The word on the street (well Reddit actually) is that the BellKor's Pragmatic Chaos team today submitted the first qualifying solution for the Netflix Prize. If nobody submits a better solution within the next 30 days then they will claim the $1 million reward that has so far eluded the best efforts of thousands of programmers and researchers since the competition was launched in October 2006.
Netflix is a US-based online DVD rental service. One of their features is that they make movie recommendations to customers based on their previous viewing history. In order to improve their recommendations system, Netflix has been offering a million dollar reward to any individual or team that is able to develop software that increases the accuracy of these recommendations by at least 10%.
The financial rewards and intellectual challenge of the Netflix Prize have encouraged almost 50,000 individuals and teams to attempt to solve the problem using a vast array of different AI and data-mining techniques.
The BellKor team have overcome such obstacles as the Napolean Dynamite problem and will no doubt have the champagne on ice while they nervously wait to see if anybody else is able to surpass their results within the next month.
Opera Software would have you believe that yesterday they reinvented the web. The launch of their new Opera Unite service has received a decent amount of publicity. By now you've probably heard all about it, but if not you can read the details here.
The 10 second summary is that version 10 of Opera's web browser contains a web server that allows users to serve web content directly from their desktop machines or laptops. However, this description doesn't really capture the potential of the platform.
Some commentators have dismissed the announcement with a "so what?". Opera Unite content is only going to be available while the user's computer is switched on and running Opera and will be constrained by their available upload bandwidth (which often isn't much thanks to the 'A' in ADSL). That doesn't really cut it when compared to low-cost web hosting packages capable of serving thousands of users, but then the comparison isn't particularly helpful.
I don't need Opera Unite to host my personal website from my desktop. I can install and configure Apache, tweak my firewall/router settings and find a solution to dynamic IP address issues. The point is that with Opera Unite, you don't have to do any of that. Opera have completely eliminated all of that hassle and in doing so have made web serving accessible to even non-technical users. But that's only half of the story. Serving your personal home page via Opera Unite is still sub-optimal. If you want (semi-)permanent web hosting, pay for some cheap PHP hosting or get a WordPress.com account.
If somebody gives you an Opera Unite URL, you shouldn't expect that resource to be still around tomorrow or next year like you would with a link to Wikipedia. The real value in Opera Unite is in ad hoc sharing and transient collaboration. Things that were possible but bothersome previously are now trivial because you don't have to worry about server configuration and networking issues.
For example, say I wanted to invite every reader of this blog to join a chat session. I could try to find out which IM clients you all use and try to arrange something via MSN Messenger, Skype or Google Talk. Or I could install and configure my own IRC server. Or I could try to find a third-party server to host the chat room. With Opera Unite I can simply open up my lounge and give you all the URL (regardless of which browser you happen to be using). It just takes a few clicks. The service is transient. When we're done, I kick you all out.
In our chat session I might decide to share some photos or other files with you. I could send them via e-mail or upload them to an FTP server or a service like Flickr, but again it's simpler with Unite. I just enable the appropriate service and share the URL. You can browse my shared directory and grab what you want directly from my machine. The link probably won't work tomorrow, but you won't need it tomorrow. Temporary is fine when it's this easy.
The other service that I'm already finding useful is the media player, which enables me to remotely play my home MP3 collection from the office. The Unite platform is based on open standards, so it will be interesting to see what other ideas for services people come up with.
The two weeks are up. The Twitter experiment is complete. Did I find the dolphin, or am I still waiting for the magic?
If nothing else, I've achieved a greater understanding of the dynamics of Twitter, but I don't think that it has yet had a significant impact on the way that I communicate or the way that I consume information. I have to admit that the experience was less awful than I thought it might be.
The first thing that I discovered is that the web interface to Twitter is just not usable. It's a decidedly less confusing and more dynamic experience using one of the many desktop clients. I'm currently on TweetDeck having previously tried Twhirl, though neither is the one Twitter client to rule them all. The static nature of the website and the way that it displays conversation fragments out of context was one significant reason why I didn't see much value in the service.
I don't feel that my initial complaints about the general unimportance of most tweets, and the plain pointlessness of many, were unfounded. And when somebody starts tweeting every minute about the film that they are currently watching (a film that I am not watching), it becomes incredibly irritating. They say that on the web Content is king. Well, since the advent of Twitter, Content has abdicated and crown prince Banality is now running the show.
However, I did find that I had a higher than expected tolerance for tedium, mostly because I could easily consume/ignore most of the tweets that I received without suffering much distraction. And even if the tweets were mostly superfluous, they did occasionally raise a chuckle, such as Wez's new software development methodology.
They have real people on Twitter now?
I was not expecting to be able to interact with people I knew in the real world on Twitter, because two weeks ago none of them were on Twitter, but Wez and David have signed up since I started. David is already well ahead of me in terms of followers, and all without the help of a series of self-promoting blog posts. He is the next microblogging celebrity. Meanwhile, Wez is using Twitter to stimulate the global economy.
But what do you actually use it for?
From the start of this experiment I've struggled with what to tweet. I wanted to stay on-topic. I thought maybe I could use Twitter to complement this blog. I don't think that this approach is particularly easy or even that useful. It's easier just to go down the stream-of-conciousness route and write anything that comes to mind.
In this regard, I wouldn't be surprised if, for many, Twitter is effectively a write-only medium where everybody's contributions are welcomed and few are valued – a kind of voluntary collective delusion.
Moreso than with blogging, you are subscribing to people rather than topics. If you want to use Twitter, you have to accept that even if you pick compatible people to follow, a lot of what they write will not be of interest to you, particularly when it concerns the trivialities of daily life.
One use case for Twitter that does makes sense to me is within a development team for posting status updates that can easily be consumed and responded to by other team members. Yammer offers a Twitter-like service well suited to this niche (access can be restricted to selected people only).
If I could change one thing about Twitter it would be the 140 character limit. Countless times I've sat there trying to figure out how to remove 13 characters from a message without altering its meaning. This involves creatively removing punctuation and finding abbreviations or shorter synonyms. A limit is good for keeping messages concise and to the point, but a few more characters would go a long way to improving the quality of the content.
I found the global eavesdropping aspect kind of interesting, although it's a bit hit-and-miss as there is no way to filter by quality.
Twitter is mostly harmless but, as far as I can see, does not deliver on much of the hype that surrounds it. I'm still indifferent to Stephen Fry getting stuck in a lift and wary of news organisations such as the BBC treating it as a reliable journalistic source. Twitter is not the harbinger of a communications revolution, it's an occasionally relevant diversion.
I suppose that the big question is will I continue to use it now that the two weeks are up? I don't know. Probably to some extent. It's there, I have an account, it won't take much effort to continue. On the other hand, if Twitter disappeared tomorrow I wouldn't miss it. I might not even notice for a while.
It's been over a week since my previous post on my Twitter experiences. In the meantime I've only been using it sporadically (so much for being addictive). Time flies and I've almost reached the end of the two-week period that I had assigned to this little experiment.
Ask a rhetorical question on Twitter and somebody will answer it within a couple of minutes. What surprised me when I pondered the usefulness of OSGi is that the person who responded was not one of my followers but somebody who I had not interacted with before. This highlighted an aspect of Twitter that I had not previously paid much attention to. As well as following individuals, you can track particular search terms. So anybody monitoring Twitter for discussions about OSGi would have been alerted by my tweet.
This is particularly interesting to me because my number one complaint about Twitter has been the utter pointlessness of most of the content (including that which I have been contributing). Focusing on this aspect, you don't have to follow anybody. You could use Twitter in a similar way to Google Alerts, surfing the zeitgeist ready to pounce on any discussions that include your favoured keywords. This way you participate only in on-topic conversations and avoid the what-I-just-ate messages. Unfortunately, there's still no quality control. No Digg, Reddit or DZone equivalent to promote the good content and ignore the bad.
On a related note, you can get an overview of what topics are presently occupying the thoughts of the planet's bored masses via TwitScoop, which provides a real-time word cloud and top 10 topics.
140 characters should be enough for anybody. Really?
One thing that I've held back until this penultimate post is something that I knew would irritate me right from the start: the 140 character limit. I don't care what anybody says, it's not enough. I understand the benefit of having a limit; it forces people to keep their entries concise. However, 140 characters is too restrictive. Sometimes not even enough for a fully-formed sentence. Twitter doesn't need to be restricted by SMS limits. The future of Twitter does not lie with SMS. Everybody who is using it from a mobile phone has Internet access. A limit of 250 or 300 characters would be altogether more civilised.
When you start adding links to your tweets it leaves less room to provide context. The URLs are necessarily shrunk and obfuscated to save room, making each link a leap into the unknown. It would be very nice to be able to attach the link to particular words in the message (you know, like we've been doing since 1992). Twitter takes you back to the days before hypertext.
Time for another status report from Twitterland (is that the correct name, or is it "twitosphere" or "information super bridleway" or something?). Here are some more disjointed thoughts (is Twitter affecting my ability to combine multiple sentences into coherent prose?).
Writing about Twitter is the journalistic equivalent of eating the fluff from your navel.
…The rest of the world, however, completely ignores it. But with the journalists' attention fixed firmly on each others' navels, they don't seem to realise what a fringe activity Twitter is.
…Twitter is a bit of a charity-case itself: both technically and financially, it's a lost cause. That's plain to everybody, it seems, except the journalists who use it and who can't stop Twittering about Twitter.
Orlowski's piece references "Twestival". I tracked down this disturbing footage of the London event via the BBC (who else?). It's a few dozen geeks with iPhones standing around ignoring each other while sending tweets to other people who aren't there. These people need to get out less.
After 5 days, the initial novelty has worn off. Maybe I should approach tweeting in a different way? Perhaps every message should be a haiku?
One problem with Twitter content, regardless of who you are following, is that each obfuscated URL is a leap of faith and the messages are usually too truncated to provide any meaningful context.
I haven't posted many Twitter messages in the last two days. I'm still trying to figure out how best to use Twitter. What should I tweet? Should I stay on-topic (software development and tangentally related things) or should I branch out to anything that comes to mind? I'm thinking this would be counter-productive as people who are following me mostly came via this blog and are unlikely to share my other interests. Without some kind of focus it becomes Facebook without the functionality. I'm also proud of the fact that I'm 5 days in and I have yet to tweet the details of anything that I have ingested.
I also need to find more people to follow. I've been through Jurgen's list and picked out a few more people that might be of interest.
Previously on New Adventures in Software: Dan signs-up for Twitter to try to figure out the attraction of self-stalking.
I'm starting to get a feel for Twitter now. Not so much in terms of finding it useful, or even particularly interesting, but I have a better appreciation of what it is.
Twitter inhabits a space somewhere between a feed reader and an instant messaging client. If you use it via the Twitter website it shows its more reader-like tendencies. It aggregates messages in a very static way. You just go there and see what's been said since you last checked it. If you use one of the myriad clients (today's client is Twhirl), the experience is closer to using MSN Messenger or similar. Messages pop up in the corner of your screen, not in real-time but via polling.
I rarely have IM programs running because I find them to be incredibly damaging to productivity. Conversations spawning at random, all requiring attention, distract you from whatever you were trying to do on the computer. Twitter is not quite as distracting. Messages arrive but you don't have to respond, whereas on IM it would be rude to ignore them. Then again, on Twitter, the messages usually aren't directed at you. You are just tapping into other people's stream-of-conciousness thoughts. I wouldn't be surprised if that is the real attraction of Twitter, though people might not like to admit it. It's nice to get these little reassurances that you are not alone in the world, right now there are other people out there doing "stuff". You select a set of people that you like, or admire, or find interesting and you tune into their stuff. The nature of that stuff is unimportant, just so long as you are in the loop.
Of course, there is also a conversational aspect to Twitter. The people you are following might not have addressed their messages to you, they may not even know that you exist, but you can jump in at any point and respond to something that they have said. This is the "global conciousness" aspect that Twitter fans highlight. Yes, you can ignore what your parents and teachers told you and talk to strangers. It's not a proper conversation though. It lacks the depth of e-mail and it lacks the immediacy of instant messaging.
You also get to see the conversations that don't involve you. This is incredibly irritating when somebody you are following replies to somebody you are not following. It's like when you are on a train and the person next to you is talking on their mobile phone and you are forced to listen to one half of a conversation. You just get some out-of-context sentence. You can try to track down the original message, but that's just one more distraction. It would be better if the Twitter clients defaulted to not showing you messages that were addressed to other people.
I now have 13 followers, and I am following 19 people. It seems that there are a few people who signed up for Twitter in response to my original post. This is no longer an experiment, it's a movement. They too are trying to see what all the fuss is about.
I also have to abandon the "nobody in the real world uses Twitter" argument now since David has signed up and I can confirm that he is a real person that I know. Go on, you can follow him too. Maybe he'll say something.
I'm not going to write a blog post for every single day of this 2-week experiment. I will report back again in a few days.
I've said it before, I don't get Twitter. For me, the hysteria generated by the flat-lined signal-to-noise ratio of this limited medium is deeply confusing. The last time I felt like this was back in the early 90s as I stared cross-eyed and frustrated at one of those Magic Eye pictures, trying to find the dolphin. How come everybody else can see something in it while to me it's just nonsense?
Since I last wrote on the subject of Twitter, the hype has increased still further. Somebody used TwitPic to post a picture of the AirBus that landed in the Hudson River in New York. As a result, this "citizen journalist" earned himself 15 minutes of international fame, including featuring on the BBC's television news at least twice. I somehow suspect that had he chosen to upload his snap to Flickr instead, the BBC would not have been nearly as interested. Somebody at BBC News is a Twitter lover. The corporation's online coverage of the recent attacks in Mumbai prominently featured information sourced from Twitter, whether accurate or not.
If further evidence were needed that with Twitter the medium really is more important than the message, it arrived last week. What was this seismic event that many are heralding as the tipping point for the microblogging revolution? Stephen Fry got stuck in a lift. No, really, that's it. Had General Melchett used his Blackberry to phone a journalist instead of to tweet, he could not have bribed them to write about this unfortunate but utterly banal occurrence.
Twitter may have novelty value but it is more than mere surface silliness. It is anti-thought, the deadening white noise of modern life with all its pointless business. As for the dotty idea that short computer messages are full of wit, insight or observation – that is, to quote the master twitter himself, "arse, poo and widdle".
…the manifold possibilities of Twitter are enough to make you giddy. This is a new world, people! We are officially in the future, not with jetpacks, but with something much cooler – the hive mind. Ignore those grumpy luddites in the broadsheets and elsewhere, who don't understand it, can't be bothered to learn how it works and are frightened at the prospect that people are entertaining themselves in a way that doesn't involve accepted media forms.
By now, I think that I've firmly established that I don't really see the point of Twitter, but I don't want to be dismissed as a "luddite" who "can't be bothered to learn how it works". So it's time to take the red pill and see for myself how deep this rabbit hole goes. Today I'm embarking on an experiment: a two-week trial to see whether there is any substance to the Twitter hype. I'm deeply sceptical but also approaching it with an open mind. Will I experience a higher level of conciousness or will I endure and proliferate a fortnight of pointless anti-thought?
I've just signed up for a Twitter account. If you're already a Twitter user, I need some followers (sounds like I'm starting my own religion here). I also need interesting people to follow. Please also send me tips on how to get the most out of Twitter. If you are one of the many people who responded to my previous post agreeing that Twitter was pointless, I will report back here at regular intervals in the next couple of weeks and let you know how it's going on the other side.
WordPress is great. In some ways. Sometimes. It has all these plugins that add all kinds of neat features. It even has a really easy-to-use auto-update feature for plugins. So when I saw that a new version of Ryan McGeary's very useful WP-Syntax plugin was available, I let it do the upgrade for me.
Unfortunately, this made a mess of my previous post (thanks to David for pointing this out to me – I wasn't actually diligent enough to check for myself that the upgrade hadn't broken anything). All the < and > characters in my Java code had been replaced by HTML entities (> and <). Rolling back to WP-Syntax 0.9.1 didn't fix the problem, which was odd. Then a few neurons flickered into life and I had a vague recollection of having solved this problem previously. It turns out that I had modified the PHP source for the WP-Syntax plugin (as described here). I simply had to make the same change for the new version. I'm ignorant as to why WP-Syntax does not include this modification by default. Maybe it breaks something else, but it works for me.
I can't really understand how this happened. Even less gifted "webmasters" should be able to grasp the concept of 10 without taking their shoes and socks off.
I'm certainly not the first person to ask this question, but what exactly is the point of Twitter (I mean aside from being the poster child for scalability problems)?
Most Twitter feeds consist of messages like "Cheese sandwich for lunch", "Just watched the latest episode of [some TV show]" and "Put more RAM in my PC, much faster now". Who on earth wants to read this stuff? Yet people on Twitter are each following hundreds of other people, getting bite-sized updates about the most mundane details of the lives of huge numbers of strangers.
Perhaps, like reading blogs, the secret is to filter out the rubbish? There are an awful lot of blogs and, it has to be said, a lot of awful blogs, but eventually you find the ones you like. Maybe I just need to find the right people to follow on Twitter? Fortunately, Jurgen Appelo has produced another one of his lists. This time it's the Top 50 Twitterers to Follow for Developers. There are several instantly recognisable names on the list; many people whose blogs I read. So I took a look at most of their Twitter feeds and no, these people can't make it interesting either. There are confusing fragments of conversations with other people that you don't know, half-formed thoughts, obfuscated hyperlinks and yet more mundane life details that nobody needs to know.
Can it really be that the emperor is naked? Has the medium become more important than the message? I'd really like to know what the appeal of it is. Is it the constant reassurance that there are hundreds of people out there who have lives as equally dull as your own?
Online it's everywhere. Even the BBC has started using it. BBC News' coverage of the recent events in Mumbai included contributions sourced from Twitter (with no indication of the validity of these contributors or guarantees as to the veracity of their information).
Then again, is Twitter really that popular? Nobody that I know in the real world uses Twitter. They all use Facebook, some have blogs but not one person uses Twitter, not even the software developers. Where does the buzz come from? Why are there dozens of imitations trying to repeat Twitter's "success"?
So this is an invitation. Please tell me (in the comments below) why I should care about Twitter. What am I missing? I'm even prepared to give it a trial, if somebody can convince me that it is worthwhile. I've no problems sharing the trivial events of my daily existence (I'm thinking of maybe having soup for lunch today). It's the other bit that confuses me. How can I extract value from other people's Twittering?


