separation of variables for the quantum SL(2,R) spin chain

We construct representation of the Separated Variables (SoV) for the quantum SL(2,R) Heisenberg closed spin chain and obtain the integral representation for the eigenfunctions of the model. We calculate explicitly the Sklyanin measure defining the scalar product in the SoV representation and demonstrate that the language of Feynman diagrams is extremely useful in establishing various properties of the model. The kernel of the unitary transformation to the SoV representation is described by the same "pyramid diagram" as appeared before in the SoV representation for the SL(2,C) spin magnet. We argue that this kernel is given by the product of the Baxter Q-operators projected onto a special reference state.

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arXiv2003

The Uses of Conformal Symmetry in QCD

The Lagrangian of Quantum Chromodynamics is invariant under conformal transformations. Although this symmetry is broken by quantum corrections, it has important consequences for strong interactions at short distances and provides one with powerful tools in practical calculations. In this review we give a short exposition of the relevant ideas, techniques and applications of conformal symmetry to various problems of interest.

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arXiv2003

Gauge/string duality for QCD conformal operators

Renormalization group evolution of QCD composite light-cone operators, built from two and more quark and gluon fields, is responsible for the logarithmic scaling violations in diverse physical observables. We analyze spectra of anomalous dimensions of these operators at large conformal spins at weak and strong coupling with the emphasis on the emergence of a dual string picture. The multi-particle spectrum at weak coupling has a hidden symmetry due to integrability of the underlying dilatation operator which drives the evolution. In perturbative regime, we demonstrate the equivalence of the one-loop cusp anomaly to the disk partition function in two-dimensional Yang-Mills theory which admits a string representation. The strong coupling regime for anomalous dimensions is discussed within the two pictures addressed recently, -- minimal surfaces of open strings and rotating long closed strings in AdS background. In the latter case we find that the integrability implies the presence of extra degrees of freedom -- the string junctions. We demonstrate how the analysis of their equations of motion naturally agrees with the spectrum found at weak coupling.

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arXiv2002

Noncompact Heisenberg spin magnets from high-energy QCD: III. Quasiclassical approach

The exact solution of the noncompact SL(2,C) Heisenberg spin magnet reveals a hidden symmetry of the energy spectrum. To understand its origin, we solve the spectral problem for the model within quasiclassical approach. In this approach, the integrals of motion satisfy the Bohr-Sommerfeld quantization conditions imposed on the orbits of classical motion. In the representation of the separated coordinates, the latter wrap around a Riemann surface defined by the spectral curve of the model. A novel feature of the obtained quantization conditions is that they involve both the alpha- and beta-periods of the action differential on the Riemann surface, thus allowing us to find their solutions by exploring the full modular group of the spectral curve. We demonstrate that the quasiclassical energy spectrum is in a good agreement with the exact results.

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arXiv2002

Noncompact Heisenberg spin magnets from high-energy QCD: II. Quantization conditions and energy spectrum

We present a complete description of the spectrum of compound states of reggeized gluons in QCD in multi-colour limit. The analysis is based on the identification of these states as ground states of noncompact Heisenberg SL(2,C) spin magnet. A unique feature of the magnet, leading to many unusual properties of its spectrum, is that the quantum space is infinite-dimensional and conventional methods, like the Algebraic Bethe Ansatz, are not applicable. Our solution relies on the method of the Baxter Q-operator. Solving the Baxter equations, we obtained the explicit expressions for the eigenvalues of the Q-operator. They allowed us to establish the quantization conditions for the integrals of motion and, finally, reconstruct the spectrum of the model. We found that intercept of the states built from even (odd) number of reggeized gluons, N, is bigger (smaller) than one and it decreases (increases) with N approaching the same unit value for infinitely large N.

