1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill...

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1 From the Littlest to From the Littlest to the Largest: QCD to the Largest: QCD to the LBT the LBT The intersection of HEP and The intersection of HEP and Cosmology Cosmology M.S.S. Gill M.S.S. Gill OSU Astronomy Department Colloquium OSU Astronomy Department Colloquium Thursday, November 30, 2006 Thursday, November 30, 2006

Transcript of 1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill...

Page 1: 1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill OSU Astronomy Department Colloquium Thursday, November.

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From the Littlest to the From the Littlest to the Largest: QCD to the LBTLargest: QCD to the LBT

The intersection of HEP and CosmologyThe intersection of HEP and Cosmology

M.S.S. GillM.S.S. GillOSU Astronomy Department ColloquiumOSU Astronomy Department Colloquium

Thursday, November 30, 2006Thursday, November 30, 2006

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Talk PlanTalk Plan

A short history of HEP (high energy physics)A short history of HEP (high energy physics) The Standard Model edificeThe Standard Model edifice My work on form factors (i.e. the B meson My work on form factors (i.e. the B meson

internal wavefunction) and relation to QCD internal wavefunction) and relation to QCD A very significant era coming up for HEPA very significant era coming up for HEP Analogies and connections with cosmologyAnalogies and connections with cosmology Where weak lensing fits inWhere weak lensing fits in Our plans for using the LBT for a lensing surveyOur plans for using the LBT for a lensing survey

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The things to take awayThe things to take awayAfter evolving separately After evolving separately

for decades, physics and for decades, physics and astronomy have strongly astronomy have strongly rejoined as one field – rejoined as one field – overlap in DM especially..overlap in DM especially..

http://img-fan.theonering.net/rolozo/images/howe/oldwillow.jpghttp://watershed.ucdavis.edu/skeena_river/images/photos/Skeena/day02/images/AR_143.jpg

Essentially how the Essentially how the Universe came to be, Universe came to be, and what it’s made, of and what it’s made, of are inextricably linked are inextricably linked ideas at root.ideas at root.

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DM in many spheresDM in many spheres

Galaxy Dynamics

Colliders

Cosmological Component

Particle Theory

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Beginnings of HEPBeginnings of HEP 1869 Periodic table finalized1869 Periodic table finalized 1897 e- = electron (UK)1897 e- = electron (UK) 1910’s proton (UK etc.)1910’s proton (UK etc.) 1932 neutron (UK)1932 neutron (UK) 1932 e+ = positron (cosmic rays -- CA)1932 e+ = positron (cosmic rays -- CA) 1936 1936 Whoa! - (c. rays – CO and Whoa! - (c. rays – CO and

Panama )Panama ) 1947 1947 (c. rays – Pic du Midi, France (c. rays – Pic du Midi, France

and Chacaltaya, Bolivia (!) )and Chacaltaya, Bolivia (!) ) 1947 Kaon (c. rays – Mt. Wilson, CA)1947 Kaon (c. rays – Mt. Wilson, CA) 1947 Lambda (c. rays – UK)1947 Lambda (c. rays – UK)

http://www.physicscentral.com/action/2000/images/antimatter-img2.jpghttp://www.physicscentral.com/action/2000/images/antimatter-img2.jpghttp://nssdc.gsfc.nasa.gov/image/astro/hst_ngc3314_0014.jpg

[ By 1932: quite neat, tidy picture of three basic particles that explained everything in the Universe people had seen up to that point]

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More and More ParticlesMore and More Particles

1956 Electron neutrino (reactor – WA, GA)1956 Electron neutrino (reactor – WA, GA) 1950’s: Many, many more particles seen 1950’s: Many, many more particles seen

Picture has become complicated!!Picture has become complicated!! 1960’s: Quark theory proposed1960’s: Quark theory proposed Late 1960’s: Quarks confirmed (SLAC)Late 1960’s: Quarks confirmed (SLAC)

Known by late 60’sKnown by late 60’sKnown by late 60’s

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Finally: the “congealing” of the SM Finally: the “congealing” of the SM (The (The Standard ModelStandard Model))

Finally: the “congealing” of the SM Finally: the “congealing” of the SM (The (The Standard ModelStandard Model))

