I'm going to start this post by saying I'm really no expert when it comes to Pinterest, social media, SEO or anything of the kind, my boyfriend studies IT and the first thing he said when he looked at my blog was "you could really improve your SEO" - whatever that means, but I'm learning and trying to discover the best ways to market my blog and boost traffic. Recently in a bloggers chat the topic was the best way to gain traffic and bloggers use of social media, there were several bloggers discussing Pinterest and how they want to start using it or they don't understand, I tweeted a few people saying it's my main source of traffic and a few people replied asking for tips, so I thought I'd do my 5 easy tips for helping boost your traffic.
1. Try to join a bloggers board! MissMakeupMagpie created one, here, it has over half a million followers making it great exposure for you and your blog. It's currently closed to new members but if you are part of it start making use of it, if half a million people see it and only ten of them pin your post, all of their followers will see it, then if 3 of them pin it all of their followers will, and so forth. If you can't join at the moment still follow the board because she may open up to new members again, plus it's a great way to find new blogs, which leads me on to my next tip.
2. Follow and pin other peoples posts. If you're not going to follow and pin other peoples blog pictures, why should they follow and pin yours? Not only are you helping other bloggers out by getting their name out there, it's also getting your name out there to them. If you're their only new follower that day or you're one of only 3 people that pin their post, odds are they'll check your page out and will hopefully stick around.
3. Try to make your pictures look as nice as you can. I'm not saying I'm a photography maestro, but Pinterest is a vain little part of the Internet, the people like things to be pretty, bright and clear, or to at least look like they've been taken by a DSLR expert. If you look at pictures on the bloggers board the ones with the most interactions are the bright and sharp pictures. Of course certain pictures such as MAC products are always going to get a lot of pins, but if you can make a unfamiliar product look interesting people are more likely to become interested.
4. Post links to your blog and the posts. I'm honestly not patronising you here, because when I started using Pinterest I forgot to do this myself, it was only weeks later I decided to go back and change them, however by then they'd become lost in the abyss of Pinterest. Have your blog and Twitter linked up in your bio and I would recommend installing a Pinterest button to your blog, such as this one here, so you can automatically pin pictures from your blog and then don't have to worry about putting the link to the blog post manually. Pinning through a button will do it all for you, put the link, the title and your name, it's so simple!
5. Post at the right times! Just like your blog posts and tweets, you need to post pins at the optimal time to ensure you're reaching the largest amount of people possible. From experience I've found around 10am/11am and 7pm-9pm the best times to post, sometimes the 10am one can be a bit hit and miss, you'll either got loads of people or just a couple, but some of my most popular posts have been through pinning at 10am. The best way to find out is through your own trial and error, but as a starting point I would say 7pm.
Hopefully you found these helpful, these are just the basic ways I've helped boost my traffic. I've basically doubled the amount of traffic I receive since signing up to Pinterest and like I said, it's now become my main traffic source. These tips won't bring in millions of people, but I feel like following these few steps will help anyone to increase traffic, even if it's only a small proportion of their regular views.
Let me know if you found these useful, or your best tips!
I've really been trying to up my Pinterest game recently so have read dozens of tips and tricks articles, but this one was really original! I agree that timing is incredibly important, but I can never seem to get it quite right so thanks for the 7pm trick. Pinterest definitely has a lot of potential as I've discovered a lot of new blogs through it; it's just mastering good photography and Pinning the right things! Given you a follow on Pinterest - looking forward to your Pins!
Grab Yourself A Free Burberry Lipstick!


Green charity Friends of the Earth denies it was forced to stop publishing an anti-fracking leaflet after energy giant Cuadrilla complained to the advertising watchdog.
The campaign group said the Advertising Standards Agency (ASA) dropped the case without a ruling when the charity confirmed the ad is no longer in use.
Energy firm Cuadrilla, a leading fracking firm in the UK, complained to the ASA about "false" claims allegedly made in a Friends of the Earth (FoE) leaflet.
The leaflets were distributed in Lancashire, where Cuadrilla was given permission by the central government to frack for shale gas after the local council rejected the application and subsequent appeals.
Cuadrilla is a privately owned company chaired by former BP chief Lord Browne. It was itself censured by the ASA in 2013 for using misleading advertising and was ordered to tone down its claims on the safety of fracking.
The Advertising Standards Authority (ASA) says it has "informally resolved" the more recent dispute between Cuadrilla and Friends of the Earth (FoE), after the energy firm complained.
FoE claimed in a leaflet that chemicals involved in fracking can cause cancer and that there would be "plummeting house prices" as a result of the drilling.
They also claimed in the ad that drinking water would likely be contaminated.
"No ruling has been made against us. The ASA offered to drop the case without ruling after we confirmed that a particular leaflet was no longer being used," senior FoE campaigner Donna Hume said, as quoted in the Guardian.
"We continue to campaign against fracking because burning fossil fuels is dangerous for the climate. As well as that, the process of exploring for and extracting shale gas is inherently risky for the environment, this is why fracking is banned or put on hold in so many countries," Hume added.
"We approached Friends of the Earth with the concerns that had been raised about its ad," said a spokesman for the ASA.
"After many attempts by Friends of the Earth to delay this decision, the charity's admission that all of the claims it made, that we complained about, were false should hopefully put a stop to it misleading the UK public on fracking," Cuadrilla Chief Executive Francis Egan said.


Scientist Imagines Elevator Reaching 62,000 Miles Into Space: This seems so wrong on so many levels.
President Bush wants to return to the moon and put a man on Mars. But scientist Bradley C. Edwards has an idea that's really out of this world: an elevator that climbs 62,000 miles into space.
Edwards thinks an initial version could be operating in 15 years, a year earlier than Bush's 2020 timetable for a return to the moon. He pegs the cost at $10 billion, a pittance compared with other space endeavors.
A space elevator would present a considerable navigational hazard, both to aircraft and spacecraft. Aircraft could be dealt with […], but spacecraft are a more difficult problem. Over a long period of time all satellites with perigees below geostationary altitude would eventually collide with the space elevator, as their orbits precess around Earth.
There is a Star Trek: Voyager episode where they use something like this.
How's that for lame; not only that I remember that Voyager episode, but know off the top of my head where to find a picture of it.


In August, you'll see back-to-school ads from virtually every store. These ads will try to convince you that you need to buy clothes, shoes, computers, school supplies, sporting equipment, lunch making materials, cleaning wipes and a myriad of other products. Children legitimately need some of these items. Other items are in the nice to have category.
The average family will spend in excess of $600 per child for back-to-school items — and significantly more for college-bound students, especially when they need to furnish that freshman dorm room. Back-to-school has become the second largest shopping season in the year.
There is one item that may not be on your back-to-school list: Immunizations! Immunizations are something every child and young adult should have before they head back to school. That may be why August is National Immunization Awareness Month!
In recent years, we've looked eagerly for vaccines for HIV, Hepatitis C, Ebola, the Zika virus, and other emerging diseases, just as in the past people looked for vaccines for polio, measles, mumps, rubella and smallpox.
Many of the vaccinations we receive in this country are for "childhood illnesses." Despite the inoffensive title, these illnesses can be quite serious or even deadly, especially for the very young, the elderly, or those with immune systems compromised by diabetes, cancer, lung diseases or other illnesses. Many people currently live with long term effects of diseases acquired in childhood—some of which, like polio—have been largely eradicated thanks to immunizations.
Add this one extra item to that back-to-school list. Make sure your child is fully immunized. While you're at it, check to see if your immunizations are all up to date — immunity to many diseases, such as whooping cough and tetanus — can dissipate over time, and the flu vaccine is different each year.
There is good news with this back-to-school item though — recommended vaccinations are available as a preventive health service through Marketplace plans, so this won't add to your back-to-school expenses. Just be sure to follow your plan's guidance on where you should get your vaccinations to be sure the cost is covered.
The state of Washington provides excellent resources for parents, including Vaccine Requirements for Child Care, Preschool, and School in a variety of languages, Recommended Immunizations for Children from Birth through 6 Years Old and Recommended Immunizations for Children from 7 through 18 Years Old in English and Spanish, Vaccine Information for College Students, Recommended Adult Immunization Schedule, Plain Talk about Childhood Immunization, Immunization Data that allows you to see immunization rates, and Immunization News and Hot Topics.
Every child (and parent) should have a safe and healthy school year. Immunizations are an easy way to start out at the head of the class!


Raise the IL statewide minimum wage to $15 per hour.
The only one of these many factors important to IL WC professionals is the $15 per hour minimum wage. If that passes, I assure you IL WC wage loss differential benefits are certain to change in many industries, because anyone who can work, even with severe restrictions, will be making at least $15 per hour.
I assure my readers reserves for wage loss differential claims are going to have to change if the new minimum wage becomes law. If you aren't sure why/how, send a reply.
As a long-time IL WC Commission observer, I hope the secret-powers-that-be who run the Commission keep our State in the middle of the pack of United States for work comp costs. We don't need to get on everyone's radar for being too expensive, PLEASE!!
Allows HSA-compatible plans to provide pre-deductible coverage for services and medications for chronic conditions and for services at on-site clinics and retail clinics (e.g., clinics in pharmacies).
Permits employees to use HSA funds to pay for wellness activities, equipment and gym memberships.
Conforms HSA rules to other tax code rules to allow parents to use their HSA funds to pay for medical expenses of children who are not dependents through the end of the year in which the child turns 26.
Permits employees to contribute to HSAs even if the employee's spouse participates in a general-purpose health flexible spending arrangement (health FSA).
Makes it easier for employers to add an HSA-compatible plan when the employer sponsors a health reimbursement arrangement (HRA) or health FSA.
These proposals, if they become law, may significantly change the U.S. landscape on non-work-related healthcare coverage.
On another front, the Equal Employment Opportunity Commission (EEOC) recently advised a federal court it is not likely to meet its self-imposed August deadline to issue updated regulations describing how the Americans with Disabilities Act (ADA) and Genetic Information Nondiscrimination Act (GINA) apply to corporate wellness programs. Regulations issued in 2016 were recently vacated by the court effective Jan. 1, 2019.
One problem for the EEOC is all regulations must be voted on by the five-member commission. Two seats on the commission are vacant and one commissioner is up for re-nomination. Nominees for those seats are being held up in the U.S. Senate, pending the outcome of the current mid-term election.
Whatever you do folks, keep the faith. The United States will rise again! I appreciate your thoughts and comments. No, I don't like Donald Trump. Please post them on our award-winning blog.
Synopsis: Dreaded Consecutive IL WC Claim(s)—Who Knows Who Owes?
Editor's comment: In Par Electric v. Illinois Workers' Compensation Comm'n, 2018 IL App (3d) 170656WC, issued October 19, 2018, the IL WC Appellate Court considered a claim where Claimant filed workers' compensation claim for a June 2014 injury to his right arm while in the employ of Par Electric Company. He returned to work elsewhere and later filed IL workers compensation claims for April 1, 2015 and April 3, 2015 injuries to his right shoulder while working for the other company. The events leading to new problems were not severe trauma—one event was simply tossing a tool to another worker.
The IWCC in its wisdom, reached the conclusion the two April 2015 accidents did not constitute intervening and superseding accidents sufficient to break the causal connection from the June 2014 accident. In short, Par Electric, the first employer got stuck with all three claims, even though Claimant recovered sufficiently to return to construction electrician work.
In my opinion, the new Appellate ruling follows a solid trend—they let the IWCC, as the primary IL administrative agency entrusted to determine medical causation make they call. In short, the Appellate Court ruled the IWCC decision was not against manifest weight of evidence. Our Appellate Court, WC Division noted the evidence supported a finding Claimant had not completely and fully recovered from his 1st injury and surgery despite being released to return to work.
My final whiny, court-watchers comment is to note it took almost four years to resolve who was going to have to take care of this worker—one would think we are smart enough to get such decisions done quicker. I do feel the ruling by the Appellate Court, WC Division does send a message—they are going to follow the IWCC's lead on such issues so, don't waste time and money appealing.
Synopsis: From Brad Smith, our KCB&A GL defense team lead—New Cook County HIPAA order.
Editor's comment: This was just disseminated and we want clients and colleagues to be aware of it.
Cook County HIPAA Order to view the Law Division Administrative Order 18-1 HIPAA order.
Please contact Brad Smith at bsmith@keefe-law.com for concerns.


