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Get Illinois Fighting Illini Men's Basketball
Haddonfield, illinois is a fictional town that was used as the setting for the cult classic film "halloween." the film, which debuted in 1978 and starred jamie lee curtis, was set in the idyllic midwestern surroundings but was actually shot. Oct 28 (fri) 7 pm ct b1g+ (stream) · eastern illinois . 1800 s 1st st, champaign, il 61820. People can pay for traffic tickets through the judici system or browse a number of different court cases that are available for public. Find out the latest on your .
Ohio State Buckeyes vs Illinois Fighting Illini Prediction & Match from staticg.sportskeeda.com
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Coverage of the men's and women's university of illinois teams and big ten basketball. Haddonfield, illinois is a fictional town that was used as the setting for the cult classic film "halloween." the film, which debuted in 1978 and starred jamie lee curtis, was set in the idyllic midwestern surroundings but was actually shot. State farm center is proud to be the home court of the university of illinois fighting illini! Within the service industry, community, health care and personal services industries lead the way in illinois. @coach_underwood · 3,064 posts · 101k followers · 239 . Your source for the top illini basketball news stories. Get the latest news and information for the illinois fighting illini. Keep up with the fighting illini on bleacher report.
Other strong services are finance.
Like most states in the united states, the major industries in illinois are service industries. State farm center is proud to be the home court of the university of illinois fighting illini! 2022 season schedule, scores, stats, and highlights. Within the service industry, community, health care and personal services industries lead the way in illinois. Judici of illinois is the online portal of 71 different judicial courts throughout the state of illinois. Official twitter account for university of illinois fighting illini men's basketball | 18 big ten championships . People can pay for traffic tickets through the judici system or browse a number of different court cases that are available for public. @coach_underwood · 3,064 posts · 101k followers · 239 . Official instagram account of university of illinois fighting #illini men's basketball head coach: 1800 s 1st st, champaign, il 61820. The official men's basketball page for the university of illinois fighting illini. Oct 28 (fri) 7 pm ct b1g+ (stream) · eastern illinois . Coverage of the men's and women's university of illinois teams and big ten basketball.
Formerly the assembly hall, state farm center has provided a home . Like most states in the united states, the major industries in illinois are service industries. Judici of illinois is the online portal of 71 different judicial courts throughout the state of illinois. Visit espn to view the latest illinois fighting illini news, scores, stats,. The illinois fighting illini men's basketball team is an ncaa division i college basketball team competing in the big ten conference.
Other strong services are finance. Judici of illinois is the online portal of 71 different judicial courts throughout the state of illinois. Like most states in the united states, the major industries in illinois are service industries. Official twitter account for university of illinois fighting illini men's basketball | 18 big ten championships . Haddonfield, illinois is a fictional town that was used as the setting for the cult classic film "halloween." the film, which debuted in 1978 and starred jamie lee curtis, was set in the idyllic midwestern surroundings but was actually shot. 2022 season schedule, scores, stats, and highlights. State farm center is proud to be the home court of the university of illinois fighting illini! The official men's basketball page for the university of illinois fighting illini.
Visit espn to view the latest illinois fighting illini news, scores, stats,.
Formerly the assembly hall, state farm center has provided a home . The illinois fighting illini men's basketball team is an ncaa division i college basketball team competing in the big ten conference. Find out the latest on your . Your source for the top illini basketball news stories. Within the service industry, community, health care and personal services industries lead the way in illinois. Coverage of the men's and women's university of illinois teams and big ten basketball. Keep up with the fighting illini on bleacher report. The official facebook home of university of illinois fighting illini basketball. 2022 season schedule, scores, stats, and highlights. Judici of illinois is the online portal of 71 different judicial courts throughout the state of illinois. Oct 28 (fri) 7 pm ct b1g+ (stream) · eastern illinois . Other strong services are finance. Haddonfield, illinois is a fictional town that was used as the setting for the cult classic film "halloween." the film, which debuted in 1978 and starred jamie lee curtis, was set in the idyllic midwestern surroundings but was actually shot.
Get Illinois Fighting Illini Men's Basketball. Get the latest news and information for the illinois fighting illini. Official twitter account for university of illinois fighting illini men's basketball | 18 big ten championships . Oct 28 (fri) 7 pm ct b1g+ (stream) · eastern illinois . Your source for the top illini basketball news stories. The illinois fighting illini men's basketball team is an ncaa division i college basketball team competing in the big ten conference.
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Visit espn to view the latest illinois fighting illini news, scores, stats,. The official men's basketball page for the university of illinois fighting illini. Oct 28 (fri) 7 pm ct b1g+ (stream) · eastern illinois .
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Visit espn to view the latest illinois fighting illini news, scores, stats,. Coverage of the men's and women's university of illinois teams and big ten basketball. Within the service industry, community, health care and personal services industries lead the way in illinois.
Coverage of the men's and women's university of illinois teams and big ten basketball. Other strong services are finance. Keep up with the fighting illini on bleacher report.
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Keep up with the fighting illini on bleacher report. Official instagram account of university of illinois fighting #illini men's basketball head coach: Get the latest news and information for the illinois fighting illini.
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The illinois fighting illini men's basketball team is an ncaa division i college basketball team competing in the big ten conference. Haddonfield, illinois is a fictional town that was used as the setting for the cult classic film "halloween." the film, which debuted in 1978 and starred jamie lee curtis, was set in the idyllic midwestern surroundings but was actually shot. Find out the latest on your .
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Get the latest news and information for the illinois fighting illini.
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The official men's basketball page for the university of illinois fighting illini.
@coach_underwood · 3,064 posts · 101k followers · 239 .
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The official facebook home of university of illinois fighting illini basketball.
Formerly the assembly hall, state farm center has provided a home .
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The Waldbühne in Berlin, one of the most appealing outdoor amphitheatres in Europe, is the home of the Berlin Philharmonic's annual summer concert. With over 22,000 in attendance, these are some of the most popular classical music concerts in the world.
On this recording, Estonian conductor Neeme Järvi takes the audience on a trip through A Thousand and One Nights. Works by Grieg, Rimsky-Korsakov, Nielsen, Saint-Saëns and Massenet explore Arabian images in music. High-ranking soloists like rising star Dutch violinist Janine Jansen join the outstanding orchestra. Neeme Järvi can be counted as one of the world's leading musical personalities, having conducted more than 350 CD productions. Recorded live at the Waldbühne Berlin in 2006, Sheherazade offers a sensational concert to all those who want to relive the atmosphere of a this relaxed and high-quality open-air event.
Florentiner Marsch (Florentine March), Op. 214, "Grande marcia Italiana"


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The change in numbering for last year's models compared to previous iterations of the iPhone, resulting in the skipping of the "iPhone 7s" name in favor of the iPhone 8 and the introduction of the iPhone X, may lead to "potentially simpler branding" for the popular smartphones, Cihra writes in an investor note received by AppleInsider.
"We think Apple may use this upcoming cycle to formally change its iPhone naming/branding pattern," according to the analyst, with the "mid-market LCD-based iPhone" simply called "iPhone" without any numbering. The high-end iPhone for the generation will apparently keep the "X" suffix to denote its increased specifications.
Making a change to the way it names its successive product releases is not a new idea, as evidenced by the main iPad line. The range moved from the iPad name to iPad 2 then back to The New iPad, then switching to the iPad Air name by the fifth generation, before returning to being simply called iPad.
A switch to simplify the name to iPhone and retaining the X branding could also be confusing to consumers down the line, as it could become harder to refer to specific models without some sort of identifying term.
Highlighting the lack of a "plus-sized" iPhone X last year, caused through a limited supply of OLED panels, the firm believes the existence of a 6.5-inch model in the upcoming refresh can remedy what is considered a "notable miss." There are also the "makings of a solid refresh" for the LCD-equipped model, with features carried over from the iPhone X including 3D sensing and more native optimization of on-device machine learning and augmented reality likely to help its cause.
Current rumors and speculation point to three iPhones shipping this fall, with a lower-specification 6.1-inch LCD model accompanied by 5.8-inch and 6.5-inch OLED versions.
For the current iPhone generation, Guggenheim has lowered its annual iPhone unit growth forecast from 3 percent year-on-year to flat, citing "softer-than-expected iPhone X uptake" and broadly weaker smartphone market demand in China. "It appears Apple ultimately cannot outgrow what is now a no-growth smartphone market," writes Cihra.
The expected iPhone average selling price (ASP) increase of 15 percent year-over-year is thought to help continue driving iPhone revenues up year-on-year by 14 percent.
Ahead of Apple's second quarter results, due for release on May 1, Guggenheim expects in-line results with no changes to its estimates, including revenue growth of 15 percent year-on-year to $60.9 billion, and earnings per share of $2.69, up 28 percent on last year.
Estimates for the June quarter, however, have been trimmed, with expected revenue down from $52.7 billion to $49.4 billion and EPS dropping from $2.15 to $1.93. Shipments of iPhones in that quarter are also thought to go down from the previous expectation of 42.7 million to 39.4 million.
Guggenheim continues to maintain a "buy" rating for AAPL stock, with the 12-month price target unchanged at $215.
Oh so no 'iPhone Quadra 840 av X' model, drat!
25% of the year over and Apple has far released a cut down iPad and no new macs.
Naming the OLED the "X" really blew out their naming structures... But I'm sure that somebody at Apple thought of that and they knew where they were going back last September.
Having an iPhone "Pro" line fits with their other product lines -- but somehow the idea of a "Pro" grade iPhone doesn't make sense like it does with Macs and iPads where professionals can have increased demands that standard consumers do not.
2018 iPhone X and X Plus. 2018 iPhone and iPhone Plus. 2018 iPhone SE. That would be more in line with both their desktop/laptop lines and the iPad line.
I think they "X" models will be considered "Pro" from here on out. As you suggested, the "Pro" nomenclature just doesn't fit well with smartphones as it does with computers where an emphasis on performance and capacity is used to differentiate models.
So the article could be right that the current numbering scheme has run its course and from here on out we'll have "iPhone" and "iPhone X". With the iPhone models on a two year upgrade cycle as the SE currently is, and the X models continuing a yearly update with the latest and greatest features.
Not giving models a unique name makes no sense. Literally everyone has to refer to the products in some way that differentiates one model from the other. If Apple does not name the models, they receive unofficial names (which, BTW, kinda become the official names and, in my experience, are even used without hesitation by employees at Apple Stores).
Whatever artistic reason Apple may have for not wanting to name the models needs to take a backseat to the reality of models needing names.
long overdue imho, I'd just call them all iPhone; available in 4" (i wish), 4.7" and 5.5".
If need be, the X could remain differentiated as "iPhone X" alongside the standard "iPhone" range.
Wasn't the X because it was the 10th anniversary model? This year won't be the 10th anniversary any more.
I've said this before: I won; be surprised if "iPhone" becomes Phone.
Obviously the designations like "SE" could be different. But you get the idea.
In my opinion it was. They skipped 9 altogether and on announcing it, tied the presentation into the first ten years of iPhone.
However, it could vanish as a product, leaving an inheritance for the other lines or mark the tenth anniversary in a 'new dawn' sense and continue in its own right.
I was saying this last year before last year iPhones were released. Why does there need to be numbers? Apple doesn't release a new iPhone more than once a year. Apple ended up making the problem even worse last year. First they skipped the 7S and jumped to 8. I kind of think Apple did that because of Samesung releasing their 8's also. If they're 8 and Apple is just a 7s, people think that 8 must be newer, faster, better. That's just how people think.
But then Apple also released a phone that's a X or TEN. So this year, Apple cold I guess go 8s or 9 I suppose, and the X could be names XI? But at some point, Next year or the year After for a 8S, 9, and 9s, they'll hit the X wall which they already used. It's just dumb at this point.
So I was saying last year, all Apple needs to do is name them, iPhone, iPhone Plus, and iPhone Pro. That's it. With a iPhone SE thrown in also. There is ZERO need for numbers. It's the 2017, 2018, 2019, iPhone's. If you've noticed, Apple doesn't number the iPad's!!! When you go to Apple's site, you are really only picking size of iPad and Storage and color options. There's no Numbers. There's the older 12.9" iPad Pro 2015, and now the newer 2017 model. There's no numbers!!!!
Apple made the whole number issue worse last year when Apple could have just tossed the numbers right out of the Window. There's ZERO need for numbers.
They like to keep the previous years models hanging around though, you can still buy the iPhone 6S and 7. How would we deal with that without numbers? Maybe part of the planned simplification will be not doing that any more.
If they do this it won't be guaranteed that the models will all update at the same time every year, or even every year. The SE is a case in point.
Also they may not continue with last years version for all models, the SE is an example of that too.
This would reduce the pressure on their suppliers every Christmas. Of course one Christmas is going to see a drop in revenue if they do that, so it may not happen, but they are extremely pressurised by the system as it is now set up. Any failure is catastrophic.


