The Standard Model and Beyondvmsstreamer1.fnal.gov/VMS_Site_03/Lectures/LPC/...LPC Lectures, Feb.,...

LPC Lectures, Feb., 2010 1

LPC Particle Physics LecturesLPC Particle Physics LecturesLPC Particle Physics Lectures

The Standard Model and Beyond

LHC PhysicsDan GreenFermilab


Outline –

I, The Standard Model

Outline Outline ––

I, The Standard I, The Standard ModelModel

•

Tools•

Comphep

•

Calchep

•

SM Particles and Forces•

V-V Interactions

•

SM Questions•

The LHC

•

ATLAS and CMS•

First Data –

Soft Interactions

•

Hard Scattering


Tools for These LecturesTools for These LecturesTools for These Lectures

http://comphep.sinp.msu.ru/overview

http://theory.sinp.msu.ru/~pukhov/calche p.html

These tools can reside on your desktop. They can be used to compute many fundamental processes. What they lack is only the “hadronization”

of the final state quarks and gluons and the “underlying event”

soft particles. (interface to Pythia)

What they provide is a rapid understanding of the basics of collider physics.

http://comphep.sinp.msu.ru/overview

http://theory.sinp.msu.ru/~pukhov/calchep.html

http://theory.sinp.msu.ru/~pukhov/calchep.html


“Particle Physics”

in the 20th

Century

““Particle PhysicsParticle Physics””

in the 20in the 20thth

CenturyCentury•

The e-

was discovered by Thompson ~ 1900. The nucleus was discovered by Rutherford in ~ 1920. The e+, the first antiparticle, was found in ~ 1930. The μ , indicating a second “generation”, was discovered in ~ 1936.

•

There was an explosion of baryons and mesons discovered in the 1950s and 1960s. They were classified in a "periodic table" using the SU(3) symmetry group, whose physical realization was point like, strongly interacting, fractionally charged "quarks". Direct evidence for quarks and gluons came in the early 1970s.

•

The exposition of the 3 generations of quarks and leptons is only just, 1996, completed with the top quark discovery and the observation of the neutrino associated with the tau lepton in 2002 at Fermilab. In the mid 1980s the unification of the weak and electromagnetic force was confirmed by the W and Z discoveries at CERN.

•

The LHC, starting in 2009, will be THE tool to explore the origin of the breaking of the electroweak symmetry (Higgs field?) and the origin of mass itself. The Higgs boson is postulated to be responsible for

the mass of all the known elementary particles.


The Standard Model of Elementary Particle Physics

The Standard Model of Elementary The Standard Model of Elementary Particle PhysicsParticle Physics

•

Matter consists of half integral spin fermions. The strongly interacting fermions are called quarks. The fermions with only electroweak interactions are called leptons. The uncharged leptons are called neutrinos.

•

The forces are carried by integral spin bosons. The strong force

is carried by 8 gluons (g), the electromagnetic force by the photon (γ), and the weak interaction by the W+

Zo

and W-. The g and γ

are massless, while the W and Z have ~ 80, 91 GeV

mass. The postulated Higgs boson is a scalar.

J = 1 g,γ, W+,Zo,W- Force Carriers

J = 1/2

u

d

c

s

t

b

e

νe

μ

νμ

τ

ντ

Q/e=

2/3

-1/3

1

0

Quarks

Leptons

HJ= 0


Fundamental Forces -

Strong Fundamental Forces Fundamental Forces --

Strong Strong

2 / 4 ~ 0.12( ) , ~ 0.2( ) 0

3 3 1 8, 3 3 3 1 8 8 10

s s

s

s

gGeV

α παα

=Λ → ∞ Λ∞ →

⊗ = ⊕ ⊗ ⊗ = + + +

Strong interactions : quarks carry color as do gluons. Because of this non-Abelian

property the strong coupling diverges at low mass scales and vanishes at high mass scales. The latter property makes perturbative

calculation in p-p

possible. There are 3 low mass quark flavors ( u, d, s) that bind into the observed low mass mesons and baryons in SU(3) multiplets.


