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65
Solving high energy evolution equation including running coupling corrections, Phys
 Rev
"... We study the solution of the nonlinear BK evolution equation with the recently calculated running coupling corrections [1,2]. Performing a numerical solution we confirm the earlier result of [3] (obtained by exploring several possible scales for the running coupling) that the high energy evolution w ..."
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We study the solution of the nonlinear BK evolution equation with the recently calculated running coupling corrections [1,2]. Performing a numerical solution we confirm the earlier result of [3] (obtained by exploring several possible scales for the running coupling) that the high energy evolution with the running coupling leads to a universal scaling behavior for the dipolenucleus scattering amplitude, which is independent of the initial conditions. It is important to stress that the running coupling corrections calculated recently significantly change the shape of the scaling function as compared to the fixed coupling case, in particular leading to a considerable increase in the anomalous dimension and to a slowdown of the evolution with rapidity. We then concentrate on elucidating the differences between the two recent calculations of the running coupling corrections. We explain that the difference is due to an extra contribution to the evolution kernel, referred to as the subtraction term, which arises when running coupling corrections are included. These subtraction terms were neglected in both recent calculations. We evaluate numerically the subtraction terms for both calculations, and demonstrate that when the subtraction terms are added back to the evolution kernels obtained in the two works the resulting dipole amplitudes agree with each other! We then use the complete running coupling kernel including the subtraction term to find the numerical solution of the resulting full nonlinear evolution equation with the running coupling corrections. Again the scaling regime is recovered at very large rapidity with the scaling function unaltered by the subtraction term.
Database Abstractions
 Aggregation and Generalization”, TODS
, 1977
"... We present a method for deriving shape space parameters that are consistent with immunological data, and illustrate the method by deriving shape space parameters for a model of crossreactive memory. Crossreactive memory responses occur when the immune system is primed by one strain of a pathogen a ..."
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Cited by 9 (1 self)
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We present a method for deriving shape space parameters that are consistent with immunological data, and illustrate the method by deriving shape space parameters for a model of crossreactive memory. Crossreactive memory responses occur when the immune system is primed by one strain of a pathogen and challenged with a related, but different, strain. Much of the nature of a crossreactive response is determined by the quantity and distribution of the memory cells, raised to the primary antigen, that crossreact with the secondary antigen. B cells with above threshold affinity for an antigen lie in a region of shape space that we call a ball of stimulation. In a crossreactive response, the intersection of the balls of stimulation of the primary and secondary antigens contains the crossreactive B cells and thus determines the degree of crossreactivity between the antigens. We derive formulas for the volume of intersection of balls of stimulation in different shape spaces and show that the parameters of shape space, such as its dimensionality, have a large impact on the number of B cells in the intersection. The application of our method for deriving shape space parameters indicates that, for Hamming shape spaces, twenty to twentyfive dimensions, a three or four letter alphabet, and balls of stimulation of radius five or six, are choices that match the experimental data. For Euclidean shape spaces, five to eight dimensions and balls of stimulation with radius about twenty percent of the radius of the whole space, match the experimental data.
Lightcone quantization of string theory duals of free field theories,” arXiv:hepth/0212041
 Rev. D
, 2003
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Quark loop contribution to BFKL evolution: Running coupling and leadingN(f) NLO intercept, accepted for publication at Nucl. Phys. A
, 2006
"... We study the sea quark contribution to the BFKL kernel in the framework of Mueller’s dipole model using the results of our earlier calculation. We first obtain the BFKL equation with the running coupling constant. We observe that the “triumvirate ” structure of the running coupling found previously ..."
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Cited by 7 (7 self)
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We study the sea quark contribution to the BFKL kernel in the framework of Mueller’s dipole model using the results of our earlier calculation. We first obtain the BFKL equation with the running coupling constant. We observe that the “triumvirate ” structure of the running coupling found previously for nonlinear evolution equations is preserved for the BFKL equation. In fact, we rederive the equation conjectured by Levin and by Braun, albeit for the unintegrated gluon distribution with a slightly unconventional normalization. We obtain the leadingNf contribution to the NLO BFKL kernel in transverse momentum space and use it to calculate the leadingNf contribution to the NLO BFKL pomeron intercept for the unintegrated gluon distribution. Our result agrees with the wellknown results of Camici and Ciafaloni and of Fadin and Lipatov. We show how to translate this intercept to the case of the quark dipole scattering amplitude and find that it maps onto the expression found by Balitsky. 1
SLAC–PUB–15366 Threefold Complementary Approach to Holographic QCD
"... A complementary approach, derived from (a) higherdimensional anti–de Sitter (AdS) space, (b) lightfront quantization and (c) the invariance properties of the full conformal group in one dimension leads to a nonperturbative relativistic lightfront wave equation which incorporates essential spectros ..."