text:
In August 2008, after another fun-filled day at the office processing personal injury claims, I was driving home from Raleigh when a random call came through on my cell. I was not in the habit of answering my cell if I didn't recognize the number, but Megan had lost her phone in Hawaii while on deployment and I was answering all calls. Megan who had been in the Navy almost four years was assigned to the Helicopter Mine Countermeasures Squadron Fourteen out of Norfolk, Virginia. She was part of two crews flying two H-53 Sea Dragons (Sirkosky H-53 Series Helicopters) cross county. I understood they would be fueling periodically and hadn't expected to hear from her until that evening.
I had just crossed the overpass of Interstate 540 and was approaching Norwood Road. I made the transition onto Norwood and pulled over to a roadside stand that had landscape plants for sale for the new homeowners in the area. Azaleas of every color were situated in neat rows to better attract the commuters. My appreciation of the painstaking efforts by the vendor to entice buyers was about to be lost in the forthcoming minutes.
"Hey, Mija!" (short for "my daughter" Mi Hija. Spanish) I answered, sure that my surprise registered in my voice.
"Mom!" Her voice was high pitched and full of laughter. "I am in the middle of some farmers field in…wait a minute…" she paused.
"Where are we?" she asked someone nearby. " Mississippi? We're in Mississippi, Mom!"
"What?" I asked, at first not understanding why she wasn't certain where she was. Next breath, my worst fears, suppressed since the day she chose to be an aircrewman, eating at the edge of memories.
"We had to put down the "bird"," she explained, using her vernacular for the helicopter. "We landed in the middle of some farmer's, I don't know what this is, field, I guess. You should have seen his face! He came out on a four-wheeler with his shotgun and his dog!"
"Ok, so you are not supposed to call me when you have to emergency land," I responded even-toned, feeling anything but. It wouldn't do to get excited. She was fine. She was on the other end of the line.
Breathe, Liz. She's on the other end of the line.
"You are supposed to call your mother, after you've been rescued, taken to the clinic, examined and released!" I said, trying to keep the emotion out of my voice. I was looking at the pots of boxwood, crepe myrtle, azalea and gardenia plants lined neatly under an awning, but I was seeing a large corn/milo/soy field stretched far before me with the huge beautiful Vanguard Sea Dragon sitting still, blades silent, a trail of smoke wafting upward to the blue sky. The same blue sky I was under.
Hours later, in lodging for the night, Megan spoke to her Dad. I watched patiently from my perch on the couch, as he listened intently. My only indication of how serious it was, was when his eyebrows lifted, but took forever to descend. She had been sleeping when a vibration and knocking sounds woke her up. Where she had been resting was situated half-way between the middle of the bird and the cockpit. The other "maintainers" (maintenance crew) were still sleeping but the crew member toward the front of the cabin and pilot heard what she heard and could feel vibrations coming from the left side of the helicopter. When she started to move forward, flames started shooting to the ground of the cabin from overhead. The only reason she could see the flames was that there happened to be a hole in the airframe that had not been sufficiently patched. She pulled the fire extinguisher off the deck of the bird, gave it to her crew chief who went to work on the flames. During this time, the pilot and co-pilot are looking for a safe place to land and picked a field somewhere in Mississippi. The second helicopter landed nearby as all the crew from the damaged helicopter exited and allowed the bird to wind down.
The farmer, who owned the field, came out to investigate, in his overalls, on his ATV with his dog and his shotgun. After the crews identified themselves and updated the farmer on the problems, they secured the damaged bird before they all boarded the functioning H-53 and continued to the base in Tennessee. The wounded bird remained behind until a maintenance crew could be flown back to work on it from the Naval Base in Norfolk.
A couple of days after the incident I drove to Norfolk to a soccer game where Megan was scheduled to play on her co-ed team. Emergency land an H-53, life continued, and soccer was on the calendar. I wanted to put eyes on her. As she played, a friend of hers who was also a mechanic in the same squadron handed me a small packet of pictures. I looked at them, understanding and not understanding what I was seeing. A clutch had disengaged from the gearbox located above the cabin. Fuel and oil power these behemoths that weigh around 33,000 pounds empty. Her friend was silent as I flipped through the photos, pausing to look at what once had been the gearbox.
"She did good." He told me when I silently handed the pictures back. "No one got hurt". The entire crew received the 2008 NHA Region FOUR, Aircrew of the Year (Non-Deployed) Award. She gave it to me, as she has done with all her paperwork, reenlistments and evaluations for safekeeping. She dismissed my praise after I read it.
"I did exactly what I was trained to do. We all did."
I would remember that exchange years later, when an H53 Sea Dragon crashed off the coast of Virginia on January 8, 2014. For my daughter, now almost ten years in service, the threat of deconstruction loomed. She knew each of them. She trained two of them. She had flown with all of them.
"I trained them. I trained them how to handle this sort of emergency. I can't help but think I missed something" she told me her voice low and clear, but her eyes just missed meeting mine. I had seen that haunted look before.
That evening when I told Chester about her remark, it took him a moment to comment. When he did, his voice was low and clear, as Megan's had been earlier.
"You train with folks. You believe you have people who are going to be all right under fire. You believe you are going to be all right under fire. But you don't know. You don't really know until the moment you are under fire who you are and who you have next to you. Training is just that. Training. It's supposed to kick in under emergency and life-threatening circumstances, but you don't know who you have next to you until it does."
It had been an accident of a different sort. It mattered not to those who knew these men, those who worked, lived, loved and drank with these men. Megan withdrew, internalizing her grief, attending the memorial and services alone. I had asked if she wanted her dad or I there with her, but realized though we were her blood family, those men she went to honor and mourn and those she stood with who did the same, were her Navy family. The Squadron tightened ranks during this tragedy, tending to the families of the fallen crew, tending to each other. But the residuals ate at the edges of memories.
Exerpt from Train's Comin' - Our Struggle with PTSD Manuscript.
The Interview, Part 2
The Announcement

redpajama_set_name: RedPajamaCommonCrawl


text:
function usage {
  printf "Usage: %s: -m marvinCfg -p <pr id> [ -b <branch: default to master> -s <skip compile> -t <run tests> -f test-file-to-run -T mvn-T-flag -S <use simulator> ]\n" $(basename $0) >&2
}

# Options
skip=
run_tests=
test_file=
compile_threads=
while getopts 'm:p:T:b:f:Sst' OPTION
do
  case $OPTION in
  S)    simulator="-S"
        ;;
  m)    marvinCfg="$OPTARG"
        ;;
  p)    prId="$OPTARG"
        ;;
  s)    skip="-s"
        ;;
  t)    run_tests="-t"
        ;;
  f)    test_file="-f $OPTARG"
        ;;
  T)    compile_threads="-T $OPTARG"
        ;;
  b)    branch_name="$OPTARG"
        ;;
  esac
done

echo "Received arguments:"
echo "skip = ${skip}"
echo "use simulator = ${simulator}"
echo "run_tests = ${run_tests}"
echo "test_file = ${test_file}"
echo "marvinCfg = ${marvinCfg}"
echo "prId = ${prId}"
echo "compile_threads = ${compile_threads}"
echo "branch_name = ${branch_name}"

# Check if a marvin dc file was specified
if [ -z ${marvinCfg} ]; then
  echo "No Marvin config specified. Quiting."
  usage
  exit 1
else
  echo "Using Marvin config '${marvinCfg}'."
fi

if [ ! -f "${marvinCfg}" ]; then
    echo "Supplied Marvin config not found!"
    exit 1
fi

# Default to master branch
if [ -z "${branch_name}" ]; then
    branch_name="master"
    echo "branch_name = ${branch_name}"
fi

echo "Started!"
date

# Check if a pull request id was specified
if [ -z ${prId} ]; then
  echo "No PR number specified. Quiting."
  usage
  exit 1
fi

# Check if a marvin dc file was specified
if [ -z ${marvinCfg} ]; then
  echo "No Marvin config specified. Quiting."
  usage
  exit 1
fi

# Perpare, checkout and stuff
/data/shared/helper_scripts/cloudstack/prepare_cloudstack_compile.sh

# Go the the source
cd /data/git/${HOSTNAME}/cloudstack
git pull
git reset --hard
git checkout ${branch_name}
git branch --set-upstream-to=origin/${branch_name} ${branch_name}
git pull

git branch -D try/${prId}
git branch try/${prId}
git checkout try/${prId}
# Get the PR
tools/git/git-pr ${prId} --force
if [ $? -gt 0  ]; then
  echo "ERROR: Merge failed!"
  exit 1
fi

# Build, run and test it
/data/shared/helper_scripts/cloudstack/build_run_deploy_test.sh -m ${marvinCfg} ${run_tests} ${test_file} ${skip} ${compile_threads} ${simulator}

redpajama_set_name: RedPajamaGithub


Economist Burton Malkeil has called the index fund "the most important financial innovation that has been created for the individual investor." And one look at index-fund pioneer Vanguard's performance over the past decade shows that many individual investors agree.
For the past 12 years, Vanguard has taken in more money on a net basis than any other fund firm, according to data from Morningstar. Only one other firm, BlackRock BLK, -0.39% subsidiary iShares, has appeared on the list of top five net-flow recipients every year since 2007, and at nearly $2 trillion in net inflows since that time, Vanguard has attracted more than double the dollar amount iShares has over the past 12 years.
Ben Carlson, director of institutional asset management at Ritholtz Wealth Management labeled Vanguard "the Amazon of wealth management," when learning of the magnitude of Vanguard's lead over the competition, saying in an interview with MarketWatch that the comparison is appropriate not only because both companies were leading innovators in their respective industries, but because they have used their scale to drive prices lower and build unprecedented brand loyalty.
"Amazon is the first place you go to buy something, whether it's the cheapest or not. And Vanguard is the first place that comes to mind when shopping for low-fee investments," he said.
Vanguard, and specifically John Bogle, was a pioneer of so-called passive investing strategies, marketing the first-ever index mutual fund in 1975, which sought to track the performance of benchmarks like the S&P 500 SPX, +0.16% rather than actively picking stocks in an attempt to outperform an index. Because the fund wasn't actively managed, Vanguard was able to offer funds at rock-bottom prices, compared with other mutual-fund firms, which typically employ teams of analysts and star stock pickers to identify investments.
Todd Rosenbluth, senior director for ETF and mutual fund research at CFRA, told MarketWatch that the popularity of such index funds has grown steadily since that time, with the trend toward low-fee index investing intensifying over the past decade.
Vanguard is a client-owned company, wherein the shareholders own the funds offered by Vanguard, which in turn own the company itself.
On top of that, a Feb. 18 op-ed in the New York Times argued that passive investing funds may be vulnerable to manipulation and conflicts of interest. "Conflicts of interest should worry anyone who is invested in index funds, which includes many Americans with retirement accounts. Index providers have enormous power. The decision to include a company in the S.&P. 500, for example, results in a reallocation of billions of dollars of investors' money. The average company added to the S.&P. 500 gains value; when it's removed, its share price drops as index funds sell their holdings," wrote authors of the article Robert J. Jackson Jr. and Steven Davidoff Solomon.
CFRA's Rosenbluth makes the case that passive funds are abundantly transparent and perhaps even more than individual stocks.