Forces -

GravityForces Forces --

GravityGravity•Gravitational coupling constant is not dimensionless as in EM, weak and strong. Coupling is universal, however as in EM, e. There are non-Abelian

features –

“gravity

gravitates”

-> non-linear GR.

•

Gravity becomes strong only at a very high mass scale•

Very bad high energy behavior. Not

renormalizable. Impossible for 4-D point particles -> strings, extra dimensions?.

GeVxM

cMGNG19

2

103.1~

4/1.0~ hπα =


Forces -

Weak InteractionsForces Forces --

Weak InteractionsWeak Interactions•Fermi theory –

a universal coupling G between 4

fermions. Use muon

lifetime to find value for G. G is not dimensionless.•[G] –

1/M2

.

Low energy weak interactions grow rapidly with mass scale.

•

Bad high energy behavior. Violates unitarity

at a few 100 GeV

CM energy

πννσ /)( 2sGee =+→+

Gs

s

/2

/42

π

ππσ

<

=< D


Electro -

Weak UnificationElectro Electro --

Weak UnificationWeak Unification•In the 1980’s we found that weak interactions only appear to be weak at low energies.

•At energies above the W and Z mass the electromagnetic and weak forces are ~ equal. The coupling constants are ~ equal and the forces are unified.

8( ) / ( ) ~ 3 10o xμπ γ γ π μ ν+ +Γ → + Γ → +

2 2/W Wg M

2 2 2

2 2 /

1/ , 1/( )/ , /

sin

rW

W W

q q me r g e re g θ

−

+

=

D


Weak Interactions -

IIWeak Interactions Weak Interactions --

IIII•Partially solved by having G arise from a coupling constant (dimensionless, universal) and a propagator for a massive gauge boson

•This is not enough to preserve unitarity. W+W scattering diverges badly. S wave scattering amplitude violates unitarity

at a mass scale ~ 1

TeV

-> hence the LHC. What is EWSB?

2

2

2/

30/1~4/

sin

WW

WW

WW

MG

g

eg

πα

πα

θ

=

=

=

2( ) ~ 3 /16

4 / 3 ~ 1o W W

W W

W W W W s M

M s M TeV

α

α

Α + → +

= <


Strong and Weak are non-Abelian, Photon is Uncharged

Strong and Weak are nonStrong and Weak are non--AbelianAbelian, , Photon is UnchargedPhoton is Uncharged

2 2 2,E P M P P Mμμ= + ⋅ =

2( ) Mφ φ φφ= ∂ ∂ −l

To describe quantum fields we will use ψ for fermion (J = ½) fields, φ for scalar (J = 0)fields, and ϕ for vector (J = 1) gauge fields. For masses, m is used for fermions and M forbosons.

2

( )( ) ( )( )~ ( ) ,I

D Dg g

ϕ ϕ ϕ ϕ

ϕ ϕϕ ϕϕϕϕ

∂ ∂ →

∂l

Pr

by AePrr

−

μμμμ ieAD −∂=→∂

ggggggg, ZWWWW −+−+ ,γ −+−+−−+−+ WWWWZZWWZWWWW ,,, γγγ

Classical

Lagrangian

density

Classical gauge replacement

Quantum gauge replacement


WW Cross Section at LEPWW Cross Section at LEPWW Cross Section at LEP

COMPHEP point shown. Proof that the WWZ triple gauge boson coupling is needed. The LEP result has established the non-

Abelian

nature of the EW coupling of vector bosons.


ZZ at LEPZZ at LEPZZ at LEP

SM has only the single Feynman diagram. There are no relevant triple or quartic

couplings. Use the data to set limits on couplings beyond the SM.


Higgs Width -

WW + ZZHiggs Width Higgs Width --

WW + ZZWW + ZZ

Higgs decays to V V have widths Γ

~ M3

Try this as a COMPHEP example ?

Note that Higgs width ~ Mass at 1 TeV

-> unitarity

violation if Higgs mass is too large.


A Few Unresolved Fundamental Questions in HEP

A Few Unresolved Fundamental A Few Unresolved Fundamental Questions in HEPQuestions in HEP

•

How do the Z and W acquire mass and not the photon?