Oh, my dear lad..thank you for your cover of "Etta's" I'd Rather Go Blind..with tears running down my face..you have done her justice and then some..please put this on your new album or offer as a single!!!!......also what a surprise to hear you do Buona Sera..Louie Prima, Keely Smith and especially Sam Butera were close friends of my father,,What a treat. I am a new fan but a fan forever. I thank you for your passion, your interpretation of the songs you sing and of course your original music. You are truly gifted.
love to hear some new music, we all miss it!
Paolo please come to NYC!!!!!
i have seen paolo twice in the usa, he is awesome for sure. but it would be nice to have another album out there. he says he has no friends across the pond. but every concert i went to, he was a sell out! but he is going to have to put himself out there again, sometimes it looks like just another show to him. i can tell when he is having fun with it. but yes he is unique.
Today it is a special day.
and a splendid, healthy, happy New Year.
Two unique musicians I adore and make me happy.
Always been a fan, PLEASE DO A GIG IN NOTTINGHAMMMMM!!!!!!!!!
ive been a fan for a long time and never got a chance to see you live but was in ibiza on the 8th aug and thought your live performance was superb , had a brilliant night along with all the fans , hail hail .
Its true what they say Big man. "You can take the man out of Paisley but you cant take etc...."
Paisley thinks you're no bad.
CANADA LOVES YOU! There! I spelt it right this time! See what you do to my fingers! Bad Boys!
PLEASE come to Canda soon, Paolo! We will rocket you into the realm called legendary!
I never thought that I would in my lifetime get the honor of listening and watching an original, musical genius after the tragic death of Freddie Mercury; but God has given us another rare, and exciting gift with you and your wonderful band. Give it all you got guys, you are fantastic!
I first saw you on The Tonight Show and I was hooked.
Please come back to L.A. and give this older woman a thrill.


Ben provides a brief introduction to The Cornucopia Institute and the important work they do.
Nature's Gourmet Farm "In The News"
In February 2017 Joel McNair, editor of Graze Magazine, visited our farm and recently published his article about our farm. Click the following link to read his article.
Ben discusses the GMO snowball effect and updates numerous farm activities.
Ben updates farm soil health based on test from Ward Labs.
Ben discusses the difference between conviction and belief. Also, Nature's Gourmet Farm "Goes To Washington"
Recap of Ben & Beth's visit to MS State Capital on Feb 16th to engage Senator's & representatives.
2017 0218 Spring is just around the corner!
We are now taking deposits for Custom Half Beef orders.
Ben lays our the best value for your family dollar in purchasing a Half-Pig Custom Processed. Additionally, Ben updates customers on legislative issues that affect our food choices.
Ben updates Facebook Like's, Gabe Brown quote, Jason & Lindsay comment received, and calving season update.


text:
Rihanna sent ventilator to dad in Barbados after Covid 19 confirmation
Last Modified: Apr 16, 2020
After Rihanna's father Ronald Fenty tested positive for coronavirus in his home country of Barbados, she was there to help in every way. Now, thanks to the superstar, Fenty has beat the SARS COV-2 infection.
Speaking to the Sun, Fenty, 66, said, "My daughter Robyn was checking in on me every day. "I thought I was going to die to be honest. I have to say, I love you so much, Robyn. She did so much for me. I appreciate everything she has done."
Ronald Fenty in his St. James home (Image: Pagesix)
According to him, the Fenty Beauty founder sent a ventilator to his Caribbean home, giving him "more than enough" to battle the illness. Fenty further added, "I got a fever up inside of my nose. I had a fever across my lips. It was just a lot of fever. I feared the worst. I thought I was going to die, honestly."
Having quarantined at the Paragon Isolation Center for two weeks Ronald Fenty was declared virus-free, discharged and is now resting in his St. James home.
Ronald Fenty was treated at the Paragon Isolation Center (Image: Pagesix)
He also asked the public to stay home and take the coronavirus pandemic seriously, "I want everybody to stay home. This is a serious situation. More serious than people realize. Please stay home."
Rihanna, born as Robyn Rihanna Fenty, is also known for her philanthropic work. Since the outbreak, she has donated $5 million via her Clara Lionel Foundation. With rapper Jay-Z, she teamed up to donate $1 million each to those affected in Los Angeles and New York while with Twitter boss Jack Dorsey she teamed up to help domestic abuse survivors who may have been affected during the ongoing pandemic.
Tags : Rihanna Robyn Rihanna Fenty Singer Fenty Fenty beauty Clara Lionel Foundation Coronavirus Covid 19


Merry christmas everyone 🙂 I hope you got everything you wished for!
I've done the Quileute High Protectors shirt so far, for the pricely sum of £1.47 and I've had the transfer paper for a while now, so I won't count that, but the top was from Primark. It's not 100% cotton though, so the image has cracked, and it smudged after the backing moved and I accidentally caught it with the iron… Doh! Still, I have 2 more shirts from Matalan (£3 each) to have a go at the Forks Spartans one.
I've actually bookmarked some freezer paper on ebay, although someone has mentioned that Hobby Craft do it, so I might just check out my local HC sometime. The best news is we're moving to nice clean offices, within walking distance of HC. I can imagine I will spend many winter lunches there!
In the meantime, I'm about to jump in the shower and put on some new PJs. My favourite pair (I've had since 2002) have got a hole in the knee. They'll last a little longer but I have a new pair and a Nightie… I don't do nighties lol, so want to give it a go, and some new fluffy white slippers. Then I have a Yankee Candle wax tart burning in the background. Been a pretty good Sunday!
I do apologise for the terrible lighting in the photos. I don't think we've seen sunlight in a long time. Horrible British weather.
Cough is back… with a vengeance. Well the Bronchial mixture worked for 2 whole days. That was 2 days peace that I enjoyed, even if it was like drinking tar. Blood test came back fine, so everyone is still completely stumped. I'm still in so much pain and I can feel an irritation on my chest.


text:
\section{Introduction}
In recent years, jet physics has played a prominent role at high energy colliders, particularly the Large Hadron Collider (LHC).
Jets provide an opportunity to test our understanding of Quantum Chromodynamics (QCD) and appear in
both Standard Model and beyond the Standard Model cross sections, making them important for searches of new physics as well.
Due to the enormous energies available at the LHC, top quarks, $W^\pm$, $Z^0$, and Higgs bosons are frequently
produced with transverse momenta much greater than their mass, and studies of jet substructure have proved essential
in identifying these highly boosted particles when they decay hadronically \cite{Altheimer:2013yza,Sapeta:2015gee}.
For all these reasons, precision jet calculations have become increasingly important in particle physics. At the heart of
analytic calculations of jets are factorization theorems which separate jet cross sections into perturbative and
non-perturbative pieces. Non-perturbative functions such as parton distribution functions (PDFs), fragmentation
functions (FFs), and fragmenting jet functions (FJFs) offer ways to analytically probe the structure of the proton as well as the nature of hadronization.

FJFs were first introduced in Ref.~\cite{Procura:2009vm} within the framework of Soft-Collinear Effective Theory (SCET)~\cite{Bauer:2001yt,Bauer:2000ew,Bauer:2000yr,Bauer:2001ct}.
They appear in factorization theorems for cross sections for jets containing an identified hadron $h$ carrying a
fraction $z$ of the jet energy
($z=2E_h/\omega$, where $E_h$ is the hadron energy and $\omega=\sum_{i \in jet} p^-_{i}$). Ref.~\cite{Procura:2009vm}
also showed that one can construct a factorization theorem in
SCET for the differential cross-section $d \sigma^h / dz$ from the inclusive jet cross section by applying
a simple replacement rule,
\begin{equation}
  \label{eq:rule}
J_i(s,\mu)\rightarrow \frac{1}{2(2\pi)^3}{\cal{G}}_{i/h}(s,z,\mu) dz,
\end{equation}
where $J_i$ is the standard jet function and ${\cal{G}}_{i/h}$ is a FJF. In Eq.(\ref{eq:rule}), $s$ is the jet
invariant mass and $\mu$ is the renormalization scale.
Additionally in the limit $\Lambda_{\text{QCD}} \ll \sqrt{s}$ we can evaluate the FJF as a convolution of perturbative
short distance coefficients and the more commonly studied
fragmentation functions (FFs).
\begin{equation}
{\cal{G}}_{i/h}(s,z,\mu)= \sum_{j} \int_{z}^{1} \frac{dx}{x} \; {\cal{J}}_{i/j}(s,x,\mu) D_{j/h}\left(\frac{z}{x},\mu \right) + {\cal{O}}(\Lambda_{\text{QCD}}^2/s).
\end{equation}
Past studies of FJFs involve the jet invariant mass~\cite{Jain:2011xz,Procura:2009vm,Liu:2010ng} and were generalized to
angularities~\cite{Berger:2003iw} in Ref.~\cite{Bain:2016clc}. In Ref.~\cite{Procura:2011aq,Baumgart:2014upa,Chien:2015ctp}
FJFs independent of jet substructure observables were used to study the production of light quarks, heavy mesons, and quarkonia.
The properties of FJFs have also been studied
in Refs.~\cite{Jain:2011iu, Jain:2012uq, Bauer:2013bza, Dai:2016hzf, Kang:2016ehg, Ritzmann:2014mka, Kang:2016ioz, Metz:2016swz}.
In this work we extend FJFs to transverse momentum dependent distributions (TMDs). Recently, TMDs have been studied extensively
within and outside the framework of SCET~\cite{GarciaEchevarria:2011rb,Echevarria:2012pw,Echevarria:2014rua,Echevarria:2015usa,Echevarria:2016scs,Anselmino:2013lza,Procura:2014cba,Musch:2010ka,Chiu:2012ir}.
TMDs offer a new technology for the study of hadron substructure in hadron colliders (TMD parton distribution functions
(TMDPDFs)) and hadron production (TMD fragmentation functions (TMDFFs)). TMDPDFs have been used in SCET for studies of
Higgs production in the small transverse momentum limit at the
LHC~\cite{Neill:2015roa, Chiu:2012ir, Luebbert:2016itl,Becher:2012yn, Becher:2012uya,Ahrens:2008nc}. TMD fragmenting
jet functions (TMDFJF) depend on three kinematic variables: the jet energy, $\omega/2$, the fraction of this energy
carried by the identified hadron, $z$, and the hadron transverse momentum with respect to the axis of direction
of the original parton, $\veb{p}^h$.
The modes that give important contributions to the transverse momentum are
\begin{align}
\text{collinear-soft:} &\;\;\; p_{cs}^{\mu}\sim \omega(\lambda r,\lambda/r, \lambda),\;\;\;\; \lambda=p_{\perp}/\omega\nonumber \\
\text{collinear:}&\;\;\;p_{n}^{\mu} \sim \omega (\lambda^2,1,\lambda),
\end{align}
where collinear-soft modes are soft modes collinear to the direction of the jet axis first introduced in Ref.~\cite{Bauer:2011uc} and  $r \equiv \tan{\left(R/2\right)}$ for jet
cone size $R$. Similar modes are also studied in~\cite{Chien:2015cka}. To incorporate contributions from soft-collinear modes, we make use of the $\text{SCET}_+$ formalism. $\text{SCET}_+$ and other similar extensions of SCET
have been used to study processes with multiple well-separated scales and distinct phase space regions (e.g.~\cite{Bauer:2011uc,Pietrulewicz:2016nwo,Procura:2014cba,Chien:2015cka}).

