# Hints for lepton flavor violation in B-hadron decays

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Dedu
Hi everyone,

I have to write a paper (like an essay) where I have to discuss the hints for lepton flavor violation (LFV) in B-hadron decays from LHCb, BaBar, Belle experiments.

I have found that there are (rare) B-decays, mostly B-mesons, forbidden in the SM that signal flavor lepton violation such as: $$B^0_{s} \rightarrow e^{\pm} \mu^{\pm}, B^0 \rightarrow e^{\pm} \mu^{\pm}$$
and also (+charge conjugates) $$B^+ \rightarrow K^+ e^{\pm} \mu^{\mp}, B^+ \rightarrow \pi^+ e^{\pm} \mu^{\mp}$$
These seem to be the only ones searched for in the literature (maybe also B0 to tau electron/tau muon).

Is there a source where I could find a general description of B-hadron decays which then goes more particularly into lepton flavor violating B decays? How would you go about writing this paper? I am thinking of writing a description of what lepton flavor conservation is with decay examples, the experiments at LHCb and BaBar, general B-decays, particular LFV B-decays with all the braching ratio current upper limits + discussion whether this is just background or hints for new physics and finally some models that could explain the observed (very low) branching ratios such as leptoquarks.

Please tell me if I have a wrong understanding of the topic based on what I wrote. Is there an essential point that I missed and should be included in such an essay?

Thank you

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Gold Member
Possible Research Sources

For background information, Wikipedia is always a good starting point, although it should never be your ending point and should only rarely be the reference that you end up actually citing in your article. For example, the articles on Lepton Number, Meson and B Meson in Wikipedia are probably the best starting points in your search because they define key terms and summarize the state of current knowledge at a big picture level.

A comprehensive listing of experimental data on lepton family violating phenomena is found at the Particle Data Group (on the linked page, with different kinds of decays each having a hyperlink to more citations to the relevant literature and materials). There is also a related review article at PDG related to that page. There are also a number of review articles at PDG that discuss the decay of mesons in general and the decay of B mesons in particular.

The most useful resources for reviewing the literature of a search of the arXiv papers for HEP-EX, Google, and Google scholar.

If you haven't found at least three or four fairly recent published articles or pre-prints from respectable authors you haven't researched the literature thoroughly enough and you need to keep looking and you need to try different key words.

A search of posts at Physics Stack Exchange (near the top left of the page, the field kind of blends into the background visually) is also a good way to review available information in a relatively up to date way from people who are on average very knowledgeable.

How would you go about writing this paper?

Start With The Basics Of What Is Known Before Discussing New Or Speculative Ideas

In my experience, there is a strong temptation to start out by discussing the mystery and its solutions, and in general, what is unknown. But, this is usually not the best way to organize an essay on new BSM physics discoveries or evidence.

The Basic Outline Of An Essay Discussing Hints Of New Physics

Instead, it is usually better to develop as much of a foundation of what is known, what has been measured, what there is consensus upon, and what exactly the Standard Model predicts and allows regarding the matter being discussed.

Many writers omit this assuming that the audience knows it, but this introduction section is easy to write, it grounds all readers in the common set of shared assumptions are taken for granted and the context you are coming at the issue from, its familiarity helps you build solidarity with the reader who shares this knowledge with you making you seem more credible because you and the reader agree on the basics, and it helps a reader build up a little momentum with familiar material before getting into the more challenging new information.

Provide A Brief History Of What Led Up To The Current Experimental Results

Also, in an essay type format discussing new developments, after you lay out the basics or in connection with doing so, it is also often helpful to outline a brief history of the experiments in this area both in terms of who, when and where they too place and how they helped the field make progress and other more tangentially related discoveries. This does several things. One is that it makes it easier for a reader to evaluate references seen in your paper and elsewhere in light of how far developed this line of inquiry was when a particular paper was written. Passing mention of the key researchers in the field will also protect you from accusations that you have failed to attribute work of a researcher whose work you implicitly are relying upon. And, this format also makes it possible to highlight the "where was this point published first by whom" issue, which makes you come across as more authoritative and knowledgeable.

This doesn't have to be in narrative form. A timeline or set of bullet points is also acceptable.

For example, unless you are really pressed for words, it would be helpful to discuss in your chronology in LFV in B meson decays, who discovered neutrino oscillation when and where that happened. This is because lepton flavor number is violated pervasively in neutrino oscillation. Until then, it wasn't entirely clear from the experimental data that LFV ever really took place at all, while after this discovery it was manifestly clear that LFN was not a perfectly conserved quantum number in nature.

Lay Out The Essentials Of The Methodology Used And Key Definitions Clearly

Once you get into the new material, in which you will be discussing several related experiments and measurements, it is a good time to discuss as concretely as possible, the experimental setup that the experimenters used in their more recent experiments, simplified so that only the conceptually fundamental key elements of the set up are explained. In this way, you can be clear about where the date come from and what the numbers in your tables and charts are defined to mean.

Always be meticulous about defining your terms and the units involved, even though more advanced researchers often assume a great deal when they write, and leave a lot to the reader to figure out. If you don't have a PhD or Nobel Prize, you have to prove that you know these things, not force the reader to figure them out.

