119188644
QCD bulk thermodynamics and conserved charge fluctuations with HISQ fermions
After briefly reviewing recent progress by the HotQCD collaboration in studying the 2+1 flavor QCD equation of state, we will focus on results on fluctuations of conserved charges by the BNL-Bielefeld and HotQCD collaborations. Higher order cumulants of the net-charge distributions are increasingly dominated by a universal scaling behavior, which arises due to a critical point of QCD in the chiral limit. Considering cumulants up to the 6^{th} order, we observe that they generically behave as expected from universal scaling laws, which is quite different from cumulants calculated within the hadron resonance gas model. Taking ratios of these cumulants, we obtain volume independent results that can be compared to the experimental measurements. We will argue that the freeze-out chemical potentials and the freeze-out temperature, usually obtained by a HRG model fit to the measured hadronic yields, can also be obtained in a model independent way from ab-initio lattice QCD calculations by utilizing observables related to conserved charge fluctuations. Further, we will show that the freeze-out strangeness and electric charge chemical potentials can be fixed by imposing strangeness neutrality and isospin asymmetry constraints in the lattice QCD calculations, in order to accommodate conditions met in heavy ion collisions. All results have been obtained with the highly improved staggered quark action (HISQ) and almost physical quark masses on lattices with temporal extent of N_\tau=6,8,10,12. 
After briefly reviewing recent progress by the HotQCD collaboration in studying the 2+1 flavor QCD equation of state, we will focus on results on fluctuations of conserved charges by the BNL-Bielefeld and HotQCD collaborations. Higher order cumulants of the net-charge distributions are increasingly dominated by a universal scaling behavior, which arises due to a critical point of QCD in the chiral limit. Considering cumulants up to the 6(th) order, we observe that they generically behave as expected from universal scaling laws, which is quite different from cumulants calculated within the hadron resonance gas model. Taking ratios of these cumulants, we obtain volume independent results that can be compared to the experimental measurements. We will argue that the freeze-out chemical potentials and the freeze-out temperature, usually obtained by a HRG model fit to the measured hadronic yields, can also be obtained in a model independent way from ab-initio lattice QCD calculations by utilizing observables related to conserved charge fluctuations. Further, we will show that the freeze-out strangeness and electric charge chemical potentials can be fixed by imposing strangeness neutrality and isospin asymmetry constraints in the lattice QCD calculations, in order to accommodate conditions met in heavy ion collisions. All results have been obtained with the highly improved staggered quark action (HISQ) and almost physical quark masses on lattices with temporal extent of N(τ) = 6, 8, 10, 12.
17537588
Lattice simulations with chemical potential
After giving an overview of recently invented methods for simulating lattice QCD at small mu/T, we discuss some results for bulk thermodynamic quantities of QCD matter coming from those methods. We focus on the transition line and the critical endpoint in the QCD phase diagram.
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.
16120128
Bulk thermodynamics and charge fluctuations at non-vanishing baryon density
We present results on bulk thermodynamic quantities as well as net baryon number, strangeness and electric charge fluctuations in QCD at non-zero density and temperature obtained from lattice calculations with almost physical quark masses for two values of the lattice cut-off aT = 1/4 and 1/6. We show that with our improved p4fa3-action the cut-off effects are under control when using lattices with a temporal extent of 6 or larger and that the contribution to the equation of state, which is due to a finite chemical potential is small for {mu}{sub q}/T < 1. Moreover, at vanishing chemical potential, i.e. under conditions almost realized at RHIC and the LHC, quartic fluctuations of net baryon number and strangeness are large in a narrow temperature interval characterizing the transition region from the low to high temperature phase. At non-zero baryon number density, strangeness fluctuations are enhanced and correlated to fluctuations of the net baryon number. If strangeness is furthermore forced to vanish, as it may be the case in systems created in heavy ion collisions, strangeness fluctuations are significantly smaller than baryon number fluctuations.
16115905
Flavor and quark mass dependence of QCD thermodynamics
We calculate the transition temperature in 2 and 3-flavor QCD using improved gauge and staggered fermion actions on lattices with temporal extent Nτ = 4. We find Tc = 173 (8) MeV and 154 (8) MeV for nf = 2 and 3, respectively. In the case of 3-flavor QCD we present evidence that the chiral critical point, i.e. the second order endpoint of the line of first order chiral phase transitions, belongs to the universality class of the 3d Ising model.
119274896
Quark number susceptibilities at high temperatures
We calculate second and fourth order quark number susceptibilities for 2+1 flavor QCD in the high temperature region. In our study we use two improved staggered fermion formulations, namely the highly improved staggered quark formulation, and the so-called p4 formulation, as well as several lattice spacings. Second order quark number susceptibilities are calculated using both improved staggered fermion formulations, and we show that in the continuum limit the two formulations give consistent results. The fourth order quark number susceptibilities are studied only using the p4 formulation and at non-zero lattice spacings. We compare our results on quark number susceptibilities with recent weak coupling calculations, and find that these agree reasonably well with the lattice calculations within the estimated uncertainties.
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.
17264957
An Effective Higgsless Theory: Satisfying Electroweak Constraints and a Heavy Top Quark
The main challenge faced by Higgsless models of electroweak symmetry breaking is to reconcile the experimental constraints imposed by the precision electroweak data and the top quark phenomenology with the unitarity constraints imposed by longitudinal gauge boson scattering amplitudes. In this paper we expand on previous work, giving details of how delocalized fermions can be used to adjust the S parameter to zero, while keeping the T and U parameters naturally suppressed. We also show that it is possible to obtain the top quark mass, without affecting the delay of unitarity violation of the W{sup +}W{sup -}{yields}W{sup +}W{sup -} scattering amplitude, by separating the mass scales of the fermion sector (1/R{sub f}) from that of the gauge sector (1/R{sub g}). The fermion sector scale 1/R{sub f} is only weakly constrained by unitarity of the tt{yields}W{sup +}W{sup -} scattering amplitude; thus the ratio R{sub g}/R{sub f} can be quite large, and the top mass can be achieved easily. Anomalous right-handed couplings involving the third generation quarks also avoid constraints from experimental data if 1/R{sub f} is sufficiently large.
59063827
Emittance Measurement Techniques used in the 1 MeV RFQ for the PET Isotope Linac at Fermilab
Beam emittance measurements have been performed on the {sup 3}He{sup +} beam at the PET isotope production accelerator, being commissioned at Fermilab for the Biomedical Research Foundation in Shreveport, Louisiana, USA. Emittances have been measured at injection to and extraction from the first RFQ, at 20 keV and 1 MeV, respectively. A single slit followed by a 48 electrode collector is used in the standard way to measure the divergence of the {sup 3}He{sup +} beam as a function of position. Noise reduction operations have been developed, both in hardware and software. These techniques and the emittance measurement results are presented.
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].
117019402
BFKL versus O (alpha-s**3) corrections to large rapidity dijet production
We examine dijet production at large rapidity intervals at Tevatron energies by comparing an exact ${\cal O}(\alpha_s^3)$ calculation with the BFKL approximation, which resums the leading powers of the rapidity interval $y$ to all orders in $\alpha_s$. We analyze the dependence of the exact ${\cal O}(\alpha_s^3)$ calculation on the jet cone-size as a function of $y$, and use this cross section to define an ``effective rapidity'' $\hat y$ which reduces the error that the large-$y$ approximation induces on the kinematics. Using $\hat y$ in the BFKL resummation, we reexamine jet production at large transverse momenta and the transverse momentum decorrelation of the tagging jets. We find less dramatic, but still significant, effects than found previously using the large-$y$ approximation.