Building Blocks for Subleading Helicity Operators

On-shell helicity methods provide powerful tools for determining scattering amplitudes, which have a one-to-one correspondence with leading power helicity operators in the Soft-Collinear Effective Theory (SCET) away from singular regions of phase space. We show that helicity based operators are also useful for enumerating power suppressed SCET operators, which encode subleading amplitude information about singular limits. In particular, we present a complete set of scalar helicity building blocks that are valid for constructing operators at any order in the SCET power expansion. We also describe an interesting angular momentum selection rule that restricts how these building blocks can be assembled.Comment: 22 pages without references, 2 figures v2. Updated minor typo in Table

A Precise Determination of αs\alpha_s from the C-parameter Distribution

We present a global fit for $\alpha_s(m_Z)$, analyzing the available C-parameter data measured at center-of-mass energies between $Q=35$ and $207$ GeV. The experimental data is compared to a N$^3$LL$^\prime$ + $\mathcal{O}(\alpha_s^3)$ + $\Omega_1$ theoretical prediction (up to the missing 4-loop cusp anomalous dimension), which includes power corrections coming from a field theoretical nonperturbative soft function. The dominant hadronic parameter is its first moment $\Omega_1$, which is defined in a scheme which eliminates the $\mathcal{O}(\Lambda_{\rm QCD})$ renormalon ambiguity. The resummation region plays a dominant role in the C-parameter spectrum, and in this region a fit for $\alpha_s(m_Z)$ and $\Omega_1$ is sufficient. We find $\alpha_s(m_Z)=0.1123\pm 0.0015$ and $\Omega_1=0.421\pm 0.063\,{\rm GeV}$ with $\chi^2/\rm{dof}=0.988$ for $404$ bins of data. These results agree with the prediction of universality for $\Omega_1$ between thrust and C-parameter within 1-$\sigma$.Comment: 24 pages, 19 figure

C-parameter Distribution at N3{}^3LL′^\prime including Power Corrections

We compute the $e^+ e^-$ C-parameter distribution using the Soft-Collinear Effective Theory with a resummation to N${}^3$LL$^\prime$ accuracy of the most singular partonic terms. This includes the known fixed-order QCD results up to ${\cal O} (\alpha_s^3)$, a numerical determination of the two loop non-logarithmic term of the soft function, and all logarithmic terms in the jet and soft functions up to three loops. Our result holds for $C$ in the peak, tail, and far tail regions. Additionally, we treat hadronization effects using a field theoretic nonperturbative soft function, with moments $\Omega_n$. In order to eliminate an ${\cal O} (\Lambda_{\rm QCD})$ renormalon ambiguity in the soft function, we switch from the $\overline {\rm MS}$ to a short distance "Rgap" scheme to define the leading power correction parameter $\Omega_1$. We show how to simultaneously account for running effects in $\Omega_1$ due to renormalon subtractions and hadron mass effects, enabling power correction universality between C-parameter and thrust to be tested in our setup. We discuss in detail the impact of resummation and renormalon subtractions on the convergence. In the relevant fit region for $\alpha_s(m_Z)$ and $\Omega_1$, the perturbative uncertainty in our cross section is $\simeq 3\%$ at $Q=m_Z$.Comment: 34 pages, 20 figure

Soft Functions for Generic Jet Algorithms and Observables at Hadron Colliders

We introduce a method to compute one-loop soft functions for exclusive $N$-jet processes at hadron colliders, allowing for different definitions of the algorithm that determines the jet regions and of the measurements in those regions. In particular, we generalize the $N$-jettiness hemisphere decomposition of [Jouttenus 2011] in a manner that separates the dependence on the jet boundary from the observables measured inside the jet and beam regions. Results are given for several factorizable jet definitions, including anti-$k_T$, XCone, and other geometric partitionings. We calculate explicitly the soft functions for angularity measurements, including jet mass and jet broadening, in $pp \to L + 1$ jet and explore the differences for various jet vetoes and algorithms. This includes a consistent treatment of rapidity divergences when applicable. We also compute analytic results for these soft functions in an expansion for a small jet radius $R$. We find that the small-$R$ results, including corrections up to $\mathcal{O}(R^2)$, accurately capture the full behavior over a large range of $R$.Comment: 33 pages + appendices, 17 figures, v2: journal version, v3: fixed typo in eq.(4.37

Factorization for jet radius logarithms in jet mass spectra at the LHC

To predict the jet mass spectrum at a hadron collider it is crucial to account for the resummation of logarithms between the transverse momentum of the jet and its invariant mass mJ . For small jet areas there are additional large logarithms of the jet radius R, which affect the convergence of the perturbative series. We present an analytic framework for exclusive jet production at the LHC which gives a complete description of the jet mass spectrum including realistic jet algorithms and jet vetoes. It factorizes the scales associated with mJ , R, and the jet veto, enabling in addition the systematic resummation of jet radius logarithms in the jet mass spectrum beyond leading logarithmic order. We discuss the factorization formulae for the peak and tail region of the jet mass spectrum and for small and large R, and the relations between the different regimes and how to combine them. Regions of experimental interest are classified which do not involve large nonglobal logarithms. We also present universal results for nonperturbative effects and discuss various jet vetoes.German Science Foundation (Emmy-Noether Grant No. TA 867/1-1, the Collaborative Research Center (SFB) 676 Particles, Strings and the Early Universe)United States. Dept. of Energy. Office of Nuclear Physics (Grant No. DE-SC0011090)Simons Foundation (Investigator grant 327942)MIT International Science and Technology Initiative

