\documentclass[
aps,
prl,
reprint,
preprintnumbers,
showpacs,
groupedaddress,
amsmath,
amssymb,
floatfix]{revtex4-1}
%% \RequirePackage{lineno}
\usepackage{graphicx,epsfig,dcolumn,multirow}
\usepackage{natbib}
\newcolumntype{d}[1]{D{.}{.}{#1}}
\RequirePackage{xspace}
%\input{babarsymMerge-chka}
%\input{defsMerge-chka}
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%
% Definitions
%
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
\newcommand\rfit{{\em R}fit}
\newcommand\ckmfitter{{CKMfitter}}
\newcommand{\simgt}{\,\hbox{\lower0.6ex\hbox{$\sim$}\llap{\raise0.6ex\hbox{$>$}}}\,}
\newcommand{\simlt}{\,\hbox{\lower0.6ex\hbox{$\sim$}\llap{\raise0.6ex\hbox{$<$}}}\,}
%
%
%\newcommand{\Bbar} {\kern 0.18em\overline{\kern -0.18em B}{}\xspace}
\newcommand{\bra}[1]{\ensuremath{\langle #1 |}}
\newcommand{\ket}[1]{\ensuremath{| #1 \rangle }}
\newcommand{\CP}{\ensuremath{C\!P}}
\newcommand{\lt}{\left}
\newcommand{\rt}{\right}
\newcommand{\imag}{\mathrm{Im}\,}
\newcommand{\real}{\mathrm{Re}\,}
\newcommand{\dm}{\ensuremath{\Delta M}}
\newcommand{\dg}{\ensuremath{\Delta \Gamma}}
\newcommand{\ov}[1]{\bar{#1}}
\newcommand{\braket}[2]{\langle#1|#2\rangle}
\newcommand{\braOket}[3]{\langle#1|#2|#3\rangle}
\newcommand{\Bag}{\mathcal{B}}
\newcommand{\HatBag}{\hat{\mathcal{B}}}
\newcommand{\eq}[1]{Eq.~(\ref{#1})}
\newcommand{\eqsand}[2]{Eqs.~(\ref{#1}) and (\ref{#2})}
\newcommand{\fig}[1]{Fig.~\ref{#1}}
\newcommand{\bb}{\ensuremath{B\!-\!\Bbar{}\,}}
\newcommand{\dd}{\ensuremath{D\!-\!\Dbar{}\,}}
\newcommand{\kk}{\ensuremath{K\!-\!\Kbar{}\,}}
\newcommand{\bbms}{\bbs\ mixing}
\newcommand{\bbmd}{\bbd\ mixing}
\newcommand{\bbmq}{\bbq\ mixing}
\newcommand{\bbm}{\bb\ mixing}
\newcommand{\ddm}{\dd\ mixing}
\newcommand{\kkm}{\kk\ mixing}
\newcommand{\bbd}{\ensuremath{B_d\!-\!\Bbar{}_d\,}}
\newcommand{\bbs}{\ensuremath{B_s\!-\!\Bbar{}_s\,}}
\newcommand{\bbq}{\ensuremath{B_q\!-\!\Bbar{}_q\,}}
\newcommand{\Bbar}{\,\overline{\!B}}
\newcommand{\Dbar}{\,\overline{\!D}}
\newcommand{\Kbar}{\,\overline{\!K}}
\newcommand{\eins}{\mbox{$1 \hspace{-1.0mm} {\bf l}$}}
\newcommand{\gev}{\ensuremath{\, \mathrm{GeV}}}
\newcommand{\tev}{\ensuremath{\, \mathrm{TeV}}}
\newcommand{\etal}{\emph{et al.}\xspace}
\newcommand{\Dzero}{D\O\xspace}
%\newcommand{\TeVatron}{Te$\mskip-.2\thinmuskip$Vatron\xspace}
\newcommand{\TeVatron}{Tevatron\xspace}
\newcommand{\OnlyBabarColl}{\babar\ collaboration\xspace}
\newcommand{\OnlyBelleColl}{Belle collaboration\xspace}
\newcommand{\OnlyDzeroColl}{\Dzero collaboration\xspace}
\newcommand{\OnlyCDFColl}{CDF collaboration\xspace}
\newcommand{\BabarColl}{[\babar\ collaboration]\xspace}
\newcommand{\BelleColl}{[Belle collaboration]\xspace}
\newcommand{\DzeroColl}{[\Dzero collaboration]\xspace}
