A Methodological Handbook for a Work-Team Based Learning and Teaching Approach

A methodological handbook for a work-team based learning and teaching approach

The iTHEPHY Collaboration

April, 25, 2020

1 Contents

1 Introduction 3

2 The iTHEPHY project 5

3 The platform for enhancing teacher-student collaboration 7 3.1 How to implement an e-learning platform ...... 7 3.2 Cloud Migration and Software Maintenance ...... 8 3.3 The Moolde implementation under the iTHEPHY project ...... 9 3.4 Exercise example in Latex ...... 10

4 How to implement a Tandem-Project learning and teaching activities 17 4.1 The Tandem-Project in 2018/2019 academic year as an example ...... 18 4.2 The research projects ...... 19

5 How to organise a Summer/Winter School 21 5.1 How selecting the right location ...... 21 5.2 Participants ...... 21 5.3 A eﬃcient and well oriented agenda ...... 22

6 Conclusions 23

2 1 Introduction

The Innovative Team-Teaching in Physics (iTHEPHY) project is an international high- energy physics teaching program for master’s degree students in physics. It started in 2017 and was co-funded by the Erasmus+ program of the European Union. The careers of students enrolled in physics courses after the degrees normally evolve in an international research context (universities, research institutes, private industries, etc.). However, the small number of exchanges are limited by crossing cultural and language boundaries, which prevent students and the master courses to have the right level of internationalization during their studies. In order to increase the internationalization of physics master courses and to promote student and staff mobility an international consortium started the iTHEPHY project. The consortium is realized on the basis of strong national synergies between academic and research institutions, with the aim of straightening the link between teaching and research. In particular the consortium consists of the following institutions: Alma Mater Studiorum - Universitàdi Bologna (UNIBO) Bologna, Italy; UnversitéClermont Auvergne (UCA), Clermont-Ferrand, France; Technische UniversitätDortmund (TUD), Dortmund, Germany; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Centre National De La Recherche Scientifique and Institute National des physique nucléaireet de physique de particules (CNRS/IN2P3), France; Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany. Thanks to its European flavour founded on a long-term collaboration between all involved institutions the partnerships and activities in the iTHEPHY project motivated the students to be more in favour of mobility. For the realization of the iTHEPHY project innovative student-centered learning methodologies were developed. A central element were the so called Tandem projects where teams of high qualified European professors and researchers experienced in international research projects drove international teams of students working on specific research tasks. In the Tandem projects both students and teachers improved their collaboration skills. iTHEPHY also included two intensive teaching and learning activities (the ISHEP Sum- mer Schools) where new pedagogical methodologies were tested. These methodologies gave to the student’s instruments to develop critical thinking, problem-solving attitude, and collaboration skills, strengthening the links between higher education institutions and the research, enhancing the quality and relevance of students’ knowledge and skills. For a successful realization of the iTHEPHY project information and communication technologies (ICTs) were of fundamental importance. Therefore several new ICT tools supporting the teams of students and teachers during the project were developed as drivers of improvements in education. In particular, a customized Moolde platform integrated into a web-based virtual environment with additional tools useful for sharing documents, meeting virtually through chat/video rooms, tracking the project and scheduling meetings was set up. iTHEPHY promotes ICT-based educational tools and content for deep learning and teaching in physics in a digital era. The iTHEPHY Moolde page was partially published, providing access to a broad range of learning and teaching contents. In particular, an exercise database as well as a glossary for high-energy physics were set up. For the exercises different level hints as well as detailed solutions are also available. Furthermore, technical terms occurring in the exercises are auto- linked to the glossary containing plenty of definitions, additional explanations and references to literature. Therefore, the Moolde platform does not only offer valuable resources for the use in university courses but also provides an ideal environment for auto-didactic studying.

3 This handbook aiming at setting out the procedures to be followed to facilitate other master degree in Physics and in more in general of STEM disciplines to achieve the objectives of iTHEPHY. The goal of this document is to provide guidelines to replicate the methodologies. It includes a critical guidance on how to set up a web-based platform with tools developed and tested during the iTHEPHY project; a section dedicated to explain how eﬃciently organise an intensive learning and teaching activities (i.e. Summer/Winter Schools); a section to guide newcomers to use the tandem-project approach for a team-based learning; a section on methodologies necessary for student’s evaluation in order to assess the quality assurance at program implementation level.

4 2 The iTHEPHY project

The project aims at building a strategic partnership to promote an innovative educational environment and exchange of good practices in the field of higher education. The project main goal, from the computing point of view, is the development of e-learning tools for teaching particle physics to students attending the second year of the master degree, in order to allow them to work together in real research projects supervised by international teachers and researchers belonging to the iTHEPHY Consortium. The innovative educational approach proposed promotes internationalization, enhances team-work skills and boosts mobility worldwide. The project foresees three so-called Intellectual Outputs: 1. a web-based platform to support the team during the project, which integrates a video web-conference plug-in, a chat room, a shared storage area for files, a scheduler/agenda for planning meetings between teachers and students and a project management tool to effectively organise projects, enabling to sub-tasks assignments and progress tracking; 2. guided exercises with full solutions on an e-learning platform; 3. a handbook describing the implementation of the project for future replications. iTHEPHY is a project funded by the European Commission on higher education methodologies with the aim of addressing some of the most urgent priorities, recently pointed out in the Report on Public Consultation of the EU Modernization Agenda for Higher Education (2016) [1]: promoting internationalization, recognition and mobility supporting • changes in line with Bologna principles [2]. This priority is justified by an essential need of students enrolled in master courses. After the master degree, students’ careers normally evolve in an international research context. Universities, international research institutes and laboratories, and private industries are the most fre- quent employers. However, the level of labour mobility is limited by cross-cultural and language boundaries, which prevents students from having the right level of internationalization during their studies. In order to overcome this issue, the Consor- tium is realized on the basis of strong international synergies between academic and research institutions, that strengthen the link between teaching and research in an international environment. Its European flavour, rooted in a long lasting collaboration between all partners in High Energy Physics (HEP) experiments, such as the ones undertaken at the CERN, strongly motivates students to be more open to EU and non-EU mobility. All these characteristics are key ingredients for successfully promoting the development of international mind-set. The recognition of the training goals, assured by assigning ECTS (European Credit Transfer System) credits, and the mobility required to attend the school, both contribute to overcome language and cultural barriers. Enhancing the quality and relevance of students’ knowledge and skills. The • innovative learning and teaching methodologies promoted by iTHEPHY enhance the quality and relevance of student’s knowledge and skills. Learning and teaching activities are carried out by teams of highly qualified professors and researchers experienced in international research projects. In this context, both students and teachers will improve their collaboration skills. With this goal in mind, iTHEPHY has organised two

5 intensive teaching and learning activities culminated in two editions of the ISHEP Spring School, where the pedagogical methodologies have been tested and reﬁned to be adopted in future editions of the school. The new methodologies provide students with the right instruments to develop critical thinking, problem-solving attitude and collaborative perspectives.

Open and innovative practices in a digital era. A fundamental aspect of the • project is the development of ICT tools to support groups of students and teams of teachers during their learning and teaching activities. In particular, a customized Moolde [3] platform, based on open-source software, has been developed to integrate, on a web-based virtual environment, a standard Moolde installation with additional tools useful for sharing documents, meeting virtually trough chat/video rooms, tracking projects and scheduling meetings.

6 3 The platform for enhancing teacher-student collaboration

3.1 How to implement an e-learning platform The e-learning platform developed under the iTHEPHY project follows the Infrastructure as a Service (IaaS) deployment model. It mainly consists of a framework where various open source educational services are integrated in a unique virtual space. The platform has been developed in the HEP context, but it is general purpose and it could be adopted by research groups of any discipline. In order to meet the iTHEPHY requirements, we deployed and tested additional functionalities on top of a standard Moolde environment, namely:

a video web-conference plugin for meetings, remote lectures, live events; • a chat room to have a real-time, quick and synchronous discussion; • a shared area, as central resource repository to share ﬁles, documents and notes related • to the project;

an appointment scheduler for planning meetings between teachers and students and • between students;

a project management tool for implementing projects, assigning sub-tasks and tracking • their progress, assigning roles to team members, giving reports about the progress of the project, handling with Gantt chart.

Some of these functionalities were not available in the public releases and additional development was needed to eﬀectively integrate all the needed features in a unique web platform. Software integration has been realized developing some software modules, using common programming and markup languages such as HTML5, CSS3, PHP, and PYTHON. The building blocks shown in Fig. 1 are integrated in a unique virtual space consisting of:

Moolde [4] as LMS, used worldwide for educational purposes; • BigBlueButton [5], a Moolde plug-in, that allows users to create interactive video • lessons and webinars, and to record them;

Rocket.Chat [6], a chat system with channels and rooms integrated with Jitsi (video • conference) and BigBlueButton;

Redmine [7], a project management software with calendar, agenda and Gantt charts • functionalities;

Sharelatex [8], a real-time shared latex editing platform. • The front-end applications include an authentication system based on Indigo DataCloud [9] IAM using OAuth2 protocol. In contrast, the back-end ones are authenticated trough a JWT API call by the front-end interfaces. Thanks to Indigo DataCloud IAM, students and teachers can take advantage of a standard authorization and user management system. The platform has been installed in two versions: one is a stable release for the production deployment, it is updated annually (except for security updates which are applied when necessary), while the second version is used for testing and development. The BigBlueButton software has been chosen because it can be easily integrated into Moolde, it has interesting features such as the use of multi-platform HTML5 webrtc clients and the integration of Etherpads

7 Figure 1: iTHEPHY Platform Building Blocks. for shared notes together with a whiteboard for interactive lectures. Rocket.Chat is a chat system which has all the requirements needed by the project, such as easy integration with Jitsi and BigBlueButton. Jitsi fully respects the platform requirements for audio and video conferencing; it is technologically advanced and widely supported. Sharelatex/Overleaf is the only solution for shared editing in latex so far. INDIGO DataCloud IAM authentication system allowed us to manage authorizations and authentications in an integrated and con- venient way. It exploits OAuth2/OpenID-Connect for applications and provides a module for federation integration (IDEM/EDUGAIN). Redmine is a project management system. Even if other competitors exist, the choice was driven by the fact that it is open-source software and provides all the necessary features needed.

3.2 Cloud Migration and Software Maintenance Cloud services (both private and public) are evolving rapidly and efficiently and the need for users (teachers and students) to have fast, easy and highly flexible deployment sys- tems encouraged the Consortium to build up a microservices based PaaS platform. Natural choices were Kubernetes [10] and Rancher [11]. These tools exploit the HELM Charts [12] for rapid deployment and there is a large number of recipes publicly available and providing integrated monitoring and logging functionalities. Other useful features are Load Balancer ingress, automatic NGINX, integrated Letsencrypt certificates, integrated resource provi- sioning and RBAC (Role Based Access Control). Two platforms are deployed: the Test Platform and the Production Platform. The iTHEPHY test platform is installed inside the INFN private cloud infrastructure Cloud at CNAF, where the Openstack resources are instantiated manually and added to the Rancher cluster using a script developed for this purpose. All the resources needed (floating IP, security groups, L4 load balancers) are configured separately and supplied to Rancher from the outside. Permanent volume class provided by Longhorn are used as persistent storage. Longhorn is a k8s application that manages cluster nodes and local disks to provide repli- cation. The system is a beta testing implementation running since months without showing

8 any significant issue. The applications installed so far are Moolde, RedMine, Rocket.Chat, Letsencrypt and Longhorn. Soon the IAM authentication system (INDIGO-DataCloud), Jitsi and BigBlueButton will be also added. The production platform has been deployed at the INFN Corporate Cloud. It is Hybrid cloud environment where all resources are automatically provisioned in a dynamic way. Ap- plications were deployed using Rancher and HELM catalogues. In this configuration, public applications are reachable from the general Internet via Openstack L4 and/or Rancher L7 load balancer and proxies by Rancher nginx service. All necessary security group configurations are made from application receipts. Moolde, Redmine, Rocket.Chat from official HELM repository are installed and configured. In the near future, it will be necessary to create, test and distribute a chart or a YAML for the configuration of environment starting from docker-compose receipts of Jitsi, BigBlueButton and the IAM authentication system.

