SUSY/BSM  I

SUSY/BSM  I  

Mario  Mar-nez    

HASCO  SUMMER  SCHOOL  2017  

Outline  for  Part  I  

•  Why  SUSY  ?   –   SM  Glory   –   Higgs    

–   Hierarchy  Problem  

•  SUSY  primer  

–  Basic  Concepts   –  SUSY  Breaking   –  MSSM    

–  Mixing    

–  SUSY  spectrum  

•  Experimental  Approach  

SM  Glory  

Just  to  illustrate  the  Glory  of  the  SM  

(processes  relevant  for  searches  later  on…)  

Physics  Menu  

à To  access  the  interesTng  physics  one  needs  to    

fight  with  SM  backgrounds    and  control  the  tail  of  the  distribuTons    

SM  Cross  SecTon  Summary  

Top  producTon   Dibosons  

As  by  June  2016  

SM  Cross  SecTon  Summary  

Dibosons   W/Z+jets  

As  by  June  2016  

Changing  pp  energy..  

SM  Higgs  

Some  results  

The  Hiearchy  problem  

Higgs  Couplings  to  SM    

Couplings  proporTonal  to  masses  of    parTcles   à  This  determines  the  phenomenology  

and  via     loops..  

So  close  to  1…    

Higgs  Couplings  vs  mass  

The  hierarchy  Problem  

Hierarchy Problem

From EWK to Planck scale ? < H > = 172 GeV → m_H² ≈ O(−100 GeV²)

...]

) m / ln(

m 6 2

16 [

|

m_H² | ^f ₂² − Λ²_UV + _f² Λ_{UV f} + π

= λ Δ

H ^f

!! 10 in tuning fine

M

if Λ_UV ≈ _planck → ³⁰

Already a serious problem at 5 TeV scale

(cancellation among top, gauge and Higgs loops)

This kind of conspiracy has name in Physics…

SuperSymmetry ?

TeV 5

= Λ

H2

M to

ons contributi

relative Δ

(taken from C. Quigg, hep-ph/0704.2232)

12/07/17   14  

                                                   UnificaTon  of  Forces  ?  

BHE  mechanism  makes  the  small  range  and      weak  interacTon    (massive  Ws  and  Z  )  

à  EWK  symmetry  breaking….  

à  Can  we  unify  all  forces  ?  

€

σ ∝ 1 Q⁴

€

σ∝ 1 (Q²+ M_W²)²

UnificaTon  of  Forces…  

15  

Some  of  the  open  quesTons  

(i.e.,  the    need  for  new  physics)  

H  

•  Who  ordered  3  generaTons?  

•   Macer/AnT-­‐Macer  ?  

•   ……..    

•   Hierarchy  Problem  …    

•    UnificaTon  at  Large  Scale?  

•   Dark  Macer  in  the  Cosmos?  

•   ……….    

•   What  about  Gravity  ?  

•     ……….  

New  Physics  (!)

O(TeV)  scale  phenomenology  

16  

SUSY  Primer  

•  SUSY  version  of  a  QM    harmonic  oscillator  

•  Super-­‐Symmetry    

QM  raising/lowering  operators    

For  fermions…  

SUSY  transformaTons  

SUSY  Hamiltonian  

Energy  Spectrum    

Lessons  from  SUSY  oscillator    

Super-­‐Symmetry  

Super-­‐Symmetry  

Some  Theorems  

à  Supersymmetry    is  regarded  as  a  "loophole"  of  the  theorem  because    it  contains  addi8onal  generators  (supercharges)  that  are  not  scalars     but  rather  spinors.  

-­‐>  Coleman  &  Mandula  not  applicable  to  conserved  charges  transforming  as  spinors.  

“The”  Theorem  

à Pure  mathema8cal  argument…    but  invites  to  consider  Nature  could  not  ignore  it..  

SUSY  Algebra  

SUSY  invariance….    

Hierarchy  Problem  

•  Electron  case  

•  Higgs    

In  electrodynamics  

à  In  principle  this  points  into  a  problem  of  fine-­‐tuning  !  

Fine  tuning  ??..not  really.  

Scalar  (Higgs)  case  

Huge  fine-­‐tuning…  

SUSY  coming  to  rescue  you..  

SUSY  coming  to  rescue  you..  