\newcommand{\CDFColl}{[CDF collaboration]\xspace}
\newcommand{\arxiv}[1]{{arxiv:{#1}}}
\newcommand{\epm}[2]{
\raisebox{-0.5ex}{\shortstack[l]{$\scriptstyle+#1$\\$\scriptstyle-#2$}}}
\newcommand{\nn}{\nonumber\\}
\newcommand{\Bcal}{\mathcal{B}}
\usepackage{pstricks}
\newcmykcolor{darkgreen}{1 0 0.6 0.5} %% cyan magenta yellow black
\newcommand{\rd}{\color{red}}
\newcommand{\uli}{\rd} %% change to \newcommand{\uli}{} to switch off color
\newcommand{\martin}{\color{blue}} %% change to \newcommand{\martin}{} to switch off color
\def\journalL#1#2#3#4#5{\journal{#1 #2}{#3}{#4}{#5}}
\def\journal#1#2#3#4{#1~{\bf #2}, #3 (#4)}
\bibliographystyle{apsrev4-1}
%%%%%%%%%%%%%%%%% Begin document %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
%% \linenumbers
\preprint{TTP12-010}
\title{
%======
Joint analysis of Higgs decays and electroweak precision observables\\
in the Standard Model with a sequential fourth generation
}
\author{Otto Eberhardt$^{\,a}$, Geoffrey Herbert$^{\,b}$, Heiko
Lacker$^{\,b}$,\\ Alexander
Lenz$^{\,c}$, Andreas Menzel$^{\,b}$, Ulrich
Nierste$^{\,a}$, and Martin Wiebusch$^{\,a}$
\vspace{0.6cm}}
\affiliation{
\mbox{$^{a}$ Institut f\"ur Theoretische Teilchenphysik,
Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany,}
\mbox{email: otto.eberhardt@kit.edu, ulrich.nierste@kit.edu,
martin.wiebusch@kit.edu}\\
\mbox{$^{b}$ Humboldt-Universit\"at zu Berlin,
Institut f\"ur Physik,
Newtonstr. 15,
D-12489 Berlin, Germany,}\\
\mbox{e-mail: geoffrey.herbert@physik.hu-berlin.de,
lacker@physik.hu-berlin.de, amenzel@physik.hu-berlin.de}\\
\mbox{$^{c}$ CERN - Theory Divison, PH-TH, Case C01600, CH-1211 Geneva 23,
{e-mail: alenz@cern.ch}}
}
\date{\today}
\begin{abstract}
We analyse the impact of LHC and Tevatron Higgs data on the viability of the
Standard Model with a sequential fourth generation (SM4), assuming Dirac
neutrinos and a Higgs mass of 125 \gev. To this end we perform a combined fit to
the signal cross sections of $pp\to H\to \gamma\gamma,ZZ^*,WW^*$ at the LHC, to
$p\bar p\to VH\to Vb\bar b$ ($V=W,Z$) at the Tevatron and to the electroweak
precision observables. Fixing the mass of the fourth generation down-type quark
$b^\prime$ to 600$\,\gev$ we find best-fit values of $m_{t^\prime}=634\,\gev$,
$m_{l_4}=107.6\,\gev$ and $m_{\nu_4}=57.8\,\gev$ for the other fourth-generation
fermion masses. We compare the $\chi^2$ values and pulls of the different
observables in the three and four-generation case and show that the data is
better described by the three-generation Standard Model. We also investigate the
effects of mixing between the third and fourth-generation quarks and of a
future increased lower bound on the fourth-generation charged lepton mass
of $250\;\text{GeV}$.