3.3 The Moolde implementation under the iTHEPHY project The e-learning platform based on the open-source Moolde framework is the central tool of the iTHEPHY project. The platform can be found at the following website [4] and is divided in a public and a private part. The public part is directly accessible whereas for the private part an authentication is needed. The public part of the platform and contains a broad range of learning and teaching materials for high-energy physics. As mentioned, those materials are free accessible for everyone and we encourage teachers and students to use those resources in their university courses and self-studies, respectively. As a central element of the platform, an exercise database was set up. It contains plenty of exercises from diﬀerent ﬁelds of theoretical and experimental high-energy physics sorted by categories. The categories are

Quantum Field Theory and Group Theory • Electroweak Unification and Electroweak Symmetry Breaking • Detector and Accelarator Physics • General Relativity and Cosmology • Flavour Physics • Top-quark Physics • Statistics • Quantum Chromo Dynamics • Computing. • The exercises are presented such that auto-didactic studies are explicitly supported. The exercise layout is standardized and starts with a header containing the title, type, difficulty and keywords. The type of exercises varies from short questions to calculations and mathematical proofs. The difficulty is divided in the three levels easy, intermediate and advanced. The inclusion of keywords in the header allows for a precise search for exercises on a specific topic. Within an exercise, for each task there are hints at two different levels available. The hints are implemented such that they are hidden by default but available by

9 a single click. Furthermore, detailed standard solutions are provided, allowing to check and fully comprehend the solution to the exercise under consideration. Moreover, all technical terms occurring in the exercises are directly linked to a glossary. The glossary contains definitions and short explanations for a lot of technical terms from high-energy physics as well as cross references to the relevant literature. In order to simplify the use of the exercise database in university courses, the possibility to submit solutions online was included. Last but not least, for each exercise a short feedback sheet can be filled in and submitted. Examples for the pdf versions of exercises and glossary entries can be found at the end of this report. The private part of the Moolde platform is accessible after log in with IAM Authentica- tion Service. It contains courses of the ISHEP Summer Schools and the Tandem Projects. In the ISHEP course at first the schedule, a list of participants and other general information can be found. Moreover, the course contains the slides and a graded test for each lecture held in the framework of the ISHEP summer school. Furthermore, the slides of all ISHEP student talks are included. The second central element of the private part of the Moolde platform are the Tandem projects. At first, general information on the formal aspects of the Tandem projects are provided. Then, for each year a list of all Tandem projects including the names of all involved students and supervisors is given. For the Tandem projects information and communication technologies (ICTs) are of central importance. Therefore a virtual area used as a central resource repository to share files, documents, and notes related to each project is also installed. Several different ICT tools have been integrated in the e-learning platform. E.g. it is possible to perform web-live interactive lectures using BigBlueButton. Moreover, an appointment scheduler for planning meetings between teachers and students and between students is available. As communication features, a video conference system and a chat room with the possibility to directly start a video session are built in. Finally, a project management tool based on Redmine is available. All in all, the Moolde e-learning platform as the central tool supports the iTHEPHY project in several ways. An exercise database and a glossary have been made public available for everyone. In addition, there is a private section used for the ISHEP summer schools and Tandem projects. The private section is strongly supported by several different ICT tools.

3.4 Exercise example in Latex The following Latex template can be used to design exercises in a consistent way. The idea is that each of the lecturers provides one or two (small) problems that will then be worked on by the students during the lectures. The template includes two tex-files and a makefile (tested to work on Linux and Mac enviroment) to produce PDF versions of the exercises. It is possible to modify the file exercise.tex to implement an exercises into the Moolde page. Please also see the readme.txt. As visible in the template, the exercises should also include literature references for further reading and might also contain hints for solving the problems or even control results. Using the Moolde implementation of the exercises, the students can decide whether they want to see the hints and control results, or not. (see the attached pictures of an example implementation: ”hidden.png” and ”shown.png”) A full solution to the problems should also be provided.

% Please define your exercise here

10 %===== General information about the exercise \renewcommand{\title} {Spherical coordinates: jacobian matrix and metric}

\renewcommand{\subject}{theoretical particle physics} % possible subjects: theoretical particle physics / experimental particle physics / experimental methods / statistical methods / accelerator physics / detector physics

\renewcommand{\topic}{General coordinate changes} % detailed topic of this exercise (e.g. continuity equation, top quark mass, ... )

\renewcommand{\keywords}{General relativity, curved coordinates, Jacobian matrix, tensor transformations} % comma separated

\renewcommand{\type}{Calculation} % possible types: Calculation / Short question / Concept / Proof

\renewcommand{\level}{intermediate} % possible levels: easy / intermediate / advanced / difficult

\renewcommand{\literature}{ $\bullet$ P.A.M. Dirac, General Theory of Relativity, Ch.11, Princeton University Press, 1996, \\ $\bullet$ S. Carroll, Lecture Notes on General Relativity, Ch. 3, gr-qc/9712019 } %===== End of general information about the exercise ======

%===== Exercise tasks ======\newcommand{\tasks}{ % Define exercise tasks here: In the 3 dimensional Euclidian space, a point $P$ is usually labeled by 3 cartesian coordinates $x^i=(x^1,x^2,x^3)=(x,y,z)$. Sometimes, these can be usefully replaced by spherical coordinates $x’^{i’}=(x’^1,x’^2,x’^3)=(r,\theta,\phi)$ with the relations \begin{eqnarray}\nonumber x&=&r\,\sin\theta\,\cos\phi\\\nonumber y&=&r\,\sin\theta\,\sin\phi\\\nonumber x&=&r\,\cos\theta \end{eqnarray}

\begin{enumerate}[a)] \item obtain the 9 components of the Jacobian matrix

11 $J^i_{i’}=\frac{\partial x^i}{\partial x’^{i’}}$

\item If $V$ is a contravariant vector field that has constant components $V^{i’}$ in the spherical basis, e.g. $V^{i’}=(0,1,0)\Leftrightarrow V=0\times e’_{(r)}+1\times e’_{(\theta)}+0\times e’_{(\phi)}$, show that $V$ is not a constant vector field.

\item More generally, use the Jacobian matrix $J^i_{i’}$ to express the basis vector fields of spherical coordinates $e’_{(r)}$, $e’_{(\theta)}$ and $e’_{(\phi)}$ in terms of the basis vectors of cartesian coordinates $e_{(x)}$, $e_{(y)}$ and $e_{(z)}$.

\item Check that each of these basis vector fields points in the direction where the corresonding coordinate is increasing.

\item A symmetric (0,2)-tensor field $g=g_{ij}\,\theta^{(i)}\otimes \theta^{(j)}$ called the metric can be defined if the length $dl$ of any given interval $dx^i=(dx^1,dx^2,dx^3)$ is known, and consistent with $dl^2=g_{ij}(x)dx^idx^j$. Assuming this length is given by the euclidian metric $dl^2=dx^2+dy^2+dz^2$, obtain the components $g_{i’j’}(x’)$ of the metric in spherical coordinates.

\end{enumerate}

% Plots or other graphics can be included using: \includegraphics{}

} %===== End of exercise tasks ======

%===== Full solution ======\newcommand{\solution}{

% Please provide the full solutions to the exercise here.

Complete step-by-step solution. \begin{enumerate}[a)] \item Solution for the first subtask: \begin{align} A+B=C \end{align} \item Solution for subtask 2. \end{enumerate}

12 } %===== End of full solution ======

%===== First-level hints ======% If you want to provide hints to the exercise (or only to specific subtasks), you can do this here. % The first-level hints should not be too specific and just give a small hint towards the right direction for solving the task. % If no first-level hints should be given, comment out the line "\newcommand{\firstlevelhints}{}" \newcommand{\firstlevelhints}{

\begin{enumerate}[a)] \item Apply the general expression for the differential of a function $df=\partial_{i’} f\, dx’^{i’}$ to the 3 particular functions $x^1=x(r,\theta,\phi)$, $x^2=y(r,\theta,\phi)$ and $x^3=z(r,\theta,\phi)$.

\item By definition, the components of a (contravariant) vector $V$ transform as $V^{i}=Jî_{i’}\,V^{i’}$, like the components of the tangent vector $Tî=\frac {dxî}{d\lambda}$ to a curve $xî(\lambda)$. (This generalizes the particular case of spatial Lorentz transformations where $Jî_{i’}=\Lambdaî_{i’}$ is a constant rotation matrix with 3 independent parameters).

\item The so-called ‘‘co-variant’’ transformation $e’_{(i’)}= Jî_{i’}e_{(i)}$ guarantees that $V=Vî e_{(i)}$ is a basis-independent object. Indeed, \begin{eqnarray} \label{eq:3} V&=&Vî e_{(i)}\\ &=&(Jî_{i’}\,V^{i’})e_{(i)}\\ &=&V^{i’}(Jî_{i’}e_{(i)})\\ &=&V^{i’} e_{(i’)} \end{eqnarray}

\item Identify the family of curves $x^i(\lambda, j)$ tangent at every point to the basis vector $e_{(j)}$.

\item Apply the transformation law for the components of a

13 (0,2)-tensor: \begin{equation} \label{eq:4} g_{i’j’}=J^i_{i’}J^j_{j’}g_{ij}=J^i_{i’}g_{ij}J^j_{j’} \end{equation} where $g_{ij}=\delta_{ij}$ in cartesian coordinates. Notice that some care is needed in order to write the double sum on $i,j$ as a matrix product: $J^j_{j’}$ can be seen as a matrix $J$ with $j$ as line number and $j’$ numbering columns; similarly $g_{ij}$, can be seen as a matrix $g$, but line number $i$ is down, sort of transposed. This is why the matrix product expression of (\ref{eq:4}) is $g’=J^T.g.J$. As a cross-check, compute the squared length $dl^2$ of an arbitrary interval $(dr,d\theta,d\phi)$.

\end{enumerate}

} %===== End of First-level hints ======

%===== Second-level hints ======% The second-level hints should be a bit more specific and guide the students towards the right approach. % If no second-level hints should be given, comment out the line "\newcommand{\secondlevelhints}{}"

% \newcommand{\secondlevelhints}{

% \begin{enumerate}[a)] % \setcounter{enumi}{1} % \item Second hint to subtask 2. % \end{enumerate}

%} %===== End of Second-level hints ======

%===== Control results ======% Control results can be provided for specific tasks. % If no control results should be given, comment out the line "\newcommand{\controlresults}{}"

\newcommand{\controlresults}{

14 \begin{enumerate}[a)] \item \item \item \item \item $dl^2=dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2$

\end{enumerate}

} %===== End of control results ======

\subsubsection{Make file} #======# This makefile produces two PDF files: # One PDF with only the exercise (and with hints and control results, if provided) # and a second PDF also including the full solution. #======

#======# Change the inputname and outputname (no file extensions needed):

# tex-file containing the exercise: INPUTNAME="exercise" # outputname for the PDF files: OUTPUTNAME="exercise" #======

#======# The following lines should not be changed! #======PDFLATEX = pdflatex LATEX = latex MAKEINDEX = makeindex BIBTEX = bibtex SED = sed MV = mv all: exer solu

15 CONTENTSFILES=$(shell find . -name "template.tex")

OUTPUTFILEBASE=$(shell basename ${CONTENTSFILES} .tex)

OUTPUTFILE=${OUTPUTFILEBASE}.pdf targets: $(OUTPUTFILE) additional: $(OUTPUTFILE) $(ADDOUTPUTFILES) clean: $(RM) -f *.glo *.gls *.idx *.ilg *.ind *.toc *.log *.lof *.lot *.aux *.blg *.bbl *.nav *.snm *.vrb *.out allclean: clean $(RM) -f $(OUTPUTFILE) $(ADDOUTPUTFILES) solu: $(CONTENTSFILES) $(BIBLIOGRAPHY) $(LATEXSTYLES) @ $(SED) ’s/.*\\\def.printsolution/\\\def\\\printsolution/’ $< > solu.tex @ $(PDFLATEX) "\\def\\inname{$(INPUTNAME)}\\include{solu}" @ $(PDFLATEX) "\\def\\inname{$(INPUTNAME)}\\include{solu}" @ $(MV) "solu.pdf" $(OUTPUTNAME)"_solution.pdf"; @ rm *.aux *.log *.out solu.tex exer: $(CONTENTSFILES) $(BIBLIOGRAPHY) $(LATEXSTYLES) @ $(SED) ’s/.*\\\def\\\printsolution/% \\\def\\\printsolution/’ $< > exer.tex @ $(PDFLATEX) "\\def\\inname{$(INPUTNAME)}\\include{exer}" @ $(PDFLATEX) "\\def\\inname{$(INPUTNAME)}\\include{exer}" @ $(MV) "exer.pdf" $(OUTPUTNAME)".pdf"; @ rm *.aux *.log *.out exer.tex #======

16 4 How to implement a Tandem-Project learning and teaching activities

Educating-through-research is one of the main goals of the iTHEPHY project and is pursued through the Tandem-Project (TP). In this document, it is summarised the main aspects of this learning and teaching activity with the aim of replicating the same experience in different master’s degrees. To efficiently achieve this goal, the iTHEPHY experience is reported. Figure 3 shows the logo used to advertise the activities among students. This innovative educational methodology was tested for the first time in October 2018. Eigh- teen students, enrolled in the second year of the master’s degree in physics from the three partner universities were engaged to be part of TPs. They were combined to form seven cross-national teams (made of two or three students and two or three supervisors). Interna- tional research projects based on HEP research were assigned to each group. To achieve the expected results, students and supervisors organized regular virtual meetings (bi-weekly). Also, two video-conferencing meetings were organized, gathering all the students and supervisors together to share the status of their research. The project-based learning and teaching activities were supported by an advanced collaboration platform, integrated into a customized, open source Moolde site. Figure. 2 shows a view of the Moolde web page, in particular the main page of the Summer School held on May-June 2020.

Figure 2: A view of the Moolde web page.

The standard Moolde installation has been extended with the integration of additional educational tools. In more details a TP consists in: defining a project: a small research project from HEP context, like data analysis, a • simulation of a detector, etc.; defining a target: a result to be presented at the end of the project; • defining a time-line: organizing a calendar, scheduling meetings, considering all the • intermediate steps to achieve the expected results, indicating when the results are ready to be shown to other colleagues and supervisors; realizing a presentation with final results to be presented at the ISHEP Spring School; • realizing a report, following the scheme of a scientific paper, where students describe • in details methodologies and results.