Late 60’s: Electroweak theory combines QED (Quantum Late 60’s: Electroweak theory combines QED (Quantum Electrodynamics) and Fermi theory of weak interactionsElectrodynamics) and Fermi theory of weak interactions

Also late 60’s: quarks + gluons = QCD (Quantum Also late 60’s: quarks + gluons = QCD (Quantum Chromodynamics)Chromodynamics)

1970’s-1990’s: all other predicted SM particles tracked 1970’s-1990’s: all other predicted SM particles tracked down (c,b,t quarks / down (c,b,t quarks / __ g; W+, W- ,Z0 force carriers) g; W+, W- ,Z0 force carriers)

The only “new” particles fit as an extra generation into The only “new” particles fit as an extra generation into the already existing theorythe already existing theory

Known by late 60’sKnown by late 60’sKnown by late 60’s

Found 70’s-90’s

“1974 November Revolution”

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By 1994: We Knew the Basic By 1994: We Knew the Basic Constituents of ALMOST Constituents of ALMOST Everything Everything in the SM in the SM

Matter particles: Force exchange carriers:

Only one particle remains: the elusive Higgs Boson :Only one particle remains: the elusive Higgs Boson :

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Building up from the blocksBuilding up from the blocks

How to make up hadrons from quarksHow to make up hadrons from quarks Now we see it’s back to being simple!Now we see it’s back to being simple! (My Thesis Particle!)

Both are Hadrons

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Why we know quarks are realWhy we know quarks are real

But instead of an isotropic But instead of an isotropic distribution of final state distribution of final state particles, we see jets = particles, we see jets = directions of original quarksdirections of original quarks

The two pictures are from 2-The two pictures are from 2-jet events at Aleph from jet events at Aleph from LEP (CERN LEP (CERN [“Where the Web was [“Where the Web was born” :-> ])born” :-> ])

Jets are one of the clearest Jets are one of the clearest demonstrations of initial demonstrations of initial state free quarksstate free quarks

Quarks can never be Quarks can never be isolated freely!!isolated freely!!

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The Higgs Mechanism and Cocktail The Higgs Mechanism and Cocktail PartiesParties

Analogy: the people “crowd around” a speaker giving her “mass” and slow her downHer “mass” is proportional to her popularity – different for different individualsThe Higgs field fills all space, yet is difficult to understand and find! Analogy with dark energy (field)..?! Higgs is sometime called the “God Particle”, tongue-in-cheekily

http://www.hep.ucl.ac.uk/~djm/higgsa.html

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Known Unknowns in the SMKnown Unknowns in the SM

What do we know, and not know, in the SM?What do we know, and not know, in the SM? Know contents: Exchange bosons + fermions + Know contents: Exchange bosons + fermions +

Higgs Higgs mechanismmechanism Don’t Don’t know if a single Higgs scalar is responsible know if a single Higgs scalar is responsible

for the Higgs mechanismfor the Higgs mechanism

}{),,(),,,,( 00 HlqgZW

We know every single parameter (quite well) – except for We know every single parameter (quite well) – except for is what determines the HIGGS MASS (as )is what determines the HIGGS MASS (as )

v

Full set of 18 SM Parameters:

(NB: Strong CP Problem ignored Here)

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top quark

anti-top quark

ZW+, W-

. . . .

e e- u d s c b

gluons

Unknowns Example: Elementary Particles and Masses

( Mass proportional to area shown: proton mass = )

Why are there so many? Where does mass come from? (Slide credit: Y.K. Kim)

“Crazy” Huge Mass!!