text:
\section{Introduction}

The Next-to-Minimal Supersymmetric Standard Model
(NMSSM)~\cite{Nilles:1982dy,Frere:1983ag,Ellis:1988er,Drees:1988fc,Ellwanger:1993hn,Ellwanger:1993xa,Elliott:1993bs,Pandita:1993tg,Ellwanger:1995ru,King:1995vk,Franke:1995tc,Ellwanger:1996gw,Miller:2003ay}
extends the particle content of the Minimal Supersymmetric Standard
Model (MSSM) by one singlet superfield.  The NMSSM has several
attractive features beyond the MSSM.  First, the NMSSM elegantly
solves the so-called $\mu$ problem~\cite{mu-problem}: the scale of the
$\mu$ parameter is dynamically generated at the electroweak or SUSY
scale when the singlet Higgs acquires a Vacuum Expectation Value
(VEV).  Second, the fine-tuning and little hierarchy problems of the
NMSSM are greatly diminished compared to the
MSSM~\cite{Dermisek:2005ar}.  In the NMSSM, the upper mass limit on
the lightest CP-even Higgs boson is higher than in the MSSM, making it
less constrained experimentally.  Another attractive feature of the
NMSSM is that the lightest CP-even Higgs can have a significant
branching fraction for the new $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1$ decay ($h_1$ and
$a_1$ are the lightest CP-even and CP-odd Higgs bosons, respectively).
This weakens the LEP-II constraints on the allowed Higgs parameter
space, as this new decay channel reduces the branching fractions of
$h_1$ into the modes used in direct Higgs searches.  In addition,
there are interesting implications in the cosmological Dark Matter
sector of the model due to the appearance of the fifth neutralino, the
``singlino.''  It has been shown~\cite{nmssm-dm} that the NMSSM is
consistent with the experimentally measured relic density, and the
data provide important constraints on the allowed NMSSM parameters.

