A. Hinzmann

Jet substructure has emerged to play a central role at the Large Hadron Collider, where it has provided numerous innovative ways to search for new physics and to probe the Standard Model, particularly in extreme regions of phase space. In this article we focus on a review of the development and use of state-of-the-art jet substructure techniques by the ATLAS and CMS experiments.

Over the past decade, a large number of jet substructure observables have been proposed in the literature, and explored at the LHC experiments. Such observables attempt to utilize the internal structure of jets in order to distinguish those initiated by quarks, gluons, or by boosted heavy objects, such as top quarks and W bosons. This report, originating from and motivated by the BOOST2013 workshop, presents original particle-level studies that aim to improve our understanding of the relationships between jet substructure observables, their complementarity, and their dependence on the underlying jet properties, particularly the jet radius and jet transverse momentum. This is explored in the context of quark/gluon discrimination, boosted W boson tagging and boosted top quark tagging.

This document summarises the talks and discussions happened during the VBSCan Split17 workshop, the first general meeting of the VBSCan COST Action network. This collaboration is aiming at a consistent and coordinated study of vector-boson scattering from the phenomenological and experimental point of view, for the best exploitation of the data that will be delivered by existing and future particle colliders.

The structure of liquid Sn was investigated up to $19.4\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ by synchrotron x-ray diffraction. Upon compression up to about $3--6\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, the structural features, which reflect the anisotropic local structure, become less prominent, i.e., the hump on the high-$Q$ side of the first peak in the structure factor $S(Q)$ becomes smaller, the position of the second peak relative to that of the first peak in $S(Q)$, ${Q}_{2}∕{Q}_{1}$, decreases, and the coordination number increases. These features indicate that the liquid structure changes toward a simple liquid metal upon compression. However, at higher pressures, the structural parameters are nearly unchanged. The parameters in this pressure range are still deviated from their respective values for simple liquid metals. These findings suggest that, contrary to previous expectations, the liquid does not monotonically approach a simple liquid metal but takes a relatively stable intermediate form with an anisotropic local structure before approaching a simple liquid metal. The high-pressure behavior of liquid Sn is compared to those of liquid Si and liquid Ge and the systematics in liquid group 14 elements are discussed.

Jet substructure techniques are playing an essential role in exploring the TeV scale at the Large Hadron Collider (LHC), since they facilitate the efficient reconstruction and identification of highly-boosted objects. Both for the LHC and for future colliders, there is a growing interest in using jet substructure methods based only on charged-particle information. The reason is that silicon-based tracking detectors offer excellent granularity and precise vertexing, which can improve the angular resolution on highly-collimated jets and mitigate the impact of pileup. In this paper, we assess how much jet substructure performance degrades by using track-only information, and we demonstrate physics contexts in which calorimetry is most beneficial. Specifically, we consider five different hadronic final states—W bosons, Z bosons, top quarks, light quarks, gluons—and test the pairwise discrimination power with a multi-variate combination of substructure observables. In the idealized case of perfect reconstruction, we quantify the loss in discrimination performance when using just charged particles compared to using all detected particles. We also consider the intermediate case of using charged particles plus photons, which provides valuable information about neutral pions. In the more realistic case of a segmented calorimeter, we assess the potential performance gains from improving calorimeter granularity and resolution, comparing a CMS-like detector to more ambitious future detector concepts. Broadly speaking, we find large performance gains from neutral-particle information and from improved calorimetry in cases where jet mass resolution drives the discrimination power, whereas the gains are more modest if an absolute mass scale calibration is not required.

The Visual Physics Analysis (VISPA) project integrates different aspects of physics analyses into a graphical development environment. It addresses the typical development cycle of (re-)designing, executing and verifying an analysis. The project provides an extendable plug-in mechanism and includes plug-ins for designing the analysis flow, for running the analysis on batch systems, and for browsing the data content. The corresponding plug-ins are based on an object-oriented toolkit for modular data analysis. We introduce the main concepts of the project, describe the technical realization and demonstrate the functionality in example applications.

This contribution gives an overview of scenarios beyond the standard model and their signatures searched for at the LHC.New results presented at the EPS conference 2021 are used as examples to point out new routes explored in searches.