17 Figure 3: Tandem-Project logo.

A team of international supervisors guided students during the various TPs, exploiting the ICT tools developed in the first part of the project which allowed them to communicate, exchange files, documents and ideas. When all these activities were completed, and the reports delivered, six ECTS were awarded by UNIBO to all students, comprising the ones coming from the foreign Universities of the Consortium. Both supervisors and students were extremely motivated, as most of the projects might continue as a thesis project. Un- fortunately, no official recognition of teaching hours has been assigned by Universities to the supervisors so far. However, there are plans for future acknowledgement. This innovative didactical methodology was for the first time tested starting in October 2018, when 18 students enrolled at the second year of the master’s degree in physics from the three partner universities (University of Bologna, Dortmund, and Clermont-Ferrand) are engaged to be part of the TP. They are combined to form 7 cross-national teams (made of 2/3 students and 2/3 supervisors). An international research project based on the real high-energy-physics research life has been assigned to each team. To achieve the expected results, students and supervisors from different countries organised regular virtual meetings to discuss the status of their project. Besides, two general virtual (by a video conference system) meetings, gathering all the students and supervisors together to share the status of each project have been also organized. A final oral presentation, to show the results of the TPs, was given by each team at the V edition of the International Summer School on High Energy Physics (ISHEP) that have been held in Cargese (Corsica, France) from 8th to 12th of April 2019. TP foresees also a final written report, in the form of a real scientific paper, to be delivered in the virtual environment by the end of June 2019 and reviewed by the supervisors. A final mark has been assigned to all the students who completed successfully the activities and six ECTS have been awarded by UNIBO to all of them.

4.1 The Tandem-Project in 2018/2019 academic year as an example Eighteen students, enrolled at the second year of the master’s degree in physics from the three partner universities are engaged to be part of the TP. They are combined to form seven cross-national teams (made of 2 or 3 students and 2 or 3 supervisors) as shown in Fig 4.

18 Figure 4: The ﬁgure shows name of the Students and Supervisors participating in the pilot TP

4.2 The research projects International research projects based on the real HEP research life have been assigned to each team. To achieve the expected results, students and supervisors organised regular virtual meetings (bi-weekly). Also, two video-conferencing meetings have been organized gathering all the students and supervisors together to share the status of each project.

TP-1 : BSM physics in 4-top ﬁnal states: Survey of the BSM models leading to NP in 4 tops and Implementation of the NP models in FeynRules/MadGraph.

TP-2 : Machine learning application to enhance discovery sensitivity.

TP-3 : Higgs self-coupling at the FCC: HH production.

TP-4 : Sensitivity estimates indirect searches for new physics.

TP-5 : Sensitivity estimates for rare decays.

TP-6 : SMEFT at the LHC: EFT interpretation of Top-quark measurements at the LHC and beyond.

TP-7 : Evaluation of the sensitivity for a future detector: tracking detectors with high time and space resolutions; calorimeters with high resolution and segmentation.

A ﬁnal oral presentation showing the results of the various projects have been given by each team at the V edition of the ISHEP-2019. The international attendants to the school

19 were twenty-seven, ten students from UNIBO, nine students from UCA, six students from TUD, one student from the Economic School of Moscow and one student from Universidad Nacional de Colombia. The students were selected, respecting gender principles and equal national sharing through an interview with the students, previously informed about the objectives of the project. Nine teachers attended the school. The program of the school included lectures on Standard Model, Neutrino Physics, Flavour Physics, Future High Energy Physics, Top quark physics, and Machine learning techniques. An entire day was dedicated to the students that presented the progress of their research activities to the audience in the context of the TP. The TP scheme foresees also that students conclude the experience writing a ﬁnal report, in the form of a real paper. Students delivered the documents in June 2019. The work done by the students are reported in Appendix 6 as an examples. Final marks have been assigned to all the students who complete successfully the activities above described and six ECTS have been awarded by UNIBO.

20 5 How to organise a Summer/Winter School

In this section are reported guidelines for organizing an successful International Summer School. Trough our experience we have recognised the following main criteria to be followed:

The ﬁrst step is to identify the level of student at which the School is oriented, together • with the date, the duration, the number of students that will attend the school, and the location

To have a successful international school is necessary to work on institutional commit- • ments, searching form academic support (including ECTS recognition), local logistic, and budget planning.

It is of extremely importance defining a core group of people (steering committee) in • charge of the organisation, appointing an academic committee, recruiting the teaching staff, defining the details of the budget. The academic committee should also be in charge of the recognition of students’ performance.

Few months before the start of the school is important to ﬁnalise the advertisement • and the communication of the school to target groups, the logistical organisation, and the recruitment of students.

During the event, it is extremely useful to plan a quality evaluation of the event • between students and teacher, for example with surveys. This will help to improve the future edition of the school

After the school, the steering committee analyses the result of the surveys write a • short report for future reference.

In the following sections, the experience done within the iTHEPHY project is reported with the idea to be an example for other possible school in any ﬁeld, not only in Particle Physics.

5.1 How selecting the right location The ISHEP summer schools were hosted by the Institut d’Etudes Scientiﬁques de Cargese (IESC) in Cargese, Corsica, France. The IESC oﬀers an ideal structure equipped with all the necessary facilities to achieve a successful realization of the summer schools. The institute is located in a quiet area close to the sea, an ideal place to create a friendly and close collaboration atmosphere. It provides housing facilities, lunch and breakfast as well as a fully equipped kitchen for preparing dinner. The lectures were given in the two auditoriums (capacity of 80 and 98 seats). They are equipped with a projector and a laptop computer. Two additional meeting rooms are available with boards and beamers for team-work activities. The restaurant, auditoriums, accommodation rooms are connected by pleasant paths through the diversity of the Mediterranean vegetation.

5.2 Participants The ISHEP is designed for students enrolled in second year of a Master degree in physics, with specialisation in high-energy physics. The teachers are professors and researchers that

21 are active in a broad range of ﬁelds in experimental and theoretical high-energy and particle physics. ISHEP-2018 brought together 26 students and 7 teachers from the Universities of Bologna, Clermont-Ferrand, and Dortmund as well as from research institutions (INFN, IN2P3, and DESY). In ISHEP-2019, the number of participants increased to 10 teachers and 29 students, including one student from the National University of Colombia in Bogota, Colombia. In both editions the good ratio of teachers to students allowed for an intensive mentoring to achieve the maximal possible learning outcome for the students.

5.3 A efficient and well oriented agenda The central elements of the summer schools were lectures given by the different teachers, that were organized in one lecture block in the morning, and one in the afternoon. The lectures covered a broad range of different topics in the field of high-energy physics, such as Standard Model (SM), QCD, Flavour Physics, Top Quark, Machine Learning, Neutrino Physics, Cosmology, Beyond the SM, and SM Future. They were given by teachers doing active research on the respective subject and especially focused on the most recent results and achievements, fresh from international conferences like Moriond, only a few weeks before. After each lecture there was a short catalogue of questions given to the students and the answers were discussed in the plenum. A special ”Future Project” session had the students playing the role of a funding agency, having to choose between various projects defended by the teachers. In both ISHEP editions one entire day was reserved for students talks. In those talks the students that were recently involved in a Tandem project presented the result of their work to the other students and teachers. This provided the possibility to give a scientific talk in a comfortable environment and prepared the students for talks at more challenging conferences in the future. The programme was completed by social activities in the evening like a welcome cocktail, a workshop dinner and a volleyball tournament. These social activities accelerated the opportunity get to know the other participants in an informal atmosphere and to create a network. The ISHEP summer schools held in Cargese were a central part of the iTHEPHY project and essential for the achievement of project objectives. The students acquired a great deal of scientific knowledge on high energy physics through the lectures, and improved their presentation skills in the Tandem talks. Furthermore the students experienced the international character of scientific research. The summer schools provided the perfect environment to make contact with students and researchers from other countries and allowed the participants to build an international network of people working in their field. Many of those connections among participants made during the ISHEP summer schools also lasted afterwards.

22 6 Conclusions

We can here summarise the main results obtained by the iTHEPHY project as reference for different implementation of similar activities in other master’s degrees. The first main result is the Virtual environment able to support international stu- • dent teams in all phases of the development of their research projects and therefore contributing to the internationalization of the students’ mindset although not mobile (internationalization @ Home). The second main result of the project so far is the official recognition of the ECTS by • UNIBO to all international students who developed their tandem-project and completed the research attending the Summer School. Students can obtain credit points participating in the tandem-project and the Summer School. This has a high impact on the students participating in the project so far, but also for all the other students that in the future will be part of this programme. Besides, thanks to this official achievement, all the academic institutions of the Consortium have been starting the process to integrate the teaching and learning activities proposed by this project in their master’s degree curricula. Not strictly connected with the ECTS, but related to the entire project, iTHEPHY had so far an important impact in strengthening the relationship among the partners, which applied to the ITN Marie Sklodowska- Curie 2019 action (European Joint Doctorate) with the same Consortium, aiming in transforming the iTHEPHY project at the level of a doctoral school. The third result is the establishment of an Intenational Master’s Degree in Parti- • cle Physics (IMAPP), a joint degree between the University of Bologna, Clermont- Auvergne and Dortmund. The program addresses students who, building up on inter- ests in particle physics, have the goal of becoming leading researchers in the academic world or in private companies. The degree aligns its program with the job market needs: it offers 36 credits in statistics and artificial intelligence, in the development of detectors and electronics, as well as in computer science. Furthermore, 36 credits are devoted to experimental techniques, 18 credits are focused on the theoretical founda- tions, and 30 credits are reserved to the final research thesis. By studying at three universities at the core of Europe, IMAPP offers a unique mobility experience. It is important to underline that, especially thanks to the start of the Tandem-Project supervision activities, the collaboration in teaching from researches belonging to research institutions increased, with an impact on the quality of the education provided by the universities. In parallel, the academic institutions started to fill up the lack of internationalization present in the master programme. In addition, to get a stronger international context, bi-lateral Erasmus plus agreements have been recently signed by the three Universities. In conclusion, this handbook summarised the methodologies adopted by the iTHEPHY project to be replicated by other master’s degrees as well its impact. After an introduction to the iTHEPHY project, a section is dedicated to the software used to implement an e-learning platform with collaborative tools for enhancing remote teacher-student collaboration. The consequent section reports on how to implement the so-called Tandem-Project learning and teaching activities. Finally, a section to describe how efficiently organise a Summer/Winter school is also present.One of the main innovative educational activity of iTHEPHY is the tandem-project. Innovative learning and teaching methodologies have been implemented for the first time with international pilot students and supervisors during the 2018/2019

23 and 2019/2020 academic years. Students participated actively at various research projects, presenting results at the V edition of the International School on High Energy Physics held in Cargese (Corsica, France) from 8th to 12th of April 2019 and writing ﬁnal reports in the form of a scientiﬁc paper. For these activities, six ECTS were awarded to the students by UNIBO.

Appendix

In this Appendix the papers written by the students participating to the 2018/2019 Tandem- Project activities are reported.

24 TP-2 Report A Machine Learning Application to Enhance the Discovery Sensitivity

Nils Abichta, Serena Di Pedeb, Louis Vaslinc, Julien Doninid, Kevin Kr¨oningere, Maximiliano Siolif

aTandem-Project student, Technische UniversitätDortmund, Germany bTandem-Project student, Universitàdi Bologna, Italia cTandem-Project student, UniversitéClermont Auvergne, France dTandem-Project supervisor, UniversitéClermont Auvergne, France eTandem-Project supervisor, Technische UniversitätDortmund, Germany fTandem-Project supervisor, Universitàdi Bologna, Italia

Abstract This project aims to improve the sensitivity and the exclusion limit of the ATLAS search for the W boson, in the W t¯b lνb¯b decay channel, applying Machine Learning 0 0 → → techniques, in particular focusing on the application of the Multilayer Perceptron, Boosted Decision Trees and Support Vector Machine methods.

1. Introduction

Experiments at the Large Hadron Collider (LHC) [1] at CERN test the Standard Model (SM) of particle physics [2] and search for Beyond the Standard Model (BSM) physics by producing elementary particles in high energy particle collisions. With data from one of these four big experiments, the ATLAS experiment, a search for heavy vector bosons W 0 was performed. This project aims to enhance the sensitivity of this search by employing diﬀerent machine learning algorithms.

2. Context

2.1. Standard Model and Beyond The SM is the current theoretical framework describing almost everything we know about the world of subatomic particles and their interactions. It is also the most consistent model we have with respect to the numerous experimental results.

However, if so far no experiment ever managed to prove it wrong to a high level of precision, it doesn’t mean that this model is perfect. In fact there are a few missing pieces that make physicists looking for another more global theory. Many possibilities are explored

22 in order to ﬁnd a model BSM. Among the variety of potentially discoverable new particles features a new heavy gauge boson, the W 0.

2.2. Looking for the W 0 boson

The W 0 can be seen as a sort of cousin of the W bosons of the SM. Just like its cousin, 1 the W 0 is either positively or negatively charged .

If we consider a purely right-handed W 0, we can assume that the W 0 will only couple to right-handed fermions. In the case of coupling to leptons, we must assume that there is a νR lighter than the WR0 . This is the reason why we will focus on the coupling to quarks (t¯b). We deal with the semi-leptonic ﬁnal state where the top quark decays into a b quark, a charged lepton and a neutrino, as it is shown in Figure 1.

Figure 1: Feynman diagram of the production and decay of the W 0 boson with the semi-leptonic ﬁnal state.

3. Latest analysis from ATLAS and project objective

We based on the ATLAS search for the W 0 boson in the semi-leptonic channel shown in [3]. The analysis preselected data with these criteria:

at least two jets and one lepton • Lepton p > 50 GeV • t Emiss > 80 GeV (el), 30 GeV (mu) • T Emiss > + m (W) > 100 GeV • T t top p > 200 GeV • t b p > 200 GeV • 1 t In this way, eight Signal Regions (SR) have been deﬁned with:

2-3 jets and 1-2 b-jets, both for the electron and the muon • W mass > 500 GeV • 0

1 + For simplicity sake, we will refer to both the ”W 0 ” and ”W 0−” as just ”W 0”.