Recent work~\cite{Baumgart:2014upa,Bain:2016clc} shows that jet substructure observables may be able to shed light on
outstanding puzzles in the production of quarkonia such as $J/\psi$ and $\Upsilon$. Our modern understanding of quarkonium
production comes from non-relativistic QCD (NRQCD)~\cite{Bodwin:1994jh}, an effective field theory that writes cross sections
and decay rates for bound states of heavy quarks as expansions in the strong coupling $\alpha_s(2m_c)$ and $v$, the relative
velocity of the quark-antiquark pair. NRQCD provides factorization theorems~\cite{Braaten:1993mp, Braaten:1993rw, Braaten:1994vv, Braaten:1996jt}
for cross sections in terms of perturbatively calculable short-distance
pieces multiplied by  non-perturbative long distance matrix elements (LDMEs). The perturbative piece describes the creation of
a heavy quark-antiquark pair in a given color and angular momentum state while the non-perturbative LDMEs
describe the hadronization of the heavy quark-antiquark pair into the physical quarkonium state. The different intermediate
color and angular momentum states of the pair define different NRQCD production mechanisms for quarkonia.

Ref.~\cite{Baumgart:2014upa} studied the dependence of the cross section for the production of $J/\psi$ within jets initiated by gluons
on $z$, the fraction of the jet's energy, $E_J$, carried by the $J/\psi$. The authors showed that the $z$ dependence is sensitive
to the underlying quarkonium production mechanism. Thus, simultaneously measuring the $z$ and $E_J$ dependence of the cross section for $J/\psi$ production within jets
provides a new and independent way of extracting the values of the LDMEs. Ref.~\cite{Bain:2016clc} extended these results
to $J/\psi$ production in $e^+e^-$ collisions where the angularity of the jet was probed. Ref.~\cite{Bain:2016clc} also found
that NLL' resummed analytic calculations of the $z$ distributions were quite different from those predicted by PYTHIA simulations.
The authors attributed this large discrepancy to an unrealistic modeling of the shower radiation from color-octet quarkonium
production mechanisms.

Intuitively, one might expect color-octet quark-antiquark intermediate states to radiate more gluons relative to color-singlet pairs.
This would result in $J/\psi$ produced with higher $p_{\perp}$ relative to the jet axis. Also, since different
color-octet production mechanisms have different FFs in NRQCD, FJFs should be able to distinguish
between the different color-octet production mechanisms. In addition to generalizing FJFs to TMD distributions, this paper
also shows that these TMDFJFs do in fact provide discriminating power between the different mechanisms.

In Section~\ref{sec:TMDFJF}, we give a definition of the TMDFJF and show how it emerges from definitions of TMDFFs in the literature. We then perform a matching calculation at next-to-leading order (NLO) onto SCET$_+$ and derive a result that is completely
factorized into hard, collinear, collinear-soft, and ultra-soft modes. We present a calculation of the matching
coefficients $\mathcal{J}_{ij}$  between the TMDFJF and the more traditionally studied FFs.
Additionally, we present a perturbative calculation of the corresponding collinear-soft function at NLO. In Section~\ref{sec:numerical},
we use renormalization group (RG) and rapidity renormalization group (RRG) techniques to resum logarithms to next-to-leading-log-prime (NLL')
accuracy. The TMDFJF formalism is applied to the production of $J/\psi$ in gluon jets where the FFs are calculated to LO in NRQCD.
We find that distributions in $p_{\perp}$  and $z$ as well as the average angle of
$J/\psi$ relative to the axis of the jet  can discriminate between the various NRQCD production mechanisms. Conclusions are given in section 4.
Appendix~\ref{sec:AppA} gives calculational details of the matching of the TMDFJF onto the FF, Appendix~\ref{sec:AppB} has an
alternative derivation of the TMDFJF from an SCET factorization theorem for a jet cross section, and Appendix~\ref{sec:AppC}
has details about the RG and RRG evolution.

\section{Transverse momentum dependent fragmenting jet function}
\label{sec:TMDFJF}
In this section we will present the definition of the TMDFJF, connecting it with definitions of TMDFFs from the literature.
We first show the matching calculation of the TMDFJF onto SCET$_+$ and its factorization into pure
collinear, soft-collinear, and hard pieces. We then present perturbative calculations of the matching coefficients, ${\cal J}_{i/j}$,
from matching the pure collinear function onto the FF as well as the one-loop expression for the soft-collinear function.
\subsection{Definition and factorization}
The operator definition of the quark  FF is given by~\cite{Collins:1981uw}:
\begin{equation}
  \label{eq:OPFF}
D_{q/h}(z,\mu)=\frac{1}{z} \sum_{X}\frac{1}{2 N_c} \delta(\omega-p^{-}_{X}-p^{-}_h)\; \Tr
\Big{\lbrack}\frac{\slashed{\bar{n}}}{2} \langle 0 \vert \psi(0)\vert X h \rangle \langle X h \vert
\bar{\psi}(0)\vert 0  \rangle  \Big{\rbrack} \Big{\vert}_{\veb{p}^{X}=-\veb{p}^h},
\end{equation}
where $\psi(x)$ is the quark field in QCD. The TMDFF is given by a similar expression but is unintegrated in the transverse components of the hadron momentum.
It is defined by~\cite{Aybat:2011zv}
\begin{equation}
   \label{eq:OPTMDFF}
D_{q/h}(\veb{p}^{h},z,\mu)=\frac{1}{z} \int \frac{d^{2} x_{\perp}}{(2 \pi)^2} \sum_{X}\frac{1}{2 N_c}
\delta(\omega-p^{-}_{X}-p^{-}_h)\; \Tr \Big{\lbrack}\frac{\slashed{\bar{n}}}{2} \langle 0 \vert
\psi(0,0,x_{\perp})\vert X h \rangle \langle X h \vert \bar{\psi}(0)\vert 0  \rangle  \Big{\rbrack},
\end{equation}
such that,
\begin{equation}
\int d^{2}\veb{p}^h \; D_{q/h}(\veb{p}^{h},z,\mu) = D_{q/h}(z,\mu).
\end{equation}
Here, $\veb{p}^{h}$ is the transverse momentum of the hadron $h$ with respect to the direction of the
original fragmenting quark. In order to identify the experimentally measured jet axis with the direction of the parton
initiating the jet, there needs to be a constraint that only ultrasoft
radiation is outside the jet. Alternative definitions of the TMDFF often involve the transverse momentum
measured with respect to different axes (e.g., the beam axis). In order to extend this concept to identified hadrons within jets we consider the collinear limit of Eq.(\ref{eq:OPTMDFF}) by matching onto SCET where now $z \equiv E_h/E_J$. This yields the operator definition of the TMDFJF
\begin{multline}
  \label{eq:OPFJF}
\hspace{-0.3cm}{\cal{G}}_{q/h}(\veb{p},z,\mu)=  \frac{1}{z} \sum_X \frac{1}{2 N_c} \delta(p^{-}_{Xh;r})\delta^{(2)}
(\veb{p}+\veb{p}^{X})
\Tr \Big{\lbrack} \frac{\slashed{\bar{n}}}{2} \langle 0 \vert \delta_{\omega,\overline{\cal{P}}}  \chi^{(0)}_{n} (0)\vert X h
\rangle \langle X h \vert \bar{\chi}^{(0)}_{n}(0)\vert 0  \rangle   \Big{\rbrack} ,
\end{multline}
where in the equation above the states $\vert X h \rangle$ corresponds to the a final state of collinear particles within a jet, in contrast with the the state $\vert X h \rangle$ in Eqs. (\ref{eq:OPFF}) and (\ref{eq:OPTMDFF}) which correspond to the inclusive case. The index $(0)$ indicates that the field has been decoupled from the ultra-soft gluons via BPS field redefinitions
\begin{equation}
  \chi_{n,\omega}^{(0)}(x)= Y_n^{\dag}(x)\chi_{n}(x) \quad \text{and} \quad A_n^{(0)}(x) = Y_n^{\dag}(x)A_n(x)Y_n(x),
\end{equation}
and $\chi_{n}\equiv  W_n^{\dag}\xi_{n}$
is defined in terms of the collinear quark fields of SCET and the ultrasoft and collinear Wilson lines are
\begin{equation}
Y_n^{\dag}(x) = \mathbb{P}\exp{\left( ig\int_0^{\infty}{ ds\; n \cdot A_{us}(x+sn) } \right)}
  \quad \text{and} \quad W_n(x) = \sum_{\text{perms}}{ \exp{\left( \frac{-g}{\bar{n}\cdot {\cal P}} \bar{n}\cdot A_n{x}\right)} }.
\end{equation}
As we show in Appendix~\ref{sec:AppB},
the expression for the TMDFJF given in Eq.(\ref{eq:OPFJF}) is closely related to the FJF introduced in Ref.~\cite{Procura:2009vm}.

