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Tag: Antony Horowitz
My Kyrosmagica Review of The House of Silk by Anthony Horowitz
Bestselling novelist and Holmes expert Anthony Horowitz will bring the great man to life again for a new generation of readers. As the creator of Foyle, recently voted the nation's favourite TV detective at the ITV Crime Thriller Awards 2010, Anthony has already displayed his talent for plotting and characterisation. Having been a lifelong fan of Conan Doyle's novels, he was the perfect choice to return to the original stories and create a new mystery for Holmes and Watson. Interest in Holmes has never been higher than right now. A blockbusting movie adaptation has coincided with the BBC's intriguing modern update and both successes are to be repeated this autumn. Horowitz says: 'I fell in love with the Sherlock Holmes stories when I was 16 and I've read them many times since. My aim is to produce a first-rate mystery for a modern audience while remaining absolutely true to the spirit of the original.'
THE GAME'S AFOOT…
It is November 1890 and London is gripped by a merciless winter. Sherlock Holmes and Dr Watson are enjoying tea by the fire when an agitated gentleman arrives unannounced at 221b Baker Street. He begs Holmes for help, telling the unnerving story of a scar-faced man with piercing eyes who has stalked him in recent weeks.
Intrigued, Holmes and Watson find themselves swiftly drawn into a series of puzzling and sinister events, stretching from the gas-lit streets of London to the teeming criminal underworld of Boston and the mysterious 'House of Silk'…
Author info on Goodreads:
Anthony Horowitz, OBE is ranked alongside Enid Blyton and Mark A. Cooper as "The most original and best spy-kids authors of the century." (New York Times). Anthony has been writing since the age of eight, and professionally since the age of twenty.
In addition to the highly successful Alex Rider books, he is also the writer and creator of award winning detective series Foyle's War, and more recently event drama Collision, among his other television works he has written episodes for Poirot, Murder in Mind, Midsomer Murders and Murder Most Horrid. Anthony became patron to East Anglia Children's Hospices in 2009.
On 19 January 2011, the estate of Arthur Conan Doyle announced that Horowitz was to be the writer of a new Sherlock Holmes novel, the first such effort to receive an official endorsement from them and to be entitled the House of Silk.
Antony Horowitz is without a doubt an excellent crime writer, one just has to look at his writing resume to see that. But moreover, he has an obvious love of Conan Doyle's original stories. The House of Silk is a novel devoted to an accurate portrayal of Sherlock Holmes, Horowitz's enthusiasm shines through, in a voice that speaks with great fluidity. In fact I'm quoting him here from his conception, inspiration and the ten rules of writing The House of Silk: "When I was asked to write the House of Silk, I realised that this would be the key. I had to become invisible. I had to find that extraordinary, authentic voice." Well, in my opinion Horowitz does that and more, he invisibly keeps the fun factor in Sherlock, keeping us quietly smiling all the way through.
I loved reading crime novels as a teenager and reading The House of Silk seems to have taken me back to my teenage self, and my love of this genre. I was a huge fan of Raymond Chandler, and Agatha Christie, so it takes no Sherlock deduction to know that this love has been well and truly rekindled!
The House of Silk is told from the perspective of Sherlock's trusted friend Dr. Watson. An air of secrecy surrounds the case of The House of Silk with many notable and powerful people wishing that its horrific and secretive nature remain forever hidden. Even though Sherlock Holmes is warned in no uncertain terms by his brother to stay out of it, Holmes disregards this advice, thriving on yet another challenge. The nature of the investigation is so horrific that it was recorded by Watson at the time, but is only revealed a century after the death of his esteemed friend Sherlock Holmes.
The year is 1890, the case begins with the familiar surroundings of 221B, Baker Street, with Sherlock enjoying, "a large plate of scones with violet honey and cream, along with a pound cake and tea," all very familiar and nice, but in stark contrast with a crime of such gruesomeness, as you will see, if you read the novel.
Mrs. Hudson's tea, scones, pound cake, honey and cream sounds wonderful, we all need a Mrs Hudson I reckon!
At a later point Mrs Hudson ushers in Edmund Carstairs, an troubled Art Gallery owner, with a nervous disposition, who is disturbed by the sudden appearance of an Irish gang member that in the past damaged his paintings. Edmund Carstairs believes that this man, a member of the flat cap gang, is out to get him. Holmes calls upon his young street urchins, including Wiggins, to assist him in his investigations, and is shocked to find that one of them is brutally murdered too.
Be aware that Horowitz loves killing off people, its one of his self-confessed fortes!
Holmes shows a touch of remorse at allowing the young lad to get involved, in fact he is so disturbed by this turn of events that he becomes even more determined to bring the killer to justice.
This ultimately leads to Holmes arrival at an Opium Den, his framing, and arrest on suspicion of murder himself. Watson has to come to his friend's rescue, he must be the one to get him out of prison, so that Holmes can find the killer, and solve the mystery of the ailing Carstairs family. In comparison to the superior intellect and keen wit of Holmes, Watson feels overwhelmed by feelings of inadequacy. I will not tell you how, or if, Holmes manages to escape that's for you to find out!
The nature of the crimes committed at The House of Silk are so shocking that even the most hardened of criminals wishes to help Holmes, and then Watson to solve the case. In the meantime, Carstair's sister is suffering from some strange malady, poison is suspected, and the two stories begin to intertwine, and the final result is both shocking and gripping. Watson's deep affection for his friend, and Holmes witty, dry, repartee, and amazing powers of observation and deduction, are all there to delight, and enthrall the reader. There is a deep sense of the social concerns, and shocking depravities that were allowed to exist at this time, making this a Sherlock Holmes novel with a different standpoint, a modern social conscience.
The book is longer than the original Conan Doyle stories but still manages to keep the reader entertained throughout. The House of Silk covers two interconnecting cases, The Man in the Flat Cap and The House of Silk. The Flat Cap appears to be a more traditional Conan Doyle type story, whereas the House of Silk, reads more like a modern day crime story, but the two work brilliantly well together. With some stunning reveals at the end of the case.
The usual characters make an appearance giving validity to the story: Mrs Hudson, Wiggins, Inspector Lestrade, Mycroft, the Baker street irregulars as well as a whole host of new characters, including Mr Carstairs, Carstair's American wife, Carstair's sister who hates Carstair's wife, Cornelius Stillman, an American millionaire, The Boston gang, led by the O'Donaghue twins, The reverend and his wife who run a home for orphaned, unfortunate boys, and a brief spell with Moriarty. There are plenty of exciting moments to keep the reader on his or her toes, I particularly loved the travelling fun fair episode.
There is a sequel, Moriarty, that I very much look forward to reading too.
4.5 stars. Loved it!! Highly recommended to readers of detective, crime, mystery and thriller.
http://www.conandoyleestate.co.uk/index.php/house-of-silk-anthony-horowitz/
http://www.publishersweekly.com/978-1-61113-689-0
http://www.richardandjudy.co.uk/books/The-House-of-Silk/208
http://www.theguardian.com/books/2011/oct/27/house-silk-anthony-horowitz-sherlock-holmes
http://www.independent.co.uk/arts-entertainment/books/reviews/the-house-of-silk-by-anthony-horowitz-6262618.html
Favourite Quotations:
"Show Holmes a drop of water and he would deduce the existence of the Atlantic. Show it to me and I would look for a tap. That was the difference between us."
"Childhood, after all, is the first precious coin that poverty steals from a child."
"He had entered a veritable miasma of evil, and harm, in the worst possible way, was to come to us all too soon."
"I think my reputation will look after itself," Holmes said. "If they hang me, Watson, I shall leave it to you to persuade your readers that the whole thing was a misunderstanding."
"It was quite elementary,' returned the detective with a languid gesture of one hand."
Have you read The House of Silk? Do leave a comment below I'd love to hear from you.
Bye for now,
Marje @ Kyrosmagica xx
Happy Puzzling Sherlock Saturday: My latest read The House of Silk
Happy Puzzling Saturday
It's Happy Puzzling Saturday. How can that be? Never heard of such a thing. Has Marje, aka, Kyrosmagica, gone bonkers? No, she's just in a playful, poetic, puzzling, Saturday kind of mood.
I think my reading The House of Silk, has done it, Watson, I've gone all Sherlock Holmes like. My detective cap's on, but don't worry I haven't started smoking a pipe, or ended up in an opium den.
Have you read The House of Silk? What did you make of it? Are you a Sherlock Holmes fan?
Can you guess where I'm at in the novel? Have a go, see if you can puzzle out the answer. Have I finished, or am I half way through, have I arrived at a particularly exciting juncture? Do feel free to leave comments below.
Let's find the key to a fantastic time this weekend! My detective work tells me that you will not be puzzled by any perplexities or stumped by any unfathomable doubts that you can't solve during your weekend break! As ever enjoy, stay out of the cold weather, keep warm, drink hot chocolate, and don't think too hard. Confound it! Sherlock, I mean it!
I'm leaving you with these pearls of Sherlock wisdom:
Top Ten Sherlock Holmes Quotes:
#1: "Excellent! I cried. "Elementary," said he.
The Memoirs of Sherlock Holmes (1893)
Watson and Holmes in "The Crooked Man" (Doubleday p. 412)
#2: "It seemed to me that a careful examination of the room and the lawn might possibly reveal some traces of this mysterious individual. You know my methods, Watson. There was not one of them which I did not apply to the inquiry. And it ended by my discovering traces, but very different ones from those which I had expected."
Sherlock Holmes in "The Crooked Man" (Doubleday p. 416)
#3. "You will not apply my precept," he said, shaking his head. "How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth? We know that he did not come through the door, the window, or the chimney. We also know that he could not have been concealed in the room, as there is no concealment possible. When, then, did he come?"
The Sign of the Four, ch. 6 (1890)
Sherlock Holmes in The Sign of the Four (Doubleday p. 111)
#4. "Good heavens!" I cried. "Who would associate crime with these dear old homesteads?"
"They always fill me with a certain horror. It is my belief, Watson, founded upon my experience, that the lowest and vilest alleys in London do not present a more dreadful record of sin than does the smiling and beautiful countryside."
The Adventures of Sherlock Holmes (1892)
Sherlock Holmes in "The Copper Beeches" (Doubleday p. 323)
#5. I had neither kith nor kin in England, and was therefore as free as air—or as free as an income of eleven shillings and sixpence a day will permit a man to be. Under such circumstances I naturally gravitated to London, that great cesspool into which all the loungers and idlers of the Empire are irresistibly drained. There I stayed for some time at a private hotel in the Strand, leading a comfortless, meaningless existence, and spending such money as I had, considerably more freely than I ought.
A Study in Scarlet, ch. 1 (1887)
Dr. Watson in A Study in Scarlet (Doubleday p. 15)
#6. To Sherlock Holmes she is always the woman. I have seldom heard him mention her under any other name. In his eyes she eclipses and predominates the whole of her sex. It was not that he felt any emotion akin to love for Irene Adler. All emotions, and that one particularly, were abhorrent to his cold, precise but admirably balanced mind. He was, I take it, the most perfect reasoning and observing machine that the world has seen…. And yet there was but one woman to him, and that woman was the late Irene Adler, of dubious and questionable memory.
Dr. Watson in "A Scandal in Bohemia" (Doubleday p. 161)
#7. At this moment there was a loud ring at the bell, and I could hear Mrs. Hudson, our landlady, raising her voice in a wail of expostulation and dismay.
"By heavens, Holmes," I said, half rising, "I believe that they are really after us."
"No, it's not quite so bad as that. It is the unofficial force—the Baker Street irregulars."
#8. She looked back at us from the door, and I had a last impression of that beautiful haunted face, the startled eyes, and the drawn mouth. Then she was gone.
"Now, Watson, the fair sex is your department," said Holmes, with a smile, when the dwindling frou-frou of skirts had ended in the slam of the front door. "What was the fair lady's game? What did she really want?"
The Return of Sherlock Holmes (1905)
Sherlock Holmes in "The Second Stain" (Doubleday p. 657)
#9. Colonel Ross still wore an expression which showed the poor opinion which he had formed of my companion's ability, but I saw by the inspector's face that his attention had been keenly aroused.
"You consider that to be important?" he [Inspector Gregory] asked.
"Exceedingly so."
"Is there any point to which you would wish to draw my attention?"
"To the curious incident of the dog in the night-time."
"The dog did nothing in the night-time."
"That was the curious incident," remarked Sherlock Holmes.
Inspector Gregory and Sherlock Holmes in "Silver Blaze" (Doubleday p. 346-7)
#10. "But one false statement was made by Barrymore at the inquest. He said that there were no traces upon the ground round the body. He did not observe any. But I did—some little distance off, but fresh and clear."
"Footprints?"
"Footprints."
"A man's or a woman's?"
Dr. Mortimer looked strangely at us for an instant, and his voice sank almost to a whisper as he answered:
"Mr. Holmes, they were the footprints of a gigantic hound!"
The Hound of the Baskervilles, ch. 2 (1902)
Dr. Mortimer in The Hound of the Baskervilles (Doubleday p. 679)
More details of these quotes can be found in full at the following link:
Link: http://www.bestofsherlock.com/top-10-sherlock-quotes.htm#elementary