The rich phenomenology offered by the NMSSM, stemming from the
extension of the scalar sector, has been the focus of numerous
studies~\cite{nmssm-ph1,nmssm-ph2,nmssm-ph2b,nmssm-ph3,nmssm-ph4,nmssm-ph5,nmssm-ph6,nmssm-ph6a,nmssm-ph7}.
In Ref.~\cite{nmssm-ph2}, the first attempt to establish a ``no-lose''
theorem for NMSSM was presented.  This theorem states that the Large
Hadron Collider (LHC) has the potential to discover at least one NMSSM
Higgs boson in the conventional mode, assuming that Higgs-to-Higgs
decay modes are not important.  However, the fact that Higgs-to-Higgs
decay modes can be important has been shown in analyses devoted to
re-establishing the `no-lose'
theorem~\cite{nmssm-ph2b,nmssm-ph3,nmssm-ph4,nmssm-ph5,nmssm-ph6,nmssm-ph6a,nmssm-ph7}
in the case where the $h_1\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1$ branching fractions are
significant and $a_1$ is light.  NMSSM scenarios with $m_{a_1}$
between the $2\tau$ and $2b$-quark thresholds ($2m_\tau < m_{a_1} <
2m_b$) have previously been considered, focusing on the
$4\tau$~\cite{nmssm-ph7} channels in Higgs-strahlung and Vector Boson
Fusion, establishing the NMSSM No-Lose Theorem at the
LHC~\cite{nmssm-ph7} for this $a_1$ mass region.  Future analysis of
the $4\tau$ channel is likely to be technically challenging and can
only be performed with large datasets (typical integrated luminosity
of 10--100 fb$^{-1}$).  A more recent study~\cite{2mu2tau-pheno} has
focused on the same region using the $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi 2\mu 2\tau$
process, which has the benefit that the invariant mass of two muons
forms a much narrower peak, improving the sensitivity of such an
analysis in spite of the large reduction in signal yield due to small
$\mathcal{B}(a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu \mu)$.  Our findings indicate a substantially higher
QCD multi-jet background contamination as compared to
Ref.~\cite{2mu2tau-pheno}, which may have a substantial effect of the
sensitivity of such a search.

In this paper, we explore the region in which the $a_1$ mass is below
the $2\tau$ threshold ($m_{a_1} < 2m_\tau$).  For this case, which has
not been studied previously, we explore the potential of the $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi
a_1 a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi 4\mu$ signature at the LHC.  Unlike searches for the
$4\tau$ signature, the invariant mass of each muon pair provides a
direct estimate of $m_{a_1}$ and the 4$\mu$ invariant mass provides
$m_{h_1}$.  Use of these kinematic constraints leads to essentially
zero background and therefore allows one to rely on direct $gg$ and
$b\bar{b}$ fusion for Higgs production instead of the subdominant
vector boson fusion or associated production processes chosen in the
$4\tau$ search~\cite{nmssm-ph2} to suppress QCD backgrounds.

\begin{figure*}[thbp]
\includegraphics[width=0.49\linewidth]{smass12_vs_mkovel}
\hfill
\includegraphics[height=0.48\linewidth,angle=90]{ma_vs_akappa_vs_lambda}

\caption{(a):~Mass of the lightest ($h_1$) and second-lightest ($h_2$)
  CP-even Higgses as a function of $\mu\kappa/\lambda$ and $\lambda$.
  The density of generated scenarios surviving constraints is shown in
  the blue color scale, and the red line represents the single-valued
  $\lambda \ll 1$ limit (mean of $\lambda < 0.01$ scenarios).
  (b):~Mass of the lightest CP-odd Higgs ($a_1$) as a function of
  $A_\kappa$ and $\lambda$.  The color scale is the average mass in
  each bin, and filled circles are the scenarios with $m_{a_1} <
  2m_\tau$. The edge of the low $m_{a_1}$ region follows a parabolic
  curve, $(\mbox{30~GeV})\lambda^2 - A_\kappa \simeq 0$.
 \label{fig:hmass_mukoverl}}
\end{figure*}

We demonstrate that the analysis of the $4\mu$ mode has excellent
sensitivity to $h_1$ production, can be performed with early LHC data,
and requires little in terms of detector performance except reasonably
robust muon tracking and identification.  To present a realistic
analysis, we use parameters of the CMS detector at the LHC to design
event selection and to estimate background contributions.

The rest of the paper is organized as follows.  In Section~II, we
study the NMSSM parameter space in which $m_{a_1} < 2m_\tau$ and
discuss the phenomenology of the model. In Section~III, we review
constraints on the NMSSM parameter space from existing data.  In
Section~IV, we outline the proposed analysis for the 4$\mu$ mode and
evaluate its sensitivity.  Final conclusions are presented in
Section~V.

\section{NMSSM Parameter Space}

In our study we consider the simplest version of the
NMSSM~\cite{Nilles:1982dy,Frere:1983ag,Ellis:1988er,Drees:1988fc,Ellwanger:1993hn,Ellwanger:1993xa,Elliott:1993bs,Pandita:1993tg,Ellwanger:1995ru,King:1995vk,Franke:1995tc,Ellwanger:1996gw},
in which the $\mu\widehat{H_1}\widehat{H_2}$ term of the MSSM
superpotential is replaced by
\begin{equation}
\lambda \widehat{S} \widehat{H}_1 \widehat{H}_2 + \frac{\kappa}{3}  \widehat{S}^3 \mbox{,}
\label{eq:superpot}
\end{equation}
making the superpotential scale-invariant.  In general, there are five
soft braking terms; in the ``non-universal'' case,
\begin{equation}
  m_{H_1}^2 H_1^2 + m_{H_2}^2 H_2^2 + m_{S}^2 S^2
  + \lambda A_\lambda H_1 H_2 S +  \frac{\kappa}{3} A_\kappa S^3.
\label{eq:soft}
\end{equation}
In the above equations, capital letters with tildes denote superfields
while symbols without tildes denote the scalar component of the
respective superfield.

Soft breaking parameters in Eq.(\ref{eq:soft}), $m_{H_1}^2$,
$m_{H_2}^2$ and $m_{S}^2$, can be expressed in terms of $M_Z$, the
ratio of the doublet Higgs VEVs, $\tan\beta$, and $\mu = \lambda s$
(where $s = \langle S \rangle$, the VEV of the singlet Higgs field)
through the three minimization equations of the Higgs potential.
Assuming that the Higgs sector is CP-conserving, the NMSSM Higgs
sector at the Electro-Weak (EW) scale is uniquely defined by
14~parameters: $\tan\beta$, the trilinear couplings in the
superpotential, $\lambda$ and $\kappa$, the corresponding soft SUSY
breaking parameters $A_\lambda$ and $A_\kappa$, the effective $\mu$
parameter $\mu = \lambda s$, the gaugino mass parameters $M_1$, $M_2$,
and $M_3$, the squark and slepton trilinear couplings $A_{t}$,
$A_{b}$, and $A_\tau$, and the squark and slepton mass parameters
$M_{f_L}$ and $M_{f_R}$.  For simplicity, we assume universality
within 3 generations for the last two parameters, leaving only 6
parameters for sfermion masses.

\subsection{Parameter Scan of the Low-$m_{a_1}$ Region of the NMSSM}

To find the parameter space for our region of interest, $m_{a_1} <
2m_\tau$, we scan the NMSSM parameters using the NMSSMTools
package~\cite{nmssmtools1,nmssmtools2,nmssmtools3}, applying all known
phenomenological and experimental constraints except the following:
the cosmological dark matter relic density measured by
WMAP~\cite{wmap}, the direct $p\bar{p} \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi 4\mu$
search by the Tevatron~\cite{Abazov:2009yi}, the direct $e^+e^- \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi Z
h_1$, $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1$ searches by
LEP~\cite{lep1exclusion,lep2exclusion}, the direct $\Upsilon \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi
\gamma a_1$ searches by CLEO~\cite{:2008hs} and
BaBar~\cite{Aubert:2009cp}, and limits set by rare $B \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi K \ell^+
\ell^-$ decays~\cite{Freytsis:2009ct}.  These important constraints
are explicitly studied in our region of interest in a later section.

\begin{figure*}[htb]
\includegraphics[width=0.49\linewidth]{pcomp12_limit}
\hfill
\includegraphics[width=0.49\linewidth]{scomp13_vs_mkoverl}

\caption{(a):~Non-singlet fraction $1-\sin^2{\theta_P}$ of the
  lightest CP-odd Higgs boson ($a_1$) as a function of $v\sin
  2\beta/s$.  (b):~Singlet fraction $\cos^2{\theta_S}$ of the lightest
  CP-even Higgs boson ($h_1$) as a function of $\mu\kappa/\lambda$.
  (The red line is the mean of $\lambda < 0.01$ scenarios.)
\label{fig:nonsingletcp1}}
\end{figure*}

In our scan, we fix parameters entering the Higgs sector at loop-level
to $M_1/M_2/M_3 = 150/300/1000$~GeV, $A_t = A_b = A_\tau = 2.5$~TeV,
and $M_{f_L} = M_{f_R} =1$~TeV.  We then sample the NMSSM model points
uniformly in a six-dimensional space.  The first four scan parameters
are conventional, broad ranges over the probable values of $\mu$,
$\lambda$, $\tan\beta$, and $A_\lambda$:
\begin{itemize}
\item 100~GeV $<$ $\mu$ $<$ 1000~GeV
\item 0 $<$ $\lambda$ $<$ 1
\item 1.5 $<$ $\tan\beta$ $<$ 50
\item $-$1~TeV $<$ $A_\lambda$ $<$ 5~TeV
\end{itemize}

For the two remaining parameters, we identify two additional
phenomenological variables that allow a more narrow selection of the
region of interest and simplify the interpretation of our
observations.  A theoretical justification of these variables is
discussed in the next section.  The first of these two parameters,
$\mu\kappa/\lambda = \kappa s$, is selected because of its correlation
with the mass of the CP-even Higgs bosons, see
Fig.~\ref{fig:hmass_mukoverl}(a).  The corresponding range used in the
scan
\begin{itemize}
\item $0 < \mu\kappa/\lambda< 120~\mbox{GeV}$\label{eq:mh1}\\
\end{itemize}
was chosen to include two equally sized but phenomenologically
different sub-domains; in the lower one $h_1$ is light and $h_2$ is
the SM-like Higgs, and in the upper one $h_1$ is the SM-like Higgs.

The final parameter and its scan range,
\begin{itemize}
\item $0~\mbox{GeV} < (\mbox{30~GeV}) \lambda^2 - A_\kappa < 3~\mbox{GeV,}$ \label{eq:ak}
\end{itemize}
are chosen to zoom into the region of low $a_1$ masses as illustrated
in Fig.~\ref{fig:hmass_mukoverl}(b).