As discussed in the introduction, the TMDFJF receives contributions from two different modes, collinear and colllinear-soft or csoft .
In order to make the contribution of the csoft modes explicit, we now match our expression onto $\text{SCET}_{+}$,
\begin{multline}
{\cal{G}}_{q/h}(\veb{p},z,\mu)= C_+^{\dag}(\mu) C_{+}(\mu)  \frac{1}{z} \sum_X \frac{1}{2 N_c} \delta(p^{-}_{Xh;r})\delta^{(2)}  (\veb{p}+\veb{p}^{X})  \\
\times \Tr \Big{\lbrack} \frac{\slashed{\bar{n}}}{2} \langle 0 \vert \delta_{\omega,\overline{\cal{P}}} V_{n}^{\dag\;(0)}(0) \chi^{(0)}_{n} (0)\vert X h \rangle
\langle X h \vert \bar{\chi}^{(0)}_{n}(0) V_{n}^{(0)}(0)\vert 0  \rangle   \Big{\rbrack} ,
\end{multline}
where
\begin{equation}
  V_{n}^{(0)}(x)=\sum_{\text{perm}} \exp \left( \frac{-g}{\bar{n}\cdot {\cal{P}}} \bar{n}\cdot A_{n,\,cs}^{(0)}(x) \right),
\end{equation}
are Wilson lines of csoft fields (the csoft analogue of $W_n$) and $C_{+}(\mu)$ are SCET$_+$ matching coefficients.
In order to decouple the collinear fields $A_n^{(0)}$ and $\chi^{(0)}_n$ from the csoft gluons, we  now perform
field redefintions similar to those of the BPS procdure~\cite{Bauer:2011uc}
\begin{multline}
{\cal{G}}_{q/h}(\veb{p},z,\mu)= C_+^{\dag}(\mu) C_{+}(\mu)  \frac{1}{z} \sum_X \frac{1}{2 N_c} \delta(p^{-}_{Xh;r}) \delta^{(2)}  (\veb{p}+\veb{p}^{X})  \\ \times
 \Tr \Big{\lbrack} \frac{\slashed{\bar{n}}}{2} \langle 0 \vert  \delta_{\omega,\overline{\cal{P}}} V_{n}^{\dag\;(0)}(0) U_n^{(0)}(0)  \chi^{(0,0)}_{n} (0)\vert X h \rangle \\ \times
\langle X h \vert \bar{\chi}^{(0,0)}_{n}(0) U_{n}^{\dag \;(0)}(0) V_{n}^{(0)}(0) \vert 0  \rangle   \Big{\rbrack},
\end{multline}
where
\begin{equation}
  U_{n}^{\dag\,(0)}(x)=\mathbb{P}  \exp \left( i g \int_{0}^{\infty} ds \; n \cdot A^{(0)}_{n,\,cs}(ns+x)  \right),
  \end{equation}
and the superscript $(0,0)$ denotes that the corresponding fields are decoupled from both ultra-soft and collinear-soft modes.
Having factorized our operators, we now factorize the phase-space into collinear and collinear-soft Hilbert states.
\begin{equation}
\vert X h\rangle \; \rightarrow\; \vert X_n h\rangle \vert X_{cs}\rangle,
\end{equation}
\begin{equation}
\sum_{X} \; \rightarrow\; \sum_{X_n}\sum_{X_{cs}},
\end{equation}
\begin{equation}
\delta^{(2)}  (\veb{p}+\veb{p}^{X}) \;\rightarrow \; \delta^{(2)}  (\veb{p}+\veb{p}^{X_n}+\veb{p}^{X_{cs}}).
\end{equation}
This allows us to factorize the TMDFJF into three pieces
\begin{equation}
{\cal{G}}_{q/h}(\veb{p},z,\mu)= H_+(\mu)\times \Big{\lbrack} {\cal{D}}_{q/h}\otimes_{\perp}S_{C} \Big{\rbrack} (\veb{p},z,\mu)\,,
\end{equation}
where $H_+$ is proportional to the square of the matching coefficient from ${\cal{G}}_{q/h}$ in SCET$_I$ to SCET$_+$, and ${\cal{D}}_{q/h}$  and $S_{C}$ are the  contributions collinear and the collinear-soft modes of SCET$_+$ to the TMDFJF, respectively. These are defined by
\begin{equation}
H_+ (\mu) = (2 \pi)^2 N_c \;C_+^{\dag}(\mu) C_+(\mu) \, ,
\end{equation}
\begin{multline}
{\cal{D}}_{q/h}(\veb{p}^{\cal{D}},z)\equiv\frac{1}{z} \sum_{X_{n}} \frac{1}{2 N_c} \delta(p^{-}_{Xh;r})\delta^{(2)}(p^{\perp}_{Xh;r})
\Tr \Big{\lbrack} \frac{\slashed{\bar{n}}}{2} \langle 0 \vert \delta_{\omega,\overline{\cal{P}}} \chi_{n} (0)\delta^{(2)}  ({\cal{P}}_{\perp}^{X_n}+\veb{p}^{\cal{D}})\vert X_n h \rangle \\ \times
\langle X_n h \vert \bar{\chi}_{n}(0) \vert 0  \rangle \Big{\rbrack},
\end{multline}
\begin{equation}
  \label{eq:soft}
 S_C(\veb{p}^S) \equiv \frac{1}{N_c} \sum_{X_{cs}}  \Tr \Big{\lbrack} \langle 0 \vert  V_{n}^{\dag}(0) U_n(0) \delta^{(2)} ({\cal{P}}_{\perp}+\veb{p}^{S})
 \vert X_{cs} \rangle \langle X_{cs}
   \vert U_{n}^{\dag}(0) V_{n}(0) \vert 0  \rangle \Big{\rbrack},
\end{equation}
where the $\Tr$ is over Dirac and color indices in ${\cal D}_{q/h}$ and color indices in $S_C$. From now on, we drop the $(0)$ and $(0,0)$ superscripts since the different
collinear, soft-collinear, and ultra-soft modes are now factorized. We also employ the following shorthand for the convolution in the $\perp$ components
\begin{equation}
{\cal{D}}_{q/h} \otimes_{\perp} S_{C} (\veb{p}) = \int \frac{d^{2}\veb{p}'}{(2 \pi)^2}  \; \;{\cal{D}}_{q/h}(\veb{p}-\veb{p}') S_{C}(\veb{p}').
\end{equation}
Analogously for gluon fragmentation we have
\begin{align}
 {\cal{D}}_{g/h}(\veb{p},z,\mu)=& -g_{\mu\nu} \frac{1}{z} \sum_X \frac{\omega}{(d-2)(N_c^2-1)} \delta(p^{-}_{Xh;r}) \delta^{(2)}  (\veb{p}+\veb{p}^{X})\nonumber \\
&\times \langle 0 \vert  \delta_{\omega,\overline{\cal{P}}} {\cal{B}}^{\nu,a}_{n,\perp} (0)\delta^{(2)}  ({\cal{P}}_{\perp}^{X_n}+\veb{p}^{\cal{D}})\vert X h
\rangle \langle X h \vert {\cal{B}}^{\mu,a}_{n,\perp}(0)\vert 0  \rangle,
\end{align}
where the collinear gluon field is
\begin{equation}
  B_{n,\perp}^{\mu}(y) = \frac{1}{g}\left[ W_n^{\dagger}(y)iD_{n\perp}W_n(y)\right] \, ,
\end{equation}
and $iD_{n\perp}= {\cal P}_{n\perp}^{\mu}+gA_{n\perp}^{\mu}$ is the standard $\perp$-collinear covariant derivative in SCET.

At this point, only the purely collinear term ${\cal{D}}_{i/h}$ contains information about the hadron $h$. The collinear-soft function ($S_C$) and the
hard function ($H_{+}$) are universal functions dependent on the fragmenting parton $i$ but not on the hadron $h$. Additionally, in the limit that
$\vert \veb{p} \vert \gg \Lambda_{\text{QCD}}$, we may use the operator product expansion to factorize ${\cal{D}}_{i/h}$ into short distance
coefficients and the more commonly studied FFs, $D_{j/h}$, via,
\begin{equation}
{\cal{D}}_{i/h}(\veb{p},z,\mu,\nu)= \int_{z}^{1} \frac{dx}{x}\;{\cal{J}}_{i/j}(\veb{p},x,\mu,\nu) D_{j/h}\left(\frac{z}{x},\mu\right)\;\;+\;\;{\cal{O}}
\left(\frac{\Lambda_{QCD}^2}{\vert\veb{p}\vert^2} \right),
\end{equation}
where ${\cal{J}}_{i/j}$ are the short distance coefficients that do not depend on the final hadron and can be calculated order by order in perturbation theory.

\begin{center}
\begin{figure}[h]
\centerline{\includegraphics[scale=0.57]{images/gg}}
\caption{Feynman diagrams that give non-scaleless contributions to the gluon TMDFJF at NLO in $\alpha_s$. Diagram (b) also has a mirror image that is
	      not explicitly shown.}
\label{fig:gg}
\end{figure}
\end{center}
\begin{center}
\begin{figure}[h]
\centerline{\includegraphics[scale=0.135]{images/qq}}
\caption{Associated non-scaleless diagrams that contribute to the quark TMDFJF at NLO. Again, Diagram (b) has a mirror image that is not explicitely drawn above.}
\label{fig:qq}
\end{figure}
\end{center}

\subsection{Perturbative results}
The $O(\alpha_s)$ diagrams contributing to the gluon and quark TMDFJFs
are shown in Figs.~\ref{fig:gg} and \ref{fig:qq}, respectively.
At NLO, the matching coefficients ${\cal{J}}_{i/j}$ are directly related to the matching coefficients ${\cal{I}}_{i/j}$ between TMDPDFs and
the more commonly studied PDFs calculated in Refs.~\cite{Procura:2014cba,Chiu:2012ir} by the substitution ${\cal I}_{i/j} \to {\cal J}_{j/i}$. See Appendix~\ref{sec:AppA} for additional
details of the matching calculation. Following Ref.~\cite{Chiu:2012ir}, a rapidity regulator is used to regulate rapidity divergences in the perturbative calculation.
This is implemented by first modifying the form of the collinear and collinear-soft Wilson lines
\begin{align}
\begin{split}
&W_n = \sum_{\text{perms}}{ \exp{\left( -\frac{g \;w^2}{\bar{n} \cdot {\cal P}} \frac{\abs{\bar{n}\cdot {\cal P}_g}^{-\eta}}{\nu^{-\eta}}
      \bar{n}\cdot A_n\right)} }\\
&V_n = \sum_{\text{perms}}{ \exp{\left( -\frac{g\; w}{\bar{n} \cdot {\cal P}} \frac{\abs{\bar{n}\cdot {\cal P}_g}^{-\eta/2}}{\nu^{-\eta/2}}
 \bar{n}\cdot A_{n,cs}\right)} },\\
\end{split}
\end{align}
with similar modifications to $U_n$. This introduces a regulator $\eta$, a bookkeeping parameter $w$, and a new dimensionful parameter
$\nu$. The dependence of our results on $\nu$ should of course cancel amongst the terms in our factorization theorem.
The renormalized results for the ${\cal{J}}_{i/j}$ in the $\overline{\text{MS}}$ scheme can be written,
\begin{multline}
  {\cal{J}}_{i/j}(\veb{p},z,\mu,\nu)= \delta_{ij}\delta(1-z)\delta^{(2)}(\veb{p})\\
  +\frac{\alpha_s T_{ij}}{\pi} \Big{\lbrace} \left( \delta_{ij}\delta(1-z)\ln\left(\frac{\omega^2}{\nu^2}\right)+\bar{P}_{ji}(z)\right) {\cal{L}}_0(\veb{p}^2,\mu^2)
  +c_{ij}(z)\delta^{(2)}(\veb{p}),
\Big{\rbrace},
\end{multline}
with
\begin{align}
&\bar{P}_{qq}(z)=P_{qq}(z)-\bar{\gamma}_q\delta(1-z)=(1+z^2){\cal{L}}_0(1-z), \nonumber \\
  &\bar{P}_{gq}(z)=P_{gq}(z)=\frac{1+(1-z)^2}{z}, \nonumber \\
  &\bar{P}_{qg}(z)=P_{qg}(z)=z^2+(1-z)^2, \nonumber \\
&\bar{P}_{gg}(z)=P_{gg}(z)-\bar{\gamma}_g\delta(1-z)=2\frac{(1-z+z^2)^2}{z}{\cal{L}}_0(1-z),
\end{align}
and
\begin{equation}
{c}_{qq}(z)=\frac{1-z}{2}, \;\;
{c}_{qg}(z)=\frac{z}{2}, \;\;
{c}_{gg}(z)=0, \;\;
{c}_{gq}(z)=z(1-z),
\end{equation}
where $T_{qq}=T_{qg}=C_F,\;T_{gg}=C_A,\;T_{gq}=T_F,\;\bar{\gamma}_q=3/2$ and  $\bar{\gamma}_g= \beta_0/(2C_A)$. For convenience we use the following
shorthand notation for the vector plus-distributions,
\begin{equation}
{\cal{L}}_n (\veb{p}^2,\mu^2)=\frac{1}{2 \pi \mu^2}{\cal{L}}_n \left(\frac{\veb{p}^2}{\mu^2}\right)=\frac{1}{2 \pi \mu^2}\left(\frac{\mu^2 }
{\veb{p}^2}\ln^{n}(\mu^2/\veb{p}^2) \right)_{+}.
\end{equation}
Performing the convolutions in the energy ratio parameter $z$ we get,
\begin{multline}
{\cal{D}}_{i/h}(\veb{p}^2,z,\mu,\nu)= D_{i/h}(z,\mu)\delta^{(2)}(\veb{p})+ \frac{\alpha_s}{\pi} \Big{\lbrace} \Big{\lbrack} T_{ii} D_{i/h}(z,\mu)
\ln \left( \frac{\omega^2 (1-z)^2}{\nu^2} \right)\\
 +f^{i/h}_{P \otimes D} (z,\mu) \Big{\rbrack} {\cal{L}}_0(\veb{p}^2,\mu^2) + f^{i/h}_{c \otimes D} (z,\mu) \delta^{(2)} (\veb{p})
\Big{\rbrace},
\end{multline}
where
\begin{multline}
  f^{i/h}_{P \otimes D} (z,\mu)= \sum_{j} \Big{\lbrace} \delta_{ij} T_{ii} \int_{z}^{1} \frac{dx}{1-x} \; \Big{\lbrack} p_{i}(x)
  D_{i/h}\left(\frac{z}{x},\mu\right)-2 D_{i/h}\left(z,\mu \right) \Big{\rbrack} \\
  + (1-\delta_{ij})T_{ij} \int_{z}^{1} \frac{dx}{x} \; P_{ji}(x) D_{j/h}\left(\frac{z}{x},\mu\right) \Big{\rbrace},
\end{multline}
with $p_q(x)=(1+x^2)/x$,  $p_g(x)=2(1-x+x^2)^2/x^2$ and
\begin{equation}
f^{i/h}_{c \otimes D} (z,\mu)= \sum_{j} T_{ij} \int_{z}^{1} \frac{dx}{x} \; c_{ij}(x) D_{j/h}\left(\frac{z}{x},\mu\right),
\end{equation}