Even though jet substructure was not an original design consideration for the Large Hadron Collider (LHC) experiments, it has emerged as an essential tool for the current physics program. We examine the role of jet substructure on the motivation for and design of future energy Frontier colliders. In particular, we discuss the need for a vibrant theory and experimental research and development program to extend jet substructure physics into the new regimes probed by future colliders. Jet substructure has organically evolved with a close connection between theorists and experimentalists and has catalyzed exciting innovations in both communities. We expect such developments will play an important role in the future energy Frontier physics program.

We have done energy-dispersive x-ray diffraction for liquid As, Sb, GeS, GeSe, GeTe, and found that there is a relationship between medium-range order (MRO) and the Peierls distortion (or charge-density-wave structure) in these liquids. The prepeak disappears when the Peierls distortion is suppressed. In this paper we explain the relationship between MRO and Peierls distortion in liquids by a tentative assumption that the prepeak could be a remnant of satellite peaks in the Peierls-distorted crystals.

Over the past decade, a large number of jet substructure observables have been proposed in the literature, and explored at the LHC experiments. Such observables attempt to utilize the internal structure of jets in order to distinguish those initiated by quarks, gluons, or by boosted heavy objects, such as top quarks and W bosons. This report, originating from and motivated by the BOOST2013 workshop, presents original particle-level studies that aim to improve our understanding of the relationships between jet substructure observables, their complementarity, and their dependence on the underlying jet properties, particularly the jet radius and jet transverse momentum. This is explored in the context of quark/gluon discrimination, boosted W boson tagging and boosted top quark tagging.

Analyzing physics data at LHC experiments is a complicated task involving multiple steps, sharing of expertise, cross checks and comparing different analyses. To maximize physics productivity, the CMS experiment at LHC has developed a collection of analysis tools called the PAT (Physics Analysis Toolkit). A comprehensive training program was designed and setup on using PAT software as an integral key part of the analysis of data from the CMS experiment. This note summarizes the requirements and the considerations that led to establish the PAT training program, the approach taken, the main organizational issues and the experience on its implementation and maintenance. The training and the feedback has proved to be very successful both for participants and the PAT development team.

The CMS Physics Analysis Toolkit (PAT) is presented. The PAT is a high-level analysis layer enabling the development of common analysis efforts across and within physics analysis groups. It aims at fulfilling the needs of most CMS analyses, providing both ease-of-use for the beginner and flexibility for the advanced user. The main PAT concepts are described in detail and some examples from realistic physics analyses are given.

We present a procedure for reconstructing particle cascades from event data measured in a high energy physics experiment. For evaluating the hypothesis of a specific physics process causing the observed data, all possible reconstruction versions of the scattering process are constructed from the final state objects. We describe the procedure as well as examples of physics processes of different complexity studied at hadron-hadron colliders. We estimate the performance by 20 microseconds per reconstructed decay vertex, and 0.6 kByte per reconstructed particle in the decay trees.

VISPA is a development environment for high energy physics analyses which enables physicists to combine graphical and textual work. A physics analysis cycle consists of prototyping, performing, and verifying the analysis. The main feature of VISPA is a multipurpose window for visual steering of analysis steps, creation of analysis templates, and browsing physics event data at different steps of an analysis. VISPA follows an experiment-independent approach and incorporates various tools for steering and controlling required in a typical analysis. Connection to different frameworks of high energy physics experiments is achieved by using different types of interfaces. We present the look-and-feel for an example physics analysis at the LHC and explain the underlying software concepts of VISPA.

VISPA (Visual Physics Analysis) is a development environment to support physicists in prototyping, execution, and verification of data analysis of any complexity. The key idea of VISPA is to develop physics analyses using a combination of graphical and textual programming. In VISPA, a multipurpose window provides visual tools to design and execute modular analyses, create analysis templates, and browse physics event data at different steps of an analysis. VISPA aims at supporting both experiment independent and experiment specific analysis steps. It is therefore designed as a portable analysis framework for Linux, Windows and MacOS, with its own data format including physics objects and containers, thus allowing convenient transport of analyses between different computers. All components of VISPA are designed for straightforward integration with experiment specific software to enable physics analysis with the same graphical tools. VISPA has proven to be an easy-to-use and flexible development environment in high energy physics as well as in astroparticle physics analyses.

