= LPAIR Analysis =

[[PageOutline]]

== Introduction ==

This investigation is meant to study the parton distribution functions (`PDF`) being used in the [[http://www.desy.de/~heramc/programs/lpair/lpair.pdf|LPAIR Monte Carlo generator]] w.r.t. the inelastic collision when the incoming proton breaks up into a hadronic final state. This analysis was motivated by the observation of a deficit on the number of events in the transverse momentum (p,,T,,) distributions of dimuons from data when compated to the predictions from `LPAIR` (Figure 6 in [[http://arxiv.org/abs/arXiv:1305.5596|CMS-FSQ-12-010]]). A possible reason for such disagreement may be related to the PDF being employed by `LPAIR` to compute the contribution of proton dissociation. 

There are currently two versions of this Monte Carlo generator (which can be found [[http://cmssw.cvs.cern.ch/cgi-bin/cmssw.cgi/UserCode/Forthomme/lpair/|here]]) studying two different kind of processes:

1. `DESY` version: developed for electron-proton collisions in HERA, with built-in option for proton-proton collisions as //test//. This version allows one to study elastic and inelastic (single dissociation) processes for the production of dileptons; and

2. `CDF` version: improved version which allows one to study elastic and double dissociation processes with more phase-space cuts available.

In this current analysis, we focus in the exclusive dimuon production, γγ -> μ^+^μ^-^, in inelastic collisions (single dissociation). LPAIR makes use of the [[http://home.thep.lu.se/~torbjorn/pythiaaux/introduction.html|JetSet]] library present in [[http://home.thep.lu.se/~torbjorn/pythiaaux/present.html|Pythia]] in order to perform the hadronization of the proton remnants.

The built-in options for proton dissociation in LPAIR make use of two parametrizations for the parton densities inside the proton, namely:

1. `SURI-YENNIE` [[http://www.sciencedirect.com/science/article/pii/0003491672902424|Ann. of Phys. 72 (1972) 243]] with option `11`; and

2. `BRASSE` [[http://www.sciencedirect.com/science/article/pii/0550321376902315|Nucl. Phys. B110 (1976) 413]] with option `12` in the `LPAIR` card. This parametrization is restricted: M,,X,, < 2 GeV and Q^2^ < 5 GeV^2^.

Due to the larger hadronic masses and p,,T,, distributions of the dimuon pair probed in the LHC kinematical regime, we employ SURI-YENNIE in this analysis.

Following the implementation made by Dariusz Bocian (IFJ-PAN, Krakow) [[http://th-www.if.uj.edu.pl/acta/vol35/abs/v35p2417.htm|Acta Phys. Polon. B35 (2004) 2417]], the current `LPAIR` code (`DESY` version) was modified in order to account for the proton-nucleus collisions from previous studies. Then, LPAIR samples are produced as `HBOOK` files, which have to be converted to `ROOT` files using the [[http://root.cern.ch/root/HowtoConvert.html|h2root]] script provided by [[http://root.cern.ch/drupal/|ROOT]].

In case one has several `ROOT` files to merge, the [[http://root.cern.ch/drupal/content/how-merge-histogram-files|hadd]] script is employed.


== Set up ==

=== Code changes ===

A few changes are made in the code to have access to more information about the particles in the event sample produced in `LPAIR`, especially to distinguish the muons from the exclusive production from the remnants from the proton break up. Then, two changes are made in the file //ilpair-cms-pp.f// in order to store information from `JetSet` in the `HBOOK` files:

1. particle status code, //ks//, at line 246; and

2. particle parentage, //icode//, at line 248.

Also, taking advantage for the fact that `LPAIR` performs the theoretical calculation in terms of Q^2^, the p,,T,, cut is internally applied by means of a Q^2^ cut in file //peripp.f// at line 29.


