One eye on the weather for pike!
WELCOME TO this week's Big Fish Blog, coming to you here every Thursday. This time it's by Dave Mutton of the Pike Anglers Club. We hope you enjoy the blog, and share it with your friends on Facebook and Twitter by clicking the icons above!
AS I write this I am trying to work out where to go piking this weekend.
I am desperately missing the Warwickshire Avon as I love wandering along its banks with a float ledger setup on a deadbait rod casting into likely looking holes. Unfortunately, for the last couple of weeks the river has been racing through and is the colour of chocolate.
Pike can still be caught when it is like this but it is far easier with a little less flow and colour. However, as the colour drops out and the flow subsides a bit the pike can often come back on the feed with a vengeance. So even though it is still high, it is now starting to drop so I may well chance my arm.
If your local river is in the same condition as the Avon, why not give it a go, a big girl may well be hungry.
On a cautionary note, if you are out on the river banks over the next couple of weeks, be careful as they will be very slippery. I would advise wearing a life jacket even when fishing from the bank in these kinds of conditions.
On the subject of location, the submission below by Matthew Perring, a PAC member from Banbury, Oxfordshire and a new contributor to our Big Fish Blog for Angler's Mail, gives some food for thought with his tactic for finding where the pike may be….
Location, location, location, I kept reading those immortal words but they never hit home until one day when I was aimlessly chucking lures on my local river Cherwell and blanking, may I add.
I must've walked 8 miles that day in search of an elusive predator, when I finally got fed up and started the long walk to my car.
Now this got me thinking. Firstly whether or not to feed a swim attracting the baitfish, which is not an unusual thing to do as I also usually target perch and this tactic can be deadly.
The second thing I thought about is perhaps if I was to read up on my local match fishing reports to see which lakes and hopefully pegs were producing plenty of silver fish, thus putting me in the perfect position to ambush the pike and usually with brilliant accuracy.
Matt Perring with proof his predator hunting via matches is working!
I even went up to one of my local lakes and fished the winning peg directly after the match which proved to be a superb and very productive session.
In fact since I started to look at the match results my results have improved so much that I haven't fished a venue for months unless I've checked on the potential first.
I'm not saying it's to everyone's liking as I used to turn up to venues and fish blind and immediately deal with the situation that I found myself faced with, but if your pushed for time or are just fed up with struggling then have a go for yourself and I think you'll be pleasantly surprised .
FANCY SOME PIKE FISHING LESSONS?
The PAC, in conjunction with the Angling Trust will be running a series of pike fishing tutorials on the Coventry Canal at the Coventry Canal Basin every Saturday from 9am to 12pm from mid-February to the end of March.
This course is open to anyone between the ages of 11-24. It is free to participate for under 18's and for 18 to 24 year olds it is only £2 a session.
Places are strictly limited to 10 people so, if you are interested in you, or your son or daughter attending the course, please email dave@catfishing-uk.com for more details.
Please note, as parental permission will be needed to attend the course can the parent or guardian please email to register interest.
That's all we have room for this time round, so hopefully we will be back next month to show you some pics of some nice pike caught off the rivers. I hope you all get a few too.
The Big Fish Blog returns next Thursday.
REPORT YOUR BIG FISH CATCHES TO ANGLER'S MAIL MAGAZINE EXCLUSIVELY! Email photos and info to anglersmail@ipcmedia.com or use the button at the top right of this website which takes you to a simple form.
Pick up your copy of the biggest read in fishing this week. This latest copy of Angler's Mail magazine is in stockists from Tuesday, January 21.


Houstonians LOVE Crawfish. We eat more than anywhere else in the world.
We are thinking Crawfish eating contests, music beer and bugs.
Only share this with your serious crawfish loving friends. No amatuers.
To celebrate bug season, please join us for Crawfish.


text:
Martín Olleta was a Chono chieftain who was an important broker between Spanish authorities in Chiloé Archipelago and indigenous people of the fjords and channels of Patagonia. He is known for rescuing the survivors of the HMS Wager wreckage in 1742. He was identified as chieftain by the British and referred to as "gobernadorcillo de dicha nación chonos" ("little governor of the Chono nation") by the Spanish governor of Chiloé Victoriano Martínez de Tineo. He used a rod with a silver handle as symbol of authority.

Rescue of HMS Wager survivors
Olleta led a party of indigenous Chono that visited Captain Cheap stranded group in Wager Island, Guayaneco Archipelago. This happened fifteen days after a group of British sailors returned to Wager Island after failing to round Taitao Peninsula with an improvised barge. The Spanish language proficiency of the Chonos, led by Martín Olleta, was enough to communicate with the Spanish-speaking surgeon of the British party. After some negotiation, the Chono agreed to guide Cheap's group to a small Spanish settlement up the coast, using an overland route to avoid the peninsula. The castaways traded the barge and iron objects for the journey. Iron was highly valued by the Chono as this metal was even scarce in the Spanish settlements further north. The survivors of HMS Wager boarded the dalcas of Olleta's party and headed north. Martín Olleta led the survivors through an unusual route across Presidente Ríos Lake in Taitao Peninsula avoiding the common route through San Tadeo River and San Rafael Lake. Before handing over the English to Spanish authorities, Martín Olleta's party stopped somewhere south of Chiloé Island to hide all iron objects, likely to avoid have them confiscated. When Spanish authorities learned that Lieutenant Hamilton had been lost in the way north, they compelled Olleta to go back south and find him, which he actually did.

Scholar Ximena Urbina conjectures that Martín Olleta must have lived close to the Spanish and heard from other natives of the wreckage. Thus the rescue was not by chance but an enterprise done with prior knowledge of the Spanish interest in foreigners and of the valuable loot to be found at the wreckage.

References

Chono people
18th century in Chile
History of Aysén Region
History of Chiloé
People from Aysén Region
18th-century indigenous people of the Americas
Chilean sailors
Indigenous leaders of the Americas
Indigenous sailors of the Americas

redpajama_set_name: RedPajamaWikipedia


Tyson is a general partner at GV. He spent his career in enterprise technology, focusing on companies in the SaaS application and data center infrastructure spaces.
Prior to joining GV, Tyson was a partner at Andreessen Horowitz, where he was on the corporate development team and advised enterprise portfolio companies. He led acquisitions in the enterprise SaaS space for Oracle's corporate Navy, serving on submarines as both as a nuclear propulsion officer and Navy scuba diver.
Tyson holds a B.S. in industrial engineering from Stanford (with honors) and an MBA from Harvard Business School.


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The Sustainable Hawaii Youth Leadership Initiative (SHYLI) is expanding its focus beyond its successful pilot program with West Hawaii Explorations Academy to partner with other educational organizations in West Hawaii. SHYLI's program will serve as capacity building for existing organizations to engage more youth and develop their leadership skills. People are invited to nominate youth (ages 15-22) who are potentially at-risk and potential leaders from their communities. They are empowered to be spokespersons and representatives of their islands — learning how to develop action plans, troubleshoot challenges, prepare presentations and develop strategies to engage people to develop sustainability projects. Youth learn to use technology, video and social media to make effective presentations about their projects and featured on TV. By engaging Hawaiian youth in envisioning, planning and creating their future, SHYLI helps them to be more hopeful and invested in their future. They will engage their friends in positive, life-affirming projects. They will be proud of their vision and prepared to share it, their concerns and ideas in constructive ways so leaders in business, community and government hear them and join with them.
• SHYLI youth delegates prepare power point presentations on sustainable agriculture/business, architecture, education, energy and environment at Youth Leadership Summit.
• Trevor Tanaka and Kynan Kawaii shared their vision on the national radio – Keeping It Moving with Marsha Reeves- Jews. WEAA 88.9FM from Morgan State University, Baltimore, MD.
• Makana Tavares wrote an inspired article that was published in the Honolulu Civil Beat.
• SHYLI youth developed Sustainability-In-Action Plans to implement in their communities.
• Kynan Kawaii made presentation at North Kohala Growing a Local Food System meeting.
• Nomination Process: SHYLI Advisory Council, schools, organizations nominate youth to be youth delegates.
• Conduct Youth Leadership Summit Orientations at high schools in West Hawaii, North Kohala, Waimea, Hilo.
• Conduct monthly workshops (video conference) to develop SHYLI presentation for Youth Leadership Summit.
• Present books, meet with community, business, civic, government leaders to listen, learn, explore partnerships.
• Jan. 13: Conduct Sustainable Hawai'i Tour with WHEA students to Waimea green initiatives.
• Jan. 14-15: Conduct Sustainable Hawai'i Tour to all island green businesses, farms, organizations and schools.
• Met with Hawaiian cultural leaders to pay respect and request blessings on SHYLI Sustainable Hawaii Tour.
• Enrolled in Na Wai Iwi Ola (NWIO) Foundation language classes, participated in Hi'uwai ceremony.
• Met with potential funding organizations in Oahu to determine priorities, timelines and process.
• Met with potential nominating organizations including: Art Souza, Superintendent, Hawai'i Department of Education, Hui Laulima coalition of agencies and organizations, and Nem Lau's Career & Technical Education colleagues, Mayor Billy Kenoi's offices of Planning and Development, Research and Development, Angela Kang, Recycling Coordinaor, Councilman Angel Pilago and Polynesian Voyaging Society, Mitch Roth and Paula De Morales, Prosecutor's Offices (Youth Action Summit), Lori Sasaki, DOE Workforce Development Division, Na Kahumoku, Kealakehe Intermediate School, Environmental Leadership Club, Kealakehe High School, Guy Toyama, NELHA, Nancy Redfeather, Kohala Center.Grif Frost, Michael Kramer, HALLE, Susan Cox, Green Power Girl, David Fuertes' Ka Hana No'eau, Partners in Development Foundation, members of Kuelana Green Committee of Kona-Kohala Chamber of Commerce and Kea'au Youth Business Center.
• Create local branch: make arrangements for local office, address, and bank account.
• West Hawai'i Explorations Academy's Green Team members complete application process: What is my dream for my life, my island and my world? What are the challenges facing Hawai'i youth? What community service projects have I been involved with in the past? What are my academic, professional, and travel goals?
• Wainani Traub represents Hawai'i youth and makes presentation at the APEC Youth Summit.
Presentation of official lei as dignitary to APEC Summit to the West Hawaii Explorations Academy.
• WHEA student Taylor Wainani Traub was selected to serve as the youth delegate. The Institute researched funding to cover her costs. (Ultimately, the Institute waived fees and paid her airfare, total contribution of $4,000). The Institute's staff supported Wai through the process of preparing a power point presentation on her island's sustainable initiatives. During the Youth Leadership Summit, we worked intensively with Wai to clarify and develop her plan for her Sustainability-in-Action Project.
• Marianne Larned, Executive Director of the Stone Soup Leadership Institute conducted a series of meetings with youth and leaders from schools, non-profit organizations and businesses including Bill Wiecking, Director HPA Energy Lab, Karen Yamasato, Hawai'i Youth Congress, Nancy Redfeather and Cindy Punihaole, Kohala Center, I'ole Center, Marcy Montgomery, One Island and West Hawai'i farmer's markets to learn about sustainable projects and challenges facing Hawai'ian youth. They were invited to nominate two Hawaiian youth to attend the Institute's 7th Annual Youth Leadership Summit for Sustainable Development.