Since 2009, the CMS experiment at LHC has provided intensive training on the use of Physics Analysis Tools (PAT), a collection of common analysis tools designed to share expertise and maximize productivity in the physics analysis. More than ten one-week courses preceded by prerequisite studies have been organized and the feedback from the participants has been carefully analyzed. This note describes how the training team designs, maintains and improves the course contents based on the feedback, the evolving analysis practices and the software development.

VISPA is a novel development environment for high energy physics analyses, based on a combination of graphical and textual steering. The primary aim of VISPA is to support physicists in prototyping, performing, and verifying a data analysis of any complexity. We present example screenshots, and describe the underlying software concepts.

Even though jet substructure was not an original design consideration for the Large Hadron Collider (LHC) experiments, it has emerged as an essential tool for the current physics program. We examine the role of jet substructure on the motivation for and design of future energy frontier colliders. In particular, we discuss the need for a vibrant theory and experimental research and development program to extend jet substructure physics into the new regimes probed by future colliders. Jet substructure has organically evolved with a close connection between theorists and experimentalists and has catalyzed exciting innovations in both communities. We expect such developments will play an important role in the future energy frontier physics program.

An overview of the CMS search program for exotic new physics is given based on a representative set of models, experimental techniques and final states. Exotic new physics models are briefly reviewed and exotic experimental techniques are introduced before the experimental results based on 8 TeV pp collision data in 9 different final states are discussed.

The project VISPA@WEB provides a novel graphical development environment for physics analyses which only requires a standard web browser on the client machine. It resembles the existing analysis environment available from the project Visual Physics Analysis VISPA, including the connection and configuration of modules for different tasks. High level logic can be programmed using the Python language, while performance-critical tasks can be implemented in C++ modules. The use cases range from simple teaching examples to highly complex scientific analyses.

The job configuration system of the CMS experiment is based on the Python programming language. Software modules and their order of execution are both represented by Python objects. In order to investigate and verify configuration parameters and dependencies naturally appearing in modular software, CMS employs a graphical tool. This tool visualizes the configuration objects, their dependencies, and the information flow. Furthermore it can be used for documentation purposes. The underlying software concepts as well as the visualization are presented.

We investigated the structure of liquid SnTe at high pressures up to 8.2 GPa by energy-dispersive x-ray diffraction. On melting at low pressures, the crystalline B1 structure changed into not B1-like but distorted-B1-like local structure. We also found that the structure changes at around 1.6-3.3 GPa. At high pressures, the bond angle and coordination number approached those for B2-based structure, but still showed clear deviations from B2-like local structure.

Visual Physics Analysis (VISPA) is an analysis environment with applications in high energy and astroparticle physics. Based on a data-flow-driven paradigm, it allows users to combine graphical steering with self-written C++ and Python modules. This contribution presents new concepts integrated in VISPA: layers, convenient analysis execution, and web-based physics analysis. While the convenient execution offers full flexibility to vary settings for the execution phase of an analysis, layers allow to create different views of the analysis already during its design phase. Thus, one application of layers is to define different stages of an analysis (e.g. event selection and statistical analysis). However, there are other use cases such as to independently optimize settings for different types of input data in order to guide all data through the same analysis flow. The new execution feature makes job submission to local clusters as well as the LHC Computing Grid possible directly from VISPA. Web-based physics analysis is realized in the VISPA@Web project, which represents a whole new way to design and execute analyses via a standard web browser.

Using the proton-proton collision data delivered by the LHC in 2010, CMS has measured a variety of jet observables. These include inclusive and dijet cross sections, angular properties of dijet events, jet shapes as well as various multi-jet event observables. Jets from heavy objects have been measured as well, including the inclusive b-jet cross section and a first demonstration of the use of jet substructure algorithms for the identification of highly boosted W and top jets.

Recent results of searches for heavy resonances decaying to pairs of Standard Model W and Z bosons at CMS using 8 TeV LHC data are presented. Several new physics scenarios predict the existence of resonances that decay with high branching ratio to pairs of bosons, including extra dimensions and composite Higgs models. The final states considered here are WW, WZ, and ZZ. The acceptance for TeV resonances is increased by applying jet substructure techniques to reconstruct W or Z bosons with high transverse momenta whose decay products merge into a single jet.