\subsection{Higgs Sector Spectrum and Mixings}

The CP-even and CP-odd Higgs mass matrices, ${\cal M}_{S}$ and ${\cal M}_{P}$,
can be written as~\cite{nmssmtools1}:
\begin{eqnarray}
{\cal M}_{S11}^2 & = & g^2 v^2 \sin\beta^2 + \mu\tan\beta(A_\lambda + \kappa s ) 				\nonumber\\
{\cal M}_{S22}^2 & = & g^2 v^2 \cos\beta^2 + \mu\cot\beta(A_\lambda + \kappa s )				\nonumber\\
{\cal M}_{S33}^2 & = & \lambda A_\lambda \frac{v^2\sin 2\beta}{2s} + \kappa s(A_\kappa + 4\kappa s )   	\nonumber\\
{\cal M}_{S12}^2 & = & (\lambda^2 - g^2/2) v^2\sin 2\beta -\lambda s (A_\lambda + \kappa s) 			\nonumber\\
{\cal M}_{S13}^2 & = & \lambda v (2\lambda  s \cos\beta - \sin\beta (A_\lambda + 2\kappa s))			\nonumber\\
{\cal M}_{S23}^2 & = & \lambda v (2\lambda  s \sin\beta - \cos\beta (A_\lambda + 2\kappa s))
\label{eq:ms}
\end{eqnarray}
\begin{eqnarray}
{\cal M}_{P11}^2 & = & {2\lambda s\over{\sin 2\beta}} (A_\lambda + \kappa s ) 				\nonumber\\
{\cal M}_{P22}^2 & = & 2\lambda\kappa v^2 \sin 2\beta + \lambda A_\lambda {{v^2\sin 2\beta}\over{2s}} -3\kappa A_\kappa s \nonumber\\
{\cal M}_{P12}^2 & = & \lambda v (A_\lambda - 2\kappa s )
\label{eq:mp}
\end{eqnarray}

In general, $a_1$ is light in the regions of the parameter space
approaching either the Peccei-Quinn (PQ) symmetry limit ($\kappa \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi
0$) or the R-symmetry (RS) limit ($A_\kappa$, $A_\lambda \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi 0$).  In
both limits, $a_1$ is a massless axion, a fact which directly follows
from Eq.(\ref{eq:mp}).  It can be decomposed in terms of the weak
eigenstates $H_{uI}$, $H_{dI}$, and $S_I$ as (see
e.g.\cite{Ellwanger:2009dp}):
\begin{equation}
a_1 = \cos\theta_P A + \sin\theta_P S_I\mbox{,}
\end{equation}
where $A = \cos\beta H_{uI} + \sin\beta H_{dI}$.  In the PQ limit,
the mixing parameters $\cos\theta_P$ and $\sin\theta_P$ are
\begin{equation}
\cos \theta_P = \frac{v \sin 2\beta}{\sqrt{v^2\sin^2 2\beta + 4 s^2}}\mbox{,}
\sin \theta_P = -\frac{2s}{\sqrt{v^2\sin^2 2\beta + 4 s^2}}\mbox{.}
\label{eq:pqmix}
\end{equation}
In the RS limit, the same parameters are
\begin{equation}
\cos \theta_P = \frac{v \sin 2\beta}{\sqrt{v^2\sin^2 2\beta + s^2}}\mbox{,}
\sin \theta_P = \frac{s}{\sqrt{v^2\sin^2 2\beta + s^2}}\mbox{.}
\label{eq:rsmix}
\end{equation}

\begin{figure*}[thb]
\includegraphics[width=0.32\linewidth]{cu1_vs_mkoverl}
\hfill
\includegraphics[width=0.32\linewidth]{cd1_vs_mkoverl}
\hfill
\includegraphics[width=0.32\linewidth]{cv1_vs_mkoverl}

\caption{Reduced couplings of $h_1$ to up-type quarks (a), down-type
  quarks (b), and vector bosons (c) as a function of $\mu\kappa/\lambda$, with
  the requirement that $m_{a_1} < 2m_\tau$.  (The red line is a mean
  of $\lambda < 0.01$ scenarios.) \label{fig:sm_mukoverl1}}
\end{figure*}

According to Eq.(\ref{eq:pqmix},\ref{eq:rsmix}), the non-singlet
component of $a_1$ is determined by the ratio $v \sin 2\beta / s$.
Figure~\ref{fig:nonsingletcp1}(a) shows evident correlation of the
non-singlet fraction $1 - \sin^2\theta_P$ of the lightest pseudoscalar
Higgs boson $a_1$ with $v \sin 2\beta / s$, corresponding primarily to
the PQ limit, as can be deduced from the slope of the correlation.
It also demonstrates that in the region of interest
$a_1$ is nearly a pure singlet, $1 - \sin\theta_P^2 < 1\%$, and that
the values of $v \sin 2\beta / s$ are always below $0.1$.  If we
define $\epsilon = {v \sin 2\beta / s}$, then up to
$\mathcal{O}(\epsilon)$, $\mathcal{O}(\kappa^2)$, and
$\mathcal{O}(\lambda^2)$, the CP-even Higgs mass matrix can be
re-written as
\begin{alignat}{2}
&M_S^2= \lambda s \\
\nonumber & \begin{pmatrix}
  (A_\lambda + s \kappa)\tan\beta  & - (A_\lambda + s \kappa)      & \epsilon ({\lambda s \over \sin\beta} -{A_\lambda + 2 s \kappa\over 2\cos\beta}) \\
       - (A_\lambda + s \kappa)  & (A_\lambda + s \kappa)\cot\beta  & \epsilon  ({\lambda s \over \cos\beta} -{A_\lambda + 2 s \kappa\over 2\sin\beta}) \\
\epsilon ({\lambda s \over \sin\beta} -{A_\lambda + 2 s \kappa\over 2\cos\beta}     )&   \epsilon ({\lambda s \over \cos\beta} -{A_\lambda + 2 s \kappa\over 2\sin\beta}) &
\kappa {A_\kappa+ 4 s \kappa \over \lambda}
\end{pmatrix}
\end{alignat}

One can see that $\epsilon$ also determines the mixing of singlet and
non-singlet CP-even Higgs states.  For small values of $\epsilon$ and
$A_\kappa$, characterizing the parameter space relevant to our study,
the mass of the singlet CP-even Higgs boson is determined by $2 s
\kappa = 2\mu\kappa/\lambda$.  This substantiates our earlier
observation depicted in Fig.~\ref{fig:hmass_mukoverl}(a) and the
relevance of the $\mu\kappa/\lambda$ parameter used in our scan
(Eq.\ref{eq:mh1}).  Further, in the sub-domain $\mu\kappa/\lambda <
60$~GeV, $h_1$ is light with $m_{h1} \simeq 2\mu\kappa/\lambda$ and has
a significant singlet component, particularly for smaller values of
$\lambda$ (and $A_\lambda$).  In the upper sub-domain $\mu
\kappa/\lambda > 60$~GeV, $h_1$ becomes the SM-like Higgs with
$m_{h_1} \simeq 120$~GeV while $h_2$ acquires a large singlet component
and mass $m_{h2} \simeq 2\mu\kappa/\lambda$.  This is illustrated in
Fig.~\ref{fig:nonsingletcp1}(b) showing the singlet fraction of $h_1$,
the lightest CP-even Higgs boson.

To derive $m_{a_1}$, we diagonalize the ${\cal M}_{P}$ matrix
(Eq.~\ref{eq:mp}).  Keeping $\mathcal{O}(\kappa)$,
$\mathcal{O}(\lambda^2)$, and $\mathcal{O}(\epsilon^2)$ terms, one has
\begin{equation}
{m_{a_1}}^2 = \frac{3}{2} \, (2 \mu \kappa/\lambda)^2 \, (\zeta \lambda^2 -A_\kappa)\mbox{,}
\end{equation}
where $\zeta = \frac{3}{2} v^2\sin 2\beta/\mu$.  Because
$2\mu\kappa/\lambda$ determines the mass of the predominantly singlet
CP-even Higgs boson, $2\mu\kappa/\lambda \geq m_{h_1}$ and is always
fairly large.  Therefore, $a_1$ is light if $(\zeta \lambda^2 -
A_\kappa)$ is low, motivating the choice of the empirical parameter
$(\mbox{30~GeV}) \lambda^2 - A_\kappa$ used in the scan.  The range of
this parameter selects a region with $m_{a_1}$ between 0 and
approximately 30~GeV, avoiding most of the theoretically inaccessible
region in which $\zeta\lambda^2-A_\kappa < 0$ and therefore $m_{a_1}^2 <
0$, as shown in Fig.~\ref{fig:hmass_mukoverl}(b).

\subsection{Higgs Couplings and Decays}

The couplings of $h_1$ and $a_1$ to each other and to Standard Model
particles are determined primarily by their singlet and non-singlet
components.  While the CP-odd $a_1$ is always nearly a pure singlet
(see Fig.~\ref{fig:nonsingletcp1}(a)), the singlet fraction of $h_1$
is correlated with $\mu\kappa/\lambda$, but also depends on the
smallness of $\lambda$.  As illustrated by
Fig.~\ref{fig:nonsingletcp1}(b), for small $\lambda$, $h_1$ is nearly
a pure singlet in the $\mu\kappa/\lambda \lesssim 60$~GeV sub-region,
while in the $\mu\kappa/\lambda \gtrsim 60$~GeV domain, $h_1$ has
negligible singlet component and is essentially the SM Higgs.
Figure~\ref{fig:sm_mukoverl1} shows a strong suppression of reduced
couplings of $h_1$ to up- and down-type quarks as well as vector
bosons in the $\mu\kappa/\lambda \lesssim 60$~GeV domain.  This
suppression leads to a severe reduction in the production rates of
$h_1$ at colliders, making this scenario challenging for experimental
exploration.  Fortunately, as will be shown later, small $\lambda$
values in the low $\mu\kappa/\lambda$ region are excluded by
cosmological observations.

\begin{figure}[htb]
\includegraphics[width=0.95\linewidth]{brhaa_vs_lambda_vs_mkoverl}
\caption{Branching fraction of $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1a_1$ in the $\lambda$
  versus $\mu\kappa/\lambda$ plane, with the requirement that $m_{a_1}
  < 2m_\tau$. \label{fig:brhaa}}
\end{figure}