\end{abstract}
\pacs{}
%========================================
\maketitle
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
While the Standard Model (SM) possesses a minimal boson field content,
it indulges itself in the luxury of replicated fermion generations. It
is difficult to predict the number of generations from fundamental
theoretical principles; the determination of the correct number of
fermion families is ultimately an experimental task. A sequential
fourth generation is non-decoupling, meaning that its effect on certain
observables does not vanish in the limit of infinitely heavy
fourth-generation fermions. Among these observables are the
gluon-fusion Higgs production cross section and the decay rate of $H\to
\gamma \gamma$. This feature makes the SM with four generations, SM4,
prone to be the first popular model of new physics on which the LHC will
speak a final verdict.
Within the three generation SM (SM3) the production cross section $\sigma(gg\to
H)$, which governs $pp\to H$ studied at the LHC, is dominated by a triangle
diagram with a top quark. While the loop diagram decreases as $1/m_t$ for $m_t
\to \infty$, this decrease is compensated by the linear growth of the top Yukawa
coupling $y_t \propto m_t$. Consequently, in the SM4 the new contributions from
the heavy $t^\prime$ and $b^\prime$ quarks will modify $\sigma(gg\to H)$ by a
term which is independent of $m_{t^\prime}$ and $m_{b^\prime}$ at the one-loop
level. One finds an increase by roughly a factor of 9, which seemingly entails a
corresponding increase in the LHC signal cross section of Higgs decays into
(virtual) gauge bosons, given by the product $\sigma(pp\to H)\,\Bcal(H\to
WW^*,ZZ^*,\gamma\gamma)$. However, higher-order corrections to the Higgs
production cross sections and branching ratios due to the fourth-generation
fermions can be substantial because of their large Yukawa couplings. In
\cite{Passarino:2011kv, Denner:2011vt} it was shown that, for light Higgs
bosons, the $H\to WW^*$ and $H\to ZZ^*$ branching ratios in the SM4 can be
suppressed by a factor of $0.2$ or less as compared to their SM3 values. In the
photonic Higgs decay rate $\Gamma(H\to \gamma\gamma)$ the destructive
interference between fermion and gauge boson mediated contributions even leads
to an accidental cancellation which would render the $H\to\gamma\gamma$ decay
unobservable. As pointed out in \cite{Djouadi:2012ae}, this leads to tensions
with the observed excesses in $H\to\gamma\gamma$ searches at LHC and the
searches for $H\to b\bar b$ in $HW$, $HZ$ associated production at the Tevatron.
In \cite{Khoze:2001ug, Belotsky:2002ym, Bulanov:2003ka, Rozanov:2010xi,
Keung:2011zc, Cetin:2011fp, Englert:2011us, Carpenter:2011wb} it was discussed
that the SM4 may permit the decay mode $H\to \nu_4\ov\nu_4$, where $\nu_4$
denotes the neutrino of the fourth generation. If the $\nu_4$ is sufficiently
long-lived, LHC triggers will not associate the $\nu_4$ decay with the primary
Higgs production and decay event, such that $H\to \nu_4\ov\nu_4$ will stay
undetected. That is, with present experimental techniques the mere effect of an
open $H\to \nu_4\ov\nu_4$ channel will be an increase of the total Higgs width
and thus a decrease of all other branching fractions. In this paper we will
only consider the case of Dirac neutrinos. The fourth-generation neutrino must
therefore be heavier than $M_Z/2$ to comply with the invisible $Z$ width
measured at LEP1. While a nonzero $H\to \nu_4\ov\nu_4$ decay rate can reconcile
the LHC data on $\sigma(pp\to H)\,\Bcal(H\to WW^*,ZZ^*)$ with the SM4, it will
only increase the tensions with the excesses in $H\to\gamma\gamma$ at the LHC
and $H\to b\bar b$ at the Tevatron.