The big day is almost here and we know the most important thing on your mind... how can I make sure I get my favourite Nutrition X supplements in time?
Don't fear - we're here to help!
Our last order date for guaranteed delivery in time for Christmas is Thursday 20th December. All orders placed between Friday 21st December 2018 - Wednesday 2nd January will be processed when we reopen on Wednesday 2nd January. All orders placed during this period will be delivered on Thursday 3rd January at the earliest.
As a thank you for your patience over the Christmas period, we'll be offering FREE UK Delivery on all orders placed between Friday 21st December - Tuesday 1st January.
Please note, Next Day UK and Saturday Delivery will not be available during this time.


Hi everyone! So my computer is finally back and fixed (oh yeah!). During the past week I've been using tones of pre-made posts and a very old computer that wouldn't allow me to edit simple shoots. But everything is fixed and I have a lot to share. On top of my list? Empties. Probably because I already have a good quantity to share and I really don't want to accumulate even more. And yes, I've been storing them on my MAC bag. I'll probably keep it in that way for now.
I actually never finished these but I'll declare them as so. The Rimmel London Accelaretor mascara was used a hand-full of times but we didn't click. I got it because of the raves from Fleur...sadly this wouldn't do much to my lashes and was too liquid for my tast. And since we can't pass mascara to no one, I'll just say goodbye.
Now the Too Faced Lash-gasm has a totally different story. I had mentioned how I didn't liked it when I reviewed the romantic collection. After that this keept smelling funky and with a weird texture. So no, I won't dare to use this in my eyes ever again. I think I got bad luck with this mascara or something. Sadly, this made me scared of Too Faced mascaras in general.
I think I'll stop talking about these in future posts. But yes, I've finished to packs of my Nivea makeup remover wipes - which I use for swatches and clean my hands after applying foundation with my hands.And I've also finished two packs of my Demak-up Duo+ cotton...they are my favourite cotton pads. What else can I say?
From the SLS-free range from L'oreal I've killed the shampoo, hair mask and conditioner. The Shampoo is very gentle - cleans my hair but isn't harsh or over stripping to my scalp. I've repurchased another tube and althought I really want to try out other brands - like Aveeno and Bumble&Bumble - but this one is a favourite. I also got another tube of the conditioner and I'll probably apply to it what I intend to do with the shampoo. Now the mask, I'm currently trying other from their range which has a different smell and texture. This mask isn't bad - it's really dense which I like - but my current mask is more hydration than this one so I'm not sure If I'm going to get another box or not.
Oh yeah, there'se a lot. Starting with those that got repurchased , I finished a tube of the La Roche-Posay Hydreane Ligere moisturiser and the Effaclar Duo - I got the new version . The only thing I have to mention is the fact that duo to packaging problems the last bits of product got wasted in the cap. ridiculous...I guess it's because the product it's so liquidly (the new version isn't).
The Nuxe produgience Nuit Night cream was a pain to finish...for some reason I just couldn't smell it and even my skin wasn't liking it...I've switch for a more simple and rich moisturiser for the night and my skin appreciated it. I won't be getting this again.
The Body Shop's Camomile Cleansing butter was a lovely treat. I'm currently using the oil but I'll probably get this bad boy again because it's really lovely to use and travel with. It cleanses my face, doesn't break me out or irritates it. Just lovely.
Inspired by the Sample Killah that some lovely Canadian Beauty Bloggers did during the month I decided to finally kill a few samples. Although there are two products that really don't count as samples - the T-zone Pore strip which I had wondering around the samples. I hate it, there's anything else I can say. It leaves tones of glue on my nose and doesn't clean. Won't be getting this again. The other Non-sample is the The Body Shop Seaweed Clay Mask which you can purchase instead of the big pot. I got this because of a promotion ( buy 3 get 30% off) when I got the Aloe Toner and the Camomile Cleansing Oil . It's a nice mask that I like to use once in a while.
The Kiehl's Ultra Facial Cleanser was given by Shayne during our SWAP. I wanted to like it but..it actually broke me out. I'm not sure if it was a specific ingredient or the fact that my skin isn't used to SLS any more (it didn't foam that much actually.)The Mini.They're Real is also gone - I didn't like it but for some reason the baby version have a different texture when compared to the full-size ones. And Lastly but not least the TonyMoly Tomatox Mask - AMAZING. I really want to get the full-size version because of this one. It's like my Cleanance mask from Avène but more gentle.
Okay, enough with my trash. I'll be working on my favourites post and other posts for August.
Take Care everyone! Have a nice day!


· Monday, January 10, 2011 from 12:30 to 2:30 pm at the Phoenix Public Library, 34 Elm Street, Phoenix.
· Tuesday, January 11, 2011 from 3:30 to 5:30 pm at Catholic Charities, 365 West 1st Street, Fulton.
· Wednesday, January 12, 2011 from 6:00 to 8:00 pm at Cornell Cooperative Extension of Oswego County, 3288 Main Street, Mexico.
· Thursday, January 13, 2011 from 6:00 to 8:00 pm at the Sandy Creek United Methodist Church, 2031 Harwood Drive, Sandy Creek.
That is Cooperative Extension, responsive to Oswego County's immediate needs, while drawing on the expertise of world-class professors at Cornell University. Cornell Cooperative Extension in Oswego County provides equal program and employment opportunities. Please contact the Cornell Cooperative Extension of Oswego County Office if there are any special needs.


Westchester, IL, February 07, 2018 --(PR.com)-- The Tandem Family of Companies' (TFC's) President, Bruce Leon, strives to inspire his employees to be philanthropically-minded and involved in their community in a significant way. Leon, the founder of four companies providing custom and high-touch human resource solutions to hundreds of businesses in and around the Chicago area, has always supported nonprofit organizations in the communities in which he lives and works.
"I feel so fortunate to be in my position. I believe sharing my blessings is the right thing to do," says Leon, who not only financially supports organizations but also volunteers his time and his human resources. Yes, that's right! Leon has over 100 employees that he wants to influence positively. He has established several charitable programs which encourage and make it easy for employees to live generously.
Like a lot of other business owners, Leon matches employees' donations made to 501(c)(3) organizations all year long. Leon has taken it a few steps further, however, by establishing a Dollars for Doers program. This program awards $250 to any non-profit organization to which an employee donates at least 30 hours. It gives employees an extra way to support their causes, encouraging them to volunteer time.
TFC employees never have the excuse that they do not have the time to volunteer either. The company allows employees to use up to 20 hours of paid work time annually to volunteer. They even organize their own volunteer events throughout the year. This winter, they sent 15 employees to A Safe Haven to work in the food pantry for four hours during the workday. For the past 20 years, A Safe Haven has been assisting homeless individuals and families address the cause of their problem and achieve sustainable self-sufficiency. In case four hours out of the office were not enough incentive, the company donated $30 on behalf of each employee that chose to volunteer.
This is a mantra of Leon's often heard around the office. His actions spoke louder than words, however, when he announced at his December all company meeting that he was going to donate $20,000 to non-profit organizations near and dear to his employees' hearts. Employees were asked to tell Leon the names of the organizations they support and give a few reasons why. With an overwhelming response, Leon ended up donating $21,250 to over 50 organizations.
Leon is a champion of charitable causes and strives to influence employees, colleagues, and clients to make a positive impact in the community.


text:
Rangers pay tribute to former Scotland goalkeeper and manager Bobby Brown
The Rangers club legend has died aged 96.
Bobby Brown was manager of Scotland during the national side's famous victory over England in 1967 (Jeff Holmes/PA)
By Conor Riordan, PA Scotland
Former Scotland goalkeeper and manager Bobby Brown has died at the age of 96.
https://www.belfasttelegraph.co.uk/news/uk/rangers-pay-tribute-to-former-scotland-goalkeeper-and-manager-bobby-brown-38866114.html
https://www.belfasttelegraph.co.uk/news/uk/9900a/38866112.ece/AUTOCROP/h342/bpanews_7c9cd658-7cf1-4188-a799-b5a6169c98a9_1
Brown, from Dunipace, joined Rangers from Queen's Park in 1946 and went on to become a club legend.
In his decade-long spell at Ibrox, he made 296 appearances, keeping 109 clean sheets and he was part of the 1948/49 side when Rangers became the first team to win the treble.
Everyone at Rangers Football Club is in mourning today after learning that club legend and former Scotland goalkeeper and manager Bobby Brown has sadly passed away at the age of 96.
Bobby Brown 1923-2020 | https://t.co/lMsDVhkDwm pic.twitter.com/9pAO0M4VY6
— Rangers Football Club (@RangersFC) January 15, 2020
He played part-time throughout his Gers career, while also working as a schoolmaster.
In February 1967 he was appointed manager of Scotland, a position he held until July 1971.
It was during his reign that the national side had a famous 3-2 victory over then-world champions England in a European Championship qualifier at Wembley in 1967.
He was inducted into the Scottish Football Hall of Fame in 2015.
Rangers chairman Dave King said: "All of us connected with Rangers are deeply saddened to hear that Mr Brown, a genuine Rangers and Scotland legend, has passed away. Our thoughts are with Mr Brown's family at this time.
"He was a wonderful servant of our club and we will remember him with great fondness.
"He was a gentleman of the game and set standards which typify what Rangers is about."
A minute's silence will be held prior to Friday's Scottish Cup tie with Stranraer at Ibrox.


text:
Dan Ackerman Joins Samba TV as CRO
Samba TV Names Ackerman Chief Revenue Officer
AOL's SVP of Programmatic TV joins the leading provider of cross platform media and measurement, shaping the future of TV, digital and programmatic advertising
San Francisco, August 15 – Samba TV, the leading provider of real-time, audience driven advertising and analytics, today announced that Dan Ackerman has been named Chief Revenue Officer.
In his new role, Dan will be responsible for leading the global revenue efforts for Samba TV, building upon the company's reputation of helping brands and agencies understand TV viewership and its impact on consumer behavior and purchase.
Prior to joining Samba TV, Dan was SVP of ONE by AOL TV where he and his team helped pioneer the TV industry's evolution into programmatic buying. Dan is a veteran executive with more than 20 years' experience driving digital and television ad sales and business development. Dan has previously held executive level sales and advertising strategy roles at CBS Corporation, WideOrbit, Ecast and Jivox.
"With a track record of success in TV, digital and programmatic advertising, and trusted relationships with brands, agencies and media companies, we are excited to have Dan on our leadership team," says Ashwin Navin, CEO of Samba TV. "Dan's experience building and leading teams in high-growth environments will be key to helping us further scale our business."
"Video viewing fragmentation and time shifting are rapidly accelerating across screens. Deterministic, cross platform content and ad exposure data is crucial for marketers to identify, target, reach and connect with their prospective audiences," according to Ackerman. "Samba TV's technology and deep understanding of how to integrate digital in a meaningful way with television viewing are helping to change the audience measurement and media landscape and set a new standard. I'm excited to be a part of this growing team."
2016 has been a year of rapid growth for Samba TV, with a focus on developing a strong management team with deep industry experience. The company recently added former YouTube executive, Serena Satyasai, as VP of Marketing, and Andy Kemp, from AddThis, to head MidWest Sales. Samba TV has experienced a 600 percent increase in year-over-year revenue and has grown to more than 150 employees across 10 global offices.
About Samba TV
Samba TV is a cross-platform media and analytics company that provides a real time understanding of TV viewership – and its impact on consumer behavior and purchase – as it truly is.
Embedded in millions of smart TVs, Samba TV's technology lets consumers discover and watch the shows they love while giving brands a holistic view of content and advertising consumption across broadcast and cable TV, OTT, apps and digital. Pairing Samba TV's second-by-second, first party, TV viewership insight with its household device map, Samba TV helps brands run TV-synchronized digital ads and confidently chart the consumer path to purchase, from online to offline, to make informed media buying decisions. Using a nationwide, census like panel that is fully representative of the U.S. population, Samba TV measures TV and digital ad exposure over time for the same household. Samba TV's proprietary household device map totals more than 180 million devices, including smart TVs, set top boxes, smartphones and other connected devices. For more information, please visit www.samba.tv or follow @samba_tv on Twitter.
Contact: Bill Daddi
Daddi Brand Communications
Bill @DaddiBrand.com