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\section{Introduction}\label{sec:intr}

Coherent diffractive hadron production in $pA$ collisions is a process $p+A\to X+h+[LRG]+A$, where $[LRG]$ stands for Large Rapidity Gap. We have
recently argued  in \cite{Li:2008bm,Li:2008jz,Li:2008se} that the coherent diffractive hadron production can serve as a sensitive probe of the low-$x$ dynamics of the nuclear matter. The coherent diffractive production exhibits a much stronger dependence on energy and atomic number  than the corresponding inclusive process. Indeed, the diffractive amplitude is proportional to the square of the inelastic one. At \emph{asymptotically} high energies the coherent diffractive events are expected to constitute a half of the total cross section, other half being all inelastic processes. Therefore, coherent diffraction  is a powerful tool
for studying the low-$x$ dynamics of QCD. In particular, we advocated using  the coherent diffraction as a tool for studying the gluon saturation \cite{Gribov:1983tu,Mueller:1986wy}.

The low-$x$ region of QCD is characterized by strong gluon fields \cite{McLerran:1993ni,Kovchegov:1996ty} and can be described in the framework of the color glass condensate\cite{Balitsky:1995ub,JalilianMarian:1997jx,Jalilian-Marian:1997dw,
Kovner:2000pt,Iancu:2000hn,Ferreiro:2001qy}. Equations describing the color glass condensate take the simplest form in the  the mean-field approximation. It is valid for a color field of a heavy nucleus in the multicolor limit; the relevant resumation parameter is $\alpha_s^2A^{1/3}\sim 1$. To the leading order in this parameter, the nuclear color field  is a coherent non-Abelian  superposition of the color fields of single nucleons. Higher order corrections arise due to the nucleon--nucleon or parton-parton correlations within a nucleon. The later contribute towards the gluon saturation in proton.

In all phenomenological applications of the CGC formalism, one usually relies on the   mean-field approximations in which only the lowest order  Green's functions are relevant. If rapidity interval $Y=\ln (1/x)$ is such that $\alpha_s Y<1$, then the low-$x$ quantum evolution effects are suppressed and the color field can be treated quasi-classically. When $\alpha_s Y\sim 1$, the quantum corrections become important and are taken into account by Balitsky-Kovchegov equation \cite{Balitsky:1995ub,Kovchegov:1999yj}, which is the first (truncated) equation in the infinite hierarchy of  the coupled integro-differential equations governing evolution of Green's functions of all orders (JIMWLK equations \cite{Balitsky:1995ub,JalilianMarian:1997jx,Jalilian-Marian:1997dw,
Kovner:2000pt,Iancu:2000hn,Ferreiro:2001qy}).

Although corrections to the mean-field approximation, i.e.\ quantum fluctuations about the classical solution,  are assumed to be small in $pA$ collisions at RHIC their detailed phenomenological study is absent. In this paper we fill this gap by calculating the differential  cross section for the incoherent diffractive gluon production which happens to be proportional to the dispersion of the quasi-classical scattering amplitude in the impact parameter space, as is expected in the Glauber theory \cite{Glauber:1955qq}. The incoherent diffractive gluon production in $pA$ collisions is a process
\begin{equation}\label{id}
p+A\to X+h+[LRG]+A^*\,,
\end{equation}
 where $A^*$ denotes the excited nucleus that subsequently decays into a system of colorless protons, neutrons and nuclei debris.

Note, that the incoherent diffraction \eq{id} measures fluctuations of the nuclear color field. At higher energies color field of proton also saturates. The mean-field approximation is not at all applicable in this case. A quantum fluctuations (e.g.\ the so-called ``pomeron loops" \cite{Iancu:2004iy,Iancu:2004es,Kovner:2005en,Kovner:2007zu}) may be the driving force of the gluon saturation   in proton. This problem is of great theoretical and phenomenological interest. However, in spite of considerable theoretical efforts solution to this problem is still illusive (see \cite{Kovner:2007zz} for a brief review of recent advances).

Motivated by theoretical and phenomenological interest to the incoherent diffraction as a measure of fluctuations of the saturated nuclear color field, we derive a formula for the incoherent diffractive hadron production \eq{id} in the framework of the color glass condensate using the dipole model of Mueller \cite{dip} and use it for numerical study in the RHIC and LHC kinematic regions.
The limiting cases of large and small invariant masses of the diffractively produced system were previously considered by many authors \cite{Wusthoff:1997fz,Bartels:1999tn,Kopeliovich:1999am,Kovchegov:2001ni,GolecBiernat:2005fe,Marquet:2004xa,Marquet:2007nf,Munier:2003zb}. Inclusion of the diffractive gluon production was recently shown to be essential for the phenomenology of diffractive DIS off heavy nuclei \cite{Kowalski:2008sa}.
We generalize there results for all invariant masses (satisfying  \eq{cL2}) and include the gluon evolution effects at \emph{all} rapidity intervals.  Unlike models based on the leading twist nuclear shadowing \cite{Frankfurt:2003zd,Guzey:2005ys}, we explicitly take into account the gluon saturation effects in the nucleus.

The paper is structured as following. In \sec{sec:glauber} we review the Glauber approach \cite{Glauber:1955qq} to the coherent and incoherent diffraction in $pA$ collisions. In \sec{sec:dipole} we discuss generalization of this approached to the case of quarkonium--nucleus scattering in high energy QCD. We then turn in \sec{sec:dgp-qc} to the main subject of the paper -- the diffractive hadron production -- and calculate contributions from coherent and incoherent channels in the quasi-classical approximation neglecting the low-$x$ evolution effects. The low-$x$ evolution effects are taken into account in \sec{sec:lowx}.

Numerical results of the diffractive cross section are presented in \sec{sec:nmf}.
Our phenomenological analyses indicates that the kinematic regions of RHIC and LHC are \emph{not} asymptotic as far as the energy dependence of the diffractive hadron production  is concerned. We observed that the ratio of the coherent and incoherent diffractive hadron production at midrapidity in $pA$ collisions  increases from RHIC to LHC. This is because  gluon  saturation effects in proton are assumed to be small. Absence of this feature in experimental measurements  can serve as an evidence for the onset of gluon saturation in proton.

It is important to emphasize that all our results are obtained without imposing any experimental constraints on the forward scattering angle measurements.
Coherent diffraction measurements require much better forward scattering angle resolution than the incoherent ones. Therefore,  incoherent diffraction may well turn out to be the only one accessible in experiment.

We summarize in \sec{sec:summary}.

\section{Diffraction in the Glauber Model}\label{sec:glauber}

\subsection{Total cross section for coherent diffraction in $pA$}

 A general approach to multiple scattering in high energy nuclear physics was suggested by Glauber \cite{Glauber:1955qq}. First, consider the $pp$ scattering and introduce the elastic $pp$ scattering amplitude $i\Gamma^{pp}(s,\b b)$, where $s$ is the center-of-mass energy squared and $\b b$ is an impact parameter. At high energies $\b b$ is a two-dimensional vector in the transverse plane. According to the optical theorem,
\begin{equation}\label{optic.pp}
\sigma_\mathrm{tot}^{pp}=2\int d^2b \, \mathrm{Re}\,\Gamma^{pp}(s,\b b )\,.
\end{equation}
The scattering amplitude $\Gamma^{pp}(s,\b b)$ can be written as
\begin{equation}\label{phase1}
\Gamma^{pp}(s,\b b)=1-e^{-i\chi^{pp}(s,\b b )}\,,
\end{equation}
where $\chi^{pp}(s,\b b )$ is a change of phase due to interaction at point $\b b$.
In the following we will always assume the isotopic invariance of the scattering amplitudes, e.g.\ $\Gamma^{pp}(s,\b b)= \Gamma^{pN}(s,\b b )$, where $N$ stands for a nucleon.

In $pA$ collisions  momenta of nucleons can be neglected as compared to the incoming proton momentum. Therefore, their positions $\b b_a$, $a=1,\ldots, A$ are fixed during the interaction. If scattering of proton on a different nucleons is independent, then the corresponding phase shifts $\chi_a^{pN}(s,\b B-\b b_a)$ add up:
\begin{equation}\label{phase.pa}
\chi^{pA}(s,\b B, \{ \b b_a\})= \sum_{a=1}^A \chi_a^{pN}(s,\b B-\b b_a)\,,
\end{equation}
where $\b B$ is proton's impact parameter.  Indeed, this result holds in QCD as was demonstrated by A.~Mueller \cite{Mue}, see \sec{sec:dipole}. The scattering amplitude of proton $p$ on a nucleus $A$ reads
\begin{equation}\label{gamma.pa}
\Gamma^{pA}(s,\b B, \{ \b b_a\})= 1-e^{-i\chi^{pA}(s,\b B, \{ \b b_a\})}=
1-\prod_{a=1}^Ae^{-i\chi^{pN}_a(s,\b B-\b b_a )}=1-\prod _{a=1}^A\left(
1-\Gamma^{pN}(s,\b B-\b b_a)\right)\,.
\end{equation}

Introduce the  nucleus-averaged amplitude
\begin{equation}\label{gii1}
\Gamma^{pA}_{if}(s,\b B )=\langle A_i|\Gamma^{pA}(s,\b B, \{\b b_a\} )|A_f\rangle\,,
\end{equation}
with $|A_i\rangle$ being the initial  and $|A_f\rangle$ the final nucleus state. Then, by the optical theorem,  the total $pA$ cross section is given by
\begin{equation}\label{optic.pa}
\sigma_\mathrm{tot}^{pA}=2\int d^2b \,\mathrm{Re}\, \Gamma^{pA}_{ii}(s,\b b )\,.
\end{equation}

Since we neglect motion of nucleons during the interaction, the
distribution of nucleons in the nucleus is completely specified by the thickness function $T(\b b)$:
\begin{equation}\label{thickness}
 T(\b b)=\int_{-\infty}^\infty\, dz\, \rho_A(\b b,z)\,,
\end{equation}
where $\rho_A(\b b,z)$ is nuclear density and $z$ is the longitudinal coordinate.  The thickness function is often written in terms of the mean density of nucleons $\rho= A/(\frac{4}{3}\pi R_A^3)$ and the  nuclear profile function $T_A(\b b)$ as
\begin{equation}\label{t2t}
T(\b b)=\rho\,T_A(\b b)\,.
\end{equation}
It is normalized as
\begin{equation}\label{nucl.den}
\int d^2b\,T(\b b)=\int d^2b\,\rho\, T_A(\b b)=A\,.
\end{equation}

Using these definitions  we write the diagonal element of \eq{gii1} as
\begin{eqnarray}\label{glaub1}
\Gamma^{pA}_{ii}(s,\b B )&=&\frac{1}{A}\int \prod_{a=1}^A\,d^2b_a\, \rho\, T_A(\b b_a)\, \Gamma^{pA}(s,\b B-\b b_a )\nonumber\\
&=&1-\left[ 1-\frac{1}{A}\int d^2b_a\, \Gamma^{pN}(s, \b b_a)\, \rho\, T_A(\b B-\b b_a)\right]^A\nonumber\\
&\approx& 1-e^{-\int d^2b_a\, \Gamma^{pN}(s, \b b_a)\, \rho\, T_A(\b B-\b b_a)}\,,
\end{eqnarray}
where we assumed that $A\gg 1$.