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Better understood: Extracting V_cb Better understood: Extracting V_cb from B->D*from B->D*l l Decay (i.e. probing the Decay (i.e. probing the

B Meson Wavefunction)B Meson Wavefunction)

Look at one specific decay -- quark level diagram:

Observed particle level diagram:

Goal: Measure precisely one of the fundamentalSM parameters (V_cb)(measures amount ofquark b to c mixing)

CKM Matrix

“hadronization”

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B0 Wavefunction impact on V_cbB0 Wavefunction impact on V_cb

Contribution to systematic error on V_cb from Form Factors (the largest source) went down from 2.7 to 0.5%

Previous Rough Measurement that went into our MC (“SP4”) (CLEO is at Cornell)

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[Our secondary goal: checking QCD models through probing B meson Wavefunction – [Our secondary goal: checking QCD models through probing B meson Wavefunction – (specifically: Heavy Quark Effective Theories) – everything checked out just fine :-> ](specifically: Heavy Quark Effective Theories) – everything checked out just fine :-> ]

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dof/dof= 7.3 / 9

(Bbr = Babar experiment at SLAC)

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Knowns Example: Experimental Knowns Example: Experimental Constraints on “Unitarity Triangle”Constraints on “Unitarity Triangle”

Many many decay modes and thousands of human-years representedhere: and everything fits

The triangle closes and all the bands overlap – the SM is too good! No significant deviations seen in any decay!

Our measurement was critical for the length of this side

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UnknownsUnknowns: Back to Incompleteness : Back to Incompleteness of SMof SM

Neutrino Masses not in Minimal SMNeutrino Masses not in Minimal SM Everything else Everything else fits so far -- but 18 fits so far -- but 18

Parameters not explained Parameters not explained GUTs? GUTs? SUSY? String Theory? XD? Something SUSY? String Theory? XD? Something Else?Else?

Theoretical issues: Hierarchy problem etc.Theoretical issues: Hierarchy problem etc. NoNo allowance for DM (let alone DE) allowance for DM (let alone DE) WHAT is DM?! (i.e. the Dark Side of the WHAT is DM?! (i.e. the Dark Side of the

Universe) – who is behind the mask??!Universe) – who is behind the mask??!

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Massive Massive ’s in HEP and Cosmo’s in HEP and Cosmo

The low mass The low mass ’s are known to be a small ’s are known to be a small component total Universe matter density component total Universe matter density from cosmological (structure formation) from cosmological (structure formation) constraintsconstraints

But heavy mass right-handed But heavy mass right-handed ’s ’s maymay well well be some component of the DMbe some component of the DM

??

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DM and GUTsDM and GUTs Massive Massive ’s ’s notnot accounted for in SM accounted for in SM But they generically fit very well into GUTs – the But they generically fit very well into GUTs – the

Holy Grail of HEPHoly Grail of HEP Would be nice to see this…!Would be nice to see this…!

But we are “only” here, currently

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LHCLHC

MostMost extensions of SM predict more extensions of SM predict more particles at LHC (Large Hadron Collider)particles at LHC (Large Hadron Collider)

LHC: collide 2 p's together at 14 TeV = 7 LHC: collide 2 p's together at 14 TeV = 7 times Fermilab CM energytimes Fermilab CM energy

MayMay find DM candidates find DM candidates [ Atlas zoom-in and collision clips ] [ Atlas zoom-in and collision clips ]

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A Most Amazing Moment for HEPA Most Amazing Moment for HEPAfter nearly 40 years of waiting – After nearly 40 years of waiting –

HEP may be in for a wild rideHEP may be in for a wild rideCould see: 1. Nothing Could see: 1. Nothing 2. one Higgs 2. one Higgs

onlyonly, , 3.Signature of one of the 3.Signature of one of the worked out extensions or..worked out extensions or..

4. Something new4. Something newCould: be within first few weeks.Could: be within first few weeks.Or several years down the roadOr several years down the roadSeeing DM candidate would once Seeing DM candidate would once

again complete the Astro-HEP again complete the Astro-HEP cyclecycle

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Precision Measurement Constraints Precision Measurement Constraints Point to a low mass HiggsPoint to a low mass Higgs

Multiple Electroweak precision Multiple Electroweak precision measurements are pointing to a low measurements are pointing to a low mass Higgs if it’s a single SM particlemass Higgs if it’s a single SM particle

If not – we still strongly believe we will If not – we still strongly believe we will see signals of whatever is the see signals of whatever is the Electroweak Symmetry Breaking Electroweak Symmetry Breaking mechanism is below 1 TeV – i.e. mechanism is below 1 TeV – i.e. within the LHC reach.within the LHC reach.

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Accelerators

BigBang

Inflation

Looking back in time: with accelerators and telescopes!

