text:
\section{Introduction}
The study of flavour physics has allowed to test the Standard Model (SM) with an enormous increase of accuracy, as shown for instance by the few percent uncertainties in the Unitarity Triangle Analysis (UTA).
An even more interesting role of flavour physics that will be extensively explored in the LHC era is the search for New Physics (NP).
The discovery of NP effects in flavour observables, originated by new particles running in loops, in fact, could provide complementary information to collider direct searches.

Among flavour physics a privileged role is played by b-physics since it presents some advantages in non-perturbative calculations due to the large beauty quark mass ($m_b >> \Lambda_{\rm QCD}$ and therefore $\alpha_s(m_b) \sim 10^{-1}$) and for the wealth of b-observables sensitive to NP.
In particular, the large energy scale $m_b$ implies that soft gluons do not resolve the  spin and flavour of the heavy quark leading to the so-called Heavy Quark Symmetry (HQS), i.e. the invariance of strong interactions under the heavy spin-flavour group $SU(2 N_h)$. The large $m_b$ scale also allows to expand physical quantities in series of $\Lambda_{\rm QCD}/m_b$ through the so-called Heavy Quark Expansion (HQE), where (perturbative) short- and (non-perturbative) long-distance effects are separated.

In what follows we will discuss the status of the theoretical predictions of some of the most interesting b-physics observables that can be accurately measured at the LHC.
These are the $B$-decays that allow to extract the angles of the unitarity triangle (UT), the $B^0_s - \bar B^0_s$ mixing whose rapid oscillations can be measured at the LHC thanks to the large boost, and radiative and rare decays that are highly sensitive to NP.
We will also comment on two recent measurements that represent hot topics as they point towards the presence of NP.
One is the tagged analysis of $B_s \to J_{\Psi} \phi$ by the CDF~\cite{Aaltonen:2007he} and $D \emptyset$~\cite{:2008fj} collaborations that shows a significant deviation of the $B_s$ mixing phase from the SM one~\cite{Bona:2008jn}. The other is the difference between the direct CP-violation in charged $B^{\pm} \to K^{\pm} \pi^0$ decay and the neutral counterpart, which has been measured by the Belle collaboration to be significantly larger than in the SM~\cite{:2008zza}.

\section{Angles of the unitarity triangle}
The UTA has achieved an accuracy of few percent, without revealing any evidence for NP. In particular, a great success of the SM is represented by the good agreement between the measured UT sides and angles.
We note that a precise determination of the CKM parameters is not only an important test of the SM but also a key ingredient to improve the accuracy of the SM predictions in processes sensitive to NP.
In this section we focus on the three angles of the UT, that can all be determined from $B$ decays.

The golden method to determine the angle $\beta$ involves the $B \to J_{\Psi} K_S$ time-dependent CP-asymmetry that, dominated by one tree-level amplitude $b \to c \bar c s$, shows a simple and theoretically clean dependence on $\beta$.
Similar simplifications occur in other $b \to c \bar c s$ channels like $B$-decays to $\psi(2S) K_S$, $\chi_{c1} K_S$, $\eta_c K_S$, $J_{\Psi} K_L$, and $J_{\Psi} K^*$.
There are also determinations of $\beta$ that are sensitive to NP.
They can involve the decays $B \to \eta' K_{S,L}$  and $B \to \phi K_S$, described by the charmless $b \to s$ one-loop (penguin) amplitude.
The ambiguity between the angles $\beta$ and $\pi/2-\beta$, then, has been solved by measuring the positive sign of $\cos (2 \beta)$ from the time-dependent analysis of $B \to J_{\Psi} K^*$ and $B \to D \pi^0$ decays.
On the basis of the measurements mentioned above, the Heavy Flavour Averaging Group (HFAG) quotes the experimental value $\sin (2 \beta)=0.681\pm0.025$~\cite{HFAG}.
From the UTA, excluding the $\beta$ direct measurement, the UTfit collaboration finds $\sin (2 \beta)=0.744\pm0.039$~\cite{UTfit} that is larger than the experimental value, although compatible within the uncertainties.
It has been pointed out that this tension would disappear if instead of the inclusive-exclusive average for $|V_{ub}|$, only the exclusive $|V_{ub}|$ determination was used in the UTA.
The tension, indeed, originates from the difference between $|V_{ub}|_{\rm incl}=(43.1\pm3.9) \cdot 10^{-4}$ and $|V_{ub}|_{\rm excl}=(34.0\pm4.0) \cdot 10^{-4}$, with the inclusive determination affected by a model-dependence in the non-perturbative contribution of the threshold region.
This explanation is supported by a recent inclusive result $|V_{ub}|_{\rm incl}=(36.9\pm1.3\pm3.1)\cdot10^{-4}$~\cite{Aglietti:2007ik}, lower than the previous inclusive average and in agreement with the exclusive one, obtained with a model based on soft-gluon resummation and an analytic time-like QCD coupling.
More recently, in~\cite{Lunghi:2008aa} the experimental value of $\beta$ has been compared to a $V_{ub}$-independent determination based on the measurements of $|V_{cb}|$, $\Delta M_s/\Delta M_d$ and $\epsilon_K$.
They use for the kaon bag parameter the unquenched lattice result obtained by the RBC collaboration~\cite{Antonio:2007pb} at fixed lattice spacing, $\hat B_K =0.720 \pm 0.013 \pm 0.037$, thus finding $\sin (2 \beta)=0.82 \pm 0.09$, which deviates by around $1.5 \sigma$ from the experimental average.
We believe, however, that before interpreting this deviation as a NP signal, it is important to extrapolate $B_K$ to the continuum limit to further control lattice discretization effects that have been found to be relevant in quenched determinations of $B_K$.

