The production of a Higgs boson at the LHC proceeds through many different sub-processes. While gluon fusion is the dominant one, at least for Higgs bosons with SM-like couplings, other processes, though with a smaller cross-section, 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 Higgs-strahlung 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.*

**Project objectives**

- Acquire knowledge of the SM Higgs boson phenomenology.
- Acquire knowledge of the 2HDM Higgs sector phenomenology.
- Learn how to use the code SuShi, for the computation of the Higgs boson production cross-section at the LHC in gluon fusion and quark associated production.
- Learn how to use the code 2HDMC, a general purpose 2HDM calculator.
- Study the phenomenology of the process
**b\bar b\to ZH_{125}**.

### SM Higgs boson phenomenology TO BE COMPLETED

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 p p \to Z H process.

**Task list**

- Follow the lectures on the SM of particle physics (these lectures are quite advanced in the calendar, we will start the work before them and you can return on the topics later).
- Go through the relevant references in the Useful resources page.
- Discuss with your supervisors on the subject.
**(optional)**Derive the relation between the bottom mass, the bottom Yukawa and Higgs Vacuum Expectation Value (vev) from the Lagrangian.**(optional)**Write the amplitude for the p p \to Z H process.

### 2HDM Higgs boson phenomenology TO BE COMPLETED

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 \tan\beta). Moreover, you can understand how the Higgs phenomenology is changed by the presence of the multiple Higgs states.

**Task list**

- Follow the lectures on Beyond Standard Model (BSM) physics (these lectures are quite advanced in the calendar, we will start the work before them and you can return on the topics later).
- Go through the relevant references in the Useful resources page.
- Discuss with your supervisors on the subject.
**(optional)**Derive the relation between the bottom Yukawa, the bottom mass and the Higgs vevs in the 2HDM**(optional)**Understand how is the p p \to Z H affected by the structure of the 2HDM.

**The b\bar b\to ZH_{125} process TO BE COMPLETED**

In models in which the coupling of Higgs bosons to bottom-quarks is enhanced, as it can happen in the 2HDM, the Higgs-strahlung process \mathrm{pp\,\to\,ZH_{125}} some of the contribution that are negligible in the SM (due to the smallness of the bottom Yukawa coupling) can become relevant.

Indeed, apart from the Drell-Yan like contribution q\bar q\to ZH_{125} and the gluon-initiated contribution gg\to ZH_{125} also the process b\bar b\to ZH_{125} is of relevance. Therein the Higgs can directly couple to b-quarks (in contrast to Drell Yan, which is mediated through an s-channel Zboson only).

This process was only rudimentary discussed in the literature. As a reference, see the paper " Higgs Strahlung at the Large Hadron Collider in the 2-Higgs-Doublet 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. b\bar b \to A \to ZH_{125}.

**Task list**

- Read the literature and get familiar with the process.
- Discuss with your supervisors on the subject.

### Cross-section computation for b\bar b \to A using SusHi TO BE COMPLETED

Get familiar with Higgs production through bottom-quark annihilation b\bar b \to A, where A is a pseudoscalar Higgs boson of a Two-Higgs-Doublet Model.

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 center-of-mass energy of 13TeV produce cross sections as a function of the pseudoscalar mass.

**Task list**

- Install SusHi and familiarize with it.
- Compute the cross sections for a variety of bosons/processes such as a pseudoscalar production in bottom quark annihilation.
- Discuss with your supervisors on the subject.

### An 2HDM calculator: 2HDMC TO BE COMPLETED

Install 2HDMC from its own page, http://2hdmc.hepforge.org and familiarize with it.

Then calculate the partial width A\to ZH_{125} in the physical basis, where \sin(\beta-\alpha) and \tan\beta as well as all masses of the Higgs bosons can be set.

2HDMC calculates the total width of the pseudoscalar as well as the branching ratio A\to ZH_{125}.

SusHi can also be linked to 2HDMC in order to obtain cross sections for A directly.