\begin{center}
\begin{figure}[h]
\centerline{\includegraphics[scale=0.57]{images/soft}}
\caption{Real gloun emission diagrams that contribute to the collinear-soft function $S_C^{i}(\veb{p},z,\mu,\nu)$ at ${\cal{O}}(\alpha_s)$.
The gluons passing through the shaded oval indicate they are contained within the phase-space of the jet.}
\label{fig:soft}
\end{figure}
\end{center}
At NLO, the collinear-soft function, defined by Eq.~(\ref{eq:soft}), receives contributions from the two diagrams shown in Fig.~\ref{fig:soft}.
The real gluon is contained within a jet defined by a cone or $k_T$-type jet algorithm with cone size parameter $R$. A global soft funciton of similar form
has been calculated at NLO in Ref.~\cite{Chiu:2012ir} and at NNLO in Ref.~\cite{Luebbert:2016itl} in studies of Higgs $p_{T}$ spectrum. The two diagrams in Fig.~\ref{fig:soft}
yield identical contributions and thier sum is given by,
\begin{align}
S_{C}^{i, B(1)}(\veb{p})&=+g^2 w^2 \left(\frac{e^{\gamma_E}\mu^2}{4 \pi}\right)^{\epsilon} \nu^{\eta}\;C_{i} \int\frac{dk^+ dk^- d^{d-2}k_{\perp}}{2(2\pi)^{d-1}}\;
\frac{2}{k^+ (k^-)^{1+\eta}} \delta(k^2)\delta^{(2)}(\veb{k}+\veb{p})\;\Theta_{\text{alg}} \nonumber \\
& = +\frac{\alpha_s w^{2} C_{i} }{\pi} \frac{e^{\gamma_E\epsilon}}{\Gamma(1-\epsilon)} \left( \frac{\nu r}{\mu}\right)^{ \eta} \frac{1}{\eta} \frac{1}{2 \pi \mu^2}
\left(\frac{\mu^2}{\veb{p}^2} \right)^{1+\epsilon+\eta/2},
\end{align}
where $\Theta_{\text{alg}}$ defines the jet algorithm, $r \equiv \tan(\mathrm{R}/2)$, and $C_q=C_F,\;C_g=C_A$. After an expansion in $\eta$ followed by an
expansion in $\epsilon$ and summing both diagrams we get,
\begin{align}
S_{C}^{i,B} (\veb{p},\mu,\nu)= & \delta^{(2)}(\veb{p})+ \frac{\alpha_s w^2 C_{i}}{\pi}
\Big{\lbrace} \frac{2}{\eta}\left(-\frac{1}{2\epsilon}\delta^{(2)}(\veb{p})+{\cal{L}}_0(\veb{p}^2,\mu^2) \right) \nonumber \\
&+ \delta^{(2)}(\veb{p})\left(\frac{1}{2\epsilon^2}+\frac{1}{2\epsilon}\ln \left(\frac{\mu^2}{r^2\nu^2}\right) \right)-{\cal{L}}_0(\veb{p}^2,\mu^2)
\ln \left(\frac{\mu^2}{r^2\nu^2}\right)+{\cal{L}}_1(\veb{p}^2,\mu^2)\nonumber \nonumber \\
&-\frac{\pi^2}{24}\delta^{(2)} (\veb{p})
\Big{\rbrace},
\end{align}
The renormalized result (where we have now set $w\to 1$)in the $\overline{\text{MS}}$ scheme is thus
\begin{equation}
S_{C}^{i,R} (\veb{p},\mu,\nu)=  \delta^{(2)}(\veb{p})- \frac{\alpha_s C_{i}}{\pi}
\Big{\lbrace} {\cal{L}}_0(\veb{p}^2,\mu^2)\ln \left(\frac{\mu^2}{r^2\nu^2}\right)-{\cal{L}}_1(\veb{p}^2,\mu^2)+\frac{\pi^2}{24}\delta^{(2)} (\veb{p})
\Big{\rbrace}.
\end{equation}
While in general this expression receives contributions from virtual gluon emission diagrams at NLO, these diagrams yield scaleless integrals when
using this particular set of regulators. Thus virtual diagrams are neglected and all singularities from these real emission diagrams are interpreted as UV divergences.
We also verified, using a set of regulators where such virtual gluons give non-zero contributions, that the result is identical.\footnote{In order to verify that
all IR divergences do indeed cancel, we used a gluon mass, rapidity regulator, and dimensional regulator where diagrams with virtual
gluons give non-scaleless contributions.} Note if  pure dimensional  regularization is used for ultraviolet and infrared divergences then $H_+=(2\pi)^2 N_c$ as discussed in~Ref.~\cite{Procura:2014cba}.

\section{Numerical Results}
\label{sec:numerical}
\subsection{Renormalization Group (RG) and Rapidity Renormalization Group (RRG)}
Individual diagrams for the collinear-soft function $S_C$ and the matching coefficients $\mathcal{J}_{i/j}$ suffer from infra-red (IR), ultra-violet (UV) and rapidity divergences (RD).
We use dimensional regularization and a rapidity regulator (as introduced and developed in Ref.~\cite{Chiu:2011qc,Chiu:2012ir}) to regulate these divergences.
IR divergences in the collinear-soft function cancel when summing over all diagrams. In the matching coefficients ${\cal{J}}_{i/j}$,
IR divergences cancel in the matching  of the collinear functions ${\cal D}_{i/h}$ onto traditional FFs, $D_{j/h}$.
The remaining poles (UV and rapidity), are removed by renormalization. In addition to the scale $\mu$ introduced by dimensional regularization
our use of a rapidity regulator requires the introduction of an additional scale, $\nu$. With this scale are associated rapidity renormalization group (RRG) equations
which can be used to resum  large logarithms by evolving each function from its canonical scale to a common scale.
Bare and renormalized quantities are related through the following convolution with the renormalization factor $Z$,
\begin{equation}
F^{B}(\veb{p})=Z_{F}(\veb{p},\mu,\nu) \otimes_{\perp} F^{R}(\veb{p},\mu,\nu),
\end{equation}
where $F$ can be either ${\cal{D}}_{i/h}$ or $S_C^i$ and satisfies the following RG and RRG equations,
\begin{align}
& \frac{d}{d \ln \mu}F^{R}(\veb{p},\mu,\nu) = \gamma^{F}_{\mu} (\mu,\nu) \times F^{R} (\veb{p},\mu,\nu) \nonumber \\
& \frac{d}{d \ln \nu}F^{R}(\veb{p},\mu,\nu) = \gamma^{F}_{\nu} (\veb{p},\mu,\nu) \otimes_{\perp} F^{R} (\veb{p},\mu,\nu).
\end{align}
Here $\gamma_{\mu}^F$ and $\gamma_{\nu}^{F}$ are the anomalous dimensions associated to RG and RRG respectively and are defined by,
\begin{align}
  \label{eq:AD}
   \Big{\lbrack} (2 \pi)^2 \delta^{(2)}(\veb{p}) \Big{\rbrack}  \times \gamma_{\mu}^{F} (\mu,\nu) &=- Z_{F}^{-1}(\veb{p},\mu,\nu) \otimes_{\perp} \frac{d}{d \ln \mu}Z_F(\veb{p},\mu,\nu) \nonumber \\
   \gamma_{\nu}^{F}(\veb{p},\mu,\nu) & =- Z_{F}^{-1}(\veb{p},\mu,\nu) \otimes_{\perp} \frac{d}{d \ln \nu}Z_F(\veb{p},\mu,\nu).
  \end{align}
For the renormalization factors we find,
\begin{align}
  Z^{\cal{D}} (\veb{p},\mu,\nu)=&(2\pi)^2 \delta^{(2)}(\veb{p})+(4 \pi)\alpha_s w^2 C_F
\Big{\lbrace}
-\frac{2}{\eta}\left(-\frac{1}{2 \epsilon}\delta^{(2)}(\veb{p})+{\cal{L}}_0(\veb{p}^2,\mu^2) \right)\nonumber\\
  &+\frac{1}{2\epsilon}\left(\ln\left(\frac{\nu^2}{\omega^2}\right)+\bar{\gamma}_i \right)\delta^{(2)}(\veb{p})
\Big{\rbrace}
\end{align}
\begin{align}
  Z^{S_C} (\veb{p},\mu,\nu)=&(2\pi)^2 \delta^{(2)}(\veb{p})+(4 \pi)\alpha_s w^2 C_F
\Big{\lbrace}
+\frac{2}{\eta}\left(-\frac{1}{2\epsilon}\delta^{(2)}(\veb{p})+{\cal{L}}_0(\veb{p}^2,\mu^2) \right)\nonumber\\
& +\frac{1}{2\epsilon}\left(\ln \left(\frac{\mu^2}{r^2\nu^2}\right)+\frac{1}{\epsilon} \right)\delta^{(2)}(\veb{p}),
\Big{\rbrace}
\end{align}
The $\mu$ anomalous dimensions are found using Eq. (\ref{eq:AD}),
\begin{equation}
\gamma_{\mu}^{\cal{D}}(\nu)=\frac{\alpha_s C_i}{\pi} \left(\ln\left(\frac{\nu^2}{\omega^2}\right)+\bar{\gamma}_i \right)
\end{equation}
\begin{equation}
\gamma_{\mu}^{S_C}(\nu)=\frac{\alpha_s C_i}{\pi} \ln\left(\frac{\mu^2}{r^2\nu^2}\right),
\end{equation}
For the $\nu$ anomalous dimensions, our bookkeeping parameter $w$ plays an analogous role to the coupling $g$ for the case of the
$\mu$ anomalous dimension, although $w$ itself is not a coupling, such that,
\begin{equation}
  \nu \pf{}{\nu}w = -\frac{\eta}{2}w,
\end{equation}
thus yielding
\begin{equation}
\label{eq:nuAD1}
\gamma_{\nu}^{\cal{D}}(p_{\perp},\mu)=-(8 \pi) \alpha_s C_i\; {\cal{L}}_0(\veb{p},\mu^2)
\end{equation}
\begin{equation}
\label{eq:nuAD2}
\gamma_{\nu}^{S_C}(p_{\perp},\mu)=+(8 \pi) \alpha_s C_i\; {\cal{L}}_0(\veb{p},\mu^2).
\end{equation}
The anomalous dimensions satisfy
\begin{equation}
\gamma_{\mu}^{\cal{D}}(\nu)+\gamma_{\mu}^{S_C}(\nu)=\gamma_{\mu}^{J}=\frac{\alpha_s C_i}{\pi} \left(\ln\left(\frac{\mu^2}{r^2 \omega^2}\right)+\bar{\gamma}_i \right),
\end{equation}
where $\gamma_{J}$ is the anomalous dimension of the unmeasured quark jet function~\cite{Ellis:2010rwa} and
\begin{equation}
\gamma_{\nu}^{\cal{D}}(\veb{p},\mu)+\gamma_{\nu}^{S}(\veb{p},\mu)=0.
\end{equation}
In order to resum our results to NLL' accuracy we evolve the purely collinear function and the collinear-soft function from their characteristic scales where logarithms are
minimized to common scales in $\mu$ and $\nu$ using the RG and RRG respectively. To perform the evolution, we first solve the Fourier transforms of both the RRG and RG equations.
We then perform the evolution using the RG and RRG before finally performing the inverse Fourier transform.
The simplest resummation procedure is, in this case, to first evolve our collinear-soft function in RRG space and choose the common scale to be $\nu=\nu_{\cal{D}}$.
We then evolve both functions in RG space to the common scale $\mu=\omega r$. Notice that $S_C$ and ${\cal D}$ have the same characteristic renormalization
scale $\mu_{S_C}=\mu_{\cal{D}}\equiv \mu_C$. The equivalence of the virtualities of the soft and collinear modes is a defining feature of $\mathrm{SCET_{II}}$.