The angle $\alpha$, related to the phase of $V_{ub}$ ($\alpha \equiv arg[-V_{td} V_{tb}^* / (V_{ud} V_{ub}^*)]$), appears in tree-level $b \to u \bar u d$ transitions which describe charmless B decays like $B \to \pi \pi$, $B \to \rho \rho$, and $B \to \rho \pi$.
These decays receive also a contribution from penguin amplitudes with different CKM factors, that can disentangled by analysing a large set of branching ratios and CP-asymmetries.
The measurements in the $\pi \pi$, $\rho \rho$ and $\rho \pi$ channels have led to the direct determination $\alpha=(91\pm4)^\circ$~\cite{Bona:2005vz} where the main theoretical uncertainty comes from final state interactions and isospin violations in electroweak penguins.
From the UTA, excluding the $\alpha$ direct measurement, the UTfit collaboration finds $\alpha=(91\pm6)^\circ$~\cite{UTfit}, in perfect agreement with the direct experimental determination.
We note that the region $\alpha \sim 0^\circ$, that would be unphysical as it would imply no CP-violation, is ruled out by simple observations on the hadronic matrix elements~\cite{Bona:2007qta}.

The angle $\gamma$, defined by $V_{ub} = |V_{ub}| e^{-i \gamma}$, can be determined from $B \to D K $ decays, where an amplitude interference occurs.
In fact, the decay $B^+ \to D K^+$ can produce both a $D^0$ and a $\bar D^0$, via the tree-level $\bar b \to \bar c u \bar s$ and $\bar b \to \bar u c \bar s$ amplitudes. The $D^0$ and $\bar D^0$ can decay to a common final state and the two corresponding amplitudes interfer with a relative phase $\delta_B \pm \gamma$ (for $B^\pm$), being $\delta_B$ the strong phase.
The irreducible theoretical uncertainty of this procedure comes from the neglection of $D^0-\bar D^0$ mixing effects and is very small, of the order of $0.1$\%.
The methods that have been proposed consider different final states: CP-eigenstates, doubly Cabibbo suppressed $D$ modes or three-body $D$ decaying modes.
The best direct determination of $\gamma$ comes from a combined analysis of many $D$ and $D^*$ modes and yields: $\gamma = (88\pm16)^\circ$~\cite{Bona:2005vz}, compatible with the result $\gamma = (65.1\pm6.5)^\circ$~\cite{UTfit} of the UTA with the exclusion of the direct $\gamma$ measurement.

\boldmath
\section{$B^0_q-\bar B^0_q$ ($q=d,s$) mixing and b-hadron lifetimes}
\unboldmath
The $B^0_q$-$\bar B^0_q$ system is described by an effective $2 \times 2$ Hamiltonian $\hat H^q = \hat M^q -i \hat \Gamma^q/2$ with the $\hat M^q$ and $\hat \Gamma^q$ matrices describing $B^0_q$-$\bar B^0_q$ oscillations and meson decays, respectively.

The oscillation frequency, given by the meson mass difference $\Delta M_q=2|\hat M_{12}^q|$ between the heavy and light mass eigenstates, requires the calculation of the so-called box-diagrams. The short-distance contribution is well known as the Wilson coefficient has been computed at the NLO in QCD~\cite{Buras:1990fn}.
The operator matrix element involves the decay constant $f_{B_q}$ and the bag parameter $B_{B_q}$, whose uncertainties have been reduced to the ten percent level thanks to recent lattice unquenched calculations (see~\cite{DellaMorte:2007ny} and refs. therein).

The $B_q$ meson lifetimes are calculated, instead, from the diagonal ($\Delta B=0$) elements of the $\hat \Gamma^q$ matrix, while the off-diagonal ($\Delta B=2$) elements provide the width difference $\Delta \Gamma_q$ and the semileptonic CP-asymmetry $A_{SL}^q$.
Both the $\Delta B=0$ and $\Delta B=2$ Wilson coefficients have been computed at the NLO in QCD and at the subleading order in the HQE.
The matrix elements of the leading (in the HQE) operators are known from lattice QCD, while some of the subleading operators are only estimated in the Vacuum Saturation Approximation and represent the main source of theoretical uncertainty.

We now discuss the comparison between theoretical predictions and experimental measurements, paying attention to possible signals of NP.
The $B^0_q-\bar B^0_q$ oscillation frequency has been measured for the first time in 2006 by the CDF collaboration, that found $\Delta M_s = (17.77 \pm 0.10 \pm 0.07)\cdot {\rm ps^{-1}}$~\cite{Abulencia:2006ze} in good agreement with the indirect determination $\Delta M_s = (17.5 \pm 2.1)\cdot {\rm ps^{-1}}$, from the UTA~\cite{UTfit}.
Among b-hadron lifetimes, particular attention goes to the $\Lambda_b$ baryon since, after the new CDF measurement~\cite{Abulencia:2006dr}, the experimental average has increased, leading to the experimental lifetime ratio $\tau(\Lambda_b)/\tau(B_d)=0.904 \pm 0.032$~\cite{HFAG} that is in agreement and slightly larger than the theoretical prediction $\tau(\Lambda_b)/\tau(B_d)=0.88 \pm 0.05$~\cite{Tarantino:2007nf}.
Concerning width differences and semileptonic CP-asymmetries, the theoretical predictions, though including corrections of NLO in QCD and subleading contributions in the HQE, are affected by a theoretical uncertainty of about $30$\% due to strong cancellations between them (see~\cite{Tarantino:2007nf} and refs. therein).
The corresponding experimental measurements still present much larger uncertainties that prevent from significant comparisons with the theoretical predictions. More accurate measurements are certainly looked forward.

The study of $B^0_q$-$\bar B^0_q$ mixing is particularly interesting for its sensitivity to NP. While the $\hat \Gamma^q$ matrix, describing the meson decay to lighter (SM) particles, is expected to be practically insensitive to NP, the $\hat M_{12}^q$ amplitude can receive visible contributions from NP particles running in the box-diagrams.
These effects can be parametrised in terms of a modulus $C_{B_q}$ and a phase $\phi_{B_q}$, respectively equal to one and zero in the SM, by $\hat M_{12}^q=(\hat M_{12}^q)_{\rm SM} C_{B_q} e^{2 i \phi_{B_q}}$.
We note that Minimal Flavour Violation (MFV) models, which do not introduce new sources of flavour violation in addition to the SM Yukawa couplings, are characterised by $\phi_{B_q}=0$.

