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Unraveling duality violations in hadronic tau decays

Description: There are some indications from recent determinations of the strong coupling constant alpha_s and the gluon condensate that the Operator Product Expansion may not be accurate enough to describe non-perturbative effects in hadronic tau decays. This breakdown of the Operator Product Expansion is usually referred to as being due to"Duality Violations." With the help of a physically motivated model, we investigate these duality violations. Based on this model, we argue how they may introduce a non-negligible systematic error in the current analysis, which employs finite-energy sum rules with pinched weights. In particular, this systematic effect might affect the precision determination of alpha_s from tau decays. With a view to a possible future application to real data, we present an alternative method for determining the OPE coefficients that might help estimating, and possibly even reducing, this systematic error.
Date: March 3, 2008
Creator: Cata, Oscar; Cata, Oscar; Golterman, Maarten & Peris, Santiago
Partner: UNT Libraries Government Documents Department

Introduction into QCD Sum Rule Approach

Description: In these lectures, I describe basic techniques of the QCD sum rule approach. The basic concepts of the approach are introduced using a simple model of quantum-mechanical oscillator in 2+1 dimensions. Then I discuss their field-theoretical extension and the construction of the operator product expansion for current correlators in QCD. The calculation of static parameters is illustrated on the example of sum rules in the vector and axial meson channels. Finally, the QCD sum rule calculation of the pion electromagnetic form factor is presented as an example of application of the method to dynamic characteristics of the hadrons.
Date: September 1, 1999
Creator: Radyushkin, A.
Partner: UNT Libraries Government Documents Department

Next-to leading order analysis of target mass corrections to structure functions and asymmetries

Description: We perform a comprehensive analysis of target mass corrections (TMCs) to spin-averaged structure functions and asymmetries at next-to-leading order. Several different prescriptions for TMCs are considered, including the operator product expansion, and various approximations to it, collinear factorization, and xi-scaling. We assess the impact of each of these on a number of observables, such as the neutron to proton F{sub 2} structure function ratio, and parity-violating electron scattering asymmetries for protons and deuterons which are sensitive to gamma-Z interference effects. The corrections from higher order radiative and nuclear effects on the parity-violating deuteron asymmetry are also quantified.
Date: October 1, 2011
Creator: L. T. Brady, A. Accardi, T. J. Hobbs, W. Melnitchouk
Partner: UNT Libraries Government Documents Department

HADRONIC SCATTERING IN THE COLOR GLASS CONDENSATE.

Description: Multi-particle production in QCD is dominated by higher twist contributions. The operator product expansion is not very effective here because the number of relevant operators grow rapidly with increasing twist. The Color Glass Condensate (CGC) provides a framework in QCD to systematically discuss ''classical'' (multiple scattering) and ''quantum'' evolution (shadowing) effects in multi-particle production. The apparently insuperable problem of nucleus-nucleus scattering in QCD simplifies greatly in the CGC. A few examples are discussed with emphasis on open problems.
Date: May 15, 2005
Creator: Venugopalan, R.
Partner: UNT Libraries Government Documents Department

Semileptonic Decays and Sides of the Unitarity Triangle

Description: The elements of the CKM matrix enter the expressions for the decay rates and mixing amplitudes of hadrons. In some cases, the theoretical expressions are free of strong interaction effects, for example the CP asymmetry in B {yields} J/{psi} K{sub S}{sup 0}, so that measuring the CP asymmetry directly gives the value of sin 2{beta}, with the error in the result given by the experimental error in the measurement. In most cases, however, the experimentally measured quantities depend on strong interactions physics, and it is absolutely essential to have accurate model-free theoretical calculations to compare with experiment. A number of theoretical tools have been developed over the years which now allow us to compute B decays with great accuracy, sometimes at the level of a few percent or better. These calculations are done using effective theory methods applied to QCD, and do not rely on model assumptions. Inclusive decays can be treated using the operator product expansion (OPE). The total decay rate is given by twice the imaginary part of the forward scattering amplitude, using the optical theorem. In heavy hadron decays, the intermediate states in the forward scattering amplitude can be integrated out, so that the decay rate can be written as an expansion in local operators. The expansion parameter is 1/m{sub B}, the mass of the decaying hadron. OPE techniques have been well-studied in the context of deep-inelastic scattering, where the expansion in powers of 1/Q{sup 2} is called the twist expansion. In inclusive B decays, the leading term in the 1/m{sub B} expansion gives the parton decay rate, and nonperturbative effects enter at higher orders in 1/m{sub B}.
Date: May 1, 2003
Creator: Ligeti, Zoltan; Bauer, C.; Bernard, C.; Bigi, I.; Datta, M.; del Re, D. et al.
Partner: UNT Libraries Government Documents Department

