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Combination of CDF and D0 measurements of the $W$ boson helicity in top quark decays (open access)

Combination of CDF and D0 measurements of the $W$ boson helicity in top quark decays

We report the combination of recent measurements of the helicity of the W boson from top quark decay by the CDF and D0 collaborations, based on data samples corresponding to integrated luminosities of 2.7-5.4 fb{sup -1} of p{bar p} collisions collected during Run II of the Fermilab Tevatron Collider. Combining measurements that simultaneously determine the fractions of W bosons with longitudinal (f{sub 0}) and right-handed (f{sub +}) helicities, we find f{sub 0} = 0.722 {+-} 0.081 [{+-} 0.062 (stat.) {+-} 0.052 (syst.)] and f{sub +} = -0.033 {+-} 0.046 [{+-} 0.034 (stat.) {+-} 0.031 (syst.)]. Combining measurements where one of the helicity fractions is fixed to the value expected in the standard model, we find f{sub 0} = 0.682 {+-} 0.057 [{+-} 0.035 (stat.) {+-} 0.046 (syst.)] and f{sub +} = ?0.015 {+-} 0.035 [{+-} 0.018 (stat.) {+-} 0.030 (syst.)]. The results are consistent with standard model expectations.
Date: February 1, 2012
Creator: Aaltonen, T.; Abazov, V. M.; Abbott, B.; Acharya, B. S.; Adams, M.; Adams, T. et al.
System: The UNT Digital Library
Measurement of the $WZ$ Cross Section and Triple Gauge Couplings in $p \bar p$ Collisions at $\sqrt{s} = 1.96$ TeV (open access)

Measurement of the $WZ$ Cross Section and Triple Gauge Couplings in $p \bar p$ Collisions at $\sqrt{s} = 1.96$ TeV

This Letter describes the current most precise measurement of the WZ production cross section as well as limits on anomalous WWZ couplings at a center-of-mass energy of 1.96 TeV in proton-antiproton collisions. The WZ candidates are reconstructed from decays containing three charged leptons and missing energy from a neutrino, where the charged leptons are either electrons or muons. Using data collected by the CDF II detector (7.1 fb{sup -1} of integrated luminosity), 64 candidate events are observed with the expected background contributing 8 {+-} 1 events. The measured total cross section {sigma}(p{bar p} {yields} WZ) = 3.93{sub -0.53}{sup +0.60}(stat){sub -0.46}{sup +0.59}(syst) pb is in good agreement with the standard model prediction of 3.50 {+-} 0.21. The same sample is used to set limits on anomalous WWZ couplings.
Date: February 1, 2012
Creator: Aaltonen, T.; Alvarez Gonzalez, B.; Amerio, S.; Amidei, D.; Anastassov, A.; Annovi, A. et al.
System: The UNT Digital Library
Search for a dark matter candidate produced in association with a single top quark in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV (open access)

Search for a dark matter candidate produced in association with a single top quark in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV

We report a new search for dark matter in a data sample of an integrated luminosity of 7.7 fb{sup -1} of Tevatron p{bar p} collisions at {radical}s = 1.96 TeV, collected by the CDF II detector. We search for production of a dark matter candidate, D, in association with a single top quark. We consider the hadronic decay mode of the top quark exclusively, yielding a final state of three jets with missing transverse energy. The data are consistent with the standard model; we thus set 95% confidence level upper limits on the cross section of the process p{bar p} {yields} t + D as a function of the mass of the dark-matter candidate. The limits are approximately 0.5 pb for a dark-matter particle with mass in the range of 0 - 150 GeV/c{sup 2}.
Date: February 1, 2012
Creator: Aaltonen, T.; Alvarez Gonzalez, B.; Amerio, S.; Amidei, D.; Anastassov, A.; Annovi, A. et al.
System: The UNT Digital Library
Search for Anomalous Production of Multiple Leptons in Association With $W$ and $Z$ Bosons at Cdf (open access)

Search for Anomalous Production of Multiple Leptons in Association With $W$ and $Z$ Bosons at Cdf