For the $B_s$ system a very recent analysis~\cite{Bona:2008jn} finds that $\phi_{B_s}$ deviates by more than $3 \sigma$ from zero, signalling the presence of NP that violates MFV. This analysis combines all the available experimental information on $B_s$  mixing, including the new tagged analysis of $B_s \to J_{\Psi} \phi$ by the CDF~\cite{Bona:2008jn} and D$\emptyset$~\cite{:2008fj} collaborations. While no single measurement has a $3\sigma$ significance yet, all the constraints show a remarkable agreement with the combined result.
Updated Tevatron analyses and future high-precision measurements at the LHCb will be then of utmost importance.
We note that, due to the large dominance of the real part of $\Gamma_{12}^s/M_{12}^s$ over the imaginary part, also the semileptonic CP-asymmetry $A_{\rm SL}^s \simeq -Re(\Gamma_{12}^s/M_{12}^s)\,\sin(2\phi_{B_s})/C_{B_s}$ is highly sensitive to $\phi_{B_s}$.
Finally, some examples of NP models where a non-zero value of $\phi_{B_s}$ compatible with the Tevatron measurements is allowed, are the Minimal Supersymmetric Standard Model (MSSM) with a general flavour structure and the Littlest Higgs model with T-parity (LHT) where an enhancement of $A_{\rm SL}^s$ by $10$-$20$ times relative to the SM has been found to be possible~\cite{Blanke:2006sb}.

\section{Radiative and rare decays}
In this section we discuss the radiative and rare $B$ decays $b \to s \gamma$, $B^0_q \to \ell^+ \ell^-$ and $b \to s(d) \ell^+ \ell^-$, whose measurement at the LHC could provide a strong evidence of NP.

The inclusive decay $B \to X_s \gamma$ is highly sensitive to NP, being a FCNC decay forbidden at tree-level in the SM, and is also theoretically very clean.
The Wilson coefficients have been calculated at the NNLO in QCD and the large logarithms $\log(M_W^2/m_b^2)$ have been resummed using the renormalization group so that the remaining theoretical uncertainty is dominated by unknown $\mathcal{O}(\alpha_s \Lambda_{\rm QCD}/m_b)$ non-perturbative effects in four-fermion operators.
The theoretical prediction reads $Br(B \to X_s \gamma)=(3.15 \pm 0.23) \cdot 10^{-4}$~\cite{Misiak:2006zs} to be compared to the experimental average $Br(B \to X_s \gamma)=(3.55 \pm 0.24) \cdot 10^{-4}$~\cite{HFAG}, with the photon energy cut $E_{\gamma}>1.6$.
The theoretical and experimental results are compatible but a small positive NP effect is still allowed, which significantly constraints NP models.
It represents, for example, the strongest constraint on the one-universal extra-dimension model, yielding the lower bound on the inverse compactification scale $1/R >600\, {\rm GeV}$~\cite{Haisch:2007vb}.
Also in the MSSM the $B \to X_s \gamma$ decay represents an important constraint. Within MFV it points towards a light Higgs mass ($m_h \simeq 110\, {\rm GeV}$)~\cite{Buchmueller:2007zk} compatible with the LEP limit, and beyond MFV it can be translated within the mass insertion approach into a constraint on the non-diagonal entry $(\delta^d_{23})_{LR}$~\cite{Ciuchini:2006dx,Silvestrini:2007yf}.
In LHT it has been found that small ($\sim 4$\%) effects, in the direction of reducing the difference between theoretical and experimental results for $Br(B \to X_s \gamma)$, are possible~\cite{Blanke:2006sb}.

 The exclusive $b \to s \gamma$ decays are also very sensitive to NP, but theoretically less clean as they require the use of QCD factorization, where the main source of theoretical uncertainty is represented by non-perturbative form factors and light-cone distribution amplitudes.
They are known from lattice QCD~\cite{Becirevic:2006nm} and QCD sum rules on the light cone~\cite{Ball:2006eu}, respectively.
We note that the $B \to K^* \gamma$ decay is theoretically cleaner than $B \to \rho \gamma$ where $\mathcal{O}(\Lambda_{\rm QCD}/m_b)$ corrections turn out to be relevant, and that the t-dependent CP-asymmetries $A_{\rm CP}(B \to K^*(\rho) \gamma)$ are highly sensitive to NP due to their helicity suppression within the SM.
Recently, it has been pointed out that also the $B_s \to \phi \gamma$ channel is very promising~\cite{Muheim:2008vu}.
In the t-dependent $B_s \to \phi \gamma$ decay rate, in fact, the sizable $\Delta \Gamma_s$ width difference allows one to measure the coefficient of the $\sinh (\Delta \Gamma_s /2t)$ term, which is very sensitive to right-handed currents in $B \to V \gamma$ transitions.

Among $B_q \to \ell^+ \ell^-$ decays the $\mu^+ \mu^-$ modes are experimentally the most favourable, while the $e^+ e^-$ modes are suppressed by a further factor $m_e^2/m_{\mu}^2$ and the $\tau^+ \tau^-$ have other missing neutrinos from decaying $\tau$'s.
The CDF collaboration has found the experimental upper bounds $Br(B_d\to\mu^+ \mu^-)<1.8\cdot 10^{-8}$ and $Br(B_s\to\mu^+ \mu^-)<5.8\cdot 10^{-8}$ at the $95$\% confidence level~\cite{:2007kv}.
From the theoretical side these decays are very clean, because leptonic modes are affected by small non-perturbative uncertainties, and highly sensitive to NP, being FCNC processes forbidden at tree-level in the SM and dominated by a penguin operator with Wilson coefficient known at the NLO in QCD.
The SM theoretical predictions read $Br(B_d\to\mu^+ \mu^-)=(1.03\pm0.09)\cdot 10^{-10}$ and $Br(B_s\to\mu^+ \mu^-)=(3.35\pm0.32)\cdot 10^{-9}$~\cite{Blanke:2006ig} and, compared to the present experimental bounds above, show that there is still a lot of room for NP.
A promising way to look for NP in $B_q \to \mu^+ \mu^-$ decays is based on correlations between $Br(B_q\to\mu^+ \mu^-)$ and $\Delta M_q$ and between the $B_s$ and the $B_d$ branching ratios, that in the SM gives $Br(B_s \to \mu^+ \mu^-)/Br(B_d \to \mu^+ \mu^-)=32\pm2$~\cite{Blanke:2006ig}.
These correlations remain valid in MFV models without new operators in addition to the SM ones.
It will be very interesting to see if the LHC will find some deviations, signalling new operators or new sources of flavour violation w.r.t the SM.
Such deviations could represent a smoking gun for Higgs effects in the  MSSM with large $\tan \beta$, that induce $\tan^6 \beta$ enhanced contributions of new scalar and pseudoscalar operators~\cite{Babu:1999hn,Isidori:2006pk,Huang:1998vb}.

