Home / Featured / Natural Remedy for Poison Ivy – Immediate Itch Relief! Works on Bites, Stings & Rashes, too!
Natural Remedy for Poison Ivy – Works on bug bites, stings & rashes, too!
This past weekend I got poison ivy for the first time in my life! Ugh! I was SO itchy, red and uncomfortable and I just needed some relief.
I initially tried a few different natural poison ivy remedies, but nothing was giving me the relief that I needed.
So I reached for my 2, all-time favorite, natural remedies: Raw Apple Cider Vinegar and Bentonite Clay. I've used this powerful combination for years as a weekly deep cleaning face mask (best face mask ever!!!) and also as a remedy for bug bites, bee stings, rashes and wounds and it always works so immediate and so well. I thought it made sense that it would work well for poison ivy, too.
And wow, was I right about that! It immediately took away the itch and completely healed my poison ivy in 3 days. That's super fast considering most poison ivy rashes generally stick around for about 12 days. I was so impressed!
Bentonite Clay is made up of over 50 minerals from the earth and it has the unique ability to pull toxins, impurities and poisons from underneath the skin. How cool is that?! It's able to draw out the toxins that are causing the itch and it also accelerates healing by bringing nutrients and extra blood flow to the infected areas. I love this stuff! Bentonite clay is sometimes called Green Clay or Healing Clay. I buy THIS Bentonite Clay – it's a really good, high quality brand.
Raw Apple Cider Vinegar breaks down the oil and promotes healing. Make sure you get the kind with "the mother," as that is the kind with all the medicinal properties. I use THIS. You can usually find it at most health stores and grocery stores, often in the organic aisle.
I hope I don't get poison ivy ever again, but if I do, I know exactly what I'm reaching for!
Mix together the apple cider vinegar and bentonite clay using non-metal utensils until it forms a smooth paste.
Spread the paste onto infected area(s) and let dry for 10-15 minutes. You'll feel a pulsing and tightening sensation as it dries.
Rinse off with a warm washcloth. The area with the paste will probably be red after you wash it off - that is normal (and a good thing!) and the redness will subside in 30 minutes to an hour.
Hi Carol, No I don't think that was me!
I have some type of poison that has stayed on my hand for a couple of weeks. I will definitely try your remedy! Thanks for sharing!
LeRaye, I think this will do the trick! Keep me posted!
You mentioned in your video that you use this on your face once a week. Do you mix the Bentonite Clay with the raw apple cider vinegar or do you just use water for the face mixture?
You are some kind of good. I caught poison oak last Thursday and on Sunday I get the email with this receipe! God works in mysterious ways! Searching for the products locally today. Definitely giving it a shot since I am allergic to it. Thanks!
Oh awesome, Monica (well not awesome that you have poison oak, but you know what I mean lol). I don't know if it's just my imagination, but it seems like poison ivy/poison oak is SO bad this year – much worse than previous years. Please let me know if you find the clay locally. A few people have been asking if they could get it at stores and I wasn't sure if anywhere carried it locally.
Do you think this will work on hot spots on dogs?
Vicki, I think this has a really good chance of working on hot spots. Please keep me posted if you try it!
How often do you apply this? I just got around to reading this email and my husband got into some poison ivy a couple of days ago and could sure use this! Thanks in advance!
Hey Laura! I applied twice the first day. It was barely there the 2nd and 3rd day but I applied it once a day on the 2nd and 3rd day.
Do you need to mix this as you go or can I mix and keep in a glass jar. Was thinking of making some to take camping. Sounds like might be our go to for mosquito bites.
Hi Jenn! You'll have to mix this as you go. The clay will start to harden almost immediately once it's mixed with a liquid. This is awesome for mosquito bites!
Hello! I have a strange poison ivy situation. As a child I faithfully had poison ivy every year badly. My legs would be covered with single blisters several inches large each. They put me on a serum as a teen so for the past thirty years all I'd get (every year) is a few tiny blisters between my fingers. Sometimes as minimal as two tiny blisters. Of course I'd take that over the former any day but it's still annoying and consistently lasts a couple weeks. Well, just this morning I discovered a little patch on the top of my ring finger. I have bentonite clay here already as well as raw vinegar so I'm going to try the remedy and see if it goes away in three days. I'll update in a few days and let you know. Thank you for sharing!
I hope it works as well for you as it did for me, Paula! Take care!!
I'm using the remedy today as I got poison ivy on Sunday and haven't found anything to make it better. I was able to get the bentonite clay at my local health food store. Fingers crossed that it will work as well for me as it did for you! Thank you for sharing this home remedy.
Hi Kelly, found your post this morning! I don't know what rash I have, but the itching is driving me crazy. I mixed up your potion and applied it to my face. Definetly stung a bit, and then pulsated, but after rinsing it off, the itch is gone. I do have this rash on my stomach and unfortunately on my lower region. Because I did scratch…a lot, will the ACV irritate that area even more?
Hi Linda! Boy, I hope you feel better – that doesn't sound fun! The ACV *shouldn't* irritate it even more (ACV is great for skin issues, even on broken, cut skin), but I would first test a very small patch just to be sure. Feel better!!!
In 1976 a friend of mine, who was in her 70s then, told me to wear a lead fishing weight against my skin either on a chain or pined inside of my bra. She said this would keep me from getting the poison oak and it worked. I was one of those people who got it w/o getting near it, and ended up at the Dr's office covered in poison oak. I wore the lead weight for about a year. Goodness that was 40 years ago, but have not had it since.
That is so interesting, Starr! Thank you for sharing!
I dont. Have organic….will the regular apple cider work? I have it all over my face.
I just read through all the comments and I noticed that no one follows up with how it worked for them. I have the worst case of poison EVER – all over my tummy (even covering my stretchmarks-from pregnancy – which is ultra sensitive, thin skin). I was using essential oils, then spoke to a friend who said they might be driving the urushiol (the poison ivy oil) deeper yet into my skin! Ugh! She told me to google Bentonite clay treatment for poison ivy and this is how I came to this post. Thank you for sharing your ideas! I have some on as I write this and yes, it is cooling and soothing. I will try to follow up and let you know how well it worked. Once again, this is a HORRIBLE case of poison and spreading like a massive red, agonizingly itchy monster!!!
ohmigoodness, Julie, I hope this gives you some relief quickly!!!


At one point or another, most of my clients ask me something about how my home looks. I usually say something along the lines of 'It's pretty organized, but I'm still human, so it's not perfect.' Well, I figured it would be even better to show you what my home looks like. Let's take a look at my closet/wardrobe.
The first wardrobe consists of all my hanging, short items. On the bottom rung, you'll find my sleeveless tops, long sleeved tops and cardigans/jackets. Above that are my 3/4 length sleeved tops, short sleeved tops and skirts. The top shelf has a couple different bins: out of season shoes, bags and mementos. Stacked above is my swimwear. Note that each category of clothing is color coded.
them folded in opposite directions is an easy way for me to differentiate pants when I'm looking for a certain style in a rush. I don't have to flip through them all or try a bunch on to figure out which is which. Next to the pants are a couple baskets above and below a stacking shelf. The bottom basket has underwear, the top has bras. Hanging above on an extra rod are fashion, not winter, scarves. The upper most shelf has linens of all kinds - beach towels, sheets, blankets. There is no other linen closet in the apartment!
And, finally the only real closet in the apartment. Here I have my dresses and winter coats (when out of season). Above are winter accessories and an umbrella (there's also no other coat closet in the apartment). The black bin are my past years' taxes and the handful of files next to the bin are the only papers I have left to keep from transitioning to a paperless office years ago. There's a hook on the wall where I hang belts. Below are two bags of clothes that I've been adding to that will go to donation or a clothes swap. If something doesn't fit quite right when I try it on, into the bags it goes!


text:
This list of pterosaur type specimens is a list of fossils serving as the official standard-bearers for inclusion in the species and genera of the reptile clade Pterosauria, which includes the famous winged reptiles of the Mesozoic. Type specimens are definitionally members of biological taxa, and additional specimens can only be "referred" to these taxa if an expert deems them sufficiently similar to the type.

The list

Pterosaur

redpajama_set_name: RedPajamaWikipedia


Xavier Wade and West Ottawa play Clarkston Saturday.
Xavier Wade 6-3 180 Jr WR West Ottawa: It was a perfect convergence for Wade, who in Ryan Oshnock's two seasons as West Ottawa's coach has thrived in the system. He's had a career that rivals any receiver in O-K Red history. As a junior Wade put up big numbers and flashed talent. As a senior he's a better football, quicker into top gear of that smooth, long stride, and doing it for the first district championship team in school history. He had 11 catches for 185 yards and a TD in the district final win over Rockford. Wade was also the starting point guard on the school's first-ever district champion basketball team. One of myriad targets for QB Isaac VanDyk. Good size and ball skills who is just too big a target coming out of the slot against one-on-one coverage he can heat you up with underneath routes but also can break long and make catches on the move. Could be an All-MAC player in four years. He was the top available senior in the Lake Area before La'darius Jefferson decommitted from Central Florida.
Boone Bonnema 6-3 215 Jr LB/TE Zeeland East: One of two FBS prospects on defense (Chix junior D-end Adam Berghorst was recently offered by WMU) who'll be returning in 2018 for what should be another very good Zeeland East team. Bonnema is already a three-year starter. In any high school games he's one of the biggest, most athletic kids on the field, and he plays up to that profile. He's best when going full throttle, blitzing and making life hard on QBs or taking on blockers. He embraces the physical confrontation not much subtlety to it whether from his middle linebacker spot or coming out from his H-back spot to hit his corresponding defenders .Best college fit may be as ted linebacker in traditional 3-4. His main value on offense is as a blocker, he runs kind of looping routes but is athletic to make plays after the catch.
Enrique Gonzalez 6-4 185 Jr ATH Jenison: Received his varsity baptism against an at times brutal 2017 schedule — Forest Hills Central, Mona Shores, Muskegon, West Ottawa. In this case 'athlete' means 'tweener.' He's a safety and receiver for the Wildcats. With frame and versatility could end up a linebacker or tight end.Tends to play too upright, so he'll face the tough task of putting on strength while increasing flexibility to get the college coaches noticing.
Bryce Stark 5-11 175 Jr RB Montague: Fittingly given the surname Stark, he's played his best with winter coming. He ran for 254 yards and four TDs in a 47-0 opening round win over Lakeview then 227 yards and two touchdowns in the 37-13 district final against Kent City. For the year Stark has 161 rushing attempts for 1,501 yards and 28 touchdowns. He'll see his toughest defense yet in the regional with Ithaca, which is strong on all three levels. Montague spreads it out but uses a power running game with Stark the only back. He's a quick cut-back runner with good power for his size and the speed to finish, especially at the small-school level. Will have to show coaches he can catch the ball, though to his credit Stark's only reception this year went for a TD.