As long as the observed excesses are inconclusive one must resort to a global
fit to all relevant observables to assess the viability of the SM4. The
non-decoupling property of the SM4 implies that the SM3 can not be considered as
a special case of the SM4 where some parameters are fixed. This actually
represents a conceptual problem for a standard frequentist analysis as the
choice of a suitable test statistic for the definition of $p$-values is no
longer straightforward. We do not attempt to solve this issue here. Instead we
simply compare the $\chi^2$ values of the two models and the pulls of the
individual observables. In all our fits we assume that the observed excesses in
$H\to\gamma\gamma$ and $H\to b\bar b$ searches are not statistical fluctuations
and we therefore fix the Higgs mass at $m_H=125\;\text{GeV}$.
Stringent constraints on the SM4 are also found from analyses of the electroweak
precision observables \cite{Nakamura:2010zzi}, because the extra fermions induce
non-decoupling contributions to the $W$ mass, partial $Z$ decay widths and
asymmetries which are very sensitive to the mass splittings within the fermionic
isospin doublets. It has been shown in Ref.~\cite{Novikov:2002tk, Frere:2004rh,
Novikov:2009kc, Kribs:2007nz, Eberhardt:2010bm} that the SM4 is compatible
with the experimental constraints from LEP if the $m_{t^\prime}$--$m_{b^\prime}$
and/or $m_{l_4}$--$m_{\nu_4}$ mass splittings are chosen properly. Here $l_4$
denotes the charged lepton of the fourth generation. In this letter we perform a
global fit to the parameters of the SM4, using the LHC data on the
abovementioned Higgs decays, Tevatron data on $H\to b \ov b$ and electroweak
precision data. We also discuss the impact of mixing between the third and
fourth-generation quarks as well as the impact of an increased lower bound on
the fourth generation charged lepton mass. For our fits we use the CKMfitter
package, which implements the Rfit procedure \cite{Hocker:2001xe}, a frequentist
statistical method.
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Methodology}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
The main topic of this letter is a combined fit of the following
(pseudo-)observables, which defines our analysis A1:
\begin{itemize}
\item[i)] the signal strengths $\hat\mu(pp\to H\to WW^*)$ measured by CMS
\cite{CMS-PAS-HIG-12-008} (defined below) and $\hat\mu(pp\to H\to ZZ^*)$
measured by CMS \cite{CMS-PAS-HIG-12-008} and ATLAS \cite{ATLAS:2012ac},
\item[ii)] the signal strengths $\hat\mu(VV\to H\to\gamma\gamma)$ and
$\hat\mu(gg\to H\to\gamma\gamma)$ for Higgs production via vector boson fusion
and gluon fusion, respectively, and subsequent decay into two photons as
measured by CMS \cite{CMS-PAS-HIG-12-001},
\item[iii)] the signal strength $\hat\mu(p\bar p\to HV\to Vb\bar b)$ for Higgs
production in association with a vector boson and subsequent decay into
a $b\bar b$ pair, as measured by CDF and D0 \cite{FisherMoriond},
\item[iv)] the electroweak precision observables (EWPOs) $M_Z$, $\Gamma_Z$,
$\sigma_\text{had}$, $A_\text{FB}^l$, $A_\text{FB}^c$, $A_\text{FB}^b$, $A_l$,
$A_c$, $A_b$, $R_l=\Gamma_{l^+l^-}/\Gamma_\text{had}$, $R_c$, $R_b$,
$\sin^2\theta_l^\text{eff}$ measured at LEP and SLC \cite{EWWG:2010vi} as well
as $m_t$, $M_W$, $\Gamma_W$ and $\Delta\alpha_\text{had}^{(5)}$
\cite{Nakamura:2010zzi}.