Though isn't a huge sprawling city, but it's all the better for it. Its incredible nightlife has transformed it into one of Ireland's must-visit party towns, giving this small city a big party atmosphere. The best clubs, pubs and bars are found around Eyre Square and there's no better place to be. So, that's exactly where we'll be putting you.
Yep, we don't mess around. On your special weekend you don't want to waste time traipsing around town and with our fabulous centrally located Galway hen hotels, you won't have to.
At the risk of sounding like a broken B*witched record, Galway isn't the biggest place so more often than not, the best way to get around is on your own two dancing feet. That way you can put any money bigger cities might take for taxis towards more cocktails at the bar. Pina colada o'clock?
Although if you do fancy taking the weight off your feet after a girl's night out, or you're just weighed down by all those shopping bags (Galway has some fabulous shops to explore) then there's a fabulous bus network that you can hop-on and off at very affordable prices.
Here at GoHen we're all about helping you squeeze as much value as possible out of your hen party budget and we have some fantastic deals on our Galway hen hotels for you to take advantage of.
Because of our long-standing relationships with hoteliers, we're often given lower rates that we can pass on to our groups, helping them save money and getting them a better stay for less.
Not convinced? Put us to the test today and find out how much you could save.
If you could book your Galway hen hotels for less on your own, we'd be telling you. But unfortunately, there are some hoteliers out there that try to take advantage of large groups of travelling party people by charging them unfair premium prices.
Not only do we help you dodge these price hikes, we'll often work to drive down costs even further to make sure you're getting the best deal possible for your special weekend.
Let's be honest. Life is busy, there are dinners to cook, nails to polish and Netflix to watch… You really, really don't have time to spend trawling the web, looking for the perfect Galway hen hotels for you and the girls.
Luckily, here at GoHen we've already found the best hotels that can take large hen groups, for the best prices, in the best locations. Taking the stress of hunting for them yourself away, so you can sit back and relax knowing that all the hard work is taken care of.
Managing everybody's money when planning a weekend as big as this can get a teensy bit stressful at times (and that's putting it mildly). But when you book with GoHen, you can rest assured that you're dealing with an ABTA bonded and ATOL protected travel provider, offering the highest standards of financial protection available in our industry.
So, you can wave goodbye to pre-hen-do panic and enjoy planning the bride's farewell as much as the rest of the girls.
As soon as possible! It's a story as old as Ross and Rachel. A group of hens take forever to decide where they want to stay, they finally choose only to find out that while they were deliberating, everybody else snuck in and now everywhere's fully booked.
The alternative? Get your booking in early!
We can even hold your places in the Galway hen hotels of your choice for a limited amount of time in certain situations, giving you a chance to work out who is/isn't coming and who still needs to pay.
Just send us your enquiry. No, seriously, it's that easy. Then while you're messaging the bridesmaids group chat, letting everybody know that you're the Queen of Parties and have everything in hand, we'll be doing the hard work for you. It's fast, simple and best of all, completely free until you decide that you want the amazing GoHen weekend that you, the bride and the rest of her special guests deserve.
Or you can talk to one of our expert destination specialists today by calling 01225 474200.


I visited Withlacoochee Park in Dade City, Florida in March 2015. It was hot, humid, and covered in flies, but other than that it was pretty cool.
There are several large parking lots, picnic shelters, two playgrounds, and a canoe launch. The good playground has plastic drums and metal "bowls" built into it, just in case your children aren't loud enough already. Much of the structure has hornets growing on it, just in case your children like to pet animals. Also, the highest point of the structure, from which two covered slides attach (very slippery and fun, I might add), can only be accessed by a short ladder through a tight hole in the floor – I assume to keep fat kids and grown-ups out, because nobody wants either of them around.
There are long trails looping around the park, but the flies wore me out before I could explore them all. I did climb the observation tower and traverse one swamp boardwalk while I was there though. I saw several interesting things. I saw some very red Christmas lichen, which is usually pink around here. I saw a rather large owl at a close distance that stared at me long enough for me to wave, but not long enough for me to take its picture or get an autograph. I also saw a tiny tan skink, a very large burrowing turtle, and a tiny grey-and-black toad. I found a leaf that looked as if it had been bitten by a cookie-cutter shark – which is very unlikely this far inland. I also took a picture of a cluster of two species of lichen on the forest floor that I meant to be the cover picture for this report. It was the best picture I took, but it somehow must have fallen out of my phone because it didn't make it home. I'm very silly.


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I'm interested in the ways people organise their Therion datasets. Feel free to add your own templates or add your own page to explain your own approach to organising your cave survey data, or how mine can be improved.
These pages do not describe 'the official word' on Therion. For that you should refer to The Therion Book, or pages on this wiki by those more knowledgeable. This is just my attempt to tame the beast, or a least understand it a little so that I can keep it under control.
Bruces data structure An incomplete and not yet well thought out description of concepts and ways to organise Therion data.
Extended Elevations Manage extended elevations independently of survey trip data and drawings.
Therion by Examples Playground Simple examples that demonstrate particular features one at a time using 'bare bones' data structures.
When I first found the Therion website (2007-2008) I thought that my 15+ year search for cave drawing software was over. (Having suffered that many years of what I imagine were similar frustrations and wasted effort that prompted a Cave Surveying Group article on Sustainable Mapping of Caves) Straight away I had visions of, from a single set of input, many types of cartographed maps of the same piece of cave, various symbol sets, orientations, levels of text detail and symbol visibility depending on scale, languages, comprehensive data reporting, etc etc.
With the exception of the drawing files, Therion never writes to the input files, so a bug in the software can never trash your data. Drawing files are textual, so if there is a problem, you can generally get in there with a text editor and figure out what is wrong, and then fix it.
Text files, and hence Therion, are version control software friendly. Go back to inspect any change ever made to the input data, or recreate the dataset as it was five years ago. Simultaneously edit and process your dataset while others in the survey team are doing the same on different sides of the mountain. Merge and share all your edits later on with removable media or via a central web repository.
Symbolic representation of entities. The output language and drawings can be chosen from a number of predetermined sets, or they can be customized quite readily.
Batch processing (make one or more changes, propagate them easily to selected outputs).
Features are added or modified on request of, or in consultation with users.
All that a wannabe cave geek could wish for!
In hindsight my expectations were too high. Some of my wishes were met easily and others are above what Therion can (readily) deliver (5.3.9 Nov 2011). I now realize that Therion is still in the early stages of it's development cycle, and many of the features are only developed to a rudimentary level. So, new users need to be prepared for this, and either have the faith and patience to wait for development to evolve, or move on to other cave documentation tools, that may sacrifice some of the above advantages.
Back when I first started exploring Therion, I struggled with understanding how it all worked. I still have 'game changing' insights after 5 years of tinkering. The Therion (reference – not instruction) Book and wiki provide basic and advanced information, but there is little direct guidance on how to organize large projects. Therion provides a means of producing cave maps, but allows the user complete freedom to create long tangled files with spaghetti like dependencies. At present, to manage a modest cave dataset, you need a good working knowledge of computing best practices (not me), or be satisfied with all your maps at similar scales, preview arrangements and orientations. While these pages are quite likely to be just as confusing as the rest of the documentation, they (will hopefully eventually) contain stuff that I think would have got me going much quicker.
So if like me you are tempted to incorporate all of the features at once, here is some advice regarding those things that don't yet work as well as they might.
Plan view maps and atlases can be produced rotated to any angle, but if you want to produce maps of a particular cave at a variety of angles you are probably making things difficult for yourself (5.3.9 Nov 2011).
and, when scanning sketches as background to scraps (or collecting data with PocketTopo – see the cautions at the bottom of data_transfer_from_pockettopo_to_therion) ensure that north is approximately towards the top of the page.
The reasoning for sketch scans is because point insertion alignments (left, top-left, right etc) are based on the orientation of the scrap (sketch) and not on the orientation of the output produced. (Thus rotate 160 deg, -align top-left for a north aligned sketch will likely produce an output aligned bottom-right, very confusing).
The reasoning for map and atlas outputs is because, unless you use the default alignment (centre) the position of the symbol will vary with respect to the cave depending on the rotation. In both cases this mainly causes problems with text labels.
Short of creating independent scraps for labels at different rotations (which I think is unreasonable duplication) I cannot think of a way to resolve this. My approach has been to choose a rotation for all map and atlas outputs at the start of a project, ensure all sketches are scanned at this rotation (not essential, but helpful) and accept that all future maps and atlases will be produced at that rotation unless you want to check and tweak the position of every label each time you change the rotation.
Therion support for elevations in atlas is not finished yet (5.3.9 Nov 2011) see forum post If you want to produce an atlas in elevation, you will find that only the x part and z part of the origin is used for positioning pages, regardless of the projection angle.
The easy way is to only produce elevation atlases looking north.
You can fudge an elevation in any direction, but you will have to experiment with the x part of the origin to get a good result. It's a long time since I tried, but from memory non-orthogonal elevation projection atlases are next to impossible to control with any degree of refinement.
The easy way is to accept that you will only produce a good looking map with labels within a narrow range of scales (5.3.9 Nov 2011).
While the size of the text naturally scales with the map, the positioning that works at one scale will be too far from, or overlap the cave at other scales. In order to minimise this effect, always make careful use of label and symbol insertion points, ie -align top, bottom, left, right, center, tl, tr, bl, br.
As of 5.4.1 Apr 2017 you can use the layout option min-symbol-scale to progressively hide small text at smaller scales.
b) the title does not match very closely the id.
b) ensure that the first several characters of the title match exactly the id (except for top level surveys that need to 'read nicely' on the outputs produced).
This one still eludes me, although to be honest, once I came up with a system I have not experimented too widely. Too time consuming to make changes to large projects, especially when new cave is constantly being added to the dataset! Somewhere there is a balance between having many modular codependent components that are linked together, ensuring consistent outputs and the alternative of having a few independent components which require duplication of edits to migrate changes through to all appropriate outputs.
I started out trying to use a single thconfig file that was capable of producing any output possible for a particular cave, with only minor edits such as commenting or uncommenting particular lines. It works pretty well, and can be reasonably compact provided most of the layouts and indexes are in referenced files, but inevitably they require edits in a number of places (usually only about 3 lines or blocks of lines) that need to be consistent else you don't get what you want.
refer to the relevant export statements.
It might be better to have multiple thconfig files, referencing the same sets of layout and index files as above, but avoiding the need to comment and uncomment so many lines. Anyway, if you can see what could be done better, or even just differently, add a page here, or make a suggestion on the forum.


