LPAIR Analysis

Introduction

This investigation is meant to study the parton distribution functions (PDF) being used in the ​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 ​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 ​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 ​JetSet library present in ​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 ​Ann. of Phys. 72 (1972) 243 with option 11; and

2. BRASSE ​DESY 76/11 (1976) with option 12 in the LPAIR card. This parametrization is restricted: M_X < 2 GeV and Q² < 5 GeV².

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) ​Acta Phys.Polon. B35 (2004) 2417-2424, 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 ​h2root script provided by ​ROOT.

In case one has several ROOT files to merge, the ​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 Q², the p_T cut is internally applied by means of a Q² 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 Q²: 0-1, 1-5, 5-20, 20-50, and 50-100 GeV². The production of each of the sample with 1M events follows the same procedure as for 1M events for the whole Q² 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 built-in PDFs in LPAIR are replaced by two paramatrizations for the parton densities:

1. Glueck-Reya-Vogt (GRV) ​Eur.Phys.J. C5 (1998) 461-470: version GRV95 at leading order (LO) in α_s.

   * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
   *                                                                   *
   *     G R V  -  P R O T O N  - P A R A M E T R I Z A T I O N S      *
   *                                                                   *
   *                          1998 UPDATE                              *
   *                                                                   *
   *                  For a detailed explanation see                   *
   *                   M. Glueck, E. Reya, A. Vogt :                   *
   *        hep-ph/9806404  =  DO-TH 98/07  =  WUE-ITP-98-019          *
   *                  (To appear in Eur. Phys. J. C)                   *
   *                                                                   *
   *   This package contains subroutines returning the light-parton    *
   *   distributions in NLO (for the MSbar and DIS schemes) and LO;    * 
   *   the respective light-parton, charm, and bottom contributions    *
   *   to F2(electromagnetic); and the scale dependence of alpha_s.    *
   *                                                                   *
   *   The parton densities and F2 values are calculated from inter-   *
   *   polation grids covering the regions                             *
   *         Q^2/GeV^2  between   0.8   and  1.E6 ( 1.E4 for F2 )      *
   *            x       between  1.E-9  and   1.                       *
   *   Any call outside these regions stops the program execution.     *
   *                                                                   *
   *   At Q^2 = MZ^2, alpha_s reads  0.114 (0.125) in NLO (LO); the    *
   *   heavy quark thresholds, QH^2 = mh^2, in the beta function are   *
   *            mc = 1.4 GeV,  mb = 4.5 GeV,  mt = 175 GeV.            *
   *   Note that the NLO alpha_s running is different from GRV(94).    * 
   *                                                                   *
   *    Questions, comments etc to:  avogt@physik.uni-wuerzburg.de     *
   *                                                                   *
   * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
   

2. Parametrization by Fiore et al ​Eur. Phys. J. A 15, 505-515 (2002).

Abstract: An explicit model realizing parton-hadron duality and fitting 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 Q² region, reproducing the resonances of low-mass mesons. The figure below shows the distribution F₂ vs. x for Q² = 0.5 GeV²:

Variables

The final-state kinematics is used to make the distributions in terms of the variables of the interacting particles, like the photon virtuality, Q², by:

Q² = [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 = Q²/(M_X²-M_p²+Q²),

with ξ given by

ξ=log₁₀(x)

Results

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

(Right-click on the images and select 'Open in a new Tab' in order to enlarge them)

No experimental cuts

1M events
SURI-YENNIE	GRV	FIORE

5M events
SURI-YENNIE	GRV	FIORE

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)| < 2.4.

3. M(μ⁺μ^-) > 10. GeV.

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.

1M events
MX < 100 GeV
SURI-YENNIE	GRV

1M events
MX < 300 GeV
SURI-YENNIE	GRV

Ratio

The comparisons are performed by, first, the ratio between the distributions with and without experimental acceptance and, next, the SURI-YENNIE and GRV parametrizations.

1M events
MX < 300 GeV
SURI-YENNIE	GRV
to be added

1M events
MX < 300 GeV
RATIO SURI-GRV

LPAIR++

to be added