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Tools for Xtra Dimensions

Discover generators & simulation tools for accelerator searches of extra dimensions. Explore calculation programs & event generation models for cosmology & accelerators. Learn about various generator tools such as CalcHEP & CompHEP for particle interaction studies. Delve into models like Universal Extra Dimensions (UED) & Randall Sundrum (RS), and understand the relation between weak scale & Planck scale in physics.

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Tools for Xtra Dimensions

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  1. Tools for Xtra Dimensions GDR Bruxelles 12-14 novembre 2007 - Helenka Przysiezniak CNRS LAPP

  2. 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…

  3. CalcHEP • A program for calculation of cross sections and widths, • and for event generation for any model of particle interaction. • Alexander Pukhov http://theory.sinp.msu.ru/~pukhov/calchep.html • 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 http://comphep.sinp.msu.ru/ • PANDORA • Physics event generator for linear collider studies • M.Peskin etal. http://www-sldnt.slac.stanford.edu/nld/New/Docs/Generators/PANDORA.htm • PYTHIA • Simulates Randall Sundrum excitations, amongst many other things. • Peter Skands etal. http://projects.hepforge.org/pythia6/ • 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) 035002], 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. http://wwwlapp.in2p3.fr/~przys/PythiaUED.html • And most certainly other tools-generators (private as well as public) • which I have and haven’t heard about…

  4. 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 and in the meantime, the RS graviton has been implemented thanks to some ATLAS collaborators.

  5. Looking for the Randall Sundrum Model

  6. A reminder of the Randall Sundrum Model How can the weak scale be related to the Planck scale Mweak Mplanck ? 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 5th dimension warped exponentially ds2 = e -2krc|y|dx dx -r2c dy2 1/k ~ 1/1017-18GeV : curvature radius rc : bulk radius m=m0e-krc  Mweak/ MPlanck~1  krc ~ 35 “y” is the massless graviscalar radion while “” is the massless graviton

  7. 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. Pythia production of lowest excited graviton state G* : KF = 5000039 qq and gg intial states: ISUB = 391 ffbar  G* 392 gg  G* 393 qqbar  gG* 394 qg  qG* 395 gg  gG* Default parameter: k/MPlanck=0.01 Universal decay modes: ffbar, gg, , ZZ, WW Free parameters: G* mass, k/MPlanck CMS example So you see that the CMS private Herwig works as well

  8. Universal Extra Dimensions (UEDs)

  9. 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 mn2=n2/R2 + mSM2 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 3rd generation first level particles Q(0)3(t,b)L U(0)3tR and D(0)3bR For each fermion 1 tower/chiral state == 2 towers/quark flavor, 2 towers/lepton, 1 tower/neutrino Bosons W3j and Bj 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 Mj and 1 scalar CP-even of mass (M2j+m2h) The interactions between the Higgs field, the gauge bosons and the fermions are described by the same couplings as those for the SM

  10. “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

  11. 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) : *

  12. (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 5th D the splitting between adjacent levels is of order eV

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

  14. 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). 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 • Variables – Constants • Lagrangian • Particles • Squaring • View diagrams • Fortran Code • Reduce code • Mathematica code • C code • View Squared Diagrams • Symbolic calculation • Write results • Reduce Program • Numerical calculator • Enter new Process • View/Change Data • Set angular precision • Parameter dependence • Total cross section • Show plot • Save results in file • Show plot • Save results in file It’s possible but rather complicated…

  15. PYTHIA_UED • UED particle spectrum and production mechanisms matrix elements • (inspired by and Xchecked with ATL-PHY-PUB-2005-003 Beauchemin+Azuelos for the ME) • 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, 056006 (2002) and Macesanu private communication) • Gravitational decay widths (e.g.for * G) and graviton mass expression • (Phys.Rev.D68, 084008 (2003) hep-ph-0305029 • and Phys.Lett. B482 (2000) 195-204. hep-ph-0001335) N.B. It’s rather simple but somehow ATLAS software makes it rather complicated…

  16. Production cross sections pp g*g*,g*q*,q*q* KK + KK From Macesanu, McMullen and Nandi Phys.Rev.D62 (2002) 015009,hep-ph/0201300. Pythia_UED □ : 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 == 100 fb-1 @ LHC 1 evt == 1 fb-1 @ LHC

  17. Decay widths for bosons and fermions Gravity mediated decay widths (N=2,6) Phys.Lett.B546(2002)253 hep-ph-0207269 PYTHIA_UED gkk Dqbar+q,Sqbar+q Wkk l+Dbar,+Dlbar Zkk  l+Dlbar Gauge bosons Gauge bosons Dq q’ W*, qZ* Fermions Sq q* Fermions Dll* Mass splitting decay widths

  18. Outlook • Many of the existing tools are private • and maybe something should be done about this • e.g. HDECAY adapted to RS radion • was never made public… • e.g.2 UED-Pythia not yet divulged to the Pythia authors • For collider experimentalists (for myself…), • Pythia is still the easiest tool to modify privately and to use • i.e. just one tool for simulation of production-hadronization-decay • Nonetheless valuable Xsection calculations with CompHEP (CalcHEP) • By the way, a special thanks to all authors and theoreticians.