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Five Useless Characters and How to Fix Them
Let's find the smallest edit that will get these protagonists contributing to the team.
Analysis, Agency, Characters
When your story is about a group of characters working toward a shared goal, it's important for everyone to contribute. If one character is off doing their own thing, they'll feel superfluous. Likewise, if two characters offer the same thing, one of them will almost always overshadow the other. Unfortunately, it's often difficult to make sure each character actually brings something useful and distinct to the table, especially in large casts. So today we're covering five notable examples of useless characters and looking for the smallest edit possible that would fix it. That's how I approach content editing, and it's a good skill for any writer working on revisions.
1. Neelix: Voyager
Neelix is one of the most annoying characters to ever grace speculative fiction TV, and there are several reasons for that. He's entitled, he flies into a rage at the slightest provocation, and the other characters have to explain jealousy to him like he's 10 years old. But the quality we're most interested in today is that Neelix contributes almost nothing to Voyager's journey through the Delta Quadrant.
You might not expect that because, to hear Neelix tell it, he does four separate jobs on the ship. He's Voyager's cook, guide, survival expert, and self-appointed morale officer. How can he not be contributing? The secret is that he can't actually do any of those jobs. Not even a little.
Voyager's most prominent running joke is that no one likes Neelix's cooking. There are occasional episodes that buck the trend,* but they're overwhelmed by scenes of everyone being grossed out by whatever bizarre concoction Neelix serves up that day. We also have multiple jokes about how gross his ingredients are, and at least one episode where his cheese makes the ship break down. Admittedly, I don't blame Neelix for that one; it's not his fault Starfleet built a lactose intolerant computer system.
Neelix can't guide Voyager through a field of dandelions, let alone the Delta Quadrant. One time, he leads the ship to a dilithium mining site, only for them to discover that there's no dilithium at all and it's a trap by organ-harvesting aliens. In another episode, his supposedly trustworthy contact immediately calls the cops on him. When he does have information, it's usually too vague to be helpful, and it's not long before Voyager leaves the part of space where he has experience anyway.
He's probably the worst as a survival expert. This skill doesn't come up often, but the one time it does, he gets a crewmate killed by not recognizing that a pile of bones outside a cave probably means there's a predator inside. His problems as a morale officer are self-explanatory: he can't raise anyone's morale because he's very annoying. Most of the time it comes across more like he's trying to bully the crew into acting happy.
How to Fix Him
Despite everything wrong with Neelix, he's very easy to fix: just make him good at some of his supposed jobs! Not all of them, mind you, as four separate roles* are too much for any character. But if he were a competent cook and a skilled guide, there'd be no problem.
Making Neelix a better guide would also solve another problem Voyager has: they often say they're low on one type of supplies or another, but we rarely see them actually replenish those supplies. If Neelix knew where to find those supplies, that would give a lot more weight to the idea that Voyager is operating far from home and without support. Plus, Neelix could still be good at finding replacement parts in scrap yards due to his background as a salvager, something that would be useful even after Voyager left his region of space.
We could even keep the occasional joke about bad food, but they would have to be rare and due to clear misunderstandings, like Neelix not being used to Alpha Quadrant gastronomy. As it is, Neelix often deliberately sabotages the crew's food orders based on what he thinks is best, and that's just not a good idea. Alternatively, we could actually have stories where Voyager is low on supplies and Neelix is making due with what little he has, but I don't want to be too ambitious here.
2. Leslie Vann: Lock In
John Scalzi's novel Lock In is about two FBI agents: protagonist Chris Shane and their* partner, Leslie Vann. Together they fight crimes! Specifically, they unravel a murder mystery involving a billionaire, disability advocates, body sharing, and a virtual-reality world called the Agora. Shane has plenty to do, which is good because they're the main character. Unfortunately, for most of the book, Vann can best be described as "around."
Shane handles almost all of the actual investigating, as they are much more physically capable than Vann. You see, Shane can remotely pilot robot bodies anywhere in the world, and they're rich enough to afford the best. Not only does this mean that Shane can galivant across the globe while Vann is stuck in Washington, DC, but it also means that Shane can get into fights without risking their personal safety.
So Shane does all the fight scenes and physical investigations, but maybe Vann can help with putting together the clues? No, there's a different side character for that. During the investigation, Shane meets a hacker named Tony. From that point on, Tony is the one in charge of connecting any clues Shane doesn't have time for. This turns out to be a lot because the bad guy's plan is absurdly complicated, but that's another article.
What does Vann actually contribute? Well, in a few scenes, she and Shane discuss what might be happening, which brings her up to the level of a glorified sounding board. She also participates in Shane's plan to trick the villain, but only after Shane has already set everything up and just needs someone to have a misleading conversation with.
Given all this, you could reasonably assume that Vann is a minor character, but she's not. She easily has more screen time than any character besides Shane, and the story makes a big deal about her tragic backstory. There's even a secondary antagonist out to ruin her reputation, though that plot never goes anywhere. Plus, Vann is actually the senior partner, with Shane having just graduated from FBI school.* This raises the expectations for her participation even higher, as she should have more experience than Shane does.
How to Fix Her
The good news is that as an experienced FBI agent, it's not difficult to find more ways for Vann to contribute. The simplest option would be for her to take over most of Tony's role in the story. There's really no reason to bring in a whole new character for hacking when you've got a perfectly good FBI agent right there. Just give Vann a few tech skills, say she specializes in electronic investigations, and you're set. If it's important for Tony to still be in the story, he can be one of Vann's contacts.
Another option would be to make Vann's backstory more important. Before joining the FBI, she was a professional integrator, someone who lets others experience life through her body. That's a neat scifi concept, and since the mystery plot involves several integrators, it could certainly be important, but it never is. The closest we get is when she tries to build rapport with a suspect through their shared professional experience, an attempt that immediately fails.
But there could easily have been more for Vann to contribute with her integrator expertise. Perhaps she has to go undercover in her old profession, letting the villain integrate with her so she can gather evidence. Or we might just let her actually build rapport with a fellow integrator. Any of these options would still leave Shane with the protagonist's share of the story's focus while allowing Vann to be something other than technically present.
3. Xander Harris: Buffy the Vampire Slayer
Xander is in a tough position in this vampire hunting TV show. He and Willow both start out as the normal kids who stumble onto Buffy's team, but while Willow's usefulness continues to grow until she's actually overpowered, Xander's stays almost the same for seven seasons. That is to say, he's completely useless. Unless the good guys ever find a magical weapon powered by sarcasm, I guess.
The main reason is that there aren't any obvious ways for him to contribute. The characters' shared goal is fighting monsters, and all the obvious jobs are already taken. Buffy is the main fighter, occasionally backed up by Angel, Faith, or Spike when they aren't being evil. Giles does the research, sometimes with Willow's help. Anya has her old demonic contacts. Willow and Tara handle the magic, and there are a host of characters who've got the "monster on team good" angle locked down. Even Dawn, another perpetually useless character, has a side gig as the MacGuffin in season five. There are even entire episodes about Xander feeling useless,* but while they often give Xander more candy, they never give him more to contribute.
The writers seem aware of this problem, and I think their intent is for Xander to be the team's moral support character, providing insights to help other characters on their journeys. That would make him similar to Guinan on TNG or Iroh for much of Avatar. As evidence, I present this exchange from the season seven episode Potential:
Xander: They'll never know how tough it is, Dawnie, to be the one who isn't chosen. To live so near to the spotlight and never step in it. But I know. I see more than anybody realizes because nobody's watching me. I saw you last night. I see you working here today. You're not special. You're extraordinary.
Dawn: Maybe that's your power.
Xander: What?
Dawn: Seeing, knowing.
Xander: Maybe it is… Maybe I should get a cape.
The problem with this idea is that it's not actually present in the show. Xander almost never helps another character with their problems. Other than the above quote, the closest moment I could think of is in season four, when Xander tells Buffy to go after her soon-to-be ex-boyfriend Riley. This is terrible advice, as Riley and Buffy clearly don't work as a couple, and it only seems to be there so Buffy will feel worse when she doesn't arrive at the helipad in time. There might be a few other instances scattered across the show's 144 episodes, but when a character actually needs emotional support, they usually go to someone like Giles or Tara.
So what would it take for Xander to actually be the emotional support character he's apparently supposed to be? For one thing, he'd have to be less of a creep. Granted, that's something I'd change regardless, but it's even more important if Xander is going to help other characters with their problems. There's no room for him to get mad over Buffy not dating him if he's the one she's supposed to turn to for help.
More fundamentally, Xander would need to be more emotionally mature, and I suspect this would be the sticking point. In addition to self-deprecating jokes, not understanding how other characters feel is a big part of Xander's comedy routine. While emotional support characters don't always have to be wise and spiritual, they do have to be insightful, something Xander specifically isn't.
That's why if I were content editing Buffy the Vampire Slayer, I'd make Xander the team's crafter. This is something the good guys don't already have, and it would be very useful. We even see hints of it in season seven, when Xander adds some modest fortification to Buffy's house. These are almost comically useless, but they show what could have been. Buffy and her comrades are in constant need of new weapons, which they currently pull from the ether. But if Xander took up smithing and got serious about carpentry, he could be the one arming the slayer while also making it harder for the bad guys to break in after sundown.
4. Charles Gunn: Angel
Moving on to Buffy's dark and gritty(ish) spin off, we meet Charles Gunn, a young man who fights vampires on the streets of LA. Originally, Gunn actually leads his own team of vampire hunters, but it's not long before that gig peters out and he becomes a full-time member of Angel Investigations. That's too bad for Gunn, as it's immediately apparent he has nothing to do there.
Like its parent show, Angel's main cast is clearly delineated in its roles. Angel does the fighting, Wesley and Fred do the researching, and Cordelia has her visions. Gunn's most obvious skill is fighting, which puts him at war with Angel for screen time. Pro tip: it's never a good idea to be competing with the titular character for screen time. Gunn doesn't have superstrength; Angel does. You can guess who makes the real difference in fights, leaving Gunn to throw an occasional backup punch.