An overview of the CMS search program for exotic new physics is given based on a representative set of models, experimental techniques and final states. Exotic new physics models are briefly reviewed and exotic experimental techniques are introduced before the experimental results based on 8 TeV pp collision data in 9 different final states are discussed.

The Visual Physics Analysis (VISPA) project provides a graphical development environment for data analysis. It addresses the typical development cycle of (re-)designing, executing, and verifying an analysis. We present the new server-client-based web application of the VISPA project to perform physics analyses via a standard internet browser. This enables individual scientists to work with a large variety of devices including touch screens, and teams of scientists to share, develop, and execute analyses on a server via the web interface.

We present results on the performance of jet reconstruction in CMS, using charged tracks only. Jet reconstruction with tracks is completely independent from jet finding with calorimeter towers and is an extremely clean and efficient way to find jets, and determine their directions with good precision. A commissioning analysis using approximately 100 μb −1 of minimum bias pp collision data at [Formula: see text] shows that for jets with p T > 10 GeV/c the agreement between the data and PYTHIA predictions for properties of minimum bias events appears to be good, and there is consistency of track jets and calorimeter-based jets.

Recent results from CMS on searches for new heavy resonances decaying into hadronic final states are summarized.A variety of final states ranging from two jets up to six jets have been analyzed using the data samples of 5 fb -1 of pp collisions at √ s =7 TeV and 4 fb -1 at √ s =8TeV collected with CMS in 2011 and 2012.In addition to the resonance production of final states with jets from light quarks and gluons, also final states enriched with b-quarks and hadronically decaying W or Z bosons are examined using b-tagging and jet substructure techniques.

VISPA (Visual Physics Analysis) is a development environment to support physicists in prototyping, execution, and verification of data analysis of any complexity.The key idea of VISPA is to develop physics analyses using a combination of graphical and textual programming.In VISPA, a multipurpose window provides visual tools to design and execute modular analyses, create analysis templates, and browse physics event data at different steps of an analysis.VISPA aims at supporting both experiment independent and experiment specific analysis steps.It is therefore designed as a portable analysis framework for Linux, Windows and MacOS, with its own data format including physics objects and containers, thus allowing convenient transport of analyses between different computers.All components of VISPA are designed for straightforward integration with experiment specific software to enable physics analysis with the same graphical tools.VISPA has proven to be an easy-to-use and flexible development environment in high energy physics as well as in astroparticle physics analyses.

A summary of recent searches by the ATLAS, CMS and LHCb experiments at the LHC for new physics signatures that involve the production of bosons is given. The results are based on the first data collected at the LHC in 2015 at a center of mass energy of 13 TeV, corresponding to an integrated luminosity of 2.2-3.2/fb. Statistical combinations with previous data collected at 8 TeV are also presented. Particular focus is given to two hints of resonances in di-boson final states at 750 GeV and 2 TeV.

The VISPA programm supports particle physicists and astroparticle physicists in their data analysis projects.VISPA combines elements off graphical and textual programming to enable fast development cycles of physics analyses.

A search is presented for narrow resonances decaying to dijet final states in proton–proton collisions at s√=13TeV using data corresponding to an integrated luminosity of 12.9 $fb{−1}$. The dijet mass spectrum is well described by a smooth parameterization and no significant evidence for the production of new particles is observed. Upper limits at 95% confidence level are reported on the production cross section for narrow resonances with masses above 0.6 TeV. In the context of specific models, the limits exclude string resonances with masses below 7.4 TeV, scalar diquarks below 6.9 TeV, axigluons and colorons below 5.5 TeV, excited quarks below 5.4 TeV, color-octet scalars below 3.0 TeV, W′ bosons below 2.7 TeV, Z′ bosons below 2.1 TeV and between 2.3 and 2.6 TeV, and RS gravitons below 1.9 TeV. These extend previous limits in the dijet channel. Vector and axial-vector mediators in a simplified model of interactions between quarks and dark matter are excluded below 2.0 TeV. The first limits in the dijet channel on dark matter mediators are presented as functions of dark matter mass and are compared to the exclusions of dark matter in direct detection experiments.