23 ∆R(lepton, b ) < 1.0 • 2 In particular, the condition on the W 0 mass removes the small number of low-mass events, while the last condition is quite discriminant against the background, mainly in the muon-channel for higher W 0 masses. Hence, starting from the results of the ATLAS analysis our objective was to achieve the maximum separation between the signal and background events.

4. The Machine Learning technique

In order to improve the previous analysis, Machine Learning algorithms have been applied, using the TMVA package [4], to the Monte Carlo simulated Signal and Background samples provided2. The Machine Learning technique consists of two steps: 1. the Training phase, which produces the weight ﬁles, used both in the Training and Application phase of the methods, and also provides an objective evaluation of the trained method (e.g. ROC curve) 2. the Application phase, where the trained methods are applied to the full datasets, providing an output value that determines if an event is of class ”Signal” or ”Back- ground”

4.1. ML algorithms Serena Di Pede (Bologna) used the Multi-Layer-Perceptron (MLP), one of the Feed- Forward Artiﬁcial Neural Network (ANN) implemented in TMVA. A MLP is implemented with: (1) an input layer with its input variables; (2) an output layer with only one neuron (or node); (3) eventually hidden layers with variable number of neurons (nodes). Keeping in mind the Weierstrass theorem (according to which, you should construct a MLP with only one hidden layer and increase the number of hidden neurons until improvement in performance) for the architecture, the others hyperparameters considered for the MLP implementation and evaluation are:

the NCycles (number of training cycles) • the Training Method • the TestRate (tests performed for overtraining performed at each epoch) • Louis Vaslin (Clermont-Ferrand) used a method called Boosted Decision Tree (BDT) [5]. This algorithm is well known in Particle Physics and is reputed for its robustness. The hyperparameters of interest of this method are:

The number of trained trees • The maximum depth of the trees • The minimum allowed size for the nodes •

2The Signal sample consists of W’ generated with masses ranging from 1 TeV to 5 TeV, while the Back- ground sample included all the background processes of the analyzed decay, such as tt¯ events (dominant), W + jets, multijets (instrumnetal background)

24 The learning rate of the algorithm • Nils Abicht (TU Dortmund) implemented a Support Vector Machine (SVM) [6]. This algorithm is a linear classiﬁer that uses a kernel function to map the input features into a higher dimension. Usually a gaussian kernel function is used. Important hyperparameters are:

The kernel parameter γ, which deﬁnes the size of the kernel • The cost parameter C, which balances the impact of misclassiﬁcation on the learning • process

5. Application

5.1. Preprocessing Taking the dataset from the ATLAS analysis (events with two or three jets, at least one of them b-tagged and a reconstructed W 0-mass mW 0 of at least 1000 GeV), we applied then miss miss the cuts on Et and Et + mt(W ), as deﬁned in section 3.

5.2. Training and performance For the training of the algorithms, a total of seven variables are used. The training is performed with the Monte Carlo generated Signal samples that are based on only mW 0 = 4 TeV. It appears that training with other W 0-masses does not signiﬁcantly improve the performance of the algorithms.

For the MLP, the training phase is performed using diﬀerent Neural Networks available in TMVA, in order to test their performance and choose the best method: (1) the Clermont Ferrand Neural Network (CFMlpANN), (2) the TMultilayer Perceptron (TMlpANN), (3) the MultiLayer Perceptron (MLP). The ROC-curves of each method are shown in Figure 4 of the Appendix B. The method MLP2 shows the best performance, looking also at its response in the overtrainig check (left side of Figure 6, Appendix C) with the hyperparameters:

NCycles: 700 • 1 Hidden Layer with 107 hidden neurons • Training Method: Back-Propagation method • TestRate: 10 • For the BDT, the training is performed in the electron and muon channels separately. The hyperparameters are optimized using TMVA default algorithm. The optimal values obtained are the following:

number of trained trees : 500 • maximum depth : 3 • minimum node size : 2% • learning rate : 0.05 •

25 For the SVM, the variables used are normalized to the range between 1 and 1. With − TMVA a grid search for the optimal hyperparameters C and γ is performed. The search yields C = 0.93 and γ = 0.15. Other hyperparameters do not make much of a diﬀerence and are left to their default values.

Appendix C shows the response of the algorithms on the test sample as well as the training sample. All three algorithms show good discrimination strength. Overtraining does not appear to be a problem, since the responses on the test and the training samples are quite similar. When applied to signal samples with other W 0-masses, the discrimination strength gets worse for lower W 0-masses. This is to be expected, as the features at lower masses get more similar to the background.

6. Results

6.1. Significance As a figure of merit, the significance “Signal/√Background” is used. The algorithms are applied to each sample and the significance is calculated depending on the classification cut value. The maximum significance achieved for each W 0 mass is shown on the left side of Figure 2. For reference, the significance achieved in the previous analysis is also included. The maximum significance curves are obtained by applying a single cut on the output value of the different methods. We can see that, at low mass, only the MLP methods achieve a better significance. But for masses greater than 2000 GeV, all methods seems to improve the reference results.

6.2. Exclusion limit 6.2.1. Deﬁnition The exclusion limit is a statistical method that tells us if we are sensible to the physics we want to probe with respect to the theoretical model we consider. Thus, even if we are not able to observe a W 0 in the data, this allow us to put limits on the theoretical model we consider.

The tool we use for our analysis is a complex method called Likelihood Proﬁle Ratio [7], [8]. For the reference analysis, the calculation is done using the reconstructed invariant mass distributions of the W 0. For our Machine Learning analysis, we use the output distributions given by each method. The distributions must be normalized using the normalization information provided with the samples.

Thus, the tool calculates the limit on the cross-section of the process we are studying at 95% of conﬁdence level. The comparison of this limit with the cross-section predicted by the theoretical model allows us to say if we can exclude the model at 95% of conﬁdence level. The objective is to obtain a limit on the cross-section as low as possible.

6.2.2. Obtained limit The limits on the cross-section have been calculated for each W 0 mass hypothesis. The results is the combination of the calculation realized in each signal regions. Figure 2 shows

26 Significance - All analysis Expected exclusion limit - All analysis

3 )B 10 Significance BDT 10

Significance SVM ) [pb]b t → 102 Significance MLP

Significance cuts R 1 Significance (S/ 10 )*BR(W’ R W’ → (pp σ

1 10-1

10-1

10-2 Theoretical 10-2 Expected BDT Expected SVM Expected MLP Expected cuts 10-3 1000 1500 2000 2500 3000 3500 4000 4500 5000 1000 1500 2000 2500 3000 3500 4000 4500 5000 W’R mass [GeV] W’R mass [GeV]

Figure 2: On the left side, maximum signiﬁcance curves obtained for all three methods. The result obtained with the reference analysis is also shown for comparison. On the right side, the exclusion limit at 95% of conﬁdence level obtained for BDT, MLP and SVM. The limit obtained with the reference cut-based analysis is also shown for comparison. the limit on the cross-section obtained for each analysis methods together with the theoretical cross-section of the process.

The results show that, for a low W’ mass (< 2000 GeV), the results of the BDT and SVM are not competitive with the reference analysis, while MLP gives better results at 1000 GeV. However, as long as the limit stays bellow the theoretical line, we can still exclude the considered model at 95% of conﬁdence level. For masses between 2000 and 4000 GeV, all Machine Learning methods gives better results than the reference analysis. And for higher W 0 masses (> 4000 GeV), the performance of BDT and MLP deteriorates while SVM remains competitive with respect to the reference.

The intersection between the theoretical cross-section and the limit tells us how far we can exclude the model. Thus, we can interpret it as a limit on the W 0 mass for the considered model. Here we can observe that this limit on the W 0 mass is improved by around 100 GeV with MLP and 200 GeV with BDT and SVM.

7. Conclusion

To improve the sensitivity in the search for heavy W 0 bosons, diﬀerent Machine Learning methods, i.e. the MLP, BDT and SVM algorithms were deployed on data from a previous ATLAS analysis. Showing strong discrimination strength between signal and background, the signiﬁcance was improved, especially for higher W 0-mass hypotheses. Exclusion limits on the mass of the W 0 were improved by around 200 GeV.

References

[1] L. Evans and P. Bryant. LHC Machine. JINST, 3, 2008.

[2] W. Cottingham and D. Greenwood. An Introduction to the Standard Model of Particle Physics. Cambridge University Press, 2007.

27 [3] The ATLAS Collaboration. Search for vector-boson resonances decaying to a top quark and bottom quark in the lepton plus jets ﬁnal state in pp collisions at √s = 13 TeV with the ATLAS detector. Physics Letters B, 2019.

[4] K. Albertsson et. al. TMVA 4, Toolkit for Multivariate Analysis with ROOT : User Guide, 2018.

[5] B. Roe, H. Yang, and J. Zhu. Boosted decision trees, a powerful event classiﬁer. In Statistical Problems in Particle Physics, Astrophysics and Cosmology (PHYSTAT 05): Proceedings, Oxford, UK, September 12-15, 2005, 2005.

[6] C. Cortes and V. Vapnik. Support-vector networks. Machine Learning, 20, 1995.

[7] A.L. Read. Presentation of search results: the CLs technique. Journal of Physics G: Nuclear and Particle Physics, 28, 2002.

[8] G. Cowan et. al. Asymptotic formulae for likelihood-based tests of new physics. The European Physical Journal C, 71, 2011.

28 APPENDIX

A. Deﬁnition of variables

In Particle Physics, there are many variables defined to describe the state of an event and of all the objects that are involved within this event. One of the most important variable is the transverse momentum pT of the different particles defined as the projection of the total momentum in the transverse plan:

2 2 pT = px + py q We also deﬁne the invariant mass of a particle as the norm of its energy-momentum four-vector, expressed in natural units:

M = E2 + p2

Another important point is that, givenp the cylindric geometry of the detector, we usually work with the coordinates Φ (azimuthal angle) and η (pseudo-rapidity). The pseudo- rapidity η being deﬁned as a function of the usual θ angle as follow:

θ η = ln tan − 2 With the angular coordinates, we define the angular distance between two particle tracks as follow: ∆R = ∆Φ2 + ∆η2 With ∆Φ the difference of azimuthal anglep between the momentum of the two particles and ∆η the difference of pseudo-rapidity.

Using the diﬀerence ∆Φ, we can also calculate the transverse mass of a particle P from the four-vectors of its decay products as follow:

m (P ) = 2p p [1 cos(∆Φ)] T T,1 T,2 − q With pT,1 and pT,2 the transverse momentum of the two decay products of the particle P .

29 B. ROC curves

Background rejection versus Signal efficiency Background rejection versus Signal efficiency 1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6 Background rejection Background rejection

0.5 0.5

0.4 0.4 MVA Method: MVA Method: 0.3 BDT 0.3 BDT

0.2 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Signal efficiency Signal efficiency

Figure 3: ROC curves obtained for the method BDT for the electron channel (left) and muon channel (right)

30 Figure 4: ROC curves obtained for the trained Neural Networks (left) and SVM (right).

31 C. Overtraining checks

TMVA overtraining check for classifier: BDT TMVA overtraining check for classifier: BDT

dx/ Signal (test sample) Signal (training sample) dx/ Signal (test sample) Signal (training sample) 16 12 Background (test sample) Background (training sample) Background (test sample) Background (training sample) Kolmogorov-Smirnov test: signal (background) probability = 0.023 (0.104) 14 Kolmogorov-Smirnov test: signal (background) probability = 0.032 (0.556) 10 (1/N) dN (1/N) dN 12

8 10

6 8

6 4 4 2 2

0 U/O-flow (S,B): (0.0, 0.0)% / 0 U/O-flow (S,B): (0.0, 0.0)% / 0.8− 0.6− 0.4− 0.2− 0 0.20.8 0.4 0.6 0.8− 0.6− 0.4− 0.2− 0 0.20.8 0.4 0.6 BDT response BDT response

Figure 5: BDT response on the training and test samples for the electron channel (left) and muon channel (right)

32 Figure 6: MLP2 response (left) and SVM response (right) on the training and test sample.

33 TP-3 Report Measurement of Higgs Boson Self-coupling at the FCC-hh Collider

Noemi Cavallia, Saad Tailb, Djamel Boumedienec, Sylvie Braibantd, Elisa Fontanesid

aTandem-Project student, Universitàdi Bologna, Italia bTandem-Project student, UniversitéClermont Auvergne, France cTandem-Project supervisor, UniversitéClermont Auvergne, France dTandem-Project supervisor, Universitàdi Bologna, Italia

Abstract The prediction of the Higgs boson, in 1964, was a huge breakthrough in physics; moreover, its discovery in 2012 was even a great validation for the Standard Model (SM). In this report, a closer look is taken at the self-coupling of the Higgs Boson. To start, an overview on the di-Higgs features is provided. Next, a presentation of the chosen signature process to study the Higgs self-coupling. Finally, two data analyses are performed: the cut-based analysis and the multivariate analysis.

1. Introduction

One substantial topic described by the SM is the Higgs mechanism. In fact, the discovery of the Higgs boson, at the Large Hadron Collider (LHC) at Cern [1] in 2012, is one of the major conﬁrmations of the SM. The Higgs boson was ﬁrst predicted by Robert Bout, Fran¸coisEngler and Peter Higgs in 1964, since then an important amount of focus and research have been dedicated to study the characteristics of this particle. Among the several features that fall under the scope of Higgs mechanism is the Higgs self coupling. This work is intended to present the way this type of coupling takes place and explore some dynamics of the Higgs boson such as its production and decay. The Higgs selfcoupling is studied assuming the conditions of the hypothetical hadron Future-Circular- Collider (FCC-hh) where physicists aim to achieve collispionsion energies of 100 TeV in the search for new physics.