Soft functions for generic jet algorithms and observables at hadron colliders

We introduce a method to compute one-loop soft functions for exclusive N - jet processes at hadron colliders, allowing for different definitions of the algorithm that determines the jet regions and of the measurements in those regions. In particular, we generalize the N -jettiness hemisphere decomposition of ref. [1] in a manner that separates the dependence on the jet boundary from the observables measured inside the jet and beam regions. Results are given for several factorizable jet definitions, including anti-k[subscript T], XCone, and other geometric partitionings. We calculate explicitly the soft functions for angularity measurements, including jet mass and jet broadening, in pp → L + 1 jet and explore the differences for various jet vetoes and algorithms. This includes a consistent treatment of rapidity divergences when applicable. We also compute analytic results for these soft functions in an expansion for a small jet radius R. We find that the small-R results, including corrections up to O(R[superscript 2]), accurately capture the full behavior over a large range of R.United States. Dept. of Energy. Office of Nuclear Physics (Grant DE-SC0011090)United States. Dept. of Energy. Office of Nuclear Physics (Grant DE-AC02-05CH11231)United States. Dept. of Energy. Office of Nuclear Physics (Grant DEAC52-06NA25396)Los Alamos National Laboratory. Laboratory Directed Research and Development ProgramSimons Foundation (Investigator Grant 327942)Massachusetts Institute of Technology (Global MISTI Collaboration Grant

Accuracy and precision in collider event shapes

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2016.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 159-167).In order to gain a deeper understanding of the Standard Model of particle physics and test its limitations, it is necessary to carry out accurate calculations to compare with experimental results. Event shapes provide a convenient way for compressing the extremely complicated data from each collider event into one number. Using eective theories and studying the appropriate limits, it is possible to probe the underlying physics to a high enough precision to extract interesting information from the experimental results. In the initial sections of this work, we use a particular event shape, C-parameter, in order to make a precise measurement of the strong coupling constant, s. First, we compute the e+e- C-parameter distribution using the Soft-Collinear Eective Theory (SCET) with a resummation to N³LL' accuracy of the most singular partonic terms. Our result holds for C in the peak, tail, and far-tail regions. We treat hadronization effects using a field theoretic nonperturbative soft function, with moments [omega]n, and perform a renormalon subtraction while simultaneously including hadron mass effects. We then present a global fit for [alpha]s(mZ), analyzing the available C-parameter data in the resummation region, including center-of-mass energies between Q = 35 and 207 GeV. We simultaneously also fit for the dominant hadronic parameter, [omega]1. The experimental data is compared to our theoretical prediction, which has a perturbative uncertainty for the cross section of ~/= 2:5% at Q = mZ in the relevant t region for [alpha]s(mZ) and [omega]1. We find [alpha]s(mZ) = 0:1123 +/- 0:0015 and [omega]1 = 0:421 +/- 0:063 GeV with X² / =dof = 0:988 for 404 bins of data. These results agree with the prediction of universality for [omega]₁ between thrust and C-parameter within 1-[sigma]. The latter parts of this study are dedicated to taking SCET beyond leading power in order to further increase the possible precision of calculations. On-shell helicity methods provide powerful tools for determining scattering amplitudes, which have a one-to-one correspondence with leading power helicity operators in SCET away from singular regions of phase space. We show that helicity based operators are also useful for enumerating power suppressed SCET operators, which encode subleading amplitude information about singular limits. In particular, we present a complete set of scalar helicity building blocks that are valid for constructing operators at any order in the SCET power expansion. We also describe an interesting angular momentum selection rule that restricts how these building blocks can be assembled.by Daniel W. Kolodrubetz.Ph. D

A complete basis of helicity operators for subleading factorization

Abstract Factorization theorems underly our ability to make predictions for many processes involving the strong interaction. Although typically formulated at leading power, the study of factorization at subleading power is of interest both for improving the precision of calculations, as well as for understanding the all orders structure of QCD. We use the SCET helicity operator formalism to construct a complete power suppressed basis of hard scattering operators for e + e − → dijets, e − p → e − jet, and constrained Drell-Yan, including the first two subleading orders in the amplitude level power expansion. We analyze the field content of the jet and soft function contributions to the power suppressed cross section for e + e − → dijet event shapes, and give results for the lowest order matching to the contributing operators. These results will be useful for studies of power corrections both in fixed order and resummed perturbation theory