Selected topics in

Phenomenology

Stefano Moretti

Scho ol of Physics and Astronomy

Univ ersity of Southampton

Southampton SO BJ UK

and

Particle Physics Departmen t

Appleton Lab oratory Rutherford

Didcot Oxon OX QX Chilton

Foreword

The tradition is that this course is given using transparencies

unlike the other courses in the scho ol and that the transparen

cies are simply repro duced in the pro ceedings This year I

have used a mixture of slides and whiteb oard These notes at

tempt to combine all the material I used throughout the course

and also contain some which I could not treat extensively in

the lecture theater In preparing my course I used material

from Nigel Glover Mike Seymour and Michael Kramer who

course I am preceded me as lecturers of the Phenomenology

greatly indebted to them for letting me using it I have also

ripp ed o some slides from Gavin Salams talks and presenta

tions for some of the QCD topics and from Laura Reina in the

case of Higgs physics A sp ecial thank go es to Dan Tovey for

letting me use many slides from one of his talks for that very

last lecture the day after the scho ol dinner and aftermath

The references I have used to prepare the course are collected

at the end and should ideally provide a go o d starting p oint

for those who want to learn more ab out some of the topics I

would like to thank Tim Greenshaw for organising the scho ol

so well and for his supp ort throughout Lots of thanks also

go to the other lecturers to the tutors and primarily to the

students Finally I am grateful to Margaret Evans for all the

practical arrangements and for coping with my extreme late

ness in preparing these notes I was again the last one

Intro duction

Kants Critique of Pure Reason as interpreted by Wikip edia

Phenomenon Phenomena constitute the world as we ex

p erience it as opp osed to the world as it exists inde

p endently of our exp eriences thinginthemselv es das

cannot according to Kant know ding an sich Humans

thingsinthemselves only things as we exp erience them

Noumenon Thing in itself Ding an sich is an al

legedly unknowable undescribable reality that in some

way lies b ehind observed phenomena Noumena are

sometimes sp oken of though the very notion of individ

uating items in the noumenal world is problematic

since the very notions of numb er and individuality are

among the categories of the understanding which are

supp osed to apply only to phenomena not noumena

The concept of Phenomena led to a tradition of philos

ophy known as Phenomenology Hegel Heidegger etc

which we will ignore here

Phenomenon in the general sense stands for any observable

event phenomena make up the raw data of science

Famous quotes No phenomenon is a phenomenon until it

is an observed phenomenon Niels Bohr

I will nonetheless discuss Sup ersymmetry

My denition of high energy phenomenology

Branch of highenergy physics that seeks knowledge by

Exploiting the hints and clues available in observable phe

nomena aka exp erimental data without any preconception

on the theory governing the latter

Parametrise theories into a set of observables predictions

that can directly b e tested by exp eriment thus conrming or

disproving the former

Phenomenology bridge b etween theory and exp eriment

Outline

Intro duction The Standard Mo del Beyond

Tests of the Standard Mo del

QCD running coupling infrared safety factorisation parton dis

tribution functions jet pro duction searches for new physics

ElectroWeak EW Physics weak interactions from uni

tarity Z lineshap e precision tests W b oson pro duction indirect

b oson search for the Higgs

Higgs Boson Hunting

The Higgs mechanism

The Higgs picture

The Higgs prole

Collider searches

Sup ersymmetry SUSY

Why sup ersymmetry

The hierarchy problem and gauge coupling unication

The Minimal Sup ersymmetric Standard Mo del MSSM

Indirect searches g

Collider searches

Epilogue

Intro duction

Current theoretical framework of particle physics is

Standard Mo del SM

SM is S U SU U gauge theory with

Matter elds

s b u

d u s c b t quarks

R R R R R R

d c t

L L L

e

e leptons

R R R

e

L L

L

Force elds

W Z g Vector b osons

and a

Higgs scalar H

Q Why do we b elieve in the Standard Mo del

A Because conrmed by exp eriment

Q Why lo ok Beyond the Standard Mo del BSM

A Because SM lacks explanation of fundamental quantities

 

SM Flaws

 

SM do es not explain quantum numb ers

EM charge weak isospin hyp ercharge and colour

Contains at least arbitrary parameters

gauge couplings

CPviolating vacuum angle

quark masses

charged lepton masses

weak mixing angles

CPviolating CKM phase

W mass

Higgs mass

and p ossibly more parameters in the neutrino sector

neutrino masses

neutrino mixing angles

CPviolating phases

More crucially it do es not incorp orate gravity

 

Beyond the Standard Mo del

 

Three kind of problems

Mass

What is the origin of particle masses

Are the masses due to a Higgs b oson

What sets the scale of fermion masses

Unication

Is there a theory unifying all particle interactions

Flavour

Why are there so many typ es of quarks and leptons

What is the origin of CPviolation

gravity spacetime originstructure Solutions should incorp orate

String theory b est only candidate but not yet predictive

Sup ersymmetry SUSY to play a role in solving problems

Gauge coupling unication b est with light sparticles

Mass hierarchy needs light sparticles for stabilisation

SUSY seems essential for the consistency of string theory

Jargon a sparticle is a SUSY particle

 

What New Physics NP

 

Which way to go ab out

Come up with theory devise mo del for it get out pre

dictions compare with exp eriment

e theory b elow some high scale Treat SM as eectiv

NP describ ed by op erators of dimension suppressed

E relevant energy by p owers of E

Historic example Fermis theory of weak interactions

e decay describ ed by eective Lagrangian

e

G

F

p

L e

e

From exp eriment G Fermi coupling GeV

F

As M W app ears as deviations from eective theory

W

   

e e

µ =

¦

Ï

 e  e

 

Hence precision tests of the SM can reveal NP

Crucial question for phenomenology is

What is the scale of new physics TeV Higher

We do not know for sure so we push up collider energies

Test of the SM QCD

Outline

Imp ortance of QCD

The QCD coupling

e hadrons e

Infrared safe quantities

Jets

Parton shower

Hadronisation

Deeply inelastic scattering

HadronHadron collisions

New physics searches

 

Imp ortance of QCD

 

QCD is the correct theory of strong interactions



in the describ ed sense of a lowenergy eective theory

! Why QCD studies

A Quantum Field Theory QFT with unique features

asymptotic freedom

infrared slavery connement

We need to understand QCD also to search for NP

for new particles hadropro duction Tevatron and LHC

to predict the SM backgrounds to NP signals

QCD degrees of freedom quarks gluons aka partons

Will study their interactions in e e e p pp and pp

See Nicks course for Lagrangian Feynman rules

The QCD Lagrangian is given by

X

A A

L F F iD m q q

ab b a

avours

L L

host gaugexing g

A

where F is the eld strength tensor derived from the gluon

a

eld A

A A A AB C B

g f A A F A A

B C run over the eight colour degrees of and the indices A

freedom of the gluon eld The quark elds q are in the

a

triplet representation of the SU colour group and D is the

covariant derivative

c c

ig t D A

ab ab ab

The t are matrices in the fundamental representation of SU

and satisfy

A B AB C C

t t if t

For a discussion of the gaugexing and ghost terms of the

QCD Lagrangian see Nicks course

The Feynman rules can b e derived from the QCD La

grangian

p p i

A p B

AB

g

          

2 2

p i p i

i

A p B

AB

2

p i

i

i p b j a

ab

6 p m i

i j

h

B

AB C

g f g p q

q



g q r



 




i

 




 

g r p




 

p r




 




all momenta incoming

A C

A B



 











 




2 X AC XBD

 

g g g g ig f f




 






2 X AD XBC 

 

ig f f g g g g




 




 

2 X AB XCD




 

ig f f g g g g




 




C D

A



AB C

g f q

R

q

B C

A



A

ig t

j i

cb

R

b i c j

ß ÌÝÔ e×eØ bÝ FÓiÐÌ X ß ½7 E AB A B AB 1 Tr(t t ) = TRδ , TR = 2

2 − A A Nc 1 4 A tabtbc = CFδac , CF = = a c 2Nc 3 P AB ACD BCD AB C,D f f = CAδ , CA = Nc = 3 P b a 1 1 1 −1 A A − = tabtcd = δbcδad δabδcd (Fierz) 2 2N 2 2Nc c d

 

The QCD coupling

 

 

is running

 

Quantum corrections alter particle masses and couplings

Ultraviolet divergences removed by renormalisation

Renormalisation intro duces a mass scale the subtraction

coupling p oint of UV divergences and the renormalised

s

dep ends on

s s

ln

N n of active avours N n

C f C f

MeV is an integration constant

QCD

d

s

s

s

d

Asymptotic freedom as

s

we can use p erturbation theory for pro cesses involving

large momentum scales small distances

is crucial in QED and increases as Sign of

Infrared slavery as

s

connement quarks gluons are only found in

coloursinglet b ound states

we have to use nonp erturbative metho ds eg lattice

at low momentum scales large distances

Running of has b een established exp erimentally s

0.5 Theory Data NLO NNLO αs(Q) Lattice Deep Inelastic Scattering e+e- Annihilation 0.4 Hadron Collisions Heavy Quarkonia

Λ(5) MS α s (Μ Z ) 251 MeV 0.1215 0.3 QCD 4 213 MeV 0.1184 O(α s ) { 178 MeV 0.1153

0.2

0.1

1 10 100

Q [GeV]

Compilation of data by Siggi Bethke

Measurements of are reviewed in ESW The more

S

But how do we measure

compilation of Bethke is shown ab ove Evidence recent

s

that ( Q) has a logarithmic fallo with Q is p ersuasive

S

Typ eset by FoilT X E

 

e ! e hadrons

 

But QCD Feynman rules tell us only ab out partons

Hadron formation long distance is not p erturbative

how to calculate e e hadrons

Plenty of physics b etween partons and hadrons

Parton Shower e+

γ/Z

Hadronization

-

e Resonance Decays

O α 2

electro-weak ( s ) Leading-Log QCD

Each event has dierent hadronic nal state

how to sum over all of these

Symmetries can help us

Matrix Element ME to pro duce n hadrons h h

n

g

+

n q fp T M fvp e up g p g

h h

e e

1 n

q

with T parametrisation of the unknown part

Gives total cross section

e

+

Tr p p

e e

s s

Z

X

dPS T n q fp p g T n q fp p g

n h h h h

1 n 1 n

n

R

P

H q dP S T T Dene

n

n

covariance Imp ose Lorentz

H Ag B q q A B f unctions only of q

Imp ose gauge invariance

q H q H A q B

2

e

Hence B s and B s dimensionless

s

Gives fundamental prediction

e e hadrons

constant R R e e

e e

without knowing anything ab out hadron interactions

e e ! hadrons at leading order

X

N if f q e

C

q

s

q

X

e e hadrons

R e N

C

Q

 ½=£

e e

q

rst evidence for colour N

C

p p

Kinematically allowed if s m steps at s m

q q

6

5 γγ 2 MARK I {MARK I/LGW

4 MEA

¼ ·



Z e e ! f f R

3

2

J/ψ(1S) ψ(2S)

1 2 3 4 5 6 7

5

¾

4 «

¾

=  É ¼

4 f

R

¿×

3 AMY CRYSTAL BALL JADE MARK J TOPAZ CELLO CUSB LENA PLUTO VENUS (nS)

n=1234 CLEO DASP II MAC TASSO

¿ = Æ = Õ Õ

2 10 15 20 25 30 35 40 45 5055 60

Ecm (GeV)

È

·

·

p

X

e ! Õ Õµ  ´e

 ´e e ! µ

eg s GeV R cf PETRA data

Õ

¾

Ê  É : = = ¿

Õ

· · · ·

 µ e !  e !   µ  ´e  ´e

Õ

Ô

¼

Z × = Å ­ =Z

Z

¾ ¾

4 « 

¾ ¾ ¾ ¾

 = · Ú µ ´a · Ú µ ´a

¼

e e f f

¾

¿

Z ¾

R at the Z p eak

Can also tell us ab out EW couplings

P

A

q

q

a R N A v

C f

f f

A

cf LEP average

In general sensitive to Z interference

in fact R on Z p eak

Ô

¾

¾

 G Å = « =  ³ :

F Ï

Z

È È

¾ ¾

a Z ! Õ Õ Ú

Z !