•

What is MH

and how do we measure it?•

Why are the known mass scales so different? ΛQCD

~ 0.2 GeV

<< EW <φ> ~ 246 GeV

<< MGUT

~ 1016

GeV

<< MPL

~ 1019

GeV•

Why is charge quantized?

•

Why is matter (protons) ~ stable?•

Why is the Universe made of matter?

•

What is “dark matter”

made of? Dark energy?•

Why is the cosmological constant small?

•

How does gravity fit in with the strong, electromagnetic and weak forces? Are there extra dimensions in the Universe, as yet unobserved?


Why the LHC ?Why the LHC ?Why the LHC ?

Higher energy means larger mass –

up to the TeV

mass scale where we know new physics must appear. LHC experimental designs follows from the plan to find the SM Higgs boson.


Back to the BeginningBack to the BeginningBack to the Beginning


CERN SiteCERN SiteCERN Site

Lake GenevaLake GenevaLarge Hadron

Collider

27 km circumferenceLarge Large HadronHadron

ColliderCollider

27 km circumference27 km circumference

CMSCMS

ATLASATLAS

LHCbLHCb

ALICEALICE


LHC Accelerator -

DipolesLHC Accelerator LHC Accelerator --

DipolesDipoles

To reach the required energy in the existing tunnel, the dipoles operate at 8.3 T & 1.9 K in superfluid

helium. That makes the LHC the coldest extended place in the entire universe

wrt

Tevatron

(USA)Energy

x 7 luminosity x 20


Detection of Fundamental Particles

Detection of Fundamental Detection of Fundamental ParticlesParticles

Particletype

Tracking ECAL HCAL Muon

γ

e

μ

Jet

Etmiss

EM force

(Bremm

+ pair )

leptons

(ionize)

q, g

ν


The Large LHC ExperimentsThe Large LHC ExperimentsThe Large LHC Experiments


Cosmic Ray CommissioningCosmic Ray CommissioningCosmic Ray Commissioning

Both CMS and ATLAS have taken several 100 million cosmic ray events in order to align and calibrate the detectors while awaiting the LHC collisions.


Cosmic Rays -

IICosmic Rays Cosmic Rays --

IIII


Cosmic Muon

-

SpectraCosmic Cosmic MuonMuon

--

SpectraSpectra

Magnet test: alignment of the muon

system. Movement in 3.8 T field tracked. Checked to be “elastic”. Extract charge ratio for cosmic rays.


2008 First Events: Collimators Closed

2008 First Events: Collimators 2008 First Events: Collimators ClosedClosed

~2.109

protons on collimator ~150 m upstream of CMSECAL-

pink; HB,HE -

light blue; HO,HF -

dark blue; Muon

DT -

green; Tracker Off


2008 Beam Halo Events 2008 Beam Halo Events 2008 Beam Halo Events


2009 -

Start to Rediscover the SM

2009 2009 --

Start to Rediscover the Start to Rediscover the SMSM

L for 1 month run (106

sec)

Integrated L Trigger Process Comments

1023 100 mb-1 NoneσI

~ 50 mbInelasticnon-diff

Input to tweak Pythia

1024 1 μb-1 Setup Jet Inelasticnon-diff

Calib

in azimuth

1025 10 μb-1 Jetσ(gg) ~ 90 μbσ(ggg) ~ 6 μb

g+g

-> g+gg+g

-> g+g+gEstablish JJ

cross section

1026 100 μb-1 Jet g+g

-> g+gg+g

-> g+g+gDijet balance for polar angle –

Establish MET

1027 1 nb-1 JetSetup Photonσ(qγ) ~ 20 nb

g+g

-> g+gg+g

-> g+g+gq+g

-> q+γ

Dijet masses > 2 TeV, start discovery search.J+γ

calib


Kinematics -

RapidityKinematics Kinematics --

RapidityRapidityOne Body Phase Space

NR

φddPPdPdPdPPd TT||2 =Ω=

r

( ) EPdmPPd /224r

=−δ( )2

TPdydπ=EdPdy /||=

Relativistic

6.9,7.7,14,2@

,0max

cosh

max

222

=

=+=

=

yTeVpp

momentumbeamPatyPmm

ymE

T

TT

T

Rapidity

If transverse momentum is limited by dynamics, expect a uniform distribution in y