This paper presents a search for anomalous production of multiple low-energy leptons in association with a W or Z boson using events collected at the CDF experiment corresponding to 5.1 fb{sup -1} of integrated luminosity. This search is sensitive to a wide range of topologies with low-momentum leptons, including those with the leptons near one another. The observed rates of production of additional electrons and muons are compared with the standard model predictions. No indications of phenomena beyond the standard model are found. A 95% confidence level limit is presented on the production cross section for a benchmark model of supersymmetric hidden-valley Higgs production. Particle identification efficiencies are also provided to enable the calculation of limits on additional models.
Date: February 1, 2012
Creator: Aaltonen, T.; Alvarez Gonzalez, B.; Amerio, S.; Amidei, D.; Anastassov, A.; Annovi, A. et al.
System: The UNT Digital Library
Combined upper limit on Standard Model Higgs boson production at CDF (open access)

Combined upper limit on Standard Model Higgs boson production at CDF

The Higgs boson is the only elementary particle predicted by the Standard Model (SM) that has neither been confirmed nor refuted. The CDF collaboration has performed SM Higgs searches in many channels using p{bar p} collisions at a centre-of-mass energy {radical}s = 1.96 TeV. We present the latest combined Higgs boson search at CDF. Since the previous year's combination, the sensitivity is increased through the addition of new channels, the improvement of existing channels and the addition of new data samples. We also use the latest parton distribution functions and gg {yields} H theoretical cross sections when modelling the signal event yields. Using integrated luminosities of up to 8.2 fb{sup -1}, we observe a good agreement between data and the background prediction. Since we do not see a Higgs boson excess, we set 95% CL upper limits on the Higgs boson cross section in the range between 100 and 200 GeV/c{sup 2}, with 5 GeV/c{sup 2} increments. The observed (expected) limits for a 115 and a 165 GeV/c{sup 2} Higgs boson are 1.55 (1.49) and 0.75 (0.79) x SM, respectively. Since last year, the Higgs boson excluded range by CDF is extended to 156.5 - 173.7 and 100 - 104.5 …
Date: February 1, 2012
Creator: Adrian, Buzatu
System: The UNT Digital Library
Charge independence, charge symmetry breaking in the S-wave nucleon-nucleon interaction, and renormalization (open access)

Charge independence, charge symmetry breaking in the S-wave nucleon-nucleon interaction, and renormalization

We study the interplay between charge symmetry breaking and renormalization in the NN system for S-waves. We find a set of universality relations which disentangle explicitly the known long distance dynamics from low energy parameters and extend them to the Coulomb case. We analyze within such an approach the One-Boson-Exchange potential and the theoretical conditions which allow to relate the proton-neutron, proton-proton and neutron-neutron scattering observables without the introduction of extra new parameters and providing good phenomenological success.
Date: February 1, 2012
Creator: Alvaro Calle Cordon,Manuel Pavon Valderrama,Enrique Ruiz Arriola
System: The UNT Digital Library
Building an Efficient Model for Afterburn Energy Release (open access)

Building an Efficient Model for Afterburn Energy Release

Many explosives will release additional energy after detonation as the detonation products mix with the ambient environment. This additional energy release, referred to as afterburn, is due to combustion of undetonated fuel with ambient oxygen. While the detonation energy release occurs on a time scale of microseconds, the afterburn energy release occurs on a time scale of milliseconds with a potentially varying energy release rate depending upon the local temperature and pressure. This afterburn energy release is not accounted for in typical equations of state, such as the Jones-Wilkins-Lee (JWL) model, used for modeling the detonation of explosives. Here we construct a straightforward and efficient approach, based on experiments and theory, to account for this additional energy release in a way that is tractable for large finite element fluid-structure problems. Barometric calorimeter experiments have been executed in both nitrogen and air environments to investigate the characteristics of afterburn for C-4 and other materials. These tests, which provide pressure time histories, along with theoretical and analytical solutions provide an engineering basis for modeling afterburn with numerical hydrocodes. It is toward this end that we have constructed a modified JWL equation of state to account for afterburn effects on the response of …
Date: February 3, 2012
Creator: Alves, S; Kuhl, A; Najjar, F; Tringe, J; McMichael, L & Glascoe, L
System: The UNT Digital Library
Searching for $Z'$ bosons decaying to gluons (open access)