Õ Õ

Õ Õ

Ê

Z

· ¾ ¾ ·

Z !   Z !   a Ú

 

e e ! hadrons b eyond leading order



¼

largest coupling exp ect QCD corrections largest

s

start with them

Ê Ê Ç «

Z Ë

At O

s

Virtual corrections interfere treelevel diagrams with one

lo op ones in a

can b e negative

Real corrections square treelevel diagrams in b

p ositive denite

d :::℄d« d¬ d­ dÜ dÜ ;

¿ ½ ¾ ¿

b real gluon emission

b o dy phase space d d d d dx dx

p p

are Euler angles and x s and x E s where E

q q

quark and antiquark are energy fractions of nalstate

Applying Feynman rules and integrating over Euler angles

Z

x x

s

q g q

C dx dx

F

x x

with integration region x x

Integral is divergent at x x

x x x cos

q g

x x x cos

q g

p

where x E s E gluon energy and i are angles

g ig g

b etween gluon and quarks

collinear divergence or

q g q g

soft divergence E

g

Singularities indicate breakdown of p erturbation theory

when mass scales approach

Fortunately collinearsoft regions do not make imp ortant

contributions to total cross section

they cancel

Make integral nite using eg dimensional regularisation

D

Z

x x x

s

q q g

H dx dx C

F

x x x

2

O where H

Hence

s

q q g

C H O

F

softcollinear divergences are regulated app earing as p oles

at D

b virtual gluon exchange

s

q q

C O H

F

Adding real and virtual corrections the infraredcollinear

p oles cancel and the result is nite as

o n

s

O R R

s

Other regularisation schemes available eg nite g mass

m s nongauge invariant

g

infrared safe quantity R is an

R is nite and regularisation schemeindep endent

e e ! hadrons cross section at NLO

First measurement

s

R LEP

R M

Z

M

s Z

measurement Second

s

R PETRA

R GeV

s

M up on running

s Z

PETRA agrees with LEP

test of QCD in intervening energy range

Note decays

BR hadrons

Related measurement R R

BR electrons muons

one of b est measurements

s

m GeV

s

M up on running

s Z

Cross section now known through NNNLO g

And theoretical errors Where are they Dependence of total cross section on onlyhard gluons is reflected in ‘good behaviour’ of perturbation series:

2 3 Q Q Q σ αs( ) αs( ) αs( ) tot = σqq¯ 1 + 1.045 + 0.94 − 15 + ··· π  π   π  !

(Coefficients given forQ = MZ)

Renormalisation scale dep endence

Recall arbitrary would disapp ear to all orders

s

Use dep endence as estimate of uncertainty due to trun

cating p erturbative series smaller at each order

Vary by some factor to estimate theoretical uncertainty

What scale to use for central value

s

p

s Physical scale

Principle of Minimal Sensitivity where d d

Fastest Apparent Convergence where NLOLO

theoretical predictions rather sub jective

 

Infrared safe quantities

 

R e e and R are very inclusive quantities total cross

sections or decay rates

Infrared safety guaranteed by theorems eg Blo ch and

Nordsieck BN plus Kinoshita Lee and Nauenb erg KLN

suitably dened quantities are free of singularities

Physical meaning events with hadrons give approximately

the same measurement as parton ones

Computational meaning innities cancel when adding real

gluon emission and virtual gluon exchange

BN KLN apply also to more exclusive quantities eg

njets cross section n

Eventshap e variables like thrust

 

Jets

 

Naively exp ect most events to lo ok like

Run:event 4093: 1000 Date 930527 Time 20716 Ct rk(N= 39 Sump= 73.3) Ecal (N= 25 SumE= 32.6) Hcal (N=22 SumE= 22.6) Ebeam 45.658 Evis 99.9 Emiss -8.6 Vtx ( -0.07, 0.06, -0.80) Muon(N= 0) Sec Vtx(N= 3) Fdet (N= 0 SumE= 0.0) Bz=4.350 Thrust=0.9873 Aplan=0.0017 Oblat=0.0248 Spher=0.0073

Y

X Z

200. cm. 5 10 20 50 GeV

Centre of screen is ( 0.0000, 0.0000, 0.0000 )

with a fraction more like s

Run:event 2542: 63750 Date 911014 Time 35925 Ct rk(N= 28 Sump= 42.1) Ecal (N= 42 SumE= 59.8) Hcal (N= 8 SumE= 12.7) Ebeam 45.609 Evis 86.2 Emiss 5.0 Vtx ( -0.05, 0.12, -0.90) Muon(N= 1) Sec Vtx(N= 0) Fdet (N= 2 SumE= 0.0) Bz=4.350 Thrust=0.8223 Aplan=0.0120 Oblat=0.3338 Spher=0.2463

Y

X Z

200. cm. 5 10 20 50 GeV

Centre of screen is ( 0.0000, 0.0000, 0.0000 )

and even a fraction fourjet like etc s

Jet denition

Intuitively jet is a spray of collimated particles

clustering algorithms Need a pro cedure in e e use

p p Start with a list of momenta p

n

In p erturbative calculations they are parton momenta

Three ingredients

measure of interjet distance y A

ij

for each pair of nal state momenta calculate eg

y m s Invariant Mass

ij

ij

y E E cos s JADE

ij i j ij

y minfE E g cos s Durham

ij ij

i j

A resolution for the latter y

cut

minfy g y combine i and j into k

ij cut

A recombination pro cedure eg

p p p Escheme

i j

k

p p j p p pscheme j p

i j i j

k

E E

i j

p p Escheme jE E j p

i j i j

k

p j jp

i j

Rep eat till minfy g y remaining ob jects are jets

k l cut

A nparton nal state can give any numb er of jets b etween n

all partons wellseparated and eg two energetic quarks

accompanied by soft and collinear gluons

Jet rates

Dene njet fraction f y by y y

n cut

y y

n n

P

f y

n

y

m tot

m

If then

tot s

X

f y

n

n

p

s and n and For

s s

f y Ay B y C y Ay

s s

Ay f y B y Ay

s

f y C y

Coupling constant and functions Ay B y and C y

s

MS scheme dened in some renormalisation scheme eg

Terms of order O involving Ay take account of the

s

normalisation to rather than to

tot

Example of njet event rates vs OPAL s

The dep endence of the threejet rate is intro duced by

Q

B y B y Ay ln

s s

Event shap e variables

Attempt to nd a more global measure of jet separation

Eg Thrust T

P

jp n j

i

P

T max

n

jp j

i

Through order

s

d

s

AT

dT

s

AT log B T

s

z

renormalisation scale dep endence

LO term

T T T

log AT C

F

T T T

T T

T

T

log C

F

T T T

NLO term B T computed numerically

M compilations

s Z

O s

 

Parton shower

 

ÉCD EÚeÒØ GeÒeÖaØÓÖ×

● hard jetsubprocess jet

p p

underlying

event

●

Z0

e+ e−

ß ÌÝÔ e×eØ bÝ FÓiÐÌ X ß ½ E

●

●

l l

W/Z

●

PS

ME

PS

ß ÌÝÔ e×eØ bÝ FÓiÐÌ X ß 4 E

● CÓÑÔaÖi×ÓÒ× ÛiØh ÌeÚaØÖÓÒ daØa:

pp W

D0

pp Z

CDF

ß ÌÝÔ e×eØ bÝ FÓiÐÌ X ß 6 E

 

Hadronisation

 

The formation of hadrons long distance physics is not

describ ed by p erturbative QCD

Spacetime picture

p

e and e form or Z with virtual mass Q s

which uctuates into q and q

By the uncertainty principle uctuation o ccurs at

short distancetimescale Q

At large Q the rate e e q qg is given by p er

turbation theory

At much later times quarks form hadrons

Hadronisation mo dies the outgoing state but o c

curs to o late to change the original probability for

the event to happ en

e e hadrons

n

e e partons O Q p ower corrections

e e hadrons can b e calculated in p erturbative

QCD for Q

Need Monte Carlo MC approach for Q

Quarks and gluons pro duced in a shortdistance pro cess

hadronisation form themselves into hadrons

Hadronisation mo delled to data in MC programs like

HERWIG cluster hadronisation

PYTHIA ARIADNE string hadronisation

General approach to hadronisation based on partonhadron

duality the ow of momentum and quantum numb ers at

hadron level follows that established at the partonic stage

Eg avour of quark initiating a jet found in hadron near

the jet axis

Approach works b ecause hadronisation is longdistance pro cess

which only involves small momentum transfers

 

Deeply Inelastic Scattering DIS

 

First test of p erturbative QCD was breaking of Bjorken

scaling in deeply inelastic lepton hadronscattering DIS

DIS structure functions provide among most precise tests

of QCD determine Parton Distribution Functions PDFs

of hadrons

can b e used in predicting hadronic cross sections

Kinematics of DIS

Consider l k hp l k X via W or Z

Standard DIS variables are dened by

q q p

Q q x and y

p q k p

if Q Scattering is called deeply inelastic

Structure functions parametrise target as seen by W Z

Consider photon only

k q W p q cross section can b e written as d L

Structure of lepton tensor is determined by QED

L Tr k k

Hadronic tensor W contains instead information ab out

photon interaction with hadronic target and cannot b e cal

culated in p erturbation theory

Symmetry prop erties give restrictions on W form

Dene two scalar structure functions F and F dep endent

only on invariants x and Q

q q

F x Q W g

q

p q p q

p q p q F x Q

q q p q

Neglecting hadron mass wrt Q DIS cross section is

d y

F y F

dx dy Q xy

In principle can use y dep endence to determine structure

functions F in a DIS exp eriment

i

Additional structure function F needed for W Z

¾

F ´Ü; É µ

i

 

¾ ¾ ¾

 Å d 8 « E ½ · ´½ Ý µ

= ¾ÜF

½

4

dÜdÝ É ¾



·´½ Ý µ´F ¾ÜF µ ´Å =¾E µÜÝ F :

¾ ½ ¾

¾

É Ô ¡ Õ ! ½ Ü

Ü

Bjorken scaling limit dened as Q with x xed

¾

structure functions ob ey approximate scaling law ie

F ´Ü; É µ ! F ´Üµ:

i i

F x Q F x

i i

Even though the Q values vary by three orders of magni

¾

tude data approximately lie on universal curve

scattering o Scaling implies p ointlike constituents

Otherwise dimensionless structure functions would dep end

on QQ with Q some length scale characterising size of

constituents

Observation of scaling was the motivation for parton mo del

Parton mo del p made of p ointlike constituents partons

Their interactions are over time scales of O longer

wrt time it takes e to traverse Lorentz contracted proton

Can therefore consider partons as approximately free par

over the very short interaction time ticles

Mo del leads to intuitive formula

Z

lh la

X

d d

f d

ah

dxdQ dxdQ

a

lh

d inclusive cross section for leptonnucleon scattering

la

partonelectron one d to

p parton momentum

Function f is called PDF

f d gives the probability to nd a parton with

ah

avour a g uu d in hadron h carrying momentum

fraction within d of

PDFs are universal ie indep endent of particular hard

scattering pro cess and can b e determined from exp eriment

Hard scattering cross sections from p erturbation theory

Using QED Feynman rules

e

d

q

y

dQ Q

Massshell constraint for outgoing quark

p q q p q p q x

implies x

R

Write dx x and obtain

d

e x y

q

dxdQ Q

At lowest order structure functions are given by

X

F x Q e xf x xF x Q

h

q

q

CallanGross relation from spin of partons

Do not confuse structure functions and PDFs

In higher order QCD structure functions F are Q dep endent

i

and scaling is broken by logarithms of Q

Through O

s

Quark acquires large transverse momentum k with prob

T

at large k k ability dk

T s

T T

Q and Integral extends up to the kinematic limit k

T

gives rise to contributions ln Q which break scaling

s

Also k integral logarithmically divergent as jk j

T T

Intro ducing k cuto

T

Z

X

d x

f F x Q x e

q h

q

x

q

x x Q

s

C P ln

q q

and P C called splitting function

q q F

C is nite term due to virtual gluon exchange

Limit k corresp onds to longrange non

T

p erturbative QCD however

factorisation theorem can separate from hard scattering

QCD factorisation theorem

Perturbative expansion can b e rearranged such that con

tributions from longrange physics app ear in PDFs while

those shortdistance app ear in the hardscattering cross sec

tion Collins Sop er Sterman

Separation requires intro duction of factorisation scale

F

is part of f while Eg gluon emission with k

q h

F T

is part of p erturbative scattering with k

F T

Through O

s

Z

X

x d

F x Q x e f

q h

q F

x

q

x Q x

s

P ln C

q q FS

F

C factorisationscheme dep endent nite correction

FS

Arbitrariness in how much of C is factored into PDFs

FS

denes socalled factorisation scheme

While PDFs and hard scattering cross section dep end on

physical cross section do es not

F

The more terms included in the p erturbative expansion the

weaker the dep endence on

F

Factorisation turns QCD into a reliable calculational to ol

QCD scaling violation observed exp erimentally

x 16

10 ZEUS 96/97 Preliminary H1 96/97 H1 94/00 Prel. -log 2 em NMC, BCDMS, E665, SLAC F 14 ZEUS QCD Fit (Prelim.) H1 QCD Fit