  19. Bibliography RS Search for the radion using the ATLAS detector,EPJ C, 4, C16, 1-13(2002), Azuelos etal. The Hierarchy Problem and New Dimensions at a Millimiter Phys.Lett. B429 (1998) 263-272, Arkani-Hamed, Dimopoulos, Dvali. A Large Mass Hierarchy from a Small Extra Dimension, Phys.Rev.Lett. 83 (1999) 3370-3373,Randall and Sundrum. Bulk Fields in the Randall-Sundrum Compactification Scenario, hep-ph/9907218v2, hep-ph/9907447, hep-ph/9911457 (best one), Goldberger and Wise. Graviscalars from higher-dimensional metrics and curvature-Higgs mixing hep-ph/0002178v2, Giudice,Rattazzi,Wells. Radion effects on unitarity in gauge-boson scattering, Phys.Rev. D64 (2001) 076003, Han, Kribs,McElrath. Shifts in the Properties of the Higgs Boson from Radion Mixing, hep-ph/0202155, Hewett and Rizzo. The Scalar-Sector of the Randall-Sundrum Model, hep-ph/0206192, Dominici, Grzadkowski, Gunion, Toharia. ADD Model  Randall Sundrum Model  Goldberger Wise stabilization scheme  Phenomenology

  20. Bibliography RS

  21. Bibliography RS Arkani-Hamed-Dimopoulos-Dvali (ADD): The gravitational and gauge interactions become united at the weak scale, which we take as the only fundamental short distance scale in nature. n>=2 new compact spatial dimensions large compared to the weak scale. The Planck scale M_PL~G_N^-1/2 is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. SM particles must be localized to a 4d submanifold. The only fields propagating in the 4+n-d bulk are the 4+n-d graviton. Randall-Sundrum: the large Planck scale (weakness of gravity) arises because of the small overlap of the graviton wave function in the 5th dimension (which is the warp factor) with our brane. This is the only small number produced. All other scales are set by the TeV scale. KK gravitational modes in the RS spacetime have TeV scale mass splittings and couplings, in sharp contrast to KK decomposition in product spacetimes (e.g.ADD) which or large compactified dimensions gives rise to a high number of light modes with splittings of the order of the compactification scale (very small). Goldberger and Wise: KK decomposition of a non-gravitational scalar bulk field propagating in the RS spacetime. The mass spectrum of the 4d KK modes is suppressed by a factor exp(-kr_c) relative to the 5d scalar mass. If kr_c is around 12, the low-lying KK modes would be characterized by a scale which is on the order of a TeV: SM particles could be low-lying KK excitations of bulk fields. (voir suite)

  22. Bibliography RS Goldberger and Wise (suite): In RS, r_c is associated with the vacuum expectation value of a massless 4d scalar field. r_c is not determined by the dynamics of the model. For this scenario to be relevant, it is necessary to find a mechanism for generating a potential to stabilize the value of r_c. Such a potential can arise classically from the presence of a bulk scalar with interaction terms that are localized to the 2 3-branes. The minimum of this potential can be arranged to yield a value of kr_c~10 without fine tuning of parameters. A bulk scalar with  (5th dimension) dependent VEV can generate a potential to stabilize r_c without having to fine tune the parameters of the model. However, there is still one fine tuning associated with the 4d cosmological constant. Giudice,Rattazzi,Wells: When the radion and higgs have about the same mass, they mix heavily. For L=10TeV and =1/6 and for radion mass~higgs mass, (gg) falls rapidly. This is because the trace anomaly contribution cancels the one-loop top quark contribution for this highly mixed state at that mass. When the radion is much heavier than the higgs and =1/6, radion->ww,zz become close to 0. But the photon BR climbs since it also couples to the trace anomaly (as for BR(gg)). For =0 there is no Higgs-radion mixing. For  close to 1/6, tree level couplings of the radion to fermions and weak gauge bosons are suppressed and gg branching fraction becomes dominant even for a very heavy radion. Therefore, for a generic  not too close to 1/6 the radion branching fraction phenomenology mostly follows what we find for =0, except for the region of large mixing (m_h~m_), where our discussion of the =1/6 case applies.

  23. Bibliography UED Bounds on Universal Extra Dimensions, Appelquist, H.C.Cheng, B.A.Dobrescu hep-ph/0012100 Bosonic Supersymmetry, Getting Fooled at the LHC, Cheng, Matchev, Schmaltz hep-ph/0205314 New Signal for Universal Extra Dimensions, Macesanu, McMullen, Nandi hep-ph/0207269 C.Macesanu private communication

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