Other FCNC processes that are very sensitive to NP are the rare $b \to s(d) \ell^+ \ell^-$ decays, that in the SM are dominated by the electromagnetic dipole operator $Q_7^{\gamma}$ and the electroweak penguin operators $Q_9$ and $Q_{10}$.
In order to treat the long-distance contribution of $c \bar c$ resonances, two approaches have been used leading to a good control of the hadronic uncertainties of both inclusive and exclusive observables in certain phase-space regions.
The first one consists in introducing appropriate energy cuts, while in the second approach the resonances are modeled and some dispersion relations are used.
Concerning the inclusive $B \to X_s \ell^+ \ell^-$ decays, the Wilson coefficients are known at the NNLO in QCD, and the HQE contributions of order $\Lambda_{\rm QCD}^2/m_c^2$, $\Lambda_{\rm QCD}^2/m_b^2$ and $\Lambda_{\rm QCD}^3/m_b^3$ have been computed as well as QED corrections and bremmstrahlung effects.
The SM theoretical predictions read $Br(B \to X_s \mu^+ \mu^-)=(1.59 \pm 0.11) \cdot 10^{-6}$ and $Br(B \to X_s e^+ e^-)=(1.64 \pm 0.11) \cdot 10^{-6}$~\cite{Huber:2005ig}.
The comparison with future experimental measurements will be of great interest as these branching ratios are sensitive, through the interference between the Wilson coefficients $C_7$ and $C_9$, to NP.
A measurement of the corresponding forward-backward asymmetries would provide complementary information on possible NP effects, being sensitive to the products $C_7 C_{10}$ and $C_9 C_{10}$.
Within the exclusive channels the most promising one is $B \to K^* \ell^+ \ell^-$, and special attention, in the search for NP, is focused on the differential decay widths and the forward-backward and isospin asymmetries.
The SM theoretical predictions for the differential decay widths come from a study in terms of transversity amplitudes~\cite{Lee:2006gs} based on QCD factorization, with the main source uncertainty due to $\mathcal{O}(\Lambda_{\rm QCD}/m_b)$ corrections. NP effects will be visible here if the $C_9$ and $C_{10}$ coefficients turn out to be significantly modified w.r.t. the SM and/or the chirally flipped operators with Wilson coefficients $C'_9$ and $C'_{10}$ are present in the NP model.
A clean way to look for this effects consists in considering the muon to electron ratio where the theoretical uncertainty is enormously reduced up to $0.2$\% and it has been shown in a MFV analysis that NP effects of around $13$\% are possible~\cite{Hiller:2003js}.
In the forward-backward asymmetry and its zero $q_0^2$ the main source of uncertainty is represented by the hadronic inputs that have been obtained from QCD sum rules~\cite{Beneke:2001at} or from the experimental results on $B \to K^* \gamma$~\cite{Ali:2006ew}. A comparison with future measurements will be very useful in constraining NP, in particular the MSSM where significant deviations from the SM are expected~\cite{Ali:1999mm,Feldmann:2002iw}.
The isospin asymmetry plays a peculiar role as it is very small in the SM (it vanishes in the factorization approximation) and, therefore, could easily reveal a NP contribution.

We conclude this review commenting on a very recent result of the Belle collaboration~\cite{:2008zza} that could point out a signal of NP.
Belle has measured the charged and neutral direct CP-violating decay rate asymmetries, denoted as $A_{K^{\pm}\pi^0}$ and $A_{K^{\pm}\pi^{\mp}}$, respectively. For the charged $B$ meson $A_{K^{\pm}\pi^0}$ is the difference between the number of observed $B^- \to K^- \pi^0$ events versus $B^+ \to K^+ \pi^0$ events, normalized to their sum, and the analogous definition is valid for $A_{K^{\pm}\pi^{\mp}}$ in the neutral case.
The surprising result found by Belle is that the $A_{K^{\pm}\pi^0}$ and $A_{K^{\pm}\pi^{\mp}}$ are measured to be equal to $+7$\% and $-10$\%, respectively, with $A_{K^{\pm}\pi^0}-A_{K^{\pm}\pi^{\mp}}=+0.164\pm0.037$, in contrast with the vanishing result expected in the SM given the current uncertainties.
It will be of great interest to understand the origin of this discrepancy, if this is an evidence of NP or, instead, it reveals that our understanding of strong interaction effects need further clarification.

\vspace*{0.5cm}
I would like to thank the organizers of the {\it V Italian Workshop on the p-p Physics at the LHC} for the invitation to the pleasant workshop held in Perugia.


text:
\section{Inclusive diffraction measurement at the LHC}
In this section, we discuss potential measurements at the LHC that can constrain
the Pomeron structure, the colorless object which is exchanged in diffractive
interactions. The Pomeron structure in terms of quarks and gluons has been
derived from QCD fits at HERA and at the Tevatron and it is possible to probe this structure and the
QCD evolution at the LHC in a completely new kinematical domain.