12

10

8

6

4

2

0 2 3 4 5 1 10 10 10 10 10

Q2 (GeV2)

¯

Ô

ÜÕ Ü aÜ Ü d Ü eÜ℄

¯

« µ

PDFs can b e dened in terms of quark and gluoneld

op erators

PDFs app ear in QCD formulae for any pro cess with n

hadrons in initial state

PDFs could in principle b e calculated in lattice QCD yet

determined from exp eriment

Dep endence of PDFs on determined by Renormalisation

F

Group Equation RGE DokshitzerGrib ovLipatovAltarel

liParisi DGLAP equation

d

f x

F

ah

d ln

F

Z

X

d

P x f

ab s F F

bh

x

b

Splitting function P has p erturbative expansion

ab

s F s F

x x P x P P

ab s F

ab ab

First two terms known and used in numerical solutions

DGLAPequation

enables to relate PDFs measured at one scale to other

scales and make corresp onding predictions

PDFs

Constrain PDFs by using many dierent b eamstargets

Nomenclatureisospin

x Q f x Q etc x Q f x Q f f

d

dp un

dp

ep

xf xf xf xf xf x Q F

d u u s

d

en

F x Q xf xf xf xf xf

d u u s

d

p

F x Q xf xf xf xf

d u s c

p

F x Q xf xf xf xf

d u s c

p

F xf xf x Q xf xf

c s u

d

p

F xf xf x Q xf xf

c s u

d

etc

global ts g

Eg MRST CTEQ GRV etc

httpdurpdgduracukhepdatapdfhtml

 

Hadronhadron collisions

 

Cross section for eg Z b oson pro duction

can b e factored

Z

X

d p p d d f f

A B A B A F B F

aA bB

ab

d p p

ab A A B B F

Characteristic scale of hard scattering Q could b e

T

eg M or p

Z

Z

Factorisation formula holds up to Q corrections

To prove factorisation one needs to sum over graphs and

use unitarity causality and gauge invariance Collins Sop er

and Sterman

   

¼

Ü ½ Ô · Ô ½

¿ ½

ÐÒ Ý  ÐÒ =

¼

¾ Ô Ô ¾ Ü

¿ ¾

Historically conrmed by leptonpair hadropro duction A

 



Ô = Ô · Ô

½ ¾

B l l X or DrellYan pro cess DY using the parton

picture and the PDFs from DIS

Distribution is lepton pair invariant mass squared ½6

NP in DY pro cesses

a d dM distribution of e e CDF and DO and

CDF SM dashed normalized to CDF data in

Z mass region b CDF A versus mass compared to

FB

SM dashed Also shown are theoretical curves for

0

b oson with M GeV d dM and A for extra E

Z FB

o

0 0

and for M solid and dotted

Z Z

Top mass

Measured by Tevatron exp eriments CDF D

Hadropro duction mo des

g g tt dominates at LHC

q q tt dominates at Tevatron

e Top decays eg semileptonic j jet

tt bW bW bj j b CC

jet signatures has worse combinatorics

Reconstruct m from bj j invariant mass eg D t

10 20

log(L) 5 ∆ - ) 2 15

0 125 150 175 200 2 10 Mtop (GeV/c ) Events/(10 GeV/c

5

0 100 150 200 250 300 350 Reconstructed Mass (GeV/c2)

Top pair pro duction cross section

Measured by b oth Tevatron exp eriments CDF D

Achieved consistency with SM prediction required NLO

and resummation

Many dierent channels

Compare to lo ok for NP

Currently statistics limited pb

Assume m GeV t

8 2 Cacciari et al. JHEP 0404:068 (2004) Assume mt=175 GeV/c * Kidonakis,Vogt PRD 68 114014 (2003) CDF Preliminary

*Dilepton -1 8.3±1.5±1.0±0.5 (L= 750 pb )

*Lepton+Jets: Kinematic ANN -1 6.0±0.6±0.9±0.3 (L= 760 pb )

*Lepton+Jets: Vertex Tag -1 8.2±0.6±0.9±0.5 (L= 695 pb )

Lepton+Jets: Soft Muon Tag 1.3 -1 5.3±3.3 ± ±0.3 (L= 193 pb ) 1.0 12 -1 CDF II Preliminary 760 pb ) (pb)

* t 10

MET+Jets: Vertex Tag 1.4 t -1 6.1±1.2 ± ±0.4 → (L= 311 pb ) 0.9 p 8 (p σ *All-hadronic: Vertex Tag 3.3 -1 8.0±1.7 ± ±0.5 6 (L= 311 pb ) 2.2

4 *Combined Cacciari et al. JHEP 0404:068 (2004) -1 7.3±0.5±0.6±0.4 Cacciari et al. ± uncertainty (L= 760 pb ) 2 (stat) ± (syst) ± (lumi) Kidonakis,Vogt PIM PRD 68 114014 (2003) Kidonakis,Vogt 1PI 0 0 160 162 164 166 168 170 172 174 176 178 180 0 2 4 6 8 10 12 14 2 σ(pp → tt) (pb) Top Quark Mass (GeV/c )

Top mass Tevatron Summary

5

Run initial goal 4.5 (GeV) t m

∆ 4 Statistical uncertainty

as m GeV

w JES systematic uncertainty (from M only) t W 3.5 Remaining systematic uncertanties Total uncertainty

Projected 3

p er exp eriment

2.5

2

1.5

1

0.5

0 0 1 2 3 4 5 6 7 8

Integrated Luminosity (fb-1)

Large systematics from jet energy scale

19 CDF (*Preliminary) Run 1 Dilepton (Run 1 only) 167.4 ±10.3 ± 4.9 Run 1 Lepton+Jets 176.1 ± 5.1 ± 5.3 (Run 1 only) Best Tevatron Run II (*Preliminary) Run 1 All-hadronic ± ± (Run 1 only) 186.0 10.0 5.7 * Dilepton: Matrix-1 Element b-tag ± ± * (L= 955 pb ) 167.3 4.6 3.8 D0 Dilepton 178.1 ± 6.7 ± 4.8 * -1 Dilepton: Matrix-1 Element ± ± (L=1030 pb ) 164.5 3.9 3.9 (L= 370 pb )

Dilepton: Combined-1 (L= 360 pb ) 167.9 ± 5.2 ± 3.7 * ν 6.9 ± ± Dilepton: -1weighting ± ± D0 Lepton+Jets 170.3 2.5 3.8 (L= 360 pb ) 170.7 6.5 3.7 -1 7.7 (L= 370 pb ) Dilepton: P-1z(t )t ± ± (L= 340 pb ) 169.5 7.2 4.0 Dilepton: φ of ν 8.9 -1 169.7 ± ± 4.0 * (L= 340 pb ) 9.0 CDF Dilepton 164.5 ± 3.9 ± 3.9 * 7.3 Dilepton: DLM-1 ± ± -1 (L= 340 pb ) 166.6 6.7 3.2 (L=1030 pb ) 2.6 Lepton+Jets:-1 DLM ± ± (L= 318 pb ) 173.2 2.4 3.2 * 15.7 * Lepton+Jets:-1 Lxy ± ± ± ± (L= 695 pb ) 183.9 13.9 5.6 CDF Lepton+Jets 170.9 1.6 2.0 * -1 Lepton+Jets:-1 Matrix Element ± ± (L= 940 pb ) (L= 940 pb ) 170.9 1.6 2.0 * top → Lepton+Jets:-1 Mreco+W jj ± ± (L= 680 pb ) 173.4 1.7 2.2 * * CDF All hadronic 174.0 ± 2.2 ± 4.8 All hadronic:-1 Template ± ± (L=1020 pb ) 174.0 2.2 4.8 -1 * (L=1020 pb ) All hadronic:-1 Ideogram ± ± (L= 310 pb ) 177.1 4.9 4.7 * CDF Summer-1 2006 ± ± * (L=1030 pb ) 170.9 1.4 1.9 Tevatron July'06 171.4 ± 1.2 ± 1.8 * Tevatron Summer'06 171.4 ± 1.2 ± 1.8 (CDF+D0 Run I+II Average)(stat) ± (syst) (CDF+D0 Run I+II) (stat.) ± (syst.) 0 0 150 160 170 180 190 200 155 160 165 170 175 180 185 190 Top Quark Mass (GeV/c2) Top Quark Mass (GeV/c2) t¯t production at the LHC

6 −1 √s = 14 TeV σ(pp t¯t) 800 pb 8 10 events @ low = 10 fb → ≃ ⇒ · L −1 8 107 events @ = 10 5 pb ⇒ · Lhigh g x1  t  g x1   t  90 %   – – t g x  2 t   x  g 2   q t x1   10 %   – – x2  q t  Lars Sonnenschein Lehrstuhl B, III. Phys. Inst., RWTH Aache n CERN,14.10.1999/2 Systematical uncertainties of the top mass Crucial cuts: (only hadronic decay in semileptonic channel) p⊥(ℓ) > 20 GeV

-1 p⊥ > 20 GeV Simulated data (PYTHIA/CTEQ4M) CMS 10fb CTEQ5M 6 MRST99 4 jets: ______p⊥ > 40 GeV mW-100MeV m +100MeV ηjet axis < 2.4 W | | ______Hadronic energy scale +2% demand 2 b jets Hadronic energy scale -2% ______

Minimum Bias (UA5), p ⊥min=3GeV M. B. (UA5), p ⊥min=1,55GeV M. B. (PYTHIA/default), p ⊥min=3GeV ______

Qmin(FSR)=0,5GeV Qmin(FSR)=2,0GeV

FSR off (soon) ISR off (soon)

170 172 174 176 178 ∆mtop = 2.16 GeV mtop(GeV) Lars Sonnenschein Lehrstuhl B, III. Phys. Inst., RWTH Aache n CERN,14.10.1999/6 ' $ At LHC it is possible to produce top quarks singly via the • weak interaction

q q′ Wg large LHC x-sec 245 pb W ≈ high rate, Vtb, polarized tops, b t etc. Wt b W LHC x-sec 50 pb b ≈ g t Vtb, new theoretical results re- cently.....

W∗ q W t ± ± LHC x-sec 10 pb q′ b ≈ low th. errors, Vtb

“New Physics” can affect each rate differently • Single top provides the best opportunity to study W-t-b • vertex: 2 - cross-section Vtb ∝| | - source of polarized tops (precise prediction)

& % 1 Threshold Results

" Mass: ∆mt = 16 MeV, ∆αs = 0.0011

– Using cross section only: ∆mt = 24 MeV, ∆αs = 0.0017.

– Γ , g fixed at SM values; assume m =120 GeV, α (M )=0.120. t tth h s Z

– Theory error: ~100 MeV.

" Width: allow to vary in a 3 −parameter fit.