**Task list**

- Install 2HDMC and familiarize with it.
- Compute the decay width for the process A\to ZH_{125} and tabulate the results for a variety of masses and parameters.
- Link 2HDMC directly with SusHi to obtain the cross-section directly.
- Discuss with your supervisors on the subject.
- Study the dependence on \sin(\beta-\alpha), \tan\beta, M_A
- Plot the BR to Z H_{125}, t \bar{t}, b \bar{b} the total width in the \tan\beta - \sin(\beta-\alpha) plane for mA = 250, 400, 1000 GeV.
- Try to understand how the search at the experiments interplay with the results.

### Combine production and decay using a Breit-Wigner-improved narrow-width approximation TO BE COMPLETED

Combine the results by using a Breit-Wigner improved narrow width approximation (see e.g. arXiv:1502.07970):

\frac{d\sigma(b\bar b\to ZH_{125})}{d\sqrt{s}} = \sigma(b\bar b\to A)(m_A)\frac{2\sqrt{s}}{(s-m_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):

\frac{d\sigma(b\bar b\to ZH_{125})}{d\sqrt{s}} = \sigma(b\bar b\to A)(s)\frac{2\sqrt{s}}{(s-m_A^2)^2+m_A^2\Gamma_A^2}\frac{\sqrt{s}\Gamma(A\to ZH_{125})(s)}{\pi} |

Therein \sqrt{s} corresponds to the mass of the pseudoscalar. It allows to take into account QCD and electroweak corrections in production and decay separately. Check which parameters, probably \sin(\beta-\alpha) and \tan\beta, enhance the total cross section and which ones influence the width of the pseudoscalar for a few pseudoscalar benchmark masses like m_A=300, 750, 1500GeV.

**Task list**

- Use the Breit-Wigner narrow width approximation to combine the results of the previous steps.
- Understand the parameter dependence of the process for a few pseudoscalar masses.
- Discuss with your supervisors on the subject.

### Computation of the b\bar b\to ZH_{125} TO BE COMPLETED

Get familiar with FeynArts and FormCalc and try to calculate b\bar b \to A\to ZH_{125} and then b\bar b\to ZH_{125} at leading order. Compare this result with the result from the previous steps. which employs only leading order for production of a A boson and then for its decay.

One can think about a combination of this calculation, that neglects the interference with the t-channel b\bar b\to ZH_{125} contribution, with the interference calculated at LO QCD.

In order to obtain the hadronic cross section one needs to convolve with the parton distribution function by

\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 s in the partonic cross section \sigma(b\bar{b}\to HZ) has to be set to s=x_1x_2 \hat{s} with the center-of-mass energy of the collider \hat{s}.

The parton distribution function are evaluated at the scale \mu_F=m_\phi/4.

Here the link to the kinematics writeup of PDG:

**Task list**

- Install the FeynArts and FormCalc Mathematica package and familiarize with them.
- Compute the process b\bar b \to A\to ZH_{125} at LO.
- Compute the process b\bar b\to ZH_{125} at LO.
- Compute the full process including the interference terms.
- Compare the results above between them and with the results of the previous steps.
- Discuss with your supervisors on the subject.

### Computing **b\bar b\to ZH_{125}** @ NLO-QCD using MadGraph_aMC@NLO OPTIONAL

The public tool MadGraph_aMC@NLO (home page) allows to compute automatically the matrix elements for a given process at NLO-QCD 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 NLO-QCD for simple SM processes such as Z boson production.

Then, to compute the process **b\bar b\to ZH_{125}** at NLO-QCD in MadGraph_aMC@NLO, you will first need to verify the availability of the 2HDM model file for NLO-QCD computation.

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.

**Task list**

- Install and compile MadGraph_aMC@NLO.
- Simulate a few simple SM processes to acquire the necessary skills to run the program for a physics study.
- Verify that the 2HDM model file supports NLO-QCD computation.
- Simulate the process
**b\bar b\to ZH_{125}**at NLO-QCD.

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