-- AndreAsevedoNepomuceno - 22-Mar-2010

TorsionWithATLAS

Introduction

Although the Standard Model (SM) is very successful in describing the available data, it is well known its inability of incorporating quantum gravity, which is also the case for the natural SM extensions. If a consistent quantum theory of all four fundamental interactions is really possible, it should include certain extension of the known physics, that is SM plus General Relativity (GR). However, a consistent and generally accepted formulation of the quantum theory of gravitation is still lacking, and so far our description of the gravitational phenomena is classical. Therefore, while waiting for a completely consistent theory of gravitation, it seems to be interesting to study new effects that could appear when the Standard Model is formulated in a classical gravitational background with torsion. Any future theory could contain this approach as some kind of low-energy limit. In this situation, we can apply a phenomenological approach considering the most natural extensions of GR assuming they might come from an unknown fundamental theory. We will be concentrated on the phenomenological aspects of torsion gravity theory, which is traditionally considered as one of the most natural extensions of GR.

Torsion Field

It is well known that in general relativity matter interacts with gravitational field through the energy-momentum tensor. On the other hand, spin tensors, which are independent of energy-momentum tensors, are not connected with gravity. As spin and mass are fundamental characteristics of elementary particles, it is natural that a theory that treats matter and gravitational filed in a microscopical level should take into account both fundamental quantities. By assuming that the sources of gravitational field are energy-momentum and spin tensors, one can build a theory where the gravitational field is described by two geometrical objects, a metric and a torsion. In such theory, the spin of the elementary particles are the source of the torsion.

In a phenomenological point of view, torsion can be treated as a fundamental propagating field, either of vectorial or pseudo-vectorial nature, characterized by its mass and the coupling values between torsion and fermions. Despite there are strong theoretical restrictions on the possible parameters of the propagating torsion field there is still room for detecting this field on high energy colliders, and it can be investigated with ATLAS through its interaction with the fermions.

Model Implementation in CompHep

Torsion (TS) described as pure vectorial and pure pseudo-vectorial field was implemented in CompHep event generator. Using this package, we calculate the cross-section for the process pp → TS → e+e− with a center-of-mass energy of 7 TeV. The cross section is calculated for torsion masses between 1 and 2.2 TeV and for three values of the coupling: 0.2, 0.5 and 0.8. The plot below shows the cross-section for torsion signal. The Drell-Yan cross-section (SM) is also shown for comparison.

cross_section.gif

Validation Plots

Electrons (with Z/gamma interference)

* *

Release E CM TS Mass M cutoff Couplings N Evts Cross Sections (pb) Validation plots
15.6.14.5 7 TeV 0.5 TeV 250 GeV 0.2/ 0.5/ 0.7 10 000 3.11/ 16.5/ 29.9 Torsion0.5TeV_mass
Electron PT
Electron eta
15.6.14.5 7 TeV 0.75 TeV 375 GeV 0.2/ 0.5/ 0.7 10 000 0.56/ 2.94/ 5.34 Torsion0.75TeV_mass
Electron PT
Electron eta
15.6.6.5 7 TeV 1.0 TeV 500 GeV 0.2/ 0.5/ 0.7 20 000 0.14/ 0.76/ 1.39 Torsion1.0TeV_mass
Electron PT
Electron eta
15.6.14.5 7 TeV 1.25 TeV 625 GeV 0.2/ 0.5/ 0.7 10 000 0.05/ 0.24/ 0.44 Torsion1.25TeV_mass
Electron PT
Electron eta
15.6.6.5 7 TeV 1.5 TeV 750 GeV 0.2/ 0.5/ 0.7 20 000 0.016/ 0.084/ 0.159 Torsion1.5TeV_mass
Electron PT
Electron eta
15.6.14.5 7 TeV 1.75 TeV 875 GeV 0.2/ 0.5/ 0.7 10 000 6.16E-3/ 0.032/ 0.062 Torsion1.5TeV_mass
Electron PT
Electron eta
15.6.6.5 7 TeV 2.0 TeV 1000 GeV 0.2/ 0.5/ 0.7 20 000 4.43E-3/ 0.013/ 0.026 Torsion2.0TeV_mass
Electron PT
Electron eta

*Electrons (Torsion Signal Only) *

Release E CM TS Mass M cutoff Couplings N Evts Cross Sections (pb) Validation plots
15.6.14.5 7 TeV 0.5 TeV 250 GeV 0.2/ 0.5/ 0.7 10 000 2.66/ 16.0/ 29.5  
15.6.14.5 7 TeV 0.75 TeV 375 GeV 0.2/ 0.5/ 0.7 10 000 0.46/ 2.82/ 5.09  
16.6.6.3 7 TeV 1.0 TeV 500 GeV 0.2/ 0.5/ 0.7 10 000 0.11/ 0.72/ 1.35 Torsion1.0TeV_mass
Electron PT
Electron eta
Electron Phi