Impact parameter dependence of the $pp$ collisions is usually parameterized as
\begin{equation}\label{bpp}
\Gamma^{pp}(s,\b b)=\frac{1}{2}\sigma_\mathrm{tot}^{pp}(s)\,S_p(\b b)\,,
\end{equation}
where we neglected a small imaginary part of $\Gamma^{pp}(s,\b b)$ and
introduced the proton profile function $S_p(\b b)$ as
\begin{equation}\label{sp}
S_p(\b b)= \frac{1}{\pi R_p^2}\,e^{-\frac{b^2}{R_p^2}}\,.
\end{equation}
Phenomenologically, $R_p=\sqrt{2B}\approx 1$~fm, where $B=12.6$~GeV$^{-1}$. Since the proton radius  $R_p$ is much smaller than the radius of a heavy nucleus $R_A$,  we can approximate the proton profile function by the delta-function in which case the overlap integral appearing in \eq{glaub1} becomes simply the nuclear thickness function
\begin{equation}\label{overlap}
\int d^2b\, S_p(\b b)\,\rho\, T_A(\b B-\b b)\approx \rho\, T_A(\b B)\,.
\end{equation}
This approximation holds when $R_p\ll R_A$, i.e.\ $A^{1/3}\gg 1$. Actually, this condition follows from a requirement that  the quasi-classical approximation holds. Indeed, in the quasi-classical approximation
 $\alpha_s\ll 1$ and $\alpha_s^2 A^{1/3}\sim 1$ implying that $A^{1/3}\gg 1$.

Using \eq{bpp} and \eq{overlap} in \eq{glaub1} we derive
\begin{equation}\label{glaub2}
\Gamma^{pA}_{ii}(s,\b b )= 1-e^{-\frac{1}{2}\sigma^{pN}_\mathrm{tot}(s)\, \rho\, T_A(\b b)}\,.
\end{equation}
The cross section of coherent diffraction is given by  the elastic cross section
\begin{equation}\label{cd2}
\sigma_\mathrm{CD}^{pA}(s)= \int d^2b \, \left|\Gamma^{pA}_{ii}(s,\b b )\right|^2=
\int d^2b \left( 1-e^{-\frac{1}{2}\sigma^{pN}_\mathrm{tot}(s)\, \rho\, T_A(\b b)}\right)^2 \,.
\end{equation}

\subsection{Total cross section for incoherent diffraction in $pA$}

Consider  incoherent diffraction of proton $p$ on a nucleus $A$.  In this processes the nucleus gets excited from the initial state  $|A_i\rangle$ to any colorless final state $|A_f\rangle$. It may then decay, but it is essential that its constituent nucleons remain intact as color objects.
The corresponding cross section reads
\begin{eqnarray}\label{aa1}
\sigma^{pA}_\mathrm{ID}(s)&=& \int d^2B\sum_{i\neq f}\langle A_f|\Gamma^{pA}(s,\b B, \{\b b_a\})|A_i\rangle ^\dagger
\langle A_f|\Gamma^{pA}(s,\b B, \{\b b_a\})|A_i\rangle\nonumber\\
&=& \int d^2B\sum_{f}\langle A_f|\Gamma^{pA}(s,\b B, \{\b b_a\})|A_i\rangle ^\dagger
\langle A_f|\Gamma^{pA}(s,\b B, \{\b b_a\})|A_i\rangle \nonumber\\
&&\,-\,
\int d^2B  \left|\langle A_i|\Gamma^{pA}(s,\b B, \{\b b_a\})|A_i\rangle\right|^2\nonumber\\
&=& \int d^2B \left[ \langle A_i|\left|\Gamma^{pA}(s,\b B, \{\b b_a\})\right|^2|A_i\rangle-\left|\langle A_i|\Gamma^{pA}(s,\b B, \{\b b_a\})|A_i\rangle\right|^2\right]\,
\end{eqnarray}
where in the last line we used the completeness of the set of nuclear states.
We arrived at the well-known result that the cross section for the incoherent diffraction at a given impact parameter $\b B$ is given by the square of the standard deviation of  the scattering amplitude $\Gamma^{pA}(s,\b B, \{\b b_a\})$ from its mean-field value $\langle A_i|\Gamma^{pA}(s,\b B, \{\b b_a\})|A_i\rangle$ in a space span by  impact parameters $\{\b b_a\}$. Clearly, in the black-disk limit, corresponding to the asymptotically high energies $s\to \infty$,  this deviation vanishes because $\Gamma^{pN}(s,\b B, \{\b b_a\})\to 1$ for $|\b B- \b b_a|<R_A$ and is zero otherwise, see \eq{gamma.pa}. The standard deviation is a measure of quantum fluctuations near the mean-field value.

Since, $\Gamma^{pN}(s,\{\b b_a\})$ is approximately real, we have using \eq{gamma.pa}
\begin{eqnarray}\label{aa2}
\left( \Gamma^{pA}(s,\b B, \{\b b_a\}\right)^2&= &\left( 1-\prod_{a=1}^A\left[ 1- \Gamma^{pN}(s,\b B-\b b_a)\right]\right)^2\nonumber\\
&=& 1-2\prod_{a=1}^A\left[  1- \Gamma^{pN}(s,\b B-\b b_a)\right]+
\prod_{a=1}^A \left[  1- \Gamma^{pN}(s,\b B-\b b_a)\right]^2
\end{eqnarray}
Averaging over the nucleus and taking the large $A$ limit we obtain
\begin{eqnarray}\label{aa3}
&&
\langle A_i|\left|\Gamma^{pA}(s,\b B, \{\b b_a\})\right|^2|A_i\rangle=\nonumber\\
&&
1-2\,e^{-\int d^2b\, \Gamma^{pN}(s,\b B-\b b)\rho\, T_A(b)}+
e^{-\int d^2b\, \left[2\Gamma^{pN}(s,\b B-\b b)-(\Gamma^{pN}(s,\b B-\b b))^2\right] \rho\, T_A(b)}\nonumber\\
&&= 1-2\, e^{-\frac{1}{2}\sigma_\mathrm{tot}^{pN}(s)\,\rho\, T_A(\b b)}+e^{-\sigma_
\mathrm{in}^{pN}(s)\,\rho\, T_A(\b b)} \,,
\end{eqnarray}
where we used  \eq{bpp} and denoted the inelastic  $pN$ cross section as $\sigma_\mathrm{in}^{pN}(s)$.  Substituting \eq{aa3} into \eq{aa1} and using \eq{cd2} we derive
\begin{equation}\label{id2}
\sigma_\mathrm{ID}^{pA}(s)=\int d^2b\, e^{-\sigma_\mathrm{in}^{pN}(s)\,\rho\, T_A(\b b)}\,
\left[ 1- e^{-\sigma_\mathrm{el}^{pN}(s)\,\rho\, T_A(\b b)}\right]\,.
\end{equation}

Elastic cross section $\sigma_\mathrm{el}^{pN}$, which appears in \eq{id2}, can be found by taking square of  \eq{bpp} and integrating over the impact parameter:
\begin{equation}\label{el}
\sigma^{pN}_\mathrm{el}=\int d^2b \left|\Gamma^{pN}(s,\b b)\right|^2=
\frac{1}{4}(\sigma_\mathrm{tot}^{pN})^2\int d^2b\, S_p^2(\b b)=
\frac{(\sigma_\mathrm{tot}^{pN})^2}{8\pi R_p^2}\,,
\end{equation}
where we used \eq{sp}.

It is seen from \eq{cd2} and \eq{id2} that since the $pN$ cross sections increase with energy, at asymptotically high energies the incoherent diffraction cross section vanishes, whereas the coherent one reaches a half of the total cross section. This well-known conclusion is a consequence of unitarity of the scattering amplitude and thus is independent of interaction details.

\section{Diffraction in the dipole model}\label{sec:dipole}

It is phenomenologically  reasonable to approximate the proton light-cone wave-function (away from fragmentation regions) by a system of color dipoles \cite{Avsar:2005iz,Kopeliovich:2005us,Li:2008se}. If separation of quark and anti-quark is small, one can apply the perturbation theory to calculate the scattering amplitude of quarkonium on the nucleus. It was demonstrated by Mueller in \cite{dip} that at high energies the $q\bar q A$ forward elastic scattering amplitude takes exactly the same form as \eq{glaub2} with the $pA$ cross section replaced by the $q \bar qA$ one. By virtue of the optical theorem, the total quarkonium--nucleus cross section reads
\begin{equation}\label{sig.tot.dm}
\sigma_\mathrm{tot}^{q\bar qA}(s;\b r)=2\int d^2b \, N_A(\b r, \b b, Y)=
 2\int d^2b \, \left( 1-e^{-\frac{1}{2}\sigma^{q\bar qN}_\mathrm{tot}(s;\b r)\, \rho\, T_A(\b b)}\right)\,,
\end{equation}
where
\begin{equation}\label{NA}
N_A(\b r, \b b, Y)=\mathrm{Re}\, \Gamma_{ii}^{q \bar qA}(s,\b b;\b r)
\end{equation}
is the imaginary part of the forward elastic $q\bar qA$ scattering amplitude and $Y=\ln(1/x)=\ln (s/s_0)$ is rapidity with $s_0$ a reference energy scale.  Eq.~\eq{sig.tot.dm} is called the Glauber--Mueller formula. Let us note that it is far from obvious that the high energy amplitude in \eq{sig.tot.dm} must have the same form as the low energy one \eq{glaub2}. In this correspondence it is crucial that the color dipoles are identified as the relevant degrees if freedom at high energies.
Eq.~\eq{sig.tot.dm} holds when $ \ln(m_NR_A)\ll Y\ll 1/\alpha_s$, where $m_N$ is a nucleon mass. This condition guarantees that  the coherence length $l_c$ is much larger than the nuclear radius, see \eq{cL1}, and  that the low-$x$ gluon evolution is suppressed. In this case
 $q\bar q N$ cross section can be calculated in the Born approximation  (two-gluon exchange) as
\begin{equation}\label{born}
\sigma_\mathrm{tot}^{q\bar qN}(s;\b r)= \frac{\alpha_s}{N_c}\pi^2\b r^2\, xG(x, 1/\b r^2)\,,
\end{equation}
with the gluon distribution function
\begin{equation}\label{xG}
xG(x,1/\b r^2)=\frac{\alpha_s C_F}{\pi}\ln \frac{1}{\b r^2\mu^2}\,,
\end{equation}
where $\mu$ is an infrared cutoff.  We can re-write \eq{born} in terms of the \emph{gluon} saturation scale $Q_{s0}^2$  defined as
\begin{equation}\label{sat.sc}
Q_{s0}^2= \frac{4\pi^2\alpha_s N_c}{N_c^2-1}\,\rho\, T_A(\b b)\,xG(x,1/\b r^2)\,.
\end{equation}
Subscript $0$ indicates that the low-$x$ evolution is suppressed. Eq.~\eq{xG} implies that in the Born approximation the $q\bar qN$ total cross section \eq{born} and hence the  saturation scale \eq{sat.sc} are energy  independent. Using this definition we have
\begin{equation}\label{rss}
\rho\, T_A(\b b)\,\sigma_\mathrm{tot}^{q\bar q N}(s;\b r)=\frac{C_F}{2N_c}\, \b r^2\, Q^2_{s0}\,,
\end{equation}
where $C_F=(N_c^2-1)/(2N_c)$.  Substituting \eq{rss} into  \eq{sig.tot.dm} we derive another representation of the total quarkonium--nucleus cross section
\begin{equation}\label{dm1}
\sigma_\mathrm{tot}^{q\bar qA}(s;\b r)=
 2\int d^2b \, \left( 1-e^{-\frac{1}{4} \frac{C_F}{N_c}\,\b r^2\, Q_{s0}^2}\right)\,.
\end{equation}