– ∆Γ = 32 MeV, ∆m = 18 MeV, ∆α = 0.0015 t t s

– 2% exp. uncertainty on width

David Gerdes, University of Michigan Top/QCD at the Linear C ollider: Experimental Aspects Page 8 ttH− production and the Top Yukawa Coupling e+e−→ ttH→ WbWb bb

Very complicted final state: Up to 8 jets 4 b’s Many kinematic constraints Tiny cross section (~2 fb), with backgrounds ~3 orders of magnitude higher. Interfering backgrounds from EWK (ttZ), QCD (g →bb)

Non−interfering backgrounds Dominantly e +e−→ tt

Formally smaller number of partons, but can enter the selection due to hard gluon radiation, detector effects, and their very large cross sections

David Gerdes, University of Michigan Top/QCD at the Linear C ollider: Experimental Aspects Page 11 K. Desch M. Schumacher Top Yukawa Coupling hep-ph/0407159 2m = top = ± SM prediction is gttH .1 02 .0 02 246 GeV Important to test coupling between Higgs and top qua rk Combine LHC and LC for model independent measurement LHC: pp ttH+X – measure (ttH)xBR(H WW) to 20-50% ILC: e +e- ZH - measure BR(H WW) to 2% σ ∝ 2 (ttH ) gttH Can do with 500 GeV Linear Collider

p. 59

 

New physics searches

 

NP can intro duce new terms in SM eective Lagrangian

Imagine quarks scattering by gluon exchange to pro duce

two jets supplemented by quarks exchanging new ob ject with

mass M O TeV

p

At s M NP details cannot b e resolved

Eect can b e emulated by new terms in QCD Lagrangian

g

L

M

g strength of coupling b etween q and NP

Factor M needed for dimensional reasons and implies

that eect of NP is small

To observe deviation from SM need

highprecision exp eriment or

exp eriment lo oking for some eect forbidden in SM or

p

s M an exp eriment at

jet

of jet Eg consider pp jet X as a function of E

T

jet

For E M

T

Data Theory E

T

g

Theory M

Compare exp erimental jet cross section to NLO QCD

1

CTEQ3M CDF (Preliminary) * 1.03 D0 (Preliminary) * 1.01

0.5

0 (Data - Theory)/ Theory

-0.5 50 100 200 300 400

Et (GeV)

Beware observed eect can most likely b e explained by

theoretical uncertainty on gluon PDF at large x

Test of SM EW Physics

Outline

Weak interactions from unitarity

SM renormalisation

e e annihilation near Z p ole

W pro duction

Indirect search for top and Higgs

 

Weak interactions from unitarity

 

Weak interactions discovered in decay and describ ed by

eective Lagrangian Fermi theory

For e Lagrangian is

e

G

F

p

L e

e

with G GeV Fermi coupling

F

Fermi theory as an eective lowenergy theory and cannot b e

extended to arbitrarily high energies

Applying eective Lagrangian at high energies

G s

F

p

M e

e

Scattering amplitude must resp ect unitarity b ound

jReMj

Theory cannot b e applied at s GeV

Can deduce structure of weak interactions from unitarity con

straints Llewellyn Smith and Cornwall Levin and Tiktop oulos

Unitarity problem in e solved by assuming

e

weak interactions mediated by heavy charged vector b osons

   

e e

= µ

¦

Ï

 e  e

 

W propagator damp ens rise of scattering amplitudes as

p

s if M GeV

W

M G s

F

W

p

M e

e

s M

W

Consider pro duction of W W pairs in e e annihilation

· ·

Ï Ï Ï Ï

¿

Ï ·



e

· ·

e e e e

Neutrino term grows quadratically and violates unitarity

Bad highenergy b ehaviour cured by exchange of a new

neutral vector b oson W in schannel

Amplitude for W W W W as mediated by virtual

L L L L

W exchange and quadrilinear W b oson coupling

Ï Ï Ï Ï

Ï ·

Ï Ï Ï Ï

grows quadratically with energy

WW scattering amplitude can b e damp ed by new interac

b etween W b osons at highenergy tions

If theory is to remain weakly interacting up to high energies

a new scalar particle Higgs b oson must b e intro duced which

couples to a particle with a strength prop ortional to particle

mass

Higgs b oson exchange cancels bad highenergy b ehaviour so

M TeV that amplitude fullls unitarity requirement if

H

Ï Ï

G M

F

H

p

M

À

Ï Ï

Unitarity requirements can b e exploited further to deter

mine quartic W Higgs interactions and Higgs selfinteraction

p otential

 

SM renormalisation

 

Structure of EW interactions emerged from requirement of

unitarity at high energies

Theoretically SM is a nonAb elian gauge eld theory

SM observables can b e calculated to arbitrarily high preci

sion in a systematic expansion after a few basic parameters

are xed exp erimentally

Quantum corrections in interacting eld theories mo dify

particle masses and couplings ie interactions renormalise

the fundamental parameters

Describ ed by Feynman diagrams including lo ops

Z

d k

ln

cut

k

Æ Æ

Selfenergy and vertex corrections are logarithmically di

vergent for large lo op momenta and lead to contributions

ln where is energy scale up to which SM is valid

cut

cut

Quantum corrections add to unobservable bare mass m

and bare coupling g to generate the observable physical mass

m and coupling g ie m m m and g g g

Renormalisation is sucien t to absorb all divergences and

render all observables nite if

cut

renormalisable t Ho oft and Veltman SM is

Once massescouplings are xed exp erimentally all other

observables are calculable to arbitrarily high precision

 

e e annihilation near Z p ole

 

LEP and SLC exp eriments allowed tests of EW theory at

quantum level

Consider e e f f f q in SM

·

e f

­ ; Z



e f

s Q N N N N

f q C

f

s

s

A A N s

f e f Z

s s M M

Z Z Z

with

t t Q sin

W f f

f

A v a

f

f f

sin cos

W W

Include leading logarithmic radiative corrections

s improved Born approximation

SM cross section

s s

s

Z

z

s M s s M

Z Z Z

s

Z interference Q N

f

f

s

also use running width

Most imp ortant EW corrections near Z resonance

· ·

e f e f

¼

f

Z

­ Z ; Z

 

e e f f

Lead to ultraviolet divergences which have to b e absorb ed

into renormalised masses and couplings

In addition QCD corrections have to b e included in q q

QED corrections due to photon Initial State Radiation

ISR are crucial near resonance ] σ0 nb [ 40

had ALEPH

σ DELPHI L3 30 OPAL

Γ 20 Z

measurements, error bars increased by factor 10

10 σ from fit QED unfolded

MZ 86 88 90 92 94 [ ]

Ecm GeV

First nontrivial SM test

given measurements of M G and predicts

Z F Z

M A A

SM Z f e

Z

Total Z Width

Consider width to given nal state fermion

M A

f Z f

Total width comes all p ossible nal states

X X X X

Z f q

q

f

GeV

Z

Gives further nontrivial test of SM

Gives measurement of numb er of neutrino sp ecies

N

Or limit on width to additional invisible particles

MeV

inv

ForwardBackward asymmetry

Lineshap e and widths only sensitive to combinations of

A v a

f

f f

cos dep endence also contains

B v a

f f f

Construct forwardbackward asymmetry

SM SM

A

FB

SM SM

B B

e f

A A

e f

more and complementary tests

Leftright asymmetry

SLC had unique feature highly p olarized electrons

P

e

New asymmetry

e e e e

B

e SM SM

R L

A

LR

A

e e e e

e

SM SM

L R

Note

indep endent of nal state

indep endent of angular range

much larger than A

FB

almost systematically errorfree

Just need to measure p olarisation well

SLD worlds b est sin W

 

W pro duction

 

Consider e e W W LEP

· · ·

Ï Ï Ï Ï Ï Ï

Z ­



e

· · ·

e e e e e e

Large cancellations at high energies ditto

2

G s

F

each diagram s M

W

4 2

m G

s

F w

but sum log s M

2

W

s

M

W

Very sensitive to Triple Gauge Couplings TGCs

other very p owerful SM test

W mass in e e

Predicted by SM once G and M measured

F Z

another strong SM test symmetry breaking mechanism

Near threshold

r

M

M G

W F

W

WW

s

z

velo city of W

p

s M rapidly varying for

W

Very clean theoretically but few events

large statistical errors g

Ab ove threshold

Measure invariant mass of W decay pro ducts g

LEP average

M GeV W 30 11/07/2003 LEP

(pb) PRELIMINARY WW σ 20

10

YFSWW/RacoonWW no ZWW vertex (Gentle) ν only e exchange (Gentle) 0 160 180 200 √s (GeV)

2 80 ALEPH Preliminary √s = 188.6 GeV 70 eνqq selection Data (Luminosity = 174.2 pb-1) 60 2 MC (mW = 80.35 GeV/c ) Non-WW background 50 Events per 1 GeV/c

40

30

20

10

0 50 55 60 65 70 75 80 85 90 95 2 MW (GeV/c )

W mass in hadronhadron

W b oson mass measured at hadron colliders Tevatron

W decays provide small but clean sample

Neutrino lost p reconstructed from rest of event

Many hadrons lost in b eam directions

only transverse momentum conservation can b e used

Use

g lepton transverse momentum p

T

e

cos p p transverse mass M g

T T T

Insensitive to W transverse momentum

Tevatron average

M GeV

W

World average

M GeV W 700

600

500 events/0.5 GeV 400

300

200

100

0 30 35 40 45 50 55 pT(e) (GeV)

500 χ2 < < CDF(1B) Preliminary /df = 158/139 (50 MT 120) χ2 < < 400 /df = 62/69 (65 MT 100) # Events Mw = 80.430 +/- 0.100 (stat) GeV 300

200

100 Fit region

0 50 60 70 80 90 100 110 120 Transverse Mass (GeV)

Precision observables

Summer

Measurement Fit |Omeas−Ofit|/σmeas 0 1 2 3 ∆α(5) ± had(mZ) 0.02758 0.00035 0.02766 [ ] ± mZ GeV 91.1875 0.0021 91.1874 Γ [ ] ± Z GeV 2.4952 0.0023 2.4957 σ0 [ ] ± had nb 41.540 0.037 41.477 ± Rl 20.767 0.025 20.744 0,l ± Afb 0.01714 0.00095 0.01640 ± Al(Pτ) 0.1465 0.0032 0.1479 ± Rb 0.21629 0.00066 0.21585 ± Rc 0.1721 0.0030 0.1722 0,b ± Afb 0.0992 0.0016 0.1037 0,c ± Afb 0.0707 0.0035 0.0741 ± Ab 0.923 0.020 0.935 ± Ac 0.670 0.027 0.668 ± Al(SLD) 0.1513 0.0021 0.1479 2θlept ± sin eff (Qfb) 0.2324 0.0012 0.2314 [ ] ± mW GeV 80.392 0.029 80.371 Γ [ ] ± W GeV 2.147 0.060 2.091 [ ] ± mt GeV 171.4 2.1 171.7

0 1 2 3

Pull is dened as deviation from theoretical prediction in

units of corresp onding onestandard deviation exp erimental

uncertainty

Includes latest top mass

M and NuTeV anomaly

W

Direct vs indirect M determinations W W-Boson Mass [GeV]

TEVATRON 80.452 ± 0.059

LEP2 80.376 ± 0.033

Average 80.392 ± 0.029 χ2/DoF: 1.3 / 1 NuTeV 80.136 ± 0.084

LEP1/SLD 80.363 ± 0.032 ± LEP1/SLD/mt 80.361 0.020

80 80.2 80.4 80.6 [ ]

mW GeV

NuTeV

ratio of neutral to charged currents in neutrinonucleon

Measurement from NuTeV collab oration when interpreted

as a measurement of M shows deviation

W

Some sort of SM inconsistency

Can b e viewed as PDF problem etc

Also W width W-Boson Width [GeV]

TEVATRON 2.078 ± 0.087

LEP2 2.196 ± 0.083

Average 2.147 ± 0.060 χ2/DoF: 1.0 / 1 − pp indirect 2.141 ± 0.057

LEP1/SLD 2.091 ± 0.003 ± LEP1/SLD/mt 2.091 0.002

2 2.2 2.4 Γ [ ]

W GeV

Can correlate m and M in global EW t

t W

LEP1 and SLD 80.5 LEP2 and Tevatron (prel.) 68% CL ] GeV

[ 80.4

W m

80.3 [ ] ∆α mH GeV 114 300 1000 150 175 200 [ ]

mt GeV

Summer combination for m GeV t

 

Indirect search for top and Higgs

 

Precision observables are aected by quantum uctuations

give access to two high mass SM scales m and M

t H

t H enter in lo op corrections to EW observables

relation Eg radiative corrections to M M vs sin

W W Z

M

W

sin

W

M

Z

Quadratic dep endence on m and logarithmic on M

t H

À Ø

Ï Ï

b Ï

/ m / log M

H

t

Sensitivity also to BSM physics EW precision fits : perturbatively calculate observables in terms of few parameters:

MZ , GF ,α(MZ ), MW , mf , (αs(MZ )) extracted from experiments with high accuracy.