Wherever you choose to stay, you will be very well looked after.
We know that your accommodation and the welcome and cuisine you receive from your hosts is as important as the walks themselves. Over the past 31 years, we have built lasting partnerships with some fine accommodation providers. All are on the spectacular north coast of Cornwall, in and around the lovely unspoilt village of St Agnes. You can either enjoy Half Board or B&B accommodation and during 2019, our week long walking holidays will range from £768 per person (staying with a local family in a B&B) – up to £1,180 per person (luxury hotel, with dinner, bed and breakfast included). Please request our 2019 brochure and detailed accommodation list for the latest prices.
Whatever your choice, you will find yourself a short walk from splendid cliffs and beaches and the charming North coast village of St Agnes. This is the fictional village of 'St Annes', which Winston Graham wrote about in his popular "Poldark" novels, made later into 2 very successful TV series. It is situated some 9 miles west of Cornwall's charming cathedral city of Truro, where the trains from London arrive. The National Trust own large tracts of the local landscape, including the prominent 700 foot high St Agnes Beacon – with stunning views all over mid Cornwall and up and down the spectacular north coast. From here, one can see all the way down the north coast – past Godrevy Lighthouse (where Virginia Woolf found the inspiration to write "To The Lighthouse") to St Ives and beyond – and right up the north coast to Trevose Head and its lighthouse.
With Dinner, Bed & Breakfast included.
The Beacon Hotel is a lovely 3 star privately owned hotel, situated on the southerly slopes of St Agnes Beacon, just outside the village of St Agnes. It stands in extensive grounds of 2 acres and enjoys one of the more spectacular vistas in the area. The panorama encompasses a wide sweep of countryside, from St Austell and Bodmin Moors in the east, to the blue waters of the Atlantic, past Godrevy Lighthouse to St Ives in the west, some 13 miles distant as the crow flies.
The 11 rooms are tastefully furnished and well appointed, with "en-suite" facilities. Each room has colour television, direct dial telephones, tea and coffee making facilities and a standard of comfort commensurate with their AA 3 star rating. Both the dining room and lounge take full advantage of the view. Great pride is taken in the cuisine, which offers the very best of English and Cornish dishes, presenting a varied menu making full use of fresh local produce. There is also an extensive wine selection available with dinner. The three lounge areas are spacious and offer great comfort, where you may enjoy a quiet moment or two. For your convenience, the whole hotel has been designated as non-smoking and has Wi-Fi access. The well stocked bar is a pleasant place in which to relax in the evenings.
During the lighter months, it is quite feasible to take a stroll in the evening up to the top of St Agnes Beacon (10 mins) via the nearby footpath. From here, really spectacular views of the sunset can be observed. Also, the village, cliffs and Chapel Porth beach are all about 15-20 mins walk away. If you would like to be in a nice quiet location, with great panoramas and very comfortable rooms, with a superbly friendly family service, then this might be your choice of accommodation. Always very good reviews from our guests.
Ted and Jeannie Ellis will welcome you into their eclectic former Country Gentleman's residence, now tastefully converted into a hotel which now only offers B&B. However, the central location of The Cleaderscroft places it within 5 mins walks of many of St Agnes's fine eating places and pubs. There are 5 tastefully furnished rooms (including two four posters) and 2 self contained apartments. Please contact us (or them) to enquire as to suitability. Always highly enjoyed by those who choose to stay there.
Neil and Sue York extend a very warm welcome to all our guests at their modern self-built home. Kimberley is situated on a quiet lane in the beautiful village of St Agnes, a ten minute level walk from all the eating places the village has to offer. It is also a ten minute wooded walk down to the lovely beach at Trevaunance Cove, the main beach of St Agnes. The open cliff tops are 10 minutes walk away too.
The bedrooms (with private bathrooms) are mostly situated on the ground floor, which provides easy access to the dining room and sun lounge. Guests are welcome to relax in the garden, which includes a pond and a large terrace. Many of our guests choose to stay with Neil and Sue and we highly recommend it.
Anne and Duncan Pascoe will make you feel completely welcome at their home and be part of their family. Their charming cottage style home is situated a few minutes walk from Kimberley, in a quiet wooded setting, tucked away in a sheltered glen. It is also about a ten minute walk into the village proper and it's also a similar distance down to Trevaunance Cove. Everyone who has ever stayed with them has been blown away by their kindness and the effort they put in to make your stay nothing but excellent!
We can also offer other B&B's and pubs – please request the fully detailed accommodations and 2019 prices' list by email.
We are confident that wherever you choose to stay, you will be very well looked after. Hope you can join us on one of our wonderful walks during 2019!


text:
\section{Introduction}

Exclusive double charmonium production at $e^+e^-$ collider is among the simplest
hard exclusive reactions in perturbative QCD. The benchmark processes, exemplified by
$e^+e^-\to J/\psi+H$, with $H=\eta_c, \chi_{c0,1,2},\ldots$ representing a
$C$-even charmonium that recoils against $J/\psi$,
are first observed at two $B$ factories in the beginning of this century~\cite{Belle:2002tfa,BaBar:2005nic}.
This somewhat unexpected discovery has stimulated long-lasting theoretical interests,
since these types of hard exclusive reactions serve a novel and fertile playground for
unravelling the interplay between perturbative and non-perturbative aspects
in the heavy flavor sector of QCD.
In the following years, it became gradually clear that the conventional collinear factorization
approach~\cite{Lepage:1980fj,Chernyak:1983ej} is of rather limited use for these types of  processes,
especially problematic when handling the helicity-suppressed one such as $e^+e^-\to J/\psi+\eta_c$.
On the contrary, the nonrelativistic QCD (NRQCD) factorization approach~\cite{Bodwin:1994jh},
a modern effective-field-theory-based approach that explicitly exploits
the nonrelativistic nature of heavy quarkonium,  provides a much more powerful and
systematic tool kit to tackle double charmonium production processes.
NRQCD factorization approach organizes the predictions in a double expansion form, where the expansion parameters
are $v$, the typical velocity of heavy quark inside
a heavy quarkonium, and $\alpha_s$, the strong coupling constant.

To date the best studied exclusive charmonium production process is the one that
involves two $S$-wave charmonia in the final state, {\it i.e.}, $e^+e^-\to J/\psi+\eta_c$.
The severe discrepancy between initial \texttt{Belle}
measurement~\cite{Belle:2002tfa} and the lowest order (LO) NRQCD
predictions~\cite{Braaten:2002fi,Liu:2002wq,Hagiwara:2003cw} has spurred a flurry of theoretical investigations over years
(for a partial list, see Refs.~\cite{Braaten:2002fi,Liu:2002wq,Hagiwara:2003cw,Zhang:2005cha,Gong:2007db,Ma:2004qf,Bondar:2004sv,Braguta:2008tg}).
Among a variety of theoretical efforts, one key step in reconciling the discrepancy
is the discovery of a significant positive NLO perturbative correction in NRQCD factorization approach~\cite{Zhang:2005cha,Gong:2007db}.
The effect of relativistic corrections was also carefully addressed in \cite{Bodwin:2007ga}.
The joint NLO perturbative and relativistic correction, that is, the ${\cal O}(\alpha_s v^2)$ correction,
was also investigated in \cite{Dong:2012xx,Li:2013otv}. Very recently, as a technical breakthrough,
the very challenging NNLO perturbative correction to this process have also been considered in \cite{Feng:2019zmt}~\footnote{To appreciate the challenge
of NNLO calculation for double charmonium production processes, we quote one remark
from the 2010 review article on quarkonium physics~\cite{Brambilla:2010cs}:
"The uncalculated correction to $\sigma(e^+e^-\to J/\psi+\eta_c)$ of relative order $\alpha_s v^2$ is potentially large, as is the uncalculated correction of relative order $\alpha_s^2$. While the calculation of the former correction may be feasible, the calculation of the latter correction is probably beyond the current state of the art".}.
After piecing all kinds of available higher-order corrections together,
it appears promising that the NRQCD approach can yield a largely satisfactory description of the $B$ factory measurements for
this process, notwithstanding large uncertainties in both theory and experiment.

It is also worth noting that, the double charmonium production processes where a $P$-wave charmonium recoils
against the $J/\psi$, {\it e.g.}, $e^+e^-\to J/\psi+\chi_{cJ}$ ($J=0,1,2$),
was also reported by two $B$ factories in the early days~\cite{Belle:2002tfa,BaBar:2005nic}.
The $J/\psi+\chi_{c0}$ signals have been clearly observed,
however the $J/\psi+\chi_{c1,2}$ events, even with the more recent data set~\cite{Belle:2009bxr},
have never been established. Consequently, an upper bound has been placed on the
joint production rate $\sigma(J/\psi+\chi_{c1})+\sigma(J/\psi+\chi_{c2})$.
Fortunately, the ongoing \texttt{Belle 2} experiment, also dubbed the Super $B$ factory,
has a designed integrated luminosity about
$50\;{\rm ab}^{-1}$, about 40 times greater than that of the terminated \texttt{Belle} experiment.
It is thus very likely that \texttt{Belle 2} experiment will be able to observe all the
$e^+e^-\to J/\psi+\chi_{cJ}$ channels with decent accuracy,
and also measure the angular distribution of the $J/\psi$.
Therefore, explaining these $S$+$P$-wave double charmonium production is interesting on its own right,
which, supplementary to the $e^+e^-\to J/\psi+\eta_{c}$ channel, constitutes a rich arena
for critically testing NRQCD factorization approach.

More than a decade ago, the NLO perturbative corrections to $e^+e^-\to
J/\psi+\chi_{cJ}$ have been computed by several groups~\cite{Zhang:2008gp, Wang:2011qg, Dong:2011fb}.
The impact of ${\cal O}(\alpha_s)$ corrections is found to be substantial for $J/\psi+\chi_{c0}$,
albeit modest for $J/\psi+\chi_{c1,2}$. Incorporating the NLO perturbative corrections appears to be
helpful to bring the NRQCD prediction in better agreement with the measurement. Subsequently, some attempt to reduce the renormalization scale uncertainty in
these NLO corrections has also been conducted~\cite{Wang:2013vn}.
Recently, the contribution due to QED interference has also been investigated for these processes,
which has noneligible effect~\cite{Jiang:2018wmv}.
Furthermore, a comparative analysis of the $J/\psi$ angular distributions in a number of
double charmonium production processes has been conducted between the ${\cal O}(\alpha_s)$
NRQCD prediction and $B$ factory data~\cite{Sun:2021tma}.
It turns out that the NRQCD prediction of the $J/\psi$ angular distribution
in $e^+e^-\rightarrow J/\psi+\chi_{0}$ is in sheer contradiction to the \texttt{Belle} measurement.

Curiously, many quarkonium production and decay processes appear to suffer from substantial
higher-order radiative corrections, in particular are plagued with
large NNLO perturbative corrections~\cite{Czarnecki:1997vz,Beneke:1997jm,Marquard:2014pea,Beneke:2014qea,Czarnecki:2001zc,Feng:2015uha,Sang:2015uxg,Feng:2017hlu}.
Stimulated by the significant one-loop radiative corrections to $e^+e^-\to J/\psi+\eta_c(\chi_{c0})$,
one naturally wonders how important the two-loop QCD corrections would be for various
exclusive double charmonium production processes.
Very recently, the two-loop QCD correction to $e^+e^-\to J/\psi+\eta_c$ has been explored for the first time~\cite{Feng:2019zmt}.
The aim of this work is to continue to calculate the NNLO perturbative corrections to $e^+e^-\to J/\psi+\chi_{cJ}$ ($J=0,1,2$),
at lowest order in $v$. With the aid of very recent technical advancement in computing multi-loop integrals, we are able to present
NNLO corrections with very high numerical accuracy. In addition to assessing the impact of the
NNLO corrections on the unpolarized cross sections,
we also consider the impact of the NNLO corrections on the polarized cross sections as well as
the angular distributions, and confront the available \texttt{Belle} measurements.
We hope that these studies will provide important theoretical
guidance for future \texttt{Belle 2} measurements.

The rest of the paper is organized as follows.
In Sec.~\ref{sec-general-formula}, we employ the helicity amplitude formalism to analyze
the $e^- e^+ \to J/\psi + \chi_{cJ}$ ($J=0,1,2$) processes, and build the polarized and unpolarized cross sections
out of various helicity amplitudes. The angular distribution parameters
are also introduced in terms of the helicity amplitudes.
In Sec.~\ref{sec-NRQCD:fac}, we succinctly review the NRQCD factorization formula at the
helicity amplitude level, and parameterize the corresponding short-distance coefficients through NNLO in $\alpha_s$.
In Sec.~\ref{Technical:strategy:calc:SDC}, we briefly describe the key technical ingredients of
extracting the short-distance coefficients affiliated with each helicity amplitude through ${\cal O}(\alpha_s^2)$.
We devote Sec.~\ref{Phenomenology} to a detailed numerical analysis of the size of the NNLO perturbative
corrections to the $e^- e^+ \to J/\psi + \chi_{cJ}$ processes, including the (un)polarized cross sections and
$J/\psi$ angular distributions. Comparison between the most refined NRQCD predictions and the existing
$B$ factory measurements is also made.
Finally, we summarize in Sec.~\ref{Summary}.