To make the interpretation of our plots easier, we study the quantity ${\cal{G}}_{i/h}(p_{\perp},z,\mu)$ which is related to the TMDFJF by the change
of variables from vector transverse momenta ($\veb{p}$) to the amplitude ($p_{\perp}=\vert \veb{p}\vert$). Performing the evolutions described above we find,
\begin{multline}
  \label{eq:finalev}
  {\cal{G}}_{i/h}(p_{\perp},z,\mu)= (2 \pi)^2 \; p_{\perp} \int_{0}^{\infty} db \;b J_{0}(bp_{\perp}){\cal{U}}_{S_C}(\mu,\mu_{S_C},m_{S_C}){\cal{U}}_{\cal{D}}(\mu,\mu_{\cal{D}},1)
  \\ \times {\cal{V}}_{S_C}(b,\mu_{S_C},\nu_{\cal{D}},\nu_{S_C}) {\cal{FT}} \Big{\lbrack} {\cal{D}}_{i/h}(\veb{p},z,\mu_{\cal{D}},\nu_{\cal{D}})
  \otimes_{\perp}S_C^{i}(\veb{p},\mu_{S_C},\nu_{S_C}) \Big{\rbrack},
\end{multline}
where $\boldsymbol{b}$ is the Fourier conjugate variable of $\veb{p}$, $J_0$ is a Bessel function of the first kind,
\begin{equation}
 {\cal{U}}_F (\mu,\mu_0,m_{F})=\exp\left(K_F(\mu,\mu_0)\right) \left( \frac{\mu_0}{m_F} \right)^{\omega_F(\mu,\mu_0)},
\end{equation}
\begin{equation}
  \text{and}\;\;{\cal{V}}_F(b,\mu,\nu,\nu_{0})= \left( \frac{\mu}{\mu_C(b)} \right)^{\eta_F(\mu,\nu,\nu_0)} \quad \text{where} \quad \mu_C(b)=2 \exp(-\gamma_E)/b,
\end{equation}
are the evolution kernels resulting from solving the RG and RRG equations respectively.
The pure collinear term ${\cal{D}}_{i/h}$ in Eq.(\ref{eq:finalev}) involves the convolution of
the perturbatively calculated short distance coefficients and the standard fragmentation
functions evolved from their canonical scale to the canonical scale of the collinear term in
momentum space, $\mu=p_{\perp}$. The form of the fragmentation functions is fixed during the
Fourier transforms in Eq.(\ref{eq:finalev}). The scales $\mu_F$, $\nu_F$ and $m_F$ for each of
the functions are given in Table~\ref{tb:scales} and more details of the RG and RRG evolution
are provided in Appendix~\ref{sec:AppC}.
\begin{table}[h]
\begin{center}
\begin{tabular}{|c|c|c|c|}
  \hline
Function $(F)$     & RG scale ($\mu_F$) &  RRG scale ($\nu_F$) & $m_F$             \\
\hline{}
 ${\cal{D}}_{i/h}$ & $\mu_C(b)$         & $\omega$              & n.a.              \\
\hline
$S^{i}_C$          & $\mu_C(b)$         & $\mu_C(b)/r$          & $ \nu r $            \\
\hline
\end{tabular}
\end{center}
\caption{Characteristic scales of the different functions in the factorization theorem.}
\label{tb:scales}
\end{table}
\subsection{Applications to quarkonium production}
In this section we apply our TMDFJF formalism to the production of quarkonium in jets. We will focus on $J/\psi$ production within
jets initiated by gluons, though our results can be easily generalized to $\Upsilon$ or other quarkonia and jets initiated by quarks.
For $J/\psi$ production the leading production mechanism in the NRQCD $v$ expansion is ${}^3S_1^{[1]}$, where $^{2S+1}L_{J}^{[1,8]}$ indicates
 the color and angular momentum quantum numbers of the $c\bar{c}$ produced in the short-distance process. This mechanism scales as $v^3$,
whereas the leading color-octet mechanisms, ${}^3S_1^{[8]}, {}^1S_0^{[8]},$ and ${}^3P_J^{[8]}$, scale as $v^7$.
Table \ref{tb:LDME} shows this scaling along with numerical values of the corresponding LDME extracted from the fits  in Ref.~\cite{Butenschoen:2011yh, Butenschoen:2012qr} (which we use below).
The extracted LDME are consistent with the $v^4$ suppression expected from NRQCD. As was done for the FJF's
in Ref.~\cite{Bain:2016clc} we use the leading order NRQCD~\cite{Bodwin:1994jh} FFs for gluon fragmentation to $J/\psi$
for each of the four mechanisms.
In the $\alpha_s$ expansion the leading order contribution to gluon fragmentation to $J/\psi$ via the ${}^3S_1^{[1]}$ mechanism scales as $\alpha_s(2m_c)^3$, while for ${}^1S_0^{[8]}$ and ${}^3P_J^{[8]}$ the leading contribution scales as $\alpha_s(2 m_c)^2$ and for the ${}^3S_1^{[8]}$ mechanism the fragmentation function scales as
$\alpha_s(2m_c)$. Thus for gluon fragmentation the $v^4$ suppression of color-octet mechanisms is compensated for by fewer powers of $\alpha_s$ and all four contributions
are roughly the same size. Our goal is to see if the $z$ and $p_\perp$ dependence of the TMDFJF can discriminate between these competing mechanisms.

\begin{center}
\begin{figure}[h]
\centerline{\includegraphics[scale=0.62]{images/plot100all}}
\caption{The TMDFJF as a function of the $p_{\perp}$ of the $J/\psi$ for the ${}^3S_1^{[1]}, {}^3S_1^{[8]}, {}^1S_0^{[8]}, {}^3P_J^{[8]}$ production mechanisms where the
 for jet energies $E_J=100\; \text{GeV}$. Theoretical uncertainties are calculated by varying the renormalization
 scales by factors of  $1/2$ and $2$.}
\label{fig:plotpT1}
\end{figure}
\end{center}
\begin{table}[h]
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
$\langle\mathcal{O}^{J/\psi}(^3S_1^{[1]}) \rangle$  & $\langle \mathcal{O}^{J/\psi}(^3S_1^{[8]}) \rangle $ & $\langle \mathcal{O}^{J/\psi}(^1S_0^{[8]}) \rangle$ & $\langle \mathcal{O}^{J/\psi}(^3P_0^{[8]}) \rangle $ \\
\hline
$\sim v^3 $  & $\sim v^7 $ & $ \sim v^7  $& $\sim v^7  $\\
\hline{}
1.32 GeV$^3$& 2.24 $\times 10^{-3}$ GeV$^3$ & $4.97 \times 10^{-2}$ GeV$^3$ & $-1.61\times 10^{-2}$GeV$^5$\\
\hline
\end{tabular}
\end{center}
\caption{LDMEs for NRQCD production mechanisms. Here $v$ is the relative velocity of $c \bar{c}$ pair. For charmonium $v \sim 0.3$. For the numerical result we use central values taken from global fits in Refs.~\cite{Butenschoen:2011yh, Butenschoen:2012qr}. }
\label{tb:LDME}
\end{table}

The TMDFJF as a function of $p_\perp$ for fixed $z$, for $z=0.3,0.5,0.7,$ and $0.9$, are shown Figs.~\ref{fig:plotpT1} and~\ref{fig:plotpT2}, for jet energies of
100 ${\rm GeV}$ and 500 GeV, respectively. In order to make it easier to view all distributions simultaneously, we have rescaled the ${}^3S_1^{[8]}$, ${}^1S_0^{[8]}$, ${}^3P_J^{[8]}$,and ${}^3S_1^{[1]}$ distributions, by factors of $10^6$, $10^6$, $3.0 \, 10^5$ and $4.0 \, 10^5$, respectively. The same rescaling factor is used in all eight plots in Figs.~\ref{fig:plotpT1} and~\ref{fig:plotpT2}, and
theoretical uncertainties are calculated by varying the RRG and RG scales $\nu_{S_C},\;\nu_{{\cal D}},\;\text{and}\;\mu$ by a factor of $2$ and $1/2$.
The central dashed lines in the figures correspond to the scale choices $\nu=\nu_{{\cal D}}=\omega$ and  $\mu=\omega r$. Though we plot our distributions in the
range $0 < p_\perp < 20$ GeV, it is important that to keep in mind that our calculations are only reliable for $p_\perp \geq 2 m_c = 3$ GeV.

These plots show that the TMDFJF does in fact provide discriminating power amongst the four mechanisms. For $z = 0.3$, all four distributions look similar
for both $E_J =100 $ GeV and 500 GeV. The distributions peak at roughly the same location and they have same slope for large $p_\perp$. For $z\geq 0.5$, the color-singlet ${}^3S_1^{[1]}$ mechanism and the color-octet ${}^1S_0^{[8]}$ mechanism peak at lower values of $p_\perp$ and  fall more steeply
with $p_\perp$ than the ${}^3S_1^{[8]}$ and ${}^3P_J^{[8]}$ color-octet mechanisms. The ${}^3P_J^{[8]}$ mechanism has the peculiar feature that in order to obtain a positive FF we need to have a negative LDME, as is found in the fits of Refs.~\cite{Butenschoen:2011yh, Butenschoen:2012qr}.  The peaks in the $p_\perp$ distribution for the ${}^3S_1^{[1]}$ and ${}^1S_0^{[8]}$ mechanisms are at very low $p_\perp$ where perturbation theory is not reliable. On the other hand, the peaks of the
${}^3S_1^{[8]}$ and ${}^3P_J^{[8]}$ distributions are at larger values of $p_\perp \sim 6-8$ GeV where perturbation theory can be trusted. The  ${}^3P_J^{[8]}$ gives a slightly harder $p_\perp$ distribution than  ${}^3S_1^{[8]}$ mechanism, and both are significantly harder than the other mechanisms.

It is interesting to study the dependence of the TMDFJF as a function of $z$ with $p_\perp$ fixed to be a perturbative scale. In Fig.~\ref{fig:plotz} we plot the TMDFJF as
a function of $z$ for $p_\perp = 10$ GeV for jets with energy $E_J=$ 100 and 500 GeV. Large logarithms and shape function effects will affect these distributions
in both the $z \to 0$ and $z \to 1$ limits, but our calculations should be reliable for intermediate values of $z$.  While for $z<0.5$ the distributions have similar shapes,
in the range $0.5 < z < 0.9$, the shapes of all four mechanisms are different. The $z$ dependence of the TMDFJF for fixed $p_\perp$ can be used to differentiate between the NRQCD production mechanisms.

\begin{figure}[t]
\centerline{\includegraphics[scale=0.62]{images/z_distributions.pdf}}
\caption{The TMDFJF as a function of the $z$ of the $J/\psi$ for the $^3S_1^{[1]}, {}^3S_1^{[8]}, {}^1S_0^{[8]}, ^3P_J^{[8]}$ production mechanisms,
with $p_\perp = 10$ GeV for $E_J = 100$ and $500$ GeV.  Theoretical uncertainties are calculated by varying the renormalization
 scales by factors of $1/2$ and $2$. }
\label{fig:plotz}
\end{figure}

\begin{center}
\begin{figure}[h]
\centerline{\includegraphics[scale=0.62]{images/plot500all.pdf}}
\caption{The TMDFJF as a function of the $p_{\perp}$ of the $J/\psi$ for the $^3S_1^{[1]}, {}^3S_1^{[8]}, {}^1S_0^{[8]}, ^3P_J^{[8]}$ production mechanisms where the
 for jet energies $E_J= 500 \,\text{GeV}$. Theoretical uncertainties are calculated by varying the renormalization
 scales by factors of $1/2$ and $2$.}
\label{fig:plotpT2}
\end{figure}
\end{center}