SM needs Higgs boson to cancel infinities , e.g. •

H MW , MZ −→ W,Z W,Z

Finite logarithmic contributions survive, e.g. radiative corrections • 2 2 2 to ρ = MW /(MZ cos θW ): 2 11g MH ρ = 1 2 2 ln − 96π tan θW µ MW ¶ Main effects in oblique radiative corrections (S,T-parameters)

New physics at the scale Λ will appear as higher dimension effective • operators .

EW precision observables led to m prediction

t

Determinations of m from

t

ts to EW observables op en circles

condencelevel CL lower b ounds on m from

t

direct searches in e e annihilations solid line

direct searches in pp collisions broken line

from in pp W or Z X dotdashed line

W

direct measurements of m by CDF triangles and D

t

inverted triangles 250

200 ] 2 150 2 [GeV/c t

100 ] [GeV/c m m

50

0 1988 1990 1992 1994 1996 1998

Year

Compare to latest PDG compilation

m direct observation

t

m SM EW ts

t

Phenomenology: Higgs Physics Precision Indirect Higgs Mass Indirect constraints 24 Try same trick to find Higgs mass: Summer 2004

H Γ Z σ0 had 0 Rl 0,l A Z, W Z, W fb Al(Pτ) M 0 2 H R δM ∼ b W ln 0 R MW c 0,b Afb 0,c A Much weaker dependence onMH fb Ab mt than on . Ac

Al(SLD) ¯ 2θlept Task is harder and requires as sin eff (Qfb) m much EW precision data as you can W Γ 0 W get your hands on. . . 2 3 10 10 10 [ ] MH GeV LEP+SLD EW Working Group ’04 (adapted)

Sensitivity to M only logarithmic still limits available H

Γ Z σ0 had 0 Rl 0,l Afb

Al(Pτ) 0 Rb 0 Rc 0,b Afb 0,c Afb

Ab

Ac

Al(SLD) 2θlept sin eff (Qfb)

mW* Γ W*

QW(Cs) 2θ−−θ − − sin MS(e e ) 2θ ν sin W( N) 2 ν gL( N) g2 (νN) R *preliminary 2 3 10 10 10 [ ]

MH GeV

Allowed region in m M plane

t H

2 High Q except mt 68% CL 200 ] GeV [

t 180 m

mt (Tevatron)

Excluded 160 2 3 10 10 10 [ ]

mH GeV

A SM Higgs b oson with mass M GeV is already

Higgs

excluded from direct LEP searches at CL see later

Possible LEP evidence of SM Higgs at GeV see later

Fixing m to exp erimental value from direct measurement

t

at Tevatron precision data lead to

SM

GeV approx at CL M

H

Best t M GeV

H

Summer combination for m GeV t

6 Theory uncertainty ∆α(5) had = 5 0.02758±0.00035 0.02749±0.00012 4 incl. low Q2 data 2 3 ∆χ

2

1

Excluded Preliminary 0 30100 300 [ ]

mH GeV

Minimal impact of NuTeV anomaly

2

M

H

cos O m M log O Recall M

2

W

t

Z W

M W

Compare to plot larger m limited Run stats

t

SM

M GeV at CL

H

LEPEWWGLEPHWG Winter

Dramatic shift downwards of b est M t and upp er limit H

Higgs Boson search

Outline

The Higgs mechanism

The Higgs picture

The Higgs prole

Collider searches

 

The Higgs mechanism

 

Unitarity of EW interactions requires existent of a scalar

Higgs eld which couples to other particles prop ortional to

their mass

In Higgs sector of theory scalar elds interact with each

other in such a way that ground state acquires a nonzero

eld strength breaking EW symmetry sp ontaneously

Masses of gauge b osons V and fermions f build up by

innitely rep eated interactions with the background Higgs

eld

Such interactions masses from zero to nite values

À

· · · ¡ ¡¡

=µ

Î

j

X

g v v

W

p M g

V W

q q q q q M

V

j

À

f · · · ¡ ¡¡

=µ

j

X

g v

v

f

p p m g

f f

q q q q q m

f j

 

The Higgs picture

 

 

The Higgs prole

 

v M from curvature of selfenergy p otential V M

H

H

SM cannot predicted it since quartic coupling is unknown

Nevertheless restrictive b ounds on M follow from hyp o

H

thetical assumptions on energy scale up to which SM is

valid b efore NP emerges

quantum uctuations intro duce energy dep endence

À À

À À À À

Ø

À

À À À À

À À

running from renormalisation group equation RGE

d

g g

t t

dln

p

v and g v with v M m v

t t

H

For mo derate m large M

t H

ddln

and b ecomes strong shortly b efore Landau p ole

v

2

2

v

ln

2 2

v

Requirement SM b e p erturbative up to a scale

Can b e translated into upp er b ound on M

H

v

M

H

ln v

Lower b ound on M derived from requirement of vacuum

H

stability

toplo op corrections reduce for increasing m b ecomes

t

negative if m to o large

t

Selfenergy p otential would b ecome deeply negative and

ground state would no longer b e stable

To avoid instability M must exceed minimal value for

H

given m to balance negative contribution

t

Lower b ound dep ends on cuto value

.

For m GeV

t

M

H

TeV GeV M GeV

H

GeV GeV M GeV

H

If SM valid up to grand unication theory GUT scale

GeV M GeV

H

Observation of M outside this range would demand a new

H

strong interaction scale b elow GUT scale Unitarity : longitudinal gauge boson scattering cross section at high energy grows with MH .

Electroweak Equivalence Theorem : in the high energy limit ( s M 2 ) ≫ V 2 1 n 1 m n m 1 n 1 m MV (VL ...V L VL ...V L ) = (i) ( i) (ω ...ω ω ...ω )+O A → − A → µ s ¶ i i (VL=longitudinal weak gauge boson; ω =associated Goldstone boson).

+ − + − Example : WL WL → WL WL

2 2 − − 1 s t A W + W → W + W ∼ − −s − t ( L L L L ) v2 + s M 2 + t M 2 µ − H − H ¶ M 2 s t A ω+ ω− → ω+ ω− − H ( ) = v2 s M 2 + t M 2 µ − H − H ¶ ⇓ 2 + − + − + − + − MW A(WL WL → WL WL ) = A(ω ω → ω ω ) + O µ s ¶ Using partial wave decomposition: ∞ = 16π (2l + 1)Pl(cos θ)al A Xl=0 ∞ dσ 1 2 16π 2 1 = σ = (2l + 1) al = Im [ (θ = 0)] dΩ 64π2s |A | −→ s | | s A Xl=0

⇓ 2 1 al = Im( al) Re(al) | | −→ | |≤ 2 Most constraining condition for W +W − W +W − from L L → L L M 2 M 2 M 2 s s≫M 2 M 2 a ω+ ω− → ω+ ω− − H H − H −→H − H 0( ) = πv 2 2 + s M 2 s log 1 + M 2 πv 2 16 · − H µ H ¶¶ 8

1 Re(a0) < MH < 870 GeV | | 2 −→ + − Best constraint from coupled channels (2 WL WL + ZLZL):

2 2 s≫MH 5MH a0 MH < 780 GeV −→ − 32πv 2 −→ Observe that : if there is no Higgs boson, i.e. MH s: ≫ 2 + − + − MH ≫s s a0(ω ω ω ω ) → −→ − 32πv 2

Imposing the unitarity constraint √sc < 1.8 TeV −→

Most restrictive constraint √sc < 1.2 TeV −→

⇓ New physics expected at the TeV scale

Exciting !! this is the range of energies of both Tevatron and LHC Triviality : a λφ4 theory cannot be perturbative at all scales unless λ =0.

In the SM the scale evolution of λ is more complicated: dλ 3 3 9 32π2 = 24λ2 (3g′2 + 9g2 24y2)λ + g′4 + g′2g2 + g4 24y4 + dt − − t 8 4 8 − t ··· 2 2 (t =ln(Q /Q ), yt = mt/v top quark Yukawa coupling). 0 → Still, for large λ ( large MH ) the first term dominates and (at 1-loop): ↔ λ(Q0) λ(Q)= 3 Q2 1 4π2 λ(Q0)ln Q2 − ³ 0 ´ when Q grows λ(Q) hits a pole triviality −→ → Imposing that λ(Q) is finite , gives a scale dependent bound on MH : 1 > M 2 < 8π2v2 λ(Λ) 0 H Λ2 −→ 3 log v2 ³ ´ where we have set Q Λ and Q0 v. → → Vacuum stability : λ(Q) > 0

For small λ ( small MH ) the last term in dλ/dt = ... dominates and: ↔ 2 3 2 Λ λ(Λ) = λ(v) yt log − 4π2 µ v2 ¶ from where a first rough lower bound is derived:

2 3v2 2 Λ2 λ(Λ) > 0 MH > 2π2 yt log v2 −→ ³ ´ More accurate analyses use 2-loop renormalization group improved Veff .

H couplings to EW gauge b osons and fermions

h i

p

g G m

f f H F f

i h

p

G M g

F VH V

V

and Branching Ratios BRs determined by these H

Γ [ ] 10 2 (H) GeV

10

1

-1 10

-2 10

-3 10 50 100 200 500 1000 [ ] MH GeV 1 _ bb WW BR(H) ZZ

-1 10 τ+τ− _ cc tt- gg -2 10

γγ Zγ

-3 10 50 100 200 500 1000 [ ]

MH GeV

M GeV Higgs to o wide to resolve exp erimentally

H

Best decay channel dep ends on collider environment

leptonicphotonic decays needed at hadron colliders

can also use hadronic decays at lepton colliders

Muon colliders could scan resonance like LEP with Z

 

Collider searches

 

LEP SLC

e Z

Z

·

À

e

Higgsstrahlung

Inclusive Higgs cross section LEP

M =90 GeV e+e- -> Zh h Mh=100 GeV 0.6 Mh=110 GeV

0.4 (pb) σ

0.2

0.0 180.0 190.0 200.0 210.0 ECM (GeV)

Lo ok for H bb use btagging and Z X no evidence

M GeV at CL g

H

Small excess can b e interpreted as pro duction of a SM Higgs

b oson with M GeV g

H

Signicance insucient to claim Higgs observationdiscovery

Most candidates from fourjet nal states

e e Z q qH bb

DALI_F1 ECM=206.7 Pch=83.0 Efl=194. Ewi=124. Eha=35.9 BEHOLD Run=54698 Evt=4881 ALEPH Nch=28 EV1=0 EV2=0 EV3=0 ThT=0 00−06−14 2:32 Detb= E3FFFF 5 Gev EC (φ −138)*SIN(θ) 5 Gev HC o

o o x x o − −

− o ox xo−o o ox ooox o x x − − x o−oxo o

o o o o o o x xx− o − x o x − x − − − o − o 0.6cm o o o o x Y"

µ 0.3cm 15 GeV x −1cm 0 1cm X" P>.50 Z0<10 D0<2 F.C. imp. θ=180 θ=0 RO TPC RO Phenomenology: Higgs searching Data v. expected signal & background LEP

2 25 ± 2 ± LEP√s = 200-209 GeV Loose 7 LEP√s = 200-209 GeV Tight

Data Data 6 20 Background Background Signal (115 GeV/c2) Signal (115 GeV/c2) 5

15 all > 109 GeV/c2 all > 109 GeV/c2 Data 119 17 4 Data 18 4 Backgd 116.5 15.8 Backgd 14 1.2 Events / 3 GeV/c Events / 3 GeV/c 10 Signal 10 7.1 3 Signal 2.9 2.2

2 5 1

0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 2 2 rec rec mH (GeV/c) mH (GeV/c)

LEP Higgs WG conclusions: statistical analysis: signal at.7 1 standard dev., corresponding toMH ≃ 116 GeV