Analyticity and the Holographic S-Matrix

Description: We derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and the bulk S-Matrix in the flat spacetime limit, proving a conjecture of Penedones. As a consequence of the Operator Product Expansion, the Mellin amplitude for any unitary CFT must be a meromorphic function with simple poles on the real axis. This provides a powerful and suggestive handle on the locality vis-a-vis analyticity properties of the S-Matrix. We begin to explore analyticity by showing how the familiar poles and branch cuts of scattering amplitudes arise from the holographic description. For this purpose we compute examples of Mellin amplitudes corresponding to 1-loop and 2-loop Witten diagrams in AdS. We also examine the flat spacetime limit of conformal blocks, implicitly relating the S-Matrix program to the Bootstrap program for CFTs. We use this connection to show how the existence of small black holes in AdS leads to a universal prediction for the conformal block decomposition of the dual CFT.
Date: April 3, 2012
Creator: Fitzpatrick, A.Liam; /Stanford U., Phys. Dept.; Kaplan, Jared & /SLAC
Partner: UNT Libraries Government Documents Department

A Study of Semileptonic B Decays And of Lepton Flavor Violating Tau Decays at BaBar

Description: The study of the semileptonic B decays at BABAR is presented. The results shown include measurements of the moments of hadronic-mass and electron-energy of the decay B {yields} X{sub c}{ell}{nu}; a determination of the |V{sub cb}| CKM matrix element and other heavy quark parameters from a simultaneous fit to the moments using kinetic scheme of Operator Product Expansion; a measurement of the inclusive branching fraction of B {yields} X{sub u}{ell}{nu} and determination of |V{sub ub}|. The most recent BABAR search for the lepton flavor violating decays {tau} {yields} {ell}{ell}{ell} is presented as well.
Date: June 10, 2005
Creator: Igonkina, O. & U., /Oregon
Partner: UNT Libraries Government Documents Department

Wakimoto realizations of current algebras: an explicit construction

Description: A generalized Wakimoto realization of $\widehat\cal G_K$ can be associated with each parabolic subalgebra $\cal P=(\cal G_0 +\cal G_+)$ of a simple Lie algebra $\cal G$ according to an earlier proposal by Feigin and Frenkel. In this paper the proposal is made explicit by developing the construction of Wakimoto realizations from a simple but unconventional viewpoint. An explicit formula is derived for the Wakimoto current first at the Poisson bracket level by Hamiltonian symmetry reduction of the WZNW model. The quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate $\widehat\cal G_K$ by means of commutators. The affine-Sugawara stress-energy tensor is verified to have the expected quadratic form in the constituents, which are symplectic bosons belonging to $\cal G_+$ and a current belonging to $\cal G_0$. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold $P\backslash G$. The effect of this choice is investigated in detail by constructing quantum coordinate transformations. Finally, the explicit form of the screening charges for each generalized Wakimoto realization is determined, and some applications are briefly discussed.
Date: November 12, 1996
Creator: de Boer, Jan & Feher, Laszlo
Partner: UNT Libraries Government Documents Department

Comments on Worldsheet Theories Dual to Free Large N Gauge Theories

Description: We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in [1]. The modular invariance of these CFTs is shown to be built into the formalism. We show that correlation functions in these CFTs which are localized on subspaces of the moduli space may be interpreted as delta-function distributions, and that this can be consistent with a local worldsheet description given some constraints on the operator product expansion coefficients. We illustrate these features by a detailed analysis of a specific four-point function diagram. To reliably compute this correlator we use a novel perturbation scheme which involves an expansion in the large dimension of some operators.
Date: March 21, 2007
Creator: Aharony, Ofer; /Weizmann Inst. /Stanford U., ITP /SLAC; David, Justin R.; Gopakumar, Rajesh; Inst., /Harish-Chandra Res.; Komargodski, Zohar et al.
Partner: UNT Libraries Government Documents Department