However, Gunn does have another skill: knowing what's happening in LA's street scene. Unfortunately, he only knows what's going on in LA's human street scene. This is an urban fantasy show about fighting monsters; no one cares what the humans are doing! Whenever team good needs to get information, they go to Lorne, the green-skinned lounge singer with his ear to the demonic grapevine.
As with Xander, it's clear that Angel's writers know Gunn has a problem. In season five, feeling useless to the team, Gunn strikes a magical bargain to gain lawyer skills. Unfortunately, this turns out to be a temptation arc that resolves with Gunn giving his skills up and going back to being useless. Sigh. It's always frustrating when writers lampshade an issue instead of fixing it.
Like with Xander, the most immediate option is to take the show's own material and run with it. Giving Gunn lawyer skills is a great idea. It would not only allow him to contribute more, but it would also let Angel expand into more legal drama. There's a surprising lack of legal drama in this show, considering that the main bad guy is a prestigious law firm.
The trick is that Gunn's skills need to be genuine, and he needs to get them earlier. The simplest option is for him to simply be a lawyer. Perhaps after law school, he found out that his old neighborhood was under attack by vampires, so he came back to help. That preserves Gunn's introduction as a street fighter, and then allows him to contribute once he's joined Angel Investigations.
This leaves us one problem though: the Angel writers probably weren't interested in legal dramas, or they'd have added some. To make Gunn more useful without disrupting the show's formula, he'll need a magic power of some sort, but not to make him better at fighting. Believe it or not, the writers actually add another superpowered fighter in season two, and he's quickly sidelined in favor of Angel until he leaves in season three.*
Instead, I would give Gunn the power to heal others. It doesn't matter where he gets the power from; maybe a magical artifact exploded near him and he woke up with healing hands. This would not only give Gunn a way to contribute that doesn't compete with another character, but it would answer the question of how Angel's good guys are always ready to fight after getting beaten up in the previous episode.
5. Finn: Star Wars Episodes VII-IX
Poor Finn is one of many casualties from Disney's inexplicable decision not to plan its Star Wars sequel trilogy ahead of time. Finn does okay in The Force Awakens, where he teams up with Rey to get BB8 back to the Rebellion. Excuse me, I mean the Resistance. Very different. After that, his knowledge of Starkiller Base is useful, in terms of both planning the space battle and rescuing Rey. He even gets into a sword fight with Kylo Ren, which is pretty cool.
Things really go wrong in The Last Jedi, when Finn is sent off on a side quest for half the movie. Most of this side quest is taken up by how unjust Canto Bight's wealth distribution is, which could be a great story in a different movie. In this movie, it's got nothing to do with the main plot, which is the Resistance fighting the First Order. After wasting all that time, Finn is finally able to secure a tech expert who can hopefully stop the First Order from tracking the Resistance through hyperspace. This plan completely fails and results in most of the Resistance getting killed as the bad guys pick off their escape ships. Oof.
That is a real low point for Finn. Naturally, he'll get a big moment later to make up for it, right? It looks like he will, as he lines up for a heroic sacrifice to stop the First Order's army, but then another character gets in the way, which has to be one of Last Jedi's most baffling moments. I think the message is supposed to be that you shouldn't be eager to throw your life away, but in the context of that scene, everyone will die if he doesn't. I also don't want Finn to die, but that's the situation the film created. Instead, Finn is left to stew with all the Resistance fighters who died because of his side quest.
Then The Rise of Skywalker rolls around and makes us long for the days that Finn was relegated to unrelated side quests. Finn's most significant contribution to this film is having something he wants to tell Rey, but then not telling her. Did they think I was gonna buy a tie-in comic to find out about that? Cause I'm not. Okay, to be completely fair, he does also lead an assault on the bad guy's navigation buoy, but the movie's almost over by then. It's also impossible to tell how important the buoy is because Rise of Skywalker's final battle seems purposely designed to be confusing. If Finn had done nothing, would Lando's fleet still have arrived and wiped out all the Star Destroyers? I legitimately don't know.
Other than that, Finn's main contribution is firing off a few blaster bolts, something everyone else does too. I guess he also yells Rey's name a lot? Heck, C-3PO has more to do than Finn. That's really disappointing for a character who was originally pitched as one of the big three in this new trilogy.
Why did this happen? Racism probably, but also because neither Last Jedi nor Rise of Skywalker have any room for Finn's most obvious plot: inspiring a stormtrooper rebellion. As a former stormtrooper himself, that's where it looked like Finn was going. He even meets others with a similar backstory in Rise of Skywalker. It just doesn't go anywhere. At this point, doing a stormtrooper rebellion justice would require significant rewrites, so what can we do while keeping the films' existing shape?*
A common idea is that Finn should also go through Jedi training, as he's clearly Force sensitive. That's a possibility, but it would risk making him compete with Rey for screen time and relevance, as they'd be doing the same thing. To avoid that, their arcs would need to either play off or contrast with each other, which requires more significant rewriting. One option that quickly comes to mind: maybe Rey is in danger of going dark, and Finn is the one who pulls her back? Unfortunately, that would likely interfere with Kylo's redemption* arc. These films have so much going on that it's difficult to find ways to improve them. If I were hired to do a content edit on them, I'd probably say that the writers need to work on figuring out what their stories are actually about before any other progress could be made.
However, I do have one relatively painless option to help Finn contribute to the plot: give him the leadership arc instead of Poe. Poe is an ace pilot, which means he'll always have plenty to do in a Star Wars movie. He doesn't need command skills to properly contribute. Finn definitely does though, as by default he's just a guy with a blaster. If Finn is the one giving the orders, then his stormtrooper background would also be more relevant, as it would help him predict the First Order's tactics and counter them. This would be even better if stormtroopers were a real threat and not easily dispatched cannon fodder, but let's not get too ambitious.
Whew, that was a lot of editorial theorizing for one post. Of course, in a real content edit, we'd also have to contend with the author's goals and how compatible they were with a good story. Even so, this type of exercise is useful because it helps us look at stories as complex machines rather than unknowable enigmas. If one piece isn't working, sometimes you can fix or replace it without taking the whole engine block apart. That's a particularly useful approach for characters who aren't contributing enough, as often all you need to do is give them a new power or skill set.
The 37's is the only one I could find.
Plus a few more that I didn't have time to mention.
Chris's gender and pronouns are never given, which is pretty cool.
That's Quantico to you FBI nerds.
The Zeppo and The Replacement come to mind.
Farewell, Groo.
I don't have any attachment to the new trilogy as it is, but for the sake of the exercise.
For lack of a better word.
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Comments on Five Useless Characters and How to Fix Them
I felt really bad for Rose in TLJ too. It almost feels like they made her useless and annoying on purpose, and then RoS basically forgot she existed.
I disagree about Nelix being useless. It's been a while since I saw the series but I remember a few times his knowledge of the peoples in the area came in handy. I remember an episode where they're on-planet looking for supplies and someone hands him "some kind of apple". Nelix then tells him that one bit could kill him.
And despite the "bad" cooking, no one else stepped up to take over and people were still complaining about the food after he left. Remember the episode Tuvix when there were several crewmen trying to cook and making a mess of things until Tuvix came in and cleared everyone out to do it himself? Nelix was a dang good sport about the insults to his cooking by a bunch of spoiled crewmates who didn't like their food replicator usage limited. He did a great job given what he had available.
Semi-counterpoint, real life is often filled with people that are useless in a given situation but can't just leave for one reason or another. Many of us might have been this useless person at one time or another. Having a useless character does add a certain realism.
In reply to Esq
Arix
Counter-semi-counterpoint, as has often been discussed including on this very blog, realism is rarely if ever a good justification for doing something in a story, because stories should be narratively satisfying but real life rarely is.
Koconut
I'm with Arix on this one! Even realistic art tends to act as a focused facsimile of real life, with a message or an impression.
Having a useless character works when it's done with intention and payoff. Sokka from A:tLA frequently laments how useless he feels, and is often relegated to "sarcasm funny guy," but he's also given a character arc that shows he's more than that, as well as direct contributions to the plot, comedy relief, and character interactions — and not through contrivance, like the above examples!
In reply to Koconut
Sokka may feel useless because he doesn't have cool powers like his fellows, but as you mentioned, he actually isn't useless since he makes plot contributions – logistics, planning, even inventing devices sometimes. Those contributions are what we're talking about in posts like these.
Dave L
Easy way to fix a useless character:
Get rid of them altogether
Kill them early or just never introduce them. Or just have them not show up and nobody misses them
The more useless the character is, the easier the rewrite will be
I know this isn't always an option, but sometimes a character just isn't worth fixing
Of course, if the useless person is the only, or one of the few, POC, (as in two out of the five examples) then, yeah, maybe try a different fix first
In reply to Dave L
Star of Hope
You could have the character be in a certain situation useless or in the beginning not really that useful and they develop a new skill to become more useful. Take for instance Superman, he cannot do anything with Kryptonite and needs the help of others to save the day. This also works with the many He-Man shows , where He-Man has not the power of Grayskull and his friends have to help him. Speaking about He-Man, the recent Netflix show "Masters of the Universe:Revelation" has a character named Orko, who was so bad at magic, every spell failed and ended up causing more trouble. Then he became much better in magic and actually saved the group. I won't spoil much,, but just watch it.
Another good example is something of both like Rutherford in Lower decks, where he no longer wanted to be engineer and wanted to do a new job on the ship. He failed at being a ships Captain and doctor, but found out that he was good as a security guard. The episode ends with him returning to his old job, but in a different story, this would be the start of something new.
DeepSpacer
I said it at the beginning. Poe and Finn can easily be combined into one, main character. In TFA, Finn could've done it all from the beginning. Absolutely no need for Poe in any part of that film. Actually, I would say that Poe, and not Finn, is the useless character in the story. Finn and Rey actually had chemistry.
Why Disney had to switch directors is beyond me. Abrams, Johnson, Abrams again– what was the thinking there? Two different directors means two different visions means two different plots means that there's no way they're keeping track of the side characters' arcs. Poe suffered from a lot of FInn's same issues, too, in TLJ his job is primarily to cause problems for Holdo.