Muons (Torsion Signal Only)

* *

Release E CM TS Mass M cutoff Couplings N Evts Cross Section Validation plots
15.6.14.5 7 TeV 0.5 TeV 250 GeV 0.2/ 0.5/ 0.7 10 000 2.66/ 16.0/ 29.5 Torsion1.0TeV_mass
Muon PT
Muon eta
15.6.14.5 7 TeV 0.75 TeV 375 GeV 0.2/ 0.5/ 0.7 10 000 0.46/ 2.82/ 5.09 Torsion1.0TeV_mass
Muon PT
Muon eta
15.6.14.5 7 TeV 1.0 TeV 500 GeV 0.2/ 0.5/ 0.7 10 000 0.11/ 0.72/ 1.35 Torsion1.0TeV_mass
Muon PT
Muon eta
15.6.14.5 7 TeV 1.25 TeV 750 GeV 0.2/ 0.5/ 0.7 10 000 0.03/ 0.22/ 0.43 Torsion1.0TeV_mass
Muon PT
Muon eta
15.6.14.5 7 TeV 1.5 TeV 750 GeV 0.2/ 0.5/ 0.7 10 000 0.017/ 0.078/ 0.152 Torsion1.5TeV_mass
Muon PT
Muon eta
15.6.14.5 7 TeV 1.75 TeV 875 GeV 0.2/ 0.5/ 0.7 10 000 4.16E-3/ 0.029/ 0.059 Torsion1.5TeV_mass
Muon PT
Muon eta
15.6.14.5 7 TeV 2.0 TeV 1000 GeV 0.2/ 0.5/ 0.7 10 000 1.54E-3/ 0.012/ 0.024 Torsion2.0TeV_mass
Muon PT
Muon eta


Generator Parameters

The CompHep batch files with all the parameters and PDF used to generate the events can be found in the attachments below (files batchSignalTorsion*.zip)

Generator Validation

The presentation below have some validation plots. These comparisons are: CalcHEPxCompHEP, ECM=7 TeV versus ECM=8 TeV, Pythis 8 versus Pythia6 and PDF's CTEQ6L1 versus MSTW2008lo.

Generator validation plots

References

F. M. L. de Almeida Jr., A. A. Nepomuceno, M. A. B. do Vale. "Torsion Discovery Potential and Its Discrimination at CERN LHC", Phys. Rev. D 79, 014029 (2009)

A.S. Belyaev, I.L. Shapiro, M.A.B. do Vale. "Torsion Phenomenology at the LHC", Phys.Rev.D75, 034014 (2007)

Antonio Dobado, Antonio L. Maroto. "Some aspects of the Standard Model in gravitational backgrounds with torsion", arXiv:hep-ph/9810541