\section{(Un)polarized cross sections and angular distributions\label{sec-general-formula}}

Exclusive production of $J/\psi+\chi_{cJ}$ at $B$ factories proceeds with a simple $s$-channel spacetime route,
{\it i.e.}, that the $e^+ e^-$ first annihilate into a virtual photon, subsequently the timelike photon decays
into two charmonium final states (the latter is also referred to as the time-like electromagnetic form factor of charmonium).
Assume the $e^-$ and $e^+$ move along the $\hat{z}$ direction. We work in the center-of-mass (CM) frame with the CM energy $\sqrt{s}$.
Let $\theta$ denote the polar angle between the direction of the outgoing $J/\psi$ and the $e^-$ beam.
It is convenient to express the differential $J/\psi+\chi_{cJ}$ production rates in terms
of the differential decay rates of a time-like photon.
Moreover, to retain as much polarization information of the outgoing charmonia as possible,
it is advantageous to employ the {\it helicity amplitude formalism} following \cite{Dong:2011fb}.
Let $\lambda_1$ and $\lambda_2$ represent the helicities of the $J/\psi$ and $\chi_{cJ}$, respectively.
The differential rate of a timelike photon decay into $J/\psi(\lambda_1)+\chi_{cJ}(\lambda_2)$ becomes
\begin{equation}
\label{Polarized:Diff:Decay:Rate}
\frac{d\Gamma\left[\gamma^*(S_z)\to J/\psi(\lambda_1)+\chi_{cJ}(\lambda_2)\right]}{d\cos\theta}
  =\dfrac{|{\bf P}|}{16\pi s} \left|d_{S_z,\lambda}^1(\theta)\right|^2
  |{\mathcal A}_{\lambda_1,\lambda_2}^J|^2,
\end{equation}
with $\lambda\equiv\lambda_1-\lambda_2$. $S_z$ signifies the magnetic number of the timelike photon
with the $+\hat{z}$ direction as the spin quantization axis.
${\mathcal A}_{\lambda_1,\lambda_2}^J$ is the intended helicity amplitude that encapsulates
all nontrivial strong interaction dynamics,
which depends upon $\lambda_1$ and $\lambda_2$ yet not upon $S_z$.
The angular distribution is solely governed by the Wigner function $d^j_{m_1,m_2}(\theta)$ which depends upon the
quantum number $S_z$ and $\lambda$.
Note that angular momentum conservation enforces $|\lambda|\leq 1$.
$|{\bf P}|$ in \eqref{Polarized:Diff:Decay:Rate} signifies the magnitude of the 3-momentum of the
$J/\psi$ ($\chi_{cJ}$) in the CM frame:
\begin{equation}
|{\bf P}|= \sqrt{\dfrac{\lambda(s,M_{J/\psi}^2,M_{\chi_{cJ}}^2)}{4 s}},
\end{equation}
where $\lambda(x,y,z)=x^2+y^2+z^2-2xy-2xz-2yz$ is the K\"allen function.

Parity invariance relates various helicity amplitudes with opposite helicities of $J/\psi$ and $\chi_{cJ}$:
\begin{equation}
{\cal A}^J_{\lambda_1,\lambda_2} = (-)^J {\cal A}^J_{-\lambda_1,-\lambda_2}.
\end{equation}
Consequently, as constrained by angular momentum conservation,
there are left with only 2, 3 and 5 {\it independent} helicity amplitudes for a timelike photon decay
into $J/\psi+\chi_{c0}$, $J/\psi+\chi_{c1}$ and $J/\psi+\chi_{c2}$, respectively. Note that parity
invariance enforces $A^1_{0,0}=0$.

For a definite helicity configuration of $J/\psi$ and $\chi_{cJ}$,
it is straightforward to covert
the differential decay rate of a timelike photon into the differential polarized cross section in $e^+e^-$
annihilation~\cite{Dong:2011fb}:
\begin{eqnarray}
\label{Diff:Pol:X:Section:Angular:Distribution}
&&\frac{d\sigma\left[e^+e^-\to J/\psi(\lambda_1)+\chi_{cJ}(\lambda_2)\right]}{d\cos\theta}= \frac{2\pi\alpha}{s^{3/2}}
\sum_{S_z=\pm1} \frac{d\Gamma\left[\gamma^*(S_z)\to J/\psi(\lambda_1)+\chi_{cJ}(\lambda_2)\right]}{d\cos\theta}
\\
  && \qquad =\dfrac{\alpha}{8 s^2} \left(\dfrac{|{\bf P}|}{\sqrt{s}}\right)
|{\mathcal A}_{\lambda_1,\lambda_2}^J|^2\times \Bigg\{
\begin{array}{c}
\dfrac{1+\cos^2\theta}{2},\qquad\lambda={\pm 1}
\nonumber\\
\nonumber\\
1-\cos^2\theta,\qquad \lambda=0,
\end{array}
\end{eqnarray}
where $\alpha$ signifies the QED fine structure constant.
We have averaged upon the polarizations of the $e^-$ and $e^+$. Since helicity conservation in QED warrants the virtual photon
must be transversely polarized, we only need sum over two transverse polarization of the timelike photon.
It is this partial sum that is responsible for the anisotropic angular distribution patterns in \eqref{Diff:Pol:X:Section:Angular:Distribution}.
Note that regardless of the helicity configurations of two outgoing charmonia,
the angular distributions of $J/\psi$ always fit in the pattern $\propto 1\pm \cos^2\theta$.

So far $B$ factories only measured the unpolarized double charmonium production cross sections.
Summing over all possible helicities of $J/\psi$ and $\chi_{cJ}$ in \eqref{Diff:Pol:X:Section:Angular:Distribution},
we are ready to obtain the differential unpolarized  $J/\psi+\chi_{cJ}$ production rates,
which can be generically parameterized as
\begin{equation}
\label{Unpolar:Diff:X:Section:Parametrization}
\dfrac{d\sigma(e^+e^-\to J/\psi+\chi_{cJ})}{d\cos\theta} = A_J \left(1+\alpha_J\cos^2\theta\right),
\qquad J=0,1,2
\end{equation}
where $\alpha_J$ is a dimensionless parameter that governs the profile of the
angular distribution, subject to the constraint $|\alpha_J|\leq 1$.

After some simple massage from \eqref{Diff:Pol:X:Section:Angular:Distribution},
we obtain
\begin{equation}
\label{Unpolar:Diff:X:Section:Parametrization:chic0}
A_0=\dfrac{\alpha}{8s^2} \left(\dfrac{|{\bf P}|}{\sqrt{s}}\right)
\left\{ |{\mathcal A}_{0,0}^0|^2+ |{\mathcal A}_{1,0}^0|^2\right\},\qquad\:
\alpha_0= -\dfrac{|{\mathcal A}_{0,0}^0|^2 -|{\mathcal A}_{1,0}^0|^2}{|{\mathcal A}_{0,0}^0|^2 +|{\mathcal A}_{1,0}^0|^2}
\end{equation}
for $J/\psi+\chi_{c0}$,
\begin{equation}
\label{Unpolar:Diff:X:Section:Parametrization:chic1}
A_1 =\dfrac{\alpha}{8s^2} \left(\dfrac{|{\bf P}|}{\sqrt{s}}\right)
\left\{ |{\mathcal A}_{1,0}^1|^2+|{\mathcal A}_{0,1}^1|^2 + 2|{\mathcal A}_{1,1}^1|^2  \right\},
\qquad\:
\alpha_1= { |{\mathcal A}_{1,0}^1|^2+|{\mathcal A}_{0,1}^1|^2 -2|{\mathcal A}_{1,1}^1|^2
\over  |{\mathcal A}_{1,0}^1|^2+|{\mathcal A}_{0,1}^1|^2 + 2|{\mathcal A}_{1,1}^1|^2 },
\end{equation}
for $J/\psi+\chi_{c1}$,
\begin{subequations}
\label{Unpolar:Diff:X:Section:Parametrization:chic2}
\begin{eqnarray}
& & A_2 = {\alpha\over 8s^2} \left({|{\bf P}|\over \sqrt{s}}\right)
\left\{ |{\mathcal A}_{0,0}^2|^2 +|{\mathcal A}_{1,0}^2|^2+ |{\mathcal A}_{0,1}^2|^2 +2|{\mathcal A}_{1,1}^2|^2 + |{\mathcal A}_{1,2}^2|^2    \right\},
\\
&& \alpha_2= - { |{\mathcal A}_{0,0}^2|^2 -|{\mathcal A}_{1,0}^2|^2 - |{\mathcal A}_{0,1}^2|^2  + 2|{\mathcal A}_{1,1}^2|^2 - |{\mathcal A}_{1,2}^2|^2
\over  |{\mathcal A}_{0,0}^2|^2 +|{\mathcal A}_{1,0}^2|^2+ |{\mathcal A}_{0,1}^2|^2 +2|{\mathcal A}_{1,1}^2|^2 + |{\mathcal A}_{1,2}^2|^2   }
\end{eqnarray}
\end{subequations}
for $J/\psi+\chi_{c2}$.

Integrating \eqref{Unpolar:Diff:X:Section:Parametrization} over the polar angle,
one finds that the total unpolarized cross sections to be $\sigma(J/\psi+\chi_{cJ})=2 A_J (1+\alpha_J/3)$.
Substituting the expressions of $A_J$ and $\alpha_J$ in
\eqref{Unpolar:Diff:X:Section:Parametrization:chic0},
\eqref{Unpolar:Diff:X:Section:Parametrization:chic1} and \eqref{Unpolar:Diff:X:Section:Parametrization:chic2},
we finally arrive at
\begin{subequations}
\label{Total:Unpol:X:section:ChicJ}
\begin{eqnarray}
\sigma(J/\psi+\chi_{c0})&=&\frac{\alpha}{6s^2}\frac{|{\bf P}|}{\sqrt{s}}\bigg(|{\mathcal A}_{0,0}^0|^2 + 2|{\mathcal A}_{1,0}^0|^2\bigg),
\\
\sigma(J/\psi+\chi_{c1})&=&
\frac{\alpha}{6s^2}\frac{|{\bf P}|}{\sqrt{s}}\bigg( 2|{\mathcal A}_{1,0}^1|^2+2|{\mathcal A}_{0,1}^1|^2 +2|{\mathcal A}_{1,1}^1|^2\bigg),
\\
\sigma(J/\psi+\chi_{c2})&=&
\frac{\alpha}{6s^2}\frac{|{\bf P}|}{\sqrt{s}}\bigg(  |{\mathcal A}_{0,0}^2|^2 +2|{\mathcal A}_{1,0}^2|^2+
2|{\mathcal A}_{0,1}^2|^2 +2|{\mathcal A}_{1,1}^2|^2 + 2|{\mathcal A}_{1,2}^2|^2
\bigg).
\end{eqnarray}
\end{subequations}

The central task of this work is then to compute all the 10 helicity amplitudes ${\mathcal A}^J_{\lambda_1,\lambda_2}$,
which are functions of several entangled energy scales: $\sqrt{s}$, $m_c$, and $\Lambda_{\rm QCD}$.
Nevertheless, in the high energy limit, {\it e.g.}, $\sqrt{s}\gg m_c$, each helicity amplitude
obeys definite power law scaling~\cite{Chernyak:1980dj,Brodsky:1981kj},
$A_{\lambda_1,\lambda_2}^J \propto s^{-{1\over 2}(1+|\lambda_1+\lambda_2|)}$.
Therefore, one anticipates that the double charmonium cross section for
any prescribed helicity configuration
should exhibit the asymptotical scaling behavior~\cite{Dong:2011fb}:
\begin{equation}
\label{Polarized:X:Section:Helicity:scaling}
\sigma(J/\psi(\lambda_1)+\chi_{cJ}(\lambda_2))\propto s^{-3-|\lambda_1+\lambda_2|}.
\end{equation}

A direct consequence of (\ref{Polarized:X:Section:Helicity:scaling}) is that, the polarized cross section that
exhibits slowest asymptotic decrease, $\sigma\propto 1/s^3$, is the one with $|\lambda_1+\lambda_2|=0$,
which corresponds to the unique helicity configuration $(\lambda_1,\lambda_2)=(0,0)$ by angular momentum conservation.
Therefore, at asymptotic high energy limit, the total cross section of double charmonium production is saturated by
the $(0,0)$ helicity configuration~\footnote{An interesting exception is for the channel $J/\psi+\chi_{c1}$.
Since the $(0,0)$ configuration is forbidden by parity, the leading contributions arise from either $(1,0)$ or $(0,1)$
channels, thus, according to \eqref{Polarized:X:Section:Helicity:scaling}, we anticipate that
the cross section for $J/\psi+\chi_{c1}$ is suppressed by an extra power of $1/s$
with respect to $J/\psi+\chi_{c0,2}$.}. Since the $B$ factory energy is not much bigger than the charmonium mass,
one should not be too surprised if the hierarchy of different polarized cross sections from our actual calculation
differs considerably from what is  anticipated in \eqref{Polarized:X:Section:Helicity:scaling}.

After incorporating higher-order perturbative corrections, the scaling behavior in
\eqref{Polarized:X:Section:Helicity:scaling} still holds,
yet up to mild logarithmic violation (modulo powers of $\ln s$).

