Feedback for my grad school SOP for theoretical particle physics

[KH_137]

Hi, I would like some feedback on my draft of a SOP for a grad school application for particle physics. I am mostly targeting places in the US. I am finding it difficult to identify areas I should focus on and areas that are not as important. I read that such a statement should focus on research experience (particularly what I did and what I learnt) and how that influences my future work/choices. The current draft is somewhat incomplete because I want to tailor the ending paragraph depending on the department I am applying to.

(I think conciseness is an issue - but it is derived from my confusion regarding what needs to be highlighted and what doesn't)

 

[Vanadium 50]

First, you should start by reading all the other threads on this subject so you aren't starting from zero.

Second, post what you write as text. Who wants to open a virius-ridden attachment.

Finally, if you are smart enough to get a PhD in physics, you are smart enough to know that reading the answer without the question is a waste of time. What are the instructions for the SOP for the school you are applying to?

 

[Vanadium 50]

And one more thing - you are asking people for a favor. You are asking them to spend their time and effort helping you out. You are not entitled to anyone's help. A little courtesy, like "please" and "thank you" go a long way.

If you don't learn this before you get to grad school, your time there will be unpleasant and short. Possibly very short.

 

[KH_137]

@Vanadium 50
Thank you for your response - I apologise about the courtesy thing. I usually get words like "thanks" and "please" removed by moderators on the Physics stack exchange which is the only other place I have posted on before and assumed a similar directness was preferred here as well. Albeit, incorrectly.

To answer your question - I did read some of the threads here and outside this site as well and that just added to my confusion because some of the advice seemed contradictory. I don't have a specific school in mind right now, but am rather focusing on a general draft that I will tailor to each prompt specifically. I come from a system where SOPs are not scrutinised carefully (if at all) and its the grades that matter, so I do not have a good idea of how much detailed such a statement should be. This is what I want feedback on - whether it is too detailed, just right or whether I am focusing on the wrong details, whether the tone is right (I read that I am supposed to sell myself but also not sell myself - I am worried I might come off as a braggart).

I attached a PDF because it seemed long to me:
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Beyond the Standard model (BSM) theories pack a real punch – not only are they intriguing as standalone theoretical models, but they also offer a tangible way to test for new physics beyond what we already know. My research in particle physics, particularly axion-like particles (ALPs) and Randall–Sundrum (RS) models, has allowed me to engage with both and has informed my decision to look for graduate positions with similar goals.

Despite being interested in particle physics, my research began with nonlinear physics. As a greenhorn undergraduate, I worked with Prof. [] on nonlinear oscillators - I learnt analytic and computational techniques (for example, solving systems of differential equations). I also learnt to collaborate effectively –initially, I worked with a classmate, while for the second project, I collaborated with Prof. [] online after his relocation. Ultimately, my work led to a presentation at [] and a first-author paper in [peer-reviewed journal].

I was, however, always interested particle physics - my group theory and quantum field theory courses only made my conviction stronger. So, I joined Prof. []'s group for my Master’s thesis, focusing on the mixing between axion-like particles (ALPs) and photons. I focused on estimating Stokes parameters since they give us an observational signal to look for - photon polarization. Having gained a solid background, I wanted to explore how additional smaller turbulent magnetic fields in a helical model would affect the conversion probability - and whether the changes would be observationally significant. The motivation for this was a discussion with a graduate student in our group who had recently worked on a similar idea and found significant enhancement in results. I wrote the relevant codes and generated the smaller fields, but, unfortunately, since the intergalactic magnetic field (IGMF) is weak, the even weaker turbulent components led to no discernible change. While there were no significant observational changes, the project sharpened my skills and deepened my understanding of the limitations inherent in our models. It also reinforced the need to be adaptable in research, leading me to explore RS models, later.

After investigating axion/photon mixing, I was intrigued by the possibility of extending the formalism to the less discussed graviton/photon scenario, drawing on my General Relativity course. I found that, analytically, it was more interesting and verified my analytical results numerically. Initially, there were some discrepancies, but I resolved them after revisiting the assumptions behind the calculations. While the analytical results were cool, I wanted to figure out a way to use them in a real physical system – this proved difficult as the coupling strength was too weak, rendering most systems futile. I worked on this for several days, however – tinkering with domain sizes to see how they affect probabilities. I found that even though the probabilities do get enhanced, the effect was not strong enough to provide any stringent constraints.

After discussing these issues with my supervisor, we decided to tackle the problem by looking into RSmodels which include a 5-dimensional spacetime with an exponential warp factor that could provide the boost we needed. I worked through the formalism – I realized that current observational bounds on the axion/photon coupling could be translated to the size of the extra dimension – this would enable us to correlate RS models, axions and actual experimental data together. This work is being modified for future publication and I plan to extend my graviton calculations to RS models.