\item[v)] the lower bounds $m_{t^\prime,b^\prime}\gtrsim 600\;$\gev
(from the LHC) \cite{Aad:2012xc, Aad:2012us, CMS:2012ye, CMS-PAS-EXO-11-099}
and $m_{l_4}>101\,\text{GeV}$ (from LEP2) \cite{Nakamura:2010zzi}.
\end{itemize}
Here and in the following, the term ``signal strength'' refers to the ratio of
SM4 and SM3 signal cross sections evaluated with the same Higgs mass
\begin{equation}\label{eq:signalstrength}
\hat\mu(X\to H\to Y) = \frac{\sigma(X\to H)\Bcal(H\to Y)|_\text{SM4}}
{\sigma(X\to H)\Bcal(H\to Y)|_\text{SM3}}
\quad.
\end{equation}
where a signal cross section is given by the product of the Higgs production
cross section and a branching fraction into a certain final state.
When confronting the SM4 with electroweak precision data, the usual method is to
compute the oblique electroweak parameters $S$ and $T$ \cite{Peskin:1991sw}, and
compare the results to the best-fit values for $S$ and $T$ provided by the LEP
Electroweak Working Group \cite{EWWG:2010vi}. For the SM4, such studies were
done, for example, in Refs.~\cite{Nakamura:2010zzi, Kribs:2007nz, Erler:2010sk,
Eberhardt:2010bm}. However, it is well-known that the parametrisation of the
EWPOs (iv) by $S$ and $T$ becomes inaccurate when some of the fourth-generation
fermion masses are close to $M_Z$ or when the fourth-generation fermions mix
with the fermions of the first three generations. Since here, we are interested
in a scenario where $m_{\nu_4}250\;\text{GeV}$ as a function of $m_{\nu_4}$, minimized with respect
to all other parameters. We see that the $\chi^2$ is constant at a value of
$36$ for $m_{\nu_4}\gtrsim 160\;\text{GeV}$. For neutrino masses below
$160\;\text{GeV}$ the electroweak fit can no longer accomodate the large mass
splitting in the lepton sector and the $\chi^2$ blows up. Thus, for
$m_{l_4}>250\;\text{GeV}$ (and the case of Dirac neutrinos) the scenario with
the invisible $H\to\nu_4\bar\nu_4$ decay is completely ruled out by electroweak
precision observables.
\begin{figure}
\includegraphics[width=0.4\textwidth,bb=132 476 484 715,clip=true]{mnu4250.pdf}
\caption{Minimum $\chi^2$ values in the analysis A1 for
$m_{l_4}>250\;\text{GeV}$ as a function of the (fixed) neutrino mass
$m_{\nu_4}$. The dotted lines indicate the corresponding SM3 minimal
$\chi^2$ value.}
\label{fig:chi2}
\end{figure}
The impact of mixing between the third and fourth generation quark is negligible
in the analysis A1. The fit prefers $\theta_{34}=0$ and therefore cannot be
improved by letting $\theta_{34}$ float. The constraint on $\theta_{34}$ imposed
by EWPOs and Higgs signal strengths can be studied by using the difference
between the minimal $\chi^2$ in the SM4 with $\theta_{34}$ free and
$\theta_{34}$ fixed as a test statistic. Since we are now comparing two
different realisations of the same model (SM4) there is no problem with the
conversion of $\chi^2$ values to $p$-values. Fig.~\ref{fig:theta34} shows the
$p$-value as a fuction $\theta_{34}$. We see that Higgs signal strengths and
EWPOs require $\theta_{34}\lesssim 0.08$. However, this picture could change
dramatically if flavour observables were included in the fit: A recent analysis
shows that the SM3 fails to describe flavour physics observables at the level of
$2.7\sigma$ \cite{Lenz:2010gu, Lenz:2012az, Bevan:2010gi, Lunghi:2010gv}. Since
the SM4 can alleviate the discrepancies in the flavour data, the overall picture
may still change in favour of the SM4 in a complete analysis of Higgs decay,
electroweak precision, and flavour data. Such an analysis is beyond the scope of
this letter.