\section{NRQCD factorization of the $\gamma^*\to J/\psi+\chi_{cJ}$ helicity amplitude\label{sec-NRQCD:fac}}

NRQCD factorization not only holds for inclusive quarkonium production processes, but also
for hard exclusive quarkonium production processes.
For $\gamma^*\to J/\psi+\chi_{cJ}$ process, NRQCD factorization is also applicable at helicity amplitude level.
Concretely speaking, at lowest order in $v$, the helicity amplitude for timelike photon decay into $J/\psi(\lambda_1)+\chi_{cJ}(\lambda_2)$
can be put in a factorized form:
\begin{eqnarray}
\label{NRQCD:factorization:helicity:ampl}
{\mathcal A}_{\lambda_1,\lambda_2}^J =  {\mathcal C}^J_{\lambda_1,\lambda_2}(s, m_c^2, \mu^2_\Lambda)\,{ \langle J/\psi|
\psi^{\dagger} {\bm\sigma}\cdot {\bm\varepsilon}_{J/\psi} \chi(\mu_\Lambda) |0\rangle \langle \chi_{cJ}|
\psi^{\dagger}{\cal K}_{^3P_J} \chi(\mu_\Lambda) |0\rangle \over m_c^3}.
\end{eqnarray}
$\mathcal{C}^J_{\lambda_1,\lambda_2}$ in \eqref{NRQCD:factorization:helicity:ampl} signifies the {\it dimensionless}
short-distance coefficient (SDC) for each corresponding helicity amplitude. $\mu_\Lambda$ denotes NRQCD factorization scale, which
enters both the SDC and the nonperturbative vacuum-to-charmonium NRQCD matrix element.
$\psi^\dagger$ and $\chi$ in \eqref{NRQCD:factorization:helicity:ampl} denote the Pauli spinor fields creating a charm quark and anticharm quark,
$\bm{\varepsilon}_{J/\psi}$ denotes the polarization vector of $J/\psi$ in the rest frame,
and
\begin{subequations}
\begin{eqnarray}
{\cal K}_{^3P_{0}}&=&\frac{1}{\sqrt{3}}\left(-\frac{i}{2}\overleftrightarrow{{\bf
D}}\cdot {\bm\sigma}\right),
\\
{\cal K}_{^3P_1}&=&\frac{1}{\sqrt{2}}\left(-\frac{i}{2}\overleftrightarrow{{\bf
D}}\times\bm{\sigma}\right)\cdot  {\bm\varepsilon}_{\chi_{c1}},
\\
{\cal K}_{^3P_2}&=&-{i\over 2}\overleftrightarrow{D}^{(i}\sigma^{j)} \varepsilon_{\chi_{c2}}^{ij},
\end{eqnarray}
\end{subequations}
where  $\varepsilon_{\chi_{c1}}$ ($\varepsilon_{\chi_{c2}}$) represent the
polarization vector (tensor) for $\chi_{c1}$ ($\chi_{c2}$) at rest.

In phenomenological analysis, those long-distance NRQCD matrix elements occurring in \eqref{NRQCD:factorization:helicity:ampl}
are often approximated by the radial Schr\"odinger wave functions at the origin ($J/\psi$) and the first derivative of the $P$-wave radial wave functions at the origin ($\chi_{cJ}$):
 \begin{subequations}
\label{NRQCD:vac:to:onium:ME:wvfn:at:origin}
\begin{eqnarray}
\langle J/\psi|
\psi^{\dagger} {\bm\sigma}\cdot {\bm\varepsilon}_{J/\psi} \chi(\mu_\Lambda) |0\rangle &\approx& \sqrt{ N_c\over 2\pi} \overline{R_{J/\psi}}(\mu_\Lambda),
\\
\langle \chi_{cJ}|
\psi^{\dagger}{\cal K}_{^3P_J} \chi(\mu_\Lambda) |0\rangle &\approx& \sqrt{3 N_c\over 2\pi} \overline{R^\prime_{\chi_{cJ}}}(\mu_\Lambda),
\end{eqnarray}
\end{subequations}
where $N_c=3$ denotes the number of color, We have also tacitly assumed
$\overline{R^\prime_{\chi_{c0}}}\approx \overline{R^\prime_{\chi_{c1}}} \approx \overline{R^\prime_{\chi_{c2}}}$
by appealing to approximate heavy quark spin symmetry. Due to renormalization effect, these phenomenological (derivative of) wave functions
at the origin in quark potential model must be promoted as scale-dependent NQCD matrix elements.

Through ${\cal O}(\alpha_s)$, the SDC associated with each helicity amplitude
is expected to take the following structure:
\begin{eqnarray}
\label{SDCs:power:series:in:alphas}
&& \mathcal{C}_{\lambda_1,\lambda_2}^J \left( r, {\mu_R^2\over m_c^2}, {\mu_\Lambda^2\over m_c^2} \right)
= \dfrac{64\pi e\alpha_s}{27\sqrt{3}} \: r^{(1+|\lambda_1+\lambda_2|)/2} \: \mathcal{C}_{\lambda_1,\lambda_2}^{J(\rm tree)}\bigg\{1+\frac{\alpha_s(\mu_R)}{\pi}
\bigg(\frac{1}{4}\beta_0\ln\frac{\mu_R^2}{m_c^2}+ c_{\lambda_1,\lambda_2}^{J(1)}\bigg)
\nonumber\\
&&+ \frac{\alpha_s^2(\mu_R)}{\pi^2}\bigg(\frac{1}{16}\beta_0^2\ln^2\frac{\mu_R^2}{m_c^2}+\frac{1}{16}
(8 c_{\lambda_1,\lambda_2}^{J(1)}\beta_0+\beta_1)\ln\frac{\mu_R^2}{m_c^2}+(\gamma_{J/\psi}+\gamma_{\chi_{cJ}})
\ln\frac{\mu_\Lambda^2}{m_c^2}+ c_{\lambda_1,\lambda_2}^{J(2)}\bigg)\bigg\},
\nonumber\\
\end{eqnarray}
where $r\equiv 4m_c^2/s$ is a dimensionless ratio, $\mu_R$ and $\mu_\Lambda$ refer to the renormalization scale and NRQCD factorization scale, respectively.
$\beta_0=11C_A/3-4T_F n/3$ and $\beta_1=34C_A^2/3-20C_A T_F n/3-4C_F T_F n$ (with $T_F=1/2$, $C_F=(N_c^2-1)/2N_c$, $C_A=N_c$)
are the first two coefficients in the QCD $\beta$ function.
$n$ signifies he number of the active flavors $n=n_H+n_L$, with the number of light quarks
$n_L=3$, and the number of heavy quarks $n_H=2$~\footnote{Since the $B$ factory energy exceeds
twice bottom quark mass, we explicitly include the $b$ quark contribution inside the loop diagrams.}.
Note that the occurrence of $\ln \mu_R$ terms guarantees the renormalization group invariance of the
$\mathcal{C}_{\lambda_1,\lambda_2}^J$ at two-loop accuracy. We have deliberately pulled out the $r$-dependent factor in front to make
the helicity scaling rule manifest,
so that the SDCs $\mathcal{C}_{\lambda_1,\lambda_2}^{J(\rm tree)}$ scale as $r^0$.

The tree-level SDCs $\mathcal{C}_{\lambda_1,\lambda_2}^{J(\rm tree)}$ have been known long ago~\cite{Braaten:2002fi, Dong:2011fb}:
\begin{subequations}
\label{SDC:helicity:amplitude:tree}
\begin{eqnarray}
\mathcal{C}_{0,0}^{0({\rm tree})}&=&1+10 r-12 r^2,\qquad
\mathcal{C}_{1,0}^{0({\rm tree})}={9-14 r},
\\
\mathcal{C}_{1,0}^{1({\rm tree})}&=&{-\sqrt{6} r},\qquad
\mathcal{C}_{0,1}^{1({\rm tree})}= -{\sqrt{6} (2-7r)},\qquad
\mathcal{C}_{1,1}^{1({\rm tree})}=  -{2\sqrt{6} (1-3r)},
\\
\mathcal{C}_{0,0}^{2({\rm tree})}&=&-\sqrt{2}(1-2 r-12 r^2), \qquad \mathcal{C}_{1,0}^{2({\rm tree})}= -\sqrt{2} (3-11r),
\\
\mathcal{C}_{1,1}^{2({\rm tree})}&=&-2\sqrt{6} (1-3r),\qquad
\mathcal{C}_{0,1}^{2({\rm tree})}=-\sqrt{6} (1-5r) , \qquad \mathcal{C}_{1,2}^{2({\rm tree})}= -2\sqrt{3}.
\end{eqnarray}
\end{subequations}
Accidently, the helicity amplitudes $\gamma^*\to J/\psi(\pm 1)+\chi_{c1}(0)$ are more suppressed than as suggested
from the helicity scaling rule.

The coefficients $c_{\lambda_1,\lambda_2}^{J (1)}$ in \eqref{SDCs:power:series:in:alphas} encode
the ${\cal O}(\alpha_s)$ corrections to each of 10 helicity amplitudes, which were first computed in \cite{Dong:2011fb}.
The exact expressions are somewhat cumbersome to be presented in the text, yet the asymptotic ones of  $c_{\lambda_1,\lambda_2}^{J (1)}$
become quite succinct, whose analytic form can also be found in \cite{Dong:2011fb}. A noteworthy fact is that,
the helicity-conserving $(0,0)$ channels are always accompanied by the single logarithm $\ln s/m_c^2$,
while the helicity-suppressed channels are always accompanied by the double logarithm $\ln^2 s/m_c^2$.

The central theme of this work is to compute $c_{\lambda_1,\lambda_2}^{J(2)}$,
the two-loop perturbative corrections to the SDC $\mathcal{C}_{\lambda_1,\lambda_2}^J$.
If the NRQCD factorization remains valid  for this exclusive double charmonium production,
we expect that the SDC should develop
a logarithmic dependence on NRQCD factorization scale $\mu_\Lambda$ start at ${\cal O}(\alpha_s^2)$,
with the form as exactly prescribed in \eqref{SDCs:power:series:in:alphas}.
The coefficients $\gamma_{J/\psi}$ and $\gamma_{\chi_{c0}}$ signify the
anomalous dimensions associated with the NRQCD
bilinear operators carrying the quantum numbers of $^3S_1$ and $^3P_J$,
which have already been known from various sources~\cite{Czarnecki:1997vz,Beneke:1997jm,Hoang:2006ty,Sang:2015uxg,Sang:2020fql}:
\begin{subequations}\label{eq-snomalous-dimension}
\begin{eqnarray}
\gamma_{J/\psi}&=&-\pi^2\bigg(\frac{C_AC_F}{4}+\frac{C_F^2}{6}\bigg),\\
\gamma_{\chi_{c0}}&=&-\pi^2\bigg(\frac{C_AC_F}{12}+\frac{C_F^2}{3}\bigg),\\
\gamma_{\chi_{c1}}&=&-\pi^2\bigg(\frac{C_AC_F}{12}+\frac{5C_F^2}{24}\bigg),\\
\gamma_{\chi_{c2}}&=&-\pi^2\bigg(\frac{C_AC_F}{12}+\frac{13C_F^2}{120}\bigg).
\end{eqnarray}
\end{subequations}

\section{Description of the steps to deduce NRQCD SDCS\label{Technical:strategy:calc:SDC}}

\begin{figure}[tbh]
  \begin{center}
    \includegraphics[width=0.9\textwidth]{Jpsi_chicJ_Feynman-diagrams}
\caption{Representative diagrams for $\gamma^*\to c\bar{c}({}^3S_1^{(1)})+c\bar{c}({}^3P_J^{(1)})$
through NNLO in $\alpha_s$.
\label{feynman:diagrams}}
  \end{center}
\end{figure}

In principle the SDCs $\mathcal{C}_{\lambda_1,\lambda_2}^J$ can be inferred by the perturbative matching procedure,
{\it i.e.}, by replacing the physical $J/\psi$ and $\chi_{cJ}$ with the
fictitious quarkonia composed of the free $c\bar{c}$ pairs with quantum numbers ${}^3S_1^{(1)}$ and ${}^3P_J^{(1)}$,
and computing both sides in \eqref{NRQCD:factorization:helicity:ampl} in perturbative QCD and NRQCD,
then solving for the SDCs order by order in perturbation theory~\footnote{For a rigorous perturbative matching calculation for $P$-wave quarkonium exclusive production,
we refer the interested readers to \cite{Brambilla:2017kgw} that computes the leading realativistic corrections to $e^+e^-\to \chi_{cJ}+\gamma$.}.
Nevertheless, since here we are only concerned with the lowest order in velocity expansion, practically it is more efficient
to utilize the well-known covariant color/spin/orbital projector technique to expedite the matching calculation~\cite{Petrelli:1997ge}.
This covariant projector method is a standard tool in computing quarkonium production and decay, which has been previously employed to compute the LO
and NLO perturbative contributions to the $e^+e^-\to J/\psi+\chi_{cJ}$ processes~\cite{Braaten:2002fi,Dong:2011fb}.
In this work, we also employ this shortcut to project out the intended quark amplitude
$\gamma^*\to c\bar{c}({}^3S_1^{(1)})+c\bar{c}({}^3P_J^{(1)})$.
To further extract all ten helicity amplitudes, we find it convenient to employ various covariant helicity projectors constructed in \cite{Xu:2012uh}.

