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Tools for Xtra Dimensions

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Tools

for

Xtra

Dimensions

GDR Bruxelles 12-14 novembre 2007 - 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 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…

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.

Looking for the Randall Sundrum Model

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 bulkKK 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-krc Mweak/ MPlanck~1 krc ~ 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.

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

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

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)3tR and D(0)3bR

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

“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 5th D

the splitting between adjacent levels is of order eV

“Doing” Universal Extra Dimensions using :

CompHEP + PYTHIA

and PYTHIA_UED

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).

- 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…

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…

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

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+Dbar,+Dlbar

Zkk l+Dlbar

Gauge bosons

Gauge bosons

Dq q’ W*, qZ*

Fermions

Sq q*

Fermions

Dll*

Mass splitting decay widths

- 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.

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

Bibliography RS

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(-kr_c) relative to the

5d scalar mass. If kr_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)

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.

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