Hadron colliders Tevatron and Large Hadron Collider LHC

a gluon fusion g g H

b WW Z Z fusion W W Z Z H

c Higgsstrahlung o W Z q q W Z W Z H

d Higgs bremsstrahlung o b t q q g g bbtt H

Inclusive pro duction cross sections

10 2 _ σ(pp→H+X) [pb] √s = 2 TeV 10 Mt = 175 GeV gg→H CTEQ4M 1

-1 _ qq’→HW 10 qq→Hqq

-2 _→ 10 qq HZ

_ _ gg,qq→Htt -3 10

_ _ gg,qq→Hbb -4 10 80 100 120 140 160 180 200 [ ] MH GeV σ(pp→H+X) [pb] 2 10 √s = 14 TeV

gg→H Mt = 175 GeV 10 CTEQ4M

1

→ -1 _ → qq Hqq 10 qq’ HW

-2 10 _ _ gg,qq→Htt -3 10 _ _ → _ gg,qq Hbb qq→HZ -4 10 0 200 400 600 800 1000 [ ] MH GeV

Sensitivity for Higgs searches at Tevatron b est for Higgs

strahlung with H bb and Z other channels to o

gs

Integrated luminosity p er exp eriment required for SM Higgs

b oson exclusion and evidence as function of M

H

Note legends in reverse order with resp ect to curves

Can do b etter than LEP Luminosity problems Final State Modes and Backgrounds

Signal Production and Final State: Primary Background Processes: gg → H →bb QCD Dijet Background…Huge pp →WH →qq'bb QCD Jet Background/W+jets pp →WH →νbb W+bb/cc, Single top, tt pp →ZH →qqbb QCD Jet Background/W+jets + − pp →ZH →  bb W/Z+bb/cc, tt (Poor BR) pp → ZH →ννbb W/Z+bb/cc, tt, QCD Jets

Essentials: Lepton Acceptance, b-tagging eff/Acceptance, dijetass MResolution April 2, 2004 Moriond QCD: B. L. Winer Page 3 Event Rates/fb -1

Rates determined from a combination of MC and data. Missed No Mass WindowMass Window Chg Lepton WH Signal(115) 1.7 1.5 ZH Signal(115) 2.5 2.3 Total Signal 4.2 3.8 tt 8.8 2.2 t(W*) 3.3 0.7 t(Wg) 2.4 0.5 W/Z bb 22.3 3.3 WZ/ZZ 16.5 2.7 QCD 61.2 10.2 Total Bkg 114 19.6 S / B 0.39 0.85 April 2, 2004 Moriond QCD: B. L. Winer Page 11 S / B 0.037 0.19

R(bb) > 0.75) ∆ -1 =105-135 GeV) H (b)>20 GeV, T bb bb ν ν e e → → (Wbb) < 6.6 pb (for P (WH) < 9.0-12.2 pb (for M σ σ

• DØ DØ : 6 double b-tag events in pb 174 spectra describedwell by SM • hep-ex/0410062 Leptons + jets: + Leptons WH Leptons + jets: + Leptons WH Stefan Grünendahl Tevatron Searches @ Aspen 2005

15

Now CDF can do also

ttH l v j j bbbb lepton missing E jets with btag T

Observed Event - Kinematics

Event with an identified, central muon and three ¡ -tagged jets:

CDF II Preliminary Run 167551, Event 3626393

2

1.5 Jet 1: 73.8 GeV

1

Lxy = 7.6 mm Muon 26.9 GeV MET 48.1 GeV

Y (cm) L = 3.4 mm 0.5 xy Lxy = 3.5 mm Jet 4: 23.6 GeV

0 Jet 2: 41.4 GeV Jet 3: 27.9 GeV

Jet 5: 15.0 GeV -0.5

-1.5 -1 -0.5 0 0.5 1 1.5

X (cm) APS 9 Tevatron Run II Preliminary

– – – WH→eνbb ZH→ννbb H→WW(*)→lνlν -1 -1 -1 D0: 382 pb D0: 261 pb CDF: 184 pb WH→WWW CDF: 194 pb-1 10 Br (pb) ×

– – ZH→ννbb – -1 → ν (*) CDF: 289 pb WH l bb H→WW →lνlν -1 -1 1 WH→WWW CDF: 319 pb D0: 299-325 pb D0: 363-384 pb-1

→ → (*) – SM gg H WW SM WH→Wbb -1 10 →

Cross-Section Cross-Section SM WH WWW – SM ZH→Zbb

-2 10 110 120 130 140 150 160 170 180 mH (GeV) ± t → H b search CDF Run II Preliminary 2 -1 Excluded 95 %CL m= 175 GeV/c ∫ L dt = 192 pb 160 t 160

SM Expected

140 SM± 1σ Expected 140

) Excluded CDF Run II 2

120 Excluded LEP 120 inaccessible inaccessible Theoretically 100 Theoretically 100 (GeV/c + H

M 80 80

LEP (ALEPH, DELPHI, L3 and OPAL) ± ± 60 Assuming →Hντ or H→ cs only 60

-1 2 10 1 10 10 tan(β)

2 µ 2 2 2 MSUSY=1000 GeV/c, =-500 GeV/c, At=Ab=2000 GeV/c, Aτ=500 GeV/c M=0.498*M, M=M=M=M=M=M=M=M 1 2 2 3 Q U D E L SUSY

Huge QCD background at LHC requires triggering on lep

tonic decays of W Z and t and exploiting H and

H ZZ resonances g

Exp ected discovery limits from ATLAS

LHC exp ected to cover entire canonical SM Higgs mass

range M GeV

H 1500

20000

1000 Events / 2 GeV 17500

500 15000

12500 0 Signal-background, events / 2 GeV

10000 105 120 135105 120 135

mγγ (GeV) mγγ (GeV)

To rmly establish Higgs nature need measuring

mass

p ossibly lifetimewidth

couplings to gauge b osons and fermions g

Higgs selfcouplings

spinparity quantum numb ers eg H ZZ g

Higgs couplings at LHC

1 g2(H,Z) (H,X)

2 2 (H,X)

2 g (H,W) g

g 0.9 ∆ g2(H,τ) 2 0.8 g (H,b) g2(H,t) Γ 0.7 H without Syst. uncertainty

0.6 2 Experiments

-1 L dt=2*30 fb 0.5 ∫

0.4

0.3

0.2

0.1

0 110 120 130 140 150 160 170 180 190

mH [GeV]

Higgs Parity at LHC

³

f f

¾ ½

 

¾ ½

Z À Z

 

f f

½ ¾

0.22 → → – – H ZZ (f1f1)(f2f2) MH = 280 GeV 0.2

0.18 ϕ

/d ½ Γ 0.16 d Γ 1/

0.14

0.12 SM pseudoscalar 0.1 0 π/2 π 3π/2 2π ϕ

Higgs Spin at LHC

d M G M M M

Z H

Z F H Z

M dM M M M

H

Z Z Z

where is the Z Z threemomentum in H rest frame in

units of Higgs particle mass M H

30 → * → – – H Z Z (f1f1)(f2f2) MH = 150 GeV 25

20

15 No. of Events 10

5 SM Spin 1 Spin 2 0 30 35 40 45 50 55

M* (GeV) Example of Precision of Higgs Measurements at The next LinearCollider

-1 For MH = 140 GeV, 500 fb @ 500 GeV

-4 Mass Measurement δ MH ≈ 60 MeV ≈ 5 x 10 MH Total width δ ΓΗ / ΓΗ ≈ 3 % Particle couplings tt (needs higher √s for 140 GeV, except through H→ gg)

bb δ gΗbb / gΗbb ≈ 2 % cc δ gΗcc / gΗcc ≈ 22.5 % ++ −− ττ ττ δ gΗττττ / gΗ ττττ ≈ 5 % * WW δ gΗww/ gHww ≈ 2 % ZZ* ??

gg δ gΗgg / gΗgg ≈ 12.5 % γγγγ δgΗγγγγ / gΗγγγγ ≈ 10 % Spin-parity-charge conjugation establish JPC = 0++ Self-coupling

δλHHH / λHHH ≈ 32 % (statistics limited)

If Higgs is lighter, precision is often better

J.Brau, Snowmass, July 3, 2001 8 The Higgs Production Cross section at The next LinearCollider

Higgs-strahlung

WW fusion

2 Recall, σpt = 87 nb / (Ecm) ~ 350 fb @ 500 GeV

J.Brau, Snowmass, July 3, 2001 9 The Higgs Production Cross section at The next LinearCollider

Higgs-strahlung

e+e− → ZH → l+ l− X @ 500 GeV

MH events/ (GeV) 500 fb-1 120 2020 140 1910 160 1780 180 1650 200 1500 250 1110

J.Brau, Snowmass, July 3, 2001 11 Higgs studies -- The power of simple reactions

The LC can produce the Higgs recoiling from a Z, with known CM energy⇓, which provides a powerful channel for unbiassed tagging of Higgs events, allowing measurement of even invisible decays ⇓ ( - some beamstrahlung)

•Tag Z® l+ l-

•Select Mrecoil = MHiggs

Invisible decays are included

500 fb-1 @ 500 GeV, TESLA TDR, Fig 2.1.4 J.Brau, Snowmass, July 3, 2001 12 Higgs studies -- The Mass Measurement

MH δ MH(Recoil) δ MH(Recon & fit) 120 GeV 40 MeV (3.3 x 10-4) 150 GeV 90 MeV 70MeV ( 2 x 10-4 ) 180 GeV 100 MeV 80 MeV ( 4 x 10-4 )

500 fb-1 @ 350 GeV, TESLA TDR, Table 2.2.1

J.Brau, Snowmass, July 3, 2001 14 Total width

ΓTOT = ΓX /BR(H → X) ______

* • BR(H → WW ) = ΓWW / ΓTOT

• ΓWW from WW fusion cross section

MH WW fusion Higgs-strahlung 120 GeV 6.1% 5.6% 140 GeV 4.5% 3.7% 160 GeV 13.4% 3.6%

500 fb-1 @ 350 GeV, TESLA TDR, Table 2.2.4

ΓΓTOT to few%

J.Brau, Snowmass, July 3, 2001 15 Higgs Couplings - the branching ratios

+ − MH H → bb H → cc H → gg H→τ τ

120 GeV 2.9 % 39 % 18 % 7.9 % 140 GeV 4.1 % 45 % 23 % 10 % (through Higgs-strahlung, only) 500 fb-1 @ 500 GeV, LC Physics Resource Book, Table 3.1

From likelihood using At lower energy, including e+e− → Hνν, along with e+e− → ZH vertex, jet mass, shape information + − MH H → bb H → cc H→ gg H→τ τ BR’s

120 GeV 2.4 % 8.3 % 5.5 % 5.0 % (Mh = 120 GeV) 140GeV 2.6 % 19.0 % 14.0 % 8.0 % 160GeV 6.5 % 500 fb-1 @ 350 GeV, TESLA TDR, Table 2.2.5

Measurement of BR’s is powerful indicator of new physics e.g. in MSSM, these differ from the SM in a characteristic way. Higgs BR must agree with MSSM parameters from many other measurements.

J.Brau, Snowmass, July 3, 2001 18 Higgs spin parity and charge conjugation (JPC)

H →γγ or γγ → H rules out J=1 and indicates C=+1

Threshold cross section (e+ e− → Z H)for J=0 σ ∼ β , while for J > 0, generally higher power of β (assuming n = (-1)J P)

Production angle (θ) and Z decay angle in Higgs-strahlung reveals JP (e+ e− → Z H → ffH) JP = 0+ JP = 0− LC Physics Resource Book, dσ/dcosθ sin2θ (1 - sin2θ ) Fig 3.23(a) dσ/dcosφ sin2φ (1 +/- cosφ )2 φ is angle of the fermion, relative to the Z direction of flight, in Z rest frame

21 TESLA TDR, Fig 2.2.8 J.Brau, Snowmass, July 3, 2001 Higgs self couplings

Measures Higgs potentialλ

Study ZHH production and decay to 6 jets (4b’s ). Cross section is small; premium on very good jet energy resolution. Can enhance x5 with positron polarization.