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arXiv2002

Power corrections in deep inelastic structure functions at large Bjorken x

We study power corrections to the spin-averaged structure functions F_2 and F_L in the semi-inclusive region. The dramatic breakdown of the operator product expansion at large Bjorken x due to the formation of a narrow jet with invariant mass W (W^2=Q^2(1-x)/x) calls for an alternative approach. Our main conjecture is that the dominant contribution at each twist is the one which mixes under renormalization with the leading twist (ultraviolet dominance). At twist two the dominant perturbative corrections at large x due to soft and collinear radiation can be factorized into a jet function. From the ultraviolet dominance conjecture it follows that the twist two parton distribution as well as the jet function actually factorize to any order in the twist expansion. This factorization suggests that non-perturbative corrections ~1/W^{2n} exponentiate together with the leading twist. We verify explicitly, at the level of a single dressed gluon, the cancellation between ambiguities due to infrared renormalons in the twist-two coefficient functions and those due to the ultraviolet divergence of twist-four matrix elements. Independently of the renormalon analysis, we show that the dominant contribution to twist four at large x is associated with a twist-two like configuration: the final states are identical to those of twist two, whereas the initial states differ just by additional partons carrying small momentum fractions. This picture is consistent with the ultraviolet dominance conjecture.

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arXiv2002

Solution of the multi-reggeon compound state problem in multi-colour QCD

We study the properties of the colour-singlet compound states of reggeized gluons in multi-colour QCD using their relation with noncompact Heisenberg spin magnets. Applying the methods of integrable models, we calculate their spectrum and discuss the application of the obtained results to high-energy asymptotics of the scattering amplitudes in perturbative QCD.

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arXiv2001

Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables

We analyze a completely integrable two-dimensional quantum-mechanical model that emerged in the recent studies of the compound gluonic states in multi-color QCD at high energy. The model represents a generalization of the well-known homogenous Heisenberg spin magnet to infinite-dimensional representations of the SL(2,C) group and can be reformulated within the Quantum Inverse Scattering Method. Solving the Yang-Baxter equation, we obtain the R-matrix for the SL(2,C) representations of the principal series and discuss its properties. We explicitly construct the Baxter Q-operator for this model and show how it can be used to determine the energy spectrum. We apply Sklyanin's method of the Separated Variables to obtain an integral representation for the eigenfunctions of the Hamiltonian. We demonstrate that the language of Feynman diagrams supplemented with the method of uniqueness provide a powerful technique for analyzing the properties of the model.

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arXiv2001

Energy flow in QCD and event shape functions

Hadronization corrections to the thrust and related event shape distributions in the two-jet kinematical region of e+e- annihilation are summarized by nonperturbative shape functions. The moments of shape functions are given by universal matrix elements in QCD, which describe the energy flow in QCD final states. We show how the nonperturbative structure of these matrix elements may be inferred from resummed perturbation theory and Lorentz invariance. This analysis suggests the same functional forms for the shape functions as were found in phenomenological studies, and sheds light on the physical significance of the parameters that characterize these functions.

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arXiv2001

Evolution equation for the structure function g_2(x,Q^2)

We perform an extensive study of the scale dependence of flavor-singlet contributions to the structure function g_2(x,Q^2) in polarized deep-inelastic scattering. We find that the mixing between quark-antiquark-gluon and three-gluon twist-3 operators only involves the three-gluon operator with the lowest anomalous dimension and is weak in other cases. This means, effectively, that only those three-gluon operators with the lowest anomalous dimension for each moment are important, and allows to formulate a simple two-component parton-like description of g_2(x,Q^2) in analogy with the conventional description of twist-2 parton distributions. The similar simplification was observed earlier for the nonsinglet distributions, although the reason is in our case different.

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arXiv2000

Gluon contribution to the structure function g_2(x,Q^2)

We calculate the one-loop twist-3 gluon contribution to the flavor-singlet structure function g_2(x,Q^2) in polarized deep-inelastic scattering and find that it is dominated by the contribution of the three-gluon operator with the lowest anomalous dimension (for each moment N). The similar property was observed earlier for the nonsinglet distributions, although the reason is in our case different. The result is encouraging and suggests a simple evolution pattern of g_2(x,Q^2) in analogy with the conventional description of twist-2 parton distributions.