Outside of this, I participated in the [summer program] 2024 at [foreign country], where I worked with Prof.[] on the baryon asymmetry problem. I explored the possibility of a 1st order electroweak phase transitionin the two Higgs doublet model (THDM). I calculated the finite temperature contributions to the effective potential and corrections due to the heavier Higgs particles, finding significant deviations in the parameter space that could be probed by colliders. I also explored gravitational wave generation by such phase transitions - a direct connection to my Master's project. This experience was invaluable as it introduced meto new areas of particle physics and a whole different culture – I adapted to the change well and enjoyed my stay in []. At [], I engaged in thought-provoking discussions on BSM phenomenology with Prof.[] and his group while gaining insights into the current frontiers of particle physics through the group meetings, seminars and arXiv club talks. Academically, I broadened my exposure and gained a solid background in the Higgs mechanism, THDM, electroweak symmetry breaking, and learnt about Coleman -Weinberg corrections, effective potential calculations and how to derive higher-order corrections from such potentials.

My work with axions, RS models and electroweak phase transitions has made me more interested in thevarious approaches used to resolve open problems in physics. The question of massive neutrinos, on top ofthis, provides further motivation to focus on BSM approaches and their connection to observations. Axions, in particular, are also dark matter candidates while the THDM and electroweak phase transition scenarios often incorporate additional CP violating contributions. In the end, these theories connect different problems to each other and these connections can reveal more questions. I am interested in these questions, since they might lead to potential experimental signatures. We are entering an age of GW astronomy along with upgrades for the HL – LHC and proposals for a muon collider and the ILC. Experimental observations in the coming decades will point out more disagreements with the standard model and I want to be a part of a theoretical effort to identify these shortcomings and look for solutions.

Throughout my research, I have encountered setbacks, for instance, in connecting theory to observations, like for gravitons. This has taught me the importance of bridging theory to physical observations - something I had not given much thought earlier. This understanding will guide my future work, where I aim to relate BSM theories to experimental signatures, ensuring that the results remain impactful both theoretically and phenomenologically. Along the way, I have also learnt to work independently and challenge myself. I enjoy working independently – it gives me the freedom to try out different things and the flexibility to work at my own pace. However, I do not work alone - my work is actively shaped bydiscussions with my supervisor, group members and the valuable feedback they provide. I have also learnt to keep an open mind – even though my primary interests are theoretical, I have learnt the importance ofbeing informed on experimental techniques. On a similar theme, I actively discuss ideas with my peers from different backgrounds – condensed matter or pure math – and incorporate new techniques and ideas in myown work. This openness to cross-disciplinary techniques will inform my future work as well, especially as BSM theories often require innovative approaches that span different fields of physics, math and even computer science.

I feel that XYZ university is a great fit for me because of the perfect blend of theoretical and phenomenological research carried out in the particle physics group in the university. I feel that it is the perfect place to hone my mathematical interests while focusing on real world observations and phenomenological techniques. I wish to work more on BSM theories – specifically, on electroweak symmetry breaking, the Higgs sector, axions, neutrinos and the nature of dark matter. XYZ has some of the best people working on these areas – Prof. [...] on [...] and Prof. [...] on [...]. I have gone through some ofthe recent publications from the department and I came upon several interesting ideas - for example, [...]. My specific interests seem to be at the forefront of the kind of work being actively carried out at XYZ. This is why I believe that the graduate program at XYZ would be an amazing fit for me.
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Thank you in advance!

 

[Vanadium 50]

I doubt very much this answers the question, although you didn't post it. However, they probably did not ask "Please rehash the rest of your application" which is pretty much what you did. The questions usually asked are some variant of "Why do you want a PhD?" and "Why do you want to go here."

I would start over, with those questions (or whatever thet actually asked) in mind.

 

[Vanadium 50]

Let me add that some students think "longer is better". Just the opposite. Don't make the reader fish around for what they want to know.

 

[KH_137]

@Vanadium 50
Thank you for your answer, I appreciate it. In other words, my focus should be on the last paragraph (where I discuss why that specific PhD program is suitable for me) while cutting down everything else to one paragraph or less.
As for "why you want to do a PhD" - do you think the third paragraph from the last is a decent answer to that? I have thought about this a lot but honestly, the reason I want to do a PhD is because I love doing physics and just want to continue doing it in the future too. I don't have any other sophisticated reason or anything.
Finally, do you think the opening is decent (I want to go with it in the revised statement too)?

Thanks again.

 

[KH_137]

As an example of what you asked me to do, I am working with these questions:

Why are you aiming for a PhD degree? Why are you applying at the [ ]? Are there particular areas of research you are especially excited about for a PhD? Describe a highlight of your MSc work.

My response:
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A PhD signifies a commitment to long term research – I love physics, I love working on questions day and night and thinking of new ways to attack them. I have been a part of long terms projects before and I know I love working on questions and finding some answers. My passion and love for the field combined with the urge to know more and contribute to the existing pool of human knowledge is what drives me to a PhD position – a position where I my primary job will be to research, almost like a dream.

Beyond the Standard model (BSM) theories pack a real punch – not only are they intriguing as standalone theoretical models, but they also offer a tangible way to test for new physics beyond current knowledge. My research in axion-like particles (ALPs), Randall–Sundrum (RS) models and electroweak phase transition has allowed me to engage with both and informed my decision to look for PhD positions with similar goals. These are the areas I am specifically targeting for my PhD – BSM theories but with a focus on the Higgs sector, electroweak symmetry breaking and phase transitions and the link to dark matter candidates (like axions) and their phenomenology.