Topic attachments
I Attachment History Action Size Date Who Comment
PDFpdf MC12_validation.pdf r1 manage 279.8 K 2012-09-13 - 03:45 SimaoPauloSilva Some validation plots
Compressed Zip archivezip batchSignalTorsion_ee.zip r1 manage 31.2 K 2011-06-30 - 18:20 AndreAsevedoNepomuceno  
Compressed Zip archivezip batchSignalTorsion_mumu.zip r1 manage 31.3 K 2011-06-30 - 18:21 AndreAsevedoNepomuceno  
GIFgif cross_section.gif r1 manage 7.1 K 2010-03-30 - 22:59 AndreAsevedoNepomuceno  
GIFgif electron_eta.gif r1 manage 6.4 K 2010-07-01 - 13:57 AndreAsevedoNepomuceno  
GIFgif electron_phi.gif r1 manage 8.5 K 2010-07-01 - 13:57 AndreAsevedoNepomuceno  
GIFgif electron_pt.gif r1 manage 8.6 K 2010-07-01 - 13:57 AndreAsevedoNepomuceno  
GIFgif eta3_mm_TS1000_eta02_7tev_f1.gif r1 manage 7.6 K 2010-10-14 - 21:13 YaraCoutinho  
GIFgif eta3_mm_TS1500_eta02_7tev_f1.gif r1 manage 8.1 K 2010-10-14 - 21:14 YaraCoutinho  
GIFgif eta3_mm_TS2000_eta02_7tev_f1.gif r1 manage 7.6 K 2010-10-14 - 21:14 YaraCoutinho  
GIFgif eta_ts1000_eta02.gif r1 manage 7.8 K 2010-07-05 - 20:18 AndreAsevedoNepomuceno  
GIFgif eta_ts1500_eta02.gif r1 manage 7.8 K 2010-07-05 - 20:19 AndreAsevedoNepomuceno  
GIFgif eta_ts2000_eta02.gif r1 manage 8.5 K 2010-07-05 - 20:19 AndreAsevedoNepomuceno  
GIFgif inva_mass.gif r1 manage 8.5 K 2010-07-01 - 13:58 AndreAsevedoNepomuceno  
GIFgif mee_mm_TS1000_eta02_7tev_f1.gif r1 manage 8.0 K 2010-10-14 - 21:04 YaraCoutinho  
GIFgif mee_mm_TS1500_eta02_7tev_f1.gif r1 manage 8.6 K 2010-10-14 - 21:15 YaraCoutinho  
GIFgif mee_mm_TS2000_eta02_7tev_f1.gif r1 manage 8.5 K 2010-10-14 - 21:15 YaraCoutinho  
GIFgif mee_ts1000_eta02.gif r1 manage 8.3 K 2010-07-05 - 20:20 AndreAsevedoNepomuceno  
GIFgif mee_ts1500_eta02.gif r1 manage 8.1 K 2010-07-05 - 20:20 AndreAsevedoNepomuceno  
GIFgif mee_ts2000_eta02.gif r1 manage 8.3 K 2010-07-05 - 20:21 AndreAsevedoNepomuceno  
GIFgif pt3_mm_TS1000_eta02_7tev_f1.gif r1 manage 8.3 K 2010-10-14 - 21:10 YaraCoutinho  
GIFgif pt3_mm_TS1500_eta02_7tev_f1.gif r1 manage 8.6 K 2010-10-14 - 21:15 YaraCoutinho  
GIFgif pt3_mm_TS2000_eta02_7tev_f1.gif r1 manage 8.3 K 2010-10-14 - 21:16 YaraCoutinho  
GIFgif pt_ts1000_eta02.gif r1 manage 8.5 K 2010-07-05 - 20:21 AndreAsevedoNepomuceno  
GIFgif pt_ts1500_eta02.gif r1 manage 8.2 K 2010-07-05 - 20:21 AndreAsevedoNepomuceno  
GIFgif pt_ts2000_eta02.gif r1 manage 9.1 K 2010-07-05 - 20:22 AndreAsevedoNepomuceno  
GIFgif torsion_ele1_eta.gif r1 manage 15.3 K 2011-10-05 - 21:15 AndreAsevedoNepomuceno  
GIFgif torsion_ele1_phi.gif r1 manage 16.6 K 2011-10-05 - 21:15 AndreAsevedoNepomuceno  
GIFgif torsion_ele1_pt.gif r1 manage 14.9 K 2011-10-05 - 21:15 AndreAsevedoNepomuceno  
GIFgif torsion_invmass.gif r1 manage 15.3 K 2011-10-05 - 21:16 AndreAsevedoNepomuceno  
GIFgif ts0500_02.eta.gif r1 manage 4.0 K 2011-05-20 - 15:46 AndreAsevedoNepomuceno  
GIFgif ts0500_02.mass.gif r1 manage 4.2 K 2011-05-20 - 15:47 AndreAsevedoNepomuceno  
GIFgif ts0500_02.pt.gif r1 manage 4.2 K 2011-05-20 - 15:47 AndreAsevedoNepomuceno  
GIFgif ts0750_02.eta.gif r1 manage 3.9 K 2011-05-20 - 15:48 AndreAsevedoNepomuceno  
GIFgif ts0750_02.mass.gif r1 manage 4.1 K 2011-05-20 - 15:48 AndreAsevedoNepomuceno  
GIFgif ts0750_02.pt.gif r1 manage 4.1 K 2011-05-20 - 15:48 AndreAsevedoNepomuceno  
GIFgif ts1250_02.eta.gif r1 manage 3.9 K 2011-05-20 - 15:49 AndreAsevedoNepomuceno  
GIFgif ts1250_02.mass.gif r1 manage 4.1 K 2011-05-20 - 15:49 AndreAsevedoNepomuceno  
GIFgif ts1250_02.pt.gif r1 manage 4.3 K 2011-05-20 - 15:50 AndreAsevedoNepomuceno  
GIFgif ts1750_02.eta.gif r1 manage 3.9 K 2011-05-20 - 15:50 AndreAsevedoNepomuceno  
GIFgif ts1750_02.mass.gif r1 manage 3.9 K 2011-05-20 - 15:51 AndreAsevedoNepomuceno  
GIFgif ts1750_02.pt.gif r1 manage 4.6 K 2011-05-20 - 15:51 AndreAsevedoNepomuceno  
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