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arXiv2000

On power corrections to the event shape distributions in QCD

We study power corrections to the differential thrust, heavy jet mass and C-parameter distributions in the two-jet kinematical region in e^+e^- annihilation. We argue that away from the end-point region, e>> Λ_{QCD}/Q, the leading 1/Q-power corrections are parameterized by a single nonperturbative scale while for e Λ_{QCD}/Q one encounters a novel regime in which power corrections of the form 1/(Qe)^n have to be taken into account for arbitrary n. These nonperturbative corrections can be resummed and factor out into a universal nonperturbative distribution, the shape function, and the differential event shape distributions are given by convolution of the shape function with perturbative cross-sections. Choosing a simple ansatz for the shape function we demonstrate a good agreement of the obtained QCD predictions for the distributions and their lowest moments with the existing data over a wide energy interval.

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arXiv2000

Evolution of twist-three parton distributions in QCD beyond the large N_c limit

We formulate a consistent 1/N_c^2 expansion of the QCD evolution equations for the twist-three quark distributions g_2(x,Q^2), h_L(x,Q^2) and e(x,Q^2) based on the interpretation of the evolution as a three-particle quantum-mechanical problem with hermitian Hamiltonian. Each distribution amplitude can be decomposed in contributions of partonic components with DGLAP-type scale dependence. We calculate the 1/N_c^2 corrections to the evolution of the dominant component with the lowest anomalous dimension - the only one that survives in the large-N_c limit - and observe a good agreement with the exact numerical results for N_c=3. The 1/N_c^2 admixture of operators with higher anomalous dimensions is shown to be concentrated at a few lowest partonic components and in general is rather weak.

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arXiv1999

New representation for the odderon wave function

New representation of the odderon wave function is derived, which is convergent in the whole impact parameter plane and provides the analytic form of the quantization condition for the integral of motion q_3. A new quantum number, triality, is identified. This, together with the choice of the conformal basis, allows for simple calculation of eigenvalues of a wide class of operators.

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arXiv1999

Baryon Distribution Amplitudes in QCD

We develop a new theoretical framework for the description of leading twist light-cone baryon distribution amplitudes which is based on integrability of the helicity $λ=3/2$ evolution equation to leading logarithmic accuracy. A physical interpretation is that one can identify a new `hidden' quantum number which distinguishes components in the $λ=3/2$ distribution amplitudes with different scale dependence. The solution of the corresponding evolution equation is reduced to a simple three-term recurrence relation. The exact analytic solution is found for the component with the lowest anomalous dimension for all moments $N$, and the WKB-type expansion is constructed for other levels, which becomes asymptotically exact at large $N$. Evolution equations for the $λ=1/2$ distribution amplitudes (e.g. for the nucleon) are studied as well. We find that the two lowest anomalous dimensions for the $λ=1/2$ operators (one for each parity) are separated from the rest of the spectrum by a finite `mass gap'. These special states can be interpreted as scalar diquarks.

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arXiv1999

Power corrections to event shapes and factorization

We study power corrections to the differential thrust, heavy mass and related event shape distributions in $e^+e^-$-annihilation, whose values, $e$, are proportional to jet masses in the two-jet limit, $e\to 0$. The factorization properties of these differential distributions imply that they may be written as convolutions of nonperturbative "shape" functions, describing the emission of soft quanta by the jets, and resummed perturbative cross sections. The infrared shape functions are different for different event shapes, and depend on a factorization scale, but are independent of the center-of-mass energy $Q$. They organize all power corrections of the form $1/(eQ)^n$, for arbitrary $n$, and carry information on a class of universal matrix elements of the energy-momentum tensor in QCD, directly related to the energy-energy correlations.

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arXiv1998

Shape functions and power corrections to the event shapes

We show that the leading power corrections to the event shape distributions can be resummed into nonperturbative shape functions that do not depend on the center-of-mass energy and measure the energy flow in the final state. In the case of the thrust variable, the distribution is given by the convolution of the perturbative spectrum with the shape function. Choosing the simplest ansatz for the shape function we find that our predictions for the thrust distribution provide a good description of the data throughout a wide range of energies.

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