∆λ/λ error 36% 18%

J.Brau, Snowmass, July 3, 2001 22

Sup ersymmetry

Outline

Why Sup ersymmetry

The hierarchy problem and gauge coupling unication

The Minimal Sup ersymmetric Standard Mo del MSSM

Indirect Searches g

Collider Searches

 

Why sup ersymmetry

 

No direct exp erimental evidence of SUSY exists to date

Nonetheless prime candidate for BSM physics

SUSY is a generalisation of spacetime symmetries of

QFT transforming fermions into b osons and vice versa

It also provides a framework for unication of particle

GeV physics and gravity at a scale M

k Planc

If SUSY were an exact symmetry of Nature particles and

sup erpartners would b e degenerate in mass

Thus SUSY cannot b e an exact symmetry of nature if

it is realised it must b e broken

Crucial question for phenomenology at what scale might

SUSY b e broken Is there a reason why masses of su

p erpartners should not b e as heavy as M

Planck

Most comp elling motivation for existence of TeV scale SUSY

particles at TeV scale is linked to socalled hierarchy prob

instability of Higgs mass under quadratically divergent lem

radiative corrections

Additional supp ort for TeV scale SUSY comes from uni

cation of gauge couplings in SUSY GUTs

Hierarchy problem why is Higgs mass so much smaller

than Planck scale

Quantum corrections to Higgs mass are quadratically divergent as

internal momentum in lo ops b ecomes very large

Ï F

·

m m

H F

À À À À

Cuto represents scale up to which SM remains valid

If M extreme netuning b etween bare Higgs mass

Planc k

M would b e needed to generate a and quantum uctuations

H

physical Higgs mass of order O GeV

Most elegant solution is to intro duce additional symmetry that

transforms fermions into b osons SUSY

Paulis principle additional Higher Order HO corrections due

to sup erpartners enter M with sign opp osite to SM contribu

H

tions

divergent terms cancel

f e

Ï F

·

e m m

H F

À À À À

m me any netuning is avoided for SUSY Since m

F F H

particle sparticle masses me O TeV

Argument is qualitative and do es not tell where SUSY is

In renormalisable theories all innities can b e absorb ed in bare

parameters one might not need worry ab out SM netuning

Argument tells that large hierarchy is intrinsically unstable

SUSY very plausible way of stabilising it

Coupling unication

Additional supp ort for SUSY me O TeV follows from

gauge coupling unication

GUTs seek gauge group including SU SU and U

Apparent obstacle is at EW scale yet quantum

s

corrections intro duce energy dep endence

d

i

O

i i i i

i i

d ln

functions dep end on gauge group and matter multiplets

to which gauge b osons couple

Only particles with mass contribute to and to cou

i

pling evolution at Q

SM couplings evolve with according to

SU n

g

SU n n

g h

U n n

g h

n quarklepton generations n Higgs doublets

g h

SU SU functions negative

and decrease as increases asymptotic freedom

U function negative and increases with

extrap olated to high energy couplings must converge

SM coupling evolution

60 –1 α 1

40 α–1 α–1 2

20 –1 α 3

0 104 108 1012 1016 1020

4–97 Q (GeV) 8303A2

Couplings do not come to a common value at any scale

Lo op contributions of sup erpartners change functions

hence evolution of gauge couplings in SUSY

Most economical mo del MSSM

SUSY

n SU

g

SUSY

SU n n

g h

SUSY

U n n

g h

Couplings evolution changes also b ecause SUSY requires

two Higgs doublets

n in ab ove equations ab ove h

After including SUSY

60 –1 α 1 40 –1 –1 α α 2

20 –1 α 3

0 104 108 1012 1016 1020

4–97 Q (GeV) 8303A5

Coupling implies SUSY masses me O TeV

Theoretical uncertainties eg mo deldep endent thresholds

are such that one cannot constrain me very tightly

Higgs mechanism Sup ergravity realisations of SUSY with

universal scalar masses at GUT scale one mass evolves down

to negative values inducing EWSB

 

MSSM

 

MSSM based up on

minimal particle content

Poincare invariance

gauge invariance

SUSY

MSSM particle content

Gauge b osons S Gauginos S

f e

gluon W Z gluino W Z e

Fermions S Sfermions S

e e

e u ue

L L

L L

e

e d e d

L L L L

e

u d e ue d e

R R R R R R

Higgs Higgsinos

e e

H H H H

e e

H H H H

Charged and neutral higgsinos mix with noncoloured gaug

inos to form physical mass eigenstates socalled charginos

e neutralinos e

Mixing also exp ected in b t and sfermion sector

Intro duce additional discrete symmetry R parity

forbid B L violating interactions ie no proton decay

SM particles are R even while SUSY ones are R o dd

MSSM with R parity conservation

SUSY in pairs and Lightest SUSY Particle LSP is stable

Sparticles interactions xed by gauge symmetries and SUSY

no adjustable parameters ie predictive

q g qe eg interactions determined by only

s

Ô; i

×ÕÙaÖk

; a



i g ´Ì µ ´Ô · Õ µ =

gÐÙÓÒ

× a ij

Õ ; j

×ÕÙaÖk

SUSY is nonexact symmetry of nature

SM particle and SUSY sparticles nondegenerate masses

Mechanism of SUSY breaking not understo o d

L LSUSY LSUSYbreaking

see Sachas course

Softbreaking terms terms are consistent with Poincare

quadratic and SM gauge invariance and do not reintro duce

divergences for scalar particles

free parameters to parametrise SUSY breaking

assume universality of parameters at Plank scale

Intro duce SUSYbreaking framework eg Sup ergravity

mSUGRA

SUSY breaking parameters b ecome related and numb er

of MSSM free parameters in Sup ergravity mo dels is reduced

to only ve mSUGRA

At O M

Planck

f

scalars Higgs b osons and q have common mass M

f

gauginos B W and g have common mass M

trilinear couplings have common value A

plus

Ratio of two Higgs vacuum exp ectation values tan

Higgs mass parameter in Sup erp otential sign

Evolving universal masses from M to EW scale RGEs

Planck

entire sp ectrum of SUSY particles can b e generated

Twodoublet Higgs mo dels are anomalyfree eg MSSM

SUSY structure also requires at least two Higgs dou

blets to generate masses for b oth uptyp e and downtyp e

quarks and charged leptons

MSSM Higgs sector consists of ve physical Higgs particles

0 0

two CPeven neutral Higgses h and H M M

h H

one CPo dd neutral Higgs b oson A

a charged Higgs b oson pair H

0

AT LO tan ratio of VEVs and one Higgs mass M

A

completely determine MSSM Higgs sector

0  0 0

Eg at LO and M M M M M M

W Z

H h A

H

Sparticle virtual eects enter in higher orders via

M G M

F

t

S

p

log

M

sin

t

When radiative corrections are included NLO

M M cos sin

0

Z

h

NNLO almost g

0

GeV MSSM M

h

0

Generalise existence of light Higgs b oson with M GeV

h

is generic prediction of SUSY and its search is most imp ortant

test of SUSY theories

Assume two scenarios

Minimal mixing A A dash

t b

p

Maximal mixing A A M solid

b t SUSY

[ ] 160 Mh GeV a)

140 tgβ = 30

120

100 tgβ = 1.5

80

[ ] Mt GeV 60

140 160 180 200 220

0

rather sensitive to top mass M h 120 [ ] Mh GeV b) 110 tgβ = 30

100

90

80

β 70 tg = 1.5

60 [ ] MA GeV 50 50 100 200 500 1000 1000 [ ] MH GeV c) 700

500

300

β β 200 tg = 1.5 tg = 30

[ ] MA GeV 100 50 100 200 500 1000 1000 ± [ ] MH GeV d) 700

500

300

β β 200 tg = 30 tg = 1.5

100 [ ] MA GeV 50 100 200 500 1000

0

Higgs mixing parameter is xed by tan and M

A

M M

0

Z

A

with tan tan

cos M M

0

Z

A

Higgs couplings to ordinary matter g

g g g

u

V d

SM H

MSSM h cos sin sin cos sin

H sin sin cos cos cos

A tan tan 50 50

tgβ = 30 tgβ = 30 20 20

− α β Hdd: cosα/cosβ 10 hdd: sin /cos 10

5 5

β 2 tg = 1.5 2 tgβ = 1.5 M [GeV] [ ] A MA GeV 1 1 50 100 200 500 1000 50 100 200 500 1000

1 1 tgβ = 1.5 tgβ = 1.5 0.5 0.5

α β − α β 0.2 huu: cos /sin 0.2 Huu: sin /sin

0.1 0.1

tgβ = 30 β 0.05 tg = 30 0.05 [ ] [ ] MA GeV MA GeV 0.03 0.03 50 100 200 500 1000 50 100 200 500 1000

1 1 tgβ = 1.5 β α − β α 0.5 hVV: sin( - ) 0.5 HVV: cos( - )

0.2 0.2

β 0.1 0.1 tg = 1.5 tgβ = 30 β 0.05 0.05 tg = 30 [ ] [ ] MA GeV MA GeV 0.03 0.03 50 100 200 500 1000 50 100 200 500 1000

 

Indirect searches g

 

SUSY can app ear via HO eects in precision observables

magnetic moment provides limits on BSM physics

Dirac equation for in EM eld A is given by

e A m

For external magnetic eld Hamiltonian for a is given by

e

S B H

m

S spin vector B magnetic eld

e

and magnetic mo Bohr magneton of electron

B

m

e

ment of muon g m m

B e

Dirac equation predicts g tree level

Onelo op corrections from SM QED and SUSY MSSM

µ µ µ µ µ µ γ γ˜ γ˜

µ µ µ˜L µ˜L µ˜R µ˜R

γ γ γ

(a) (b) (c)

a photon b photinolefthanded smuon c photinorighthanded smuon

SM QED at onelo op

Q g

QE D

SUSY QED at onelo op

Z

susy

e m

g x x

dx

m x M m x m M

L

Latter is quadratic in m

m and M Consider integral in limit m

L

susy

g

em

SM and SUSY contribution have opp osite sign

M m Assume light photino and heavy smuon m

L

susy

m

g

em

m

L

Realistic scenario for SUSY breaking

SUSY contribution decouples rapidly

SUSY correction fermion mass squared

suppressed for electron

BNL E exp eriment has rep orted measurement of

g a

from SM based e e hadrons data

Discrepancy is if one uses hadrons SM data

230 µ- 220 µ+ Avg.

- 11659000 210 10 [τ] 10 ×

µ 200 a + [e e-] 190

180

170 160 Experiment Theory

150

httpwwwgbnlgovindexshtml

Though situation is not conclusive a do es provide a sig

nicant constraint on lowenergy SUSY

 

MSSM Higgs collider searches

 

There exist limits from LEP and Tevatron again assume

Minimal mixing scenario g

Maximal mixing scenario g

MSSM parameter space available is reducing

gs LHC prosp ects from ATLAS and CMS

nolose theorem but large decoupling area

Ought to observe second Higgs state or make precision mea

g surements of BRs s etc

Can construct mo dications of MSSM eg

NexttoMSSM NMSSM g

Ought to include interaction b etween HiggsSUSY sectors

Higgs SUSY and SUSY Higgs signatures gs

MSSM Higgs decay rates

Γ(Φ) [GeV] 10 tgβ = 1.5

1 ± H

-1 10 H

-2 A 10

h -3 10 50 100 200 500 1000

MΦ [GeV]

Γ(Φ) [GeV] 10 tgβ = 30

A

1 ± H

-1 10

-2 10 h H

-3 10 50 100 200 500 1000

MΦ [GeV] 1 _ 1 _ bb bb BR(h) BR(h) tgβ = 1.5 tgβ = 30

-1 − -1 + − 10 τ+τ 10 τ τ WW→←gg _ ←cc

-2 _ -2 10 cc 10 ←ZZ gg gg ←γγ -3 -3 10 10 50 60 70 80 90 60 80 100 120 [ ] [ ] Mh GeV Mh GeV 1 _ - 1 _ bb Zh tt bb BR(A) BR(A) β tgβ = 1.5 tg = 30 + − -1 − -1 τ τ 10 τ+τ 10

gg -2 -2 10 _ 10 cc tt- gg

-3 -3 10 10 50 100 200 500 1000 50 100 200 500 1000 [ ] [ ] MA GeV MA GeV

MSSM Higgs pro duction rates at LHC h H

σ(pp→h/H+X) [pb] 10 4 √s = 14 TeV 3 10 Mt = 175 GeV → CTEQ4 10 2 gg h tgβ = 1.5 hW gg→H ↓ hqq 10 ↓ _ ← hbb→ hZ Hqq 1 _ htt -1 _ 10 Hbb -2 10 HZ _ -3 Htt 10 HW -4 HHh H 10 50 100 200 500 1000 [ ] Mh/H GeV

gg→h σ(pp→h/H+X) [pb] 10 4 √s = 14 TeV _ 3 hbb 10 Mt = 175 GeV _ Hbb CTEQ4 10 2 tgβ = 30 10 gg→H 1 hqq -1 hW 10 Hqq -2 hZ 10 _ -3 htt 10 HW _ -4 HHh H HZ Htt 10 50 100 200 500 1000 [ ] Mh/H GeV

MSSM Higgs pro duction rates at LHC A

σ(pp→A+X) [pb] 10 4 √s = 14 TeV 3 10 Mt = 175 GeV CTEQ4 2 10 β gg→A tg = 1.5 10

1 _ _ gg,qq→Abb -1 10 _ _ -2 gg,qq→Att 10

-3 10

-4 10 50 100 200 500 1000 [ ] MA GeV

σ(pp→A+X) [pb] 10 4 √s = 14 TeV 3 10 _ _ Mt = 175 GeV gg,qq→Abb CTEQ4 10 2 tgβ = 30 10 gg→A 1

-1 10

-2 10

-3 10 _ _ gg,qq→Att -4 10 50 100 200 500 1000 [ ] MA GeV Figure 5: Cross sections in picobarns at the LHC for the production mechanisms of a single charged Higgs boson, for tan β =1.5 (top), 7 (middle) and 30 (bottom). (The qq¯′ → ΦH± rates, with Φ = h, A, visually coincide for tan β = 30.)