At Green Country Painting in Tulsa, Oklahoma, we believe that hard work and professional workmanship is crucial to our continued growth. We strive to exceed your expectations because we want you to call us again and again for all your painting projects. Hopefully, you will also share your pleasant experience with your family, friends and neighbors. Referrals are the best compliment we can receive and we know that you will be completely satisfied with the quality of our work from start to finish.
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It's easy. Just give us a call. Don't wait any longer to schedule your free painting estimate!


text:
\section{Introduction}
The Bethe-Salpeter formalism has recently been used in various ways in
more careful investigations of quarkonium physics.  For example
Munczek and Jain\cite{munczek} have used the full Bethe-Salpeter
equation together with the Schwinger-Dyson equation to study the mass
spectrum and lepton pair decays of light and medium-heavy mesons,
Resag {\it et
al.\/}\cite{ResagochMunz1,ResagochMunz2,ResagochMunz3,ResagochMunz4}
have written a series of papers about the Salpeter equation where they
have studied mass spectra and various decay observables for both
light and heavy mesons, Kugo {\it et al.\/}\cite{kugo} have calculated
the Isgur-Wise function and Harada and Yoshida have calculated the QCD
$S$ parameter\cite{harada1} and developed a method to solve the full
Bethe-Salpeter equation\cite{harada2}.  The stability of the Salpeter
equation for various Lorentz structures of the confining potential
has been studied by Olsson {\it et al.\/}\cite{olsson_stabil} and
Parramore {\it et al.\/}\cite{parramore1,parramore2}.  Olsson {\it et
al.\/} have also studied the validity of the reduced Salpeter
equation\cite{olsson_2}.

In this paper we undertake an investigation of the radiative decays of
the lowest charmonium levels including both M1 and E1 transitions in
our study as well as the two-gamma decays of the corresponding
pseudoscalar, scalar and tensor states.

Like many other authors\cite{ResagochMunz1,murota,Ito_E1} we use the
instantaneous approximation of the Bethe-Salpeter equation -- the
Salpeter equation -- which has a well defined physical interpretation.
Our kinematical analysis uses a formalism based on the one developed
by Suttorp\cite{Suttorp}.  (Another formalism in a similar spirit has
been developed by Laga\"e\cite{Lagae}.)  This leads to a set of
coupled equations for the amplitudes which are solved numerically.  In
this paper we present a general set of eigenvalue equations and decay
amplitudes for lepton pair decays, two gamma decays and E1 and M1
transitions, which can be used in any model with a vector plus scalar
potential using the formalism of Suttorp.

Our potential consists of one short-range vector part describing the
one-gluon-exchange interaction and one scalar long-range confining
part.  Investigations of the stability of the Salpeter equation for
confining potentials with various Lorentz structures have shown that
for light quarks there are no stable solutions for a scalar
confinement\cite{olsson_stabil,parramore1,parramore2}. This problem
does not appear for heavy quarks like the charm quark.  Furthermore a
Lorentz time component vector confinement, which has been shown to be
the most stable one, gives a contribution to the spin-orbit coupling
with the wrong sign.  We have therefore chosen a scalar confinement
potential.

In quantum mechanics the spectrum itself does not uniquely determine
the potential.  We also need as input some other information
concerning the localization of the system, such as the value of the
wave function close to the origin.  As input we therefore take the
energy levels of the charmonium spectrum as well as the decay rates of
the vector $1^{--}$~states into lepton pairs.

The instantaneous approximation leads, strictly speaking, to some
problems with renormalization, since the Ward-Takahashi identities are
then not relevant for the renormalization of the vertex function in
the lepton pair decay.  Furthermore the kernel is confining and
contains a dimensionful coupling constant for the confining part.
This leads in the final analysis to a renormalization procedure where
we use the decay width for $J/\Psi\to e^{+}e^{-}$ to define the
renormalization constant.  Thus, we calculate the ratios of the
decay rates of the vector states into lepton pairs, rather than the
rates themselves.

We adopt the formalism of Mandelstam\cite{Mandelstam} to calculate the
radiative decay amplitudes.  The gauge invariance of this method in
the instantaneous approximation is not obvious, but in Sec.
\ref{m1e1decay} we show that the decay amplitudes are indeed gauge
invariant.

The paper on heavy quarkonia by Resag and M\"unz\cite{ResagochMunz3}
overlaps to some extent with our paper.  They have also used a Salpeter
model to calculate mass spectra and decay observables for charmonium.
However, they have used a somewhat different potential.  In
particular, they have introduced a cut-off in the potential at the
origin in order to renormalize the lepton pair decay widths.  In this
paper we discuss the difficulties of renormalization and conclude that
an experimental decay width has to be used to properly define the
renormalization. A cut-off also necessitates some extra
parameters in the model, and they obviously affect the
results. In particular, the lepton pair decay widths depend on the
wave function's value at the origin, and therefore one can obtain any
value for those by varying the cut-off parameters.

In addition, we present general equations in a formalism different
from\cite{ResagochMunz3} and investigate the importance of non-dominant
terms in the wave functions.

The outline of our paper is as follows.  In Section~\ref{salpeq} we
briefly discuss the Bethe-Salpeter equation to define our variables.
In Section~\ref{potential} we describe the potential used in the
model.  We use a short-range Coulomb potential plus a long-range
confining linear potential.  In Section~\ref{leptondecay} we give the
expression for lepton pair decay and discuss the problem with
renormalization.  In Section~\ref{ggdecay} we give the expressions
for the $\gamma\gamma$ decays and in Section~\ref{m1e1decay} we give
the expressions for the M1 and E1 transitions.  There we also discuss
the gauge invariance in the instantaneous approximation.  In
Section~\ref{resultat} we present the numerical results and finally in
Section~\ref{tillsist} we give a summary of our results and
conclusions.

\section{The Salpeter equation}
\label{salpeq}
The wave function $\chi(q)$ for bound states of a fermion-antifermion
pair satisfies the spinor Bethe-Salpeter equation
\begin{equation}
(\rlap{/}{q}+\frac{\rlap{/}{P}}{2}-m)\chi(q)
(\rlap{/}{q}-\frac{\rlap{/}{P}}{2}-m)=
i\sum_{i=1}^5\int\frac{d^4p}{(2\pi)^4}K^i(p,q,P)\Gamma^i\chi(p)\Gamma^i.
\label{bs-eq}
\end{equation}
Here, $P$ is the momentum of the bound state and $q$ is the relative
momentum of the constituent fermions.  The interaction kernel is
characterized by the matrices $\Gamma^i$, where $\Gamma^S=1$,
$\Gamma^V=\gamma^\mu$, $\Gamma^T=\sigma^{\mu\nu}$,
$\Gamma^A=\gamma^\mu\gamma^5$, $\Gamma^P=\gamma^5$.

We now make the instantaneous approximation, so that the kernels
$K^i=K^i({\bf p}-{\bf q})$ in the rest frame.  This reduces the
Bethe-Salpeter equation to the Salpeter equation.  It may seem like
Lorentz invariance is lost by making this approximation.  However,
although manifest Lorentz invariance is lost, the Salpeter equation
can be formulated covariantly by letting $K^i$ depend on
$q_\perp=q-\frac{q\cdot P}{M^2}P$ and $p_\perp=p-\frac{p\cdot
P}{M^2}P$ in a general frame.  In the rest frame $q_\perp$ reduces to
$(0,{\bf q})$. For details, see for example Chang and Chen\cite{kineser}.

It is most convenient to calculate the mass spectrum and wave
functions in the rest frame of the bound states, and afterwards
Lorentz transform the wave functions when needed.  We will therefore
perform the calculations in the rest frame
for the remainder of the paper.

The propagators can be written
\begin{eqnarray}
\frac{1}{\rlap{/}{q}-m}=&&\left(\frac{\Lambda_{+}^{+}({\bf q})}{(q^0-E({\bf
q})+i\epsilon)}+ \frac{\Lambda_{-}^{+}({\bf q})}{(q^0+E({\bf
q})-i\epsilon)}\right)\gamma^0\nonumber\\
=&&\gamma^0\left(\frac{\Lambda_{+}^{-}({\bf q})}{(q^0-E({\bf
q})+i\epsilon)}+ \frac{\Lambda_{-}^{-}({\bf q})}{(q^0+E({\bf
q})-i\epsilon)}\right),\label{propagator}
\end{eqnarray}
where
\begin{equation}
\Lambda_\mu^\pm({\bf q})=\frac{1}{2E({\bf q})}(E({\bf
q})+\mu(\pm\bbox{\alpha}\cdot{\bf q}+m\gamma^0)) \qquad \mu=\pm
\end{equation}
are the projection operators for the positive and negative energy
states respectively.

With the help of these projection operators we can write the Salpeter
equation as a set of four coupled equations,
\begin{eqnarray}
\Lambda_\mu^+({\bf q})\chi(q)\Lambda_\nu^-({\bf q})=&&
\frac{i}{(M/2+q^0-\mu E+\mu i\epsilon)(-M/2+q^0-\nu E+\nu
i\epsilon)}\times \nonumber\\
&&\quad\sum_i\int\frac{d^4p}{(2\pi)^4}K^i({\bf p}-{\bf q})
\Lambda_\mu^+({\bf q})\gamma^0\Gamma^i\chi(p)\Gamma^i\gamma^0
\Lambda_\nu^-({\bf q}). \label{fyrachiekv}
\end{eqnarray}
The right hand side can be integrated over $q^0$ by a simple contour
integration.  Introducing the reduced wave function
\begin{equation}
\Psi({\bf q})=\int\frac{dq^0}{2\pi}\chi(q) \label{redwave}
\end{equation}
we find that
\begin{eqnarray}
\Lambda_{+}^{+}({\bf q})\Psi({\bf q})\Lambda_{-}^{-}({\bf q})=&&
-\frac{1}{(M-2E)} \sum_i\int\frac{d{\bf p}}{(2\pi)^{3}} K^i({\bf
p}-{\bf q}) \Lambda_{+}^{+}({\bf q})\gamma^0\Gamma^i\Psi({\bf
p})\Gamma^i\gamma^0 \Lambda_{-}^{-}({\bf q}), \label{psieq1}\\
\Lambda_{-}^{+}({\bf q})\Psi({\bf q})\Lambda_{+}^{-}({\bf q})=&&
\frac{1}{(M+2E)} \sum_i\int\frac{d{\bf p}}{(2\pi)^{3}} K^i({\bf
p}-{\bf q}) \Lambda_{-}^{+}({\bf q})\gamma^0\Gamma^i\Psi({\bf
p})\Gamma^i\gamma^0 \Lambda_{+}^{-}({\bf q}),\label{litet_psi}\\
\Lambda_{+}^{+}({\bf q})\Psi({\bf q})\Lambda_{+}^{-}({\bf q})=&&0 ,
\label{psieq3}\\
\Lambda_{-}^{+}({\bf q})\Psi({\bf q})\Lambda_{-}^{-}({\bf q})=&&0 .
\label{psieq4}
\end{eqnarray}
Combining these equations with (\ref{fyrachiekv}), we can write the
wave function as
\begin{eqnarray}
\lefteqn{\chi(q)={}}\nonumber\\
=&&-\frac{i(M-2E)}{(M/2+q^0-E+i\epsilon)(-M/2+q^0+E-i\epsilon)}
\Lambda_{+}^{+}({\bf q})\Psi({\bf q})\Lambda_{-}^{-}({\bf
q})\nonumber\\
&&{}+\frac{i(M+2E)}{(M/2+q^0+E-i\epsilon)(-M/2+q^0-E+i\epsilon)}
\Lambda_{-}^{+}({\bf q})\Psi({\bf q})\Lambda_{+}^{-}({\bf
q})\nonumber\\
&&{}+\frac{i}{(M/2+q^0-E+i\epsilon)(-M/2+q^0-E+i\epsilon)}
\int\frac{d{\bf p}}{(2\pi)^{3}}
K^i\Lambda_{+}^{+}({\bf q})\gamma^0\Gamma^i\Psi({\bf
p})\Gamma^i\gamma^0\Lambda_{+}^{-}({\bf q})\nonumber\\
&&{}+\frac{i}{(M/2+q^0+E-i\epsilon)(-M/2+q^0+E-i\epsilon)}
\int\frac{d{\bf p}}{(2\pi)^{3}}
K^i\Lambda_{-}^{+}({\bf q})\gamma^0\Gamma^i\Psi({\bf
p})\Gamma^i\gamma^0\Lambda_{-}^{-}({\bf q}). \label{waveeq}
\end{eqnarray}
Thus, finding the wave function $\chi(q)$ in this formalism reduces to
finding $\Psi({\bf q})$.