In reply to Evan
As best I can figure they imagined that each director would build upon what the previous one did (originally Episode IX was supposed to be Colin Trevorrow) while bringing their own style. That can absolutely work but there needs to be a unifying thread to keep them together and the new trilogy simply doesn't have one.
That's true. I did like some of the things Rian Johnson brought into the Star Wars world (making Rey's parents nobodies felt a little more rewarding than another magic force dynasty), and Kylo's redemption felt much more real the first time– but he tried to hard to make a different show than J. J. Abrams did, forcing Abrams to re-remake the trilogy…
Rey Nobody was a great decision.
The point of Finn's side quest was to transform him into a true rebel. He almost gets there on his own – but still wants to hurt the badguys for the sake of causing pain to those who hurt him and his friends. Rose's final line mirrors the message the film wanted to give – Luke wins through sparing every life present rather than tearing their machines all apart or killing Kylo Ren. Or a single trooper.
I could agree it's not handled smoothly, but that was my take from it. The most offensive scene to me in the whole of RoS was Finn and Poe blasting troopers as they race to escape Kylo Ren's destroyer. No sparing of life. Message lost. No plan amongst the directors or other creators. Oh well…
In reply to Jonathan
They blew it. TLJ wasn't perfect, but it was a story with a direction– ROS tried to change that direction when it was too late.
Can I add my list of useless character?
It's Clay from Xiaolin Showdown:
In this avatar-esque show with children having each power over 1 of the 4 elements in a setting that takes inspiration from east asian (mainly Chinese culture) culture and aesthetics with a lot of western flare as well. It is basically a show that revolves around McGuffins called Sheng Gong Wu with amazing power like twisting your body parts, creating storms or shooting lasers and enhancing elemental powers. They are won in a contest called Xiaolin Showdown, which is basically Kung Fu Mario party, it's very entertaining.
There we have the only White team member of the good guys, Clay Bailey! He can control the Earth and is generally characterized as a strong musclely big guy from Texas, who can penetrate a valley and shake the Earth. The problem is that his physical strength is outshines by his other teammates like Omi, who is in generally the most experienced and perhaps strongest fighter, something he has not been humble off at all. Kimiko is also more gifted in Combat and a tech genius, who can come up with clever plans. Then we have our wildcard Raimundo, who while starting out as quite rebellious became such a competent teamleader, he upstaged Omi's role as the central protagonist of the story in the end and was before that a skilled and cunning fighter, which made him more dangerous than Omi. Clay's strength came only in some episodes handy and in comparison to his teammates, he falls much quicker in battle and has overall the least amounts of victory, only having participated in like 3 Xiaolin showdowns alone and won, whereas his friends won more than that. He also was a bit of a sexist in the beginning, refusing to hurt girls, even if they are evil. Overall a mediocre to useless companion to have.
They could have fixed that by giving him more victories and plot relevance. They could have made him participate in strength based contests more, where he is undoubtedly unmatched in such battles or where they need to get rid of huge obstacles. This would have cemented his role of the big guy, which is what the show was poorly attempting to go far with him.
Now we have Quinn from Final Space.
In the first season, she was relatively useful and actually helped in the final season to stop the rift from the final space to open by sacrificing herself with a piece of final space and ended up in said space, thus starting the story arc of the second season to get into Final space to save her. Once Gary and his friends found her in Final space in season 3…she hardly contributes to the story at all. Most of it revolves around Gary and Ash with their personal conflict and thus she had very little to do in the story. She tried to stop the evil Invictus to break free from his prison, while almost undoing the sacrifice of Clarence, who sacrificed his life to help the crew to leave this dimension as repentance for his betrayal of that group in season 2. Thus they do not leave final space and activate the KVN net, but it fails and after she tried to recharge the dimensional gate, it ends in a failure, which contributed to Ash's growing dislike towards her.
They could have made her a bit more competent or better, having the KVN net work and dealing a huge blow to Invictus instead of failing. The true problem is something different and this should be discussed on a different article.
And finally almost every dragon ball character ever and it needs no explaining why it is that way and how to fix it, due to cultural osmosis and simple logic telling you everything you need to know.
How did you find that list? Was is good or did I missed something? Tell me in the comments below!
Thank you for bringing up the issues with Gunn. He was the reason I wanted to even watch Angel, and watching the creators just drop the ball with him constantly is still a sore spot.
While I agree that LA's human street scene clearly wasn't important to the writers, it still had a lot of potential. Having occasional human antagonists would out Team Angel on a whole different playing field.
Even the fact this was Los Angeles (a major metropolitan area vs a small town like Sunnydale) could have lead to a lot more possibilities and threats to Team Angel. In fact, if I'm not mistaken, none of the main cast besides Gunn and Lorne would even be familiar with LA all that much. So why not make him a guide? Hell, use the same "survival expert" fix from Neelix, since he's shown as not only a resident but from the wrong side of the tracks as well.
Hell, even his initial backstory as a leader of vampire hunters and his status as a regular human fighter could still work if they had him lean more into strategy and guerilla warfare. Have him be the Lancer to Angel, pointing out flaws in the latter's dependency on his vampire physiology to muscle his way through challenges. Make him the guy who is used to fighting physically stronger opponents, who find more asymmetrical paths to victory. This would even help tie him into the legal thriller aspect, because it would highlight how the situation just can't be solved with punching sometimes.
I would disagree about Xander. He does a few things.
First, he's a normal person, with a normal person's understanding of the world. He doesn't understand demons, vampires, Slayers, magic, etc. So he serves a narrative purpose by presenting the writers with a way to explain things in-universe. This is a common enough use for a character–see Tolkien's explanation of the hobbits. Willow and Buffy did the same thing, but they have different perspectives (Willow as a mage and Buffy as the Slayer); neither could give the perspective of the average every-day person.
Second, he creates drama. His attraction to various characters creates inter-personal drama, which affects the fight-bad-guys bit and creates tension during non-combat periods. Okay, it's not a great purpose to have, but without Xander the show could have easily devolved into a plodding supernatural procedural drama. The show focused a lot on interpersonal drama as much as on beating up monsters, so it fit narratively.
Third, he sometimes acted as a damsel in distress. He didn't have supernatural powers, so he got beat up, captured, and otherwise tormented quite a bit. Again, this created drama and tension that would otherwise be lacking. It allowed relatively low-level threats to actually have consequences. Let's face it, the monster-of-the-week isn't going to do much against the more powerful people; by focusing on Xander the random mooks could realistically attempt to hurt the Scooby Gang. It limited the options of the more powerful characters in ways that didn't appear forced.
Fourth, he was an effective member of the team in many situations. He had a perspective the rest lacked, which often did help ("This isn't riding around with your friends dead" is a great line). And he had the most room to grow. Xander of later seasons was not Xander of Season 1 by an stretch. Again, this creates narratives that would otherwise not be possible.
Maybe the show didn't use Xander effectively. I was never a huge fan, so I don't really remember. But I don't think it's fair to classify him as useless.
If Finn is the one giving the orders, then his stormtrooper background would also be more relevant, as it would help him predict the First Order's tactics and counter them.
That sounds good. It's also a way of letting him partner up with Leia as a general without one of them overshadowing the other, because it accounts for different knowledge bases.
Interestingly/even more frustratingly, the Last Jedi included what looks like the beginning of an inspiration arc. At the beginning of Finn's confrontation with Phasma, she's accompanied by four troopers – Finn calls her on the fact that she sold out Starkiller base once her own life was on the line – Phasma sees the troopers exhanging glances and shoots them all. But this was cut in the theatrical release.
(A moment I really really wanted in Rise of Skywalker was something like this; Finn and Kylo Ren fighting in a First Order facility, with Kylo getting upper hand, until:
Finn: "It doesn't have to be this way. You can choose better, like I did."
Kylo: "My father couldn't turn me. Rey couldn't turn me. You think you'll be the one?"
Finn: "I wasn't talking to you."*
Stormtrooper shoots Kylo: "We're with you, sir."
As well as where Finn seemed to be going, it would also fulfill the democratisation that was going on in Last Jedi – with Rey Nobody and Broom Kid – a redemption arc for (some of) the stormtroopers suits better than reserving it for the "officer class" or members of important bloodlines – plus the climax of the Last Jedi looked like it was slamming the door pretty hard on Kylo being redeemable (using a literal door to underscore the point).
And Kylo going down to stormtroopers would be a parallel to Palpatine going down to Vader. (Even if he did come back, which I think I'm one of the five people in the world to actually like).
* I'm a sucker for that line.
Re Charles Gunn:
Something else he could have been is an investigator. True, they are all investigators on one level, but they're investigators in the sense of knowing about demons and having contacts in the demon demimonde. But Gunn could have been someone who knows how to work a crime scene, and knows the layout and history of the city. Investigation is a skill set rather than just intelligence (even Sherlock Holmes described his mind as quite ordinary).
In reply to SunlessNick
I like that stormtrooper redemption arc instead of one for Kylo (who had oodles of choices and blew them). I think it would work especially well as the stormtroopers, like Finn, were essentially child soldiers who grew into their job. It's not as if they were adults who decided that they'd rather serve the first order. Finn gives them a way out, an inspiration for a better life, so why wouldn't at least some choose that?
One way to fix a useless character is to take his most interesting traits and composite them into another more purposeful character
Rey and finn being one character would have solved so many problems with TFA and TLJ that it wouldn't even be funny.
Rose tico and Poe Cameron would go to canto bight, where Rose reminds Poe about why they fight the first order, while finn develops feelings for Kylo
In reply to Steven
It's interesting that you would combine Rey and Finn into Finn, not Rey…
Sedivak
I have only seen the first movie of the new trilogy but from that I would say that Finn was interesting due to his stormtrooper background and him having to adapt to a completely oposite role, gaining trust of the resistance, proving himself etc. Rey was just sort of … there – not a bad character but overshadowed by Finn in terms of viewer expectations. At least that was what I took away from it.
In reply to Sedivak
There are additional female stormtroopers to Plasma, so why not have a female stormtrooper? Finn's background, but another level by having a woman in the role.