Branching fractions of $h_1$ are determined by relative strength of
the $h_1$ couplings to SM particles and the $h_1 a_1 a_1$ coupling,
which is specific to the NMSSM.  Because $a_1$ has a high singlet
fraction, the singlet content of $h_1$ is directly related to the
strength of the $h_1 a_1 a_1$ coupling. If this were the only effect,
$\mathcal{B}(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1)$ would have been close to 100\% in the
lower half of the $\mu\kappa/\lambda$ domain and negligible in the
upper half.  However, this coupling is also proportional to $\lambda$
(see Eq.~\ref{eq:soft}), which creates a competing effect as larger
values of $\lambda$ smear the nearly perfect separation of singlet-
and doublet-type $h_1$ in the lower and upper halves of the
$\mu\kappa/\lambda$ domain.  The overall result is illustrated in
Fig.~\ref{fig:brhaa}, showing average $\mathcal{B}(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1)$
for NMSSM models with $m_{a_1} < 2m_\tau$ as a function of
$\mu\kappa/\lambda$ and $\lambda$.  It is evident that the suppression
of $h_1$ SM couplings for $\mu\kappa/\lambda < 60$~GeV makes
$\mathcal{B}(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1)$ substantial as long as $\lambda$ is not
too small.  For the upper part of the $\mu\kappa/\lambda$ domain,
$\mathcal{B}(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1)$ is small except for large values of
$\lambda$ where the $h_1$ singlet fraction is enhanced.

\begin{figure}[htb]
\includegraphics[height=0.95\linewidth, angle=90]{bra_vs_ma}
\caption{Branching fraction of $a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu \mu$ for generated models
  as a function of $m_{a_1}$.  The red line is a mean of all scenarios
  as a function of $m_{a_1}$.  The threshold at 3.55~GeV/$c^2$ is $2m_\tau$.
  For $2m_\mu < m_{a_1} < 3m_\pi$ (the grey box), the branching
  fraction would be nearly 100\%. \label{fig:bramm}}
\end{figure}

As the lightest Higgs boson, $a_1$ can only decay to SM particles,
even though its coupling to SM particles is strongly suppressed due to
its nearly singlet nature.  One should also notice that $a_1$
couplings to down-type fermions are proportional to $\tan\beta$ while
its couplings to up-type fermions are suppressed as $1/\tan\beta$.
Therefore, $a_1$ branching fractions follow the standard mass
hierarchy of open decay channels to down-type fermions.
Figure~\ref{fig:bramm} shows the the branching fraction for $a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi
\mu\mu$ as obtained using NMSSMTools package.  For $m_{a_1} <
2m_\tau$, the $a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu\mu$ channel becomes significant, making an
analysis in the four-muon mode viable for experimental searches.

\begin{figure*}[htb]
\includegraphics[width=0.87\linewidth]{fourconstraints_params}
\caption{Sampled points with $m_a < 2m_\tau$ and experimental constraints successively applied
in the $\lambda$ vs.\ $\mu\kappa/\lambda$ plane. The low energy $e^+e^-$ data (CLEO and
BaBar) have essentially no impact on the allowed parameter space. Color scale is number density
and filled points are 100 models (before application of experimental
constraints). \label{fig:exclusion_params}}
\end{figure*}
\begin{figure*}[hbt]
\includegraphics[width=0.87\linewidth]{fourconstraints_masses}
\caption{Sampled points with $m_a < 2m_\tau$ and experimental constraints successively applied
similar to Fig.~\ref{fig:exclusion_params} but in the $m_a$ vs. $m_h$ plane.  The low
energy $e^+e^-$ data (CLEO and BaBar) have essentially no impact on the allowed parameter space.
Color scale is number density and filled points are 100 models (before application of experimental
constraints). \label{fig:exclusion_mass}}
\end{figure*}

It is important to note that the NMSSMTools calculation of
$\mathcal{B}(a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu \mu)$ shown in Fig.~\ref{fig:bramm} does not
include hadronization effects important in the region $m_{a_1} <
1$~GeV/$c^2$, and therefore is not reliable.  One should also notice
that for $2m_\mu < m_{a_1} < 3m_\pi$, $\mathcal{B}(a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu\mu)$ is expected
to be about 100\% because $q\bar{q}$ and $gg$ decays are prohibited by
hadronization and spin effects, and because $\gamma\gamma$ is small.
Since the status of $\mathcal{B}(a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu \mu)$ in NMSSMTools for
$m_{a_1} < 0.5$~GeV/$c^2$ is not well-established and requires further
development, we present our results only for the $m_{a_1} > 0.5$~GeV
region.  We would like to notice that $\mathcal{B}(a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu \mu)$
is model-dependent in general and can be somewhat different in, for
example, the Little Higgs model~\cite{LHiggsADecays} used by the $D\O$
collaboration in Ref.~\cite{Abazov:2009yi}.  Therefore, we present our
results as limits on production cross-section times branching ratios
for the $4\mu$ signature as a model-independent limit for a given
topology and signature under study.

\section{Current Experimental Constraints}

Existing experimental data restrict the NMSSM parameter space for the
scenario studied here.  In the following, we discuss experimental
measurements relevant to this scenario and evaluate their impact in
restricting the allowed parameter space for models with low $m_{a_1}$.

\subsection{Cosmological Constraints}

The lightest NMSSM neutralino is a candidate for Cold Dark Matter
(CDM).  The WMAP measurement of the CDM relic density therefore serves
as an important constraint on the allowed NMSSM parameter space.  In
our scan, we used the MicrOmegas package~\cite{micrOmegas} linked to
NMSSMTools to calculate $\Omega_{\mbox{\scriptsize NMSSM}}h^2$ and
determine if a particular model is consistent with the experimental
data.  We considered a model to be consistent with the CDM measurement
if $\Omega_{\mbox{\scriptsize NMSSM}}h^2 \le 0.1131 + 2\times0.0034$,
corresponding to the 95\% upper limit obtained using the latest WMAP
5-year dataset~\cite{wmap}.  The NMSSM neutralino relic density need
not account for all CDM observed by WMAP, but it cannot exceed it.

To illustrate the effect of the WMAP constraints,
Fig~\ref{fig:exclusion_params}(a) shows the density of generated NMSSM
models in the $\lambda$ versus $\mu\kappa/\lambda$ plane under the
constraint that $m_{a_1} < 2m_\tau$.  Models that were determined to
be consistent with the WMAP data are shown in
Fig.~\ref{fig:exclusion_params}(b).  The comparison shows that the
WMAP bound excludes the region of small $\mu\kappa/\lambda$ and
$\lambda$.  In that region, the lightest neutralino is light and
weakly interacts with SM particles, suppressing the neutralino
annihilation rate and enhancing the neutralino relic density to
unacceptably large values.  Figures~\ref{fig:exclusion_mass}(a) and
(b) make the same comparison but in the $m_{a_1}$ versus $m_{h_1}$
plane.

\subsection{Constraints from Direct Searches at Colliders}

Several searches for $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1$ have been performed at collider
experiments, with the strongest impact on the allowed NMSSM models
coming from LEP-II data~\cite{lep2exclusion}.  Although the singlet
component of $h_1$ at low $\mu\kappa/\lambda$ and $\lambda$ (and
correspondingly low $m_{h_1}$) would severely suppress $h_1$
production in $e^+e^- \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1 Z$, these extreme scenarios are excluded
by the WMAP data.  LEP limits~\cite{lep2exclusion} on NMSSM models are
inferred from $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1$, $a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi$ pairs of charm, gluon, and
$\tau$ jets; $a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu\mu$ limits were not quoted.  The LEP-II
upper limit on $e^+ e^- \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1 Z$ with $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1$ excludes
models that predict $m_{h_1}$ within the kinematic limits, $45 <
m_{h_1} < 86$~GeV/$c^2$, and $m_{a_1}$ in the region of significant
detector efficiency, $m_{a_1} > 2$~GeV/$c^2$.

In addition to LEP data, there were direct searches for $\Upsilon \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi
\gamma a_1$ by CLEO and BaBar at low energy $e^+e^-$
colliders~\cite{cleo-low-ma,babar-low-ma}.  Neither of these searches
significantly constrain the NMSSM models with low $m_{a_1}$ because
$a_1$ has a high singlet component, and thus negligible $bba_1$
coupling (see Fig.~\ref{fig:nonsingletcp1}(a)), for all sampled
parameter values.  Because CLEO and BaBar results have negligible
effect on the allowed parameter space,
Figs.~\ref{fig:exclusion_params}(c) and~\ref{fig:exclusion_mass}(c)
show combined LEP+CLEO+BaBar constraints, but the reader is reminded
that only LEP constraints are relevant.

\begin{figure*}[htb]
\includegraphics[width=0.48\linewidth]{crosssec_vs_mukoverl_gg}
\hfill
\includegraphics[width=0.48\linewidth]{crosssec_vs_mukoverl_bb}

\caption{Contributions to the $pp \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1$ production cross-section at
  $\sqrt{s}=14$~TeV as a function of $\mu\kappa/\lambda$ and
  $\lambda$, from $gg$ (a) and $b\bar{b}$ (b), with the requirement
  that $m_{a_1} < 2m_\tau$.  (The red line is a mean of $\lambda <
  0.01$ scenarios.)
  \label{fig:sm_mukoverl2}}
\end{figure*}

The flat $\ell^+\ell^-$ distribution of rare $B \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi K \ell^+\ell^-$
decays~\cite{:2008sk} could potentially set a limit on the parameter
space under study through the bound on $\mathcal{B}(B \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi K a_1)
\times \mathcal{B}(a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu\mu)$. However, this limit does not
actually bound the region of our interest because the coupling of
$a_1$ to up-type and down-type quarks in $b \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi s a_1$ penguin
diagrams is suppressed due the highly singlet nature of $a_1$.  For
$f_a = \tan\theta_P \, v \sin(2\beta)/2$, the quantity $f_a \tan^2\beta$
is above 100~TeV in our scan while the charged Higgs mass is typically
above 200~GeV/$c^2$.  Thus, the bound set in Fig.~2 of
Ref.~\cite{Freytsis:2009ct} is not relevant to the parameter space of our
study.