à  Note  the  cancella8on  does  not    depend  on  the  SUSY  masses  or  A_f  

Sok  SUSY  breaking…  

This  term  breaks  supersymmetry    but  will  not  create  a  quadra@c  divergences  ~Λ²  

à  SUSY  spectra  at  the  TeV  scale  ??  

SUSY  Breaking  

•   UnificaAon  of  Forces  ?  

•   MSSM  

•  SUSY  Spectrum  &  Mixing  

•  R  parity  

UnificaTon  of  Forces…  

39  

Unification of Forces (?!)

MSSM  

MSSM  with  mixing  

Mixing     neglected  

Mixing     neglected  

Neutralinos   X⁰_{1  ….}    X⁰₄   Charginos     X_1,2  

Sok  SUSY  Breaking  

(sok  to    keep  solving  the    hierarchy  problem)  

Constrained  MSSM    

The  masses  of  W  and  Z  bosons  will    fix  B  and  |µ| à    reduced  to  5  parameters

M₀:  common  scalar  mass  at  GUT  

M_1/2:  the  common  gaugino  mass  at  GUT   tanβ:  Ra@o  of  Higgs  VEVs  

A₀:  common  (scalar)³  coupling   Sign(µ):  Higgs  mass  term  

SUSY  spectra  

Heavy  

 squarks/gluinos      

Not  so  heavy   Charginos    

 Light    

neutralinos  

Mixing  

Lightest  squark  

“Natural  SUSY  in  1984”  

47  

1.  Squarks  and  Gluinos  are  heavy     2.  mixing  of  third  generaTon  leads                  to  light  stop  and  sbocom  

 3.               Lightest  supersymmetric  parTcle                                

4.  One  higgs  is  very  light  (  <  135  GeV)  

SUSY  Spectra  

Picture  taken    aker  Tevatron     and  before  LHC  era  

10

χ

12/07/17   48  

In summary….

>

=

>

>

=

>

fermion |

boson

| Q

boson

| fermion

| Q

• Fermion/Boson symmetry

• Exact cancellation between

fermion & boson loops for Higgs

..SUSY must be broken….. model-dependent phenomenology

Double Spectra of Particles

..will mix to form mass eigenstates..

Higgs sector with 2 doublets

±

⎯→

⎯ h, H, A, H H

, H

G G ~

R-Parity

s 2 + ) L B (

P

= ( 1 )

R -

Most  general  superpoten@al  includes  terms     Viola@ng    Baryon  number  and  Lepton  number      

New  symmetry  is  postulated…  

•   SUSY  par@cles  produced  in  pairs    

•   The  lightest  SUSY  par@cle  stable  

•     Valid  candidate  for  Dark  Mader  

•     Dis@nc@ve  Signature  at  Colliders  

E

Missing Large

−

− −

= Δ

− −

= Δ

λ

=

µ + λ

+ λ

=

j k ijk i

1 B

i u k i

i j k ijk

i j 1 ijk

L

d d u 2 ''

W 1

H L

´ d

Q L

´ e

L 2 L

W 1

) sparticles (

1

= R

) particles (

1 +

= R

P P

-

u

d

e

s~

)

( χ

RPV  scenarios    

51  

•  Something like > 700 possibilities, final state signatures involving leptons and/or jets

•  If λ, λ’,λ’’ very small, can lead to long-lived LSP

Many  final  states  to  explore:  

–  Couplings  via  λ, λ’,λ’’.  Ie:    

–  LSP  no  longer  stable    

•  Multilepton production (including taus)

•  Multijets, possibly resonances (ie 2 x 3 jets)

SUSY  ZOO  

Taken  from  T.  Rizzo  

52  

Some  references  

Basic  Guidelines  on  how  to   perform  a  Search  

Object  reconstruc8on   Background  Es8ma8on  

Likelihood  Fits  

?  

Building  Blocks  

Electrons  

Photons   Z  à  ee  ,    J/Psi  à  ee  …..  

eeγ    and  µµγ

Building  Blocks  

Detector  Material  

EM  absolute  scale    

Building  Blocks  

Alignment     of  trackers     and  muon     chambers      

Using  well-­‐known  peaks  

Z   J/Psi   Y  

Building  Blocks  

JET  ENERGY  SCALE  UNCERTAINTY  

B-­‐JET  TAGGING  EFFICIENCY  

MulTple  InteracTons  

Up  to  50  interacTons  /  crossing     (requires  enormous  efforts  to     understand    the  reconstrucTon   of  the  physics  objects…)  