With This Foundation In Place, Communicate the Results Of The New Experiments Neutrally

As you get into the results, it is key to balance whatever hints have been discovered with a discussion of the experimental uncertainties involved and any other theoretical or circumstantial reasons for skepticism (or lack of skepticism) about the results.

Do cut and paste the best available screen shots of charts and tables and graphs from your sources, but only if a casual reader will be able to make sense of them without reading the body text carefully first. Everyone looks at the pictures first, before reading the words.

Discuss Possible New Physics Explanations And Do So Very Carefully

Only after you have established all of these basic foundations in as much of a model independent manner as possible should you go on to discuss hypothetical explanations of the data with new physics.

As you do this be very careful to: (1) identify the source of each proposal typically by leading authors and paper or pre-print, (2) explain the proposal as clearly and simply as possible - take time to really understand each one rather than just trying to cut and paste from another source, (3) write in a manner that clearly distinguishes between different approaches so that a reader doesn't accidentally mash some of them together incorrectly, (4) make clear in the context that they are hypotheses or conjectures rather than proven physical laws, and (5) discuss what motivates a particular BSM approach (i.e. why it makes sense to approach the issue from a particular point of view). Avoid non-standard jargon particular to only one author.

If not one approach is a clear favorite, make a chart or table showing the pros and cons of each possible BSM solution. This makes it easy for the reader to evaluate them and absorb your conclusions.

Don't pull punches or dance around problems with any particular proposal even if you basically end up discrediting every single idea that has been proposed so far.

Also, in that chart, always include bad data or other sources of measurement or theoretical error (i.e. that the data is just a fluke or arises as from systemic error) as one of the possibilities. The more strongly the data deviates from the SM expectation, the more you should emphasize this possibility as a likely one.

Write A Conclusion

Finally, (1) sum up the main findings in a conclusion, (2) identify what new experimental data would be most helpful in determining what the correct explanation is, and (3) finally, if you are able to do so, identify when and where new experiments that would provide helpful data are expected to be done in the future.

Write The Abstract Last

Don't write the abstract until you have written everything else and crystalized what you have learned as much as possible in your mind. And, when you do, put as much meat of your conclusion there as you can. Don't just fill the abstract with phases that talk about what your study is doing, but don't convey anything about the results to the reader.

If Space Is Limited, Focus, Don't Survey

Of course, sometimes you won't have the time or space to cover all of this in a single essay. But, if that is the case, first trim material with lots of words that doesn't really communicate much information. Then, err in the direction over covering fewer topics in greater depth, rather than surveying as many subtopics as possible.

Form and Style Issues

First, read your professor's syllabus, website and paradigms, if any, and review any examples of good work from students that he has shared. A professor's preferences always override anything that a random guy on the Internet like me says.

Use headings liberally, even if this means that your essay is broken up into many chunks. Prefer multiple short paragraphs under a heading to one long paragraph unless the entire paragraph really just has one cohesive thought. If you feel a temptation to write a very long or complex sentence, break it up into separate sentences and turn that sentence into a paragraph instead.

It is frequently good form to introduce a subsection with a heading, then to provide the one word or sentence answer, and then to further justify your answer to that question or subquestion. People naturally parse question and answer formats more easily than monologs.

If you use a phrase often, consider defining a term that sums up that phrase. But, resist the urge to create acronyms for phrases or concepts or names that are used only a few times unless the abbreviations are ubiquitous in your field and will instantly be understood by every reader, and even then define them the first time that they are used.

Paper and pixels are cheap and you can cut and paste if you need to in order to save time writing your essay. Time spent puzzling over what you were referring to with an abbreviation or acronym is expensive.

If something is hard to explain in words, supplement it with your own picture. Even a rough hand drawn picture will usually be greatly appreciated and praised. In an article like this one, a Feynman diagrams are often are particularly useful in helping a reader to understand what you are discussing.

Always triple proofread your title, the abstract, your first paragraph and your last paragraph for formatting, spelling, grammar, readability, and accuracy, and have another set of eyes look at it too, because errors in these parts of the essay are particularly embarrassing.

Then, review the overall order to see that it flows smoothly, and double check every formula or number that is a result for mistakes.

Keep reviewing and revising your paper in as many drafts as necessary until you get it right. The papers of good students don't look all that great the first time. They look great because they are polished and refined and revised until no further improvements can be made. It should feel normal to have five to twenty-five drafts of a decent sized paper on a complex topic, if not more.

It is especially important to have someone who is native speaker of English read you essay (even if they are not very familiar with your field) if English is not your native language. Otherwise your essay will have awkward ways of saying things that aren't technically incorrect but aren't natural, idiomatic ways of saying something. Having a native speaker read your essay also allows you to avoid using words that have double meanings that you aren't familiar with that are often not documented in dictionaries, which can be embarrassing and distract from your scientific content.

If for some reason it is impossible to have someone else read it at least once, at a minimum, put the finished final draft aside, clear your head by doing something else (ideally sleep on it overnight) , print out the nearly final draft, and then come back to it and review it with a pen in hand, ideally away from your computer.

If you don't take this break or try to edit it entirely on a screen, your mind will often "autocorrect" errors in your head that would be obvious had you been reading your essay freshly for the first time.

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