5495552
The infrared behavior of one-loop gluon amplitudes at next-to-next-to-leading order
For the case of n-jet production at next-to-next-to-leading order in the QCD coupling, in the infrared divergent corners of phase space where particles are collinear or soft, one must evaluate (n + 1)-parton final-state one-loop amplitudes through O(ǫ2), where ǫ is the dimensional regularization parameter. For the case of gluons, we present to all orders in ǫ the required universal functions which describe the behavior of one-loop amplitudes in the soft and collinear regions of phase space. An explicit example is discussed for three-parton production in multi-Regge kinematics that has applications to the next-to-leading logarithmic corrections to the BFKL equation. ∗On leave of absence from I.N.F.N., Sezione di Torino, Italy. The quest to obtain ever increasing precision in perturbative QCD requires calculations to higher orders in the QCD coupling, αs. Over the years, significant effort has been expended on computing the next-to-leading order (NLO) contributions to multi-jet rates within perturbative QCD. An important next step in the endeavor to obtain higher precision would be the computation of next-to-next-to-leading-order (NNLO) contributions to multi-jet rates. As an example, although the NLO contributions to ee → 3 jets have been computed for some time now [1, 2], the NNLO contributions have yet to be obtained. A calculation of these NNLO contributions would be needed to further reduce the theoretical uncertainty in the determination of αs from event shape variables [3]. Considerable effort has also been expended in the computation of leading and next-to-leading logarithmic contributions to the BFKL equations for parton evolution at small x [4, 5]. These two problems are, of course, connected since the logarithms that are resummed in the BFKL equations also appear at fixed orders of perturbation theory. Indeed, the one-loop Lipatov vertex may be extracted [6, 7] from one-loop five-gluon helicity amplitudes [8]. In order to compute a cross section at NNLO, three series of amplitudes are required in the squared matrix elements: a) tree-level, one-loop, and two-loop amplitudes for the production of n particles; b) tree-level and one-loop amplitudes for the production of n + 1 particles; c) tree-level amplitudes for the production of n + 2 particles. For the case of NNLO ee → 3 jets the five-parton final-state tree [9] amplitudes, as well as four-parton final-state one-loop amplitudes exist in both helicity [10] and squared matrixelement forms [11], but as we discuss below, in order to be used in NNLO computations additional terms enter because of infrared issues. For the required two-loop three-parton final-state amplitudes no computations exist, as yet. Indeed, no two-loop amplitude computations exist for cases containing more than a single kinematic variable, except in the special cases of maximal supersymmetry [12]. Besides these amplitudes it is also important to have a detailed understanding of the infrared singularities that arise from virtual loops and from unresolved real emission when the momenta of particles become either soft or collinear. (For hadronic initial states infrared divergences are also associated with initial-state parton distribution functions.) These infrared divergences show themselves as poles in the dimensional regularization parameter ǫ = (4 − D)/2. By the Kinoshita-Lee-Nauenberg theorem [13] the infrared singularities must cancel for sufficiently inclusive physical quantities. However, it is only when the various contributions are combined that the infrared singularities cancel. At NLO the structure of the infrared singularities has been extensively studied. The singularities occur in a universal way, i.e. independent of the particular particle production amplitude considered. Accordingly, soft singularities have been accounted for by universal soft functions [14, 15], and collinear singularities by universal splitting functions [16]. A detailed discussion of the infrared singularities at NLO for ee → jets may be found, for example, in ref. [17].
6678978
Ultrahigh-energy neutrino–nucleon cross sections and perturbative unitarity
Abstract Unitarity relates the total cross section for neutrino–nucleon scattering to the neutrino–nucleon forward scattering amplitude. Assuming the validity of the perturbative expansion of the forward amplitude in the weak coupling constant, we derive a unitarity bound on the inelastic cross section. The inelastic cross section saturates this bound at a typical neutrino energy E ν ≃10 8  GeV. This implies that calculations of the inelastic cross section that use current parton distribution functions and lowest order weak perturbation theory are unreliable above this energy.
17272111
Effects of fermion localization in Higgsless theories and electroweak constraints
Abstract Extra-dimensional Higgsless models with electroweak symmetry breaking through boundary conditions generically have difficulties with electroweak precision constraints, when the fermions are localized to the “branes” in the fifth dimension. In this Letter we show that these constraints can be relaxed by allowing the light fermions to have a finite extent into the bulk of the fifth dimension. The T and U electroweak parameters can be naturally suppressed by a custodial symmetry, while the S parameter can be made to vanish through a cancellation, if the leakage into the bulk of the light gauge fields and the light left-handed fermion fields are of the same size. This cancellation is possible while allowing realistic values for the first two generations of fermion masses, although special treatment is probably required for the top quark. We present this idea here in the context of a specific continuum theory-space model; however, it can be applied to any five-dimensional Higgsless model, either with a flat or a warped background.
17090149
Higgsless electroweak symmetry breaking from theory space
We investigate unitarity of W+W− scattering in the context of theory space models of the form U(1) × [SU(2)]N × SU(2)N+1, which are broken down to U(1)EM by non-linear Σ fields, without the presence of a physical Higgs Boson. By allowing the couplings of the U(1) and the final SU(2)N+1 to vary, we can fit the W and Z masses, and we find that the coefficient of the term in the amplitude that grows as E2/mW2 at high energies is suppressed by a factor of (N+1)−2. In the N+1→∞ limit the model becomes a 5-dimensional SU(2) gauge theory defined on an interval, where boundary terms at the two ends of the interval break the SU(2) down to U(1)EM. These boundary terms also modify the Kaluza-Klein (KK) mass spectrum, so that the lightest KK states can be identified as the W and Z bosons. The T parameter, which measures custodial symmetry breaking, is naturally small in these models. Depending on how matter fields are included, the strongest experimental constraints come from precision electroweak limits on the S parameter.