\subsection{Jet production in double Pomeron exchanges processes}

The high energy and luminosity at the LHC allow the exploration of a
completely new kinematical domain. Once can first probe if the Pomeron is universal between
$ep$ and $pp$ colliders, or in other
other words, if we are sensitive to the same object at HERA and the LHC.
Tagging both diffractive protons in
ATLAS and CMS will allow the QCD evolution of the gluon and quark densities
in the Pomeron to be tested and compared with the HERA measurements. In addition,
it is possible to measure the gluon and quark densities
using the dijet and $\gamma + jet$ productions.
The different diagrams of the processes that can be studied at the LHC
are shown in Fig.~1, namely double pomeron exchange (DPE) production of dijets (left),
of $\gamma +$jet (middle), sensitive respectively to the gluon and quark contents of the
Pomeron, and the jet gap jet events (right).
As an example, we show in
Fig.2, the ratio of the number of events obtained for $\gamma+$jet and dijet production
for a luminosity of 300 pb$^{-1}$ when the protons are
tagged in the ATLAS Forward Physics detectors (AFP) at 210 m. The acceptance of the AFP
proton detectors at 210 m from the ATLAS interaction point (resp. 210 and 420 m) in terms
of proton energy loss is $0.015 <\xi<0.15$ (resp. $0.0015 < \xi < 0.15$). The acceptance is
similar for the CMS detector . Fig.~2 shows the potential of this
measurement to constrain further the quark density in the Pomeron. The QCD fits to the proton
diffractive structure functions and to the dijet cross section performed at HERA do not allow to
constrain the differences between the quark densities in the Pomeron, and the quark densities are
assumed to be equal in the fit ($u=\bar{u}=d=\bar{d}=s=\bar{s}$). At the LHC, we will be able to
test this hypothesis by constraining further the quark densities in the Pomeron as shown in
Fig.~2. Let us notice that the best observable is the ratio of the total diffractive mass computed by measuring
the two intact protons in the final state between $\gamma+$jet and dijet events since most
systematics uncertainties cancel in the ratio. Fig.~2 displays the ratio obtained for a luminosity
of 300 pb$^{-1}$ which corresponds to three weeks of data at ,low luminosity at the
LHC~\cite{matthias}.

\subsection{Jet gap jet production in double Pomeron exchanges processes}
This process is illustrated in Fig~1, right~\cite{jgjpap,fwd}. Both protons are intact
after the interaction and detected in AFP at 210 m, two jets are measured in the
ATLAS central detector and a gap devoid of any energy is present between
the two jets. This kind of event is important since it is sensitive to QCD
resummation dynamics given by the BFKL~\cite{bfkl}
evolution equation . This process has never been measured to date and will be
one of the best methods to probe these resummation effects, benefitting from
the fact that one can perform the measurement for jets separated by a large
angle (there is no remnants which `pollute' the event). As an example, the
cross section ratio for events with gaps to events with or without gaps
as a function of the leading jet $p_T$ is
shown in Fig~3 for 300 pb$^{-1}$. The measurement has to be performed at medium luminosity
at the LHC so that the gap between the jets is not ``polluted" by pile up events. The presence
of few pile up events in average is still possible for this measurement since central can be
identified using central tracks fitted to the main vertex of the event. It is worth noticing that
the ratio between the jet gap jet and the dijet cross sections in DPE events is of the order of 20\% which is
much higher than the expectations for non-diffractive events. This is due to the fact that the
survival probability of 0.03 at the LHC does need to be applied for diffarctive events.

\begin{figure}
\begin{center}
\epsfig{file=diagramme_incl.eps,width=7.5cm}
\caption{Inclusive diffractive diagrams. From left to right: jet production in inclusive double
pomeron exchange, $\gamma +$jet production in DPE, jet gap jet events}
\label{d0b}
\end{center}
\end{figure}

\begin{figure}[t]
\hfill
\begin{minipage}[t]{.45\textwidth}

\centerline{\includegraphics[width=1.2\columnwidth]{dsdmpratio_210.eps}}
\caption{Ratio between the $\gamma+$jet and dijet productions and sensitivity on the quark
structure in the Pomeron.}
\label{uncert1}

\end{minipage}
\hfill
\begin{minipage}[t]{.45\textwidth}

\centerline{\includegraphics[width=1.1\columnwidth]{dpejgj.eps}}
\caption{Ratio of DPE Jet gap jet events to standard DPE dijet events as a
function of the leading jet $p_T$~\cite{jgjpap}.}
\label{uncert2b}
\end{minipage}
\hfill
\end{figure}

\section{Exclusive jet and Higgs boson production at the LHC}

The Higgs and jet exclusive production in both Khoze Martin Ryskin~\cite{kmr}
(KMR) and
CHIDe~\cite{chide} models have been
implemented in the Forward Physics Monte Carlo (FPMC)~\cite{FPMC}, a generator
that has been designed to study forward physics, especially at the LHC. It aims
to provide a variety of diffractive processes in one common framework,
\textit{i.e.} single
diffraction, double pomeron exchange, central exclusive production and
two-photon exchange.

There are three main sources of uncertainties in exclusive models:
the gap survival probability which will be measured using the first
LHC data (in this study we
assume a value of 0.03 at the LHC for a center-of-mass energy of 14 TeV),
the unintegated gluon density which appears in the exclusive cross section
calculation and which contains the hard and the
soft part (contrary to the hard part, the soft one is not known precisely and
originates from a phenomenological parametrisation), and finally
the limits of the Sudakov integral which have not been all fixed by
theoretical calculations~\cite{usb,kmr}.

In order to constrain the uncertainty on the Higgs boson cross section,
we study the possible constraints using early LHC measurements of
exclusive jets using an integrated luminosity of 100 pb$^{-1}$. In
addition to the statistical uncertainties, we consider a conservative $3\%$ jet
energy scale uncertainty as the dominant contribution to the systematic error.
We obtain the
prediction for Higgs boson production as shown in Fig.~4 (yellow band).