redpajama_set_name: RedPajamaCommonCrawl


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text:
\section{Introduction }
Schwinger's original nonet mass formula \cite{Sch} (here the symbol for the
meson stands either for its mass {\it or} mass squared),
\beq
(4K-3\eta -\pi )(3\eta ^{'}+\pi -4K)=8(K-\pi ) ^2,
\eeq
and the Sakurai mass-mixing angle formula \cite{Sakurai},
\beq
\tan ^2\theta =\frac{4K-3\eta -\pi }{3\eta ^{'}+\pi -4K},
\eeq
both relate the masses of the isovector $(\pi ),$ isodoublet $(K)$ and
isoscalar mostly octet $(\eta )$ and mostly singlet $(\eta ^{'})$ states of a
meson nonet, and the nonet mixing angle $(\theta ).$ We alert the reader that,
although we use notation suggestive of masses below, each formula is to be
reprised in terms of mass or mass squared values in this introductory section.

The relations (1) and (2) are usually derived in the following way:
For a meson nonet, the isoscalar octet-singlet mass matrix,
\beq
{\cal M}=\left(
\begin{array}{cc}
M_{88} & M_{89} \\
M_{89} & M_{99}
\end{array}
\right ) ,
\eeq
is diagonalized by the masses of the physical $\eta $ and $\eta ^{'}$ states:
\bqry
{\cal M} & = & \left(
\begin{array}{rr}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{array}
\right) \left(
\begin{array}{cc}
\eta  & 0  \\
0 & \eta ^{'}
\end{array}
\right) \left(
\begin{array}{rr}
\cos \theta & -\sin \theta \\
\sin \theta & \cos \theta
\end{array}
\right)   \NL
 & = & \left(
\begin{array}{cc}
\cos ^2\theta \;\eta +\sin ^2\theta \;\eta ^{'} & \sin \theta \cos \theta \;\!
(\eta ^{'}-\eta ) \\
\sin \theta \cos \theta \;\!(\eta ^{'}-\eta )  & \sin ^2\theta \;\eta +\cos ^2
\theta \;\eta ^{'}
\end{array}
\right) ,
\eqry
where $\theta $ is the nonet mixing angle, which is determined by comparing
the corresponding quadrants of the matrices (3) and (4), by any of the three
following relations:
\beq
\tan ^2\theta =\frac{M_{88}-\eta }{\eta ^{'}-M_{88}},
\eeq
\beq
\tan ^2\theta =\frac{\eta ^{'}-M_{99}}{M_{99}-\eta },
\eeq
\beq
\sin 2\theta =\frac{2M_{89}}{\eta ^{'}-\eta }.
\eeq
It is easily seen that Eqs. (5) and (6) are identical, since, due to the trace
invariance of ${\cal M},$
\beq
\eta +\eta ^{'}=M_{88}+M_{99},
\eeq
and therefore, $M_{88}-\eta =\eta ^{'}-M_{99},$ and $\eta ^{'}-M_{88}=
M_{99}-\eta .$ Eliminating $\theta $ from (5),(7), or (6),(7), with the
help of $\sin 2\theta =2\tan \theta /(1+\tan ^2\theta ),$ leads, respectively,
to
\beq
(\eta -M_{88})(M_{88}-\eta ^{'})=M_{89}^2,
\eeq
\beq
(M_{99}-\eta )(\eta ^{'}-M_{99})=M_{89}^2,
\eeq
which again are identical, through (8).

We note that, under the quark model inspired conditions
\beq
M_{88}=\frac{4K-\pi }{3},\;\;\;M_{99}=\frac{2K+\pi }{3},\;\;\;M_{89}=-\frac{
2\sqrt{2}}{3}(K-\pi ),
\eeq
where the first of the three relations in (11) is the standard
Gell-Mann--Okubo mass formula \cite{GMO}, Eqs. (9),(10) have the
effectively unique solution
\bqry
\eta & = & 2K-\pi ,\;\eta ^{'}\;=\;\pi ,\;\theta \;=\;\arctan \frac{1}{\sqrt{
2}}\;\cong \;35.3^o,\;\;{\rm or}  \\
\eta & = & \pi ,\;\eta ^{'}\;=\;2K-\pi ,\;\theta \;=\;-\arctan \sqrt{2}\cong
-54.7^o,
\eqry
which corresponds to the ``ideal'' structure of a meson nonet.

For all well established meson nonets, except the pseudoscalar (and, we expect,
scalar) one(s), both linear and quadratic versions of Eqs. (5)-(10) are in good
agreement with experiment. For example, for vector mesons, if one assumes the
validity of the Gell-Mann--Okubo formula $\omega _8=(4K^\ast -\rho )/3,$ then
one obtains from Eq. (9) with the measured meson masses \cite{pdg}, $M_{89}=
-0.209\pm 0.001$ GeV$^2$ in the quadratic case, and $-0.113\pm 0.001$ GeV in
the linear case. Note that this is entirely consistent with $-0.196\pm 0.005$
GeV$^2$ and $-0.118\pm 0.003$ GeV, respectively, which follow from the third
element of (16). For tensor mesons, a similar comparison gives
$-0.305\pm 0.020$ GeV$^2$ vs. $-0.287\pm 0.015$ GeV$^2,$ and $-0.105\pm 0.008$
GeV vs. $-0.104\pm 0.005$ GeV, respectively.

However, for the pseudoscalar nonet, one obtains from Eq. (5) with meson masses
squared, $\theta \approx -11^o,$ in sharp disagreement with
experiment, which favors the $\eta $-$\eta ^{'}$ mixing angle in the vicinity
of $-20^o$ \cite{pdg,data,Abele}. Although using linear meson masses in Eq. (5)
does give $\theta \approx -24^o,$ in better agreement with
data than its mass-squared counterpart, the value of $M_{89},$ as given by (9),
is now $-0.165\pm 0.004$ GeV, vs. $-2\sqrt{2}/3\;(K-\pi )=-0.338\pm 0.004$ GeV.
This emphasizes that neither Schwinger's nonet mass formula nor the mass-mixing
angle relations (including Sakurai's) (5)-(7) hold for the pseudoscalar nonet.

It is well known, however, that the pseudoscalar (and, probably, scalar) mass
spectrum does not follow the ``ideal'' structure, Eq. (11), since the mass of
the pseudoscalar isoscalar singlet state is shifted up from its ``ideal''
value of $(2K+\pi )/3,$ presumably by the instanton-induced 't Hooft
interaction \cite{tH} which breaks axial U(1) symmetry
\cite{symbr,Dmitra,Dmitra2}. However, the use of $M_{99}=(2K+\pi )/3+A,$ $A\neq
0,$ in Eqs. (5)-(8) will again lead to Schwinger's formula (9), which does not
hold for the pseudoscalar mesons, as just demonstrated. [In fact, the
structure of this formula does not depend at all on $M_{99},$ as seen in (9).]
Therefore, instanton, as well as any other effects which may shift the mass
of the pseudoscalar isoscalar singlet state, cannot constitute the explanation
of the failure of Schwinger's quartic mass and the Sakurai mass-mixing angle
formulae for the pseudoscalar nonet. We believe, however, that the following
analysis can resolve this problem.

\section{Pseudoscalar meson mass squared matrix}
Here we suggest the following form of the mass squared matrix for
the pseudoscalar mesons:
\beq
\bar{f}^2M^2=\frac{1}{3}\left(
\begin{array}{cc}
4f_K^2K^2-f_\pi ^2\pi ^2 & -2\sqrt{2}\;(f_K^2K^2-f_\pi ^2\pi ^2) \\
-2\sqrt{2}\;(f_K^2K^2-f_\pi ^2\pi ^2) & 2f_K^2K^2+f_\pi ^2\pi ^2+3f_9^2A
\end{array}
\right) ,
\eeq
where $f$'s are the pseudoscalar decay constants defined below, and $A$ stands
for the sum of all possible contributions to the shift of the isoscalar
singlet mass (from instanton effects, $1/N_c$-expansion diagrams, gluon
annihilation diagrams, etc.).

Indeed, the form of such a mass squared matrix is determined by the form of
Gell-Mann--Okubo type relations among the masses of the isovector, isodoublet,
and isoscalar octet and singlet states (which in our case are Eqs. (17)-(19)
below), since this matrix must be equivalent to that of the form (3), which in
the case we are considering is
\beq
\bar{f}^2M^2=\left(
\begin{array}{cc}
f_8^2\eta _{88}^2 & f_8f_9\eta _{89}^2 \\
f_8f_9\eta _{89}^2 & f_9^2\eta _{99}^2
\end{array}
\right) ,
\eeq
and which we assume is diagonal in the basis of the physical $\eta $
and $\eta ^{'}$ meson masses and decay constants:
\beq
\bar{f}^2M^2=\left(
\begin{array}{cc}
f_\eta ^2\eta ^2 & 0  \\
0 & f_{\eta ^{'}}^2\eta ^{'2}
\end{array}
\right) .
\eeq
The equivalence of the matrices (14) and (16) is guaranteed by the validity of
the following relations:
\beq
f_8^2\eta _{88}^2=-\frac{1}{3}\left[ m_u\langle \bar{u}u\rangle +m_d\langle
\bar{d}d\rangle +4m_s\langle \bar{s}s\rangle \right] =\frac{4f_K^2K^2-f_\pi ^2
\pi ^2}{3},
\eeq
\beq
f_8f_9\eta _{89}^2=-\frac{\sqrt{2}}{3}\left[ m_u\langle \bar{u}u\rangle +m_d
\langle \bar{d}d\rangle -2m_s\langle \bar{s}s\rangle \right] =\frac{2\sqrt{
2}}{3}\left( f_\pi ^2\pi ^2-f_K^2K^2\right) ,
\eeq
\beq
f_9^2\eta _{99}^2=f_9^2A-\frac{2}{3}\left[ m_u\langle \bar{u}u\rangle +m_d
\langle \bar{d}d\rangle +m_s\langle \bar{s}s\rangle \right] =f_9^2A\;+\;\frac{
2f_K^2K^2+f_\pi ^2\pi ^2}{3},
\eeq
with
\beq
K^2\equiv \frac{(K^\pm )^2+(K^0)^2}{2},
\eeq
as suggested by Dmitrasinovic \cite{Dmitra2}, on the basis of the (precise)
Gell-Mann--Oakes-Renner formulae which relate the pseudoscalar
masses and decay constants to the quark masses and condensates \cite{GOR}:
\bqry
f_\pi ^2\;\pi ^2 & = & -\left[ m_u\langle \bar{u}u\rangle +m_d\langle \bar{d}d
\rangle \right] , \\
f_K^2\left( K^\pm \right) ^2 & = & -\left[ m_u\langle \bar{u}u\rangle +m_s
\langle \bar{s}s\rangle \right] , \\
f_K^2\left( K^0\right) ^2 & = & -\left[ m_d\langle \bar{d}d\rangle +m_s\langle
\bar{s}s\rangle \right] .
\eqry
(We ignore Dashen's theorem violating effects \cite{Dash}, and only
approximately take into account isospin violating effects via (20), as we are
not concerned here with accuracies better than 1\%.)

Note that in the limit of exact nonet symmetry,
\beq
f_\pi =f_K=f_8=f_9\equiv \bar{f},
\eeq
the mass squared matrix (14) reduces to (3) with the matrix elements defined
in (11) and an additional contribution in the isoscalar singlet channel $(A).$

\section{Modified Gell-Mann--Okubo mass formula}
Here, we shall only explicitly demonstrate the validity of the modified
Gell-Mann--Okubo formula (17) (the remaining relations (18) and (19) may be
checked in a similar way). This formula may be obtained in standard chiral
perturbation theory \cite{GL}, as follows.

