Variable Flavor Number Scheme for Final State Jets

We discuss a variable flavor number scheme (VFNS) for final state jets which can account for the effects of arbitrary finite quark masses in inclusive jet observables. The scheme is a generalization of the VFNS scheme for PDFs applied to setups with additional dynamical scales and relies on appropriate renormalization conditions for the matrix elements in the factorization theorem. We illustrate general properties by means of the example of deep-inelastic scattering (DIS) in the endpoint region $x\rightarrow 1$ and event shapes in the dijet limit, in particular the calculations of threshold corrections, consistency conditions and relations to mass singularities found in fixed-order massive calculations.Comment: 7 pages, 4 figures, Proceedings of the XXII. International Workshop on Deep-Inelastic Scattering and Related Subjects, 28 April - 2 May 2014, Warsaw, Polan

Factorization and Resummation for Massive Quark Effects in Exclusive Drell-Yan

Exclusive differential spectra in color-singlet processes at hadron colliders are benchmark observables that have been studied to high precision in theory and experiment. We present an effective-theory framework utilizing soft-collinear effective theory to incorporate massive (bottom) quark effects into resummed differential distributions, accounting for both heavy-quark initiated primary contributions to the hard scattering process as well as secondary effects from gluons splitting into heavy-quark pairs. To be specific, we focus on the Drell-Yan process and consider the vector-boson transverse momentum, $q_T$, and beam thrust, $\mathcal T$, as examples of exclusive observables. The theoretical description depends on the hierarchy between the hard, mass, and the $q_T$ (or $\mathcal T$) scales, ranging from the decoupling limit $q_T \ll m$ to the massless limit $m \ll q_T$. The phenomenologically relevant intermediate regime $m \sim q_T$ requires in particular quark-mass dependent beam and soft functions. We calculate all ingredients for the description of primary and secondary mass effects required at NNLL$'$ resummation order (combining NNLL evolution with NNLO boundary conditions) for $q_T$ and $\mathcal T$ in all relevant hierarchies. For the $q_T$ distribution the rapidity divergences are different from the massless case and we discuss features of the resulting rapidity evolution. Our results will allow for a detailed investigation of quark-mass effects in the ratio of $W$ and $Z$ boson spectra at small $q_T$, which is important for the precision measurement of the $W$-boson mass at the LHC.Comment: 42 pages + appendices, 21 figures; v2: journal versio

On the Cutoff Dependence of the Quark Mass Parameter in Angular Ordered Parton Showers

We show that the presence of an infrared cutoff $Q_0$ in the parton shower (PS) evolution for massive quarks implies that the generator quark mass corresponds to a $Q_0$-dependent short-distance mass scheme and is therefore not the pole mass. Our analysis considers an angular ordered parton shower based on the coherent branching formalism for quasi-collinear stable heavy quarks and splitting functions at next-to-leading logarithmic (NLL) order, and it is based on the analysis of the peak of hemisphere jet mass distributions. We show that NLL shower evolution is sufficient to describe the peak jet mass at full next-to-leading order (NLO). We determine the relation of this short-distance mass to the pole mass at NLO. We also show that the shower cut $Q_0$ affects soft radiation in a universal way for massless and quasi-collinear massive quark production. The basis of our analysis is (i) an analytic solution of the PS evolution based on the coherent branching formalism, (ii) an implementation of the infrared cut $Q_0$ of the angular ordered shower into factorized analytic calculations in the framework of Soft-Collinear-Effective-Theory (SCET) and (iii) the dependence of the peak of the jet mass distribution on the shower cut. Numerical comparisons to simulations with the HERWIG 7 event generator confirm our findings. Our analysis provides an important step towards a full understanding concerning the interpretation of top quark mass measurements based on direct reconstruction.Comment: 110 pages, 23 figures; v2: improved version, references updated, typos eliminate

Variable Flavor Number Scheme for Final State Jets in DIS

We discuss massive quark effects in the endpoint region $x \to 1$ of inclusive deep inelastic scattering, where the hadronic final state is collimated and thus represents a jet. In this regime heavy quark pairs are generated via secondary radiation, i.e. due to a gluon splitting in light quark initiated contributions starting at $\mathcal{O}(\alpha_s^2)$ in the fixed-order expansion. Based on the factorization framework for massless quarks in Soft Collinear Effective Theory (SCET), we construct a variable flavor number scheme that deals with arbitrary hierarchies between the mass scale and the kinematic scales exhibiting a continuous behavior between the massless limit for very light quarks and the decoupling limit for very heavy quarks. We show that the threshold matching corrections for all gauge invariant components at the mass scale are related to each other via consistency conditions. This is explicitly demonstrated by recalculating the known threshold correction for the parton distribution function at $\mathcal{O}(\alpha_s^2 C_F T_F)$ within SCET. The latter contains large rapidity logarithms $\sim \ln(1-x)$ that can be summed by exponentiation. Their coefficients are universal which can be used to obtain potentially relevant higher order results for generic threshold corrections at colliders from computations in deep inelastic scattering. In particular, we extract the $\mathcal{O}(\alpha_s^3)$ threshold correction multiplied by a single rapidity logarithm from results obtained earlier

Factorization of the Drell-Yan qTq_T spectrum with massive quarks

Exclusive differential spectra in color-singlet processes at hadron colliders are benchmark observables that have been studied to high precision in theory and experiment.We present an effective-theory framework utilizing soft-collinear effective theory to incorporate massive (bottom) quark effects into resummed differential distributions, accounting for both heavy-quark initiated primary contributions to the hard scattering process as well as secondary effects from gluons splitting into heavy-quark pairs.We discuss a variable flavor number scheme (VFNS) for the Drell-Yan process for the vector-boson transverse momentum $q_T$ as an example of an exclusive observable. The theoretical description depends on the hierarchy between the hard, mass, and the $q_T$ scale, ranging from the decoupling limit $q_T ≪ m$ to the massless limit $m ≪ q_T$. The phenomenologically relevant intermediate regime $m ∼ q_T$ requires in particular quark-mass dependent beam and soft functions. We find that the rapidity divergences are different from the massless case and we discuss features of the resulting rapidity evolution. Our results will allow for a detailed investigation of quark-mass effects in the ratio of W and Z boson spectra at small $q_T$, which is important for the precision measurement of the W-boson mass at the LHC

Herwig 7.3 Release Note

A new release of the Monte Carlo event generator Herwig (version 7.3) has been launched. This iteration encompasses several enhancements over its predecessor, version 7.2. Noteworthy upgrades include: the implementation of a process-independent electroweak angular-ordered parton shower integrated with QCD and QED radiation; a new recoil scheme for initial-state radiation improving the behaviour of the angular-ordered parton shower; the incorporation of the heavy quark effective theory to refine the hadronization and decay of excited heavy mesons and heavy baryons; a dynamic strategy to regulate the kinematic threshold of cluster splittings within the cluster hadronization model; several improvements to the structure of the cluster hadronization model allowing for refined models; the possibility to extract event-by-event hadronization corrections in a well-defined way; the possibility of using the string model, with a dedicated tune. Additionally, a new tuning of the parton shower and hadronization parameters has been executed. This article discusses the novel features introduced in version 7.3.0