The results of a search~\cite{d0-low-ma} for the NMSSM with a low mass
$a_1$ at the Tevatron was recently published by the $D\O$
collaboration in the channel $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi 4\mu$.  With no
excess of data over the SM expectations, the paper quotes 95\%
C.L.\ upper limits for the cross-section of this process.  To
interpret the $D\O$ result in terms of constraints on allowed NMSSM
models in our scan, we calculate the NLO production cross-section for
$p\bar{p} \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1$ in the NMSSM using the SM NLO calculations for $gg
\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi H_{SM}$~\cite{Spira:1995rr} and $b\bar{b} \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi H_{SM}$ with
QCD-improved (running) Yukawa couplings~\cite{Balazs:1998sb},
corrected for differences in coupling between the SM and the NMSSM
using NMSSMTools:
\begin{align}
\sigma(gg\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1)=\sigma(gg\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi H_{SM})\frac{\Gamma(h_1\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi gg)}{\Gamma(H_{SM}\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi gg)} \label{eq:ggcross_section} \\
\nonumber =\sigma(gg\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi H_{SM})\frac{Br(h_1\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi gg)\Gamma^{\mbox{\scriptsize tot}}(h_1)}{\Gamma(H_{SM}\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi gg)} \\
\sigma(b\bar{b}\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1)=\sigma(b\bar{b}\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi H_{SM})
\left(\frac{Y_{bbh_1}}{Y_{bbH_{SM}}}\right)^2 \label{eq:bbcross_section}
\end{align}
where $\sigma(gg \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi H_{SM})$ and $\Gamma(H_{SM} \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi gg)$ are
calculated using HIGLU~\cite{higlu}, while $\mathcal{B}(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi gg)$,
$\Gamma^{\mbox{\scriptsize tot}}(h_1)$, and the ratio of Yukawa
couplings $Y_{bbh_1}/Y_{bbH_{SM}}$ are obtained using NMSSMTools.  For
$\mu\kappa/\lambda < 60$~GeV (non-SM $h_1$ lighter than
120~GeV/$c^2$), the cross-section is strongly suppressed even compared
to the SM for low $m_{a_1}$ because $h_1$ has a large singlet fraction
and weakly couples to SM particles (see Fig.~\ref{fig:sm_mukoverl1}).
For larger $\mu\kappa/\lambda$, the lightest CP-even Higgs $h_1$
becomes the SM-like Higgs and has a small $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1$ branching
fraction.

The $D\O$ paper~\cite{d0-low-ma} quotes 95\% C.L.\ limits on
$\sigma(p\bar{p} \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1) \times B(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi 4\mu)$ for
several choices of $m_{a_1}$ with $m_{h_1} = 100$~GeV/c$^2$.  To
determine if a particular model in our scan is excluded by these data,
we linearly interpolate the published cross-section limits for values
of $m_{a_1}$ between the points in~\cite{d0-low-ma}.  To obtain the
experimental cross-section limits as a function of $m_{h_1}$, we need
to correct for variations in the experimental acceptance.  We obtain
those limits by taking the analysis acceptance to be linear as a
function of $m_{h_1}$ ``increasing by $\sim$10\% when $m_{h_1}$
increases from 80 to 150~GeV/$c^2$''~\cite{d0-low-ma} and matching it
to the full analysis acceptance given at $m_{h_1} = 100$~GeV/$c^2$.
We then calculate the production cross-section and branching fractions
for the model points and compare them to the values we derive
from~\cite{d0-low-ma}.  Figures~\ref{fig:exclusion_params}(d)
and~\ref{fig:exclusion_mass}(d) show the density of NMSSM models
surviving WMAP, LEP and Tevatron constraints.  Because of the
suppression in production rate at low $\mu\kappa/\lambda$ and small
$\mathcal{B}(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1)$ at high $\mu\kappa/\lambda$, the
Tevatron search has only a limited impact on the allowed NMSSM
parameter space, mainly excluding models with high $\lambda$.  A
significant improvement in Tevatron reach for the NMSSM would require
a large increase in integrated luminosity, thus requiring the LHC to
make a definitive discovery or exclusion of NMSSM models with low
$m_{a_1}$.

\section{A Dedicated Search for the Low-$m_{a_1}$ NMSSM at the LHC}

\begin{figure*}[htbp]
\begin{center}
\includegraphics[width=0.48\linewidth]{acceptance_vs_mh}
\hfill
\includegraphics[width=0.48\linewidth]{acceptance_vs_ma}

\caption{(a):~Acceptance as a function of $m_{a_1}$ for fixed
  $m_{h_1}$.  (b):~Acceptance as a function of $m_{h_1}$ for fixed
  $m_{a_1}$.}
\label{signal_acceptance}
\end{center}
\end{figure*}

Since $a_1$ is only weakly coupled to SM particles, it can only be
produced at the LHC via decays of the lightest scalar Higgs $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi
a_1 a_1$.  The main characteristic of such signal at the LHC is two
back-to-back (in $\phi$) di-muon pairs of spatially nearby muons.  The
reconstructed di-muon pairs should have invariant masses consistent
with one another, and their invariant masses also serve as a direct
measurement of $m_{a_1}$.  Additionally, the $4\mu$ invariant mass
distribution should have a narrow peak corresponding to the $m_{h_1}$
mass.  We use these striking features to design an analysis suitable
for early LHC running.

The four-muon final state considered in this analysis has relatively
low experimental backgrounds.  Therefore, instead of using the Vector
Boson Fusion (VBF) production process chosen in the proposed NMSSM
searches targeting the $m_{a_1} > 2m_\tau$ region~\cite{nmssm-ph7}, we
focus on the largest Higgs production modes at the LHC, $gg \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1$
and $b\bar{b} \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1$.  We calculate the NLO cross-section for $pp
\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1$ for the NMSSM by rescaling the LHC SM NLO
calculations~\cite{Spira:1995rr,Balazs:1998sb} to correct for
differences in couplings between the SM and NMSSM
(Eqs.~\ref{eq:ggcross_section} and~\ref{eq:bbcross_section}).  Like
the Tevatron case, the cross-section is strongly suppressed compared
to the SM if $h_1$ has a large singlet fraction.
Figure~\ref{fig:sm_mukoverl2} shows the production cross-section for
14~TeV $pp \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1+X$ as a function of $\mu\kappa/\lambda$.  While
this suppression makes the analysis challenging even at the LHC, the
constraints arising from the WMAP relic density measurement exclude
models with very low values of $\lambda$, so the allowed models have
small but non-negligible production cross-section.

\subsection{Analysis Selections}

We use Pythia to generate signal event templates with $m_{h_1}$ in the
range from 70 to 140~GeV/$c^2$ and $m_{a_1}$ in the range from 0.5 to
4~GeV/$c^2$.  We chose the CMS detector as a benchmark for modeling a
realistic experimental environment, with parameters described in
Ref.~\cite{cms-tdr}.  The important parameters for this analysis are
muon momentum resolution, the minimum muon momentum needed to reach
the muon system, geometric acceptance, and the average muon
reconstruction efficiencies.  Because of the large number of
reconstructed muons in the event, we take the trigger efficiency to be
100\%.

The analysis starts by requiring at least four muon candidates with
transverse momentum $p_T > 5$~GeV/$c$ and pseudorapidity $|\eta| <
2.4$ to ensure high and reliable reconstruction efficiency.  Of the
four muon candidates, at least one must have $p_T > 20$~GeV/$c$ to
suppress major backgrounds and to satisfy trigger requirements.  Each
event is required to have at least two positively charged and two
negatively charged muon candidates.  For the surviving events, we
define quadruplets of candidates, pairing the candidates by charge and
sorting them into two di-muon pairs by minimizing the quantity
$(\Delta R(\mu_i,\mu_j)^2 + \Delta R (\mu_k,\mu_l)^2)$, where $\Delta
R^2 = \Delta \eta^2 + \Delta \phi^2$.  Muon quadruplets for which
$\Delta R > 0.5$ in either of the pairs are discarded as inconsistent
with the signal topology.  Acceptance for the selections listed above
is shown in Fig.~\ref{signal_acceptance} for several representative
values of $m_{h_1}$ and $m_{a_1}$.

The requirement of four sufficiently energetic muons in the event
dramatically reduces contributions of potential backgrounds for this
analysis.  After acceptance selections, the dominant background is due
to the QCD multijet production where muons originate from heavy-flavor
resonances, heavy-flavor quark decays, or from $\pi/K$
decays-in-flight.  We use Pythia to estimate the QCD multijet
background, and obtain approximately 2.6~events/pb$^{-1}$
(approximately half containing at least one decay-in-flight).  Using
CalcHEP~\cite{calchep} to estimate $pp \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi 4\ell + X$ electroweak
backgrounds, we obtain 0.04~events/pb$^{-1}$.  Direct $J/\psi$
production is found by Pythia to be completely negligible.  Other SM
backgrounds (top, W+jets) are negligible in the region of interest of
this analysis.

\begin{figure*}[htb]
\begin{center}
\includegraphics[width=0.48\linewidth]{muon_pair_masses_new}
\hfill
\includegraphics[width=0.48\linewidth]{fourmuon_invariant_mass_new}

\caption{(a):~Invariant mass of reconstructed muon pairs for $m_{a_1}
  = 0.5$ and 3~GeV/c$^2$ (in both cases $m_{h_1}$ = 100~GeV/c$^2$).
  (b):~Invariant mass of four reconstructed muons for $m_{h_1} = 80$ and
  120~GeV/c$^2$ (in both cases $m_{a_1}$ = 3.0~GeV/$c^2$).}
\label{muon_pairs_masses_invariant_mass}
\end{center}
\end{figure*}

The backgrounds are further reduced by requiring the kinematics to be
consistent with the expected signal siganture.  We calculate the
invariant mass of each of di-muon pair, $m_{12}$ and $m_{34}$, as well
as the invariant mass of all four muons, denoted as
$m_{1234}$. Figure~\ref{muon_pairs_masses_invariant_mass}(a) shows the
invariant mass of the muon pairs passing all selections in signal
events for two choices of $m_{h_1}$ and
$m_{a_1}$. Figure~\ref{muon_pairs_masses_invariant_mass}(b) shows the
distribution of $m_{1234}$ for two benchmark points.  To focus on the
region of interest, we require $m_{1234} > 60$~GeV/$c^2$, $m_{12}$,
$m_{34} < 4$~GeV/$c^2$, which reduces the QCD background to
0.4~events/pb$^{-1}$.

To ensure the compatibility of the measured invariant masses of the
two di-muon pairs, one could require $|m_{12} - m_{34}| < 0.08 +
0.005\times(m_{12} + m_{34})$. Such cut would require the two pair
masses to be consistent with each other and would take into account
the widening of absolute resolution in the reconstructed di-muon mass
as a function of mass.  If applied, the only background that still may
be not completely negligible is the QCD multi-jet production, for
which we conservatively estimate the upper bound to be
0.02~events/pb$^{-1}$.  However, instead of applying this selection
explicitly, a better approach would be to fit the data in the 3D space
$(m_{12}, m_{34}, m_{1234})$, taking into account kinematic properties
of the signal events.  This approach maximizes the signal acceptance
and therefore the statistical power of the analysis.  It is also
convenient from an experimental standpoint as the background events
are distributed smoothly over the 3D space, allowing a fit of the 3D
distribution to estimate backgrounds directly from the data.  A
potential signal would appear as a concentration of events in a small
region of the space (a 3D peak). We use a binned likelihood defined as
a function of parameters $m_{a_1}$, $m_{h_1}$ and effective signal
cross-section $\sigma \times \mathcal{B} (h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1)
\mathcal{B}^2(a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu\mu)$ to fit the simulated data using either
background-only or signal-plus-background templates.  We estimate the
sensitivity of this analysis and present it in terms of the 95\%
C.L.\ exclusion levels for signal cross-section using a Bayesian
technique.