Poster Sessions which can monitor the rheological properties of liquids between two surfaces as a function of surface separation distance (D) from µm to contact with nm resolution.In this study, we investigated the rheological properties of a liquid crystal, 4-cyano-4'-hexylbiphenyl (6CB), under the electric field which induces the orientational change of 6CB.Resonance curves were obtained by measuring the amplitude of shear as a function of angular frequency.Polarizing microscopy confirmed that 6CB was in the planar orientation between mica surfaces without electric field, and in the homeotropic orientation under the electric field (28 V, 1 kHz).The viscosity of 6CB was larger for the case of 0 V than the case of 28 V at 370-14 nm, which agreed with Miesowicz viscosity.Below D=14 nm, the viscosity increased similarly both at 0 V and 28 V, indicating the same orientation of 6CB under confinement.1) M.

VISPA is a novel development environment for high energy physics analyses, based on a combination of graphical and textual steering. The primary aim of VISPA is to support physicists in prototyping, performing, and verifying a data analysis of any complexity. We present example screenshots, and describe the underlying software concepts.

VISPA is a novel graphical development environment for physics analysis, following an experiment-independent approach.It introduces a new way of steering a physics data analysis, combining graphical and textual programming.The purpose is to speed up the design of an analysis, and to facilitate its control.As the software basis for VISPA the C++ toolkit Physics eXtension Library (PXL) is used which is a successor project of the Physics Analysis eXpert (PAX) package.The most prominent features of this toolkit are the management of relations, a copyable container holding different aspects of physics events, the ability to store arbitrary user data, and a fast I/O.In order to support modular physics analysis, VISPA provides a module handling system using the above mentioned event container as the interface.Several analysis modules are provided, e.g. a module for automated reconstruction of particle cascades.All modules can be steered through Python scripts.Physicists can easily write their own modules to the module handling system or extend the existing ones.In this paper the concept of VISPA will be presented.

We present an algorithm for reconstructing particle cascades from event data of a high energy physics experiment. For a given physics process, the algorithm reconstructs all possible configurations of the cascade from the final state objects. We describe the procedure as well as examples of physics processes of different complexity studied at hadron-hadron colliders. We estimate the performance of the algorithm by 20 microseconds per reconstructed decay vertex, and 0.6 kByte per reconstructed particle in the decay trees.

Pixelated silicon detectors are state-of-the-art technology to achieve precise tracking and vertexing at collider experiments, designed to accurately measure the hit position of incoming particles in high rate and radiation environments. The detector requirements become extremely demanding for operation at the High-Luminosity LHC, where up to 200 interactions will overlap in the same bunch crossing on top of the process of interest. Additionally, fluences up to 2.3 10^16 cm^-2 1 MeV neutron equivalent at 3.0 cm distance from the beam are expected for an integrated luminosity of 3000 fb^-1. In the last decades, the pixel pitch has constantly been reduced to cope with the experiment's needs of achieving higher position resolution and maintaining low pixel occupancy per channel. The spatial resolution improves with a decreased pixel size but it degrades with radiation damage. Therefore, prototype sensor modules for the upgrade of the experiments at the HL-LHC need to be tested after being irradiated. This paper describes position resolution measurements on planar prototype sensors with 100x25 um^2 pixels for the CMS Phase-2 Upgrade. It reviews the dependence of the position resolution on the relative inclination angle between the incoming particle trajectory and the sensor, the charge threshold applied by the readout chip, and the bias voltage. A precision setup with three parallel planes of sensors has been used to investigate the performance of sensors irradiated to fluences up to F_eq = 3.6 10^15 cm-2. The measurements were performed with a 5 GeV electron beam. A spatial resolution of 3.2 +\- 0.1 um is found for non-irradiated sensors, at the optimal angle for charge sharing. The resolution is 5.0 +/- 0.2 um for a proton-irradiated sensor at F_eq = 2.1 10^15 cm-2 and a neutron-irradiated sensor at F_eq = 3.6 10^15 cm^-2.