=== Event samples ===

The samples are produced with 1 million (1M) events, to check the shape of all kinematic distributions, and 5 million (5M) events in order to have enough statistics for high-p,,T,, dimuons. For the former, the samples are produced by merging ten sub-samples containing 100k events, which are obtained by running `LPAIR` at a time. while for the latter, five samples of 1M events by applying cuts on Q^2^: 0-1, 1-5, 5-20, 20-50, and 50-100 GeV^2^. The production of each of the sample with 1M events follows the same procedure as for 1M events for the whole Q^2^ range.

It is worth to notice that the histograms in the distributions with 5M events are **stacked**, and each individual set of events can be distinguished by the lines crossing vertically the histogram.


=== Structure functions ===

The W,,1,, and W,,2,, structure functions are defined in terms of the parton densities in the proton:

F,,2,, = (4/9)*(u,,val,, + 2*u,,sea,,) + (1/9)*(d,,val,, + 2*d,,sea,,) + (1/9)*2*s,,sea,,

F,,1,, = F,,2,,/2x

with Q^2^ = Q^2^,,min,, for the region below the Q^2^,,min,, of each parametrization.

The built-in PDFs in `LPAIR` are replaced by two paramatrizations for the parton densities:

1. Glueck-Reya-Vogt (`GRV`) [[http://dx.doi.org/10.1007/s100520050289|Eur. Phys. J. '''C5''' (1998) 461]]: version `GRV95` at leading order (`LO`) in α,,s,,.

 * 0.4 < Q^2^/GeV^2^ < 1.E6;
 * 1.E-5 < x < 1.

[[source:trunk/plots/PDFs/GRV/README|README]]

2. Parametrization by Fiore et al [[http://epja.epj.org/articles/epja/abs/2002/10/100500505/100500505.html|Eur. Phys. J. '''A15''' (2002) 505]].

>**Abstract**: An explicit model realizing parton-hadron duality and fiting the data is suggested. Complex nonlinear Regge trajectories are important ingredients of the 
>model. The inclusion of ∆ and N^∗^ trajectories should account for all resonances in the direct channel. The exotic trajectory is responsible for the smooth background.

This parametrization is meant to fit the data for the low Q^2^ region, reproducing the resonances of low-mass mesons. The figure below shows the distribution F,,2,, vs. `x` for Q^2^ = 0.5 GeV^2^:

[[Image(source:/trunk/plots/FIORE_F2_x.png, 500px)]]

3. Parametrization by `Martin-Ryskin-Stirling-Thorne` (`MRST` 2001) at leading order [[http://www.sciencedirect.com/science/article/pii/S0370269302014831|Phys. Lett. '''B531''' (2002) 216]]

 * 0.4 < Q^2^/GeV^2^ < 1.E6;
 * 1.E-5 < x < 1.

[[source:trunk/plots/PDFs/MRST2001/README|README]]

4. Parametrization by `Martin-Stirling-Thorne-Watt` (`MSTW` 2008) at leading order [[http://link.springer.com/article/10.1140%2Fepjc%2Fs10052-009-1072-5| Eur. Phys. J. '''C63''' (2009) 189]]

 * 1.25 < Q^2^/GeV^2^ < 1.E7;
 * 1.E-5 < x < 1.

[[source:trunk/plots/PDFs/MSTW2008/README|README]]

=== Variables ===

The final-state kinematics is used to make the distributions in terms of the variables of the interacting particles, like the photon virtuality, Q^2^, by:

> Q^2^ = [P,,p,,(E)-p,,rem,,(E)]^2^-[P,,p,,(x)-p,,rem,,(x)]^2^-[P,,p,,(y)-p,,rem,,(y)]^2^-[P,,p,,(z)-p,,rem,,(z)]^2^

and the momentum fraction of the proton carried by the photon, x, by

> x = Q^2^/(M,,X,,^2^-M,,p,,^2^+Q^2^),

with ξ given by

> ξ=`log`,,10,,(x)

=== Comparison between W,,1,, and W,,2,, Structure Functions ===

[[https://cp3.irmp.ucl.ac.be/projects/LpairAnalysis/wiki/W1W2StructFunc|Distributions]]