Integrand of \eq{dm1} represents the propagator of quarkonium $q\bar q$ of size $\b  b$ through the nucleus at impact parameter $\b b$.  Since $\sigma_\mathrm{tot}^{q\bar qN}\sim \alpha_s^2$ and $\rho\, T_A(\b b)\sim A^{1/3}$  Eq.~\eq{dm1} sums up powers of $\alpha_s^2 A^{1/3}$. It has been shown by Kovchegov that this corresponds to the coherent scattering of $q\bar q$ off the quasi-classical  field of the nucleus \cite{Kovchegov:1996ty}. This is possible only if the coherence length $l_c$ of the $q\bar q$ pair is much larger than the nuclear radius. This condition certainly holds at RHIC energies. In the quasi-classical approximation the coherent diffraction cross section is given by  (cp.\ \eq{cd2})
\begin{equation}\label{cd2.dm}
\sigma_\mathrm{CD}^{q\bar qA}(s; \b r)= \int d^2b \, \left|\Gamma^{q\bar qA}_{ii}(s,\b b; \b r )\right|^2=
\int d^2b \left( 1-e^{-\frac{1}{4}\frac{C_F}{N_c} Q_{s0}^2\, \b r^2}\right)^2 \,,
\end{equation}
Eq.~\eq{cd2.dm} represents the leading  contribution to the diffraction cross section in the quasi-classical field strength. On the contrary, the incoherent diffraction cross section, see\eq{id2}, vanishes in this mean-field approximation since $\sigma_\mathrm{el}^{q\bar qN}\rho\, T_A(\b b)\sim \alpha_s^4 A^{1/3}\sim \alpha_s^2\ll 1$.  Vanishing of the incoherent diffraction cross section can also be seen directly from \eq{aa1}.
It is a consequence of vanishing relative fluctuations at large occupation numbers of classical fields. This effect has recently been studied within the Glauber framework (see \sec{sec:glauber}) in \cite{Kaidalov:2003vg,Guzey:2005tk,Kopeliovich:2005us}.

Let us emphasize to avoid a possible confusion, that the semantic distinction between the coherent and incoherent diffraction concerns the nucleus target staying intact or breaking down in the collision. As far as  the coherence length is concerned, at high enough energies such that $l_c\gg R_A$ the \emph{scattering} is coherent for both coherent and incoherent diffraction. However, unlike the incoherent diffraction that can happen in the incoherent scattering at low energies (provided only that $l_c\gg R_N$), the coherent diffraction is possible only if the scattering is coherent over the entire nucleus.

\section{Diffractive gluon production}\label{sec:dgp-qc}

 \subsection{Coherent diffractive gluon production}
Consider coherent diffractive production of a gluon of momentum $k$ in $q\bar qA$ collision. As mentioned before, coherent diffraction is possible only if the coherence length $l_c$ of the emitted gluon with momentum $k$ is larger than the nucleus size $R_A$ (in the nucleus rest frame):
\begin{equation}\label{cL1}
l_c=\frac{k_+}{\b k^2}\gg R_A\,,
\end{equation}
where + indicates the light-cone direction of the incoming proton. The invariant mass of the produced system is given by $M^2=\b k^2/x$, where $x=k_+/p_+$ and $p$ is the proton momentum. Substituting these equations in \eq{cL1} yields  the following condition on the mass of the diffractive system:
\begin{equation}\label{cL2}
M^2\ll \frac{p_+}{R_A}=\frac{s}{R_Am_p}\,,
\end{equation}
where $\sqrt{s}$ is the center-of-mass energy of the proton--nucleon collision and $m_p$ is  proton mass.

Coherent diffractive gluon production off the large nucleus was calculated in \cite{Kovchegov:2001ni,Kovner:2001vi,Kovner:2006ge}.
The corresponding cross section reads
\begin{eqnarray}\label{xsectQ}
\frac{d\sigma_\mathrm{CD}(k,y)}{d^2k\, dy}&=&\,\frac{1}{(2\pi)^2}\,\int d^2b\, d^2z_1\,
d^2z_2\,\Phi^{q\bar q}(\b x, \b y, \b z_1, \b z_2)\,
e^{-i\b k\cdot(\b z_1-\b z_2)}\,\nonumber\\
 &&\times\,
 \left( \Gamma^{q\bar q GA}_{ii}(s,\b b;\b x,\b y,\b z_1)-\Gamma^{q\bar q A}_{ii}(s,\b b;\b x,\b y)\right)\nonumber\\
 &&\times\,
  \left( \Gamma^{q\bar q GA}_{ii}(s,\b b;\b x,\b y,\b z_2)-\Gamma^{q\bar q A}_{ii}(s,\b b;\b x,\b y)\right)
  \,,
\end{eqnarray}
where  the $q\bar q \to q\bar q G$ light-cone wave function $\Phi^{q\bar q}$ is given by
\begin{equation}\label{wf}
\Phi^{q\bar q}(\b x, \b y, \b z_1, \b z_2)= \frac{\alpha_s
C_F}{\pi^2}\,\left(\frac{\b z_1-\b x}{|\b z_1-\b x|^2}-
 \frac{\b z_1-\b y}{|\b z_1-\b y|^2}\right)\cdot
 \left(\frac{\b z_2-\b x}{|\b z_2-\b x|^2}-
 \frac{\b z_2-\b y}{|\b z_2-\b y|^2}\right)\,.
\end{equation}
 The $q\bar q$ scattering amplitude $\Gamma^{q\bar q A}_{ii,\sigma}(s,\b b)$ is given by \eq{cd2.dm}, while the $q\bar q G$ one was calculated in
\cite{Kopeliovich:1998nw,Kovner:2001vi,Tuchin:2004rb} and reads
\begin{eqnarray}\label{qqG}
\Gamma^{q\bar q GA}_{ii,\sigma}(s,\b b;\b x, \b y, \b z_\sigma)&=&
\langle A_i| \Gamma^{q\bar qG A}_{\sigma}(s,\b B, \{\b b_a\};\b x, \b y, \b z_\sigma) |A_i\rangle =
1-e^{-\frac{1}{2}\sigma_\mathrm{tot}^{q\bar qGN}(s;\b x, \b y, \b z_\sigma)\,\rho\, T_A(\b b)}
\nonumber\\
&=&1-e^{-\frac{1}{8}(\b x-\b z_\sigma)^2Q_{s0}^2
-\frac{1}{8}(\b y-\b z_\sigma)^2Q_{s0}^2-\frac{1}{8N_c^2}(\b x-\b y)^2Q_{s0}^2}\,,
\end{eqnarray}
where $\b x$, $\b y$ and $\b z_\sigma$ are the transverse coordinates of quark, antiquark and gluon respectively; $\sigma =1$ in the amplitude and $\sigma=2$  in the complex conjugated one. For future reference, note that we can express the $q\bar q GN$ total cross section in terms of the $q\bar qN$ one given by \eq{rss}
\begin{equation}\label{expr}
\sigma_\mathrm{tot}^{q\bar qGN}(s;\b x, \b y, \b z_\sigma)= \frac{N_c}{2C_F}\left[
\sigma_\mathrm{tot}^{q\bar qN}(s;\b x-\b z_\sigma )+
\sigma_\mathrm{tot}^{q\bar qN}(s;\b y-\b z_\sigma )-
\frac{1}{N_c^2}\sigma_\mathrm{tot}^{q\bar qN}(s;\b x-\b y)\right]\,,
\end{equation}
where we explicitly indicated the dipole size and energy dependence of the $q\bar q N$ total cross section.

Depending on the relation between the gluon emission time $\tau_\sigma$ and the interaction time $\tau'_\sigma$ in the amplitude and in the c.c.\ amplitude  there are four possible products  of the $q\bar q$ and $q\bar q G$ amplitudes appearing in the second line of \eq{xsectQ}. Explicitly,
\begin{eqnarray}\label{pr1}
&&\langle A_i| \Gamma^{q\bar q A}(s,\b B, \{\b b_a\};\b x,\b y) |A_i\rangle^\dagger\,
\langle A_i| \Gamma^{q\bar q A}(s,\b B, \{\b b_a\};\b x,\b y) |A_i\rangle\nonumber\\
&+&
\langle A_i| \Gamma^{q\bar q GA}(s,\b B, \{\b b_a\};\b x, \b y, \b z_1) |A_i\rangle^\dagger\,
\langle A_i| \Gamma^{q\bar q GA}(s,\b B, \{\b b_a\};\b x, \b y, \b z_2) |A_i\rangle\nonumber\\
&-&
\langle A_i| \Gamma^{q\bar q A}(s,\b B, \{\b b_a\};\b x,\b y) |A_i\rangle^\dagger\,
\langle A_i| \Gamma^{q\bar q GA}(s,\b B, \{\b b_a\};\b x, \b y, \b z_2) |A_i\rangle\nonumber\\
&-&
\langle A_i| \Gamma^{q\bar qG A}(s,\b B, \{\b b_a\};\b x, \b y, \b z_1) |A_i\rangle^\dagger\,
\langle A_i| \Gamma^{q\bar q A}(s,\b B, \{\b b_a\};\b x,\b y) |A_i\rangle\,.
\end{eqnarray}