2. Theoretical Overview

The elementary particles, as described by the SM, acquire their mass via a mechanism called the Higgs mechanism. The spontaneous symmetry breaking of the Electroweak theory gives rise to the introduction of a new scalar field; the Higgs field and the mechanism by which elementary particles couple to this field provides them with masses.

34 Mass of the fermions: m = g ν/√2. • f f Mass of the Bosons W and Z: M = g ν/2 and M = g ν/2cos(θ ) • W W Z W W where: 1/2 ν = (√2GF )− GeV [2] is the vacuum expectation value of the Higgs ﬁeld, gf and gW are known as the coupling constants, and θW is called the Weinberg angle.

The excitation of the Higgs ﬁeld creates the Higgs boson which is produced through four modes [3]: Gluon fusion (which is the mode considered here), Vector Boson Fusion, Higgs-strahlung, and Associated production.

2.1. Di-Higgs Boson Production This study of the self-coupling could be probed by investigating the di-Higgs production process. Figure 1 displays Feynmann diagrams of this process, the diagrams are known as the top quark triangle and box loops.

Figure 1: diagrams for the di-Higgs production

The Potential for the Higgs scalar ﬁeld H is written as: 1 2 2 3 1 4 5 V (H) = 2 mH H + λνH + 4 λH + O(H ) It contains the term λνH3 which represents the Higgs coupling to itself, where λ represents the Higgs self coupling.

One of the tasks through which we went during this work is the calculation of the di- Higgs cross section using Madgraph. MadGraph is a framework that aims to providing all the elements necessary for SM and BSM phenomenology, such as the computations of cross sections, the generation of hard events and their matching with event generators, and the use of a variety of tools relevant to event manipulation and analysis.

3. Cut-based Analysis 3.1. Signal and background processes The ﬁrst part of the project aimed to reproduce the results published in the FCC-hh CDR [4] about the projection on the Higgs boson self-coupling measurement at FCC-hh. The channel of interest, displayed in Figure 2, considered in the analysis is: HH bbZZ(4l) −→ where one of the Higgs bosons decays in a pair of bottom quarks while the other one in a pair of weak Z bosons. The Z bosons decay then in four leptons. In this analysis only electrons and muons are considered (l = e, µ). There are several background processes which results in the ﬁnal signature searched in the analysis (bb4l) such as:

35 Figure 2: Feynman diagram for the channel of interest.

channel σ BR [fb] · HH bbZZ(4l) 0.178 −→ ttH bb4l 4.013 −→ gg(H) + bb bb4l 0.369 −→ ttZ bb4l 2594 −→ ZH bb4l 0.071 −→ Table 1: Cross section time branching ratio values for signal and background processes. The branching ratios associated to the decay of the Higgs boson in a pair of bottom quarks and in four leptons are respectively 4 BR(H bb) 0.58 and BR(H 4l) = 1.24 10− . −→ ≈ −→ ·

ttH bb4l • −→ gg(H) + bb bb4l • −→ ttZ bb4l • −→ ZH bb4l • −→ The cross section time branching ratio values for signal and background channels are presented in Table1.

3.2. Data Samples The MC samples employed in the analysis were (previously) obtained using MAD- GRSPH5 [5] for the parton level generation, PYTHIA8 for the parton showering and DELPHES [6] for the ideal detector simulation. All the samples were generated for proton-proton collisions at a center of mass energy 1 √s = 100 TeV and an integrated luminosity = 30 ab− . No pile-up was considered. L 3.3. Event selection The discrimination between signal and background events was obtained performing a cut-based analysis. Several restrictions on the values of the kinematic variables such as transverse momentum, angular distance between the b-jets and others were set in order to get the best discrimination. Signal events were selected according to the following requirements regarding the leptons:

Number of isolated leptons 4 • ≥ Number of dileptons 2 • ≥

36 1 Figure 3: Invariant mass distribution of the four lepton ﬁnal state. Events are normalized to 30000 fb− .

40 GeV M 120 GeV • ≤ Z1 ≤ 12 GeV M 120 GeV • ≤ Z2 ≤ Number of leptons = 4 • At least one lepton with p > 20 GeV • T At least one lepton with p > 10 GeV • T 120 GeV M 130 GeV • ≤ 4l ≤ where lepton pairs with same ﬂavor and opposite charge are indicated as ”dileptons”. Events were selected requiring also the following conditions on the b-jets:

Number of b-jets 2 • ≥ 80 GeV M 130 GeV • ≤ bb ≤ 0.5 ∆R 2.0 • ≤ bb ≤ 3.4. Results The invariant mass distribution of the selected events for the four-lepton system is presented in Figure 3. The ttH background (in yellow) is found to be the dominant one.

The expected precision on the Standard Model cross section as well as on the self coupling SM modifier kλ, defined as the ratio kλ = λHHH /λHHH (with λHHH being the trilinear Higgs boson self coupling), were obtained using CMS Combine tool. Figure 4 and 5 show the results obtained on these parameters. Three different assumptions on the systematic uncertainties have been made:

No systematic uncertainties in blue; • 1% of systematic uncertainty for both signal and background (∆S/S = ∆B/B = 1%) • in red;

37 Figure 4: Expected precision on the SM cross section at FCC-hh. Three diﬀerent assumptions about the systematic uncertainties are made.

3% of systematic uncertainty for both signal and background (∆S/S = ∆B/B = 3%) • in green.

4. Multivariate Analysis The most dominant background is ttH and in order to have a maximum separation between this background and the signal HH one of the multivariate analysis methods, Boosted Decision Trees (BDT), have been employed. The input variables are: number of leptons • number of jets • angular distance between the jets • angular distance between the Higgs bosons • mass of the four leptons • mass of the two jets • higgs momentum • The BDT response, as represented in Figure 6, helps pick a value at which the significance, denoted as δ = s/√s + b, is maximum: Optimal cut on BDT leads to a significance of δ = 27.15 • Assuming ttH as main background, expected statistical sensitivity on HH cross-section • = 3.7% Two different types of BDT were employed, using TMVA in ROOT: GradBoost and Ad- aBoost. The signal and background efficiencies values obtained from these two BDT are showed in Table 2.

38 Figure 5: Expected precision on the kλ factor at FCC-hh. Three diﬀerent assumptions about the systematic uncertainties are made.

Figure 6: Signal and background separation by the AdaBoost BDT.

BDT signal eﬃciency background eﬃciency GradBoost 87% 18% AdaBoost 88% 15%

Table 2: Signal and background eﬃciencies obtained from the BDT employed in the analysis.

39 5. Conclusions

This project aimed to get a projection on the Higgs boson self-coupling measurement at the FCC-hh. The study of signal associated to di-Higgs boson production is of great importance in High Energy Physics since it could probe information on the Higgs potential and furthermore it could be employed to test the SM, since any deviation from the SM trilinear Higgs coupling could probe new BSM theories. Two analysis approaches were used to study the following decay channel associated to the di-Higgs pair: HH bbZZ(4l) −→ Firstly, a cut-based analysis was performed, following the FCC-hh CDR. From this analysis the expected precision on the measurement of the SM cross section as well as on the Higgs self coupling modiﬁer were obtained. Since, from the cut-based analysis, the ttH background is found to be the dominant one, a further multivariate analysis was performed, employing BDT to get the best discriminating power between the HH signal and the ttH background. BDT resulted in good signal eﬃciencies values, therefore their employment in future analyses could be of great help in High Energy Physics, especially to suppress the ttH background in Higgs boson studies.

References

[1] G. Bernardi and J. Konigsberg. The Higgs Boson Search and Discovery. Adv. Ser. Direct. High Energy Phys., 26, 2016.

[2] A. Kobakhidze and A. Spencer-Smith. The Higgs vacuum is unstable. 2014.

[3] S. Rahatlou. University lecture: Higgs production and search strategy. 2015-2016.

[4] L. Borgonovi et. al. Higgs measurements at FCC-hh. Technical report, CERN, 2018.

[5] J. Alwall et. al. The automated computation of tree-level and next-to-leading order diﬀerential cross sections, and their matching to parton shower simulations. JHEP, 07, 2014.

[6] DELPHES 3 collaboration. DELPHES 3, A modular framework for fast simulation of a generic collider experiment. JHEP, 02, 2014.

40 TP-4 Report Sensitivity Estimates in Direct Searches for New Physics

Eric Ballabenea, Massimiliano Gallia, Djamel Boumedieneb, Alberto Cervellic, Antonio Sidotic

aTandem-Project student, Universitàdi Bologna, Italia bTandem-Project supervisor, UniversitéClermont Auvergne, France cTandem-Project supervisor, Universitàdi Bologna, Italia

Abstract Standard Model (SM) has been proven a very solid theory for explaining elementary particle interactions; it cannot, however, explain many phenomena, such as dark matter presence and hierarchy problem and the smallness of neutrino masses: it is very interesting to look to new particles unpredicted by the model. The aim of this project is to build a realistic framework, using both real and simulated data, to optimize the selection for a search for non SM particles, to estimate backgrounds using a ﬁt between data and simulations, and then extract the sensitivity to the process of interest.

1. Introduction 1.1. Supersymmetry and case of interest In the SUSY scenario, for each SM particle there is a supersymmetric counterpart: e.g. the supersymmetric counterpart of the quark is called squark, for lepton is slepton, and we also have particles without SM counterpart, such as chargino and neutralino. Chargino is formed from the linear combination of the wino and higgsino, while neutralino from the combination of zino and higgsino. Chargino interacts exactly like a charged W, while neutralino as a Z or Higgs boson of SM. This leads to events very similar to the SM ones, which are produced in much larger numbers, so that we search for very rare events in a large amount of backgrounds, a search far away from easy. Four different categories can be distinguished for the pair production of the chargino and next-to-lightest neutralino (see Figure 1). This analysis focuses on the 1`b¯b, with a reconstructed lepton and a bottom quark-antiquark pair in the final state. It is characterized by the hadronic decay of the Higgs boson into a bottom quark antiquark pair and the leptonic decay of the W boson, accounting for the presence of one reconstructed lepton and a missing transverse energy in the final state. Other possibilities are not taken into consideration in this analysis. Appropriate selection criteria to our category region are performed in order to reject lepton-rich background processes while at the same time maximizing signal significance.

41 Figure 1: Diagrams illustrating the signal scenarios considered for the pair production of chargino and next-to-lightest neutralino [1].

1.2. Backgrounds There are three main backgrounds: the top quark-antiquark pair production (tt¯), the W+jets production and single top quark production (see Figure 2).

Figure 2: Diagrams illustrating the main backgrounds for the pair production of chargino and next-to-lightest neutralino.

In the (tt¯) production, each top quark decays into a W boson and a bottom quark, thus yielding two bottom quarks and two Ws in the final states. If the W is not well reconstructed and decays leptonically, the final state can be confused as the 1`b¯b channel. In the W+jets production, the quark-antiquark annihilation produces a W boson in association to b-jets coming from the leading interaction, showing the same final objects of signal category. Finally, the single top production whose decays has again the same final signature with a top quark in the final state with a bottom quark coming from the initial state.

2. Data Analysis

The analysis is performed through a software called HistFitter, which allows the user to perform complete analysis by using a simple configuration file written in Python. Three different regions are defined:

signal region: a region where a particular model that we want to study predicts a • signiﬁcant excess of events over the predicted background level;

control region: speciﬁcally designed to be basically free of signal contamination, here • we will perform some ﬁts in order to estimate the actual composition of the background;

validation region: it’s optional and placed between the other two regions; we use the • VR to control if the background composition that we obtained by ﬁtting the model to the data in the CR is the right one. At the very end of this process we come back to the SR and obtain the results of the analysis.

42 2.1. Analysis strategy The goal of the analysis is to reproduce ATLAS results for the 1`b¯b decay mode. The main steps (performed with HistFitter) are the following:

perform suitable cuts on multiple variables in SRs and CRs (same cuts applied by • ATLAS);

estimate the background contribution through MC simulation; • perform an exclusion fit in order to obtain an exclusion contour plot. • 2.2. Signal region In table 1 we summarize the cuts used on the variables in the SR, with the presence of one lepton whose pT > 27 GeV, 2 or 3 jets two of which are b-tagged. Cuts on the missing transverse energy and cotransverse mass are performed in order to suppress as much as possible the backgrounds. We define three different ranges corresponding to three different W values of mT , SR1Lbb-Low, SR1Lbb-Medium, SR1Lbb-High, and finally the range of the bottom quark antiquark mass be compatible with the one of the Higgs boson.

Variable SR1Lbb-Low SR1Lbb-Medium SR1Lbb-High Nleptons = 1 ` pT > 27 Njets (pT > 27 GeV) = 2 or 3 Nb jets = 2 miss− ET > 200 mCT [GeV] > 160 W mT [GeV] [100, 140] [140, 200] > 200 mbb [GeV] [105, 135]

Table 1: SR selection cuts.