In addition, it is possible to measure the exclusive jet cross section
(see the process in Fig.~6) at high jet $p_T$ at the LHC
benefitting from the high luminosity accumulated. The expectation
is shown in Fig.~5 for the ATLAS experiment as an example.
The results of the measurement are shown as
black points for a luminosity of 40 fb$^{-1}$ and 23 pile up events, assuming
the protons to be detected in AFP at 210 m~\cite{loi}.
The expected contributions from background (non-diffractive, single diffractive
with pile up and double pomeron exchange events) are shown as well as the
exclusive jet one in yellow. The statistical significance of the measurement is
up to 19$\sigma$.

\begin{figure}[t]
\hfill
\begin{minipage}[t]{.45\textwidth}

\centerline{\includegraphics[width=1.\columnwidth]{LhcHiggsGuess.eps}}
\caption{Total uncertainty for exclusive Higgs production at the LHC:
constraint provided by
the CDF measurements
and a possible measurement at the LHC with a luminosity of 100 pb$^{-1}$~\cite{usb}.}
\label{uncert1b}

\end{minipage}
\hfill
\begin{minipage}[t]{.45\textwidth}

\centerline{\includegraphics[width=1.1\columnwidth]{final2.eps}}
\caption{Measurement of the exclusive jet production at high jet $p_T$ at the LHC in the ATLAS
experiment~\cite{loi} .}
\label{uncert2}
\end{minipage}
\hfill
\end{figure}

\section{Exclusive $WW$ and $ZZ$ production}

In the Standard Model (SM) of particle physics, the couplings of fermions and
gauge bosons are constrained by the gauge symmetries of the Lagrangian.
The measurement of $W$ and $Z$ boson pair productions via the exchange of
two photons
allows to provide directly stringent tests
of one of the most important and least understood
mechanism in particle physics, namely the
electroweak symmetry breaking.

\subsection{Photon exchange processes in the SM}
The process that we intend to study is the $W$ pair production shown in Fig.~7
induced by the
exchange of two photons~\cite{us}. It is a pure QED process
in which the decay products of the $W$ bosons are measured in the central
detector and the scattered protons leave intact in
the beam pipe at very small angles and are detected in AFP.

After simple cuts to select exclusive $W$ pairs decaying into leptons, such
as a cut on the proton momentum loss of the proton ($0.0015<\xi<0.15$) --- we
assume the protons to be tagged in AFP at 210 and 420 m ---
on the transverse momentum of the leading and second leading leptons at 25 and
10 GeV respectively, on $\mbox{$\not\!\!E_{T}$}>20$ GeV, $\Delta \phi>2.7$ between leading
leptons, and $160<W<500$ GeV, the diffractive mass reconstructed using the
forward detectors, the background is found to be less than 1.7 event for 30
fb$^{-1}$ for a SM signal of 51 events~\cite{us}.

\begin{figure}[t]
\hfill
\begin{minipage}[t]{.35\textwidth}

\epsfig{file=diagramme_excl.eps,width=3.9cm}
\caption{Exclusive jet production.}

\end{minipage}
\hfill
\begin{minipage}[t]{.45\textwidth}

\epsfig{file=Fig1_anom.eps,width=5.cm}
\caption{Diagram showing the two-photon production of $W$ pairs.}

\end{minipage}
\hfill
\end{figure}

\begin{figure}
\begin{center}
\epsfig{file=ptleplead2_allcuts_hl.eps,width=8.cm}
\caption{Distribution of the transverse momentum of the leading lepton for
signal and background after the cut on $W$, $\mbox{$\not\!\!E_{T}$}$, and $\Delta \phi$ between
the two leptons~\cite{us}.}
\label{d0}
\end{center}
\end{figure}

\subsection{Quartic anomalous couplings}
The parameterization of the quartic couplings
based on \cite{Belanger:1992qh} is adopted.
The cuts to select quartic anomalous gauge coupling $WW$ events are similar as the
ones we mentioned in the previous section, namely $0.0015<\xi<0.15$ for the
tagged protons corresponding to the AFP detector at 210 and 420 m, $\mbox{$\not\!\!E_{T}$}>$ 20 GeV,
$\Delta \phi<3.13$ between the two leptons. In
addition, a cut on the $p_T$ of the leading lepton $p_T>160$ GeV and on the
diffractive mass $W>800$ GeV are requested since anomalous coupling events
appear at high mass. Fig~8 displays the $p_T$ distribution of the leading lepton
for signal and the different considered backgrounds.
After these requirements, we expect about 0.7 background
events for an expected signal of 17 events if the anomalous coupling is about
four orders of magnitude lower than the present LEP limit ($|a_0^W / \Lambda^2| =
5.4$ 10$^{-6}$) for a luminosity of 30 fb$^{-1}$. The strategy to select anomalous coupling $ZZ$ events is
analogous and the presence of three leptons or two like sign leptons are
requested.
Table 1 gives the reach on anomalous couplings at the LHC for
luminosities of 30 and 200 fb$^{-1}$ compared to the present OPAL limits~\cite{opal}. We note that we can gain almost
four orders of magnitude in the sensitivity to anomalous quartic gauge couplings
compared to LEP experiments, and it is possible to reach the values expected in
extra-dimension models. The tagging of the protons using the ATLAS Forward
Physics detectors is the only method at present to test so small values of
quartic anomalous couplings.

\begin{table}
\begin{center}
   \begin{tabular}{|c||c|c|c|}
    \hline

    Couplings &
    OPAL limits &
    \multicolumn{2}{c|}{Sensitivity @ $\mathcal{L} = 30$ (200) fb$^{-1}$} \\
    &  \small[GeV$^{-2}$] & 5$\sigma$ & 95\% CL \\
    \hline
    $a_0^W/\Lambda^2$ & [-0.020, 0.020] & 5.4 10$^{-6}$ & 2.6 10$^{-6}$\\
                      &                 & (2.7 10$^{-6}$) & (1.4 10$^{-6}$)\\ \hline
    $a_C^W/\Lambda^2$ & [-0.052, 0.037] & 2.0 10$^{-5}$ & 9.4 10$^{-6}$\\
                      &                 & (9.6 10$^{-6}$) & (5.2 10$^{-6}$)\\ \hline
    $a_0^Z/\Lambda^2$ & [-0.007, 0.023] & 1.4 10$^{-5}$ & 6.4 10$^{-6}$\\
                      &                 & (5.5 10$^{-6}$) & (2.5 10$^{-6}$)\\ \hline
    $a_C^Z/\Lambda^2$ & [-0.029, 0.029] & 5.2 10$^{-5}$ & 2.4 10$^{-5}$\\
                      &                 & (2.0 10$^{-5}$) & (9.2 10$^{-6}$)\\ \hline
    \hline
   \end{tabular}
\end{center}
\caption{Reach on anomalous couplings obtained in $\gamma$ induced processes
after tagging the protons in AFP compared to the present OPAL limits. The $5\sigma$ discovery and 95\%
C.L. limits are given for a luminosity of 30 and 200 fb$^{-1}$~\cite{us}}
\end{table}