 \subsection{Incoherent diffractive gluon production}

To calculate the propagators in the case of incoherent diffraction we need to consider each one of the four cases shown in \eq{pr1} and follow the by now familiar steps \eq{aa1}--\eq{id2}. Consider, for example, gluon emission before the interaction in the amplitude and in the c.c.\ one, i.e.\ $\tau_\sigma<\tau'_\sigma$ for $\sigma=1,2$. The detailed calculation is presented in Appendix. The result is  (cp.\ \eq{id2})
\begin{eqnarray}
&&\sum_{f\neq i} \langle A_f| \Gamma^{q\bar q GA}(s,\b B, \{\b b_a\};\b x, \b y, \b z_1) |A_i\rangle^\dagger
\langle A_f| \Gamma^{q\bar q GA}_2(s,\b B, \{\b b_a\};\b x, \b y, \b z_2) |A_i\rangle
=\nonumber\\
&&
=
 e^{-\frac{1}{2}\left[\sigma_\mathrm{tot}^{q\bar q GN}(s;\b x, \b y, \b z_1)
+\sigma_\mathrm{tot}^{q\bar q GN}(s;\b x, \b y, \b z_2)-\frac{1}{4\pi R_p^2}
\sigma_\mathrm{tot}^{q\bar q GN}(s;\b x, \b y, \b z_1)\,\sigma_\mathrm{tot}^{q\bar q GN}(s;\b x, \b y, \b z_2)
\right]
\,\rho\, T_A(\b b)}
\nonumber\\
 && \times
\left\{1-
e^{-\frac{1}{2}\frac{1}{4\pi R_p^2}
\sigma_\mathrm{tot}^{q\bar q GN}(s;\b x, \b y, \b z_1)\,\sigma_\mathrm{tot}^{q\bar q GN}(s;\b x, \b y, \b z_2)\,\rho\, T_A(\b b)}\right\} \label{U}\,.
\end{eqnarray}
This result holds in the quasi-classical approximation $\alpha_s^2A^{1/3}\sim 1$. Therefore,  contribution of elastic processes to \eq{U} are of the order
 $$
 \left(\sigma_\mathrm{tot}^{q\bar q GN}\right)^2\rho\, T_A(\b b)\sim \alpha_s^4A^{1/3}\sim \alpha_s^2\,.
$$
It is suppressed compared to the contribution of  inelastic processes which are of order $\alpha_s^2A^{1/3}\sim 1$. Note, that the contribution to the incoherent diffraction cross section   given by \eq{U} vanishes with vanishing elastic $q\bar qN$ cross section. Thus, we expand the expression in the curly brackets of \eq{U}, keeping the leading elastic term. We derive
\begin{eqnarray}
&&\sum_{f\neq i} \langle A_f| \Gamma^{q\bar q GA}(s,\b B, \{\b b_a\};\b x, \b y, \b z_1) |A_i\rangle^\dagger
\langle A_f| \Gamma^{q\bar q GA}(s,\b B, \{\b b_a\};\b x, \b y, \b z_2) |A_i\rangle
\nonumber\\
&&\approx
\frac{\rho\, T_A(\b b)}{8\pi R_p^2}\,
\sigma_\mathrm{tot}^{q\bar q GN}(s;\b x, \b y, \b z_1)\,\sigma_\mathrm{tot}^{q\bar q GN}(s;\b x, \b y, \b z_2)\,
e^{-\frac{1}{2}\left[\sigma_\mathrm{tot}^{q\bar q GN}(s;\b x, \b y, \b z_1)
+\sigma_\mathrm{tot}^{q\bar q GN}(s;\b x, \b y, \b z_2)
\right]\,\rho\, T_A(\b b)}\,. \label{pr10}
\end{eqnarray}
This approximation is valid  at not too high energies satisfying
\begin{equation}\label{cond1}
 \frac{1}{8\pi R_p^2}\left(\sigma_\mathrm{tot}^{q\bar qGN}\right)^2\,\rho\, T_A(\b b)\ll 1\,.
\end{equation}
Let us for simplicity consider a cylindrical nucleus for  which $\rho\, T_A(\b b)=2A/(\pi R_A^2)$. Since  $R_A=A^{1/3}  R_p$ and taking into account that $\frac{1}{2}\sigma_\mathrm{tot}^{q\bar qGN}\rho\, T_A(\b b)= \frac{1}{4}\,Q_s^2\, r^2$ for $N_c\gg 1$ (see \eq{sig.tot.dm} and \eq{cd2.dm})  we can re-write \eq{cond1} as
\begin{equation}\label{cond2}
\frac{1}{4}\, Q_s^2\, r^2\ll 2\, A^{1/6}\,.
\end{equation}
The saturation effects in the nucleus become important when $\frac{1}{4}Q_s^2r^2\gtrsim 1$. At rapidities $ Y\sim 1/\alpha_s$ the low $x$ evolution effects give rise to the energy dependence of the saturation scale.
Let $Y_1$ be the rapidity at which $\frac{1}{4}Q_s^2r^2= 1$ and $Y_2$ be the rapidity at which $\frac{1}{4}Q_s^2r^2= 2A^{1/6}$. Since   $Q_s^2\propto e^{\lambda Y}$ \cite{Levin:1999mw} we obtain $Y_2-Y_1= \lambda^{-1}\ln (2A^{1/6})$.
Using the phenomenological value $\lambda=0.25$ for the Gold nucleus $A=197$ we find that there are $Y_2-Y_1\approx 6$ units of rapidity between $Y_1$ where the saturation effects become important and $Y_2$ where the expansion \eq{pr10} breaks down.  This provides quite wide kinematic window in which approximation \eq{cond1} holds.

Other three cases corresponding to different relations between $\tau_\sigma$ and $\tau'_\sigma$  can be worked out in a similar way.  The result for the cross section of incoherent diffractive gluon production takes form
\begin{eqnarray}\label{xID}
\frac{d\sigma_\mathrm{ID}(k,y)}{d^2k\, dy}&=&\frac{1}{(2\pi)^2}\,\frac{1}{8\pi R_p^2}
\int d^2b\, d^2z_1\,
d^2z_2\, \Phi^{q\bar q}(\b x, \b y, \b z_1, \b z_2)\, e^{-i\b k\cdot(\b z_1-\b z_2)}\,
\rho\, T_A(\b b)
\nonumber\\
 &  \times&
 \left( \sigma_\mathrm{tot}^{q\bar qGN}(s;\b x, \b y, \b z_1)
\,
 e^{-\frac{1}{2}\sigma_\mathrm{tot}^{q\bar qGN}(s;\b x, \b y, \b z_1)\,\rho\, T_A(\b b)}
-\sigma_\mathrm{tot}^{q\bar qN}(s;\b x, \b y)\,
e^{-\frac{1}{2}\sigma_\mathrm{tot}^{q\bar qN}(s;\b x, \b y)\,\rho\, T_A(\b b)}
 \right)
 \nonumber\\
 & \times&
 \left( \sigma_\mathrm{tot}^{q\bar qGN}(s;\b x, \b y, \b z_2)\,
 e^{-\frac{1}{2}\sigma_\mathrm{tot}^{q\bar qGN}(s;\b x, \b y, \b z_2)\,\rho\, T_A(\b b)}
- \sigma_\mathrm{tot}^{q\bar qN}(s;\b x, \b y)\,
e^{-\frac{1}{2}\sigma_\mathrm{tot}^{q\bar qN}(s;\b x, \b y)\,\rho\, T_A(\b b)}\right)\,.
\nonumber \\
\end{eqnarray}

\section{Low-$x$ evolution}\label{sec:lowx}

\subsection{Incoherent diffraction}

The results derived in the previous section can be generalized beyond the quasi-classical level to include the low-$x$ evolution. This procedure follows the general strategy developed in \cite{Kovchegov:2001sc} and has been used in \cite{Li:2008bm,Li:2008jz} to derive the expression for the coherent diffractive gluon production in onium--nucleus collisions.  In this we section we derive an analogous expressions for the incoherent diffractive gluon production. For applying this general strategy it is important, that  formula \eq{pr10} can be factorized in a product of two expressions one depending on the gluon coordinate $\b z_1$ while another one on $\b z_2$.

The low-$x$ gluon evolution in the nucleus at large $N_c$ is taken into account by the following two substitutions in \eq{xID}: (i) the exponents are replaced by the forward elastic $q\bar q A$  scattering amplitude $N_A(\b r,\b b, Y)$   \cite{Kovchegov:2001sc}
\begin{equation}\label{repl}
e^{-\frac{1}{2}\sigma_\mathrm{tot}^{q\bar qN}(s;\b r)\,\rho\, T_A(\b b)}\to
1-N_A(\b r,\b b, Y)\,.
\end{equation}
 $N_A(\b r,\b b, Y)$ evolves towards higher rapidities $Y$, i.e.\ lower $x$, according to the nonlinear BK evolution equation \cite{Balitsky:1995ub,Kovchegov:1999yj} from its initial condition, given by \eq{sig.tot.dm} at some rapidity $Y=Y_0$;  (ii) the factors linear in $\sigma_\mathrm{tot}^{q\bar qN}$ have emerged in expansion \eq{pr10} where the terms of higher order (i.e.\ multiple scattering) in the elastic amplitude were neglected. Therefore, they are replaced by the forward elastic $q\bar qN$  scattering amplitude $N_p(\b r, \b b, Y)$ that evolves according to the linear BFKL equation \cite{Kuraev:1977fs,Balitsky:1978ic}. It is defined similarly to  \eq{NA}  (see \eq{bpp})
\begin{equation}\label{Np}
N_p(\b r, \b b, Y)=\mathrm{Re}\, \Gamma^{q \bar qp}(s,\b b;\b r)=\frac{1}{2}\sigma_\mathrm{tot}^{q\bar q p}(s;\b r)\,S_p(\b b)\,.
\end{equation}
Recall, that  in the heavy nucleus environment the impact parameter dependence of $q\bar qp$ cross section can be neglected, see \eq{overlap}. Thus, using \eq{sp} we have
\begin{equation}\label{W}
\sigma_\mathrm{tot}^{q\bar q N}(s;\b r)\to 2\pi R_p^2\, N_p(\b r,  0, Y)\,
\end{equation}
in agreement with the optical theorem.
The factors linear in the $q\bar qGN$ cross section are replaced similarly using \eq{expr}.  Substituting \eq{repl} and \eq{W} into \eq{xID} using \eq{expr} (in the multicolor  $N_c\gg 1$ limit) yields
\begin{eqnarray}\label{xsectID}
&&\frac{d\sigma_\mathrm{ID}(k,y)}{d^2k\, dy}=\frac{1}{(2\pi)^2}\,\frac{\pi R_p^2}{2}
\int d^2b\, d^2z_1\,
d^2z_2\, \Phi^{q\bar q}(\b x, \b y, \b z_1, \b z_2)\,
\rho\, T_A(\b b)\,
e^{-i\b k\cdot(\b z_1-\b z_2)}\,
\nonumber\\
 &&\times\,
 \bigg\{
 \left[ 1-N_A(\b z_1-\b x,\b b, y) \right]\, \left[ 1-N_A(\b z_1-\b y,\b b, y) \right]
 \, \left[ N_p(\b z_1-\b x,0, y) +  N_p(\b z_1-\b y,0, y)  \right]
 \nonumber\\
 &&
 -   \left[ 1-N_A(\b x-\b y,\b b, y) \right] N_p(\b x-\b y,0, y)
 \bigg\}
 \nonumber\\
 &&
\times\,
 \bigg\{
 \left[ 1-N_A(\b z_2-\b x,\b b, y) \right]\, \left[ 1-N_A(\b z_2-\b y,\b b, y) \right]
 \, \left[ N_p(\b z_2-\b x,0, y) +  N_p(\b z_2-\b y,0, y)  \right]
 \nonumber\\
 &&
 -   \left[ 1-N_A(\b x-\b y,\b b, y) \right] N_p(\b x-\b y,0, y)
 \bigg\}\,.
\end{eqnarray}

We can write \eq{xsectID} in a more compact form introducing the following two-dimensional vector
\begin{eqnarray}\label{iid}
&&\b I_\mathrm{ID}(\b x-\b y,\b b, y;\b k)= \int d^2 z \left(\frac{\b z-\b x}{|\b z-\b x|^2}-
 \frac{\b z-\b y}{|\b z-\b y|^2}\right)\,e^{-i\b k \cdot \b z}\,\nonumber\\
 &&
 \times\,
 \bigg\{
 \left[ 1-N_A(\b z-\b x,\b b, y) \right]\, \left[ 1-N_A(\b z-\b y,\b b, y) \right]
 \, \left[ N_p(\b z-\b x,0, y) +  N_p(\b z-\b y,0, y)  \right]
 \nonumber\\
 &&
 -   \left[ 1-N_A(\b x-\b y,\b b, y) \right] N_p(\b x-\b y,0, y)
 \bigg\}\,.
\end{eqnarray}
Then,
\begin{equation}\label{comp1}
\frac{d\sigma_\mathrm{ID}(k,y)}{d^2k\, dy}=\frac{\alpha_s C_F}{\pi^2}\, \frac{1}{(2\pi)^2}\,\frac{\pi R_p^2}{2}\,
\int d^2b\, \rho\, T_A(\b b)\, |\b I_\mathrm{ID}(\b x-\b y,\b b, y;\b k)|^2\,.
\end{equation}