The TMDFJF formalism also allows us to calculate the angle at which $J/\psi$ are produced relative to the jet axis. The average production angle for the $J/\psi$ is given by
\begin{equation}\label{eq:theta}
  \langle \theta \rangle (z) = \frac{\int \theta d\theta  (d\sigma/d\theta dz)}{  \int d\theta  (d\sigma/d\theta dz)  }.
\end{equation}
Using the small angle approximation the differential cross section can be written as
\begin{equation}
  \frac{d\sigma}{d\theta dz}=\int d p_{\perp}\; \delta \left( \theta - \frac{2 p_{\perp}}{z \omega} \right) \frac{d\sigma}{dp_{\perp} dz}.
\end{equation}
Substituting this into Eq.~\ref{eq:theta}  yields
\begin{equation}\label{eq:ratio}
  \langle \theta \rangle (z) =\frac{2\;\int dp_{\perp} p_{\perp} (d\sigma/dp_{\perp} dz)}{z \omega\;\int dp_{\perp} (d\sigma/dp_{\perp} dz) }.
\end{equation}
As discussed in Appendix~\ref{sec:AppB}, the cross section $d\sigma/d\theta dz $ can be factorized into hard, soft and collinear terms in SCET.
In general the hard and soft contributions will not cancel because there is a sum over partonic channels in both the numerator and denominator of Eq.~\ref{eq:ratio}.
However, they will if gluon fragmentation dominates production, then the expression above  can be written as
\begin{equation}
  \langle \theta \rangle (z) \sim \frac{2 \int dp_{\perp} \; p_{\perp} {\cal{G}}_{g/h}(p_{\perp},z,\mu)}{z \omega \int dp_{\perp} \; {\cal{G}}_{g/h}(p_{\perp},z,\mu)} \equiv f^{h}_{\omega}(z),
  \end{equation}
where ${\cal{G}}_{g/h}(p_{\perp},z,\mu)$ is the gluon TMDFJF. Fig.~\ref{fig:plotang} the function $f_{\omega}^{J/\psi}(z)$ is plotted at points $z=0.3,0.5,0.7,$ and $0.9$ for $\omega=2E_J =200\,\text{GeV}$ and
$\,1\,\text{TeV}$ for $J/\psi$ with $p_\perp \in [5,20]$ GeV and  $p_\perp \in [5,60]$ GeV, respectively.
As was done earlier we have fixed the scale $\mu = \omega r$. Note the typical angles are small enough that the small angle approximation is justified. The  dashed lines in figure show the results of a fit to the functional form, $C_0 \exp(-z \,C_1)$, the values of $C_0$ and  $C_1$ for each mechanism at each energy are shown in Table~\ref{tb:fit}.
Again we see that differences between the various NRQCD mechanisms become more pronounced as $z$ increases.
This shows that the average angle does in fact yield some discriminating power between the octet mechanisms. In particular the slope on the semilog plot, which is determined by the parameter $C_1$ in Table~\ref{tb:fit}, differs by as much as 20\% between the various NRQCD mechansims for $E_J = 100$ GeV and and as much as 40\% for $E_J =$ 500 GeV.
Note however that $^1S_0^{[8]}$ and  $^3S_1^{[1]}$ give very similar predictions for this observable.
\begin{figure}[h]
\centerline{\includegraphics[scale=0.62]{images/plotang.pdf}}
\caption{The  function $f^{J/\psi}_{\omega}(z)$ (as defined in the text) as a function of $z$ relative to the jet axis for each NRQCD production mechanism where the jet has $E_J=\omega/2=100$ GeV(left)  and $500\, \text{GeV}$ (right). The $J/\psi$  is restricted to have $p_{\perp}\in\left[5,\,20\right]\,\text{GeV}$ in the 100 GeV jet
and $p_{\perp}\in\left[5,\,60\right]\,\text{GeV}$ in the 500 GeV jet.}
\label{fig:plotang}
\end{figure}

\section{Conclusions}
In this paper we introduce the transverse momentum dependent  fragmenting jet function (TMDFJF) in the framework of SCET and  show how it is related to the
previously introduced TMDFFs and fragmenting jet functions (FJFs). TMDFJFs describe the transverse as well as longitudinal momentum  distribution of an identified hadron within
a jet. TMDFJFs evolve with the renormalization group (RG) scale $\mu$ and obey RG equations similar to jet functions.
Using $\text{SCET}_+$ we show that this new distribution can be further factorized into soft and purely collinear terms. The purely collinear factor can be written
as a convolution of perturbatively calculable short distance coefficients and the standard FFs, where the soft factor is given by a vacuum matrix
element of product of Wilson lines. This factorization introduces rapidity divergences that are regulated with the rapidity regulator. We check that at NLO the regulator dependance vanishes in the final product. Associated with rapidity divergences are rapidity renormalization group (RRG) equations.
By evolving the  collinear and soft terms separately using  the RG and RRG  equations all orders resummation of large logarithms in the TMDFJF can be performed.

As an example we implement this formalism for the case of quarkonium production. In the case of quarkonia the TMDFJF can be calculated in terms of the
NRQCD  FFs which are perturbatively calculable at the scale $2 m_Q$. For the gluon TMDFJF for $J/\psi$, we study the $p_\perp$ and $z$
dependence predicted by the four production mechanisms: $^3S_1^{[1]}, {}^3S_1^{[8]}, {}^1S_0^{[8]}$, and ${}^3P_J^{[8]}$. We use the leading order (in $\alpha_S$) NRQCD FF for each of these mechanisms, and the RG and RRG equations are used to calculate the TMDFJFs to next-to-leading-logarithmic-prime (NLL') accuracy. We find that the $z$ dependence
(for fixed $p_\perp$) is different for all four mechanisms. We also find that the dependence on $p_\perp$ and the average angle of the $J/\psi$ relative to the jet axis can discriminate between the various NRQCD production mechanisms.

\begin{table}
\label{tb:fit}
\begin{minipage}[h]{0.6 \linewidth}
 \centering
 \begin{tabular}{| c | c | c |}
\hline
\multicolumn{3}{|c|}{$E_J= 100\,\text{GeV}$}\\
\hline{}
 $^{2S+1}L_{J}^{[1,8]}$  &  $C_0$  &  $C_1$   \\
\hline
 $^3S_1^{[1]}$  &  $3.92 $  &  $ 0.92 $   \\
 $^3S_1^{[8]}$  &  $3.86 $  &  $ 0.84 $   \\
 $^1S_0^{[8]}$  &  $3.88 $  &  $ 0.90 $   \\
 $^3P_J^{[8]}$  &  $3.75 $  &  $ 0.74 $   \\
 \hline
 \end{tabular}
\end{minipage}
\begin{minipage}[b]{0.31\linewidth}
  \centering
\begin{tabular}{| c | c | c |}
\hline
\multicolumn{3}{|c|}{$E_J = 500\,\text{GeV}$}\\
\hline{}
 $^{2S+1}L_{J}^{[1,8]}$  &  $C_0$  &  $C_1$ \\
\hline
 $^3S_1^{[1]}$  &  $3.75 $  &  $1.68 $  \\
 $^3S_1^{[8]}$  &  $3.48 $  &  $1.39 $  \\
 $^1S_0^{[8]}$  &  $3.66 $  &  $1.64 $  \\
 $^3P_J^{[8]}$  &  $3.28 $  &  $1.20 $  \\
 \hline
\end{tabular}
 \end{minipage}
\caption{Results of fits of $\log{\left(f_{\omega}(z)\right)}$ shown in Fig.~\ref{fig:plotang} to the function $C_0 \exp(-z\, C_1)$.}
\end{table}

\acknowledgments
The authors would like to thank Aneesh Manohar for his helpful suggestions on the manuscript. TM and YM are supported in part by the Director, Office of Science, Office of
Nuclear Physics, of the U.S. Department of Energy under grant numbers DE-FG02-05ER41368. RB is supported by
a National Science Foundation Graduate Research Fellowship under Grant No. 3380012.

redpajama_set_name: RedPajamaArXiv


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González Byass "Dos Palmas" Fino
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Biscuity like the Una Palma but more salty on the nose. Wonderful power and yeasty richness. Deep and long and tangy with bitter orange. Mouth-watering finish. (JH)" (29.03.2017)
It was in 1835 when the young Manuel María González Ángel founded González Byass and started a long, and passion-filled journey, dedicated to the world of wine.
Manuel Maria found the support he needed to grow the business in his uncle, José Ángel, Tío Pepe (Uncle Joe). He showed his nephew everything he knew about Fino wines, so much so that his name was given to the winery's founding solera, where today you can still see the name, "Solera del Tío Pepe".
Inspired by the continual development in export and the growing success of his company, Manuel María González decided to join forces with Robert Blake Byass, his English agent, to whom he wrote a letter in 1844, recommending that Byass sell an "exceptionally pale…" wine. These were the very first barrels of Tío Pepe that were sent to the United Kingdom where they were very well received.
The alliance between the Byass and González families continued until 1988 when the Byass family withdrew from the business and the winery passed into the hands of the direct descendants of Manuel María González.
Today, it continues to be a family winery, presided over by the 5th generation of the González family who have always shown their passion for the world of wine, their love of nature and their care for the environment.
In 2016 Antonio Flores (pictured) was named "Best Winemaker of Fortified Wines in the World" according to the Winemaker of the Year awards, organised by the International Wine Challenge (IWC).
"Palmas" Explained:
The winemakers and winery managers have been marking the sherry casks with chalk to identify their content since 1880. They used to draw a single line on the fino casks, a circle on the oloroso wines…and there were also the 'Palma' markings. The Palmas wines are developed finos that are characterised by being exceptionally refined with a delicate aroma. The older and more refined the wine, the more 'Palmas' marked on the cask. Ever faithful to its passion for wine and in line with its innovative nature Gonzalez Byass launches every year the Fino Palmas Collection, a collection of gems comprising four very exclusive and limited production wines.
At the end of September 2016 top sommelier and wine personality Gérard Basset MW MS joined Master Blender Antonio Flores to taste over 100 casks and choose the very best for the 2016 edition of Finos Palmas. Dos Palmas 2016 was a selection of two casks, numbers 86 and 120, from a solera of 150 casks. A wine which has spent 8 years ageing in American oak and yet surprisingly is still covered with a layer of flor. This, as with last year, is due to the mild temperatures seen over the last 12 months, allowing the flor to survive longer than usual. This wine is hand bottled without filltration or clarification.
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González Byass "Una Palma" Fino


text:
Q: VBA (Ms-Access) 2013 Overflow errors I'm building a set of VBA functions to manipulate IP address strings in an MS-Access database and I am having problems with overflow errors whenever the IP address value exceeds the size of an Integer variable.  I've tried to ensure I am using only Long types, but I am still getting these errors.  Here is a very simple demo that fails with an overflow, and I can't figure out why.
Public Function BigNumber() As Long
Dim N256 As Long
N256 = 256
BigNumber = N256 * N256 * N256 * N256
End Function

I've read other thread that explained VBA may give overflow errors if any of the terms in an expression are too small for the product, but I can't see how that applies in this example.  Can anybody explain?

A: In VBA, a Long variable can store a value between -2,147,483,648 and 2,147,483,647. The result of your calculation is greater than the max, so it overflows:

256 * 256 * 256 * 256 = 4,294,967,296

redpajama_set_name: RedPajamaStackExchange


Get directions, reviews and information for Check Into Cash in San Francisco, CA.
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Candidates score on just who votes. Democrats count on women voters. Should they? Why poll workers hold a special place. Where does your candidate stand on the arts?
Those who work the polls wake up before 4 a.m. and stay on site about 14 hours to ensure residents can cast ballots.


PCYC offer recreational spaces and facilities for young people to meet or just hang out. Contact your nearest PCYC to check out what activities are available.
free access to a range of spaces and software.
Read more about support for young LGBTIQ+ people.
Your local council may list safe public places near you where you can hang out.
Libraries offer a safe environment with free access to books, magazines, movies and the internet.
Emergency housing is available for you to sleep, eat and shower.
Salvation Army drop-in centres also offer a safe and supportive place for at-risk young people.
Kids Help Line—phone 1800 551 800.


Cycling through countryside and witnessing daily life of rural rice farmers and craftsmen are the best ways to discover the real part of the island's life and beauty.
We will take you to the starting point of your cycling tour in the morning.
After a short standard safety briefing from the tour guide, you will be broken into groups of 5 to 6 people. Each group will have one tour guide. After selecting the right size bike, and helmet, you will start your adventure and follow the tour guides on a leisurely, mostly downhill trail to Ubud. You will pass the small lanes, called "gang" of the village and make a stop at local Balinese house. Along the ride, children will happily greet you. They will line up along the street (some might even follow you) and raise their hands, expecting a high/low five from you (some visitors mistakenly interpret this gesture as begging). This is a memorable part of your trip, the real encounter with the friendly local Balinese people.
Cycling tour will take about 2 hours, and end at Elephant Safari Park. Enjoy the park, visit elephant discovery museum, and have buffet lunch at Taro Restaurant.