The [ ] is one of the world’s leading institutions in research – especially particle research within the [ ]. I find the topics of research at the [ ] diverse with a perfect blend of theoretical and phenomenological groups. Prof. [ ], for example, is a leading expert on DM, baryon asymmetry issues – these are at the forefront of my interests. The structure of the [ ] program is also particularly appealing. The block courses, [ ] colloquium and [ ] workshop would be particularly beneficial for learning and discussions with experts and one’s own peers while keeping me informed on the very current research ideas and techniques. To work towards my own dream of a PhD at a place like the [ ] would be incredible. I am also interested in science popularism and I feel that the [ ]'s active commitment to it makes the program a good fit for me.

My Master’s work was based on mixing between ALPs and photons. While I explored the consequences of their interactions initially, I later focused on RS models where the size of the extra dimension is related to the axion/photon coupling strength by an exponential factor. The main highlight of my work was the realisation that current observational bounds on the axion/photon coupling could be translated to the size of the extra dimension – this would enable us to correlate RS models, axions and actual experimental data together. In many ways, this is the essence of the kind of work I want to do – bridging the gap between theory and experiments through innovative approaches and by relating different ideas together. Apart from the actual research, my work has also taught me effective collaboration and communication, working feedback into my research and trying as many things as possible without worrying about failure all of which will influence my future work.
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Thanks again for the help!

 

[Vanadium 50]

Note the question is much closer to what I guessed than what you answered in the first draft. Do not try and salvage your first draft - that's like working problem #7 and then realizing they asked for problem #8 and trying to submit the answer for #7 anyway.

The good news is that this answers the question they asked better. The less good news is that it is full of cliches and platitudes, especially in the first paragraph. It makes me wonder "Is he going to grad school by default? He just can't think of what else to do?" The first line of the 2nd paragraph says, in effect, "BSM is the way to see what is beyond the standard model". Well, I guess. But hardly an earth-shattering insight.

You also continue to make this about the past. That is not what they are asking.

 

[KH_137]

@Vanadium 50
Thank you for the input. I appreciate the consistent feedback. Writing a statement is much harder than I thought it would be - however, on deeper thought, I realised I had overlooked the science education part of a PhD training which had subconsciously informed my choices as well (the only issue is that at my current institution, we are not allowed to apply for TAships despite being Master's students so I don't have any experience tutoring).

I revised my response:
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A PhD signifies a commitment to long term research and offers significant flexibility to work on questions I personally find interesting. It is an opportunity to develop my critical thinking, to learn to independently frame and solve problems, and to carve out my identity as a physicist - an opportunity to master my own way of approaching problems. Alongside this, a PhD will also allow me to give back to society - not only through tangible research output, but also teaching, science communication and by bridging the gap between theory, experiment and real life societal benefits. My long-term goal is to be a physicist - work on what intrigues me, teach what I love, make fundamental research more accessible and contribute meaningfully to society. A PhD will provide the platform to develop the necessary skills to achieve this.

The [ ] is one of the world’s leading institutions in research – especially particle research within the [ ]. The research at the [ ] is diverse with a perfect blend of theoretical and phenomenological groups - it would allow me to explore abstract formalism while remaining connected to observations. Prof. [ ], for example, is a leading expert on DM, baryon asymmetry issues, central to my research interests. The structure of the [ ] program is also particularly appealing - the block courses, [ ] colloquium and [ ] workshop would provide excellent opportunities to engage and collaborate with experts and peers, while staying informed about the current techniques and research ideas in the field. Furthermore, [ ]'s active commitment to science popularization perfectly aligns with my own broader goals as a physicist. To pursue my PhD at [ ] would be an incredible opportunity to develop as a physicist.

I am particularly excited about Beyond the Standard Model (BSM) theories — not only are they intriguing as standalone theoretical models, but their rich phenomenology also leads to testable predictions. My research in axion-like particles (ALPs), Randall–Sundrum (RS) models and electroweak phase transition has allowed me to engage with both sides of this, shaping my decision to pursue a PhD similar opportunities. I want to focus on BSM physics and am particularly interested in the Higgs sector, electroweak phase transition and the link to gravitational waves, dark matter candidates, such as axions, and neutrinos all of which can lead to experimentally observable consequences.

My Master’s work was based on mixing between ALPs and photons. While, initially, I explored the consequences of their interactions, I later focused on RS models where the size of the extra dimension is related to the axion/photon coupling strength by an exponential factor. The main highlight of my work was the realisation that current observational bounds on the axion/photon coupling could be translated to the size of the extra dimension – this enables us to correlate RS models, axions and actual experimental data together. In many ways, this is the kind of work I want to do – bridging the gap between theory and experiments through innovative approaches and by relating different ideas together. Beyond the technical aspects, my work has taught me effective collaboration and communication, working feedback into my research and trying as many things as possible without worrying about failure all of which will influence my future work.
----------------------------------------------------------

Please let me know what you think and thank you again for the consistent feedback!

 

[Vanadium 50]

Writing a statement is much harder than I thought it would be

Yes. Yes it is.