So far we have discussed the gluon evolution in the rapidity interval $y$ between the emitted gluon and the target nucleus. The low-$x$ evolution also occurs in the rapidity interval $Y-y$ between the incident quarkonium $q\bar q$ and the emitted gluon (we now denote by $Y$  the rapidity between the quarkonium and the nucleus and by $y$ the inclusive gluon rapidity).  The low-$x$ evolution in the incident quarkonium is taken into account by convoluting \eq{comp1} with the dipole density $n_1(\b r,\b r', \b B-\b b, Y-y)$, where $\b r=\b x-\b y$:
\begin{equation}\label{all1}
\frac{d\sigma_\mathrm{ID}(k,y)}{d^2k\, dy}=\frac{\alpha_s C_F}{\pi^2}\, \frac{\pi R_p^2}{2(2\pi)^2}
\int d^2b \int d^2B \int d^2r'\, n_1(\b r, \b r', \b B-\b b, Y-y)\, \rho\, T_A(\b b)\, |\b I_\mathrm{ID}(\b r,\b b, y;\b k)|^2\,.
\end{equation}
The dipole density $n_1(\b r,\b r,\b B-\b b,Y-y)$ has the meaning of the number of dipoles of size $\b r'$ at rapidity $Y-y$ and impact parameter $\b b$ generated by evolution from the original dipole $\b r$ having rapidity $Y$ and impact parameter $\b B$ \cite{dip}. It obeys the BFKL equation \cite{Kuraev:1977fs,Balitsky:1978ic}. As the interval  $Y-y$
increases the quarkonium wave function involves increasing number of dipoles.
Although the dipole size distribution diffuses according to the BFKL equation, the typical dipole size is much smaller than the nuclear radius $R_A$, i.e.\ $|\b B-\b b|\ll b$. Integrating over $\b B-\b b$ in this approximation we derive
\begin{equation}\label{all2}
\frac{d\sigma_\mathrm{ID}(k,y)}{d^2k\, dy}=\frac{\alpha_s C_F}{\pi^2}\, \frac{\pi R_p^2}{2(2\pi)^2}
\int d^2b  \int d^2r'\, n_p(\b r, \b r', Y-y)\, \rho\, T_A(\b b)\, |\b I_\mathrm{ID}(\b r,\b b, y;\b k)|^2\,,
\end{equation}
where we defined \cite{Li:2008bm,Li:2008jz}
\begin{equation}\label{np20}
n_p(\b r, \b r', Y)=\int n_1(\b r, \b r', \b b', Y)\, d^2b'\,.
\end{equation}
Eqs.~\eq{all2} and \eq{iid} constitute the main result of this paper.

\subsection{Coherent diffraction}

The cross section for the coherent diffractive gluon production including the low-$x$ evolution was derived in \cite{Li:2008bm,Li:2008jz}. It can be written similarly to  \eq{all2} \cite{Li:2008bm,Li:2008jz}:
\begin{equation}\label{cd10}
\frac{d\sigma_\mathrm{CD}(k,y)}{d^2k\, dy}=\frac{\alpha_s C_F}{\pi^2}\, \frac{1}{(2\pi)^2}
\int d^2b  \int d^2r'\, n_p(\b r, \b r', Y-y)\, |\b I_\mathrm{CD}(\b r,\b b, y;\b k)|^2\,,
\end{equation}
where
\begin{eqnarray}\label{icd}
\b I_\mathrm{CD}(\b x-\b y,\b b, y;\b k)&=& \int d^2 z \left(\frac{\b z-\b x}{|\b z-\b x|^2}-
 \frac{\b z-\b y}{|\b z-\b y|^2}\right)\,e^{-i\b k \cdot \b z}\,\nonumber\\
 &&
 \times\,
 \bigg\{
 -N_A(\b z-\b x,\b b, y) -N_A(\b z-\b y,\b b, y)  +N_A(\b x-\b y,\b b, y)  \nonumber\\
 &&
 +N_A(\b z-\b x,\b b, y) \,N_A(\b z-\b y,\b b, y)
  \bigg\}\,.
\end{eqnarray}
In \cite{Li:2008bm,Li:2008jz} we presented a detailed analytical and numerical analysis of the the coherent diffractive gluon production.

\subsection{ Logarithmic approximation}

To obtain a working model for numerical calculations, it is useful  to estimate $\b I_\mathrm{ID}(\b r,\b b, y;\b k)$ in the logarithmic approximation. First, let us change the integration variable $\b w= \b z-\b y$ and define an auxiliary function \cite{Li:2008bm,Li:2008jz}
\begin{eqnarray}\label{QID}
Q_\mathrm{ID}(\b r', y;\b k)&=&\int \frac{d^2w}{w^2}\, e^{i\b k\cdot \b w}\,
 \bigg\{ \left[ 1-N_A(\b r',\b b, y) \right] N_p(\b r',0, y)  \nonumber\\
 &-&
 \left[ 1-N_A(\b w-\b r',\b b, y) \right]\, \left[ 1-N_A(\b w,\b b, y) \right]
 \, \left[ N_p(\b w-\b r',0, y) +  N_p(\b w,0, y)  \right]
 \bigg\}\,.
\end{eqnarray}
With this definition  \eq{iid} becomes
\begin{equation}\label{bb1}
\b I_\mathrm{ID}(\b r,\b b, y;\b k)=-e^{-i\b k\cdot \b r}\,i\nabla_{\b k}Q_\mathrm{ID}(\b r', y;\b k)+e^{i\b k\cdot \b r}\,i\nabla_{\b k}Q_\mathrm{ID}^*(\b r', y;\b k)\,.
\end{equation}
In the logarithmic approximation $Q_\mathrm{ID}(\b r', y;\b k)$ is a real function\cite{Li:2008bm,Li:2008jz}. Therefore,  we can write
\begin{equation}\label{abs}
|\b I_\mathrm{ID}(\b r,\b b, y;\b k)|^2= 4\sin^2\big(\frac{1}{2}\,\b k\cdot \b r'\big)\, (\nabla_{\b k}Q_\mathrm{ID}(\b r', y;\b k))^2\,.
\end{equation}
Notice that the integral over $\b z$  in \eq{iid} is dominated by the region $w<1/k$ since otherwise the integrand is a rapidly oscillation function. Restricting integration to this region yields results valid as long as the scales $1/r'$, $Q_s$ and $k$ are strongly ordered \cite{Li:2008bm,Li:2008jz}. Operating with $\nabla_{\b k}$ on $Q_\mathrm{ID}(\b r', y;\b k)$ yields
\begin{eqnarray}\label{log1}
&&\nabla_{\b k}Q_\mathrm{ID}(\b r', y;\b k)= -\frac{\b k}{k^3}\frac{\partial }{\partial k^{-1}}Q_\mathrm{ID}(\b r', y;\b k)=
 -2\pi\frac{\b k}{k^2}\bigg\{ \left[ 1-N_A(\b r',\b b, y) \right] N_p(\b r',0, y)
\nonumber\\
&& -
 \left[ 1-N_A(\b k\,k^{-2}-\b r',\b b, y) \right]\, \left[ 1-N_A(\b k\,k^{-2},\b b, y) \right]
 \, \left[ N_p( \b k\,k^{-2}-\b r',0, y) +  N_p(\b k\,k^{-2},0, y)  \right]
 \bigg\}\,.
\end{eqnarray}

Analogously, in the coherent diffraction case we define
\begin{eqnarray}\label{QCD}
Q_\mathrm{CD}(\b r', y;\b k)&=&\int \frac{d^2w}{w^2}\, e^{i\b k\cdot \b w}\,
 \bigg\{
N_A(\b w-\b r',\b b, y) +N_A(\b w,\b b, y) -N_A(\b r',\b b, y)
 \nonumber\\
 &&   -N_A(\b w-\b r',\b b, y)\,N_A(\b w,\b b, y)
    \bigg\}\,.
\end{eqnarray}
Then, in the logarithmic approximation,
\begin{eqnarray}\label{log2}
\nabla_{\b k}Q_\mathrm{CD}(\b r', y;\b k)&=&
 -2\pi\frac{\b k}{k^2}\bigg\{ -N_A(\b r',\b b, y) +N_A(\b k\,k^{-2}-\b r',\b b, y)+
N_A(\b k\,k^{-2},\b b, y)\nonumber\\
&&
-N_A(\b k\,k^{-2}-\b r',\b b, y)\,N_A(\b k\,k^{-2},\b b, y)
\bigg\}\,.
\end{eqnarray}
Similarly \eq{abs}  becomes
\begin{equation}\label{abs1}
|\b I_\mathrm{CD}(\b r,\b b, y;\b k)|^2= 4\sin^2\big(\frac{1}{2}\,\b k\cdot \b r'\big)\, (\nabla_{\b k}Q_\mathrm{CD}(\b r', y;\b k))^2\,.
\end{equation}

\section{Numerical calculations} \label{sec:nmf}

In  our previous paper \cite{Li:2008se} we justified using the quarkonium--nucleus $q\bar qA$ scattering  as a model of $pA$ collisions. It also serves as the QCD ingredient for the deep inelastic $eA$ scattering.  Therefore, we extend the use of this model in this section for the incoherent diffraction.

We fix the quarkonium size at $r=0.2$~fm. Dependence of all cross sections on $r$ has been discussed at length in \cite{Li:2008bm,Li:2008jz,Li:2008se} where  the interested reader is readily referred. Since our main goal in this section is to illustrate the key features of the various diffraction channels, rather than giving a detailed quantitative analyses, we approximate the nuclear profile by the step function (cylindrical nucleus).

It is clear from the discussion in the previous Section that in order to calculate the diffractive cross sections we need only to specify the dipole--nucleus scattering amplitude $N_A(\b r,\b b, y)$ and the dipole density $n_p(\b r, \b r', y)$. The  dipole--proton scattering amplitude $N_p(\b r,\b b, y)$ is obtained from $N_A(\b r,\b b, y)$ in the limit $A\to 1$.

For the forward elastic dipole--nucleus scattering amplitude $N_A(\b r, \b b, y)$ we use the KKT model \cite{Kharzeev:2004yx}, which is based on analytical analysis in \cite{Kharzeev:2003wz}. It successfully describes the inclusive hadron production in the RHIC kinematic region (at the central and forward rapidities).

For the dipole density we use the leading BFKL solution in the diffusion approximation:
\begin{equation}\label{ndiff}
n_p( r, r', Y-y)=\frac{1}{2\pi^2}\frac{1}{rr'}\sqrt{\frac{\pi}{14\zeta(3)\bar\alpha_s\,d\, (Y-y)}}\, e^{(\alpha_P-1)(Y-y)}\, e^{-\frac{\ln^2\frac{r}{r'}}{14\zeta(3)\bar\alpha_s\, d\, (Y-y)}}\,.
\end{equation}
Parameter $d$ is equal to unity in the LO BFKL. To obtain the hadron diffractive cross section we convoluted the gluon cross sections  \eq{all2} and \eq{cd10} with the LO pion fragmentation function given in \cite{Kniehl:2000hk}.