Combining the equations (\ref{psieq1})-(\ref{psieq4}) we get an equation
for $\Psi({\bf q})$,
\begin{eqnarray}
\lefteqn{(\frac{M}{2}-\bbox{\alpha}\cdot{\bf q}-m\gamma^0)\Psi({\bf
q})+\Psi({\bf q}) (\frac{M}{2}-\bbox{\alpha}\cdot{\bf
q}+m\gamma^0)}\nonumber\\
&&=-\sum_i\int\frac{d{\bf p}}{(2\pi)^{3}} K^i({\bf p}-{\bf
q})\bigl(\Lambda_{+}^{+}({\bf q})\gamma^0\Gamma^i\Psi({\bf p})
\Gamma^i\gamma^0\Lambda_{-}^{-}({\bf q})-\Lambda_{-}^{+}({\bf
q})\gamma^0\Gamma^i\Psi({\bf p})\Gamma^i\gamma^0 \Lambda_{+}^{-}({\bf
q})\bigr) .\label{psiequation}
\end{eqnarray}

For each state with a certain angular momentum, parity, and charge
parity, we expand the function $\Psi({\bf q})$ in the Dirac algebra by
imposing the correct transformation properties.  We also demand that
$\Psi({\bf q})$ fulfills the conditions (\ref{psieq3})-(\ref{psieq4}).
For example the expansion of the $0^{-+}$~state is
\begin{equation}
\Psi({\bf q})=\Psi_P(q)\gamma^5+\Psi_A(q)\left(\gamma^0\gamma^5+
\gamma^5\frac{\bbox{\alpha}\cdot{\bf q}}{m}\right).
\end{equation}
The scalar functions $\Psi_A$ and $\Psi_P$ depend only on $q=|{\bf
q}|$.  Similar expansions for other states are given in
Appendix~\ref{waveexp}.

Integral equations for the scalar functions $\Psi_i$ can be obtained
from (\ref{psiequation}) by expanding both sides in the Dirac algebra
and comparing the coefficients.  This is discussed further in
Appendix~\ref{eigenequ}, where all integral equations are given.

\section{The potential}
\label{potential}
We have chosen a potential which consists of one short-range part
describing the one-gluon-exchange interaction and one long-range
confining part. The calculations have been done both in the Feynman
gauge and in the Coulomb gauge, in an attempt to study the gauge
dependence in the instantaneous approximation. The respective
potentials are
\begin{eqnarray}
K_{\text{Feyn}}(r)=&&K^V(r)\gamma_\mu^{(1)}\gamma^{\mu(2)}
+K^S(r)+U,\\
K_{\text{Col}}(r)=&&K^V(r)\left(\gamma^{0(1)}\gamma^{0(2)}-\frac{1}{2}
\bbox{\gamma}^{(1)}\bbox{\gamma}^{(2)}+
\frac{1}{2}(\bbox{\gamma}^{(1)}\cdot{\bf\hat x})
(\bbox{\gamma}^{(2)}\cdot{\bf\hat x})\right)
+K^S(r)+U,
\end{eqnarray}
where $U$ is a constant and
\begin{eqnarray}
	K^{V}(r) & = & \frac{\bar\alpha_s}{r},  \\
	K^{S}(r) & = & \lambda r .
\end{eqnarray}
In momentum space the vector part in the Coulomb gauge becomes
\begin{equation}
	\frac{4\pi\bar\alpha_{s}}{({\bf p}-{\bf q})^{2}} \left(
	\gamma_\mu^{(1)}\gamma^{\mu(2)} +(\bbox{\gamma}^{(1)}\cdot({\bf \hat
	p}-{\bf \hat q}))(\bbox{\gamma}^{(2)}\cdot
	({\bf \hat
	p}-{\bf \hat q}))\right) \label{coulomb_mom}
\end{equation}
The color factor $4/3$ is included in $\bar\alpha_s$,
$\bar\alpha_s=4/3\alpha_s$.  We let the coupling be constant, since a
running coupling would not make any significant difference for heavy
mesons like charmonium.

There are four parameters in the model: $\bar\alpha_s$, $\lambda$, $U$,
and the quark mass $m$.  These will be determined by a least square
fit to the mass spectrum and the ratios of the lepton pair decays.

Olsson {\it et al.\/}\cite{olsson_stabil} have recently investigated
the stability of the Salpeter equation for various Lorentz
structures of the confining kernel.  They have come to the conclusion
that for light and medium-heavy quarks numerically stable solutions
exist only for a time component vector potential.  The same result has
also been found  by Parramore and
Piekarewicz\cite{parramore1,parramore2} from a similar analysis.

However, we have found no such problems for heavy quarks like in the
charmonium system. This has also been
confirmed in Ref.\cite{ResagochMunz3}.  Furthermore,
a time component vector confinement gives a contribution to the
spin-orbit coupling with the wrong sign, which speaks in favor of a
scalar confinement.

We want to be able to perform the angular integrations in the Salpeter
equation analytically.  We therefore need the expansions of the
potential in spherical harmonics in momentum space as
\begin{equation}
K^i({\bf p}-{\bf q})=\sum_{\ell m}F_\ell^i(p,q)Y^*_{\ell m}(\hat {\bf
p})Y_{\ell m}(\hat {\bf q}), \quad i=V,S.
\end{equation}
The expansion of the Coulomb potential is
\begin{equation}
K^V({\bf p}-{\bf q})=\frac{4\pi\bar\alpha_s}{({\bf p}-{\bf q})^2}=
\frac{8\pi^2\bar\alpha_s}{pq}\sum_{\ell
m}Q_\ell\left(\frac{p^2+q^2}{2pq} \right)Y^*_{\ell m}(\hat {\bf
p})Y_{\ell m}(\hat {\bf q}),
\end{equation}
where $Q_\ell$ are the Legendre functions of second kind.  Thus
\begin{equation}
F_\ell^V(p,q)=\frac{8\pi^2\bar\alpha_s}{pq}Q_\ell\left(\frac{p^2+q^2}{2pq}
\right).
\end{equation}
In the Coulomb gauge potential (\ref{coulomb_mom}) there is another
angular dependence in the second term.  However, we later choose to
give this dependence in terms of the functions $F_{\ell}^{V}$.

The Fourier transform of the linear potential can only be defined in a
distributional sense.  This causes no problems as in momentum space
the value of the potential at each point is not important, but only its
action on a wave function.  We define $K^S(r)$ as the limit
\begin{equation}
K^S(r)=\lim_{\epsilon\to0}\frac{\partial^2}{\partial\epsilon^2}
\left(\frac{\lambda e^{-\epsilon r}}{r}\right).
\end{equation}
This gives
\begin{eqnarray}
K^S({\bf p}-{\bf
q})=&&\lim_{\epsilon\to0}\frac{\partial^2}{\partial\epsilon^2}\left(
\frac{4\pi\lambda}{({\bf p}-{\bf q})^2+\epsilon^2}\right) \nonumber \\
=&&\lim_{\epsilon\to0}\frac{8\pi^2\lambda}{pq}\sum_{\ell m}
\frac{\partial^2}{\partial\epsilon^2}Q_\ell\left(\frac{p^2+q^2+\epsilon^2}{2pq}
\right)Y^*_{\ell m}(\hat {\bf p})Y_{\ell m}(\hat {\bf q}).
\end{eqnarray}
It can be shown~\cite{Hersbach}, that in a distributional sense, the
following relation holds:
\begin{eqnarray}
\lefteqn{\lim_{\epsilon\to0}\int_0^\infty
dp\frac{\partial^2}{\partial\epsilon^2}
Q_\ell\left(\frac{p^2+q^2+\epsilon^2}{2pq}\right)f(p)} \nonumber \\
&&=\text{PV}\int_0^\infty
dp\left(\frac{1}{pq}Q'_\ell\left(\frac{p^2+q^2}{2pq}
\right)f(p)+\frac{4q^2}{(p+q)^2(p-q)^2}f(q)\right),
\end{eqnarray}
where PV means the principal value.  Thus
\begin{eqnarray}
\lefteqn{\int_0^\infty\frac{dp}{(2\pi)^{3}} p^2 F_\ell^S(p,q)\Psi(p)}\nonumber \\
&&= \text{PV}\int_0^\infty \frac{dp}{(2\pi)^3}8\pi^2\lambda
\left(\frac{1}{q^2}Q'_\ell\left(\frac{p^2+q^2}{2pq}
\right)\Psi(p)+\frac{4q^2}{(p+q)^2(p-q)^2}\Psi(q)\right).
\end{eqnarray}

\section{Lepton pair decays}
\label{leptondecay}
We now continue with a discussion of the decay observables.  A general
prescription for calculating matrix elements of the electromagnetic
current operator between bound states has
been given by Mandelstam~\cite{Mandelstam}.  We begin with the lepton
pair decays, which we will use together with the mass spectrum, in
order to optimize the four parameters $\bar\alpha_s$, $\lambda$, $U$,
and $m$ in the model.  The probability for a vector particle decaying
into two light leptons is
\begin{equation}
\Gamma=\frac{4\pi\alpha^2 e_q^2}{M^3}|j^\mu j_\mu|^2,
\end{equation}
where $j^\mu$ is the vector quark current, $e_q$ is the charge of the
quark, and $M$ is the mass of the vector particle.  To lowest order in
the electromagnetic coupling the current is, in the rest frame of the
decaying particle,
\begin{equation}
j^\mu=-\text{Tr}\int\frac{d^4q}{(2\pi)^4}\gamma^\mu\chi(q)=
-\text{Tr}\int\frac{d{\bf q}}{(2\pi)^{3}} \gamma^\mu \Psi({\bf q}).
\end{equation}
The corresponding Feynman diagram is given in Fig.~\ref{leptonfig}.