Searching for $Z'$ bosons decaying to gluons

The production and decay of a new heavy vector boson, a chromophilic Z{prime} vector boson, is described. The chromophilic Z{prime} couples only to two gluons, but its two-body decays are absent, leading to a dominant decay mode of Z{prime} {yields} q{bar q}g. The unusual nature of the interaction predicts a cross-section which grows with m{sub Z{prime}} for a fixed coupling and an accompanying gluon with a coupling that rises with its energy. We study the t{bar t}g decay mode, proposing distinct reconstruction techniques for the observation of an excess and for the measurement of m{sub Z{prime}}. We estimate the sensitivity of current experimental datasets.
Date: February 1, 2012
Creator: Alwall, Johan; /Fermilab /Taiwan, Natl. Taiwan U.; Khader, Mazin; Rajaraman, Arvind; Whiteson, Daniel; Yen, Michael et al.
System: The UNT Digital Library
Legătura dintre sumele Stieltjes şi sumele simetrice elementare (open access)

Legătura dintre sumele Stieltjes şi sumele simetrice elementare

Article discussing studies of the relationship between the Stieltjes sums and the elementary symmetric sums.
Date: February 2012
Creator: Anghel, Nicolae
System: The UNT Digital Library
Composite Octet Searches with Jet Substructure (open access)

Composite Octet Searches with Jet Substructure

Many new physics models with strongly interacting sectors predict a mass hierarchy between the lightest vector meson and the lightest pseudoscalar mesons. We examine the power of jet substructure tools to extend the 7 TeV LHC sensitivity to these new states for the case of QCD octet mesons, considering both two gluon and two b-jet decay modes for the pseudoscalar mesons. We develop both a simple dijet search using only the jet mass and a more sophisticated jet substructure analysis, both of which can discover the composite octets in a dijet-like signature. The reach depends on the mass hierarchy between the vector and pseudoscalar mesons. We find that for the pseudoscalar-to-vector meson mass ratio below approximately 0.2 the simple jet mass analysis provides the best discovery limit; for a ratio between 0.2 and the QCD-like value of 0.3, the sophisticated jet substructure analysis has the best discovery potential; for a ratio above approximately 0.3, the standard four-jet analysis is more suitable.
Date: February 14, 2012
Creator: Bai, Yang & Shelton, Jessie
System: The UNT Digital Library
$B_s\to D_s/B\to D$ Semileptonic Form-Factor Ratios and Their Application to BR($B^0_s\to \mu^+\mu^-$) (open access)

$B_s\to D_s/B\to D$ Semileptonic Form-Factor Ratios and Their Application to BR($B^0_s\to \mu^+\mu^-$)

We calculate form-factor ratios between the semileptonic decays {bar B}{sup 0} {yields} D{sup +} {ell}{sup -}{bar {nu}} and {bar B}{sub s}{sup 0} {yields} D{sub s}{sup +}{ell}{sup -}{bar {nu}} with lattice QCD. These ratios are a key theoretical input in a new strategy to determine the fragmentation fractions of the neutral B decays, which are needed for measurements of BR(B{sub s}{sup 0} {yields} {mu}{sup +}{mu}{sup -}). They use the MILC ensembles of gauge configurations with 2 + 1 flavors of sea quarks at two lattice spacings of approximately 0.12 fm and 0.09 fm. We use the model-independent z parametrization to extrapolate their simulation results at small recoil toward maximum recoil. The results for the form-factor ratios are {line_integral}{sub 0}{sup (s)} (M{sub {pi}}{sup 2})/{line_integral}{sub 0}{sup (d)} (M{sub K}{sup 2}) = 1.046(44){sub stat.}(15){sub syst.} and {line_integral}{sub 0}{sup (s)} (M{sub {pi}}{sup 2})/{line_integral}{sub 0}{sup (d)} (M{sub {pi}}{sup 2}) = 1.054(47){sub stat.}(17){sub syst.}. In contrast to a QCD sum-rule calculation, no significant departure from U-spin (d {leftrightarrow} s) symmetry is observed.
Date: February 1, 2012
Creator: Bailey, Jon A.; Bazavov, A.; Bernard, C.; Bouchard, C. M.; DeTar, C.; Du, Daping et al.
System: The UNT Digital Library
Planetary Candidates Observed by Kepler, III: Analysis of the First 16 Months of Data (open access)