\begin{figure}
\includegraphics[width=0.4\textwidth,bb=133 477 477 712,clip=true]{theta34.pdf}
\caption{$p$-value scan of the CKM mixing angle $\theta_{34}$ between the
third and fourth generation quarks in the analysis A1.}
\label{fig:theta34}
\end{figure}
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Conclusions}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
Assuming a Higgs mass of $125\;\text{GeV}$ we have performed a global fit to the
parameters of the SM4, combining data on electroweak precision physics and five
different Higgs searches: $H\to\gamma\gamma$ produced by gluon fusion at the
LHC, $H\to\gamma\gamma$ produced by vector boson fusion at the LHC, inclusive
searches for $H\to WW,ZZ$ at the LHC and $W$,$Z$ associated production and decay
to $b\bar b$ at the Tevatron. With the exception of the inclusive $H\to ZZ$
search the pulls of the signal cross sections in the SM4 exceed those of the SM3
by $0.5\sigma$ or more. Also the electroweak precision observables are described
better in the SM3. With a lower bound of $100\;\text{GeV}$ on the
fourth-generation charged lepton mass the best-fit SM4 scenario has a
fourth-generation neutrino mass around $60\;\text{GeV}$, i.e.\ just below the
$H\to\nu_4\bar\nu_4$ threshold. If the lower bound on the fourth-generation
charged lepton mass moves up to $250\;\text{GeV}$ the electroweak precision
observables constrain $m_{\nu_4}$ to be larger than approximately
$160\;\text{GeV}$ and scenarios with invisible $H\to\nu_4\bar\nu_4$ decays are
ruled out. The mixing angle $\theta_{34}$ between the third and fourth
generation quarks is constrained to be smaller than $0.08$. However,
since the SM4 can alleviate the discrepancies in flavour observables, the
overall picture may still change in favour of the SM4 when flavour observables
are included in the fit. On the basis of electroweak precision data and Higgs
searches alone the SM4 is certainly disfavoured. A quantitative comparison of
the SM3 and SM4 in terms of $p$-values is problematic because the non-decoupling
nature of the SM4 fermions is fundamentally incompatible with standard
frequentist methods. We hope to shed more light on this subject in a future
publication.
\acknowledgments
We would like to thank Julien Baglio for fruitful discussions and his help with
the VBF cross sections. We acknowledge support by DFG through grants NI1105/2-1
and LA 2541/1-1. A.L.\ is further supported by DFG through a Heisenberg
fellowship.
\bibliography{sm4higgs}
%% \begin{thebibliography}{99}
%% %1
%% \bibitem{turks}
%% cite the Turkish paper on $H\to \nu_4\ov\nu_4$ here.
%% %2
%% \bibitem{ewpos}
%% Peskin, Takeuchi...
%% %3
%% \bibitem{spanno}
%% Spannowsky...
%% %4
%% \bibitem{rfit}
%% cite the CKMfitter paper explaining the Rfit method here
%% %5
%% \bibitem{cmszzww}
%% cite CMS paper on $H\to WW,ZZ$ here
%% \bibitem{atlaszzww}
%% cite ATLAS paper on $H\to WW,ZZ$ here
%% \bibitem{cmsgaga}
%% cite CMS paper on $H\to \gamma\gamma$ here
%% \bibitem{atlasgaga}
%% cite ATLAS paper on $H\to \gamma\gamma$ here
%% %
%% \bibitem{PDG}
%% K.~Nakamura {\it et al.} [Particle Data Group],
%% %``Review of particle physics,''
%% J.\ Phys.\ G {\bf 37} (2010) 075021, and 2011 partial update for the 2012 edition.
%% %%CITATION = JPHGB,G37,075021;%%
%% %6
%% \bibitem{dirsearch}
%% cite the direct search papers here, leading to the lower bound on
%% $m_{b^\prime}$.
%% \bibitem{dirsearchl}
%% cite the direct seach paper here for $m_{l_4}$ bound.