Kinematically

allowed range in y of a proton with PT

=0


Rapidity “Plateau”Rapidity Rapidity ““PlateauPlateau””Monte Carlo results are from COMPHEP -

running under Windows or Linux

Region around y=0 (90 degrees) has a “plateau”

with width Δy ~ 6 for LHC

LHC


Rapidity Plateau -

TevatronRapidity Plateau Rapidity Plateau --

TevatronTevatron

Existing data exhibits a plateau in rapidity.


Minbias

Rapidity DensityMinbiasMinbias

Rapidity DensityRapidity Density

Using data from 0.2 to 1.8 TeV

to

extrapolate the plateau rapidity density. For all pions

expect

Note –

2x extrapolation from 0.9 TeV

1/ ( / ) ~ 9o

d dρ σ σ η

π π π+ −

=

= =


Charged Particle RapidityCharged Particle RapidityCharged Particle Rapidity


Minimum Bias EventsMinimum Bias EventsMinimum Bias Events

Use dE/dx

in the CMS tracking system to do particle identification. Extract the charged particle cross section vs. particle type as a function of y and Pt

Useful for overlap to simulate high luminosity pileup. Must tune Monte Carlo models, e.g. for triggering.


Minbias

–

Pt DataMinbiasMinbias

––

Pt DataPt Data

Extrapolations of the Pt distribution and average values.

Expect <Pt> ~ 0.65Note the factor ~ 100 drop in single tracks (tracker alignment) from 14 ->0.9 TeV

for Pt = 6 GeV


First Data, 0.9 TeV, ~5 First Data, 0.9 First Data, 0.9 TeVTeV, ~5 , ~5 1bμ −


The Underlying EventThe Underlying EventThe Underlying Event

Extrapolation of the UE is uncertain. The UE is crucial for trigger strategy –

e.g. lepton isolation. Must tune the CMS Monte Carlo to have a valid representation of the UE and the minbias

pileup.


s Quark Secondary Verticess Quark Secondary Verticess Quark Secondary Vertices


Tracker dE/dx

for K, pTracker Tracker dE/dxdE/dx

for K, pfor K, p

CMS Preliminary CMS Preliminary 20092009

√√s=900GeVs=900GeV

(GeV/c)


Minbias

Pions

and ECALMinbiasMinbias

PionsPions

and ECALand ECAL

~ 0.14 /~ ~ 14 / ( )

o

GeV Pds R cm P GeV

π

π

π γ γθ

θ

→ +

Use charged pions

at moderate Pt to start tracker alignment in 2009 and start in situ HCAL. Neutral pions

can be used for ECAL.

γ

γπo


Higher Mass di-photonsHigher Mass Higher Mass didi--photonsphotons


Jets at 0.9 TeVJets at 0.9 Jets at 0.9 TeVTeV

First seem SM “objects”

are the strongly produced Jets.


“Back to Back Jets”““Back to Back JetsBack to Back Jets””

Start to establish jet resolution by comparing Pt of the 2 jets


Lepton Candidates -

eLepton Candidates Lepton Candidates --

ee

With the luminosity taken at 0.9 and 2.4 TeV

in 2009 one expects only a few leptons from b Jet semi-leptonic

decays. Can start to debug “b tagging”

and electron and muon

id (muons

from CRAFT in place already).


Lepton Candidates -

MuonLepton Candidates Lepton Candidates --

MuonMuon


Parton and Hadron

DynamicsParton and Parton and HadronHadron

DynamicsDynamicsFor large ET

, or short distances, the impulse approximation means that quantum effects can be ignored. The proton can be treated as containing partons

defined by distribution functions. f(x) is the probability distribution to find a parton

with momentum fraction x.


Parton Distribution Functions (PDF)

Parton Distribution Functions Parton Distribution Functions (PDF)(PDF)

The LHC data will probe regions of the distribution functions which are not yet explored. It is important to have a reliable set of verified PDF in order to model new physics and SM backgrounds.


p-p

Collisions -Valence?pp--pp

Collisions Collisions --Valence?Valence?