Training Baton provides a safe and reliable way to agressively train maneuvers,strikes and routines. Each of these manufacturers are a leader in the military and law enforcment industry for quality products and gear. Essential Training equipment, the training baton is a tool used to equate to a tactical baton or impact weapon but in in a safe training environment. Safe realistic training is proven and effective in preparing the officer for success in their mission. Training Batons have such as models like ASP Training Baton + Carrier (21"/26") Buy 9 Get 1 Free, RedMan Training Baton and others that offer a variety of options for your varying needs. Alternate Force carries a wide variety of equipment and gear supporting the success of your mission. Please Contact Us for assistance, quotations or with any questions about your mission needs.
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Occupational Therapy For The Older Adult A Clinical Manual is good choice for you that looking for nice reading experience. We hope you glad to visit our website. Please read our description and our privacy and policy page.
Finally I get this ebook, thanks for all these Occupational Therapy For The Older Adult A Clinical Manual can get now!


Will there be unique and distinctive ways to "slaughter your prey"?
Will it allow you quite a lot of "creative freedom" in that respect?
I'll show you the life of the mind.
Getting hyped for this now!
Here is Digital Foundry's take on it for those that are into that kind of thing, which seems pretty spoiler free to me.
Another reason why I just bought my PS4.
Really looking forward to hunting some Yeti.
Midnight can't come quick enough.
Might trade in some tosh and get this tomorrow.....I'll just close my eyes when the Activision logo comes up at the start.
@kyleforrester87 Rather have Activision than EA, to be fair.
@Kyroki I expect it of both of them to be honest. It's Ubisoft that rile me. They seem like they should know better.
I'm not in a hurry to pick this one up yet, but I'll get it eventually. There's not a whole lot to look forward to in the latter half of this year, so that's a perfect time for something like this.
@Mega-Gazz I believe it's a woman doing voice of Ash in the anime.
@kyleforrester87 Yeah, I agree with you there; Ubisoft should know better.
@Octane very possible - may be the same woman doing the boy prince?
@Mega-Gazz Do you have a link? Is it like a small child? I'm thinking of some kind of Final Fantasy character, and with that voice it sounds very silly.
@Octane yes, it is a child. I saw it on VaatiVidya's twitch stream. They actually changed to the Japanese language because of it. I'm skeptical, but curious.
I just picked a copy up coz screw it, one of those days - need something to look forward to.
I want this game but I just won't get to it for ages.
I must admit, this one has largely passed me by - far less interested after the fact when I realised that it was a From Software game.
Seen a fair amount of it now. Doubt I'll ever get it.
I hope it has that same brutal wall that Bloodborne served up. I really enjoyed not knowing what I was doing for several days when I got that.


text:
Q: Magento2: Add a custom image and link below account navigation in account dashboard below the account navigation is there an easy way for a newbie to add an image pointing to a page in the magento2?  This account navigation appears on the side of my account dashboard.
thanks!

A: For the add image and there link in the below myaccount navigation dashboard.
Follow below steps.

File path:
  magento/app/design/frontend/Namespace/theme/Magento_Customer/layout/customer_account.xml

<?xml version="1.0"?>
<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" layout="2columns-left" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd" label="Customer My Account (All Pages)" design_abstraction="custom">

         <block class="Magento\Framework\View\Element\Template" name="new-sidebar-image-block" template="Magento_Customer::imageblock.phtml"/>

</page>

File path:
  magento/app/design/frontend/Namespace/theme/Magento_Customer/templates/imageblock.phtml

<a href="<?php echo $block->getUrl()?>customer/account/" target="_self"><img src="<?php echo $block->getUrl("pub/media/myaccount/")?>image.png"/>

Put your image to below path:
pub/media/myaccount/image.png

Now run the command php bin/magento cache:flush
Check in myaccount image will appear.
Hope it help.


The smart business look is under threat, with ugly pink, green, rounded 'lifestyle' branding all over the place. Gadgets are for kids, it seems, which is why this serious-looking, serious-sounding effort from Sennheiser immediately impresses.
Perhaps it's the leather neckband and red stitching, or the dynamic drivers, but the HD1 – part of this noted German audio brand's awesome Momentum line-up – look enticing. They feature Bluetooth 4.1, AAC codec support and Qualcomm apt-X as well as machined stainless steel in-ear sound tunnel, an in-line three-button remote, and a 10-hour battery life. That's great news for long flights.
Business users will love its ability to connect to two devices, and engage in three-way calling. So forget those 'true wireless' earbuds that (a) you will lose and (b) last about four hours and put your head between the HD1's.


text:
daily; but my experience showed me soon that even that small dose not unfrequently caused salivation in the course of a mouth or so of daily treatment. I have, therefore, thought it advisable to give a smaller dose than two-thirds of a grain of the proto-iodide of mercury daily, and have, therefore, given latterly one-sixth of a grain of that salt in combination with two grains of extract of henbane in a pill, twice daily, to these young female patients.
This dose seems to be well tolerated, and not to produce salivation, even when continued for months. I have given it, with occasional interruptions, for twelve months, without any clear symptoms of mercurial poisoning appearing.
Under this treatment, the disease goes ou in general in a favorable manner. For the most part, the secondary eruptions are benignant, accompanied, occasionally, by slight alopecia and mucous tubercles, which latter symptoms are amenable to local treatment by means of chlorine lotions and isolation. Iritis bas occurred about as often as when I did not use mercury, and has usually been very amenable to belladonna and blisters. One or two cases of rupia have occurred, but have, with one exception, done well. No severe cases of sore throat have been seen. There have been cases of apparent rectal syphilis which have proved obstinate, and in one case the prognosis was bail. As far as I have followed the patients, there have been but few cases of tertiary disease seen; but I am fully aware that it is impossible to foretell when such symptoms may arise, since syphilis arises after twenty years. I conclude
1. The initial lesion requires no mercury.
2. Syphilis, when iodine is used without mercury, is usually mild.
3. Syphilis, when treated with very small duses of iodide of mercury, is usually mild.
4. Iritis supervenes whilst patients are taking courses of mercury, and is usually amenable to blisters and atropine.
5. Tertiary syphilis is rare after iodide of potassium and iodide of mercury.
6. It is best treated by large doses of iodide of potassium, adding mercury when that remedy fails.
7. Cerebro-spinal syphilis supervenes in some cases early in the disease, and we may then give both specifics, or iodide of
potassium alone, which holds good also in syphilis of the testis, liver, or lung.
8. Mercury and iodine probably act by their power of destroying the low vegetable organism in the tissues—the yeast of syphilis (Hutchinson).
9. The dose of mercury ought to be very small.
TREATMENT OF FRACTURES OF LONG BONES
INVOLVING JOINTS.
BY JAMES S. GREEN, M D.,
NEW JERSEY.
During the winter of 1875 and 1876, it was my privilege to follow closely the private and clinical practice of Professor Lewis A. Sayre, anıl during that time and afterwards, had the opportunity of witnessing him perform a number of operations for fibrous anchylosis of the knee and hip-joints, from which experience I gathered the principle, which I afterwards applied in the treatment of fractures involving joints.
The joints to which I applied this treatment were the elbow and ankle-joints, being the articulations which have suffered more frequently than any other joints from injury, and the mode of treatment laid down in the principal works on surgery with the exception perhaps of the radio-carpal articulation.
During the first years of my surgical practice I had, on more than one occasion, realized the truth that the most careful application of the following direction laid down in the text-books for the treatment of a fracture involving the elbow-joint, yielded me an imperfect result.
"Bend the forearm at a right angle to the arm, draw it forward until the parts be brought into their proper places, and into apposition, and preserve them in this condition by applying a few turns of roller round the lower part of the arın and upper part of the forearm. An angular splint is then to be applied behind the arm or forearm of wood, leather, or gutta percha, with a smaller straight one in front, fastened by a bandage lightly applierl ; with evaporating lotions and other antiphlogistic measures to be used as the case demands."
" Passive motion is to be commenced in two or three weeks, according to the age of the patient." Notwithstanding my strict observation of the rules above given, and passive motion
care.
being commenced within six days, in a case of fracture of botlı condyles of the humerus, my experience is best expressed in the words of Mr. Wm. H. Flower in his article "On Injuries of the Upper Extremity." "The remaining fractures of the lower end of the humerus are of a more serious character, as they are necessarily attended with more or less inflammation of the joint, and are consequently almost always followed by some permanent impairment of the movements of the elbow."
Strange as it may seem, and it has appeared passing strange to me, in the standard works on surgery no means have been recommended that will prevent this almost certain " traumutira synovitis," and its consequences of "some permanent impairment in the movements of the elbow."
Dr. Sayre's treatment of the joints upon which he had used "brisement force," had so invariably prevented subsequent traumatic synovitis, that I determined to apply it to the first case of fracture involving the elbow-joint which came under my
But before detailing the cases in which the principle involved was successfully used, I will quote from Dr. Sayre's work on "Orthopædic Surgery and Diseases of Joints," in which he states the principle alluded to above (page 215). In speaking of the dressing of a knee joint after "brisement force," in January, 1854, he writes: " A tight roller was applieil from the toes up to near the knee; a large sponge placed in the popliteal space, and strips of adhesive plaster were applied over the sponge and drawn tightly around the joint from the bandage below the knee to some six inches above it. The roller was then continued over the plaster snugly applied to the whole thigh. A piece of sponge about two inches in length and about the size of the forefinger, having been placed over the track of the femoral artery-as is my usual custom in this operationthe roller was carefully applied to cause partial occlusion of the calibre of the artery, and thus diminish the supply of blood to the joint without being so tight as to induce its complete strangulation."
"I wish to call especial attention to the principle involved in the dressing in this case, as I think it of cardinal importance, having witnessed its practical benefit in many serious operations. I mean the pressure on the main trunk of an artery leading to any part in danger of inflammation in such
| Holmes's System of Surgery, vol. ii. p. 544.
manner as to diminish the supply of blood, to prevent inflammation by partial starvation. Great caution is of course necessary not to produce gangrene, but little practice and close observation will soon give the vecessary tact of knowing how to use pressure without abusing it."
In following out this plan in the treatment of fractures involv. ing joints, I determined to incase the whole limb, from its lower extremities to a point at least six inches above the joint involved, in a snugly-fitting plaster-of-Paris bandage (provided the case of fracture was seen before swelling occurred), believing that the plaster bandage properly applied would prevent the swelling in the joint, and iuflux of blood to the part in sufficient quantity to allow a traumatic synovitis to be set up.
Case I.--On the 26th of June, 1876, the first opportunity presented itself in the person of H. H. I., aged twelve years, who, falling from a high fence, produced a T-shaped fracture of the humerus and a dislocation of the forearm backward.
I saw the patient within an hour of the accident, and, having fully anesthetized him, was able to reduce the dislocation and place the bones in perfect apposition. The arm and forearm were fixed at a right angle, and a snug-fitting plaster-of-Paris bandage was applied to the limb, from the fingers to the axilla. This dressing was watched carefully for the first five days, and as there were no indications requiring its removal, it was allowed to remain until the morning of the sixth day, when the mould was cut down along the front of the arm, and the cast carefully removed for the inspection and passive motion of the joint. To niy great pleasure I found that the treatment bad prevented traumatic synovitis, that the fragments were in proper position, and having moved the joints carefully I returned the arm to the splint. The cast was removed, and passive motion used daily for four weeks, when union was complete and the joint perfect in form and motion.
Case II.—May 25, 1877, C. K., aged fourteen years, fell from a tree, fracturing the external condyle of the humerus, with displacement of the head of the radius. Saw patient immediately after the accident. The same treatment was followed by a perfect result, as in the former case.
CASE III.--November 15, 1877. G. K., aged twelve years, fell from the back part of a wagon while in motion, and fractured both condyles of the left bumerus, dislocating the forearm


Since 1989 I have been sharing my passion for the American West & Southwest through my photographs. Currently, my Limted Edition Metal Photographs are only avaialble for purchase at one of the numerous art shows that I do each year. Follow the link to view my current show schedule - Thank you!