A convenient way to study the nuclear dependence of  particle production is to consider  the nuclear modification factor defined as follows
\begin{equation}\label{nmf}
R^{pA}_\mathrm{diff}(k_T,y)=\frac{\frac{d\sigma^{pA}_\mathrm{diff}(k_T,y)}{d^2k_Tdy}}{A\,\frac{d\sigma^{pp}_\mathrm{diff}(k_T,y)}{d^2k_Tdy} }\,.
\end{equation}
We calculate the diffractive gluon production in $pp$ collisions, which is required as a baseline for the calculation of the nuclear modification factor \eq{nmf},  by setting $A=1$ in the formula for the corresponding cross section in $pA$ collisions. The nuclear modification factor is defined in such a way that a completely incoherent \emph{scattering} would yield  $R^{pA}_\mathrm{diff}(k_T,y)=1$. The results of the calculations are exhibited in \fig{cd+id}
\begin{figure}[ht]
\begin{tabular}{cc}
      \includegraphics[width=8cm]{cd_rhic.pdf} &
      \includegraphics[width=8cm]{id_rhic.pdf}\\
      (a) & (b)
\end{tabular}
\caption{(Color online). Nuclear modification factor for (a) coherent diffraction, (b) incoherent diffraction for RHIC at different rapidities. }
\label{cd+id}
\end{figure}
We see that the nuclear modification factor is rapidly decreasing with rapidity  for the coherent diffraction case and is almost independent of rapidity for the incoherent case. This trend continues even at the forward LHC energies \cite{Li:2008se}. In contrast to inclusive hadron production that saturates already in the forward rapidities at RHIC \cite{Kharzeev:2004yx,Tuchin:2007pf},  we expect that the coherent diffraction cross section   saturates at much higher energies and rapidities, perhaps at the forward rapidities  at LHC (see \cite{Li:2008se} for an extensive discussion). As \fig{cd+id} implies, the incoherent diffractive gluon production is saturated already in the central rapidity region at RHIC.

We observe in \fig{cd+id} a parametric enhancement by a factor  $\sim A^{1/3}$  of the coherent diffractive cross section with respect to the incoherent one. This is a benchmark of the classical gluon field of the nucleus in which quantum fluctuations are suppressed by  $A^{1/3}$.
 This feature is also seen in \fig{fig:rat} where we show the ratio of the cross sections for coherent and incoherent diffractive gluon production for $pA$ collisions at different energies. To illustrate the atomic number dependence of this ratio we
show three cases: $A=200$, $A=100$ and $A=20$.
\begin{figure}[ht]
\begin{tabular}{cc}
      \includegraphics[width=8cm]{rat_rhic.pdf} &
      \includegraphics[width=8cm]{rat_lhc.pdf} \\
      (a) & (b)
\end{tabular}
\caption{(Color online). Ratio of the cross sections for coherent and incoherent diffractive gluon production in $pA$ collisions  at midrapidity: (a) RHIC and (b) LHC. Solid blue line: $A=200$, dashed red line: $A=100$ and dotted green line: $A=20$. }
\label{fig:rat}
\end{figure}

In \fig{fig:rat} we can see that the fraction of the incoherent diffractive events increases from RHIC to LHC. This happens because the gluon saturation effects in proton are still not strong enough to unitarize the cross section. Remember, this allowed us to expand  the scattering amplitude as shown in \eq{pr10}. Our estimate \eq{cond2} shows that this approximation is valid for about six units of  rapidity starting from the rapidity $y_1\simeq 1$ at RHIC. Therefore, our conclusion that the fraction of incoherent diffractive events increases holds up to the rapidity $y_2\simeq 3$ at the LHC. As soon as the gluon distribution of the incident  proton saturates, the incoherent diffraction cross section vanishes, as can be seen in \eq{id2}. This effect however is not included in our present model.

Finally, it may be challenging to experimentally distinguish  the
coherent and incoherent diffractive cross sections. In part it is related to the difficulty of performing measurements at very forward angles. One usually measures an event with large rapidity gap between the produced hadronic system and the target remnants in the forward direction (that may or may not be an intact nucleus). In such a likely case we consider the nuclear modification factor for a sum of coherent and incoherent diffractive channels. The result is
displayed in \fig{fig:tot}. We can see that the predictions for the total diffractive cross section are similar to those of the inclusive hadron production \cite{Tuchin:2007pf}. Therefore, it is very important to experimentally separate contributions of coherent and incoherent diffraction. The former is especially useful for studying the low $x$ QCD due to its strong and non-trivial energy, rapidity and atomic number dependence.
\begin{figure}[ht]
\begin{tabular}{cc}
      \includegraphics[width=8cm]{tot_rhic.pdf} &
      \includegraphics[width=8cm]{tot_lhc.pdf}\\
      (a) & (b)
\end{tabular}
\caption{(Color online). Nuclear modification factor for the sum of coherent and incoherent diffractive cross sections  for (a) RHIC, (b) LHC at different rapidities. }
\label{fig:tot}
\end{figure}

Let us also mention that electromagnetic interactions also contribute to diffraction processes in $pA$ collisions. If they become large, as argued in  \cite{Guzey:2008gw}, it may present an additional experimental challenge. We intend to analyze contribution of the e.m.\ interactions in a separate publication.

To conclude this section, we would like to emphasize that  Figs.~\ref{cd+id},\ref{fig:rat},\ref{fig:tot} are an \emph{illustration} of  general features expected in various diffractive channels. As we have mentioned more than once in this paper, application of  realistic experimental cuts, which are unique for every experiment, will significantly change the absolute values of the cross sections and relative importance of the coherent and the incoherent channels. A dedicated study is required in each case, although the key features displayed in Figs.~\ref{cd+id},\ref{fig:rat},\ref{fig:tot}  will perhaps remain unchanged.

\section{Summary}\label{sec:summary}

To summarize, we calculated the cross section for the incoherent diffractive gluon production in $q\bar qA$ collisions, which is a prototype of $pA$ collisions at RHIC and LHC and $\gamma^*A$ ones at EIC. We  took into account the gluon saturation, i.e.\ color glass condensate, effects. We then compared prediction of diffractive hadron production in coherent (calculated previously in \cite{Li:2008bm,Li:2008jz,Li:2008se}) and incoherent diffraction.

Coherent diffractive gluon production has a very characteristic energy, rapidity  and atomic number dependence which makes it a powerful tool for studying the leading mean-field contribution to the color glass condensate.
Incoherent diffraction arises from contributions to the gluon field correlations beyond the mean-field approximation. Its experimental study can reveal the
dynamics of quantum fluctuations in the CGC. Unlike the nuclear modification factor for coherent diffractive gluon production the nuclear modification factor for incoherent diffraction is not expected to exhibit a significant rapidity and energy dependence. Ratio of the coherent and incoherent inclusive diffractive cross sections is predicted to increase from RHIC to LHC \emph{if} the gluon saturation effects in proton are small. Otherwise, the ratio will decrease approaching the unitarity limit (i.e.\ zero).

Finally,  one may consider measuring a diffractive  event  with  large rapidity gap but without distinguishing contributions of coherent and incoherent components. Although in this case many interesting features of coherent and incoherent channels get averaged out, the corresponding cross section as well as the nuclear modification factor are expected to display a non-trivial behavior as a function of energy, atomic number and transverse momentum. This behavior is sensitive to the underlying parton dynamics and thus can serve as a discriminator  of different models. We are certain that
studying  diffraction at RHIC, LHC and EIC can become an important tool in accessing the detailed structure of QCD at low-$x$.

\acknowledgments
I would like to thank Dima Kharzeev, Yura Kovchegov  and J.-W.~Qiu for informative discussions.  I am grateful to Wlodek Guryn for encouragement and for explaining to me numerous experimental challenges in measurements of diffractive processes at RHIC.
This work  was supported in part by the U.S. Department of Energy under Grant No.\ DE-FG02-87ER40371. I would like to
thank RIKEN, BNL, and the U.S. Department of Energy (Contract No.\ DE-AC02-98CH10886) for providing facilities essential
for the completion of this work.

redpajama_set_name: RedPajamaArXiv


MrRyan2582 What's the worst car company logo you've ever seen? Vote for it now!
8 Ford The Ford Motor Company is an American multinational automaker headquartered in Dearborn, Michigan, a suburb of Detroit.
9 Cadillac Cadillac is a division of the American automobile manufacturer General Motors that designs and builds luxury vehicles.
10 Chevrolet Chevrolet, colloquially referred to as Chevy and formally the Chevrolet Division of General Motors Company, is an American automobile division of the American manufacturer General Motors.


text:
Dietary intervention with whole flaxseed or vitamin D has beneficial effects on leiomyomas in the oviduct of the laying hen
Sizemore, Courtni Renee
SIZEMORE-THESIS-2018.pdf (2MB) (no description provided) PDF
Title: Dietary intervention with whole flaxseed or vitamin D has beneficial effects on leiomyomas in the oviduct of the laying hen
Author(s): Sizemore, Courtni Renee
Advisor(s): Nowak, Romana
Contributor(s): Miller, David; Hales, Dale B
Department / Program: Animal Sciences
Discipline: Animal Sciences
Degree: M.S.
Subject(s): Leiomyoma
Abstract: Uterine leiomyomas, or fibroids, have a symptomatic incidence of around 40% and are a leading cause of reproductive morbidity in reproductively-aged women. Symptoms include menorrhagia, pelvic pain, and infertility. They are characterized by excessive production of extracellular matrix components, such as collagen. Leiomyomas are responsive to estrogen and progesterone and occur more frequently as women age. Risk factors for fibroids include obesity, race, localized injury, and stress, while parity has been shown to be protective against fibroids. Inflammation has been hypothesized to play a key role in their development. Traditionally, hysterectomy or myomectomy has been the treatment for fibroids. However, hysterectomy does not preserve a woman's fertility. Currently, there are no effective long-term, non-surgical treatments available for fibroids. Hormone therapies, such as GnRH analogs cannot be used for long-term treatment because they induce a state of hypoestrogenism which leads to post-menopausal symptoms. Researchers have turned to dietary intervention as a possible therapy for fibroids because it is non-invasive, safe for long-term use, and relatively inexpensive. Two potential candidates for dietary intervention are flaxseed and vitamin D3. Flaxseed consists of two parts: lignan and oil. The lignan portion of flaxseed contains phytoestrogens which may inhibit fibroid growth through the antagonism of estrogen. Flaxseed oil is rich in α-linolenic acid, which has known anti-inflammatory properties. Vitamin D3 is a hormone involved in calcium and bone homeostasis that also possesses anti-inflammatory and anti-fibrotic properties. Because the laying hen is the only animal to develop leiomyomas spontaneously as they age, they are an ideal animal model for the study of fibroids. Hen leiomyomas occur as polyps on the smooth muscle layer of the oviduct with increasing abundance as hens age and have the same histological and molecular markers as human uterine fibroids including desmin, smooth muscle actin, increased collagen, and steroid hormone receptors. Two studies were conducted to assess the efficacy of dietary intervention with whole flaxseed and vitamin D3. The first study involved feeding White Leghorn hens an isocaloric control (basic layer) or 15% whole flaxseed diet ad libitum from the end of their second year of lay to the completion of their third. At the end of the study, hens were euthanized and fibroids were counted, measured, and collected. Immunohistochemical analyses of fibrosis (Gomori's Trichrome Stain), proliferation (Proliferating Cell Nuclear Antigen), angiogenesis (von Willebrand Factor), NF-κB p65, oxidative stress (nitrotyrosine), cellular senescence (Sudan Black B), and prevalence of mast cells (Toluidine Blue) were performed on fibroid tissue sections. Quantitative RT-PCR was performed to determine changes in expression levels of mRNA for collagen I, transforming growth factor-β3 (TGF-β3), and prostaglandin-endoperoxide synthase 2 (PTGS2). Western blots were carried out to determine changes in protein levels for COX-2. There was a slight decrease in the incidence of leiomyomas in the flaxseed group versus the controls. There was no significant difference in the volume of leiomyomas (p=0.3), although previous work by our group demonstrated a significant decrease in the size of leiomyomas from hens fed a similar diet of 10% whole flaxseed diet for 24 months. Fibroids from hens fed the flaxseed-supplemented diet for 12 months showed a modest decrease in proliferation when compared to controls and a significant decrease in numbers of blood vessels per unit area of fibroid. There were no differences in p65 translocation to the nucleus, a measure of Nuclear Factor kappa B (NF-κB) activation, or tissue levels of nitrotyrosine, a measure of oxidative stress, between treatment groups. Sudan Black B staining showed that leiomyomas from both treatment groups were not undergoing cellular senescence while Toluidine Blue staining did show mast cell infiltration into fibroids from both groups. Fibroids from hens fed the whole flaxseed diet had slightly decreased collagen I (4-fold change, p=0.06) and TGFβ-3 expression (6-fold change, p=0.06), while PTGS2 (6-fold change, p=0.04) expression was significantly downregulated when compared to fibroids from hens fed the control diet. COX-2 analysis through western blot showed a non-significant decrease in relative COX-2 expression in leiomyomas from flaxseed-fed hens compared to those from control hens. In the second study, White Leghorn hens having completed their second year of lay were fed either an isocaloric control (basic layer), 10% whole flaxseed, or vitamin D3 (69 µg/kg/day) diet for 15 months. Twenty-five hens were sacrificed at the start of the trial to determine the baseline incidence of leiomyomas. Blood was drawn from the same subset of hens every three months until the end of the trial. After 15 months on their respective diets, hens were euthanized. Oviducts were collected, and fibroids were counted, measured, and either flash frozen in liquid nitrogen or fixed in 10% neutral buffered formalin for further analysis. Leiomyoma incidence increased from 44% at the start of the trial to 78%, 74%, and 71% in the control, whole flaxseed, and vitamin D groups, respectively after 15 months. The number of leiomyomas per hen in all three groups increased significantly after fifteen months when compared to the baseline; there were no differences between groups after fifteen months. Plasma carbonylated protein levels decreased significantly in the whole flaxseed and vitamin D3-treated hens after 6 months on their respective diets; these levels were significantly lower than those of the control hens after 9 months in both groups. qRT-PCR analysis showed a downregulation of collagen I (50-fold change, p=0.02), TGF-β3 (50-fold change, p=0.003), and PTGS2 (100-fold change, p=0.001) gene expression in leiomyomas from hens fed the vitamin D3-supplemented diet after 15 months when compared to those from control hens; there were no differences between the whole flaxseed group when compared to the control. We conclude that dietary intervention with whole flaxseed or vitamin D3 may have beneficial, therapeutic effects on leiomyomas found in the oviduct of the laying hen. Our results support further investigation into the use of these supplements in women with fibroids as they could provide a safe, effective, long-term, and non-invasive treatment option that currently is not available.
Rights Information: Copyright 2018 Courtni Renee Sizemore
Dissertations and Theses - Animal Sciences