Standard chiral perturbation theory leads to the following expressions for
the pseudoscalar meson masses and decay constants~\cite{GL}:
\bqry
\pi ^2 & = & 2m_nB\left( 1+\mu _\pi -\frac{1}{3}\mu
_8+2m_nK_3+(2m_n+m_s)K_4\right) , \NL
K^2 & = & (m_n+m_s)B\left( 1+\frac{2}{3}\mu _8+(m_n+m_s)K_3
+(2m_n+m_s)K_4\right)
, \NL
\eta _{88}^2 & = & \frac{2}{3}(m_n+2m_s)B\left( 1+2\mu _K-\frac{4}{3}\mu _8
+\frac{2}{3}(m_n+2m_s)K_3+(2m_n+m_s)K_4\right) \NL
 & + & 2m_nB\left( -\mu _\pi+\frac{2}{3}\mu _K+\frac{1}{3}\mu _8\right) +
B(m_s-m_n)^{2}K_5, \NL
f_\pi & = & \bar{f}\Big( 1-2\mu _\pi-\mu _K+2m_nK_6+(m_n+2m_s)K_7\Big) , \NL
f_K & = & \bar{f}\left( 1-\frac{3}{4}\mu _\pi -\frac{3}{2}\mu _K-\frac{3}{4}
\mu _8+(m_n+m_s)K_6+(m_n+2m_s)K_7\right) , \NL
f_8 & = & \bar{f}\left( 1-3\mu _K+\frac{2}{3}(m_n+2m_s)K_6
+(m_n+2m_s)K_7\right) ,
\eqry
where $\mu $'s are chiral logarithms, and the constants $K_i$
are\footnote{We have extracted factors absorbed into $K_{4}, K_{5}$ and
$K_{7}$ in ref. \cite{GL}, to make uniformly explicit the quark mass
factors and the overall scale.} proper combinations of the low energy
coupling constants $L_i.$ It then follows from these relations that the
standard Gell-Mann--Okubo formula is broken in first nonleading
order~\cite{GL},
\bqry
\triangle _{{\rm GMO}} & \equiv  & 4K^2 -3\eta_{88}^2 -\pi^2 \NL
 & = & 4B\Big[ m_n(\mu _\pi +\mu _8-2\mu _K)+2m_s(\mu _8-\mu _K) \Big] +\ldots
\;,
\eqry
where $\ldots $ indicates higher order terms.

However, the modified Gell-Mann--Okubo formula remains valid in this
order, and is violated only by second (non-leading) order SU(3)-flavor
breaking effects:
\bqry
\triangle ^{'}_{{\rm GMO}} & \equiv & \frac{1}{{\bar f}^2}\left( 4f_K^2K^2-
3f_8^2\eta _{88}^2-f_\pi ^2\pi ^2\right)  \NL
 & = & 4B\;(m_s-m_n) \left[ \left( \mu_K+\frac{1}{2}\mu_8 -\frac{3}{2}\mu_\pi
\right) \right.  \NL
 & &  \left. -\;(m_s-m_n)\left(\frac{1}{3}K_{3}+\frac{3}{4}K_{5}
+\frac{2}{3}K_{7}\right) \right] +\ldots \;,
\eqry
since the second factor in the first bracketed term on the r.h.s. of
(27) must vanish in the SU(3)-flavor limit.

This analysis shows, in an essentially model independent way, that the
modified Gell-Mann--Okubo formula (17) must be a more accurate relation
among the octet pseudoscalar mesons than the standard one,\footnote{A
search for a relation of a more general form, $4f_K^aK^2=3f_8^a\eta
_{88}^2+f_\pi ^a\pi ^2,$ which would hold in the first nonleading order
of standard chiral perturbation theory, results in $a= 2.$} and
therefore, use of the form of the mass squared matrix (14) is fully
justified.\footnote{It has been suggested in the literature that the
pseudoscalar decay constants should enter relations like (17)-(19) in
the first rather than second power \cite{first}. As discussed above,
such relations are expected to be less accurate than ours, according to
chiral perturbation theory.}

\section{The Schwinger and Sakurai formulae reexamined}
Starting with the mass squared matrix (14), the considerations which lead to
Eqs. (5)-(10) above, will now lead, through (17)-(19), to the following two
relations,
\beq
\tan ^2\theta =\frac{4f_K^2K^2-3f_\eta ^2\eta ^2-f_\pi ^2\pi
^2}{3f_{\eta ^{'}}^2\eta ^{'2}+f_\pi ^2\pi ^2-4f_K^2K^2},
\eeq
\beq
\left( 4f_K^2K^2-3f_\eta ^2\eta ^2-f_\pi ^2\pi ^2\right) \left( 3f_{\eta ^{
'}}^2\eta ^{'2}+f_\pi ^2\pi ^2-4f_K^2K^2\right) =8\left( f_K^2K^2-f_\pi ^2\pi
^2\right) ^2,
\eeq
where $\theta$ is the mixing angle for the valence quark wavefunctions
which produces the mass eigenstates from the octet-singlet basis, and
which we refer to as ``the Schwinger nonet mass, and Sakurai
mass-mixing angle (respectively), formulae reexamined''.

In contrast to $f_\pi $ and $f_K,$ the values of which are well
established experimentally \cite{pdg},
\beq
\sqrt{2}f_K=159.8\pm 1.6\;{\rm MeV,}\;\;\;\sqrt{2}f_\pi=130.7\pm 0.3\;{\rm
MeV},\;\;\;\frac{f_K}{f_\pi }=1.22\pm 0.01
\eeq
the values of $f_\eta ,$ $f_{\eta ^{'}}$ and $\theta $ are known rather
poorly. We now wish to calculate these values using the relations
(28),(29), and compare the results with available experimental data. It
is obvious that the two relations are not enough for determining the
three unknowns. However, the additional relation, independent of
(28),(29) (the trace condition for (14),(16)),
\beq
f_\eta ^2\eta ^2+f_{\eta ^{'}}^2\eta ^{'2}=2f_K^2K^2+f_9^2A,
\eeq
introduces yet an additional unknown, $A$. We therefore develop another
independent relation among $f_\eta ,$ $f_{\eta ^{'}}$ and $\theta$, as
follows.

The light neutral pseudoscalar decay constants are defined by the
matrix elements
\beq
\langle 0| \sum_q c^P_{q} \bar{\psi}_{q}(0) \gamma^\mu \gamma^5
\psi_{q}(0) |P(p) \rangle = i \delta^{jP} f_P p^\mu ,
\eeq
where $\psi_{q}$, $q=(u,d,s)$ are the quark field operators, and we
define the wave function of a neutral pseudoscalar meson $P$ in terms
of the quark basis states $q\bar{q}$ as:
\beq
|P\rangle = \sum _q c^P_q |q\bar{q}\rangle ,\;\;\;q=u,d,s,
\eeq
where for $P = \pi^0$, $c^3_u=1/\sqrt{2} = -c^3_d$, $c^3_s=0$, for $P =
\eta_{88}$, $c^8_u = c^8_d = 1/\sqrt{6}$, $c^8_s = -2/\sqrt{6}$ and for
$P = \eta_{99}$, $c^9_u = c^9_d = c^9_s = 1/\sqrt{3}$.

The pseudoscalar decay constants defined in (32) can now be expressed as
\beq
f_P = \sum _q(c^P_{q})^{2}f_{q\bar{q}},
\eeq
where we have introduced the auxiliary decay constants $f_{q\bar{q}}$ defined
as the decay constants of the $q\bar{q}$ pseudoscalar bound states having the
masses $M(q\bar{q}).$ In the isospin limit, $f_{u\bar{u}}=f_{d\bar{d}}=f_{u
\bar{d}}=f_{\pi ^0}=f_{\pi ^{+}}.$ Using this approximation, and evaluating
the appropriate matrix elements leads to the following relations:
\bqry
f_\eta  & = & \left( \frac{\cos \theta -\sqrt{2}\sin \theta }{\sqrt{3}}\right)
^2f_\pi \;+\;\left( \frac{\sin \theta +\sqrt{2}\cos \theta }{\sqrt{3}}\right)
^2f_{s\bar{s}}, \\
f_{\eta ^{'}} & = & \left( \frac{\sin \theta +\sqrt{2}\cos \theta }{\sqrt{3}}
\right) ^2f_\pi \;+\;\left( \frac{\cos \theta -\sqrt{2}\sin \theta }{\sqrt{3}}
\right) ^2f_{s\bar{s}}.
\eqry

Now we have four equations, (28),(29),(35),(36), which allow us to
determine the three unknowns, $f_\eta ,$ $f_{\eta ^{'}},$ $\theta ,$ as
well as the additional quantity introduced, namely, $f_{s\bar{s}}.$ The
solution to these four equations is
\bqry
\frac{f_\eta }{f_\pi } & = & 1.085\pm 0.025, \\
\frac{f_{\eta ^{'}}}{f_\pi } & = & 1.195\pm 0.035, \\
\frac{f_{s\bar{s}}}{f_\pi } & = & 1.280\pm 0.060, \\
\theta  & = & (-21.4\pm 1.0)^o.
\eqry
[The $\pi $ and $K$ electromagnetic mass differences, and the uncertainties in
the values of $f_\pi $ and $f_K,$ (see (30)), are taken as a measure of
the uncertainties of the results.]

Before comparing the solution obtained with
experiment, let us also calculate the values of $f_8$ and $f_9$ which are
obtained from (35),(36) in the no-mixing case $(\theta =0):$
\bqry
f_8 & = & \frac{1}{3}f_\pi \;+\;\frac{2}{3}f_{s\bar{s}}, \\
f_9 & = & \frac{2}{3}f_\pi \;+\;\frac{1}{3}f_{s\bar{s}}.
\eqry
Therefore, as follows from (39),(41),(42),
\bqry
\frac{f_8}{f_\pi } & = & 1.185\pm 0.040, \\
\frac{f_9}{f_\pi } & = & 1.095\pm 0.020.
\eqry

The $\eta $-$\eta ^{'}$ mixing angle, as given in (40), is in agreement with
most of experimental data which concentrate around $-20^o$
\cite{pdg,data,Abele}. Also, the values for $f_8/f_\pi,$ $f_9/f_\pi $ and
$\theta $ are consistent with those suggested in the literature, as we show in
Table I.

\begin{center}
\begin{tabular}{|c|c|c|c|c|} \hline
 Ref. & $f_8/f_\pi $ & $f_9/f_\pi $ & $\theta ,$ deg.  \\
\hline
 This work & $1.185\pm 0.040$ & $1.095\pm 0.020$ & $-21.4\pm 1.0$  \\ \hline
    [6]    & $1.11\pm 0.06$ & $1.10\pm 0.02$ & $-16.4\pm 1.2$   \\ \hline
  [15,16]  &     $1.25$     & $1.04\pm 0.04$ &   $-23\pm 3$     \\ \hline
    [17]   & $1.33\pm 0.02$ & $1.05\pm 0.04$ &   $-22\pm 3$     \\ \hline
    [18]   & $1.12\pm 0.14$ & $1.04\pm 0.08$ & $-18.9\pm 2.0$   \\ \hline
    [19]   & $1.38\pm 0.22$ & $1.06\pm 0.03$ & $-22.0\pm 3.3$   \\ \hline
    [20]   &     1.254      &     1.127      &    $-19.3$       \\ \hline
\end{tabular}
\end{center}
{\bf Table I.} Comparison of the values for $f_8/f_\pi,$ $f_9/f_\pi $ and
$\theta ,$ calculated in the paper, with the results of the papers referenced.
 \\

\section{Comparison with data}
We now wish to compare the values obtained above for the ratios
$f_8/f_\pi ,$ $f_9/f_\pi ,$ and for the $\eta $-$\eta ^{'}$ mixing
angle with available experimental data. We shall first consider in more
detail the well-known $\eta ,\eta ^{'}\rightarrow \gamma \gamma $
decays, for which experimental data are more complete than those for
other processes involving light neutral pseudoscalar mesons, and then
briefly mention the $\eta,\eta ^{'}\rightarrow \pi ^{+}\pi ^{-}\gamma
,$ and $J/\psi \rightarrow \eta \gamma ,\eta ^{ '}\gamma $ decays.

