Tools for Xtra Dimensions GDR Bruxelles novembre Helenka Przysiezniak CNRS LAPP

Tools…meaning… Calculations Generators Generators + detector simulation Cosmological XtraD’s Accelerator XtraD’s … I will concentrate on Generators for accelerator searches of XtraD’s and in a very biased way, on what I know best…

CalcHEP A program for calculation of cross sections and widths, and for event generation for any model of particle interaction. Alexander Pukhov CompHEP A package for evaluation of Feynman diagrams, integration over multi-particle phase space and event generation for hadron and lepton colliders with interface to PYTHIA, TAOLA, and FeynHiggs. Slava Bunichev, Sasha Sherstnev PANDORA Physics event generator for linear collider studies M.Peskin etal. PYTHIA Simulates Randall Sundrum excitations, amongst many other things. Peter Skands etal. PYTHIA_UED A generator tool which uses Pythia to produce events in the Universal Extra Dimensions (UED) model of Appelquist, Cheng and Dobrescu [Phys.Rev.D64 (2001) ], with 1 extra dimension and as well with additional gravity mediated decays [Macesanu etal. Phys.Lett. B546 (2002) 253]. M.ElKacimi,D.Goujdami,H.P. And most certainly other tools-generators (private as well as public) which I have and haven’t heard about…

Personally, I’ve never used: PANDORA We (ATLAS colleagues M.ElKacimi, D.Goudjdami, H.P.) have played with CalcHEP and have used CompHEP for the Universal Extra Dimensions model. Which lead us to modify PYTHIA in order to generate “UED events” PYTHIA_UED We (ATLAS colleagues G.Azuelos etal.) had used PYTHIA +an adapted HDECAY for the Randall Sundrum model with a radion but in the meantime, the RS graviton has been implemented thanks to some ATLAS collaborators

Looking for the Randall Sundrum Model

A reminder of the Randall Sundrum Model How can the weak scale be related to the Planck scale M weak  M planck ? R&S were somehow inspired by the Arkani-Hamed, Dimopoulos and Dvali (ADD) model : Planck scale is « brought down » to the TeV scale using 1 non factorisable xtraD which doesn’t need to be 16 orders of magnitude large! Universe made of two 4-dimensional branes sandwiching a slice of 5-d spacetime. SM fields live on the TeV brane (y=  ) while gravity lives everywhere : on the TeV and Planck (y=0) branes, as well as in the bulk  KK excitations of the graviton 5 th dimension warped exponentially ds 2 = e -2krc|y|   dx  dx -r 2 c dy 2 1/k ~ 1/ GeV : curvature radius r c : bulk radius m=m 0 e -k  rc  M weak / M Planck ~1  k  r c ~ 35 “y” is the massless graviscalar radion while “  ” is the massless graviton

Randall Sundrum phenomenology in PYTHIA Narrow massive graviton resonances in the TeV energy range (4D KK excitations of Graviton) First excited graviton has been implemented into Pythia. CMS example Pythia production of lowest excited graviton state G* : KF = qq and gg intial states: ISUB = 391 ffbar  G* 392 gg  G* 393 qqbar  gG* 394 qg  qG* 395 gg  gG* Default parameter: k/M Planck =0.01 Universal decay modes: ffbar, gg, , ZZ, WW Free parameters: G* mass, k/M Planck

Universal Extra Dimensions (UEDs)

A review of the Universal Extra Dimensions (UEDs) model “Universal” == ALL SM particles propagate into the XtraD(s) n=1,2,3,… Kaluza Klein (KK) excitations for each SM particle of mass m n 2 =n 2 /R 2 + m SM 2 n=0 corresponds to the SM particle R : compactification scale ; Λ : cutoff scale above which the theory is no longer valid Momentum is conserved in the extra dimensions. In 3D (3D+t), this implies conservation of the KK number: never a vertex with only one KK excitation hence KK particles are always produced in pairs A bit of UED zoology Q (Doublet), U and D (Singlets) fields describe the quarks in (4+  ) dimensions e.g. for the 3 rd generation first level particles Q (0) 3  (t,b) L U (0) 3  t R and D (0) 3  b R For each fermion 1 tower/chiral state == 2 towers/quark flavor, 2 towers/lepton, 1 tower/neutrino Bosons W 3j  and B j  mix within each level, as in the SM (level 0). Each Higgs boson KK level is composed of: 1 charged Higgs, 1 scalar CP-odd Higgs of mass M j and 1 scalar CP-even of mass  (M 2 j +m 2 h ) The interactions between the Higgs field, the gauge bosons and the fermions are described by the same couplings as those for the SM