== Results ==

=== No experimental cuts ===

==== Cross sections ====

The predicted cross sections using each PDF for the parton densities are:

||= **PDF**           =||= **Cross section (pb)** =||
||= **`SURI-YENNIE`** =||  9262.   ||
||= **`FIORE`**       =||  10557.  ||
||= **`GRV`**         =||  7749.   ||

and when producing the sub-samples by Q^2^ cuts:

||= **PDF**           =||||||||||= **Cross section (pb)** =||
||= Q^2^ (GeV^2^)     =||= 0-1.        =||= 1.-5.  =||= 5.-20. =||= 20.-50. =||= 50.-100. =||
||= **`SURI-YENNIE`** =||  3379.41      ||  387.51  ||  73.95   ||  13.10    ||  3.86      ||
||= **`FIORE`**       =||  4140.11      ||  747.88  ||  40.18   ||  0.477    ||  0.0124    ||
||= **`GRV`**         =||  2439.74      ||  484.31  ||  105.41  ||  19.22    ||  5.51      ||

==== Distributions ====

The kinematic distributions are presented below for the sets of 1M and 5M events considering the possibilities for the parton densities.

OneMillionEvents

FiveMillionEvents

One should notice that the samples with 5M events show different distributions w.r.t. the fact that the five regions are produced with Q^2^ cuts, which comnpletely changes the p,,T,, distributions of the dileptons.


=== Experimental cuts ===

In order to have results closer to the observed results in the data analysis, event samples are produced within the experimental acceptance used for at trigger level in CMS:

1. p,,T,,(μ) > 10. GeV;

2. |η(μ)| < 2.5;

3. M(μ^+^μ^-^) > 10. GeV.

==== Cross sections ====

||= **PDF**           =||||= **Cross section (pb)** =||
||= M,,X,max,,        =||= 100 GeV =||= 300 GeV =||
||= **`SURI-YENNIE`** =||  0.82     ||  0.87     ||
||= **`GRV`**         =||  0.92     ||  1.01     ||

==== Distributions ====

The first set of plots shows the events restricted to a hadronic system with mass lower than **100 GeV**, while the second consider masses up to **300 GeV**.

[[https://cp3.irmp.ucl.ac.be/projects/LpairAnalysis/wiki/1MevtCutsMx100GeV|SURI-GRV: Distributions with 1M events for Mx > 100 GeV]]

[[https://cp3.irmp.ucl.ac.be/projects/LpairAnalysis/wiki/1MevtCutsMx300GeV|SURI-GRV: Distributions with 1M events for Mx > 300 GeV]]

[[https://cp3.irmp.ucl.ac.be/projects/LpairAnalysis/wiki/5MevtSURIGRVCutsMx300GeV|SURI-GRV: Distributions with 5M events for Mx > 300 GeV]]

[[https://cp3.irmp.ucl.ac.be/projects/LpairAnalysis/wiki/5MevtSURIGRVMRSTMSTWCutsMx300GeV|MRSTlo-MSTWlo-MSTWnlo: Distributions with 5M events for Mx > 300 GeV]]


=== Ratio ===

The comparisons are performed by the ratio between the distributions with experimental acceptance for the `SURI-YENNIE` and `GRV` parametrizations:

[[https://cp3.irmp.ucl.ac.be/projects/LpairAnalysis/wiki/RatioSURIGRVCutsMx300GeV|Ratio between SURI and GRV]]

[[https://cp3.irmp.ucl.ac.be/projects/LpairAnalysis/wiki/RatioSURIGRVMSTWMRSTCutsMx300GeV|Ratio between SURI, GRV, MSTW and MRST]] and normalized by the production cross section [[https://cp3.irmp.ucl.ac.be/projects/LpairAnalysis/wiki/RatioXsecSURIGRVMSTWMRSTCutsMx300GeV|here]]

== LPAIR++ ==

to be added