17634589
Radiative electroweak symmetry breaking in a Little Higgs model
We present a new Little Higgs model, motivated by the deconstruction of a five-dimensional gauge-Higgs model. The approximate global symmetry is SO(5)0 × SO(5)1, breaking to SO(5), with a gauged subgroup of [SU(2)0L × U(1)0R] × O(4)1, breaking to SU(2)L ×U(1)Y . Radiative corrections produce an additional small vacuum misalignment, breaking the electroweak symmetry down to U(1)EM. Novel features of this model are: the only un-eaten pseudo-Goldstone boson in the effective theory is the Higgs boson; the model contains a custodial symmetry, which ensures that $ \widehat{T} = 0 $ at tree-level; and the potential for the Higgs boson is generated entirely through one-loop radiative corrections. A small negative mass-squared in the Higgs potential is obtained by a cancellation between the contribution of two heavy partners of the top quark, which is readily achieved over much of the parameter space. We can then obtain both a vacuum expectation value of v = 246 GeV and a light Higgs boson mass, which is strongly correlated with the masses of the two heavy top quark partners. For a scale of the global symmetry breaking of f = 1 TeV and using a single cutoff for the fermion loops, the Higgs boson mass satisfies 120 GeV ≲ MH ≲ 150 GeV over much of the range of parameter space. For f raised to 10 TeV, these values increase by about 40 GeV. Effects at the ultraviolet cutoff scale may also raise the predicted values of the Higgs boson mass, but the model still favors MH ≲ 200GeV.
118429632
Higgs Boson Cross Section from CTEQ-TEA Global Analysis
We study the uncertainties of the Higgs boson production cross section through the gluon fusion subprocess at the LHC (with $\sqrt s=7, 8$ and $14$ TeV) arising from the uncertainties of the parton distribution functions (PDFs) and of the value of the strong coupling constant $\alpha_s(M_Z)$. These uncertainties are computed by two complementary approaches, based on the Hessian and the Lagrange Multiplier methods within the CTEQ-TEA global analysis framework. We find that their predictions for the Higgs boson cross section are in good agreement. Furthermore, the result of the Lagrange Multiplier method supports the prescriptions we have previously provided for using the Hessian method to calculate the combined PDF and $\alpha_s$ uncertainties, and to estimate the uncertainties at the $68\%$ confidence level by scaling them from the $90\%$ confidence level.
118327970
Universal O(N) scaling and the chiral critical line in (2+1)-flavor QCD with small chemical potentials
We show that for small values of the chemical potential the curvature of the phase transition line can be deduced from an analysis of scaling properties of the chiral condensate and its susceptibilities. We make use of a recent analysis of the magnetic equation of state in (2+1)-flavor QCD where a connection between the QCD parameters and the universal scaling fields could be established. The remaining dependence of the reduced temperature on the chemical potential can be fixed by an analysis of a mixed susceptibility, obtained from a derivative with respect to quark mass and chemical potential. We extract this dependence which describes the curvature of the phase transition line, at two values of the cut-off, $aT=1/4$ and $1/8$. We find that cut-off effects are small for the curvature parameter and determine the transition line in the chiral limit to leading order in the light quark chemical potential. We obtain $T_c(\mu_B)/T_c(0) = 1 - 0.00656(66) (\mu_B/T)^2 +{\cal O}(\mu_B^4)$.
18184787
QCD THERMODYNAMICS WITH ALMOST REALISTIC QUARK MASSES.
Ongoing calculations on the QCDOC supercomputer at Brookhaven National Laboratory and the APEnext installation at the University of Bielefeld aim to determine the critical temperature of the QCD phase transition as well as the equation of state with almost realistic quark masses. We will discuss preliminary results of the quark mass and cut-off dependence of order parameters, susceptibilities, static quark potentials and the critical temperature in (2+1)-flavor QCD. All these quantities are of immediate interest for heavy ion phenomenology.
15858058
Non-zero density QCD by the Taylor expansion method: The isentropic equation of state, hadronic fluctuations and more
We discuss the Taylor expansion approach to non-zero baryon chemical potential ($\mu_B$) and present results on expanion coefficients of the pressure and energy density up to the 6-th order in $\mu_B$. Calculations have been performed with (2+1)-flavor of improved staggerd fermions (p4fat3) and almost physical masses on lattices with temporal extent of four and six time slices. We use the expansion coefficients to construct the isentropic equation of state on lines of constant entropy per baryon number and various different hadronic fluctuations. Furthermore, we estimate the radius of convegence of our expansion, which can be seen as a method to analyze the structure of the QCD phase diagram.
19037480
QCD Thermodynamics with an almost realistic quark mass spectrum
We will report on the status of a new large scale calculation of thermodynamic quantities in QCD with light up and down quarks corresponding to an almost physical light quark mass value and a heavier strange quark mass. These calculations are currently being performed on the QCDOC Teraflops computers at BNL. We will present new lattice calculations of the transition temperature and various susceptibilities reflecting properties of the chiral transition. All these quantities are of immediate interest for heavy ion phenomenology.
46056796
Fermilab electron cooling project: commissioning of the 5 MeV recirculation test set-up
An important part of the Fermilab's Recycler Electron Cooling (REC) project is a recirculation test which is performed using a 5-MV electrostatic accelerator, a Pelletron, with two tubes and a simplified beam line with one 180-degree bend. The main goal of the test is to demonstrate stable operation of a 4.4-MeV, 0.5-A DC electron beam. The paper describes the set-up and the early experimental results.