“n=1” KK states – a very degenerate situation All SM particles have practically the same mass == 1/R (compactification scale) Below : 1/R = 500 GeV

Radiative Corrections – larger mass splittings KK number is conserved at the tree level, but can be violated in first order loops First order corrections can bring large contributions to the KK masses. Tree level radiative corrections ~20% for strongly interacting particles (heaviest being the gluon) <10% for leptons and EW bosons (lightest being the photon) SM quark and gluon KK excitations will cascade decay to the Lightest Kaluza Klein Particle (LKP) :  *

(Minimal)UED scenario Fermions and bosons live in a 4+δ ( R ~ TeV -1 ) dimensional “thick” brane embedded in a larger 4+N ( size ~ eV -1 ; e.g. N=2 ) bulk where only gravitons propagate. No a priori constraints on the number of UEDs. Study the δ =1 case. With radiative corrections to the masses the KK excitations of SM quarks and gluons decay in a cascade down to the Lightest KK Particle : the LKP  * The additional ingredient of gravity mediated decays (e.g. of the LKP) KK excitations would also decay through KK number violating interactions mediated by gravity. When decay widths of first level KK excitations due to mass splitting  gravity mediated decay widths, gluon and quark excitations will decay in a cascade down to the  * which in turn will decay as  *  G Large density of states for the KK gravitons in the 5 th D the splitting between adjacent levels is of order eV

“Doing” Universal Extra Dimensions using : CompHEP + PYTHIA and PYTHIA_UED

View/Change Data Set angular precision Parameter dependence CompHEP+PYTHIA QED Fermi Model Standard Model (Unit Gauge) Standard Model (Feynman Gauge) MSSM (Unit Gauge) MSSM (Feynman Gauge) Universal Extra Dimension Any new model …. Enter process Edit model Delete changes Squaring View diagrams Variables – Constants Lagrangian Particles View Squared Diagrams Symbolic calculation Write results Reduce Program Numerical calculator Enter new Process Fortran Code Reduce code Mathematica code C code Total cross section Show plot Save results in file Show plot Save results in file 2005 : Generate events using CompHEP (CalcHEP). Output is « LesHouches » standard. Use Pythia 6.2 for the hadronization and decay while introducing UED particles into Pythia (PYTHIA_UED). It’s possible but rather complicated…

UED particle spectrum and production mechanisms matrix elements (ATL-PHY-PUB Beauchemin+Azuelos) MSEL=100 :g + g  g*+ g*(ISUB=302) g + g  Dq + Dqbar, Sq + Sqbar(ISUB=305) MSEL = 101 :g + q  g*+ Dq/Sq(ISUB=303) MSEL = 102 :q + q’  Dq + Dq’, Sq + Sq’(ISUB=304) q + qbar  Dq + Dqbar, Sq + Sqbar(ISUB=306) q + qbar’  Dq + Sqbar’(ISUB=307) q + qbar’  Dq + Dqbar’, Sq + Sqbar’(ISUB=308) q + q’  Dq + Sq’(ISUB=309) q + qbar  Dq’ + Dqbar’(ISUB=310) Radiative corrections to the particle masses and partial decay widths (Phys.Rev.D66, (2002) and Macesanu private communication) Gravitational decay widths (e.g.for  *  G) and graviton mass expression (Phys.Rev.D68, (2003) hep-ph and Phys.Lett. B482 (2000) hep-ph ) PYTHIA_UED It’s rather simple but somehow ATLAS software is rather complicated…

Production cross sections pp  g*g*,g*q*,q*q*  KK + KK From Macesanu, McMullen and Nandi Phys.Rev.D62 (2002) ,hep-ph/ Pythia_UED == 100 LHC 1 evt == 1 LHC □ : final state KK quark pair  : final state KK quark-gluon  : final state KK gluon pair + : top production  : Solid line: sum of all Initial state quark pair Initial state quark-gluon Initial state gluon pair Sum of all

Gauge bosons Fermions g kk  Dqbar+q,Sqbar+q W kk  l+D bar, +Dlbar Z kk  l+Dlbar Dq  q’ W*, qZ* Sq  q  * Dl  l  * Decay widths for bosons and fermions Mass splitting decay widths PYTHIA_UED Gravity mediated decay widths (N=2,6) Phys.Lett.B546(2002)253 hep-ph Gauge bosons Fermions

This is not a commercial for pythia. RS and UED with PYTHIA is everything in one code. Nonetheless valuable Xsection calculations with CompHEP Both groups of authors and all theoreticians were very helpful.