Our estimations show that for an early data search ($\mathcal{L}
\simeq 100$~pb$^{-1}$), the backgrounds are negligibe.  For an
analysis with higher luminosity, one can restore the zero-background
situation by adding an isolation requirement to one or both of the
di-muon pairs in the event.  Isolation can be defined by either
setting an upper bound on the sum of the transverse momenta of all
tracks in a cone around the reconstructed direction of the di-muon
pair, excluding two muon tracks, or by rejecting pairs with additional
tracks above a certain threshold.  For the analysis with $\mathcal{L}
= 1$~fb$^{-1}$ of data, we required no charged tracks with momentum
$p_T > 1$~GeV/$c$ in the $\sqrt{(\Delta \eta)^2 + (\Delta \phi)^2} <
0.3$ cone around the direction of at least one of the two muon pairs.
This requirement is 96\% efficient for signal and reduces QCD multijet
background, dominated by events with muons originating from heavy
flavor jets, by a factor of 6--7.  For high-luminosity datasets,
isolation can be further tightened to increase background suppression
with only a moderate loss in signal efficiency.

\begin{table}[t]
\caption{Expected rate of background events per 100~pb$^{-1}$ of
  luminosity after selection. \label{bckgr_cuts_number_reco_level}}
\begin{center}
\renewcommand{\arraystretch}{1.4}
\begin{tabular}{c|c|c}
\hline\hline
Selection & 4 leptons & QCD multi-jet \\
\hline
$p_T (\mu_1) > 20$~GeV/$c$ and       &                           &                        \\
$p_T (\mu_i) > 5$~GeV/$c$; $i=2,3,4$ &               $4.8\pm0.2$ &             $267\pm23$ \\
\hline
$m_{12}$, $m_{34} < 4$~GeV/$c^2$     &           $0.024\pm0.012$ &              $90\pm13$ \\
$m_{1234} > 60$~GeV/$c^2$            &           $0.010\pm0.007$ &               $39\pm9$ \\
$|m_{12} - m_{34}| < 0.08$~GeV/$c^2$ &                           &                        \\
$+0.005 \times (m_{12} + m_{34})$    & $0.000^{+0.005}_{-0.000}$ & $0.00^{+1.95}_{-0.00}$ \\
\hline\hline
\end{tabular}
\end{center}
\end{table}

\begin{figure*}[htbp]
\includegraphics[width=0.32\linewidth]{newlhcconstraints_params}
\hfill
\includegraphics[width=0.32\linewidth]{newlhcconstraints_masses}
\hfill
\includegraphics[width=0.32\linewidth]{newlhcconstraints_crosbr}

\caption{Sampled models with $m_{a_1} < 2m_\tau$ and all experimental
  constraints applied, presented as a function of model parameters
  (a), Higgs masses (b), branching fraction and LHC cross-section (c).
  With only 100~pb$^{-1}$, the LHC's reach extends beyond that of the
  Tevatron. \label{fig:lhcexclusion}}
\end{figure*}

\subsection{LHC Reach for NMSSM $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1$}

We have proposed an analysis that has a potential of discovering the
NMSSM with early LHC data in scenarios with low $m_{a_1}$.  We
estimate its sensitivity by calculating the 95\% C.L.\ upper limit on
the product $\sigma(pp \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h) \mathcal{B}(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1)
\mathcal{B}^2(a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu\mu) \, \alpha$, where $\alpha$ is the
analysis acceptance, using a Bayesian technique.  Because of the low
background, an upper limit on the signal corresponds to approximately
three reconstructed events.  This limit is 0.0293~pb for $\mathcal{L}
= 100$~pb$^{-1}$, and scales linearly with luminosity assuming that
the number of observed background events is zero.  In nearly all
pseudoexperiments, this limit is independent of $m_{h_1}$ and
$m_{a_1}$ because the effective signal region that dominates signal
significance is essentially background-free and the probability to
observe an event is small.  Note that the corresponding projection for
$\mathcal{L} = 1$~fb$^{-1}$ includes the isolation cut, slightly
reducing signal efficiency and correspondingly loosening the limit.
The upper limit on $\sigma(pp \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1) \mathcal{B}(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1)$ is
shown as a function of $m_{h_1}$ and $m_{a_1}$ in
Table~\ref{table_both_factorized}.

Figure~\ref{fig:lhcexclusion} presents the region of NMSSM parameter
space excluded by the Tevatron and the region that the LHC would
exclude with 100~pb$^{-1}$ (without isolation) and 1~fb$^{-1}$ (with
isolation), assuming no observed signal.  The regions are presented in
the $\lambda$, $\mu\kappa/\lambda$ plane (Fig.~11(a)), the $m_{a_1}$,
$m_{h_1}$ plane (Fig.~11(b)), and the plane of $h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi
4\mu$ branching fraction versus LHC $pp \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1$ cross-section
(Fig.~11(c)).  High $h_1$-singlet scenarios (which have low production
cross-section) and low $h_1$-singlet scenarios (which have low $h_1
\relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1$ branching fractions) are accessible to the Tevatron and
the LHC to different degrees, leading to a region in
Fig.~\ref{fig:lhcexclusion}(c) where high $h_1$-singlet scenarios are
excluded by the Tevatron while some low $h_1$-singlet models with the
same LHC cross-section times branching fraction are not.  The Tevatron
exclusion region has a sharp border only when viewed as a function of
the Tevatron cross-section.

\begin{table}[htbp]
\caption{95\% C.L.\ upper limit on $\sigma(pp \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi h_1) \times
  \mathcal{B}(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi 4\mu)$ (fb) at the LHC with
  $\mathcal{L} = 100$~pb$^{-1}$ (no isolation) and $\mathcal{L} =
  1$~fb$^{-1}$ (with isolation).  The limit tightens at high $m_{h_1}$
  because of the increase in acceptance with
  $m_{h_1}$. \label{table_both_factorized}}

\begin{flushright}
\renewcommand{\arraystretch}{1.4}
\begin{tabular}{c | c | c | c | c}
\hline\hline
\multicolumn{5}{c}{$m_{a_1}$ (GeV/$c^2$)} \\
\hline
\mbox{\hspace{0.19 cm}}0.5\mbox{\hspace{0.19 cm}} & \mbox{\hspace{0.25 cm}}1.0\mbox{\hspace{0.25 cm}} & \mbox{\hspace{0.34 cm}}2.0\mbox{\hspace{0.34 cm}} & \mbox{\hspace{0.33 cm}}3.0\mbox{\hspace{0.33 cm}} & \mbox{\hspace{0.25 cm}}4.0\mbox{\hspace{0.25 cm}} \\
\end{tabular}

\begin{tabular}{c c | c | c | c | c}
\hline\hline \multicolumn{1}{c |}{$\mathcal{B}(a_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi \mu\mu)$ (\%)} & \mbox{\hspace{0.25 cm}}0\footnote{Recall that $\mathcal{B}(h_1 \relax\ifmmode{\rightarrow}\else{$\rightarrow$}4\fi a_1 a_1)$ is obatined
using NMSSMTools and is not reliable for $m_{a_1} \lesssim 1$~GeV/$c^2$. Furthermore, this branching fraction is expected
to reach nearly 100\% for $2m_\mu < m_{a_1} < 3m_\tau$.}\mbox{\hspace{0.25 cm}} & \mbox{\hspace{0.25 cm}}9.8\mbox{\hspace{0.25 cm}} & \mbox{\hspace{0.25 cm}}15.2\mbox{\hspace{0.25 cm}} & \mbox{\hspace{0.25 cm}}16.2\mbox{\hspace{0.25 cm}} & \mbox{\hspace{0.25 cm}}0.7\mbox{\hspace{0.25 cm}} \\\hline\hline
& \multicolumn{5}{c}{for $\mathcal{L} = 100$~pb$^{-1}$ (no isolation)} \\
\hline
\multicolumn{1}{c |}{$m_{h_1} = 80$~GeV/$c^2$}  &  96.0 & 110.3 & 121.1 & 122.6 & 126.1 \\
\multicolumn{1}{c |}{$m_{h_1} = 100$~GeV/$c^2$} &  74.8 &  90.3 & 100.8 & 102.4 & 103.9 \\
\multicolumn{1}{c |}{$m_{h_1} = 120$~GeV/$c^2$} &  63.9 &  77.4 &  86.0 &  90.8 &  94.4 \\\hline\hline
& \multicolumn{5}{c}{for $\mathcal{L} = 1000$~pb$^{-1}$ (with isolation)} \\
\hline
\multicolumn{1}{c |}{$m_{h_1} = 80$~GeV/$c^2$}  &  10.0 &  11.5 &  12.6 &  12.8 &  13.1 \\
\multicolumn{1}{c |}{$m_{h_1} = 100$~GeV/$c^2$} &   7.8 &   9.4 &  10.5 &  10.7 &  10.8 \\
\multicolumn{1}{c |}{$m_{h_1} = 120$~GeV/$c^2$} &   6.7 &   8.1 &   9.0 &   9.5 &   9.8 \\\hline\hline
\end{tabular}
\end{flushright}
\end{table}