2.3. Control region In table 2 we summarize the cuts used on the variables in the CRs. We point out for tt¯ CR the selection of mCT < 160 GeV since this variable is built in a way so if one b-jet and one lepton belong to a top decay it has an endpoint at the top mass. The mbb is selected to be orthogonal to the signal region. For W+jets CR, the mT has a value compatible with W mass so we select mT between 40 and 100 GeV. For single top we focus on high mbb masses where tt¯ +jets contribution is small, and this also for signal.

tt¯ CR mCT < 160 GeV miss mbb < 105 GeV or mbb > 135 GeV and ET > 200 GeV mT [100-140] GeV or mT [140-200] GeV or mT > 200 GeV miss W + jets CR mCT > 160 GeV, ET 40 GeV < mT < 100 GeV, mbb < 80 GeV Single top CR mCT > 160 GeV miss ET > 200 GeV mT > 100 GeV, mbb >195 GeV

Table 2: CR selection cuts.

43 3. Fit result

The result from the exclusion fit is displayed in Figure 3. The masses of the chargino and the next-to-lightest neutralino are represented as a function of the mass of the lightest neutralino. The black dotted line is the expected value of the background computed from the MC, with a 1 σ confidence level represented by the yellow band, while the red line is the same value taken from the data. The exclusion fit permits to exclude the existence of new physics whose presence lays under the black dotted line. At low mass values the observed data follows the expected one, while at higher mass it moves below it: this means that we observed more background values than what we expected, so the limit is worse. There is also an abnormal bump in comparison to the ATLAS result due to the fact that we had some missing points. In general we obtained a good agreement with the ATLAS result.

Figure 3: The expected and observed exclusion for the 1`b¯b channel. Experimental and theoretical systematic uncertainties are applied to background and signal samples and illustrated by the yellow band and the red dotted contour lines respectively. The red dotted lines indicate the 1σ variation on the observed exclusion ± limit due to theoretical uncertainties on the signal cross-section.

Acknowledgements

We express our gratitude to the Erasmus+ funding programme and to the Department of Physics and Astronomy of the University of Bologna for allowing us to be part of the Tandem-Project activities. We acknowledge our supervisors and colleagues for all the support throughout the work.

References

[1] ATLAS Collaboration. Search for chargino and neutralino production in ﬁnal states with a Higgs boson and missing transverse momentum at √s = 13 TeV with the ATLAS detector. Phys. Rev. D, 100, 2019.

44 TP-5 Report Sensitivity Estimates for Rare Decays

Sergio Jaimes1, Assane Sambéb, Andrea Villac, Angelo Carboned, Régis Lefèvree, Diego Milanesf

aTandem-Project student, Universidad Nacional de Colombia bTandem-Project student, Université Clermont Auvergne, France cTandem-Project student, Università di Bologna, Italia dTandem-Project supervisor, Università di Bologna, Italia eTandem-Project supervisor, Université Clermont Auvergne, France fTandem-Project supervisor, Universidad Nacional de Colombia

Abstract A study of the reconstruction efficiency for the decay B0 K 0(K π+)τ (3πν )τ +(3πν¯ ) → ∗ − − τ τ is made using two methods for the reconstruction of the undetected neutrinos. The first method exploits momentum conservation and the B meson flight direction, but possibly due to vertex reconstruction dependence fails to give a reconstruction of the B0 invariant mass. The second method relays on the kinematic relations and constraints for the decay chain and is able to obtain an efficiency of reconstruction of (9.1 0.2)%. A control sample had ± been studied to validate the techniques, which proved to be as accurate on an independent sample as they are on the signal one. Efficiencies and resolutions were found to be similar for the two samples.

1. Introduction In the Standard Model (SM) the electroweak gauge bosons couple to the different lepton flavours with the same strength. This interesting property is known as Lepton Flavour Universality (LFU). Recent measurements of the ratio of branching fractions for leptonic decays of a B meson + (B Hµ µ−) R = B → (1) H (B He+e ) B → − show deviations from the SM predicted value [1, 2, 3, 4]. Since flavour changing transitions can only be mediated by charged gauge bosons, processes involving Flavour Changing Neutral Currents (FCNC) are forbidden at tree-level in the SM and are dominated at one loop by the penguin and box diagrams. This makes them a good scenario for searching New Physics [5]. In particular, decays involving pairs of τ leptons are expected to show greater deviations from the SM.

45 0 0 + In this project we study the reconstruction efficiency for the process B K∗ τ τ −. 0 + →(+) Here the K∗ is reconstructed by its decay into a K π− pair, while the τ − lepton is reconstructed by the decay to 3 pions and a neutrino ντ (¯ντ ). The SM predicted branching ratio is of (B0 K τ +τ ) 10 7 [5]. Within the LHCb B → ∗ − ∼ − acceptance this would imply around 5 events for Run I and 30 for Run II. This would make the analysis of the decay channel out of reach but some NP models that explain the flavour anomalies might increase this branching ratio by several orders of magnitude. The presence of an undetected neutrino in the reconstruction channel for each tau lepton indicates the necessity for a good method for the reconstruction of the neutrino. Here two methods for the reconstruction of the invisible neutrinos are studied. The first addresses the problem by taking geometric relations between the momentum direction of each of the involved particles while the second method solves the energy-momentum equations of the system by decomposing the momentum of the τ lepton daughters into a parallel and a perpendicular components.

2. Topological reconstruction We plan to determine, analytically, the momenta of each neutrino: for this particular decay we have two invisible neutrinos, one for each τ lepton, that means we have six degrees of freedom. We can reconstruct the B0 end vertex, the ones of each τ and the primary vertex. This allows us to deﬁne each τ ﬂight direction and the one of B0. Finally, we obtain eight constraints including the tau masses for six unknowns. So the problem is fully constrained.

2.1. Method 1 This method exploited geometric arguments and momentum conservation to reconstruct the invisible neutrinos momenta from the visible decay products of the B meson. To start, we defined the six following quantities: x px + px xτ + xB0 pτ + vis,τ + ν A = − = z = z z , (2) z + z 0 p p + p τ − B τ + vis,τ + ν y py + py yτ + yB0 pτ + vis,τ + ν B = − = z = z z , (3) z + z 0 p p + p τ − B τ + vis,τ + ν then C and D defined accordingly for the τ −, and finally x x x x x x x x x 0 x p + p + + p pK + p + + pν + p + pν B PV K∗ τ τ − ∗ vis,τ vis,τ − E = − = z z z = z z z z z , (4) zB0 zPV pK + p + + p pK + p + + pν + p + pν − ∗ τ τ − ∗ vis,τ vis,τ − y y y y y y y y y 0 y p + p + + p pK + p + + pν + p + pν B PV K∗ τ τ − ∗ vis,τ vis,τ − F = − = z z z = z z z z z , (5) zB0 zPV pK + p + + p pK + p + + pν + p + pν − ∗ τ τ − ∗ vis,τ vis,τ − which represent the slopes of the lines connecting the known decay vertices in the transverse plane. Fig. 1 shows an interpretation of two of these variables. The six equations contain the components of the two neutrino momenta, so the system is fully constrained, therefore we can obtain an analytical solution. For example, by plugging the first four equations into the last two we obtain the system:

z z x z z z (E C)pν + (E A)pν = pK EpK + (A E)p + + (C E)p − − ∗ − ∗ − vis,τ − vis,τ − z z y z z z (6) ((F D)pν + (F B)pν = p F pK + (B F )p + + (D F )p − − K∗ − ∗ − vis,τ − vis,τ −

46 휏+ 휏+ 푥 푦 퐵0 훼 = tan−1(퐴) 퐵0 훽 = tan−1(퐵) 푧 푧

Figure 1: Visual representation of the variables A and B (ﬂight distances not to scale).

푝 0 neutrino momentum antineutrino퐵 momentum 훽 = tan−1(퐹) 2500 2500 푦 Entries 151513 Entries 151513 푝 2000 True P 2000 True P Reconstructed P 푧 Reconstructed P 1500 1500

1000 1000

500 500 0 5000 10000 15000 20000 0 5000 10000 15000 20000 P [MeV] P [MeV]

Figure 2: Distribution of the events for the simulated and reconstructed neutrinos momenta. which, once solved, yields the z-components of both momenta. The other components can then easily be calculated from A, B, C, and D. Once the solution was found, we put it to test with Monte Carlo data. In Fig. 2 is shown the comparison between the simulated ν and ν momenta and those calculated with the solution using only the visible particles’ momenta. The events distributions seem to be correctly reproduced. However, when the B0 mass shape is computed, the situation in Fig. 3 shows up: on the left, the B meson is reconstructed with the solution using the Monte Carlo truth data; on the right, instead, the same procedure is applied to data after a reconstruction phase was simulated, which produced data similar to those acquired by a real-life particle detector. On these data, the resolution and eﬃciency on the B mass reconstruction are very poor. This is probably caused by the strong dependence of the solution on the vertices position resolution. Any uncertainty on the vertex position thus vastly inﬂuences the reconstruction of the neutrinos.

2.2. Method 2 2.2.1. Analytical reconstruction of the B0 invariant mass In the following, the indexes 3π and τ will correspond respectively to quantities for the 3 pions system and the neutrino. The parallel and perpendicular components of the neutrino ~ momenta will be taken about the τ decay plane (uˆ , uˆ ) such that Pτ = Pτ uˆ and Pτ = 0. k 2 ⊥ k k ⊥ Using momentum conservation, the expression of mτ allows to establish a quadratic equation for the parallel component of the neutrino momenta:

2 2 2 2 2 δmm 2 2 2 (E3π P3π )Pν + (2P3π δmm)P3π Pν P3π + E3πP3π = 0, (7) − ⊥ − k k − 2 − ⊥ ⊥ k k

47 B0 mass, true branches B0 mass, reconstructed branches

3500 Entries 13925 25 Entries 13925 3000 Mean 5.29e+03 Mean 6.76e+03 20 2500 Std Dev 164 Std Dev 1.39e+03 Overflow 1.26e+03 Overflow 1.31e+04 2000 15 Events / 20 MeV Events / 75 MeV 1500 10 1000 5 500 0 0 4500 5000 5500 6000 6500 4000 6000 8000 10000 m(K*τ+τ-) [MeV] m(K*τ+τ-) [MeV]

Figure 3: Plots of the B0 mass shape for true (left) and reconstructed (right) data.

Figure 4: Invariant mass distributions for all combinations (left) and for the good combination (right). with δ = m2 m2 . If the discriminant ∆ = δ2 4m2P 2 is positive, we obtain the mm τ − 3π mm − τ 3π following solutions: ⊥

Pν = P3π ⊥ − ⊥ 2 2 2 2  (δmm 2P3π )P3π Eπ δmm 4mτ P3π (8) P = − ⊥ k ± − ⊥  ν 2 q2 k 2(m3π + P3π ) ⊥  We apply the same for the anti-neutrino and get also two solutions. Finally, we have four possible combinations for the reconstruction of the B0 invariant mass.

2.2.2. Topological reconstruction of the B0 invariant mass After stripping, we will limit ourselves to candidates for which the reconstructed particles are matched to their Monte Carlo truth counterparts. Using the true B0 vertices, the taus 0 decay vertices and the true momenta of the tracks from τ and K∗ decays, we ﬁrst reconstruct the B0 invariant mass for the four combinations then, for each event, we identify the right (good) combination as the one that corresponds to the minimum angle between the B0 reconstructed momentum and the B0 direction estimated from its true vertices. Now, we move on from the true vertices and momenta to the reconstructed vertices and momenta including the experimental resolution. For 9% of the events we have two positive discriminants, so we are able to reconstruct the B0 candidates. For each event, the combination among the four that had been chosen from the MC truth is also considered as the good combination. The results are shown in Fig. 4. The method is promising because we obtain a peak around of the right B0 invariant mass with a width of 250 MeV/c2 for the good combination when we exclude the tail.

48 Table 1: Table of topological reconstruction eﬃciencies

Fraction of events with ∆ > 0 B0 K 0τ +τ 9.1 0.2 → ∗ − ± B0 D D+ [15.0 ; 21.9] → − s One track from D− 65.1 0.5 + ± One track from Ds [24.0 ; 33.2]

Figure 5: Invariant mass distributions of the good combinations for the best case (left) and the worst case (right).

2.2.3. Control sample We used the decay B0 D (K+π π )D+(K K+π+) as control sample for which a → − − − s − fully reconstruction can be obtained with large statistics. From this decay we can reconstruct the tertiary vertices with three tracks as for the signal. The reconstruction of the secondary + vertex is different because it is done from D− and Ds decays while for the signal it is 0 obtained from the K∗ decay. Again with matched candidates, we are substituting one track from D− and one track + from Ds by their analytically estimated momenta. To do this, we adapt the eqs. 7,8 to take into account the masses of the particles. We have nine possibilities of substitution and we get efficiencies that are comparable to the one obtained for the signal in Tab. 1. The efficiency depends on the lifetime of the concerned particle. It is easier to apply the method to a D− + than to a Ds or a τ. To separate the signal from the background on the data, we used the TMVA [6] toolkit. The input variables for the analysis are: transverse momenta, impact parameters, flight distances and quality of the end vertices. For the signal and the combinatorial background, we are using respectively matched MC candidates and reconstructed candidates with a reconstructed mass up to 5500 MeV. Four classifiers have been tested: Maximum Likelihood, Fischer, MLP and BDT. We obtained the best performances with the BDTG classifier which will be retained for the future. In the following a cut at BDTG > 0.5 will be used: it allows to eliminate most of the background by keeping 90% of the signal. To further purify the control 1845 < m < 1890 MeV 1950 < m + < 1995 MeV sample, we apply the cuts : D− and Ds . Fig. 6a shows the invariant mass distributions of B0 at the different selection levels. To evaluate the purity of our selection, we adjust the invariant mass distribution of B0 using the RooFit toolkit. We used three probability density functions (PDF): a gaussian of expectation µB0 0 σ 0 B µ 0 and standard deviation B for , a gaussian of expectation Bs and standard deviation 0 σ 0 = σ 0 B Bs B for s and a decreasing exponential for background noise. In Fig. 6b is shown

49 (a) Eﬀect of successive cuts on the B0 in- (b) B0 invariant mass distribution variant mass: stripping (black), BDT (blue), masses of D mesons (red).