Through this work we adopt the Feynman gauge and use dimensional regularization to regularize the occurring UV and IR divergences.
We apply the packages \texttt{QGraf}~\cite{Nogueira:1991ex} and \texttt{FeynArts}~\cite{Hahn:2000kx} to generate the corresponding
Feynman diagrams and amplitudes for $\gamma^*\to c\bar{c}c\bar{c}$ through NNLO in $\alpha_s$.  We implement the packages \texttt{FeynCalc}/\texttt{FormLink}~\cite{Mertig:1990an,Feng:2012tk} to handle
the Lorentz index contraction and Dirac/$SU(N_c)$ traces, in order to utilize
the spin/color/orbital/helicity projectors to project out the respective helicity amplitude for $\gamma^*\to c\bar{c}({}^3S_1^{(1)})+c\bar{c}({}^3P_J^{(1)})$.
We pause to emphasize that, in applying the covariant projection method, we have tacitly expanded the QCD amplitudes
in powers of quark relative momentum prior to conducting loop integrals.
This amounts to directly extracting the NRQCD SDCs in the context of method of region, which is considerably simpler than
the literal matching calculation.

Nearly 2000 two-loop diagrams survive for the $\gamma^*\to c\bar{c}({}^3S_1^{(1)})+c\bar{c}({}^3P_J^{(1)})$ processes.
Some representative  Feynman diagrams through NNLO in $\alpha_s$ are displayed  in Figure~\ref{feynman:diagrams}. The two-loop diagrams can be divided into two categories, the regular part and ``light-by-light" part. The latter admits a peculiar topology where a closed quark loop is linked with the timelike photon and three gluons. Since the sum of electric charge of the light flavors cancels, {\it e.g.}, $e_u+e_d+e_s=0$, so we can simply ignore the ``light-by-light" contributions stemming from the light quark loops.

Employing the package \texttt{Apart}~\cite{Feng:2012iq} for partial fractions and \texttt{FIRE}~\cite{Smirnov:2014hma}
for integration-by-parts (IBP) reduction, we end up with roughly 600 two-loop master integrals (MIs).
The biggest challenge of this work is to precisely compute these MIs, many of which bears rather complicated topology and are generally complex-valued.
It turns out that it becomes a formidable task for the traditional numerical recipes such as sector decomposition to
yield satisfactory results. Fortunately, a powerful new algorithm dubbed {\it Auxiliary Mass Flow} (AMF) has recently been pioneered by Liu and Ma~\cite{Liu:2017jxz,Liu:2020kpc,Liu:2021wks}.
The key idea is to set up differential equations with respect to an auxiliary mass variable, with the vacuum bubble diagrams as the
boundary conditions. Remarkably, the differential equations can be solved iteratively with very high numerical precision in much shorter time.
We have examined that, the AMF approach can readily tackle all the complex-valued MIs with high precision, which turns out to be much more superior to
the sector decomposition method for the MIs encountered in this work.

We thus employ the newly released package~\texttt{AMFlow}~\cite{Liu:2022chg} to compute all the 600 MIs.
After implementing the charm quark mass and field strength on-shell renormalization, and renormalizing the QCD coupling
under $\overline{\rm MS}$ scheme, we numerically verify that all the UV poles indeed cancel, yet each renormalized quark helicity amplitude is left with
a single IR pole, whose coefficients are exactly identical to $(\gamma_{J/\psi}+\gamma_{\chi_{cJ}})/2$ in \eqref{SDCs:power:series:in:alphas}.
This can be viewed as a highly nontrivial success of NRQCD factorization for exclusive double charmonium production at two loop order.
We can factor these IR divergences using $\overline{\rm MS}$ prescription, so that the two-loop SDC in each helicity channel starts to
develop an explicit logarithmic dependance on NRQCD factorization scale $\mu_\Lambda$. It is straightforward to infer the UV/IR finite
non-logarithmic part of the two-loop SDC, $c_{\lambda_1,\lambda_2}^{J(2)}$.

\section{Phenomenology\label{Phenomenology}}

\renewcommand\arraystretch{1.25}
\begin{table}[!htbp]\scriptsize
\caption{One-loop and two-loop contributions to the dimensionless SDCs, $c_{\lambda_1,\lambda_2}^{J (1,2)}$
in \eqref{SDCs:power:series:in:alphas}.
\label{Table-SDC:C:one:two:loop}
}
\setlength{\tabcolsep}{0.4mm}
\centering
  \resizebox{\textwidth}{!}{
  \begin{tabular}{|c|c|c|c|}
    \hline
      $H$ & $(\lambda_1,\lambda_2)$ &  $c_{\lambda_1,\lambda_2}^{(1)}$ & $c_{\lambda_1,\lambda_2}^{(2)}$\\

    \hline
      \multirow{4}*{$\chi_{c0}$}
        & \multirow{2}*{$(1,0)$}
        & $0.7210+0.6140 i+(0.1136-0.5236 i) n_L$
        & $-29.59+8.53 i+(-0.2621-0.1190 i) n_L^2+(-1.323+0.709 i) n_L$        \\
        &                        &                                       & $+(-0.1994+0.1361 i) _{\text{lbl},c}+(-0.0559+0.1737 i)_{\text{lbl},b}$   \\
      \cline{2-4}
        & \multirow{2}*{$(0,0)$}
        & $0.292+2.279 i+(0.0663-0.5236 i) n_L$
        & $-44.93+20.09 i+(-0.2755-0.0694 i) n_L^2+(0.1312+0.1762 i) n_L$      \\
        &                        &                                         & $+(-0.2735+0.2099 i)_{\text{lbl},c}+(-0.0711+0.1690 i)_{\text{lbl},b}$   \\
    \hline
      \multirow{6}*{$\chi_{c1}$}
        & \multirow{2}*{$(1,1)$}
        & $-6.331+5.039 i+(0.0678-0.5236 i) n_L$
        & $-67.21-43.30 i+(-0.2751-0.0710 i) n_L^2+(2.709+6.129 i) n_L$        \\
        &                        &                                         & $+(0.2348-0.0348 i)_{\text{lbl},c}+(0.4232+0.1602 i)_{\text{lbl},b}$     \\
      \cline{2-4}
        & \multirow{2}*{$(1,0)$} & $-62.87+75.74 i+(0.1423-0.5236 i) n_L$
        & $-769.4-585.4 i+(-0.2539-0.1491 i) n_L^2+(72.27+39.43 i) n_L$        \\
        &                        &                                         & $+(-0.129+1.425 i)_{\text{lbl},c}+(2.890+3.365 i)_{\text{lbl},b}$        \\
      \cline{2-4}
        & \multirow{2}*{$(0,1)$} & $-2.806+2.068 i+(0.0637-0.5236 i) n_L$
        & $-37.97-16.38 i+(-0.2763-0.0667 i) n_L^2+(-0.217+3.406 i) n_L$       \\
        &                        &                                         & $+(0.12717-0.02899 i)_{\text{lbl},c}+(0.1941+0.0208 i)_{\text{lbl},b}$   \\
    \hline
      \multirow{10}*{$\chi_{c2}$}
        & \multirow{2}*{$(1,2)$} & $-4.554+5.687 i+(0.1423-0.5236 i) n_L$
        & $-36.04-27.64 i+(-0.2539-0.1491 i) n_L^2+(4.426+3.230 i) n_L$        \\
        &                        &                                         & $+(-0.7413+0.1567 i)_{\text{lbl},c}+(-0.6149+0.2857 i)_{\text{lbl},b}$   \\
      \cline{2-4}
        & \multirow{2}*{$(1,1)$} & $-3.775+4.755 i+(0.0678-0.5236 i) n_L$
        & $-69.87-5.01 i+(-0.2751-0.0710 i) n_L^2+(2.967+3.058 i) n_L$         \\
        &                        &                                         & $+(-0.2400+0.0725 i)_{\text{lbl},c}+(-0.1554+0.1515 i)_{\text{lbl},b}$   \\
      \cline{2-4}
        & \multirow{2}*{$(1,0)$} & $-3.367+3.201 i+(0.0355-0.5236 i) n_L$
        & $-55.16-11.06 i+(-0.2843-0.0371 i) n_L^2+(1.716+2.894 i) n_L$        \\
        &                        &                                         & $+(-0.2349+0.1069 i)_{\text{lbl},c}+(-0.1166+0.1127 i)_{\text{lbl},b}$   \\
      \cline{2-4}
        & \multirow{2}*{$(0,1)$} & $-2.818+1.781 i+(-0.0467-0.5236 i) n_L$
        & $-15.87-18.98 i+(-0.3077+0.0489 i) n_L^2+(0.813+1.989 i) n_L$        \\
        &                        &                                         & $+(0.1442+0.0718 i)_{\text{lbl},c}+(0.2558-0.0429 i)_{\text{lbl},b}$     \\
      \cline{2-4}
        & \multirow{2}*{$(0,0)$} & $-4.708+4.808 i+(-0.0300-0.5236 i) n_L$ & $-67.22-28.33 i+(-0.3030+0.0314 i) n_L^2+(4.399+2.106 i) n_L$        \\
        &                        &                                         & $+(-0.1578+0.1796 i)_{\text{lbl},c}+(0.012572+0.005615 i)_{\text{lbl},b}$\\
    \hline
  \end{tabular}
  }
\end{table}

We proceed to present our numerical predictions accurate to ${\cal O}(\alpha_s)$ and confront
the available $B$ factory data. We take the following input parameters:
\begin{eqnarray}
&& \sqrt{s}=10.58\;{\rm GeV},\quad m_c=1.5\;{\rm GeV}, \quad \alpha(\sqrt{s})=1/130.9,\quad
\alpha_s(\sqrt{s}/2)=0.209,
\\
&& \left|R_{J/\psi}(0)\right|^2= 0.81\,{\rm GeV}^3,\quad \left|R_{\psi(2S)}(0)\right|^2= 0.529\,{\rm GeV}^3,
\quad \left|R^\prime_{\chi_{cJ}}(0)\right|^2 = 0.075\, {\rm GeV}^5.
\nonumber
\end{eqnarray}
We take $\mu_\Lambda=m_c$.
The radial wave functions at the origin (and first derivative) for $J/\psi$, $\psi(2S)$ and
$\chi_{cJ}$ are evaluated from the Buchm\"uller-Tye (BT) potential model~\cite{Eichten:1995ch}.
One can use \eqref{NRQCD:vac:to:onium:ME:wvfn:at:origin} to evaluate the corresponding vacuum-to-charmonium NRQCD matrix elements.
The running QCD coupling constant is automatically evaluated to two-loop accuracy
with the aid of the package \texttt{RunDec3}~\cite{Herren:2017osy}.

In Table~\ref{Table-SDC:C:one:two:loop} we enumerate the ${\cal O}(\alpha_s)$ and ${\cal O}(\alpha^2_s)$ contributions to the SDCs,
$c_{\lambda_1,\lambda_2}^{J (1,2)}$ for each helicity configuration introduced in \eqref{SDCs:power:series:in:alphas}.
The terms labeled with subscripts $\text{lbl},c$ and $\text{lbl},b$ denote the contributions from the ``light-by-light" diagrams due to charm and bottom loop,
as illustrated by some typical diagram in Figure~\ref{feynman:diagrams}. We do not include the ``light-by-light" contribution due to light quark loops, since
the net contribution vanishes after including three light quark flavors.
From Table~\ref{Table-SDC:C:one:two:loop}, we observe that the ``light-by-light" contributions are
insignificant relative to the regular part.

\begin{table}[tbh]
\caption{Polarized cross sections (in unit of fb) for each helicity channel
$e^+e^-\to J/\psi(\lambda_1)+\chi_{c0,1,2}(\lambda_2)$.
The central values of predictions are obtained by setting $m_c = 1.5\:\text{GeV}$ and
$\mu_R=\sqrt{s}/2$. The first error is estimated by varying $m_c$ from
$1.3\:\text{GeV}$ to $1.7\:\text{GeV}$, while the second error is given by varying
$\mu_R$ from $2m_c$ to $\sqrt{s}$.
\label{Table:Polarized:X:NNLO}}
 \begin{center}
  \resizebox{\textwidth}{!}{
    \begin{tabular}{ccccccc}
      \hline
          &   & $\sigma^{(0,0)}$ & $\sigma^{(1,0)}$ & $\sigma^{(0,1)} (\times 10^{-1})$ &
        $\sigma^{(1,1)} (\times 10^{-2})$ & $\sigma^{(1,2)} (\times 10^{-3})$ \\