The search for quartic anomalous couplings between $\gamma$ and $W$ bosons was
performed again after a full simulation of the ATLAS detector including pile
up~\cite{loi} assuming the protons to be tagged in AFP at 210 m only.
Integrated luminosities of 40 and 300 fb$^{-1}$ with,
respectively, 23 or 46 average pile-up
events per beam crossing have been considered. In order to reduce the
background, each $W$
is assumed to decay leptonically (note that the semi-leptonic case in under study).
The full list of background processes
used for the ATLAS measurement of Standard Model $WW$ cross-section was
simulated, namely $t \bar{t}$, $WW$, $WZ$, $ZZ$, $W+$jets, Drell-Yan and
single top events. In addition, the additional diffractive backgrounds
mentioned in the previous paragraph were also simulated,
The requirement of the presence of at least one
proton on each side of AFP within a time window of 10 ps allows us to reduce the
background by
a factor of about 200 (50) for $\mu =$ 23 (46). The $p_T$ of the leading
lepton originating from the
leptonic decay of the $W$ bosons is required to be
$p_T >$ 150 GeV, and that of the next-to-leading
lepton $p_T>$ 20 GeV. Additional requirement of the dilepton mass to
be above 300 GeV allows us to remove
most of the $Z$ and $WW$ events. Since only leptonic decays of the
W bosons are considered, we require in addition less than 3 tracks associated
to the primary vertex, which allows us to reject a large fraction of the
non-diffractive backgrounds (e.g. $t \bar{t}$, diboson
productions, $W+$jet, etc.) since they show much higher track multiplicities.
Remaining Drell-Yan and
QED backgrounds are suppressed by requiring the difference in azimuthal angle between the
two leptons $\Delta \phi <$ 3.1.  After these requirements, a similar
sensitivity with respect to fast simulation without pile up was obtained.

Of special interest will be also the search for anomalous quartic $\gamma \gamma \gamma
\gamma$ anomalous couplings which is now being implemented in the FPMC
generator. Let us notice that there is no present existing limit on such
coupling and the sensitivity using the forward proton detectors is expected to
be similar as the one for $\gamma \gamma WW$ or $\gamma \gamma ZZ$ anomalous
couplings. If discovered at the LHC, $\gamma \gamma \gamma
\gamma$ quartic anomalous couplings might be related to the existence of
extra-dimensions in the universe, which might lead to a reinterpretation of
some experiments in atomic physics. As an example, the Aspect photon correlation
experiments~\cite{aspect} might be interpreted via the existence of
extra-dimensions. Photons
could communicate through extra-dimensions and the deterministic interpretation
of Einstein for these experiments might be true if such anomalous
couplings exist. From the point of view of atomic physics, the results of the
Aspect experiments would depend on the distance of the two photon sources.

\section{Forward Proton Detectors in ATLAS and CMS}

In this section, we describe the proposal to install the ATLAS Forward
Proton (AFP)
detector in order to detect intact  protons at 206 and 214 meters on both side of
the ATLAS experiment~\cite{loi} (similar detectors will be installed around CMS
by TOTEM/CMS).
This one arm will consist of two sections (AFP1 and AFP2) contained in a special design of
beampipe or in more traditional roman pots. In the first section (AFP1),
a tracking station composed by 6 layers of Silicon detectors will be deployed.
The second station AFP2 will contain
another tracking station similar to the one already described and a timing
detector. In addition, a similar structure could be installed at about 420 m from the ATLAS
interaction point.
The aim of this setup, mirrored by an identical arm placed on the opposite side
of the ATLAS interaction point,
will be to tag the protons emerging intact from the $pp$ interactions so allowing ATLAS to exploit
the program of diffractive and photoproduction processes described in the previous sections.

\subsection{Movable beam pipes}
The idea of movable Hamburg beam pipes is quite simple~\cite{HBP}: a larger section of the
LHC beam pipe than the usual one
can move close to the beam using bellows so that the detectors located at its edge (called pocket)
can move close
to the beam by about 2.5 cm when the beam is stable (during injection, the detectors are in
parking position).
In its design, the
predominant aspect is the minimization of the thickness of the portions
called floor and window (see Fig.~ \ref{Figa}). Minimizing the depth of the floor ensures that the
detector can go as close to the beam as possible allowing us to detect protons scattered at very small
angles, while minimizing the depth of the thin window is important to keep the protons intact and
to reduce the impact of multiple interactions.
Two configurations exist for the movable beam pipes: the first one at 206 m form the ATLAS interaction
point hosts a Si detector
(floor length of about 100 mm) and the second one (floor
length of about 400 mm) the timing and the Si detectors. While it is still being discussed if the
movable beam pipe or the roman pot solution will be chosen at 210 m, it is clear that movable beam
pipes are favoured at 420 m since not enough space is available at this position and
new cryostats have been developped to host these movable beam pipes in the cold region at 420 m.
The usage of roman pots at 420 m would require a costly cryogenic bypass to be installed to isolate
the region where roman pots would be installed.

\begin{figure}
\centering
\includegraphics[width=3.5in]{hbp.eps}
\caption{Scheme of the movable beam pipe.}\label{Figa}
\end{figure}

\subsection{3D Silicon detectors}
The purpose of the tracker system is to measure points along the trajectory of
beam protons that are deflected at small angles as a result of collisions.
The tracker when combined with the LHC dipole and quadrupole magnets,
forms a powerful momentum spectrometer. Silicon tracker stations will be
installed in  Hamburg beam pipes or roman pots at $\pm$ 206 and $\pm$ 214 m from the
ATLAS interaction point (and also at 420 m later if these additional detectors are appoved).