Figure 6: Results of selection and purity.

the fit to the data. The total PDF is in good agreement with the data. The value of µB0 is very close to the mass of B0 with a resolution of about 15 MeV. We defined a signal region between 5220 and 5340 MeV, in which the purity of the control sample is 93%. The topological reconstruction method is applied, here, to the selected candidates of the control sample. As previously, the nine substitution possibilities are tested. The results obtained are compared to those of Monte Carlo by applying the same selection as on the data to the Monte Carlo sample of the control mode, while the matching criterion is no longer used. Unlike what was done previously, this choice of a solution among the four is independent of the Monte Carlo truth: it is applicable in the data as well as on the Monte Carlo. In Fig. 5 are shown the invariant mass distributions for the selected combination (only one entry per candidate) obtained on the data for the worst-case good solution and for the best-case one in terms of reconstruction efficiencies. Those are very similar to the ones obtained on the MC in terms both of reconstruction efficiency and reconstructed B mass spectra. It shows that what is obtained for the signal on the MC is trustable.

3. Conclusions

The study of the reconstruction of the neutrinos in this channel is key for the analysis of LFU in search for New Physics. In this sense two different methods were studied. The first one, which takes into account the topological features of the decay chain, seems to do good on the neutrino momentum reconstruction, but once this momentum is used to reconstruct the full B0 invariant mass the method fails, probably due to a too strong dependence of the method on the resolution of the vertices. The second method studied relies on the decomposition of the momenta of the τ lepton and its daughters into a perpendicular and a parallel components to the τ flight direction. This method produces two solutions for each τ which means that we get four different solutions for the B0 invariant mass by combining the reconstruction of the two τ’s. The combination chosen to best reconstruct the B0 is the one that has a smaller angle between the reconstructed momentum and its flight direction estimated from its MC truth. The overall efficiency of this second method is found to be 9.1 0.2% with a resolution of about ± 250 MeV.

50 A study of the control sample B0 D D+ was carried out to independently test the → − s method on a larger data sample, and resulted in reconstruction eﬃciencies from 15% to 22% and a resolution of 15 MeV after background suppression.

References

[1] E. Graverini et. al. Flavour anomalies: a review. Journal of Physics: Conference Series, 1137, 2019.

[2] LHCb Collaboration. Test of lepton universality using B+ K+`+` decays. Phys. → − Rev. Lett., 113, 2014.

[3] BELLE Collaboration. Measurement of the diﬀerential branching fraction and forward- backward asymmetry for b K( )l+l . Phys. Rev. Lett., 103, 2009. → ∗ − [4] BABAR Collaboration. Measurement of branching fractions and rate asymmetries in the rare decays b K( )`+` . Phys. Rev. D, 86, 2012. → ∗ − [5] B. Capdevila et. al. Searching for new physics with b sτ +τ processes. Phys. Rev. → − Lett., 120, 2018.

[6] P. Speckmayer et. al. The toolkit for multivariate data analysis, TMVA 4. Journal of Physics: Conference Series, 219, 2010.

51 TP-6 Report Interpretation of Top-quark Measurements at the LHC and Beyond in the SMEFT Framework

Federico Battistia, Anja Beckb, Mouad Hilalic, Kevin Kr¨oningerd, Stephane Monteile, Matteo Negrinif

aTandem-Project student, Universitàdi Bologna, Italia bTandem-Project student, Technische UniversitätDortmund, Germany cTandem-Project student, UniversitéClermont Auvergne, France dTandem-Project supervisor, Technische UniversitätDortmund, Germany eTandem-Project supervisor, UniversitéClermont Auvergne, France fTandem-Project supervisor, Universitàdi Bologna, Italia

Abstract Effective field theories offer a way to introduce new model independent six-dimensional operators in the Standard Model Lagrangian. In this paper we try to set boundaries on the values of the operator coefficients relevant in top quark production processes. We start by performing a χ2 test on top-antitop production cross-section in proton-antiproton collisions at Tevatron, and proton-proton collisions from LHC Runs I and II. We compare the cross-section values obtained by simulating the processes at the variation of the individual coefficients with the NNLO expectations and set boundaries at 95% confidence levels. We then combine the results from Tevatron and LHC and repeat the process by varying two coefficients at the same time. Finally we study single-top production processes and indi- viduate the common operators to attempt a global fit. All results obtained were in good agreement with the Standard Model.

1. Theoretical Introduction

The Standard Model (SM) is a successful theory of particle interactions that very well describes elementary particles and interactions, namely the electroweak and strong interactions. It yields a vast landscape of predictions which have not been certiﬁed by experiments so far. [1, 2, 3] However, and even with all its success, the SM still cannot explain some phenomena such as the mass of the neutrinos and the matter-antimatter asymmetry in our universe. Our ignorance can however be parameterized by additional terms of above four dimensions in addition to the SM Lagrangian in what is called the Standard Model Eﬀective Field Theory (SMEFT), which is a model independent way to look at BSM physics. In it the

52 new physics are modelled by a series of effective operators that can be of dimensions above the conventional four dimensions of the SM, these operators have an advantage over other approaches for the reasons that they preserve the SM SU(3) SU(2) U(1) gauge C × L × Y symmetry [4, 5]. On the other hand, it is known that the top quark can have a crucial role in the un- covering of physics beyond the SM. This is thanks to its unique (1) Yukawa coupling, O which makes it the heaviest particle of the SM. Conversely, its large mass might favour the coupling with BSM heavier degrees of freedom. Taking this into account, we will during this work, calculate limits on top interactions by performing a global fit of each of the dimension six operators that are relevant to the Top-Antitop and single Top production. The study in this report makes use of the LHC and Tevatron top production cross- sections. The measurements are compared to productions built from the Monte Carlo event generators tuning, namely MadGraph5 aMC@NLO. The value of a cross-section will change when new physics is taken into account, because it is dependent on the interactions of a given process, therefore, by computing the cross-section in the SM and in a model that includes SMEFT, we can constrain the coefficients attached to those higher dimension operators of the SMEFT and put limits on them if we compare the computations we perform with the experimental measurements of the cross-section. In SM EFT, the Lagrangian is expressed as follows: 1 1 = + + + ... , (1) Leff LSM ΛL1 Λ2 L2 where represents the Standard Model Lagrangian, Λ the energy up to which the SM L(SM) is no longer valid, and are higher than 4 dimension terms. L1(2) Up to dimension six the Lagrangian can be expressed in the following way [4]:

1 1 1 = + C(5)O(5) + C(6)O(6) + , (2) L LSM Λ k k Λ2 k k O Λ3 Xk Xk (n) (n) with Ok denoting dimension n operators, and Ck dimensionless Coupling constants (named Wilson coefficients). In general, a complete analysis of the SMEFT is an impossibly hard task, because at dimension six we’d have 2499 independent parameters [6], but, if one assumes baryon number conservation and minimal flavour violation, meaning, only the regular Yukawa couplings dictate the flavour violation dynamics and only the CKM phase generates the CP violation, only 59 Operators remain [4].

2. EFT for the top quark

In what follows, we will only focus on the operators that are relevant to the top physics, especially top pair-production and single top- production. We adopt the notation where qL and QL represent the first two and the third generations of left-handed isospin doublets respectively, uR and tR are the first two and third generations up-type right-handed singlets and dR and bR denote the first two and third generation down-type right-handed singlets. With these notations at hand, the relevant four-fermion operators can be expressed in the following way, stating explicitly each useful Wilson coefficient:

53 (1,1) ¯ µ (8,1) ¯ a µ a OQq = (QLγµQL)(q ¯Lγ qL) OQq = (QLγµT QL)(q ¯Lγ T qL) (1,3) ¯ i µ i (8,3) ¯ a i µ a i OQq = (QLγµτ QL)(q ¯Lγ τ qL) OQq = (QLγµT τ QL)(q ¯Lγ T τ qL) (8) ¯ a ¯ µ a (8) ¯ a µ a Otd = (tRγµT tR)(dRγ T dR) Otu = (tRγµT tR)(u ¯Rγ T uR) (8) ¯ a µ a (8) ¯ a ¯ µ a Otq = (tRγµT tR)(q ¯Lγ T qL) OQd = (QLγµT QL)(dRγ T dR) (8) ¯ a µ a (1) ¯ ¯ µ OQu = (QLγµT QL)(u ¯Rγ T uR) Otd = (tRγµtR)(dRγ dR) (1) ¯ µ (1) ¯ µ Otu = (tRγµtR)(u ¯Rγ uR) Otq = (tRγµtR)(q ¯Lγ qL) (1) ¯ ¯ µ (1) ¯ µ OQd = (QLγµQL)(dRγ dR) OQu = (QLγµQL)(u ¯Rγ uR) ¯ µν a ˜ a ¯ µν I ˜ I OtG = (QLσ T tR)φGµν OtW = (QLσ tR)τ φWµν ¯ µν I ˜ I ObW = (QLσ bR)τ φWµν

Table 1: Usefull Wilson coeﬃcients

2.1. Analysis Taking as an example the top pair production at LHC, the simulation of the top production process starts first by a pp collision at center of mass energy of 13 TeV. The relevant amplitudes of the top-pair production are then calculated, varying the values of each one of the Wilson coefficients, each one at a time while all other coefficients are set to zero. The variation of the total cross-section of the process is hence calculated for each one of the specific Wilson coefficient to obtain σMG. It was found that the FeynRules model chosen to perform the dimension six operators analysis, does not support NLO computations and only gives LO result values for the cross- sections. A normalisation of the results was required to bring the values computed by the simulation to a corresponding NLO or NNLO value from the literature. Hence, σNorm was defined and the following operation was applied on the values of the cross-section generated by MadGraph, σNNLO σNorm = σMG , (3) σSM MG +19.77 where σNorm is the value of the cross-section after the normalisation, σNNLO = 831.76 29.20 − (Scale) 35.06 (PDF and αs) pb is the NNLO value of the cross-section from the literature ± SM [7], and σMG represents the value computed by MadGraph when all coefficients are set to zero,i.e. the LO SM expectation. Note that the LHC cross section is not the only relevant observable that can be taken into account: another observable that we explored was the top pair production at Tevatron, applied, this time, with a pp¯ collision at center of mass energy of 1.96 TeV, and compared the cross-section values variation to the one measured at Tevatron. After the evaluation of the cross sections at the variation of the relevant coefficients, a chi- square test can be used to obtain limits on their values, either by considering one observable at a time or by combining them into a single test: n σ σ 2 χ2 = Norm − NNLO . (4) standard deviation 1 X From the χ2 we choose a value of the significance level α of .05 and .01 (corresponding to 95% and 99% C.L. respectively). A more ambitious approach to further constrain the coefficient limits consists of changing the values of two operators at the same time, then minimize χ2 and create a contour plot .

54 3. Results 3.1. tt¯ processes 3.1.1. Constraints for one operator As mentioned in the previous section, we started by a simple fixed constraint (one operator at a time) on the relevant operators at the LHC energy (8 and 13 TeV) and the Tevatron energy (1.96 TeV). The second step of our analysis consisted in understanding how the combination of the measurements can enhance the constraints. A χ2 statistic estimator has been defined to handle the set of measurements (constraints). The Figure 1 superim- poses the individual constraints at 95% C.L.. obtained on the Wilson coefficients and the constraint issued from the combination. It is observed that the bounds are significantly stronger in the latter.

Figure 1: The combination of both Tevatron and LHC’s 95% C.L. constraints in a χ2 test. The red lines represents limits set by Tevatron process, The blue lines are the limits deﬁned by the LHC process, and the green lines are the combinations of the two.

3.1.2. Two Wilson coefficients varied simultaneously The final aim of this analysis is to provide a framework to make a global simultaneous fit of all constraints in terms of all relevant SMEFT degrees of freedom. To gradually reach the target, we are considering in this Section two Wilson coefficients and vary their values at the same time. then look at the effect this can have on the setting of constraints on the values of the coefficients. This analysis can be simplified by observing that the four fermion operators can be divided into three groups according to the flavor of the light quarks. So, we couple the Coefficients that belong to the same group together one pair at a time, therefore we will get: six possible combinations in the first and second category, and 15 possible combinations of coefficients in the third one:

(1) (1) (8) (8) ur : Otu ,OQu,Otu ,OQu , (5) (1) (1) (1) (1) dr : Otd ,OQd,Otd ,OQd , (6) (1) (8) (1,1) (8,1) (1,3) (8,3) qL : Otq ,Otq ,OQq ,OQq ,OQq ,OQq . (7) We take this approach, ﬁrst by applying a constraint only with the LHC at 13 TeV measurment which gives us the plots on the top side of Figure 2, then we plotted the

55 dim6top_LO_UFO, pp -> tt~, CONTOUR-PLOT, cQq11-ctq1 dim6top_LO_UFO, pp -> tt~, CONTOUR-PLOT, ctd8-cQd1 dim6top_LO_UFO, pp -> tt~, CONTOUR-PLOT, ctu1-cQu1 6.64 6.64 6 6.64 10 6

5 4 4 0 2 2 5

0 3.84 3.84 0 3.84

ctq1 10 cQd1 cQu1

2 15 2

20 4 4 25 6 0.00 30 0.00 6 0.00 6 4 2 0 2 4 6 30 25 20 15 10 5 0 5 10 6 4 2 0 2 4 6 cQq11 ctd8 ctu1 (a) (b) (c)

dim6top_LO_UFO, pp -> tt~, CONTOUR-PLOT, cQq11-ctq1 dim6top_LO_UFO, pp -> tt~, CONTOUR-PLOT, ctd8-cQd1 dim6top_LO_UFO, pp -> tt~, CONTOUR-PLOT, ctu1-cQu1 6.64 6.64 6 6.64 10 6

5 4 4 0 2 2 5

0 3.84 3.84 0 3.84

ctq1 10 cQd1 cQu1

2 15 2

20 4 4 25 6 0.00 30 0.00 6 0.00 6 4 2 0 2 4 6 30 25 20 15 10 5 0 5 10 6 4 2 0 2 4 6 cQq11 ctd8 ctu1 (d) (e) (f)

Figure 2: Constrains on dimension 6 operators coefficients at 95% and 99 % C.L., (a-c) represent the LHC and Tevatron’s constraints combined, (d-f) are the coefficient limits at the LHC energy alone. constraints on the Wilson coefficient using both LHC at 13 TeV and Tevatron measurments, as portrayed in the bottom of Figure 2. We were successfully able to further limit the possible values of the coefficients on the way to a global fit.