Taking the trace we find that $j^0=0$ (whence the current is
conserved) and
\begin{equation}
{\bf j}=\int\frac{d{\bf q}}{(2\pi)^3} \left(\frac{4m}{q^2}{\bf
q}\Psi_S(q) Y_{1m}(\hat{\bf q})+4\Psi_V(q) {\bf Y}_{1m}^{(e)}(\hat{\bf
q})\right). \label{leptonstrom}
\end{equation}
We have here used the expansion (\ref{ettppexp}) of the $1^{--}$~state
given in Appendix~\ref{waveexp}.

Performing the angular integration we get
\begin{equation}
|{\bf j}|^2=\left( \int\frac{dq}{(2\pi)^{3}}
\left(8mq\sqrt{\frac{\pi}{3}}\Psi_S(q)+8q^2\sqrt{\frac{2\pi}{3}}
\Psi_V(q)\right)\right)^2.
\end{equation}

The expression for the leptonic decay is divergent and has to be
renormalized~\cite{Ito_renorm}.  This can in principle be done in
several ways.  However, here we must take into account the fact that
the theory is not fully defined.  This means that with an interaction
kernel which is instantaneous and defined by the ladder expansion
only, the Ward-Takahashi identities are not appropriate.  The
divergence of the wavefunction at the origin can therefore only be
related to the (experimental) value of the vertex function at some
suitable momentum transfer.  For non-confining potentials, such as the
Coulomb potential, there is a region of production of asymptotically
free fermions above threshold.  The production cross section can then
be calculated with the kernel and the result be taken as a measure of
the vertex function.  This is more or less the choice in
Ref.\cite{Ito_renorm}.  In our case the potential is confining and
consists of two parts, one of which has a dimensionful coupling
constant $\lambda$.  This means that the renormalization has to be
done in the deep inelastic region, where the quarks are asymptotically
free and the linear part of the potential is negligible.  This
presents several problems since the lack of manifest covariance makes
the renormalization constant depend upon both the cut-off and the
momentum.

The problem appears as follows.  We would like to define a
renormalization constant $Z_1$, such that
 \begin{equation}
\lim_{\Lambda\to\infty}Z_1(\Lambda)\int^\Lambda d{\bf
q}\,\gamma^\mu\Psi({\bf q}) =\text{finite.}
\end{equation}
Asymptotically $\Psi({\bf q})\sim q^{-3+\beta}$, and thus
$j^\mu\sim\Lambda^\beta$ for large $\Lambda$, where $\beta$ is
determined from the dynamics\cite{Ito_renorm}.

The renormalization constant, $Z_1$, is defined through the
(analytically continued) vertex function $\Gamma^\mu$ by
\begin{equation}
\bar u({\bf q})\Gamma^\mu u({\bf q})=Z_1^{-1}(q)\bar u({\bf
q})\gamma^\mu u({\bf q})
\label{zdef}
\end{equation}
and the vertex function satisfies
\begin{eqnarray}
\bbox{\Gamma}({\bf
q})=&&\bbox{\gamma}+i\int^\Lambda\frac{d^{4}p}{(2\pi)^{4}} K^V({\bf
p}-{\bf q})\gamma^\mu\frac{1}{\rlap{/}{p}-m} \bbox{\Gamma}({\bf
p})\frac{1}{\rlap{/}{p}-m}\gamma_\mu\nonumber\\
&&{}+i\int^\Lambda\frac{d^{4}p}{(2\pi)^{4}} K^S({\bf p}-{\bf
q})\frac{1}{\rlap{/}{p}-m} \bbox{\Gamma}({\bf p})\frac{1}{\rlap{/}{p}-m}.
\end{eqnarray}

The renormalization constant $Z_1$ has the correct asymptotic behavior
to cancel the $\Lambda$-dependence of the current.  However, due to
the instantaneous approximation, $Z_1$ depends on $q$.  With only a Coulomb
potential, $Z_1$ has the correct $\Lambda$-dependence to cancel the
divergence of $j^{\mu}$ as $\Lambda\to\infty$ for any momentum $q$.
However, with a confining part added to the potential this would only
be true in the region $q\to\infty$, where the linear potential is
negligible.  Unfortunately, $Z_1\sim q^\beta$ when $q\to\infty$, and
therefore the theory is not renormalizable in this way.

The electromagnetic theory can only be used in lowest order due to the
non-existence of Ward-Takahashi identities in the instantaneous
approximation since the theory is not fully defined.  Nevertheless
there is a loop contribution in the current $j^{\mu}$ which has to be
renormalized.  As the vertex function cannot be renormalized, we therefore
adopt the philosophy that, for confining potentials, the most natural
experimental datum at which to fix the normalization is the resonance
formation itself.  The renormalization should therefore be effected by
using, say, the decay width for the lowest resonance as input.  The
other decay widths are then calculated relative to this.  Thus we will
optimize only the ratios of the decay constants for successive
$nS$~states as predictable by the model.  These ratios are independent
of the cut-off $\Lambda$ for $\Lambda \geq 30 $ GeV to within $1 \%$.

Another way to avoid the problem with infinities would be to redefine
the potential to take a finite value for $r=0$.  This would make the
current (\ref{leptonstrom}) finite.  However, the theory must still be
renormalized although only a finite renormalization is necessary in
this case.  Therefore such an approach would still face the same
problem as explained above, as a new dimensionful constant must be
introduced in the cut-off of the potential.  Our opinion is that our
approach is much cleaner and conceptually more transparent.

\section{$\gamma\gamma$ decays}
\label{ggdecay}
The calculation of the $\gamma\gamma$ decays is most easily performed in the
rest frame of the bound state, which decays into two photons with
momenta $k_1=(M/2,{\bf k})$ and $k_2=(M/2,-{\bf k})$.  To lowest order
the matrix element is given by
\begin{eqnarray}
M^{\mu\nu}=&&\text{Tr}\int\frac{d^{4}q}{(2\pi)^{4}}
\chi(q)\left(\gamma^\mu \frac{1}{\rlap{/}{P}/2+\rlap{/}{q}-\rlap{/}{k_1}-m}
\gamma^\nu+\gamma^\nu \frac{1}{\rlap{/}{P}/2+\rlap{/}{q}-\rlap{/}{k_2}-m}
\gamma^\mu\right)\nonumber\\
=&&\text{Tr}\int\frac{d^{4}q}{(2\pi)^{4}} \chi(q)\left(\gamma^\mu
\frac{1}{\rlap{/}{q}+\bbox{\gamma}\cdot{\bf k}-m} \gamma^\nu+\gamma^\nu
\frac{1}{\rlap{/}{q}-\bbox{\gamma}\cdot{\bf k}-m} \gamma^\mu\right).
\end{eqnarray}
The corresponding Feynman diagrams are given in Fig.~\ref{gamgamfig}.
The decay probability is given by
\begin{equation}
\Gamma=\frac{3\pi\alpha^2e_q^4}{2(2J+1)M}\sum|\epsilon_1^\mu\epsilon_2^\nu
M_{\mu\nu}|^2,
\end{equation}
where $e_q$ is the charge of the quark, and $M$ is the meson mass and
$J$ its angular momentum.

The amplitude $\epsilon_1^\mu\epsilon_2^\nu M_{\mu\nu}$ can be
expressed in the scalar amplitudes for the different decaying states.
This is discussed in Appendix~\ref{ggdecays}.

\section{M1 and E1 transitions}
\label{m1e1decay}
In the rest frame of the initial particle the matrix element for the
M1 and E1 transitions is, in the ladder approximation, given by
\begin{eqnarray}
	M^\mu= & &
	\text{Tr}\int\frac{d^4q}{(2\pi)^4}\bar\chi_{f}(q-k/2,P_f)
	\gamma^\mu\chi_i(q,M_i) (-\frac{M_i}{2}\gamma^0+\rlap{/}{q}-m)\nonumber
	\\
	 & & +\text{Tr}\int\frac{d^4q}{(2\pi)^4}\bar\chi_{f}(q+k/2,P_f)
	 (\frac{M_i}{2}\gamma^0+\rlap{/}{q}-m)\chi_i(q,M_i) \gamma^\mu.
\end{eqnarray}

Here $\chi_i(q,M_i)$ is the wave function of the initial particle in
its rest frame, and $\bar\chi_f(q\pm k/2,P_f)$ is the wave function of
the final particle in a frame where it moves with momentum $P_f$.
This wave function is found by Lorentz transforming the one in the
rest frame, see Appendix~\ref{lorentz}.  The Feynman diagrams
corresponding to $M^\mu$ are given in Fig.~\ref{m1fig}.

The decay probability is given by
\begin{equation}
\Gamma=\frac{\alpha e_q^2 k}{2M_i^2(2J+1)}\sum|\epsilon_\mu M^\mu|^2,
\end{equation}
where $e_q$ is the charge of the quark, $k$ the photon momentum, $M_i$
the mass of the initial meson and $J$ its angular momentum.

To calculate the matrix element we use the expansions of the wave
functions given in Appendix~\ref{amplitudes}.  We first perform the
$q^0$ integration.  Since the Lorentz transformed state
$\chi(q-k/2,P_f)$ has a very complicated analytic structure we cannot
make a simple contour integration.  We have to use the principal value
technique.  The real part is given by a sum of residues
\begin{equation}
\text{Re}\ i\int dq^0 \frac{f(q^0)}{g(q^0)\pm i\epsilon}=\pm \pi
\frac{f(p^0_k)}{|g'(p^0_k)|},
\end{equation}
where $p^0_k$ is a zero of $g(p^0)$.  The imaginary part gives an
unphysical non-Hermitian contribution to the decay width.  It should
vanish in any consistent covariant theory, but in the Salpeter model
is has been verified that it does not vanish\cite{ResagochMunz4},
because of the lack of manifest covariance.  However, for the
charmonium system this unphysical contribution is negligible, and
we therefore neglect it.

The integration over the azimuthal angle $\varphi$ can also be done
analytically.  The rest of the calculation is made numerically.
Trying to take the trace analytically creates enormously complicated
expressions which are hardly of any use.

\subsection{Gauge invariance of the matrix element}
In a Bethe-Salpeter model without the instantaneous approximation
where we have an even kernel of the form $K(p-q)$, the gauge
invariance of the matrix element can be shown with the help of the
Bethe-Salpeter equation.  Let the initial meson have momentum $P_i$
and the final meson have momentum $P_f=P_i-k$, where $k$ is the photon
momentum.  Then
\begin{eqnarray}
k_\mu M^\mu=&&\int \frac{d^{4}q}{(2\pi)^{4}}\bar\chi(q-k/2,P_f
)\rlap{/}{k}\chi(q,P_i)(-\frac{\rlap{/}{P}_i}{2}+\rlap{/}{q} -m)\nonumber\\
=&&\int \frac{d^{4}q}{(2\pi)^{4}}
\bar\chi(q-k/2,P_f)(\frac{\rlap{/}{P}_i}{2}+\rlap{/}{q}-m)\chi(q,P_i)
(-\frac{\rlap{/}{P}_i}{2}+\rlap{/}{q}-m)\nonumber\\
&&{}-\int \frac{d^{4}q}{(2\pi)^{4}} \bar\chi(q-k/2,P_f
)(\frac{\rlap{/}{P}_f}{2}+\rlap{/}{q}-\frac{\rlap{/}{k}}{2}-m) \chi(q,P_i
)(-\frac{\rlap{/}{P}_f}{2}+\rlap{/}{q}-\frac{\rlap{/}{k}}{2}-m)\nonumber\\
=&&\int \frac{d^{4}q}{(2\pi)^{4}}\frac{d^{4}p}{(2\pi)^{4}}
\bar\chi(q-k/2,P_f)K(q-p)\chi(p,P_i)\nonumber\\
&&{}-\int \frac{d^{4}q}{(2\pi)^{4}}\frac{d^{4}p}{(2\pi)^{4}}
\bar\chi(p,P_f)K(q-k/2-p)\chi(q,P_i)\nonumber\\
=&&\int \frac{d^{4}q}{(2\pi)^{4}}\frac{d^{4}p}{(2\pi)^{4}}
\bar\chi(q-k/2,P_f)K(q-p)\chi(p,P_i)\nonumber\\
&&{}-\int \frac{d^{4}q}{(2\pi)^{4}}\frac{d^{4}p}{(2\pi)^{4}}
\bar\chi(p-k/2,P_f)K(q-p)\chi(q,P_i)=0
\end{eqnarray}
provided the order of integrations can be interchanged.  This proves
gauge invariance.