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Cited by 7 (4 self)
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A complementary approach, derived from (a) higherdimensional anti–de Sitter (AdS) space, (b) lightfront quantization and (c) the invariance properties of the full conformal group in one dimension leads to a nonperturbative relativistic lightfront wave equation which incorporates essential spectroscopic and dynamical features of hadron physics. The fundamental conformal symmetry of the classical QCD Lagrangian in the limit of massless quarks is encoded in the resulting effective theory. The mass scale for confinement emerges from the isomorphism between the conformal group and SO(2,1). This scale appears in the lightfront Hamiltonian by mapping to the evolution operator in the formalism of de Alfaro, Fubini and Furlan, which retains the conformal invariance of the action. Remarkably, the specific form of the confinement interaction and the corresponding modification of AdS space are uniquely determined in this procedure. 1
Lightcone Hamiltonian flow for positronium”, preprint hepth/9809143
"... The technique of Hamiltonian flow equations is applied to the canonical Hamiltonian of quantum electrodynamics in the front form and 3+1 dimensions. The aim is to generate a bound state equation in a quantum field theory, particularly to derive an effective Hamiltonian which is practically solvable ..."
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Cited by 6 (1 self)
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The technique of Hamiltonian flow equations is applied to the canonical Hamiltonian of quantum electrodynamics in the front form and 3+1 dimensions. The aim is to generate a bound state equation in a quantum field theory, particularly to derive an effective Hamiltonian which is practically solvable in Fockspaces with reduced particle number, such that the approach can ultimately be used to address to the same problem for quantum chromodynamics. Preprint: MPIHV331998 PACSnumbers are:
SDLCQ: Supersymmetric discrete light cone quantization
 AIP Conf. Proc. 494, 140
, 1999
"... In these lectures we discuss the application of discrete light cone quantization (DLCQ) to supersymmetric field theories. We will see that it is possible to formulate DLCQ so that supersymmetry is exactly preserved in the discrete approximation. We call this formulation of DLCQ, SDLCQ and it combine ..."
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Cited by 5 (0 self)
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In these lectures we discuss the application of discrete light cone quantization (DLCQ) to supersymmetric field theories. We will see that it is possible to formulate DLCQ so that supersymmetry is exactly preserved in the discrete approximation. We call this formulation of DLCQ, SDLCQ and it combines the power of DLCQ with all of the beauty of supersymmetry. In these lecture we will review the application of SDLCQ to several interesting supersymmetric theories. We will discuss two dimensional theories with (1,1), (2,2) and (8,8) supersymmetry, zero modes, vacuum degeneracy, massless states, mass gaps, theories in higher dimensions, and the Maldacena conjecture among other subjects. To be published in:
Collinear Singularities and Running Coupling Corrections to Gluon Production in CGC
, 2008
"... We analyze the structure of running coupling corrections to the gluon production cross section in the projectile–nucleus collisions calculated in the Color Glass Condensate (CGC) framework. We argue that for the gluon production cross section (and for gluon transverse momentum spectra and multiplici ..."
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Cited by 4 (3 self)
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We analyze the structure of running coupling corrections to the gluon production cross section in the projectile–nucleus collisions calculated in the Color Glass Condensate (CGC) framework. We argue that for the gluon production cross section (and for gluon transverse momentum spectra and multiplicity) the inclusion of running coupling corrections brings in collinear singularities due to final state splittings completely unaffected by CGC resummations. Hence, despite the saturation/CGC dynamics, the gluon production cross section is not infraredsafe. As usual, regularizing the singularities requires an infrared cutoff Λcoll that defines a resolution scale for gluons. We specifically show that the cutoff enters the gluon production cross section in the argument of the strong coupling constant αs(Λ2 coll). We argue that for hadron production calculations one should be able to absorb the collinear divergence into a fragmentation function. The singular collinear terms in the gluon production cross section are shown not to contribute to the energy In the recent years there has been a lot of progress in understanding running coupling corrections
Planar diagrams in lightcone gauge
 JHEP
, 2006
"... Preprint typeset in JHEP style PAPER VERSION ..."
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Triumvirate of Running Couplings in Smallx Evolution
, 2006
"... We study the inclusion of running coupling corrections into the nonlinear smallx JIMWLK and BK evolution equations by resumming all powers of αsNf in the evolution kernels. We demonstrate that the running coupling corrections are included in the JIMWLK/BK evolution kernel by replacing the fixed co ..."
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Cited by 3 (3 self)
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We study the inclusion of running coupling corrections into the nonlinear smallx JIMWLK and BK evolution equations by resumming all powers of αsNf in the evolution kernels. We demonstrate that the running coupling corrections are included in the JIMWLK/BK evolution kernel by replacing the fixed coupling constant αs in it with αs(1/r2 1) αs(1/r2 2) αs(1/R2), where r1 and r2 are transverse distances between the emitted gluon and the harder gluon (or quark) off of which it was emitted to the left and to the right of the interaction with the target. In the formalism of Mueller’s dipole model r1 and r2 are the transverse sizes of “daughter ” dipoles produced in one step of the dipole evolution. The scale R is a function of twodimensional vectors r1 and r2, the exact form of which is schemedependent. We propose using a particular scheme which gives us R as an explicit In the recent years there has been a lot of progress in smallx physics due to developments in the area of parton saturation and Color Glass Condensate (CGC) [1–21]. Among other things