3.2. Single top Processes As mentioned earlier, single top are produced through three kinds of processes: the t-channel, s-channel and Wt-related channels. In the scope of this report we will cover the t-channel and the s-channel, starting with the t-channel ﬁrst.

(a) (b)

Figure 3: The combination of both Tevatron and LHC’s 95% C.L. constraints in a χ2 test for t-channel(a) and s-channel(b). The red lines represents the constraints set by the measurements made at Tevatron. The blue lines are the limits set by the LHC (8Tev for s-channel processes and 13 Tev for t-channel), and the green lines are the combinations of both;

56 3.2.1. t-Channel The largest single-top production cross-section at the Tevatron and LHC colliders is the cross-section of t-channel production. It represents one third of the top-quark pair- production cross-section. It has been measured at the LHC. The cross-section measured by CMS at 13 TeV is 238 32 pb [8]. It has also been measured at Tevatron, for which ± a cross-section of 2.10 0.13 pb [8] is reported. The high production rate of single-top in ± these two different environment makes it a valuable use case to constrain the dimension 6 operators’ coefficients. An attempt to combine single-top production and top pair production information in a single χ2 test is reported on the Figure 3a. A significantly improved constraint is obtained.

3.2.2. s-Channel The s-Channel processes on the other hand are initiated byqq ¯ annihilation and the cross-section is therefore larger in pp¯ collisions than in pp collisions (at the same centre-of- mass energy). Quantitatively, the cross-section at Tevatron amounts to about one-half that of t-channel production with a value of 1.29 0.26 pb [8]. ± This process is by contrast a bit challenging for the LHC, due to the high backgrounds in the signal region coming from tt¯ events, making it very hard to observe at 13 TeV. Thankfully, the level of background is more easily tractable at lower energy and ATLAS and CMS were able to set upper limits on the production cross-section of the s-channel. ATLAS experiment enhanced the sensitivity with 8 TeV data set to measure the cross- section for s-channel process production [9] and obtained a value of 4.8 1.8 pb. Therefore, ± we shall use the lattermost information in our study of the Wilson coefficients. The computation of the single-top production cross-sections were performed to obtain the Figure 3b. Again, only the LO calculations were available in the model we used and a rescaling of the predictions was in order; the predicted SM values have been rescaled to the NLO predictions at the LHC 5.6 0.2 pb [8] and 1.05 0.06 pb [8] at the Tevatron. ± ± 3.3. Single Top and tt¯ Combined (1,3) (8,3) The only common relevant operators between these two processes are OQq and OQq . We hence kept varying the values of the coefficients of these two operators to predict the variation of the different cross-sections. The final objective is to perform the χ2 test taking into account the whole set of measurements. These result is displayed in Fig.4.

dim6top_LO_UFO, CONTOUR-PLOT, cQq83-cQq13 6.64

0.4

0.2

0.0 cQq13

0.2

0.4

0.00 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 cQq83

Figure 4: The combination of all the seven observables we have into one global ﬁt at 99% C.L.

57 4. Conclusion

We have performed in this project a global fit of a selection of Wilson coefficients attached to dimension-six operators relevant to tt¯ production and single-top production Physics at LHC and Tevatron. The analysis took into account the cross-section measurements from LHC at centre-of-mass energies of 13 TeV and 8 TeV and the equivalent measurements from Tevatron. The number of relevant operators to the processes considered in this work amounts to 17; the associated Wilson coefficients have been constrained by performing a χ2 fit to establish limits at 95% C.L.. We generalised the approach to the simultaneous variation of two operators and taking into account simultaneously several measurements. The strongest constraints in our study were obtained on the common operators between single top production and tt¯ production (1,3) (8,3) (OQq and OQq ) for which the available experimental information is the largest.

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[2] A. Salam. Weak and Electromagnetic Interactions. Conf. Proc., C680519, 1968.

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[4] B. Grzadkowski et. al. Dimension-six terms in the Standard Model Lagrangian. JHEP, 10, 2010.

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[8] A. Giammanco and R. Schwienhorst. Single top-quark production at the Tevatron and the LHC. Rev. Mod. Phys., 90, 2018.

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58 TP-7 Report Evaluation of the Sensitivity for Future Detectors

Leonardo Lunertia, Francesco Poppia, Johannes Albrechtb, Angelo Carbonec, Roberto Preghenellac

aTandem-Project student, Universitàdi Bologna, Italia bTandem-project supervisor, Technische UniversitätDortmund, Germany cTandem-Project supervisor, Universitàdi Bologna, Italia

Abstract In this report the ﬁnal results of the Tandem Project 7 (TP-7) are presented. The focus of the project is the study of a tracking detector and an electromagnetic calorimeter for an ideal high energy physics experiment. The particle identiﬁcation and track reconstruction performances of the tracking detector has been studied. The reconstruction of the B0 φγ → decay has been used to study the resolution of the electromagnetic calorimeter. Primary events has been simulated with PYTHIA, while DELPHES has been used to simulate the response of the detector.

1. Introduction

The project aims at studying new detectors for physics at future colliders and/or upgrades of the Large Hadron Collider (LHC). The studies has been performed in a fast- simulation framework using the latest software technologies available for High Energy Physics (HEP). This project has been carried out using PYTHIA [1, 2] as Monte Carlo (MC) event-generator coupled with the DELPHES [3] parametric detector simulator. PYTHIA allows the user to setup the physics details of the primary interaction with very high flexibility and to select specific physics processes in the interest of the study. At the same level, DELPHES allows the user to define the characteristics of the simulation of the detector by setting its geometry and response to particles and radiation. As a matter of fact, the two components are independent to each other, thus allowing a very high level of flexibility in the achievable output. The common communication interface between PYTHIA and DELPHES will be provided by the HepMC data format, which is becoming a standard in HEP. The project comprises the study of an electromagnetic calorimeter (Sec. 2) and a tracking detector (Sec. 3). The study of the tracking detector is focused on the spatial and timing resolution in order to have a detector that is able to identify particles by measuring both the momentum from the reconstructed track and the Time Of Flight (TOF). On the other

59 hand, the study of the electromagnetic calorimeter is focused on the energy resolution. The electromagnetic calorimeter and the tracking detector has been developed in perspective of both a 4π and a forward spectrometer. These two detectors are considered as independent.

2. The electromagnetic calorimeter

2.1. The calorimeter The electromagnetic calorimeter simulated and studied during this project is based on a forward spectrometer geometry detector, the baseline of the simulation was the current LHCb electromagnetic calorimeter (ECal), based on a shashlik-type technology. The current ECal consists of three regions of different granularity, the granularity increases as the region is closer to the center of the detector, therefore the inner region is characterized by an higher- density of cells, achieved with smaller cells. In order to simulate an improvement of the detector, we decided to focus on two distinct aspects: the cell size and the ECal energy resolution. The study was performed by tuning the LHCb ECal parameters in the corresponding DELPHES configuration card. In order to increase the granularity, we simulated cells of half the size for each of the three different regions. As far as the improvements on the calorimeter energy resolution, we decided to test the proposed energy resolution for the upcoming LHCb ECal upgrade. The current energy resolution

2.2. Evaluation of sensitivity Using the software PYTHIA, we generated LHC-like interactions by simulating 150000 p-p collisions with √s = 13.6T eV in the center of mass. We decided to evaluate the reconstruction of B0 particles, hence we allowed the simulations of hard QCD b ¯b interactions s − only. We forced the following decay channels: B0 φγ and φ K+K . The sensitiv- s → → − ity was evaluated as the resolution of the invariant mass reconstruction of the simulated particles in diﬀerent ECal conﬁgurations. The data analysis was performed using RooFit, in particular using the RooVoigtian model, based on a ”voigtian” function. The invariant mass resolution is a good indicator of the sensitivity improvements achieved with the ECal upgrades.

2.3. Reconstruction and results 0 The reconstruction of the Bs particles exploited the forced decay channels in φ and, consequently, in the KK pairs. The reconstruction was first tested on the MC truth and then applied to the simulated data-set. In Figure 1 the invariant masses fits are presented. The invariant mass resolution evaluated in the different ECal configurations is summarized in the following table:

Simulated ECal Sigma[MeV ] Current ECal 64.0 6.5 ± Doubled granularity 59.4 4.3 ± Improved resolution 55.7 5.3 ± Doubled granularity and better resolution 46.7 3.4 ± 0 Table 1: Sensitivity of the simulated ECal conﬁguration to the reconstruction of the Bs invariant mass.

60 0 Figure 1: RooVoigtian ﬁt of the reconstructed Bs particles in the current ECal (top-left), a doubled granularity ECal (top-right), the current ECal with the future resolution (bottom-left) and a combination of both the upgrades (bottom-right).

3. The tracking detector

The tracking detector is made of seven cylindrical tracking layers nested around the beam axis cover the barrel region, while the endcap region is empty. Each layer measures the position of the hitting particle. Two of the seven tracking layer measure also the crossing time. Each one of the layers is centered around the beam axis, that we take parallel to the z axis, and has a length of 2 m along z. Going from the most internal layer to the most external one, the radius takes the value: 5 cm, 10 cm, 20 cm, 40 cm, 60 cm, 80 cm and 100 cm. The layers also used as timing detectors are the third and the last one of the former list. A constant and uniform magnetic of 2 T is also applied and its direction is parallel to the beam axis. The main event is generated using the PYTHIA. 10 000 proton-proton collision with a center of mass energy of 14 TeV has been generated and only soft QCD processes where enabled. The particles present in the final state were protons (p), kaons (K) and pions (π). The TOF measurement combined with the momentum reconstruction has been eventually used to perform the identification task. The TOF was measured assuming the collision time known with infinite precision. Two different layers for the TOF measurement has been used in order to increase the separation for lower momentum particles, ı.e. the ones that, due to their small Larmor radius, cannot reach the outer one. The distribution of the measured velocity vs. the true (reconstructed) momentum is shown in Fig. 2a (3a), for the inner TOF layer, and in Fig. 2b (3b)for the outer one. The reconstruction of the particle momentum has been performed by first measuring the transverse momentum. Once the curvature radius is known, the transverse momentum can

61 (a) (b)

Figure 2: Two-dimensional distribution of ﬁnal particles as a function of their momentum and velocity measured using the innermost TOF layer (left) and the outermost one (right). The three most populated bands corresponds to p, K and π in the ﬁnal state.

(a) (b)

Figure 3: Two-dimensional distribution of ﬁnal particles as a function of their reconstructed momentum and velocity measured using the innermost TOF layer (left) and the outermost one (right). be inferred. A particle in a magnetic ﬁeld B [Tesla] with a curvature radius R [meters] has a transverse momentum pT [GeV]:

pT = 0.3BR. (1)

Once the transverse momentum is known, the momentum of the particle can be obtained by the vectorial sum of the transverse and the longitudinal components. The former component can be obtained by the following formula: bp p = t , (2) z ωR where b is the particle velocity along z, ω is the angular velocity and R is the curvature radius.

4. Conclusions

4.1. ECal Diﬀerent conﬁgurations of the current LHCb ECal were simulated. We evaluated the detector sensitivity as the invariant mass resolution of a certain decay channel (B0 s →

62 φγ), the results are presented in Table 1. A combination of an increased granularity and improved energy resolution (as expected from the future upgrades) will lead to a signiﬁcative improvement in invariant mass resolution, more precise analysis can be made by simulating the pile-up eﬀects.

4.2. Tracker The use of PYTHIA and DELPHES tools ended up being an excellent combination for the study of a tracking detector for HEP experiments. The simulated detector has shown good separation for the separation of the particles under study using the TOF technique. The fitting procedure for the reconstruction of particle momentum needs a significant improvement in order to be used in combination with a TOF detector for particle identification.

Acknowledgements

We express our gratitude to the Erasmus+ funding program and to the Department of Physics and Astronomy of the University of Bologna for allowing us to be part of the Tandem-Project activities.

References

[1] T. Sjostrand, S. Mrenna, and P. Skands. PYTHIA 6.4 Physics and Manual. JHEP, 05, 2006.

[2] T. Sjostrand, S. Mrenna, and P. Skands. A Brief Introduction to PYTHIA 8.1. Comput. Phys. Commun., 178, 2008.

[3] The DELPHES 3 collaboration. DELPHES 3: a modular framework for fast simulation of a generic collider experiment. JHEP, 2014, 2014.

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