However, if the kernel depends on the momentum of the bound state, as
it does in the instantaneous approximation, the terms in the last line
do not cancel.  In the first term $K$ depends on $P_i$, and in the
second term on $P_f$.

Nevertheless, in the instantaneous approximation we have verified that
${\bf k}\cdot{\bf M}=0$ and $M^0=0$ in the rest frame of the decaying
particle, by performing the angular integration of the decay
amplitude.  Thus gauge invariance is fulfilled.

\section{Numerical results}
\label{resultat}
The eigenvalue equations given in Appendix~\ref{eigenequ} were solved
numerically by expanding the wave function in cubic Hermite
splines\cite{hermite}. However, first the integration region $0\le p
<\infty$ was transformed into the finite interval $-1\le x\le 1$ by
$x=(p-p_{0})/(p+p_{0})$, where $p_{0}$ was chosen in the physically
relevant region.  The integration and the following matrix eigenvalue
problem for the expansion coefficients were solved with standard
methods.  We have tested the stability of the solutions by varying the
number of basis functions and the parameter $p_{0}$, and found that
the eigenvalues do not change.  Problems, like the ones reported in
Refs.\cite{olsson_stabil,parramore1,parramore2} for lighter quarks,
have not been seen.

The parameters $\bar{\alpha}_{s}$, $m$, $\lambda$, and $U$ of the
model are determined by making a least square fit to the mass spectrum
and the ratios of the lepton pair decay widths $J/\Psi/\Psi(2S)$ and
$\Psi(2S)/\Psi(3S)$.  As discussed in Sec.~\ref{leptondecay} we
renormalize the decay widths to the experimental value of the decay of
$J/\Psi$.  We therefore make the fit to the ratios between the widths
rather than the widths themselves.  We minimize the function
\begin{equation}
\chi^2=\sum\frac{(M_i(\text{theory})-M_i(\text{exp}))^2}{\sigma_i^2}+
\sum\frac{(\Gamma_i(\text{theory})/\Gamma_j(\text{theory})
-\Gamma_i(\text{exp})/\Gamma_j(\text{exp}))^2}{\sigma_{i/j}^{2}}.\label{chikvadrat}
\end{equation}
The first sum goes over all the charmonium masses in
Table~\ref{masstable} except $\eta_c(2S)$
and $h_{c1}$ which are not used in the fit because they still need
experimental confirmation.  The second sum is over the two ratios of
lepton pair decay widths $\Gamma(J/\Psi)/\Gamma(\Psi(2S))$ and
$\Gamma(\Psi(2S))/\Gamma(\Psi(3S))$.  We have not used the decay
widths for the higher states because their wave functions are not good
enough to be used for calculations of decay widths. The experimental
errors for the ratios, $\sigma_{i/j}$, are numerically
$\sigma_{J/\Psi/2S}=0.30$ and $\sigma_{2S/3S}=0.64$ respectively.

As many of the masses are very accurately measured, using the true
experimental error for the masses in this function would make the
masses totally dominate over the decay width.  We therefore use a
minimum value of $\sigma_{i}$ when the experimental error is small.
Two fits for both gauges have been made, one where we have used
$\sigma_i=10$~MeV for the masses when the experimental error is
smaller than 10~MeV, and one where we have used $\sigma_i=50$~MeV for
the masses when the experimental error is smaller than 50~MeV. We use
the true experimental errors for $\sigma_{i/j}$ in both fits.  In the
second fit we thus give the lepton decays a higher weight, though in
both cases the masses get a higher weight than the decay widths as the
errors of the decay widths are rather large.  The numerical results of
the four fits can be found in Tables \ref{masstable} and
\ref{decaytable}.  In these tables F and C stand for Feynman and
Coulomb gauge respectively, and 10 and 50 MeV stand for the minimum
value of $\sigma_{i}$.

Making four fits gives us a chance to see how sensitive the different
decay observables are to changes of the model parameters.  The
parameter values in the four different cases can be found in Table
\ref{parametertable}.  We see that when we change $\sigma_{i}$ from
10~MeV to 50~MeV the parameter which changes most is the constant $U$.
One would perhaps expect that $\bar \alpha_{s}$ would be the parameter
most sensitive to such a change in $\sigma_{i}$, as the lepton pair
decays should be very sensitive to $\bar \alpha_{s}$ because they
depend on the value of the wavefunction at the origin.  However, we
calculate the ratios between the decay widths rather than the widths
themselves, and these ratios are not very sensitive to the value of
$\bar \alpha_{s}$.  This can be understood by noting that in a
non-relativistic model with a Coulomb potential the ratios of the wave
functions' value at the origin are independent of the coupling
constant.  On the other hand, $\bar \alpha_{s}$ of course changes a
lot between the fits in the two different gauges to compensate for the
differences in the structure of the vector part of the potential,
while the other parameters remain almost constant.

The bottom row in Table~\ref{masstable} shows the total $\chi^{2}$ for
the four fits.  A fictitious error of 10~MeV for all masses has been
used to calculate the values in order to make them comparable.  We see
that we obtain a slightly better result in the Coulomb gauge and that
in the Feynman gauge we obtain the largest difference between the fits
with different $\sigma_{i}$.

In Table~\ref{decaytable} the $\chi^{2}$ values in the row just above
the lepton pair decays measure the quality of the calculation of the
E1, M1, and two gamma transitions. We have here excluded the decay
$\Psi(2S)\to\eta_{c}\gamma$ as it would totally dominate $\chi^{2}$.
We see that the results in the Coulomb gauge changes most and that
the Feynman gauge on average gives a better result although the Coulomb
gauge with $\sigma_{i}=50$~MeV is better than any of the two fits in
Feynman gauge.

In the last row in the same table we find the $\chi^{2}$ values for
the lepton pair decays.  The decays of the D states have been excluded
in the calculation as they depend on higher order corrections not
included in our calculations. We see that the Feynman gauge clearly
gives a better result.

In conclusion the Coulomb gauge gives better results for the masses,
the Feynman gauge gives better results for the lepton pair decays and the
results for the two gamma, E1, and M1 transitions are fairly equal,
perhaps slightly better in Feynman gauge.  The overall differences are
not so large that we can clearly tell which one of the two gauges
gives best results.

The lepton decay widths are normalized such that the value for
$J/\Psi$ agrees with the experimental value.  We see that the other
values for the S states become too large.  This indicates that we lack
a fine-tuning of the shape of the potential.  A smaller slope of the
linear confinement potential would push the wave function further away
from the origin but would on the other hand make the mass spectrum
worse.  That the decay widths for the D states are rather small is not
surprising, as they mainly come from higher order corrections not
included here.  In non-relativistic models with a Coulomb potential
the wave function for D states is zero at the origin, which give a
vanishing decay width.  In the Salpeter model this means that higher
order corrections to the kernel in the ladder approximation are very
important for the D states.

The values for the two gamma decays agree very well with experiment,
and the values for the E1 transitions agree fairly well although the
values for the decays including the $\chi_{c1}$ state all come out
about a factor of two too large.

When it comes to the M1~transitions we see that the predicted value of
the $J/\Psi\to \gamma\eta_c$ decay width agrees very well with
experimental data.  On the other hand the $\Psi(2S)$ decay width is
far too large.  This is because the wave function of the excited state
is not determined well enough, and as this decay is forbidden it is
extremely sensitive to the exact shape of the wave functions.

For light quarks, the non-relativistic quark model parameters
usually relate the magnetic moments directly to the constituent masses
and there is no room in the parameterization, so to speak, to
introduce anomalous magnetic moments.

For the charm quark the current and constituent masses should be
essentially the same and there is then a possibility to introduce an
anomalous magnetic moment as a new independent parameter.

The details of the decay mechanism are in principle sensitive to this
parameter.  In the absence so far of any measurement of the magnetic
moment of charmed baryons, the radiative decay rates therefore
constitute at present the only place where this parameter can be
studied.

Once an accurate determination of the wave functions can be made, the
anomalous magnetic moment can be calculated from the M1 transitions.
But it is important to notice that the outcome of such a calculation
depends heavily on the quark mass. Therefore a determination of
the quark mass must be made first. An estimate of the anomalous
magnetic moment have previously been made in a Salpeter model where a
non-relativistic approximation has been made\cite{Hulth_o_Hakan}.

A calculation of lepton pair decays and E1 transitions has earlier
been done by Ito\cite{Ito_E1} in a model where only the positive energy
term is used in the Salpeter equation. Recently a calculation of all
decay observables has been done by Resag et al.\cite{ResagochMunz3} in
a Salpeter model, but with a cut-off in the potential to regularize
the divergence in the lepton pair decay amplitude. The overall results
in both these calculations are of about the same quality as in ours.
As we have discussed earlier, the lepton pair decays depend
of the cut-off parameter, and therefore have to be renormalized before
they can be compared. Doing so, we see that their results for a
scalar confinement are almost identical with our results in Feynman
gauge with $\sigma_{i}=10$~MeV.

\section{Importance of non-dominant terms}
Sometimes the Salpeter equation is reduced to only the term with the
positive energy states of the quark. This is done by making the
following replacement of the propagators (\ref{propagator}) in the
Salpeter equation:
\begin{equation}
	\frac{1}{\rlap{/}{q}-m} \longrightarrow
	\frac{\Lambda_{+}^{+}({\bf q})\gamma^{0}}{(q^{0}-E({\bf
	q})+i\epsilon)}= \frac{\gamma^{0}\Lambda_{-}^{-}({\bf q})}{(q^0+E({\bf
	q})-i\epsilon)}
\end{equation}
This imposes an extra constraint on the reduced wave function $\Psi({\bf
q})$. Eq.~(\ref{litet_psi}) is replaced by
\begin{equation}
	\Lambda_{-}^{+}({\bf q})\Psi({\bf q})\Lambda_{+}^{-}({\bf q})=0
\end{equation}
For the wave function $\chi(q)$ only the first term in (\ref{waveeq})
remains:
\begin{equation}
	\chi(q)=-\frac{i(M-2E)}{(M/2+q^0-E+i\epsilon)(-M/2+q^0+E-i\epsilon)}
	\Lambda_{+}^{+}({\bf q})\Psi({\bf q})\Lambda_{-}^{-}({\bf q})
\end{equation}

Does this reduction change the results significantly?  Olsson {\it et
al.\/}\cite{olsson_2} have recently investigated the validity of the
reduced Salpeter equation by comparing the eigenvalues and wave
functions found from the full and reduced Salpeter equation.  They
found that there is only a significant difference for light quarks,
and for as heavy ones as the charm quark the difference is very small.

However, this does not completely test the validity of the reduced
Salpeter equation.  In particular this does not tell us how important
the last two terms in (\ref{waveeq}) are.  They do not appear in the
calculation of the mass spectrum, which only involves the reduced wave
function $\Psi({\bf q})$.  On the other hand, the E1 and M1
transitions do include these two terms.