Planetary Candidates Observed by Kepler, III: Analysis of the First 16 Months of Data

New transiting planet candidates are identified in sixteen months (May 2009 - September 2010) of data from the Kepler spacecraft. Nearly five thousand periodic transit-like signals are vetted against astrophysical and instrumental false positives yielding 1091 viable new planet candidates, bringing the total count up to over 2,300. Improved vetting metrics are employed, contributing to higher catalog reliability. Most notable is the noise-weighted robust averaging of multiquarter photo-center offsets derived from difference image analysis which identifies likely background eclipsing binaries. Twenty-two months of photometry are used for the purpose of characterizing each of the new candidates. Ephemerides (transit epoch, T{sub 0}, and orbital period, P) are tabulated as well as the products of light curve modeling: reduced radius (R{sub P}/R{sub {star}}), reduced semi-major axis (d/R{sub {star}}), and impact parameter (b). The largest fractional increases are seen for the smallest planet candidates (197% for candidates smaller than 2R{sub {circle_plus}} compared to 52% for candidates larger than 2R{sub {circle_plus}}) and those at longer orbital periods (123% for candidates outside of 50 day orbits versus 85% for candidates inside of 50 day orbits). The gains are larger than expected from increasing the observing window from thirteen months (Quarter 1 - Quarter 5) to …
Date: February 1, 2012
Creator: Batalha, Natalie M.; Rowe, Jason F.; Bryson, Stephen T.; Barclay, Thomas; Burke, Christopher J.; Caldwell, Douglas A. et al.
System: The UNT Digital Library
Facts About XLDB-2011 (open access)

Facts About XLDB-2011

This note provides details of the 5th Extremely Large Databases Conference and Invitational Workshop that were held in 2011 on 18-19 October and 20 October, respectively, at the SLAC National Accelerator Laboratory in Menlo Park, California. The main goals of the conference were: (1) Encourage and accelerate the exchange of ideas between users trying to build extremely large databases worldwide and database solution providers; (2) Share lessons, trends, innovations, and challenges related to building extremely large databases; (3) Facilitate the development and growth of practical technologies for extremely large databases; and (4) Strengthen, expand, and engage the XLDB community.
Date: February 22, 2012
Creator: Becla, Jacek; Lim, Kian-Tat & Wang, Daniel L.
System: The UNT Digital Library
Improvements to High-Speed Monitoring of Events in Extreme Environments Using Fiber-optic Bragg Sensors (open access)

Improvements to High-Speed Monitoring of Events in Extreme Environments Using Fiber-optic Bragg Sensors

None
Date: February 17, 2012
Creator: Benterou, J J & Udd, E
System: The UNT Digital Library
Simplifying Multi-loop Integrands of Gauge Theory and Gravity Amplitudes (open access)

Simplifying Multi-loop Integrands of Gauge Theory and Gravity Amplitudes

We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N = 4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D = 11/2, the same dimension as for N = 4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N = 8 supergravity as the subleading-in-1/N{sub c}{sup 2} single-trace divergence in N = 4 super-Yang-Mills theory.
Date: February 15, 2012
Creator: Bern, Z.; Carrasco, J.J.M.; Dixon, L.J.; Johansson, H. & Roiban, R.
System: The UNT Digital Library
NLO Vector Boson Production With Light Jets (open access)

NLO Vector Boson Production With Light Jets

In this contribution we present recent progress in the computation of next-to-leading order (NLO) QCD corrections for the production of an electroweak vector boson in association with jets at hadron colliders. We focus on results obtained using the virtual matrix element library BlackHat in conjunction with SHERPA, focusing on results relevant to understanding the background to top production. The production of a vector boson in association with several jets at the Large Hadron Collider (LHC) is an important background for other Standard Model processes as well as new physics signals. In particular, the production of a W boson in association with many jets is an important background for processes involving one or more top quarks. Precise predictions for the backgrounds are crucial to measurement of top-quark processes. Vector boson production in association with multiple jets is also a very important background for many SUSY searches, as it mimics the signatures of many typical decay chains. Here we will discuss how polarization information can be used as an additional handle to differentiate top pair production from 'prompt' W-boson production. More generally, ratios of observables, for example for events containing a W boson versus those containing a Z boson, are expected to …
Date: February 15, 2012
Creator: Bern, Z.; Diana, G.; Dixon, L.J.; Febres Cordero, F.; Forde, D.; Gleisberg, T. et al.
System: The UNT Digital Library
Bounds and self-consistent estimates for elastic constants of polycrystals of hcp solid He{sup 4} (open access)