Bootstrapping the Three-Loop Hexagon

Description: We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N = 4 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both our ansatz for the symbol and the duality between Wilson loops and MHV amplitudes. Furthermore, we predict the form of the full three-loop remainder function in the multi-Regge limit, beyond the leading-log approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an all-loop prediction for the real part of the remainder function in multi-Regge 3 {yields} 3 scattering. In the multi-Regge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic six-point kinematics other functions are required.
Date: November 8, 2011
Creator: Dixon, Lance J.; Drummond, James M. & Henn, Johannes M.
Partner: UNT Libraries Government Documents Department

Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory

Description: We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.
Date: February 15, 2012
Creator: Dixon, Lance J.; Drummond, James M. & Henn, Johannes M.
Partner: UNT Libraries Government Documents Department

Precision Studies of Duality in the 't Hooft Model

Description: The authors address numerical aspects of local quark-hadron duality using the example of the exactly solvable 't Hooft model, two-dimensional QCD with Nc ?8. The primary focus of these studies is total semileptonic decay widths relevant for extracting (Vcb) and (Vub). They compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtained in the standard 1/mQ expansion arising from the Operator Product Expansion. An impressive agreement sets in unexpectedly early, immediately after the threshold for the first hadronic excitation in the final state. Yet even at higher energy release it is possible to discern the seeds of duality-violating oscillations. They find the ''Small Velocity'' sum rules to be exceptionally well saturated already by the first excited state. They also obtain a convincing degree of duality in the differential distributions and in an analogue of Re+e-(s). Finally, they discuss possible lessons for semileptonic decays of actual heavy quarks in QCD.
Date: June 1, 2000
Creator: Lebed, R.F. & Uraltsev, N.G.
Partner: UNT Libraries Government Documents Department

Moments of Nucleon Light Cone Quark Distributions Calculated in Full Lattice QCD

Description: Moments of the quark density, helicity, and transversity distributions are calculated in unquenched lattice QCD. Calculations of proton matrix elements of operators corresponding to these moments through the operator product expansion have been performed on the 16{sup 3} x 32 lattices for Wilson fermions at Beta=5.6 using configurations from the SESAM collaboration and at Beta = 5.5 using configurations from SCRI. One-loop perturbative renormalization corrections are included. At quark masses accessible in present calculations, there is no statistically significant difference between quenched and full QCD results, indicating that the contributions of quark-antiquark excitations from the Dirac Sea are small. Close agreement between calculations with cooled configurations containing essentially only instantons and the full gluon configurations indicates that quark zero modes associated with instantons play a dominant role. Naive linear extrapolation of the full QCD calculation to the physical pion mass yields results inconsistent with experiment. Extrapolation to the chiral limit including the physics of the pion cloud can resolve this discrepancy and the requirements for a definitive chiral extrapolation are described.
Date: January 1, 2002
Creator: Dolgov, D.; Brower, R.; Capitani, S.; Dreher, P.; Negele, J.W.; Pochinsky, A. et al.
Partner: UNT Libraries Government Documents Department

Moments of Structure Functions in Full QCD

Description: Moments of the quark density distribution, moments of the quark helicity distribution, and the tensor charge are calculated in full QCD. Calculations of matrix elements of operators from the operator product expansion have been performed on 16{sup 3} x 32 lattices for Wilson fermions at {beta} = 5.6 using configurations from the SESAM collaboration and at {beta} = 5.5 using configurations from SCRI. One-loop perturbative renormalization corrections are included. Selected results are compared with corresponding quenched calculations and with calculations using cooled configurations.
Date: August 1, 2000
Creator: Dolgov, D.; Brower, R.; Capitani, S.; Negele, J. W.; Pochinsky, A.; Renner, D. et al.
Partner: UNT Libraries Government Documents Department

Introduction to heavy meson decays and CP asymmetries

Description: These lectures are intended to provide an introduction to heavy meson decays and CP violation. The first lecture contains a brief review of the standard model and how the CKM matrix and CP violation arise, mixing and CP violation in neutral meson systems, and explanation of the cleanliness of the sin 2{beta} measurement. The second lecture deals with the heavy quark limit, some applications of heavy quark symmetry and the operator product expansion for exclusive and inclusive semileptonic B decays. The third lecture concerns with theoretically clean CP violation measurements that may become possible in the future, and some developments toward a better understanding of nonleptonic B decays. The conclusions include a subjective best buy list for the near future.
Date: February 5, 2003
Creator: Ligeti, Zoltan
Partner: UNT Libraries Government Documents Department