The key requirements for the silicon  tracking system at 220~m are:
\begin{itemize}
\item Spatial resolution of $\sim$ 10 (30) $\mu$m per detector station in $x$ ($y$)
\item Angular resolution for a pair of detectors of about 1~$\mu$rad
\item High efficiency over the area of 20~mm $\times$ 20~mm corresponding to the distribution of
diffracted protons
\item Minimal dead space at the edge of the sensors allowing us to measure the scattered protons at
low angles
\item Sufficient radiation hardness in order to sustain the radiation at high luminosity
\item Capable of robust and reliable operation at high LHC luminosity
\end{itemize}

The basic building unit of the AFP detection system is a module consisting of
an assembly of a sensor array, on-sensor read-out chip(s), electrical services,
data acquisition and detector control system. The module will be
mounted on the mechanical support with embedded cooling and other necessary
services. The sensors are double sided 3D 50$\times$250 micron pixel detectors with slim-edge
dicing built by FBK and CNM companies. The sensor efficiency has been measured to be close to 100\%
over the full size in beam tests. A possible upgrade of this device will be to
use 3D edgeless Silicon
detectors built in a collaboration between SLAC, Manchester, Oslo, Bergen...
A new
front-end chip FE-I4 has been developed for the Si detector by the Insertable B Layer (IBL)
collaboration in ATLAS. The FE-I4 integrated circuit contains
readout circuitry for 26 880 hybrid pixels arranged in 80~columns on 250~$\mu$m
pitch by 336 rows on 50 $\mu$m pitch, and covers an area of about 19 mm
$\times$ 20 mm. It is designed in a 130 nm feature size bulk CMOS process.
Sensors must be DC coupled to FE-I4 with negative charge collection. The FE-I4
is very well suited to the AFP requirements: the granularity of cells provides
a sufficient spatial resolution, the chip is radiation hard enough
(up to a dose of 3~MGy),
and the size of the chip is sufficiently
large that one module can be served by just  one chip.

The dimensions of the individual cells in the FE-I4 chip are 50 $\mu$m $\times$
250 $\mu$m in the  $x$ and $y$ directions, respectively.
Therefore to achieve the required position resolution in the
$x$-direction of $\sim$ 10 $\mu$m, six layers with sensors are required
(this gives  50/$\sqrt{12}$/$\sqrt{5}\sim 7$ $\mu$m in $x$ and roughly 5 times
worse in $y$). Offsetting planes alternately to the left and right by one half
pixel will give a further reduction in resolution of at least 30\%.
The AFP sensors are expected to be exposed to a dose of 30~kGy
per year at the full LHC luminosity of 10$^{34}$cm$^{-2}$s$^{-1}$.

\subsection{Timing detectors}

A fast timing system that can precisely measure the time difference between
outgoing scattered protons is a key component of the AFP detector.  The
time difference is equivalent to a constraint on the event vertex, thus
the AFP timing detector can be used to reject overlap background by
establishing that the two scattered protons did not originate from the same
vertex as the the central system.  The final timing
system should have the following characteristics~\cite{timing}:
\begin{itemize}
\item 10 ps or better resolution (which leads to a factor 40 rejection on pile up
background)
\item Efficiency close to 100\% over the full detector coverage
\item High rate capability (there is a bunch crossing every 25 ns at the nominal LHC)
\item Enough segmentation for multi-proton timing
\item Level trigger capability
\end{itemize}

Figure~\ref{fig5_timesys} shows a schematic overview of the first proposed
timing system, consisting of a quartz-based Cerenkov detector coupled to
a microchannel plate photomultiplier tube (MCP-PMT), followed by the
electronic elements  that amplify, measure, and record the time of the event
along with a stabilized reference clock signal. The
QUARTIC detector consists of  an array of 8$\times$4 fused
silica bars ranging in length from about 8 to 12 cm and oriented at the
average Cerenkov angle.  A proton that is sufficiently deflected from the beam axis will pass
through a row of eight bars emitting Cerenkov photons providing an overall time resolution that is
approximately $\sqrt{8}$ times smaller than the single bar resolution of about 30 ps,
thus approaching the 10 ps resolution goal. Prototype tests have generally been performed on one row
(8 channels) of 5 mm $\times$ 5 mm pixels, while the initial detector is foreseen to have four rows
to obtain full acceptance out to 20  mm from the beam. The beam tests lead to a time resolution per
bar of the order of 34 ps. The different components of the timing resolution are given in
Fig.~\ref{timresol}. The upgraded design of the timing detector has equal rate pixels,
and we plan to reduce the the width of detector bins
close to the beam, where the proton density is highest.

At higher luminosity of the LHC (phase I starting in 2019), higher pixelisation of the timing detector
will be required. For this sake, a R\&D phase concerning timing detector
developments based on Silicon photomultipliers (SiPMs),
avalanche photodiods (APDs), quartz fibers, diamonds has started. In parallel, a new timing readout chip has
been developed in Saclay. It uses waveform sampling methods which give the best possible timing resolution. The
aim of this chip called SAMPIC~\cite{sampic}  (see Fig.~12) is to obtain sub 10 ps timing resolution, 1GHz input bandwidth, no dead
time at the LHC, and data taking at 2 Gigasamples per second. The cost per channel is estimated to be
of the order for \$10 which a considerable improvement to the present cost of a
few \$1000 per channel,
allowing us to use this chip in medical applications such as PET imaging detectors. The holy grail of
imaging 10 picosecond PET detector seems now to be feasible: with a resolution better than 20 ps,
image reconstruction is no longer necessary and real-time image formation becomes
possible.

\section{Acknowledgments}
The author thanks for the financial support from the CAPES/COFECUB exchange program number Ph74412 and from
the local organisers..

\begin{figure}
\centering
\includegraphics[width=3.5in]{quartic_drawing.eps}
\vspace*{-0.1in}
  \caption{A schematic diagram of the QUARTIC fast timing detector.
   } \label{fig5_timesys}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=3.in]{table_timing.eps}
  \caption{Different components of the timing detector resolution~\cite{timing}.
   } \label{timresol}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=3.in]{sampic.eps}
\caption{Scheme of the sampic chip.}\label{Figa}
\end{figure}

\input{bibliography}

\end{document}

redpajama_set_name: RedPajamaArXiv