Valence dominates quarks for x > 0.04. Sea dominates at low x for quarks.

Gluons dominate all quarks for x < 0.2.


2-->2 Formation Kinematics22---->2 Formation Kinematics>2 Formation Kinematics

θθ

βγ

τ

τ

tan/1sinhsin/1cosh

:0/,/

)/ln(2~,)/(~,sinh

cosh

/0

,/

,/2

222

||

21

212

21

||

==

===

+=

Δ=

=

===⇒=

=−==

=

yy

mEPmE

Pmm

MsyesMxymP

ymE

sMxxx

xxxsMxx

sPx

TT

yT

T

E.g. for top quark pairs at the Tevatron, M ~ 2Mt ~ 350 GeV. <x> ~ √τ~350/2000 ~ 0.18 -> valence quarks.

x1 x2

2

2 2 2 21 2 1 2

~ 4~ [( ) ( ) ]

s PM P x x x x+ − −


Hadronic

Cross SectionsHadronicHadronic

Cross SectionsCross Sections

( ) )4321(ˆ)()(/

)4321(ˆ)()(//ˆ

/ˆ)4321(ˆ)()(ˆ

210

2211

221

212211

+→+=

+→+===

==+→+==

= στττσ

στστ

τσσσ

dfCfdydd

dyddxfxCfdsMss

dydsdysddxdxddxdxxfxCfdPPd

y

BA

To form the system need x1

from A and x2

from B picked out of probability distributions with the joint probability PA

PB

to form a system of mass M moving with momentum fraction x. C is a color factor (later). On the plateau, the cross section is Δσ

~ (dσ/dy)y=0

Δy. The value of Δy varies only slowly with mass ~ ln(1/M)


Pointlike

Parton Cross Sections

PointlikePointlike

Parton Cross Parton Cross SectionsSections

Point-like cross sections for parton - parton scattering. The entries have the generic dependence already factored out. At large transverse momenta, or scattering angles near 90 degrees (y ~ 0),

the remaining factors are dimensionless numbers of order one.

Process 2A Value at θ = π⁄2 q q q q′ ′+ → + 2 2 24 [ ] /

9s u t+

2.22

q q q q+ → + 2 2 2 2 2 2 24 8[( ) / ( ) / ] ( / )

9 27s u t s t u s ut+ + + −

3.26

q q q q′ ′+ → + 2 2 24 [ ] /9

t u s+ 0.22

q q q q+ → + 2 2 2 2 2 2 24 8[( ) / ( ) / ] ( / )9 27

s u t t u s u st+ + + − 2.59

q q g g+ → + 2 2 2 2 232 8[ ] / [ ] /27 3

t u tu t u s+ − + 1.04

g g q q+ → + 2 2 2 2 21 3[ ] / [ ] /6 8

t u tu t u s+ − + 0.15

g q g q+ → + 2 2 2 2 24 [ ] / [ ] /

9s u su u s t− + + +

6.11

g g g g+ → + 2 2 29 [3 / / / ]

2tu s su t st u− − −

30.4

q q gγ+ → + 2 28 [ ] /9

t u tu+

g q qγ+ → + 2 21[ ] /

3s u su− +

Pointlike

partons

have Rutherford like behavior

σ

~ π(α1

α2

)|A|2/s

s,t,u

are Mandelstam variables. |A|2

~ 1 at y=0.


2-->2 and 2-->1 Cross Sections

22---->2 and 2>2 and 2---->1 Cross >1 Cross SectionsSections

( ) [ ] ( )

( ) [ ]

31 20

1 24 2

0 1 2 1 2

2

2

21 20

2 2 :ˆ ˆ/ 2 ( ) ( )

ˆ ˆ/

( / ) ~ [ ( ) ( )] ( )

2 1:ˆ 4 (2 1),

ˆ ˆ (2 1)( / ), int

/ ( ) ( )

y x

y x

y x

M d dydM C xf x xf x d s

d s

M d dydM C xf x xf x

J partial wave unitarity

ds J M egrate over narrow width

M d dy C xf x xf x

τ

τ

σ σ

σ πα α

σ πα α

σ π

σ π

σ

= =

= =

=

→

=

≈

→

< +

= + Γ

=

∫D

( ) [ ]