Introduction to heavy meson decays and CP asymmetries

Description: These lectures are intended to provide an introduction to heavy meson decays and CP violation. The first lecture contains a brief review of the standard model and how the CKM matrix and CP violation arise, mixing and CP violation in neutral meson systems, and explanation of the cleanliness of the sin 2{beta} measurement. The second lecture deals with the heavy quark limit, some applications of heavy quark symmetry and the operator product expansion for exclusive and inclusive semileptonic B decays. The third lecture concerns with theoretically clean CP violation measurements that may become possible in the future, and some developments toward a better understanding of nonleptonic B decays. The conclusions include a subjective best buy list for the near future.
Date: February 5, 2003
Creator: Ligeti, Zoltan
Partner: UNT Libraries Government Documents Department

Precise predictions for B -> Xs l+ l- in the large q2 region

Description: The inclusive B -> Xs l+ l- decay rate in the large q2 region (q2> m_psi'2) receives significant nonperturbative corrections. The resulting uncertainties can be drastically reduced by normalizing the rate to the B -> Xu l nu rate with the same q2 cut, which allows for much improved tests of short distance physics. We calculate this ratio, including the order 1/m_b3 nonperturbative corrections and the analytically known NNLO perturbative corrections. Since in the large q2 region an inclusive measurement may be feasible via a sum over exclusive states, our results could be useful for measurements at LHCb and possibly for studies of B -> Xd l+ l-.
Date: July 12, 2007
Creator: Ligeti, Zoltan; Ligeti, Zoltan & Tackmann, Frank J.
Partner: UNT Libraries Government Documents Department

Measurement and Interpretation of Moments of the Combined Hadronic Mass and Energy Spectrum in Inclusive Semileptonic B-Meson Decays

Description: This thesis presents first measurements of moments of the hadronic n{sub X}{sup 2} distribution measured in inclusive semileptonic decays of B mesons to final states containing a charm quark, B {yields} X{sub c}{ell}{nu}. The variable n{sub X}{sup 2} is a combination of the invariant mass of the charmed meson m{sub X}, its energy in the B-meson rest-frame E{sub X;BRF}, and a constant {tilde {Lambda}} = 0.65 GeV, n{sub X}{sup 2} = m{sub X}{sup 2}c{sup 4}-2{tilde {Lambda}}E{sub X,BRF} + {tilde {Lambda}}{sup 2}. The moments <n{sub X}{sup k}> with k = 2,4,6 are measured as proposed by theory to constrain assumptions made in the theoretical description of inclusive observables in semileptonic B-meson decays. This description uses Heavy Quark Expansion (HQE), an effective QCD combined with an Operator Product Expansion. The measurement is based on a sample of 231.6 million e{sup +}e{sup -} {yields} {Upsilon}(4S) {yields} B{bar B} events recorded with the BABAR experiment at the PEP-II e{sup +}e{sup -}-storage rings at SLAC. We reconstruct the semileptonic decay by identifying a charged lepton in events tagged by a fully reconstructed hadronic decay of the second B meson. Correction procedures are derived from Monte Carlo simulations to ensure an unbiased measurement of the moments of the n{sub X}{sup 2} distribution. All moments are measured requiring minimum lepton momenta between 0.8 GeV/c and 1.9 GeV/c in the rest frame of the B meson. Performing a simultaneous fit to the measured moments <n{sub X}{sup k}> up to order k = 6 combined with other measurements of moments of the lepton-energy spectrum in decays B {yields} X{sub c}{ell}{nu} and moments of the photon-energy spectrum in decays B {yields} X{sub s}{gamma}, we determine the quark-mixing parameter |V{sub cb}|, the bottom and charm quark masses, the semileptonic branching fraction {Beta}(B {yields} X{sub c}{ell}{nu}), and four non-perturbative heavy quark parameters. ...
Date: August 12, 2011
Creator: Klose, Verena
Partner: UNT Libraries Government Documents Department