It is worth noting that quantitative background estimates performed in
our analysis may indicate that the LHC reach for NMSSM models with
$m_{a_1} > 2m_\tau$ in the $2\mu 2\tau$ channel are substantially
weaker than suggested in Ref.~\cite{2mu2tau-pheno}, which relied on
extrapolating QCD backgrounds to avoid high-statistics simulations.
Though the $4\mu$ and $2\mu 2\tau$ analyses apply different
selections, a rough extrapolation of the simulated QCD multijet
backgrounds to the $4\mu$ channel yields an estimate of backgrounds to
the $2\mu 2\tau$ channel that is three orders of magnitude larger than
what was used in Ref.~\cite{2mu2tau-pheno}, even without considering
the much larger misidentification rate of hadronically decaying taus.
The expected number of QCD multijet events in the $m_{1234} > 60$,
$m_{12}$ and $m_{34} < 4$~GeV/$c^2$ region of the $4\mu$ analysis,
which is $390 \pm 90$~events/fb$^{-1}$ (note that the numbers in
Table~\ref{bckgr_cuts_number_reco_level} are for 100~pb$^{-1}$), could
be reduced by a factor of 10--20 using tight isolation requirements.
Unlike our analysis, the study in Ref.~\cite{2mu2tau-pheno} applies
restrictions on the transverse momentum of the di-muon pair,
$p_T^{\mu\mu} > 40$~GeV/$c$, and on the missing transverse energy
$\mbox{${E\!\!\!\!/_{\rm T}}$} > 30$~GeV.  However, the $p_T^{\mu\mu}$ selection is similar to
$m_{1234} > 60$~GeV/$c^2$ and, given typical expected $\mbox{${E\!\!\!\!/_{\rm T}}$}$
resolution for multi-jet events, a $\mbox{${E\!\!\!\!/_{\rm T}}$} > 30$~GeV requirement cannot
be powerful enough to overcome several orders of magnitude in
estimated event count.  Scaling the $4\mu$ background estimate down by
a factor of 10 to account for muon isolation, we expect about $39 \pm
9$~events/fb$^{-1}$ from QCD multijets, as opposed to the
0.03~events/fb$^{-1}$ in Ref.~\cite{2mu2tau-pheno}.  Allowing for the
larger rate of tau misidentification compared to muons only increases
the discrepancy.  Another argument can be made using the $D\O$
measurement in the $2 \mu 2\tau$ channel~\cite{d0-low-ma}, which had
1--2 expected background events in the narrow ($\pm
0.3$--$1.0$~GeV/$c^2$) windows around the selected points in the
di-muon mass.  Using common scaling estimates of background
contributions from the Tevatron to the LHC, one would expect similar
backgrounds for LHC datasets of the order of 100~pb$^{-1}$.  For
datasets with integrated luminosities of the order of 500~pb$^{-1}$,
the corresponding QCD contamination would be 5--10 events per window.
These much larger background estimates severely affect acievable
exclusion limits and, considering trial factors, would make any
discovery in the $2\mu 2\tau$ channel with early data extremely
challenging.

\section{Conclusions}

We have studied the phenomenology of the NMSSM scenarios with the mass
of the lowest CP-odd Higgs boson, $a_1$, below the $2\tau$ threshold.
Our analysis of the impact of existing data on these models has shown
that the WMAP and LEP-II data provide the most constraining power,
while recent CLEO and BaBar measurements have essentially no impact on
the allowed parameter space, and the Tevatron data has only a weak
impact on the allowed parameter space.  As a result, a large fraction
of the parameter space is not excluded by any existing data.  We
conclude that a new analysis should be performed at the LHC to
definitively confirm or exclude these models.  We propose an analysis
suitable for the LHC using the $4\mu$ signature, which has very low
backgrounds and striking kinematical features allowing direct and
precise measurement of the masses of the $a_1$ and $h_1$ bosons.
Using the CMS experiment as a benchmark, we we estimate the sensitvity
of such an analysis and demonstrate that it has the potential to
either make a discovery or significantly diminish the allowed
parameter space of the NMSSM with low $m_{a_1}$ using only
100-1000~pb$^{-1}$ of early LHC data.

\section*{Acknowledgments}

We thank Ulrich Ellwanger, Cyril Hugonie, Alexander Pukhov, Jay Wacker
for useful discussions. One of the authors (AB) would like to thank
the GGI Institute (Florence), and another (JP) would like to thank
Fermilab, where important parts of the work on the paper were
performed.  This work would not be possible without the support of the
U.S. Department of Energy, the State of Texas, and the Universities
Research Association Visiting Scholars Program.

\def\Journal#1#2#3#4{{#1} {\bf #2}, #3 (#4)}
\defNuovo Cimento{Nuovo Cimento}
\defNucl. Instrum. Methods{Nucl. Instrum. Methods}
\defNucl. Instrum. Methods Phys. Res. Sect. A{{Nucl. Instrum. Methods} A}
\def\NP{Nucl. Phys.}
\defNucl. Phys. B{{Nucl. Phys.} B}
\defPhys. Lett. B{{Phys. Lett.}  B}
\defPhys. Rev. Lett.~{Phys. Rev. Lett.}
\defRep. Prog. Phys.{Rep. Prog. Phys.}
\defPhys. Rev. D{{Phys. Rev.} D}
\defPhys. Rep.~{Phys. Rep.}
\defProg. Theor. Phys{Prog. Theor. Phys.}
\defZ. Phys. C}	% - Particles and Fields{{Z. Phys.} C}
\def{Mod. Phys. Lett.} A{{Mod. Phys. Lett.} A}
\def{Eur. Phys. J.} C{{Eur. Phys. J.} C}
\defComput. Phys. Commun.{Comput. Phys. Commun.}

\renewcommand{\baselinestretch}{1}

redpajama_set_name: RedPajamaArXiv


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text:
THE SCOUTING GUIDE TO SURVIVAL
A Licensed Product of the Boy Scouts of America
More than 200 Essential Skills for Staying Warm, Building a Shelter, and Signaling for Help
Prepared. For Life.®
In The Scouting Guide to Survival (November 6, 2018), current Scouts, Scout alumni, and readers interested in the outdoors are provided with time-tested advice on emergency preparedness. Some practical tips include:
How to build a fire
How to purify water
How to signal for help
How to build simple shelters
How to survive in different environments
How to practice survival first aid
Since 1910, the Boy Scouts of America has helped build the future leaders of this country by combining educational activities and lifelong values with fun. The BSA is committed to training youth in responsible citizenship, character development, and self-reliance through participation in a wide range of outdoor activities.
J. Wayne Fears grew up in the outdoors, as his father was a trapper. He earned the BSA rank of Eagle Scout at the age fourteen. As an adult scouter, he served for two years as the advisor to an Explorer Post that specialized in wilderness survival. He has taught wilderness survival to Boy Scout troops and BSA leaders and has served many years as a wilderness survival merit badge counselor. He received survival training both from the Army and Air Force. This is his third book on survival. He is one of America's most prolific outdoor writers with thirty-four books and over 6200 magazine articles published. In 2012 he was inducted into the Legends of the Outdoors National Hall of Fame. He resides in Tater Knob, Alabama.
To request an excerpt or to arrange an interview with the author, please contact:
Ronnie Alvarado / (212) 643-6816 x 274 / valvarado@skyhorsepublishing.com
The Scouting Guide to Survival: More than 200 Essential Skills for
Staying Warm, Building a Shelter, and Signaling for Help by J. Wayne Fears
Skyhorse Publishing paperback, also available as an e-book | On Sale: November 6, 2018
ISBN 978-1-5107-3774-7| $16.99
The AR7 – Packable Rifle for Survival
This could be called the era of the pack. In today's world there are peppers who always keep a "bug-out bag" handy in their vehicle and at home in the event of a natural or man-made catastrophe. There is the wilderness survivalist who carefully selects items for his pack in the event he is lost or stranded in the wild. There is the backpacker who carries enough lightweight high-tech gear to camp comfortably in the backcountry for days at a time. And there are the wilderness travelers who travel by bush plane, canoe, boat, dog sled, snowmobile or ATV and carry a pack equipped for almost any emergency.
One of the most popular firearms for many of these pack owners is a lightweight, takedown .22 rimfire rifle. The primary purpose for packing these rifles is for subsistence hunting for food in long term emergencies. However these same little rifles are also used for plinking and, in a pinch, protection. Since they are shoulder fired they are more accurate in most shooters hands than handguns when every shot counts. Also it is easy and lightweight to carry a good supply of .22LR ammo as 133 rounds weighs just one pound.
JAPANESE HONEYSUCKLE – THE FOOD PLOT YOU MAY ALREADY HAVE
Honeysuckle is a favorite food for deer, wild turkey, quail and rabbit. It also serves as an excellent cover for wildlife. It occurs in the wild throughout much of the U.S.
Usually, when you read about a food plot crop you read all the about all the wonderful values of the plant or plant mix. Catch words such as nutritious, high protein, drought hardy, etc. are often used to describe the plant. However, when you mention Japanese honeysuckle the first thing you hear is pest, weed, invasive, snake cover, etc. In the right place, with the correct management, this honeysuckle can be all the good things better known crops planted for wildlife are, and more.
NEW BOOK ON EVERYTHING YOU EVER WANTED TO KNOW ABOUT DUTCH OVEN COOKING
The Lodge Book of Dutch Oven Cooking By J. Wayne Fears
http://shop.lodgemfg.com/cookbooks-and-videos/dutch-oven-cookbook.asp
On April 29 and 30, 2017 during the National Cornbread Festival in South Pittsburg, Tennessee I will be at the Lodge Outlet Store autographing my new book The Lodge Book of Dutch Oven Cooking. With me will be members of the Tennessee Dutch Oven Society cooking some of the recipes from the book for you to sample. I would like to meet as many Dutch oven enthusiasts as possible those two days so put the date on your calendar.
A series of F4 tornados knocks out the electrical transmission lines, cell towers and local power lines in a five county area. For two weeks or more the area faces life without electricity and basic communications.
A small rouge nation has three "in place" radicals in the United States who rent small planes, fly to 15,000 feet above three preselected locations and each simultaneously set off small nuclear devices, an EMP attack. Everything electrical in the United States is fried. Within an instant we are living in the 1300's.
J. Wayne Fears serves as shooting columnist for Turkey Call magazine and writes the back page for GunHunter magazine and Great Days Outdoors magazine. For the past eight years he has written a column for Whitetails Unlimited magazine entitled The Food Plot Doctor. He also freelances to a number of other publications and web sites.
Cornerstone Heritage Voting Media Member

redpajama_set_name: RedPajamaCommonCrawl


Bees are like oxygen: ubiquitous, essential, and, for the most part, overlooked. And yet they lie at the heart of relationships that bind the human and natural worlds. In Buzz, award-winning author and biologist Thor Hanson explores how -- from honeybees and bumbles to lesser-known diggers, miners, leafcutters, and masons -- bees have long been central to our harvests, our mythologies, and our very existence, and, alarmingly, why they are at risk of disappearing. As informative and enchanting as the waggle dance of a honeybee, Buzz shows us why all bees are wonders to celebrate and protect. Once you read this book, you'll never overlook them again.