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H at Tevatron from Run rep ort

FIGURE 101. The likelihood of nobs = 600 (in arbitrary units), as a function of mH+ and tan β (assuming mt = 175 GeV and parameters given in Table 50).

FIGURE 102. The 95% CL exclusion boundaries in the [mH+ , tan β] plane for mt = 175 GeV and several values of −1 −1 the integrated luminosity: 0.1 fb (at √s = 1.8 TeV, cross-hatched), 2.0 fb (at √s = 2.0 TeV, single-hatched), and −1 10 fb (at √s = 2.0 TeV, hollow), if the nobs continues to be where the SM-based prediction peaks.

146

LHC search channels for MSSM Higgses

Typical discovery channels are

h inclusive pro duction and pro duction in asso ciation

th nal states with an isolated lepton in W h and t

h b b in asso ciation with an isolated lepton and bjets in

th and t W h

A H inclusive and in b bH A nal states

A H with jet and jet nal states

q H H in g b tH and in q

H tb in g b tH

ATLAS after fb of luminosity MaxMix

CMS after fb of luminosity MaxMix

Higgses SUSY

X Clean channel A H

CMS after fb assuming M GeV M GeV GeV

M GeV M GeV

q g Charged Higgs to sparticles

Analogue production mechanism for H r :

+

Analogue decay mode:

r 0 r l + E miss H oF2,3 F 1,2 o 3 T

o only 3 leptons, need to reconstruct additional top (to bjj )

Les HouchesWorkshop, May 2003 Filip Moortgat, University of Antwerpen Discovery Reach

MSSM parameters:

M 2 = 210 GeV, P = 135 GeV, M sleptons = 110 GeV, M squark, gluino = 1TeV

Les HouchesWorkshop, May 2003 Filip Moortgat, University of Antwerpen

SUSY Higgses

Possible channels

X pp gg qq qq qg

h H A H X

pp gg qq qq qg X

H h H A X

with t b t b h H A or b t H b b t pp t

pp gg qq qq qg ttX H X

½¼ ½¼

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CMS after fb assuming M GeV M GeV GeV

M GeV M GeV

q g

 

MSSM sparticle collider searches

 

To date no exp erimental evidence for SUSY

Assuming R parity conservation and LSP eg neutralino

e identication SUSY pro duction signatures

multijetsleptons plus missing transverse momentum

Limits from e e and pp colliders gs

SUSY searches at Tevatron and LHC g

At LHC q g up to masses TeV can b e discovered

Since M TeV

SUSY

LHC will either conrm or disprove lowenergy SUSY

Measurements of gross features of SUSY particle pro duc

tion will allow to determine typical mass scale of coloured

SUSY particles at the LHC

SUSY cascade decays with favorable BRs can b e exploited

to determine mass dierences of sparticles g

It is in general dicult to observe heavy weakly interact

ing particles such as at LHC need an International

i

i

Linear Collider ILC

Future LCs to ol for precise measurements of masses and

couplings of SUSY particles esp ecially noncoloured ones

g

Gluino mass from g q LEP Tevatron combined ) 2 400 ADLO ∼g

= M ∼q M UA2

300 & UA1

squark mass (GeV/c D0 LEP 200 CDF

100

∼ ∼ Mq < Mχ LEP 1 0 0 200 400 600 gluino mass (GeV/c2)

Sb ottom mass from b b LEP Tevatron combined

horizontalvertical hatching ) 2 150 ADLO 125 (GeV/c χ M b 100 + m o χ θ=0 < M θ=68o 75 CDF M sbottom 50

25

0 60 80 100 120 140 2 Msbottom(GeV/c )

Stop mass from t b LEP Tevatron combined

horizontalvertical hatching ) 2 ALO 100 θ=0o

(GeV/c o ∼ ν θ=56 M b D0 ∼ + m 80 ν

< M

stop M 60

40 60 80 100 120 140 2 Mstop (GeV/c )

SUSY searches via jets n missing energy LHC

m1/2 (GeV)

1200

~ g(2500) ∫ L dt = 100 fb-1

β µ < A0 = 0 , tan = 2 , 0 1l q ~ 1000 (2500)

~ q(2000)

~ g(2000) 2l OS

800 2l SS 3l

~ g(1500) 600 4l

5l

~ 400 g(1000)

q ~ (1000)

~ q ~ 200 g(500) (1500)

q ~ (500)

0 0 200 400 600 800 1000 1200 1400 1600 1800 2000

m0 (GeV)

SUSY pro cesses reconstruction at LHC

kinematically solves for neutralino momenta and masses

of heavier sparticles using measured jet and lepton momenta

and a few mass inputs

Eg

bb bb bb g bb

Decay chain basically free from SM background after cuts

Five mass shell conditions

p m

0 0

1 1

0

p p m

1

1

0

m p p p

0

2 1

1

2

0

p m p p p

b

1 2 1

b

1

0

m p p p p p

b b

2 1 2 1 g

1

0 0

and m measured at LHC using rst gen m Assume m

2 1

eration squark cascade decays with accuracy

For two bb events we have ten equations and ten un

0

knowns two neutralino four momenta m and m

g

1

Solution of ab ove equations can b e written

F D F F m m

g

b

D m where D D D m

b b

where F and D dep end up on p p and masses

i i b

i i

Pro cedure

In the event there are two b jets assume highest p bjet

T

from b decay

Two leptons must come from and decay

Four sets of gluino and sb ottom mass solutions together

with two lepton assignments for each decay b ecause can

not determine from which decay the lepton originates

To reduce combinatorics take event pair which satises

Only one lepton assignment has solution to equations

For a pair of events there are only two solutions and

there is a dierence GeV b etween two gluino mass solutions

41.79 / 23 Constant 214.5 300 Mean 596.2 Sigma 56.79 /10 GeV -1

200

100 Mass combinations/100 fb

0 400 600 800

m(gluino) (GeV)

Input was m GeV

g

ILC Potential in the noncoloured SUSY sector

200 120 + – ~+ ~ – ∆χ2 e e µ µ RR (a) (b) 119 1.00 150 s = 350 GeV 2.28 –1 20 fb 4.61 118

100 (GeV) 0 1 ~ χ Events 117 Input M

χ2 50 116 min

0 115 0 20 40 60 138 140 142 144 ± ± ~µ 8142A1

4–96 Eµ (GeV) M R (GeV)

An example of the p ossible accuracy of the determination

of the smuon mass and neutralino mass for an e e

p

s GeV and L fb linear collider with

1500

1000

500

# events 0

-500

-1000

0 20 40 60 80 100 120 140 160 180 200

(e- - e+) Energy Dist. (R - L Polarization) GeV

Energy sp ectrum E E + E E + for e e

e e e e

R L

e e

R L

p

s GeV L fb e e in the mo del SPS a at

R L

SUSY discovery b eginning of extensive and exciting exp er

imental research program

Crucial to make accurate measurements of SUSY masses

and couplings to constrain SUSYbreaking mechanism

Supersymmetry Flavor-blind MSSM breaking origin (Visible sector)

(Hidden sector) interactions

Dierent mo dels of SUSYbreaking can give rise to very

dierent sparticle mass sp ectra

Sup ersymmetry

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Examples of mass spectra in mSUGRA GMSB and AMSB models for Figure

tan sign The other parameters are m GeV m GeV for

=

M TeV N TeV for GMSB and m GeV mSUGRA

mess mess

GMSB Gauge Mediated SUSY Breaking AMSB Anomaly

TeV for AMSB m

=

Mediated SUSY Breaking

with the high luminosity available at Tesla It is vital to have highly p olarised elec

trons and it is very desirable to have p olarised p ositrons as well It is assumed that

Understanding SUSYbreaking mechanism will op en win

P for electrons and P for p ositrons are achievable p olarisations of

A prop er choice of p olarisations and center of mass energy helps disentangle the var

dow onto physics at Planck or GUT scales

reactions Electron p olarisation is ious pro duction channels and suppress background

essential to determine the weak quantum numb ers couplings and mixings Positron

p olarisation provides additional imp ortant information i an improved precision

on parameter measurements by exploiting all combinations of p olarisation ii an in

creased event rate factor or more resulting in a higher sensitivity to rare decays

and subtle eects and iii discovery of new physics eg spin sparticle exchange In

general the exp ected background is dominated by decays of other sup ersymmetric par

Mo del pro cesses like W ticles while the Standard W pro duction can b e kept under

control at reasonably low level

most fundamental op en question in SUSY is how sup ersymmetry is broken The

and in which way this breaking is communicated to the particles Here three dierent

schemes are considered the minimal sup ergravity mSUGRA mo del gauge mediated

GMSB and anomaly mediated AMSB sup ersymmetry breaking mo dels The phe

nomenological implications are worked out in detail The measurements of the sparticle

prop erties like masses mixings couplings spinparity and other quantum numb ers

Epilogue

The theoretical sp eculations ab out physics b eyond the Stan

dard Mo del discussed in this lecture course have centered

around sup ersymmetry and grand unied theories However

even much more radical changes could happ en as we approach

a new frontier of highenergy physics

qualitatively new degrees of freedom could app ear like

strings or extra dimensions

symmetries of the Standard Mo del like baryon and lep

ton numb er conservation could b e broken

sacred principles like lo cality microcausality or CPT

invariance could b e violated

theoretical frameworks like general relativity and quan

tum mechanics might break down under certain condi

tions

Physics b eyond the Standard Mo del will b e complex and

mayb e confusing with new interactions and a rich phenomeno

logical structure The accelerators and exp eriments planned

and envisaged for the next generation will provide the to ols

required to unravel the structure of fundamental physics at

the TeV scale and hop efully b eyond

Bibliography

General textb o oks

{ M E Peskin and D V Schro eder An Intro duction To Quan

tum Field Theory AddisonWesley

and R J Phillips Collider Physics Addison { V D Barger

Wesley

QCD

{ R K Ellis W J Stirling and B R Webb er QCD And Col

lider Physics Cambridge Monogr Part Phys Nucl Phys

Cosmol 8

{ D E Sop er Basics of QCD p erturbation theory arXivhep

ph

{ G Sterman Partons factorization and resummation arXivhep

ph

{ R Bro ck et al CTEQ Collab oration Handb o ok of p ertur

Version Septemb er bative QCD

{ M H Seymour Topics in standard mo del phenomenology

In Chilton School for young high energy physicists

eak Physics Electrow

as The standard { H Spiesb erger M Spira and P M Zerw

mo del Physical basis and scattering exp eriments arXivhep

ph

Higgs Physics

{ M Spira and P M Zerwas Electroweak symmetry breaking

and Higgs physics arXivhepph

{ S Dawson Intro duction to electroweak symmetry breaking arXivhepph

Sup ersymmetry

{ J R Ellis Beyond the standard mo del for hillwalkers arXivhep

ph Sup ersymmetry for Alp hikers arXivhepph

{ M E Peskin Beyond the standard mo del arXivhepph

{ H Dreiner Hide and seek with sup ersymmetry arXivhepph