Bounds and self-consistent estimates for elastic constants of polycrystals of hcp solid He{sup 4}

Recent advances in methods for computing both Hashin-Shtrikman bounds and related selfconsistent (or CPA) estimates of elastic constants for polycrystals composed of randomly oriented crystals can be applied successfully to hexagonal close packed solid He{sup 4}. In particular, since the shear modulus C{sub 44} of hexagonal close-packed solid He is known to undergo large temperature variations when 20 mK {<=}#20; T {<=}#20; 200 mK, bounds and estimates computed with this class of effective medium methods, while using C{sub 44} {r_arrow} 0 as a proxy for melting, are found to be both qualitatively and quantitatively very similar to prior results obtained using Monte Carlo methods. Hashin- Shtrikman bounds provide significantly tighter constraints on the polycrystal behavior than do the traditional Voigt and Reuss bounds.
Date: February 15, 2012
Creator: Berryman, J. G.
System: The UNT Digital Library
The role of members of viral quasispecies in adaptation to new host environments (open access)

The role of members of viral quasispecies in adaptation to new host environments

None
Date: February 10, 2012
Creator: Borucki, M.; Allen, J. E.; Chen-Harris, H.; Mabery, S.; Vanier, G.; Torres, C. et al.
System: The UNT Digital Library
N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops (open access)

N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops

We present the full two-loop four-graviton amplitudes in N = 4, 5, 6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in N = 0, 1, 2 supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for N = 8 supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.
Date: February 15, 2012
Creator: Boucher-Veronneau, C. & Dixon, L. J.
System: The UNT Digital Library
The Impact of Intrinsic Heavy Quark Distributions in the Proton on New Physics Searches at the High Intensity Frontier (open access)

The Impact of Intrinsic Heavy Quark Distributions in the Proton on New Physics Searches at the High Intensity Frontier

The possibility of an intense proton facility, at 'Project X' or elsewhere, will provide many new opportunities for searches for physics beyond the Standard Model. A Project X can serve a yet broader role in the search for new physics, and in this note we highlight the manner in which thus-enabled studies of the flavor structure of the proton, particularly of its intrinsic heavy quark content, facilitate other direct and indirect searches for new physics. Intrinsic heavy quarks in both light and heavy hadrons play a key role in searches for physics BSM with hadrons - and their study at the Intensity Frontier may prove crucial to establishing its existence.
Date: February 16, 2012
Creator: Brodsky, Stanley & Gardner, Susan
System: The UNT Digital Library
Atoms in Flight: The Remarkable Connections between Atomic and Hadronic Physics (open access)

Atoms in Flight: The Remarkable Connections between Atomic and Hadronic Physics

Atomic physics and hadron physics are both based on Yang Mills gauge theory; in fact, quantum electrodynamics can be regarded as the zero-color limit of quantum chromodynamics. I review a number of areas where the techniques of atomic physics provide important insight into the theory of hadrons in QCD. For example, the Dirac-Coulomb equation, which predicts the spectroscopy and structure of hydrogenic atoms, has an analog in hadron physics in the form of light-front relativistic equations of motion which give a remarkable first approximation to the spectroscopy, dynamics, and structure of light hadrons. The renormalization scale for the running coupling, which is unambiguously set in QED, leads to a method for setting the renormalization scale in QCD. The production of atoms in flight provides a method for computing the formation of hadrons at the amplitude level. Conversely, many techniques which have been developed for hadron physics, such as scaling laws, evolution equations, and light-front quantization have equal utility for atomic physics, especially in the relativistic domain. I also present a new perspective for understanding the contributions to the cosmological constant from QED and QCD.
Date: February 16, 2012
Creator: Brodsky, Stanley J.
System: The UNT Digital Library
Transversity from First Principles in QCD (open access)