Precise measurements of the mass of the $W$ boson are important to test the overall consistency of the Standard Model of particle physics. The current best measurements of the $W$ boson mass come from single production measurements at hadron colliders in its decay mode to a lepton (electron or muon) and a neutrino and pair production of $W$ bosons at lepton colliders, where also the decay mode of the $W$ boson to hadrons has been considered. In this study, prospects for a measurement of the $W$ boson mass in the all-jet final state at hadron colliders are presented. The feasibility of this measurement takes advantage of numerous recent developments in the field of jet substructure. Compared to other methods for measuring the $W$ mass, a measurement in the all-jets final state would be complementary in methodology and have systematic uncertainties orthogonal to previous measurements. We have estimated the main experimental and theoretical uncertainties affecting a measurement in the all-jet final state. With new trigger strategies, a statistical uncertainty for the measurement of the mass difference between the $Z$ and $W$ bosons of 30 MeV could be reached with HL-LHC data corresponding to 3000 fb$^{-1}$ of integrated luminosity. However, in order to reach that precision, the current understanding of non-perturbative contributions to the invariant mass of $W\to q\bar{q}'$ and $Z\to b\bar{b}$ jets will need to be refined. Similar strategies will also allow the reach for generic boosted resonances searches in hadronic channels to be extended.

The cross sections for the production of $t\overline{t}b\overline{b}$ and $t\overline{t}jj$ events and their ratio $\sigma_{t\overline{t}b\overline{b}} / \sigma_{t\overline{t}jj}$ are measured using data corresponding to an integrated luminosity of 2.3 $fb^{−1}$collected in pp collisions at $\sqrt{s}$ = 13TeV with the CMS detector at the LHC. Events with two leptons (e or μ) and at least four reconstructed jets, including at least two identified as b quark jets, in the final state are selected. In the full phase space, the measured ratio is $0.022 \pm 0.003(stat) \pm 0.006(syst)$, the cross section $\sigma_{t\overline{t}b\overline{b}}$ is $4.0 \pm 0.6(stat) \pm 1.3(syst)pb$ and $\sigma_{t\overline{t}jj}$ is $184 \pm 6(stat) \pm 33(syst)pb$. The measurements are compared with the standard model expectations obtained from a powheg simulation at next-to-leading-order interfaced with pythia.

First released in 2010, the Rivet library forms an important repository for analysis code, facilitating comparisons between measurements of the final state in particle collisions and theoretical calculations of those final states.We give an overview of Rivet's current design and implementation, its uptake for analysis preservation and physics results, and summarise recent developments including propagation of MC systematic-uncertainty weights, heavy-ion and ep physics, and systems for detector emulation.In addition, we provide a short user guide that supplements and updates the Rivet user manual.

First released in 2010, the Rivet library forms an important repository for analysis code, facilitating comparisons between measurements of the final state in particle collisions and theoretical calculations of those final states.We give an overview of Rivet's current design and implementation, its uptake for analysis preservation and physics results, and summarise recent developments including propagation of MC systematic-uncertainty weights, heavy-ion and ep physics, and systems for detector emulation.In addition, we provide a short user guide that supplements and updates the Rivet user manual.

Pixelated silicon detectors are state-of-the-art technology to achieve precise tracking and vertexing at collider experiments, designed to accurately measure the hit position of incoming particles in high rate and radiation environments. The detector requirements become extremely demanding for operation at the High-Luminosity LHC, where up to 200 interactions will overlap in the same bunch crossing on top of the process of interest. Additionally, fluences up to 2.3 10^16 cm^-2 1 MeV neutron equivalent at 3.0 cm distance from the beam are expected for an integrated luminosity of 3000 fb^-1. In the last decades, the pixel pitch has constantly been reduced to cope with the experiment's needs of achieving higher position resolution and maintaining low pixel occupancy per channel. The spatial resolution improves with a decreased pixel size but it degrades with radiation damage. Therefore, prototype sensor modules for the upgrade of the experiments at the HL-LHC need to be tested after being irradiated. This paper describes position resolution measurements on planar prototype sensors with 100x25 um^2 pixels for the CMS Phase-2 Upgrade. It reviews the dependence of the position resolution on the relative inclination angle between the incoming particle trajectory and the sensor, the charge threshold applied by the readout chip, and the bias voltage. A precision setup with three parallel planes of sensors has been used to investigate the performance of sensors irradiated to fluences up to F_eq = 3.6 10^15 cm-2. The measurements were performed with a 5 GeV electron beam. A spatial resolution of 3.2 +\- 0.1 um is found for non-irradiated sensors, at the optimal angle for charge sharing. The resolution is 5.0 +/- 0.2 um for a proton-irradiated sensor at F_eq = 2.1 10^15 cm-2 and a neutron-irradiated sensor at F_eq = 3.6 10^15 cm^-2.