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text:
Home > Categories > Art and Entertainment > Authors > Sarah Waters's Biography
Sarah Waters's Biography
Sarah Waters Facts
The Guardian on Sarah Waters
Sarah Waters was born in Pembrokeshire in Wales in 1966, and went to the local Catholic school before going to University in Canterbury, where she got a BA in English literature.
Sarah Waters followed up with an MA in gay and lesbian historical fiction from Lancaster University and a PhD on the idea of history in lesbian and gay writing from Queen Mary, University of London.
Awards and awards shortlists are not new to Sarah Waters. Fingersmith, which was adapted into a three-part drama for BBC ONE, was shortlisted for the Orange Prize and the Man Booker Prize in 2002. Affinity won Waters the Somerset Maugham Prize and the Sunday Times Young Writer of the Year Award, whilst her first novel, Tipping the Velvet, won the Betty Trask Award and was shortlisted for the Mail on Sunday / John Llewelyn Rhys Prize.
Tipping the Velvet was published to critical acclaim and was adapted by Andrew Davies for BBC drama in 2002.
The Times Literary Supplement had an interesting account of how Sarah Waters writes:
"Waters is refreshingly open about how she writes her novels. She gets to know the writing of a period very well (Tipping the Velvet came out of a PhD in late-Victorian literature). She researches the social history: the fascinating stuff about how people lived, dressed, washed their teeth, had sex; what happened inside women's prisons and private asylums. The fiction of the time gives her ideas for plot structure and motifs ..."
Asked by BBC Cambridgeshire what she liked about writing, Sarah Waters replied:
"The most exciting thing for me and the thing that I always have to come back to when I'm feeling a bit depressed about it all, is that there's something wonderful about slowly building up in my head this little world ..."
The Night Watch by Sarah Waters was shortlisted for the 2006 Booker. Set in the 1940s it has four main characters, who are linked by incidental connections. The Night Watch was also shortlisted for the Orange prize.


text:
Q: Is DOTA 2 region-locked? Is it possible for EU and NA players to play together?

A: There has been an update to DotA 2's matchmaking, which does take region into consideration, though not strictly.
Based on this thread, it looks like this was implemented in mid-January.
It's worth noting that this is more of a soft region-lock, rather than a strict one. As this article puts it:

This, in theory, would lessen the probability that a player in Tennessee on US East would be matched with a player at an internet cafe in Peru. Despite both queuing on USE, the geographical component would preferentially stack the Tennessee player with others nearby, i.e. in US states.

Apparently, there is no region lock in DOTA 2, despite this being a heavily requested feature by players (mostly NA players, from what I've found).
See this rant, simply titled "Valve, North America is begging you to region lock Dota."
Here is another post, as well as here, here, and here. Based on how old some of these posts are, it doesn't seem like a region-lock will be implemented.
So to answer your question, yes, NA players can (and apparently constantly do) play with EU players.
(Disclaimer: The views expressed in these posts do not express the views of all North American players by any means)

redpajama_set_name: RedPajamaStackExchange


text:
<?php namespace CodeIgniter\Autoloader;

use Config\Autoload;

//--------------------------------------------------------------------

class AutoloaderTest extends \CIUnitTestCase
{

	protected $loader;

	//--------------------------------------------------------------------

	protected function setUp()
	{
		$config = new Autoload();

		$config->classmap = [
			'FirstClass'        => '/app/dir/First.php',
			'Name\Spaced\Class' => '/app/namespace/Class.php',
		];
		$config->psr4 = [
			'App\Controllers' => '/application/Controllers',
			'App\Libraries'   => '/application/somewhere',
		];

		$this->loader = new MockAutoloader();
		$this->loader->initialize($config);

		$this->loader->setFiles([
			'/application/Controllers/Classname.php',
			'/application/somewhere/Classname.php',
			'/app/dir/First.php',
			'/app/namespace/Class.php',
		    '/my/app/Class.php',
		    APPPATH.'Libraries/someLibrary.php',
		    APPPATH.'Models/someModel.php',
		]);
	}

	//--------------------------------------------------------------------

	//--------------------------------------------------------------------
	// PSR4 Namespacing
	//--------------------------------------------------------------------

	public function testExistingFile()
	{
		$actual   = $this->loader->loadClass('App\Controllers\Classname');
		$expected = '/application/Controllers/Classname.php';
		$this->assertSame($expected, $actual);

		$actual   = $this->loader->loadClass('App\Libraries\Classname');
		$expected = '/application/somewhere/Classname.php';
		$this->assertSame($expected, $actual);
	}

	//--------------------------------------------------------------------

	public function testMatchesWithPreceedingSlash()
	{
		$actual   = $this->loader->loadClass('\App\Controllers\Classname');
		$expected = '/application/Controllers/Classname.php';
		$this->assertSame($expected, $actual);
	}

	//--------------------------------------------------------------------

	public function testMatchesWithFileExtension()
	{
		$actual   = $this->loader->loadClass('\App\Controllers\Classname.php');
		$expected = '/application/Controllers/Classname.php';
		$this->assertSame($expected, $actual);
	}

	//--------------------------------------------------------------------

	public function testMissingFile()
	{
		$this->assertFalse($this->loader->loadClass('App\Missing\Classname'));
	}

	//--------------------------------------------------------------------

	//--------------------------------------------------------------------

	public function testAddNamespaceWorks()
	{
		$this->assertFalse($this->loader->loadClass('My\App\Class'));

		$this->loader->addNamespace('My\App', '/my/app');

		$actual = $this->loader->loadClass('My\App\Class');
		$expected = '/my/app/Class.php';

		$this->assertSame($expected, $actual);
	}

	public function testAddNamespaceMultiplePathsWorks()
	{
		$this->loader->addNamespace('My\App', '/my/app');
		$this->loader->addNamespace('My\App', '/test/app');
		$this->loader->setFiles([
			'/my/app/Class.php',
			'/test/app/ClassTest.php',
		]);

		$actual = $this->loader->loadClass('My\App\ClassTest');
		$expected = '/test/app/ClassTest.php';
		$this->assertSame($expected, $actual);

		$actual = $this->loader->loadClass('My\App\Class');
		$expected = '/my/app/Class.php';
		$this->assertSame($expected, $actual);
	}

        //--------------------------------------------------------------------

        public function testRemoveNamespace()
        {
                $this->loader->addNamespace('My\App', '/my/app');
                $this->assertSame('/my/app/Class.php',$this->loader->loadClass('My\App\Class'));

                $this->loader->removeNamespace('My\App');
                $this->assertFalse((bool)$this->loader->loadClass('My\App\Class'));
        }

	//--------------------------------------------------------------------

	public function testLoadLegacy()
	{
	    $this->assertFalse((bool)$this->loader->loadClass('someLibraries'));
	    $this->assertTrue((bool)$this->loader->loadClass('someLibrary'));
	    $this->assertTrue((bool)$this->loader->loadClass('someModel'));
	}

	//--------------------------------------------------------------------

	public function testSanitizationSimply()
	{
		$test = '${../path}!#/to/some/file.php_';
		$expected = '/path/to/some/file.php';

		$this->assertEquals($expected, $this->loader->sanitizeFilename($test));
	}

	//--------------------------------------------------------------------

	public function testSanitizationAllowsWindowsFilepaths()
	{
		$test = 'C:\path\to\some/file.php';

		$this->assertEquals($test, $this->loader->sanitizeFilename($test));
	}

	//--------------------------------------------------------------------
}

redpajama_set_name: RedPajamaGithub


text:
Q: How to force Spring boot OAuth2 autoconfig to use another yml file instead of application.yml file? I developed a spring boot application which is using OAuth2 autoconfigure but I am not able to force it to read client configurations from a yml file other than application.yml
Thanks in advance

A: One simple solution is to use multiple profiles and one client file by profile:
The first properties files named application-my-client-1.yml :
spring:
  security:
    oauth2:
      client:
        registration:
          my-client-1:
            client-id: ${APP-CLIENT-ID}
            client-secret: ${APP-CLIENT-SECRET}
            client-name: my-client user
            provider: my-client
            scope: user
            redirect-uri: http://localhost:8080/login/oauth2/code/my-client

Activated by setting the my-client-1 profile to on when running the spring boot app:
java -jar -Dspring.profiles.active=my-client-1 myApplication.jar

The second properties files named application-my-client-2.yml :
spring:
  security:
    oauth2:
      client:
        registration:
          my-client-2:
            client-id: ${APP-CLIENT-ID}
            client-secret: ${APP-CLIENT-SECRET}
            client-name: my-client-2 email
            provider: my-client-2
            scope: user:email
            redirect-uri: http://localhost:8080/login/oauth2/code/my-client-2

Activated by setting the my-client-2 profile to on when running the spring boot app:
java -jar -Dspring.profiles.active=my-client-2 myApplication.jar

All properties can be activited by setting all profiles on:
java -jar -Dspring.profiles.active=my-client-1,my-client-2 myApplication.jar