      \hline
        \multirow{3}{*}{$J/\psi+\chi_{c0}$}
          & LO   & $1.10^{+0.59}_{-0.35}{}^{+0.51}_{-0.32}$ & $1.85^{+0.94}_{-0.62}{}^{+0.85}_{-0.54}$ & -- & -- & -- \\
          & NLO  & $2.03^{+1.26}_{-0.71}{}^{+0.51}_{-0.40}$ & $3.59^{+2.27}_{-1.36}{}^{+0.97}_{-0.74}$ & -- & -- & -- \\
          & NNLO & $1.88^{+1.33}_{-0.72}{}^{+0.003}_{-0.10}$ & $3.67^{+2.87}_{-1.56}{}^{+0.06}_{-0.24}$ & -- & -- & -- \\
      \hline
        \multirow{3}{*}{$J/\psi+\chi_{c1}$}
          & LO   & -- & $0.00116^{+0.00022}_{-0.00024}{}^{+0.00053}_{-0.00034}$ & $3.69^{+2.57}_{-1.58}{}^{+1.69}_{-1.09}$ & $3.31^{+0.77}_{-0.76}{}^{+1.52}_{-0.97}$  & -- \\
          & NLO  & -- & $0.0374^{+0.0307}_{-0.0160}{}^{+0.0468}_{-0.0199}$                  & $4.86^{+4.23}_{-2.32}{}^{+0.56}_{-0.64}$ & $2.94^{+0.94}_{-0.81}{}^{+0.009}_{-0.15}$ & -- \\
          & NNLO & -- & $0.113^{+0.101}_{-0.051}{}^{+0.088}_{-0.047}$                       & $3.59^{+4.13}_{-1.97}{}^{+0.34}_{-0.81}$ & $1.10^{+0.61}_{-0.41}{}^{+0.58}_{-0.68}$  & -- \\
      \hline
        \multirow{3}{*}{$J/\psi+\chi_{c2}$}
          & LO   & $0.430^{+0.539}_{-0.245}{}^{+0.197}_{-0.126}$ & $0.267^{+0.191}_{-0.117}{}^{+0.122}_{-0.078}$ & $0.639^{+0.587}_{-0.336}{}^{+0.293}_{-0.188}$ & $3.31^{+0.77}_{-0.76}{}^{+1.52}_{-0.97}$ & $2.31^{+0.45}_{-0.48}{}^{+1.06}_{-0.68}$ \\
          & NLO  & $0.452^{+0.610}_{-0.266}{}^{+0.020}_{-0.040}$ & $0.328^{+0.269}_{-0.153}{}^{+0.030}_{-0.039}$ & $0.808^{+0.895}_{-0.458}{}^{+0.079}_{-0.10}$  & $4.04^{+1.10}_{-1.02}{}^{+0.42}_{-0.49}$ & $2.71^{+0.58}_{-0.61}{}^{+0.28}_{-0.32}$ \\
          & NNLO & $0.225^{+0.312}_{-0.134}{}^{+0.072}_{-0.108}$ & $0.205^{+0.194}_{-0.102}{}^{+0.037}_{-0.070}$ & $0.716^{+0.921}_{-0.424}{}^{+0.014}_{-0.057}$ & $2.45^{+0.74}_{-0.65}{}^{+0.43}_{-0.70}$ & $2.11^{+0.33}_{-0.30}{}^{+0.14}_{-0.33}$ \\
      \hline
    \end{tabular}
  }
\end{center}
\end{table}

\begin{table}[htb]
\caption{Comparison between our finest predictions to the unpolarized cross sections and
the measurements in two $B$ factories (in units of fb). The sources of theoretical
uncertainties are the same as in Table~\ref{Table:Polarized:X:NNLO},
respectively. The experimental data are the double charmonium cross sections multiplied by the
branching fractions of $\chi_{cJ}$ decay into more than 2 charged tracks.
The \texttt{Belle} data for $e^+e^-\to \psi(2S) +\chi_{cJ}$ production correspond to
$\chi_{cJ}$ decay into at least 1 charged track~\cite{Belle:2004abn}. }
\label{Table:Unpolarized:X:Section:Comparison}
\begin{center}
  \resizebox{\textwidth}{!}{
    \begin{tabular}{cccc|ccc}
      \hline
        & \multirow{2}{*}{LO} & \multirow{2}{*}{NLO} & \multirow{2}{*}{NNLO} &
        \textsc{Belle} & \textsc{BaBar} \\
        & & & &
        $\sigma \times \mathcal{B}_{>2(0)}$\cite{Belle:2004abn} &
        $\sigma \times \mathcal{B}_{>2}$\cite{BaBar:2005nic} \\

      \hline
        $\sigma(J/\psi +\chi_{c0})$ &
        $4.80^{+2.47}_{-1.58}{}^{+2.20}_{-1.41}$      & $9.20^{+5.81}_{-3.43}{}^{+2.45}_{-1.87}$ & $9.22^{+7.08}_{-3.85}{}^{+0.09}_{-0.54}$       &
        $6.4 \pm 1.7 \pm 1.0$ & $10.3 \pm 2.5 ^{+1.4}_{-1.8}$ \\

        $\sigma(J/\psi +\chi_{c1})$ &
        $0.807^{+0.528}_{-0.331}{}^{+0.370}_{-0.237}$ & $1.11^{+0.93}_{-0.51}{}^{+0.21}_{-0.17}$ & $0.965^{+1.039}_{-0.503}{}^{+0.002}_{-0.015}$ &
        -- & -- \\

        $\sigma(J/\psi +\chi_{c2})$ &
        $1.16^{+1.05}_{-0.56}{}^{+0.53}_{-0.34}$      & $1.36^{+1.35}_{-0.68}{}^{+0.11}_{-0.15}$ & $0.832^{+0.898}_{-0.435}{}^{+0.157}_{-0.273}$  &
        -- & -- \\

        $\sigma(J/\psi +\chi_{c1})+\sigma(J/\psi +\chi_{c2})$ &
        $1.97^{+1.58}_{-0.89}{}^{+0.90}_{-0.58}$      & $2.46^{+2.27}_{-1.20}{}^{+0.31}_{-0.32}$ & $1.80^{+1.94}_{-0.94}{}^{+0.16}_{-0.29}$       &
        $<$5.3 at 90\% C.L. & -- \\

        $\sigma(\psi(2S) +\chi_{c0})$ &
        $3.13^{+1.61}_{-1.03}{}^{+1.44}_{-0.92}$      & $6.01^{+3.80}_{-2.24}{}^{+1.60}_{-1.22}$      & $6.02^{+4.62}_{-2.52}{}^{+0.06}_{-0.35}$      &
        $12.5 \pm 3.8 \pm 3.1$ & -- \\

        $\sigma(\psi(2S) +\chi_{c1})$ &
        $0.527^{+0.345}_{-0.216}{}^{+0.241}_{-0.155}$ & $0.722^{+0.605}_{-0.335}{}^{+0.134}_{-0.112}$ & $0.630^{+0.678}_{-0.329}{}^{+0.001}_{-0.01}$ &
        -- & -- \\

        $\sigma(\psi(2S) +\chi_{c2})$ &
        $0.759^{+0.688}_{-0.366}{}^{+0.348}_{-0.223}$ & $0.886^{+0.880}_{-0.445}{}^{+0.069}_{-0.097}$ & $0.543^{+0.586}_{-0.284}{}^{+0.102}_{-0.178}$ &
        -- & -- \\

        $\sigma(\psi(2S) +\chi_{c1})+\sigma(\psi(2S) +\chi_{c2})$ &
        $1.29^{+1.03}_{-0.58}{}^{+0.59}_{-0.38}$      & $1.61^{+1.48}_{-0.78}{}^{+0.20}_{-0.21}$      & $1.17^{+1.26}_{-0.61}{}^{+0.10}_{-0.19}$      &
        $<$8.6 at 90\% C.L. & -- \\
      \hline
    \end{tabular}
  }
\end{center}
\end{table}

\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.8]{c0.eps}
\includegraphics[scale=0.8]{c1.eps}
\includegraphics[scale=0.8]{c2.eps}
\includegraphics[scale=0.8]{c12.eps}
\caption{NRQCD predictions for the unpolarized cross sections of $e^+e^-\to J/\psi+\chi_{cJ}$ as a function of $\mu_R$ at various level of
 perturbative accuracy. For the sake of clarity, we also juxtapose the $B$ factory measurement for the $J/\psi+\chi_{c0}$ production rate
and the upper bound for combined production rate for $J/\psi+\chi_{c1}$ and $J/\psi+\chi_{c2}$.
\label{Fig:X:Section:Func:of:muR}}
\end{center}
\end{figure}

In Table~\ref{Table:Polarized:X:NNLO} and \ref{Table:Unpolarized:X:Section:Comparison},
we enumerate the NRQCD predictions at various level of perturbative accuracy for the polarized and unpolarized cross sections.
In Table~\ref{Table:Unpolarized:X:Section:Comparison} we also confront our most refined NRQCD predictions
for unpolarized $J/\psi+\chi_{cJ}$ cross sections with the existing $B$ factories measurements.
In Figure~\ref{Fig:X:Section:Func:of:muR}, we also plot the NRQCD predictions for the unpolarized production rates of
$e^+e^-\to J/\psi+\chi_{cJ}$ as function of $\mu_R$ at various levels of perturbative order.
To estimate theoretical uncertainties, we slide charm quark pole mass from 1.3 to 1.7 GeV (first error bar),
as well as vary the renormalization scale $\mu_R$ from $2m_c$ to $\sqrt{s}$ (second error bar)
(taking $\alpha_s(\sqrt{s})=0.176$, $\alpha_s(2m_c)=0.252$ by using \texttt{RunDec3}~\cite{Herren:2017osy}),
with the central values obtained by taking $m_c = 1.5\,\text{GeV}$ and
$\mu_R=\sqrt{s}/2$.  The ambiguity of charm quark pole mass turns to cause rather large
theoretical uncertainties for the predicted
cross sections, often changing the most refined NRQCD predictions by a factor of 2.

Examining Table~\ref{Table:Polarized:X:NNLO} closely, one may feel that the polarized cross sections do
not obey the hierarchy as indicated by the helicity scaling rule in \eqref{Polarized:X:Section:Helicity:scaling}.
For example, the cross section in $(1,0)$ channel is nearly twice as large as that in $(0,0)$ channel for $J/\psi+\chi_{c0}$ production,
even after including the ${\cal O}(\alpha^2_s)$ correction. A partial reason might be due to the $B$ factory energy is far from
asymptotically high, so that one may not trust too much on helicity scaling rule.
A strange pattern may be worth comment. The NLO and NNLO perturbative corrections to $\sigma^{(\pm 1,0)}$ in $J/\psi+\chi_{c1}$ production
appears to be unusually large. This might be partially traced to the fact the LO prediction $\sigma^{(0,1)}$ accidently
receives an extra suppression than what is anticipated from the helicity scaling rule (see \eqref{SDC:helicity:amplitude:tree}).
But the helicity scaling rule may be restored  after including higher-order perturbative corrections.

From  Table~\ref{Table:Polarized:X:NNLO} and \ref{Table:Unpolarized:X:Section:Comparison}, we observe that
the ${\cal O}(\alpha_s^2)$ corrections have a pronounced impact,
which lower the NLO predictions for most polarized double charmonium production rates and for all the unpolarized cross sections.
The negative NNLO perturbative corrections appear to be modest for $J/\psi(\psi(2S))+\chi_{c0,1}$ processes,
yet particularly acute for the $J/\psi(\psi(2S))+\chi_{c2}$ processes.

From Table~\ref{Table:Unpolarized:X:Section:Comparison} and Figure~\ref{Fig:X:Section:Func:of:muR}, we also observe that,
compared with the NLO predictions, the renormalization scale dependence in NNLO predictions
are considerably reduced for $\sigma(J/\psi+\chi_{c0,1})$, but slightly worsen for the $J/\psi+\chi_{c2}$ case.

It is also interesting to note that, after incorporating the ${\cal O}(\alpha_s^2)$ corrections, our most refined
NRQCD prediction for the $J/\psi+\chi_{c0}$ production are well consistent with both \texttt{Belle} and \texttt{BaBar} measurements within errors,
and our predictions for the combined production rates of $J/\psi+\chi_{c1}$ and $J/\psi+\chi_{c2}$ is also compatible with
the upper bound placed by \texttt{Belle}. Although the predicted $\sigma(J/\psi+\chi_{c1,2})$ from NRQCD is about one order of magnitude smaller than
$\sigma(J/\psi+\chi_{c0})$, with much greater integrated luminosity, we hope that future \texttt{Belle 2} experiment
will ultimately observe the $e^+e^-\to J/\psi+\chi_{c1,2}$ processes.
It will provide a more critical and comprehensive examination of NRQCD factorization approach.