Z  à  µµ  events  with    

20  interacTons  on  top  

How  to  make  your  search…  

1.  Find    good  discriminant(s)  à  signal  region  (blind  it!)   2.  Determine  your  SM  background  +  related  systemaTcs  

1.   As  much  as  possible  from  data  

2.  If  taken  from  theory/simulaTons   à  define  control  regions  in   data  (orthogonal  to  your  signal  regions)  to  constrain  the  

predicTons  with  data  (and  to  reduce  systemaTcs  from  models)   3.  Validate  your  predicTons  in  regions  close  to  the  signal  region    

(similar  kinemaTcs)  where  you  do  not  expect  new  physics   4.  Convince  your  collaborators  all  is  under  control  and  open  box  

3.  Use  a  sophisTcated  Likelihood  fit  to  determine  whether  

your  data  is  staTsTcally    consistent  with  a  background  only   hypothesis  in  the  signal  region  taking  into  account  

correlaTons  of  systemaTc  uncertainTes,  etc..    

1.   Buy  a  Tcket  to  Stockholm  or  compute  exclusion  limits  @  95%  CL      

Background  strategy      

Example:  top,  W/Z+jets    

In  ETMiss-­‐based  analyses   Example:  mulT-­‐jet,  

fake  leptons  

An  example:  0-­‐lepton  signature  

25/09/2013   64  

Region C, D, E

Region A, A’

Gluino Mass

Squark Mass

•  Searches in inclusive jets + E_t^miss events  

–  from  2  (A)  to  6  (E)  jets  

à  ≥  4  jets  

à  ≥  2  jets  

€

E_{T , jet}

jet

∑

Expect  significant    

‘’effecTve  mass’’  

Normalizations obtained in all CR and

extrapolated to signal regions simultaneously by combined maximum likelihood fit

Top  CR  

MulTjet  CR  

W+jets  CR  

Z+jets  CR  

The  mother  of  all  fits…  

•  Combine  all  info  in  a  global  fit.  Likelihood  based  on  CR  and  SR  (mutually   exclusive)  

•  Each  region  described  with  a  Poisson  p.d.f  

•  Sta@s@cal  and  systema@c  uncertain@es  on  the  expected  values  included  in   the  fit  as  nuisance  parameters  à  typically  constrained  by  a  Gaussian  

funcTon  with  width  corresponding  to  the  size  of  the  uncertainty   considered  

–  correla@ons  between  these  parameters  are  taken  into  account    

•  Inputs:  Transfer  factors  (c),  N  events  for  data  in  SR(s)  and  CRj(bj)  

StaTsTcal  facts  

Super  fast  notes  on  sta8s8cs  

Notes  on  StaTsTcal  Significance  

?  

Likelihood  raTo  

€

L( µ ^, θ ) = f

φ

^(m

) + f

φ

^(m

⁾ f

∝ µ

n

= µσ

€

p

= f (q

| µ ^)dq

q_obs

∫

Nuisance     parameters  

Only  background  ?  

€

p

= f (q

| 0)dq

q_obs

∫

If  a  real  signal  appears  …  p

 à  0  

(once  p

 <    2.87  x  10

 à  Discovery)  

Test  of  “null”  hypothesis  of  no  signal    

Only  background  ?  

€

p

= f (q

| 0)dq

q_obs

∫

If  a  real  signal  appears  …  p

 à  0  

(once  p

 <    2.87  x  10

 à  Discovery)  

Test  of  “null”  hypothesis  of  no  signal    

CL _s    

(do  not  exclude  your  signal…)  

€

CL

= p

1 − p

In  the  case  of  very  small     signals  (limited  sensiTvity)  

the  use  of  p_s  to  exclude  signals   can  lead  to  false  exclusions  if  the     data  fluctuates  down….  

In  these  cases  it  is  becer  to  use     CLs  …  which  is  conservaTve  in  the     exclusion  

 If  CLs  <  0.05    à    excluded  at  95%  CL  

EXCLUDED  

Typical  SUSY  exclusion  plot..    

Expected:  use  SM  predicTon  as  data  (yellow  band  reflects  uncertainTes  in  SM  predicTon)       Observed:    what  the  data  tells  you    (dashed  band  depends  on  the  model  uncertainTes)   Numbers  inside:  95%  CL  signal  exclusion  (if  your  signal  is  larger  than  this..  You  excluded  it)  

End  Part  I