Transversity from First Principles in QCD

Transversity observables, such as the T-odd Sivers single-spin asymmetry measured in deep inelastic lepton scattering on polarized protons and the distributions which are measured in deeply virtual Compton scattering, provide important constraints on the fundamental quark and gluon structure of the proton. In this talk I discuss the challenge of computing these observables from first principles; i.e.; quantum chromodynamics, itself. A key step is the determination of the frame-independent light-front wavefunctions (LFWFs) of hadrons - the QCD eigensolutions which are analogs of the Schroedinger wavefunctions of atomic physics. The lensing effects of initial-state and final-state interactions, acting on LFWFs with different orbital angular momentum, lead to T-odd transversity observables such as the Sivers, Collins, and Boer-Mulders distributions. The lensing effect also leads to leading-twist phenomena which break leading-twist factorization such as the breakdown of the Lam-Tung relation in Drell-Yan reactions. A similar rescattering mechanism also leads to diffractive deep inelastic scattering, as well as nuclear shadowing and non-universal antishadowing. It is thus important to distinguish 'static' structure functions, the probability distributions computed the target hadron's light-front wavefunctions, versus 'dynamical' structure functions which include the effects of initial- and final-state rescattering. I also discuss related effects such as the J = …
Date: February 16, 2012
Creator: Brodsky, Stanley J. & /SLAC /Southern Denmark U., CP3-Origins
System: The UNT Digital Library
Pair Production Constraints on Superluminal Neutrinos Revisited (open access)

Pair Production Constraints on Superluminal Neutrinos Revisited

We revisit the pair creation constraint on superluminal neutrinos considered by Cohen and Glashow in order to clarify which types of superluminal models are constrained. We show that a model in which the superluminal neutrino is effectively light-like can evade the Cohen-Glashow constraint. In summary, any model for which the CG pair production process operates is excluded because such timelike neutrinos would not be detected by OPERA or other experiments. However, a superluminal neutrino which is effectively lightlike with fixed p{sup 2} can evade the Cohen-Glashow constraint because of energy-momentum conservation. The coincidence involved in explaining the SN1987A constraint certainly makes such a picture improbable - but it is still intrinsically possible. The lightlike model is appealing in that it does not violate Lorentz symmetry in particle interactions, although one would expect Hughes-Drever tests to turn up a violation eventually. Other evasions of the CG constraints are also possible; perhaps, e.g., the neutrino takes a 'short cut' through extra dimensions or suffers anomalous acceleration in matter. Irrespective of the OPERA result, Lorentz-violating interactions remain possible, and ongoing experimental investigation of such possibilities should continue.
Date: February 16, 2012
Creator: Brodsky, Stanley J. & Gardner, Susan
System: The UNT Digital Library
Scale Setting Using the Extended Re normalization Group and the Principle of Maximal Conformality: the QCD Coupling at Four Loops (open access)

Scale Setting Using the Extended Re normalization Group and the Principle of Maximal Conformality: the QCD Coupling at Four Loops

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both the renormalization scale- and scheme-parameter transformations, provide a convenient way for estimating the scale- and scheme-dependence of the physical process. In this paper, we present a solution for the scale-equation of the extended renormalization group equations at the four-loop level. Using the principle of maximum conformality (PMC)/Brodsky-Lepage-Mackenzie (BLM) scale-setting method, all non-conformal {beta}{sub i} terms in the perturbative expansion series can be summed into the running coupling, and the resulting scale-fixed predictions are independent of the renormalization scheme. Different schemes lead to different effective PMC/BLM scales, but the final results are scheme independent. Conversely, from the requirement of scheme independence, one not only can obtain scheme-independent commensurate scale relations among different observables, but also determine the scale displacements among the PMC/BLM scales which are derived under different schemes. In principle, the PMC/BLM scales can be fixed order-by-order, and as a useful reference, we present a systematic and scheme-independent procedure for setting PMC/BLM scales up to NNLO. An explicit application for determining the scale setting of R{sub …
Date: February 16, 2012
Creator: Brodsky, Stanley J. & Wu, Xing-Gang
System: The UNT Digital Library