It is somewhat mysterious that \texttt{Belle} measurement for $\sigma(\psi(2S)+\chi_{c0})$
is twice as large as that for $\sigma(J/\psi+\chi_{c0})$. It is quite difficult to understand this pattern within NRQCD framework,
since the wave function at the origin for $\psi(2S)$ is smaller than that for $J/\psi$.
Concerning quite large experimental uncertainty of \texttt{Belle} data,
we urge future \texttt{Belle 2} experiment to conduct a more accurate measurement
to clarify this confusing situation.

\begin{table}
\caption{NRQCD predictions for the angular distribution parameter $\alpha_J$ (defined in \eqref{Unpolar:Diff:X:Section:Parametrization})
at various perturbative accuracy. The source of the theoretical uncertainties is the same as in
Table~\ref{Table:Polarized:X:NNLO} and \ref{Table:Unpolarized:X:Section:Comparison}.}
\label{Table:Angular:Distribution:Parameter}
\begin{center}
  \begin{tabular}{cccc|c}
    \hline
      & LO & NLO & NNLO & \textsc{Belle} \\

    \hline
      $J/\psi +\chi_{c0}$ & $0.252^{+0.0005}_{-0.014}$                   & $0.278^{+0.003}_{-0.020}{}^{+0.008}_{-0.006}$
      & $0.321^{+0.019}_{-0.032}{}^{+0.026}_{-0.017}$                       &   $-1.01^{+0.38}_{-0.33}$ \\
      $J/\psi +\chi_{c1}$ & $0.697^{+0.073}_{-0.083}$                    & $0.798^{+0.055}_{-0.066}{}^{+0.033}_{-0.024}$                    & $0.911^{+0.022}_{-0.027}{}^{+0.054}_{-0.048}$                       & --- \\
      $J/\psi +\chi_{c2}$ &
      ${-0.197}^{+0.070}_{-0.090}$
      & ${-0.128}^{+0.057}_{-0.077}{}^{+0.018}_{-0.014}$
      & ${0.009}^{{+0.022}}_{{-0.040}}{}^{+0.137}_{-0.065}$ & --- \\
    \hline
  \end{tabular}
\end{center}
\end{table}

Finally, in Table~\ref{Table:Angular:Distribution:Parameter} we compare the NRQCD predictions for the angular distribution patenter $\alpha_J$ with the
$B$ factory measurement. From \eqref{Unpolar:Diff:X:Section:Parametrization} to \eqref{Unpolar:Diff:X:Section:Parametrization:chic2},
we note that defined as the ratio of different combinations of the helicity amplitudes, $\alpha_J$ is insensitive to the
nonperturbative NRQCD matrix element. Theoretical uncertainties due to charm mass and renormalization scale appears to be marginal for the
$J/\psi+\chi_{c0,1}$ channels, but becomes substantial for the $J/\psi+\chi_{c2}$ channel.
We observe that, after incorporating higher-order perturbative corrections, the $\alpha_0$ predicted
from NRQCD seems to severely disagree with the \textsc{Belle} measurement.
From \eqref{Unpolar:Diff:X:Section:Parametrization:chic0}, one tells the \texttt{Belle} measurement indicates that
the $J/\psi+\chi_{c0}$ production is dominated by the helicity-conserving $(0,0)$ channel, which seems compatible with helicity scaling law.
Nevertheless,  Table~\ref{Table:Polarized:X:NNLO} indicates that the pattern is drastically opposite in NRQCD,
in which $\sigma^{(\pm 1,0)}$ is about twice bigger than $\sigma^{(0,0)}$! Needless to say, hopefully we have to wait for the
future \texttt{Belle 2} experiment to settle this disquieting discrepancy.

\section{Summary\label{Summary}}

Within the  framework of NRQCD factorization, we compute the NNLO perturbative corrections to
$e^+e^-\to J/\psi+\chi_{cJ}$ ($J=0,1,2$) production at (super) $B$ factory.
With the aid of the newly developed AMF method, we are able to present
the (un)polarized cross section and $J/\psi$ angular distribution through order-$\alpha_s^2$ with high numerical accuracy.
At $\mathcal{O}(\alpha_s^2)$, we observe that the renormalization scale dependence for $\sigma(J/\psi+\chi_{c0,1})$ are significantly reduced,
while get slightly worsen for $\sigma(J/\psi+\chi_{c2})$. Our theoretical predictions are quite sensitive to the choice of charm quark mass.
Approximating the NRQCD matrix elements by the (derivative of) wave functions at the origin in the potential model,
our most refined prediction is $\sigma(J/\psi+\chi_{c0})=9.22^{+7.08}_{-3.85}{}^{+0.09}_{-0.54}$ fb,
where the first error is estimated by varying charm quark mass and the second error originates
from sliding the renormalization scale. This prediction is consistent with two $B$ factory measurements
within uncertainties. Our predictions at NNLO accuracy for
$\sigma(J/\psi+\chi_{c1,2})$ are about one order of magnitude smaller than $\sigma(J/\psi+\chi_{c0})$,  which are
compatible with the upper limit of
the \texttt{Belle} measurement, and will likely be observed at future \texttt{Belle 2} experiment.
On the other hand, we find there also emerges severe discrepancy between the most refined NRQCD predictions and the measurements.
One example is the total cross section for $e^+e^-\to \psi(2S)+\chi_{c0}$.
The other example is the angular distribution parameter for $e^+e^-\to \psi(2S)+\chi_{c0}$.
Our prediction $\alpha_0(\chi_{c0})=0.32^{+0.02+0.03}_{-0.03-0.02}$ is in sheer contradiction to the  measured value
$-1.01^{+0.38}_{-0.33}$ by \texttt{Belle}.
Settling down these discrepancies calls for more theoretical and experimental efforts.
We hope that future \texttt{Belle 2} experiment will shed crucial light on the mechanism of
exclusive double charmonium production and the applicability of NRQCD factorization.

\acknowledgments

The work of W.-L. S. is
supported by the National
Natural Science Foundation of China under Grants No. 11975187 and the Natural Science Foundation of ChongQing
under Grant No. cstc2019jcyj-msxmX0479.
The work of F.~F. is supported by the National Natural
Science Foundation of China under Grant No. 11875318,
No. 11505285, and by the Yue Qi Young Scholar Project
in CUMTB.
The work of Y.~J., Z.-W.~Mo. and J.-Y.~Z. is supported in part by the National Natural Science Foundation of China under Grants No.~11925506, 11875263,
 No.~ 12070131001 (CRC110 by DFG and NSFC).

redpajama_set_name: RedPajamaArXiv


text:
Exclusive - India's HMEL Bought 2 Million Barrels of Iranian Oil: Sources
by Nidhi Verma
http://dubowitz.pundicity.com/17253/exclusive-india-hmel-bought-2-million-barrels
India's HMEL, part-owned by steel tycoon Lakshmi Mittal, has emerged as a new oil client of sanctions-hit Iran, potentially complicating New Delhi's bid for a renewal of its waiver from U.S. sanctions for buying crude from Tehran.
HPCL-Mittal Energy Ltd (HMEL) has taken two shipments of Iranian oil since the start of September to maximise margins at its 180,000 barrels per day (bpd) Bathinda refinery in northern India, two sources with knowledge of the deals told Reuters. The purchases came to a total 2 million barrels.
In June Washington granted India a waiver on sanctions that would have cut it off from the U.S. financial system because it had reduced its purchases of the OPEC nation's oil.
India's waiver from the sanctions, which are designed to dissuade Tehran from pursuing its nuclear programme, will only be renewed in December if imports have been cut further.
Mark Dubowitz, a U.S. lobbyist for tougher sanctions on Iran and head of the Foundation for Defence of Democracies, said HMEL was taking a significant risk in buying this oil.
"The U.S. government in December will be looking to see whether India has indeed significantly reduced its purchases of Iranian oil and the addition of one more customer - especially with significant exposure to the U.S. and Europe - will raise eyebrows in Washington," Dubowitz said.
HMEL is part-owned by Indian tycoon Mittal, who heads ArcelorMittal (ISPA.AS), the world's largest steelmaker. ArcelorMittal produces 35 percent of its steel in the Americas and 47 percent in Europe, according to the company's website.

redpajama_set_name: RedPajamaCommonCrawl


Toronto, February 27, 2019 –Building on the momentum of stakeholders' calls for a tax review, a new report by Chartered Professional Accountants of Canada (CPA Canada) sets out a clear path for undertaking an effective and successful investigation of how to overhaul our tax system to help our country grow and prosper.
In recent months, there has been a groundswell of support for an extensive tax review – something that was last carried out in the 1960s. In the most-recent CPA Canada Business Monitor (Q4 2018), 79 per cent of senior business professionals surveyed supported Canada undertaking a comprehensive review of Canada's tax system.
Beyond CPA Canada, calls for a review have come from other national business organizations, leading think-tanks, parliamentary committees, the Advisory Council on Economic Growth and international bodies such as the Organisation for Economic Co-operation and Development and the International Monetary Fund. While a range of options on how to conduct a review are being put forward, there is complete agreement that a review has been put off for too long and the time to act is now.
"With the growing chorus for change, if the government does not announce this much-needed initiative in the next federal budget, we hope it and other parties will show their commitment by making a tax system review a key pledge in their campaign platforms for the upcoming federal election," says Joy Thomas, president and CEO, CPA Canada.
Canada's Tax System: What's so Wrong and Why it Matters, which reveals the problems our out-dated and overly complex system creates for people and businesses.
To view the latest report, visit cpacanada.ca/taxreview.


The Leadership Group is composed of the Directors of Division, who meet on a monthly basis to coordinate their operations. The group appoints a coordinator from within. The Leadership Group relies on the Strategic Council.


Aston Villa manager David O'Leary has instructed his troops to raise their game and think of Europe again.
Aston Villa manager David O'Leary has instructed his troops to raise their game and think of Europe again.
Having just missed out on a Uefa Cup place when his Villa side finished sixth in his first campaign in charge two years ago, O'Leary was as disappointed as anyone when they slipped back to tenth last term.
That continued a pattern that has seen O'Leary's teams finish in a progressively worse place in the Premiership table ever since he became a manager.
But, following an efficient summer in the transfer market, which might not be over yet if Villa can land Milan Baros, O'Leary claims there is cause for optimism.
"Our sights are once again set on Europe," said O'Leary, in confident mood just days before Saturday's big kick-off at home to Bolton Wanderers. "That is definitely still the target.
"I've got three years left of my contract here and I want to get the club into Europe.
"I want to try and build a club here where eventually, year on year, it is almost taken for granted that we're going to be in Europe.
"What we are aspiring to do is to get into Europe and then keep improving. I think we are improving. We finished in tenth place last season and people ask if that would be acceptable again? Well, no it won't. I want to finish higher than that.
"Yet if we had won three games more last season it would have been so different. That's how close it can be.
"We want to finish in the top six. Anywhere from eighth upwards would be great, but our goal is Europe."


Steve joined SCS Financial Services in 2011. He has over 38 years of experience in the investment business. As CIO, Steve sets the firm's overall investment direction, strategic portfolio asset allocation, and risk management. He acts as one of the leaders in manager sourcing and due diligence, serves as the Chair of the Investment Committee, and oversees investment research across asset classes. Most recently, Steve was Managing Director and Head of Trading for Bridgewater Associates, the largest hedge fund firm in the industry. Prior to Bridgewater, Steve was the Managing Partner of TRI Asset Management, a multi-strategy hedge fund focused on equity, credit, and macro investing. Prior to TRI, Steve was the Deputy Head, then Head of Investments at Putnam Investments, where he set the investment strategy and oversaw all investment activity across fixed income, equities, and absolute return products. Prior to Putnam, he was the Global Head of Capital Markets and Fixed Income for Swiss Bank Corporation (now UBS), responsible for all interest rate, lending, and debt activities, and a senior fixed income trader for Salomon Brothers International. Altogether, Steve spent over 10 years in London for these two institutions. Steve started his career as a broker for Conti-Commodity Services in 1979. Steve is a member of several non-profit boards and advisory committees, including Etruscan Press, the Boston Book Festival, Bucknell University, and the Berklee College of Music. He earned a BSBA in Accounting from Bucknell University in 1977 and an MS in Food Economics from the University of Delaware in 1979.