2

12

2 21 2 120

(2 1) /

/ ~ " "

/ ( ) ( ) (2 1)

ff

y x

J M

M

M d dy C xf x xf x J

τ

τ

π

α

σ π α

=

= =

⎡ ⎤Γ +⎣ ⎦Γ

⎡ ⎤= +⎣ ⎦

“scaling”

behavior –

depends only on τ

and not M and s separately


2--> 2 Kinematics -

“Decays”22----> 2 Kinematics > 2 Kinematics --

““DecaysDecays””

y

y

esMx

yyyesMx−=

+==

]/[

2/)(,]/[

2

431

x1 x2 x,y,M

y3

, y4 y*, θ*

Formation System Decay CM Decay

The measured values of y3

, y4 and ET

allow one to solve for the initial state x1

and x2 and the c.m. decay angle.3 4ˆ ( ) / 2

ˆ ˆcos tanh( )

y y y

yθ

= −

=


CM Energy and Discovery “Reach”

CM Energy and Discovery CM Energy and Discovery ““ReachReach””

For masses below ~ 1 TeV

the loss of luminosity of the fundamental interactions is modest in going from 10 to 14 TeV.


2010 -

Typical Statistics for a 10 TeV

Run

2010 2010 --

Typical Statistics for a Typical Statistics for a 10 10 TeVTeV

RunRun

Assume 200 pb-1, include acceptance, initial reconstruction and id efficiency

Establish Standard Model cross sections and distributions

Log ~ 200 pb-1

at 10 TeV

in 2010. This should be reliable data taking without Physics penalty for masses < 1 TeV.

Fir 1 /fb

~ scales ( 5 x ) the factor in parton

luminosity from 10 -> 7 TeV

min bias 2 x1013

Jet Et>25 6 x 1011

Jet Et>140 6 x 107

γ+Jet

Et>20 6 x 107

W ->lν 600,000

Z -> ll 60,000

tt-> lν4q 2000


Problems -

IProblems Problems --

II

1.

Download Calchep. Read the Users manual.

2.

Compute g+g->g+g

at low Pt.3.

Compute e+E->W+W and compare to LEP data.


Hand EstimatesHand EstimatesHand Estimates

0

2 ' 30

3

4

8

'

~ /~ ln(1/ )

~ ( / )

( / ) ( )(2 1)[ ( ) ( )] /

~ 1.8 (1 )

~ 0.7 (1 )

~ 0.2(1 )

( ) ~ / 4~ 2( 2 )

y

y

v

v

s

W

v v s

x M sy x

d dy y

d dy q q M J xf x xf x M

xu x x

xd x x

xq xq x

M q q MPDF xu xq xd xq xq xq

σ σ

σ π

α

=

=

ΔΔ

= Γ + → +

−

−

= −

Γ → ++ +

Just to get started make tree level LO hand calculations for a 2 -> 1 DY process.x is the minimum value, assume a plateau cross section and a plateau width. Take simple formula for valence and sea quark distributions. Assume EW coupling and width


Cross Sections -

EstimatedCross Sections Cross Sections --

EstimatedEstimated

Note that valence quarks dominate over sea for masses above ~ 1 TeV. Line is 1/M2

scaling –

not too far off simply extrapolating for inclusive W production


Estimate vs

Theory @ NLOEstimate Estimate vsvs

Theory @ NLOTheory @ NLO

Estimate assuming allowed EW transitions to

Width in formation assumed to be SM. For decays, SM EW gives a ¼

BR of W’

-> t+b

and a 1/9 BR of W -> u + v.

At 1 TeV

( ~ CDF limit ) LHC cross section into muon

+ MET + 2 b jets is 1.7 pb. Therefore, this search is “early physics”.

3( ) ( )ud cs tb eν μν τν+ + + + +

The Standard Model and Beyondvmsstreamer1.fnal.gov/VMS_Site_03/Lectures/LPC/...LPC Lectures, Feb.,...

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