%% %6.5
%% \bibitem{dg}
%% A.~Djouadi and P.~Gambino,
%% %``Leading electroweak correction to Higgs boson production at proton
%% %colliders,''
%% Phys.\ Rev.\ Lett.\ {\bf 73} (1994) 2528
%% [hep-ph/9406432].
%% %%CITATION = HEP-PH/9406432;%%
%% A.~Djouadi, P.~Gambino and B.~A.~Kniehl,
%% %``Two loop electroweak heavy fermion corrections to Higgs boson
%% %production and decay,''
%% Nucl.\ Phys.\ B {\bf 523} (1998) 17
%% [hep-ph/9712330].
%% %%CITATION = HEP-PH/9712330;%%
%% %7
%% \bibitem{hdec}
%% ...cite H decay reference here...
%% %8
%% \bibitem{ddmpssuw}
%% A.~Denner, S.~Dittmaier, A.~Muck, G.~Passarino, M.~Spira, C.~Sturm,
%% S.~Uccirati and M.~M.~Weber,
%% %``Higgs production and decay with a fourth Standard-Model-like
%% %fermion generation,''
%% arXiv:1111.6395 [hep-ph].
%% %%CITATION = ARXIV:1111.6395;%%
%% %
%% \bibitem{Lenz:2012az}
%% A.~Lenz {\it et al.},
%% %``New Physics in B-Bbar mixing in the light of recent LHCb data,''
%% arXiv:1203.0238 [hep-ph].
%% %%CITATION = ARXIV:1203.0238;%%
%% For details of the analysis method see:
%% A.~Lenz {\it et al.},
%% %``Anatomy of New Physics in B-Bbar mixing,''
%% Phys.\ Rev.\ D {\bf 83} (2011) 036004
%% [arXiv:1008.1593 [hep-ph]].
%% %%CITATION = PHRVA,D83,036004;%%
%% %5
%% %6
%% % \bibitem{bbln}
%% \bibitem{ln}
%% M.~Beneke, G.~Buchalla, A.~Lenz and U.~Nierste,
%% %``CP asymmetry in flavor specific B decays beyond leading logarithms,''
%% Phys. Lett. B 576 (2003) 173,
%% arXiv:hep-ph/0307344.
%% %%CITATION = PHLTA,B576,173;%%
%% A.~Lenz and U.~Nierste,
%% %``Theoretical update of $B_s$--$\bar B_s$ mixing,''
%% JHEP 0706 (2007) 072,
%% arXiv:hep-ph/0612167.
%% %% CITATION = JHEPA,0706,072;%%
%% A.~Lenz and U.~Nierste,
%% %``Numerical updates of lifetimes and mixing parameters of B mesons,''
%% arXiv:1102.4274 [hep-ph].
%% %%CITATION = ARXIV:1102.4274;%%
%% %9
%% \bibitem{Abazov:2011yk}
%% V.~M.~Abazov {\it et al.} [D0 Collaboration],
%% %``Evidence for an anomalous like-sign dimuon charge asymmetry,''
%% Phys.\ Rev.\ D {\bf 82} (2010) 032001
%% [arXiv:1005.2757 [hep-ex]] and
%% %``Evidence for an anomalous like-sign dimuon charge asymmetry,''
%% Phys.\ Rev.\ Lett.\ {\bf 105} (2010) 081801
%% [arXiv:1007.0395 [hep-ex]].
%% %%CITATION = ARXIV:1007.0395;%%
%% V.~M.~Abazov {\it et al.} [D0 Collaboration],
%% %%``Measurement of the anomalous like-sign dimuon charge asymmetry with
%% %%9 fb^-1 of p pbar collisions,''
%% Phys.\ Rev.\ D {\bf 84} (2011) 052007
%% [arXiv:1106.6308 [hep-ex]].
%% %%CITATION = ARXIV:1106.6308;%%
%% \end{thebibliography}
\end{document}