\subsection{$\eta ,\eta ^{'}\rightarrow \gamma \gamma $ decays}
For these processes, the inclusion of both the $\eta $-$\eta ^{'}$ mixing and
the renormalization of the octet-singlet couplings, which leads to the
predicted amplitudes
\bqry
F_{\eta \gamma \gamma }(0) & = & \frac{\alpha N_c}{3\sqrt{3}\pi f_\pi }\left(
\frac{f_\pi }{f_8}\cos \theta -2\sqrt{2}\frac{f_\pi }{f_9}\sin \theta \right)
, \\
F_{\eta ^{'}\gamma \gamma }(0) & = & \frac{\alpha N_c}{3\sqrt{3}\pi f_\pi }
\left( \frac{f_\pi }{f_8}\sin \theta +2\sqrt{2}\frac{f_\pi }{f_9}\cos \theta
\right) .
\eqry
The values of these amplitudes, as extracted from data on widths,
are~\cite{VH}
\bqry
F_{\eta \gamma \gamma }(0) & = & 0.024\pm 0.001\;{\rm GeV}^{-1}, \NL
F_{\eta ^{'}\gamma \gamma }(0) & = & 0.031\pm 0.001\;{\rm GeV}^{-1}.
\eqry
Calculation with the help of Eqs. (30),(40),(43)-(46) yields
\bqry
F_{\eta \gamma \gamma }(0) & = & 0.025\pm 0.001\;{\rm GeV}^{-1}, \NL
F_{\eta ^{'}\gamma \gamma }(0) & = & 0.030\pm 0.001\;{\rm GeV}^{-1},
\eqry
in excellent agreement with (47).

\subsection{$\eta,\eta ^{'}\rightarrow \pi ^{+}\pi ^{-}\gamma $ decays}
These, as well as the $P^0\rightarrow \gamma \gamma ,$ processes were
extensively studied by Venugopal and Holstein \cite{VH} in chiral perturbation
theory. The analysis of experimental data for both of these processes done in
ref. \cite{VH} yields
$$\frac{f_8}{f_\pi }=1.38\pm 0.22,\;\;\;\frac{f_9}{f_\pi }=1.06\pm 0.03,\;\;\;
\theta =(-22.0\pm 3.3)^o,$$ in good agreement with our Eqs. (40),(43),(44).

\subsection{$J/\psi \rightarrow \eta \gamma ,\eta ^{'}\gamma $ decays}
These processes were studied by Kisselev and Petrov \cite{KP}. The values of
$f_8/f_\pi ,$ $f_9/f_\pi $ and $\theta $ extracted in ref.
\cite{KP} from the experimentally measured $P^0\rightarrow \gamma \gamma $ and
$J/\psi \rightarrow \eta \gamma ,\eta ^{'}\gamma $ widths, as given in the
last column of Table I of ref. \cite{KP}, which corresponds to conventional
mass-mixing angle relations, are
$$\frac{f_8}{f_\pi }=1.12\pm 0.14,\;\;\;\frac{f_9}{f_\pi }=1.04\pm 0.08,\;\;\;
\theta =(-18.9\pm 2.0)^o,$$ again in good agreement with our Eqs.
(40),(43),(44).

Thus, the three values of $f_8/f_\pi ,$ $f_9/f_\pi $ and $\theta $ agree with
experiment (at least, as far as the processes considered above are concerned).

\subsection{Comparison with CELLO and TPC/2$\gamma$ results}
As to the remaining $f_\eta /f_\pi ,$ $f_{\eta ^{'}}/f_\pi $ ratios
also calculated in the paper, the experimental values of them, as
extracted from data by the CELLO \cite{CELLO} and TPC/2$\gamma $
\cite{TPC} collaborations, are, respectively,
\bqry
\frac{f_\eta }{f_\pi } & = & 1.12\pm 0.12, \\
\frac{f_{\eta ^{'}}}{f_\pi } & = & 1.06\pm 0.10,
\eqry
and
\bqry
\frac{f_\eta }{f_\pi } & = & 1.09\pm 0.10, \\
\frac{f_{\eta ^{'}}}{f_\pi } & = & 0.93\pm 0.09.
\eqry
While the value calculated for $f_\eta /f_\pi ,$ Eq. (37), clearly agrees with
both experimental values (49) and (51), the value calculated for $f_{\eta ^{'}}
/f_\pi ,$ Eq. (38), only marginally agrees with (50), and disagrees with (52)
by almost 3 standard deviations.

To clarify the difference from the results referred to above, we recall
that the values of $f_\eta /f_\pi $ and $f_{\eta ^{'}}/f_\pi $ are
extracted by both CELLO and TPC/2$\gamma $ from experimental data on
transition form-factors $T_{\eta (\eta ^{'})}(0,-Q^ 2),$ assuming that
the pole mass $\Lambda _{\eta (\eta ^{'})},$ which parametrizes their
fits to the data, can be identified with $2\pi \sqrt{2}\;\!  f_{\eta
(\eta ^{'})}.$ Then, these pole fits to the data are presumed to join
smoothly, as $Q^2\rightarrow \infty ,$ to the perturbative QCD
predictions for $T_{\eta (\eta ^{'})}(0,-Q^2)$ \cite{BL}, i.e., these
fits would then agree with both the QCD asymptotic form $\sim 1/Q^2$
{\em and} its coefficient.

However, the values of both $f_{\eta }$ and $f_{\eta ^{'}}$ quoted by
the two groups, (in MeV) $(94.0\pm 7.1,$ $89.1\pm 4.9)$ \cite{CELLO},
and $(91.2\pm 5.7,$ $77.8\pm 4.9)$ \cite{TPC}, respectively, are all
close to $M(\rho )/(2 \pi \sqrt{2})\approx 86.5$ MeV, thus indicating a
possible connection with the vector meson dominance interpretation of
$\Lambda _{\eta (\eta ^{'})}\approx M(\rho )$ in the range of $Q^2$
investigated, which could obviate the assumptions referred to above.

On the other hand, as remarked by Klabucar and Kekez \cite{KK}, their own
bound-state calculation, as well as the model independent
calculation by Gasser and Leutwyler \cite{GL}, testing the Goldberger-Treiman
relations by Scadron \cite{Sca}, and the calculation by Burden {\it et al.}
\cite{Burden}, all agree that both $f_\eta $ and $f_{\eta ^{'}}$ should be
noticeably larger than $f_\pi .$ Our results $f_\eta \sim 1.1f_\pi ,$ $f_{
\eta ^{'}}\sim 1.2f_\pi $ are in agreement with this.

It therefore seems possible that the discrepancy with other
determinations may be due an inability to extract the values of $f_\eta
$ and $f_{\eta ^{'}}$ from the transition form-factors $T_{\eta (\eta
^{'})}(0,-Q^2)$ Sufficiently accurately, at least in the range of $Q^2$
investigated so far. That this may indeed be the case is indicated by
the experimental value $f_{ \pi ^0}=84.1\pm 2.8$ MeV \cite{CELLO},
extracted by the same method, which is again close to $M(\rho )/2\pi
\sqrt{2}.$ The central value of this $f_{\pi ^ 0},$ 84.1 MeV, is $\sim
10$\% below the well established value given in Eq.  (30), $92.4\pm
0.2$ MeV. Such a large discrepancy cannot be explained by, e.g., small
isospin violation, indicating the possibility that the extracted values
for both $f_\eta $ and $f_{\eta ^{'}}$ may well have been
underestimated also.

\section{Concluding remarks}
As a lagniappe, we note that Eq. (31) may be combined with our
extracted values for $f_9,f_\eta,f_{\eta ^{'}}$ to obtain the value of
$A:$
$$A=0.78\pm 0.12\;{\rm GeV}^2.$$
This is consistent with the usual value 0.73 GeV$^2$ determined by the
trace condition for (14),(16) without $f$'s~\cite{content}.

Let us briefly summarize the findings of this work:

i) We have found that chiral perturbation theory suggests that the
natural object to study is the pseudoscalar mass squared matrix
modified by the inclusion of the squared factors of the pseudoscalar
decay constants, rather than the mass squared matrix itself.

ii) We have shown that this modified mass squared matrix leads to new
Schwinger's quartic mass and Sakurai mass-mixing angle relations for
the pseudoscalar meson nonet.

iii) We have used these new relations to calculate the pseudoscalar
decay constants and mixing angle. We have demonstrated that, except
where questions may be raised regarding the reliability of the
extraction of the relevant quantities from direct experimental data,
the results obtained are in excellent agreement with available data.

We thank Philip R. Page for useful conversations.

\bigskip
\bigskip

redpajama_set_name: RedPajamaArXiv


The holidays have all gone and football season is officially over. Luckily you live in the city beautiful where the list of events and things to do in Orlando runs as long as the heat of summer. Get back to the 90's with some throwback jams in Downtown Orlando, watch the UFC fight with friends, or nom on some tacos. Still putting feelers out? Our local guide of things to do in Orlando this weekend has a little something for everyone. Check it out and let us know in the comments where you'll be heading.
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Did someone say BRUNCH?? The best day party in Downtown Orlando just keeps getting better! BRUNCH 2pm-6pm Unlimited Mimosas and Sangria $5 Frozà, and $10 Redbull Buckets.
Friday Light Friendzy at Altitude Trampoline Park Sanford. $25 for 4 hours of jumping, black lights, music, a slice of pizza, a bottle of water.
The most anticipated food & entertainment festival of the year is taking over the BRAND NEW Drive Shack located on Lake Nona Boulevard in Orlando, FL on Saturday, February 9, 2019! Come hungry!
On February 9th, pet lovers from all over Central Florida will gather at beautiful Lake Eola to support Pet Alliance of Greater Orlando's mission to educate, shelter, place, and heal pets and their families.
Cupid's Undie Run is the nation's largest pantsless party with a "brief" mile-ish jog (or walk) around Lake Eola in PG-13 undies, then returning for more partying… all for a great cause.
Matt Nathanson s an American singer-songwriter whose work is a blend of folk and rock and roll music. His breakout song "Come On Get Higher" launched his debut into the public eye in 2008. Matt Nathanson will be performing at The Beacham in Downtown Orlando this Saturday.
Every year, Bob Marley – A Tribute to Freedom restaurant in Universal CityWalk holds an event to celebrate the birthday of the cultural icon and music legend, Bob Marley. This year marks the 20th anniversary for the Bob Marley tribute concert inside Universal CityWalk Orlando.
Right Angle Entertainment Presents The Simon & Garfunkel Story at the Bob Carr Theater in Orlando.