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…go to India for the completion of dental work done, in India, in June. It was inconvenient from the point of view of our customers who have gotten used to our normal prompt completion of orders. I acknowledged the orders received in our absence and nearly all of you were very understanding.
One person asked why we did not think of putting a small note on our website explaining our absence. This would be tantamount to inviting people to our place , and the consequences therefrom. We did insert a note in all orders received during the past three months, advising people to keep three weeks stock of their regular order in the event of our having to be away.
Thank you for your patience and continuing support.
We wish you all that you wish for yourselves.


text:
Board index Miscellaneous From the Trenches
Answering someone else's complaints?
A case of PEBKAC (Problem Exists Between Keyboard and Chair)? Tell us about your war stories!
w9wi
Location: Pleasant View, Tennessee
Contact w9wi
Post by w9wi » Thu Apr 12, 2012 7:01 am
Well, it's happened again -- someone called us to complain about reception problems on a different station. Not one of our competitors, but a station in a completely different market.
Voice message on the engineering mailbox, tied with a strange area code. She says for some reason she can't get channel 4 -- although mostly, she's upset that she's not receiving channel 38. First head-scratcher: while we *are* channel 4, there is no channel 38 in the market.
I return the call; before I can identify myself, she repeats the entire voice message. (including something I've heard happened to other engineers but was happening to me for the first time: she complained that we should have run a story in the news about being off the air...) Luckily, she solved the mystery by mentioning she was in Cambridge, Massachusetts
(yes, I'm aware of the master antenna issues in Boston this week, affecting WBZ-TV and WSBK-TV among other stations)
This is at least the third time someone has called us complaining about problems with reception of a channel 4 station in some other market. Shortly after the digital transition, I helped a guy in Racine, Wisconsin get his WTMJ-TV reception fixed...
Doug Smith W9WI
Pleasant View, TN EM66
PID_Stop
Contact PID_Stop
Re: Answering someone else's complaints?
Post by PID_Stop » Thu Apr 12, 2012 10:21 am
I get that all the time... mainly because people tend to get little or no help when they call our competitors.
The best (?) call was a number of years ago, right after we dropped the Donahue show for Oprah. An elderly woman called up with that special brand of annoyance that only elderly women can generate:
"Donahue isn't coming in on my televison!"
"I'm sorry... but we stopped running Donahue.  We carry Oprah at 4:00 now."
"I know that."
"So... are you having trouble seeing Oprah?"
"No, I can't see Donahue."
"We don't carry Donahue any longer -- that's channel 3."
"This is channel 9 you've called..."
"I KNOW THAT!"
"Why don't you give channel 3 a call?"
"Their number is busy."
Post by NECRAT » Thu Apr 12, 2012 11:41 am
During the DTV transition, I got a call from a lady who lived in the city of Boston, in the Roxbury section. She couldn't receive any of the Boston stations. So when I asked if she called the stations, her response was "two never returned my call, one told me to visit a website, and the fourth told me to go to best buy". (Which she ended up doing).
So I helped her with her reception issues up there, and at the end of the call she was like "you know, no one would help me in this market".
I don't know how she got our number , or where she found us, but I actually felt glad to help.
Doug, your call, however, is definitely an odd one.
eadler
Location: Binghamton, NY
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Post by eadler » Thu Apr 12, 2012 12:08 pm
When the adjacent market station with the same affiliation lost their transmission facility, I received a few calls from some of their viewers. I suspect that most (if not all) of them simply once received us via cable and switched to OTA and got them. (If they live on the south side of the mountains that are in the southern part of our coverage, they have a straight shot at the transmission hill of the other market)
Eric "tonsofpcs" Adler
http://www.videoproductionsupport.com/
Twitter: @eric_adler
grich
Location: MP89.5, Mason City Subdivision
Post by grich » Thu Apr 12, 2012 4:28 pm
During the transition, I had a call from someone bitching they couldn't see Channel 13 since we flipped channels. And, she could see Channel 8 just fine.
Only thing was, our market hadn't done anything. After arguing with her for a couple of minutes, she said the name of a town I didn't recognize. I then figured out she was in Wisconsin (I'm not). Their market just happened to have an 8 and 13, too. She just googled Channel 13 and picked the first phone number that popped up...oh well, she was only a couple-hundred miles off.
Post by w9wi » Thu Apr 12, 2012 10:05 pm
Yeah, one of our techs theorized that these people are calling 411 and asking for the number for "Channel 4". The caller doesn't realize the 411 operator isn't in Boston -- and the 411 operator in Tennessee doesn't realize there's more than one Channel 4 in the United States...
Jeff: I think some viewers think all TV stations in a market are co-owned. (given the monolith that is cable, that may not be as completely unreasonable to think as it may seem) Definitely, I've had callers ask for help receiving our competitors.
And.. they think we're all network O&Os.* "NBC isn't answering their Boston number. I'll call their office in Providence & get them to fix Channel 7."
* except for viewers over age 65 in Nashville who all believe we're still co-owned with WSM Radio.
Post by Shane » Mon Apr 16, 2012 7:15 pm
What? You're not?
Post by NECRAT » Tue Apr 17, 2012 1:02 pm
I used to get that quite a bit. When I would wear my old station's logo on a jacket out in public, i'd hear "oh would you tell that Brian Williams he's a nice guy, or, I bet Pat Sajak is a nice guy to work with". Usually from very old folks.
Post by PID_Stop » Tue Apr 17, 2012 2:02 pm
NECRAT wrote: ...I bet Pat Sajak is a nice guy to work with". Usually from very old folks.
School kids (girls, mainly) touring the station were really crushed when they found out they weren't going to meet Oprah.
K9EZ
Contact K9EZ
Post by K9EZ » Thu Apr 19, 2012 10:45 pm
NECRAT wrote: I used to get that quite a bit. When I would wear my old station's logo on a jacket out in public, i'd hear "oh would you tell that Brian Williams he's a nice guy, or, I bet Pat Sajak is a nice guy to work with". Usually from very old folks.
Wait, I thought they lived in that little box I watch.......
Kent Winrich
Owner, Consultant, Floor Sweeper and Official Thread Hijacker
Broadcast and Technology Blog http://sceotech.com/blog/
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text:
China unveils world's fastest train
Source: CRRC Corporation/NewAtlas
China claims new 600 km/h(373 mph) maglev train is now the fastest ground transport service in the world.
China debuts world's first 600 km/h high-speed maglev transportation system
On July 20, 2021, a new ultra-high-speed maglev transportation system was successfully launched in Qingdao, China. Its makers, CRRC Corporation say as the fastest ground transportation vehicle at present, the 600 km/h (373 mph) high-speed maglev transportation system can further broaden the spectrum of transportation speeds and meet the diversified travel needs of the people.
China's CRRC claims its new 600 km/h maglev bullet train will be the fastest ground transport service in the world. Source: CRRC Corporation/NewAtlas
The trains were unveiled in Qingdao. Source: Corporation/NewAtlas
A maglev bullet train that can reach speeds of 600 kilometers per hour (373 miles per hour) has made its debut in Qingdao, China. Developed by the state-owned China Railway Rolling Stock Corporation, it's considered the world's fastest train.
"Maglev" is an abbreviation of "magnetic levitation." The train appears to be "floating" thanks to an electromagnetic force that sends it gliding above the tracks. Source: Facebook/CRRC Corporation L
Liang Jianying, deputy general manager and chief engineer of CRRC Sifang, told Chinese state media that in addition to its speed, the train emits low levels of noise pollution and requires less maintenance than other high-speed trains. A prototype of the new maglev train was revealed to media in 2019. That same year, China announced ambitious plans to create "3-hour transportation circles" between major metropolitan areas. Source: Facebook/CRRC Corporation
High-speed rail is a major priority in China, which aims to connect more of its large cities by train to reduce the time and expense required to travel around the world's most populous country. Currently, the average high-speed train in China can run at about 350 kph, while planes fly at 800-900 kph. Trains like the one unveiled in Qingdao this week could fill a critical middle space. Source: Facebook/CRRC Corporation
However there's one thing keeping this train from being ready to greet commuters — a lack of completed maglev track networks. Currently, China only has one maglev line in commercial use, connecting Shanghai's Pudong Airport with the Longyang Road station in the city. The 30 km (19 mile) journey takes about seven and a half minutes, with the train hitting speeds of 430 kph (267 mph). Source: Facebook/CRRC Corporation
The driver's cockpit looks very futuristic. More like a starship than a train. Source: Facebook/CRRC Corporation
How do you stop these things? According to China's Global Times, the "whirlpool" brake system on this train is considerably more efficient than previous efforts; this train will only take 10 km (6.2 miles) to pull up, where the current Shanghai maglev takes 16 km (10 miles)! Source: Facebook/CRRC Corporation
Several new maglev networks are reportedly under construction, including one linking Shanghai and Hangzhou and another connecting Chengdu and Chongqing. Source: Facebook/CRRC Corporation
The bullet train is able to travel at such high speeds because of magnetic levitation. The technology uses electro-magnetic force to levitate the body of the vehicle less than two inches from the rails and propel it forward along the tracks. By riding on a cushion of air, friction is drastically reduced, allowing it to travel faster than traditional trains where wheels and rails are constantly in contact. Source: Facebook/CRRC Corporation
The new train's record might not stand for long. The Central Japan Railway Company is currently testing a maglev train it says will be able to top out at 375 mph, but that isn't expected to make its debut until 2027 at the earliest. Source: Facebook/CRRC Corporation
It's not yet clear where exactly these machines will be rolled out. Source: Facebook/CRRC Corporation
CRRC exports trains all over the world, especially to countries that have signed onto Beijing's Belt and Road infrastructure initiative. Source: Facebook/CRRC Corporation
The trains can be configured to have between two and 10 cars, with each holding up to 100 passengers depending on fit-out. Source: Facebook/CRRC Corporation
China's new ultra-high-speed maglev bullet train is…FAST! The world's first 600 km/h high-speed maglev transportation system, the fastest ground transportation vehicle at present, was launched in Qingdao, China on July 20, 2021, by CRRC Corporation Ltd. Source: Facebook/CRRC Corporation
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text:
15 killed as major fire engulfs Pune sanitiser factory
Eyewitnesses said that while many of the male workers managed to escape, at one point, the relief teams had to bulldoze a factory wall to rescue some others trapped inside the premises
At least 15 persons, mostly women, were killed in a major fire that broke out in a sanitiser manufacturing factory in a village of Pune district on Monday afternoon, officials said.
The blaze erupted around 3.30 p.m. in the private chemical company in the MIDC area of Pirangut village and quickly spread within the enclosed premises, trapping many of those working there.
While at least 15 persons perished in the blaze mostly due to suffocation, around 10 other workers are feared trapped or missing in the incident, said an official of Pune Rural Police Control.
Earlier, Tehsildar Abhay Chauhan said that 11 persons have lost their lives and rescue operations were going on in full swing.
Fire Brigade teams from MIDC, Mulshi, disaster rescue teams and others have rushed to the spot to battle the conflagration.
Eyewitnesses said that while many of the male workers managed to escape, at one point, the relief teams had to bulldoze a factory wall to rescue some others trapped inside the premises.
fire accident


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text:
Now investors must sit an exam to invest with lending platforms
Stuart Fieldhouse
FCA, Alternative Investments, regulation
The growth in interest in lending funds and lending platforms is understandable. These can be investment funds that, instead of buying and selling stocks, instead lend money and benefit from the income in terms of interest paid. Alternatively, peer to peer lending platforms can offer investors a range of different projects they can lend to. It is a way for investors to access what we call 'uncorrelated returns' – investments that they hope make a steady return regardless of where the stock market or other public markets are going.
Lending funds and peer to peer lending platforms will tend to specialise in different types of finance – for example, lending to small businesses, or for the purposes of property development. Where the UK regulator, the FCA, has become concerned recently, is the way lending funds are explaining what they do to the general public. People frequently do not understand how the fund manager is making his money.
While investors may understand the supply and demand characteristics that drive a stock market, some peer to peer lending can be quite specialised, along with the way that risks are assessed as part of that.
Lendinvest, one of the most high profile loan management firms, which used to advertise regularly on billboards in London, is actually introducing an exam for investors interested in alternative lending opportunities before they can write a cheque. Clients will need to pass the exam to invest, and those already invested in the company's funds will also have to pass. The test will take into account current net worth, investments and the level of understanding of the investment being made. According to Christian Faes, CEO of Lendinvest, roughly 90% of its existing customers should pass.
The company is also going to restructure the loans on its platform into investment funds, more conventional legal vehicles which it hopes will reassure the regulator.
The Armchair Trader spoke to Lendinvest this morning, and they confirmed that the exam would only apply to investors in its lending platform and not to fund investors. The company's UK lending fund is already closed to new investment, but investors interested in the returns from loans to UK real estate projects can still invest via the firm's Luxembourg fund.
What is interesting is the company is moving to introduce the exam before the FCA requires one. As with the CFD trading industry, alternative lending companies are beginning to understand they must make more effort to vet their potential clients for their level of expertise, rather than simply accepting their money. It is the responsible thing to do.
Stuart Fieldhouse has spent 25 years in journalism and marketing, including as a wealth management editor for the Financial Times group, covering capital markets and international private banking, and as an investment banking correspondent for Euromoney in Hong Kong. He was the founder editor of The Hedge Fund Journal.
Stuart has worked at CMC Markets, supporting the re-launch of its global financial spread betting and CFD trading platforms. He is also the author of two books on trading, published by Financial Times Pearson. Based in The Armchair Trader's London office, Stuart continues to advise fund managers, private banks, family offices and other financial institutions.
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