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The production of a Higgs boson at the LHC proceeds through many different subprocesses. While gluon fusion is the dominant one, at least for Higgs bosons with SMlike couplings, other processes, though with a smaller crosssection, can be interesting because of the different final states and/or because they probe physics differently from gluon fusion. Among the other processes, in this project we want to improve our understanding of the so called Higgsstrahlung process. In detail, we want to consider a minimal extension of the SM where, instead of one Higgs doublet, two Higgs doublets are present in the Lagrangian and understand how the difference in Yukawa couplings and the presence of more than one Higgs alter the phenomenology of this process.
In the following sections we describe a possible project plan. It should be understood as dynamic and it can be modified as new interesting ideas and possibilities arise.
Note that you can edit the wiki to change the color and text of status message from red/"To be completed" to other statuses as you go through the tasks of the section.
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SM Higgs boson phenomenology
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A proper understanding of the theoretical predictions of the SM for the Higgs sector is necessary to study possible deviations. As a first step, you should familiarize with the SM Higgs sector.The lecture program includes a discussion of the SM, however it seems from the calendar that this might be too late for our purposes. You are therefore encouraged to go through the relevant references in the the Useful resources page. It is important to understand both production and decay processes that characterize the SM Higgs boson at the LHC.
As optional tasks, to test your understanding of the subject, you might want to derive by yourself the relation between the bottom Yukawa couplings, the bottom mass and the Higgs Vacuum Expectation Value (vev); write down the amplitude for the
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2HDM Higgs boson phenomenology
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Our Beyond Standard Model (BSM) model will be the Two Higgs Doublet Models (2HDM). It is necessary to acquire a basic knowledge of the 2HDM to perform the phenomenological analysis. Some lectures of the summer student program will be devoted to the 2HDM, however they might be too late in the calendar to be useful for our purposes. It will be therefore necessary to acquire some of this knowledge directly from the literature. In the Useful resources you can find a list of references for this task. It is important that you acquire an understanding on how the 2HDM Higgs sector phenomenology differs from the SM, besides from the presence of new states.
As an optional task, following from the one of the previous step, you can check how the MSSM bottom Yukawa is different from the SM (and how it depends on the 2HDM parameter
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process Status colour Red title To be completed
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In models in which the coupling of Higgs bosons to bottomquarks is enhanced, as it can happen in the 2HDM, the Higgsstrahlung process
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Indeed, apart from the DrellYan like contribution
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This process was only rudimentary discussed in the literature. As a reference, see the paper " Higgs Strahlung at the Large Hadron Collider in the 2HiggsDoublet Model" by Harlander et al. (arXiv link).
Therein the process was only taken into account at LO QCD. As shown in the paper, It is of particular relevance if an internal scalar/pseudoscalar can be resonant, i.e.
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Crosssection computation for
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Get familiar with Higgs production through bottomquark annihilation
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Download the code SusHi from its own page, http://sushi.hepforge.org, and familiarize with it.
As an exercise, try running the code for a centerofmass energy of 13TeV produce cross sections as a function of the pseudoscalar mass.
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An 2HDM calculator: 2HDMC
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Install 2HDMC from its own page, http://2hdmc.hepforge.org and familiarize with it.
Then calculate the partial width
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2HDMC calculates the total width of the pseudoscalar as well as the branching ratio
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SusHi can also be linked to 2HDMC in order to obtain cross sections for A directly.
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Combine production and decay using a BreitWignerimproved narrowwidth approximation
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Combine the results by using a BreitWigner improved narrow width approximation (see e.g. arXiv:1502.07970):
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\frac{d\sigma(b\bar b\to ZH_{125})}{d\sqrt{s}} = \sigma(b\bar b\to A)(m_A)\frac{2\sqrt{s}}{(sm_A^2)^2+m_A^2\Gamma_A^2}\frac{m_A\Gamma(A\to ZH_{125})(m_A)}{\pi} 
We can compare this approach also to an even more generalised version (which should give similar results):
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\frac{d\sigma(b\bar b\to ZH_{125})}{d\sqrt{s}} = \sigma(b\bar b\to A)(s)\frac{2\sqrt{s}}{(sm_A^2)^2+m_A^2\Gamma_A^2}\frac{\sqrt{s}\Gamma(A\to ZH_{125})(s)}{\pi} 
Therein
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Computation of the
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Get familiar with FeynArts and FormCalc and try to calculate
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One can think about a combination of this calculation, that neglects the interference with the tchannel
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In order to obtain the hadronic cross section one needs to convolve with the parton distribution function by
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\sigma(pp\to HZ)=2\int_0^1dx_1 \int_0^1dx_2 f_b(x_1)f_{\bar{b}}(x_2)\sigma(b\bar{b}\to HZ) 
Therein
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The parton distribution function are evaluated at the scale
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Here the link to the kinematics writeup of PDG:
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Computing LaTeX Math Inline body b\bar b\to ZH_{125}
@ NLOQCD using MadGraph_aMC@NLO
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The public tool MadGraph_aMC@NLO (home page) allows to compute automatically the matrix elements for a given process at NLOQCD accuracy, once a model file for a specific model is available. Moreover, it automatically builds what it is a called a "matched" NLO+Parton Shower Monte Carlo event generator. These kind of event generators are among the prime tools used to simulate accurately particle production processes at colliders such as the LHC.
At first, you should install the package and familiarize with it by computing and generating events for at LO and NLOQCD for simple SM processes such as Z boson production.
Then, to compute the process
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Once all the model files are in place, you can proceed to the process generation, the computation of the cross sections and the event generations.
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