To test the validity of the reduced Salpeter equation we have
therefore compared the decay widths for E1 and M1 transitions using only the
terms with positive energy states and the widths using all terms. We
have not solved the reduced Salpeter equation but only neglected all
but the dominant term. This will not give us an exact comparison with
the reduced Salpeter equation but as have been shown by Olsson~{\it et
al.\/}\cite{olsson_2} the wave functions differ very little. The
result is shown in Table \ref{positiveenergytable}.  We see that the
decay widths change considerably if we neglect all but the dominant
term, in some cases with more than 100~\%.  This
shows the importance of keeping all terms.  Although the magnitude of
the negative energy part of the reduced wave functions is small -- the
contribution to the norm is typically $<5$~\% -- there are
other terms in the decay amplitudes which make the contribution from
the non-dominant terms significant.

This can be understood if we note that the last two terms in the wave
function (\ref{waveeq}) do not appear in in the expression for the
norm (\ref{normtr}).  Using the reduced Salpeter equation leads to a
normalization condition with only the first term in (\ref{normtr}).
The omitted second term is small and thus changes the normalization
very little.

To further illustrate this we have plotted the functions
\begin{displaymath}
	\frac{m}{E(q)}\Psi_{P}(q)\pm \Psi_{A}(q)
\end{displaymath}
and
\begin{displaymath}
	\frac{I_{0}(q)}{E(q)}
\end{displaymath}
for the $0^{-+}$ state in Fig.~\ref{amplitudplot}. These functions
appears in the amplitudes of $0^{+-}$'s  wave function. We see that
negative energy amplitude $\frac{m}{E(q)}\Psi_{P}(q)- \Psi_{A}(q)$ is
considerably smaller than the positive energy amplitude. The
amplitude $I_{0}/E$ appearing in the last two terms of the wave
function (\ref{waveeq}) is somewhere in between in magnitude. However,
it should be noted that it is difficult to directly compare this
function to the other two because of the other factors in the
amplitudes coming from the propagators. But we see that it is clearly
not negligible.

Comparing the mass spectrum and wave functions is therefore not enough
to tell if an approximation is valid.  The decay widths must also be
studied.  Using the reduced Salpeter equation means that several terms
in the decay widths are omitted and we have shown that these terms are
very important in the E1 and M1 transitions.  We conclude that the
reduced Salpeter equation gives approximately the same result as the
full Salpeter equations only for those quantities which do not depend
on the last two terms in the wave function (\ref{waveeq}).

\section{Summary and conclusions}
\label{tillsist}
We have done a thorough analysis of the charmonium system in a
Salpeter model with an instantaneous potential.  We have presented
general equations for calculating the mass spectrum as well as decay
widths for lepton pair decays, two gamma decays, M1 and E1
transitions.  This has been done for a vector plus scalar potential
both in the Coulomb and Feynman gauges.  The formalism used is based
on the one developed by Suttorp\cite{Suttorp}.

We have discussed the problem with the renormalization of the lepton
pair decay amplitude in the instantaneous approximation.  This
approximation makes the renormalization constant $Z_{1}$ depend on
$q$ and $Z_{1}\to\infty$ as $q\to\infty$.  With a linear confining
potential we have to make the renormalization in the region where the
quarks are asymptotically free and the linear potential is negligible.
But since $Z_{1}\to\infty$ this leads to an inconsistency, and
therefore the only natural way to define the renormalization constant
is to normalize the calculated widths to the experimental value of the
width $J/\Psi\to e^{+}e^{-}$.

Numerically we have obtained an excellent fit to the mass spectrum of
charmonium.  Most of the decay widths agree rather well with
experiments, although the lepton pair decays of the excited S states
are too large.  The excited states are obviously more sensitive to
fine-tuning of the model.  A smaller slope of the linear confinement
potential would push the wave function further away from the origin
but would on the other hand make the mass spectrum worse.  Similarly
the poor result for the forbidden M1 transition
$\Psi(2S)\to\eta_{c}\gamma$ indicates a lack of fine-tuning of the
potential.  We conclude that before any detailed predictions can be
made from the Salpeter equation, a systematic way to improve the
kernel must be developed.

Comparing the two gauges, Feynman and Coulomb gauge, we have found the
the Coulomb gauge gives better results for the mass spectrum and that
the Feynman gauge gives better results for the lepton pair decays.
The overall difference is not large enough to clearly tell which
gauge gives the best results.

The validity of the reduced Salpeter equation has been tested, and it
has been found that the decay widths of the E1 and M1 transitions
change considerably if one uses the reduced equation.

\acknowledgments
This work was supported by the Swedish Natural Science Research
Council (NFR), contract F-AA/FU03281-308.

redpajama_set_name: RedPajamaArXiv


text:
eLessons
Cleveland and the Texas Seed Bill
Cleveland understood
Cleveland understood his constitutional legislative responsibility as preventing harmful bills from becoming law, rather than promoting what he saw as beneficial ones. Using the veto, Cleveland stopped the federal government from taking on what he saw as a "paternal" role towards citizens. This eLesson focuses on Cleveland's veto of the Texas Seed Bill, which would have provided seeds to drought-stricken farmers who had eaten their seed corn to survive.
President Grover Cleveland once told a friend that he saw his chief legislative duty to be stopping bad bills from becoming law, rather than trying to convince Congress to pass what he thought would be good ones. Cleveland used the veto more than any other US president before or since.
One of Cleveland's most famous vetoes was his veto of the Texas Seed Bill in 1887. A long and severe drought had stricken areas of Texas. With no grass to graze, eighty-five percent of cattle in the western part of the state died. Those cattle that remained were starving, often motherless calves. Many farmers were also close to starvation and had eaten their seed corn to survive. Congress authorized a special appropriation to send seeds to the drought-stricken farmers. The amount ($10,000, or approximately $223,000 in today's dollars) was small and the need was great, but Cleveland vetoed the bill.
His veto message expressed his commitment to the Constitution and the importance of private charity. He said that while he thought the intentions of the bill were good, he had to withhold his approval. He wrote,
"I can find no warrant for such an appropriation in the Constitution, and I do not believe that the power and duty of the general government ought to be extended to the relief of individual suffering which is in no manner properly related to the public service or benefit. A prevalent tendency to disregard the limited mission of this power and duty should, I think, be steadfastly resisted, to the end that the lesson should be constantly enforced that, though the people support the government, the government should not support the people."
Furthermore, Cleveland said, it would weaken the "bonds of a common brotherhood" for the government to provide assistance to individuals where individuals, families, communities and private charities otherwise would.
Finally, the veto message suggested that if Congress wanted to relieve the suffering of Texas farmers, Senators and Representatives from each state could voluntarily give up the share of grain distributed by the Department of Agriculture each year. "The constituents, for whom in theory this grain is intended, could well bear the temporary deprivation, and the donors would experience the satisfaction attending deeds of charity." Cleveland's principled stances won him the admiration of many. They also brought him many enemies. But he did not waver from his commitment to exercising only the powers warranted by the Constitution. One American author said that Cleveland's "patriotic virtues have won for [him] the homage of half a nation and the enmity of the other half. This places [his] character upon a summit as high as Washington's."
What was the Texas Seed Bill?
List two reasons for Cleveland's veto of the Texas Seed Bill.
How would you respond to Cleveland's assertion that "the lesson should be constantly enforced that, though the people support the government, the government should not support the people"?
One American author said that Cleveland's "patriotic virtues have won for [him] the homage of half a nation and the enmity of the other half. This places [his] character upon a summit as high as Washington's." From what you know, which do you think he deserves? What else would you want to know to answer the question more completely?
eLessons|


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BrandsGirard PerregauxNewsWatch Advice
Girard-Perregaux Laureato Absolute Ti 230
by Chamath Gamage 5 August, 2021
by Chamath Gamage 5 August, 2021 0 comment
2021 marks the 230th anniversary of Girard-Perregaux. As part of celebrating this incredible occasion, The Maison is going back to some of their iconic creations and recreating some beautiful new timepieces. The latest timepieces released as part of the brand's celebration is a nod to the birth year of the Manufacture and another significant event that took place in that same year.
Girard-Perregaux's story began in 1971, when Jean-François Bautte produced his first pocket watch. In this same year, an English Clergyman named William Gregor discovered black sand called menachanite in Cornwall. After analysing this black sand, he found that it contained oxides of iron and an unknown metal. This unknown metal is what we know today as titanium! In modern times, titanium is now used in various fields such as medicine, motorsport, aerospace, and of course watchmaking, showing just how important the discovery of this material is.
This newest creation by Girard-Perregaux, the Laureato Absolute Ti 230, celebrates the brand's heritage but also the story of William Gregor and titanium.
The Girard-Perregaux Laureato Absolute Ti 230 comes in a Grade 5 titanium 44mm lightly sandblasted case, which has polished facets that give off a beautiful yet subtle shine. The casing has curves that are beautifully contrasted with the sharp lines of the octagonal bezel and crown. A detail that is subtle yet familiar to those in the know is that the crown is encircled in a rubber ring. This is a first for the brand and it's done quite tastefully as the rubber ring matches the hue of the rubber strap.
The Laureato Absolute Ti 230 is offered in two different dial variants, with a choice of a blue or grey dial available. The dial itself is made up of a sandwich-type construction, which consists of an upper layer, that has several openings which sit on top of a lower layer. These openings in the upper layer give insight into the lower layer, which is made in grey. The hour indexes and date window are all made from these apertures, with the top layer cut out to show the grey indexes on the lower layer.
The strap used for these timepieces is a design that upholds the tradition of the Maison, which goes back to the original model these models were based on back in 1975. The strap is integrated and is made of GP Rubber Alloy which now contains titanium. The brand has chosen to use FKM rubber for the strap as it offers greater suppleness and resistance when compared to conventional rubber. Fitted with a micro-adjustment system on the strap, the wearer is able to get the most comfortable and optimal fit.
In regards to the design of the Laureato Absolute Ti 230, Patrick Pruniaux, CEO of Girard-Perregaux says that "With the release of the Laureato Absolute Ti 230 we wanted to create a new version of our iconic watch from 1975. This model is modern but encompasses traditional craftsmanship. The sandwich dial construction and GP's world-premiere Rubber Alloy strap, this time incorporating titanium, are further sumptuous details that also feature on this watch. Finally, while the price may be more inclusive, the quality remains typically Girard-Perregaux and the watch feels just as exclusive as our other models."
The movement used for the Girard-Perregaux Laureato Absolute Ti 230 is the self-winding mechanical Manufacture movement, the Calibre GP03300-1060. Containing 218 components, this calibre produces a frequency of 4hz (28, 800 VpH) and has a minimum power reserve of approximately 46 hours.
The blue and grey variants of the Laureato Absolute Ti 230 are both limited edition models with 230 pieces of each being released. The grey dial variant is available in all authorised Girard-Perregaux retailers along with the brand's e-commerce website. The blue dial variant however will be sold exclusively by Wempe for one month from its release. Wempe has ten boutiques across Germany as well as stores in London and New York. After this one month is over, the models will be offered like the grey variant, throughout Girard-Perregaux retailers and online.
Wempe was very proud that Girard-Perregaux wanted to offer the models exclusively for sale with them first. Managing owner of Gerhard D. Wempe KG of Wempe, Kim-Eva Wempe says that "Once again, Girard-Perregaux kindly approached us and offered exclusivity for this new model prior to its worldwide launch. We are delighted to have this opportunity and we appreciate the close working relationship we enjoy with Girard-Perregaux, forged over several years but solidified last year when we were fortunate to become their exclusive retailer across Germany."
International Pricing: 8,260 CHF
Maurice Lacroix – Timekeeper for Acea Run Rome the Marathon