E = mc2

(Slide credit: Y.K. Kim)

TelescopesTelescopes

Larger Aperture

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Shifting gears to the Shifting gears to the LargeLarge(Or:(Or: a a veryvery short history of cosmology) short history of cosmology)

Humans found: Planets Humans found: Planets Stars Stars Galaxies Galaxies Hubble Expansion Hubble Expansion

DM was known of since Zwicky, but not DM was known of since Zwicky, but not fully accepted until the 70’sfully accepted until the 70’s

Known by late 80’s that DM didn’t make Known by late 80’s that DM didn’t make =1=1

Yet a flat Yet a flat =1 =1 Universe was observed Universe was observed more and more clearly.more and more clearly.

DE had always been an options as DE had always been an options as making up the rest of the 70% of making up the rest of the 70% of -- but -- but it was “unpalatable” it was “unpalatable” (Kolb+Turner)(Kolb+Turner)

Only in the late 90’s did SN observations Only in the late 90’s did SN observations convince peopleconvince people

CFHT, 2005

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Some Types of Cosmological Some Types of Cosmological Observables Observables

Galaxy clusters / BAO : correlations Galaxy clusters / BAO : correlations [E.Rozo][E.Rozo]BBN: IGM and stellar spectra BBN: IGM and stellar spectra [G. Steigman, M. [G. Steigman, M.

Pinsonneault, T. Walker, V.Simha]Pinsonneault, T. Walker, V.Simha]

CMB: affects most cosmic parametersCMB: affects most cosmic parametersCosmic Rays: DM sources? Cosmic Rays: DM sources? [J. Cairns, H. Yuksel, [J. Cairns, H. Yuksel,

M. Kistler, G. Mack]M. Kistler, G. Mack]

SN: expansion history SN: expansion history [J. Beacom , J. Prieto][J. Beacom , J. Prieto]

Weak and Strong Lensing: galaxy clusters Weak and Strong Lensing: galaxy clusters and cosmological and cosmological [Chris K., M. Peeples, P.Martini, J.Yoo, [Chris K., M. Peeples, P.Martini, J.Yoo, D. Weinberg, MSSG]D. Weinberg, MSSG]

[ NB: NOT a comprehensive listing of all work related to cosmology at OSU, onlyA few examples here! Many other people have done related work!]

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LCDM Cosmological Parameter SetLCDM Cosmological Parameter Set

Goals are similar to SM: describe full Goals are similar to SM: describe full picture with a few parameterspicture with a few parameters

But still in the infancy, not so well But still in the infancy, not so well defined – e.g. whether the parameters defined – e.g. whether the parameters for inflation should be usedfor inflation should be used

But the minimal set people usually use But the minimal set people usually use is: is: “Vanilla” params: {_ ≈ 0.75, _m ≈ 0.25, _b ≈ 0.05,

H_0 ≈ 70 km /s/ Mpc, Σm_ <~ 1eV , w ≈ 1 , }

Extra: {_8 ≈0.9 f_nu, _k, r, n_s, z_reion, tau_reion , w_a etc. }

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Table of the Cosmological Table of the Cosmological ParametersParameters

-This indicates it is unclear just what set should be used… not as well-defined yet as the SM

Still much uncertaintyin what parameters to use in fits

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Evolution of the background densities: 1 MeV → now

photons

neutrinos

cdm

baryons

Λ

m3=0.05 eV

m2=0.009 eV

m1≈ 0 eV

Ωi= ρi/ρcrit

(Slide credit: S. Pastor)

-UL on Σm_n <~ 1eV -LL on at least one:0.05 eV

We will likely know The neutrino massesWithin 10 yrs..!

Neutrino Masses:

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Basic Weak Lensing GeometryBasic Weak Lensing Geometry

(Narayan+Bartelmann, 1997)

Mass Profile of Lens

DeflectionAngle:

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Analogy to Probing the Insides of a Analogy to Probing the Insides of a HadronHadron

Translate to mass Translate to mass profile – can analogize profile – can analogize to extracting form to extracting form factor (~wavefunction) factor (~wavefunction) of a hadron)of a hadron)

zcDD

Dd)(

2)(

2sd

ds rθ

ObserverSourceLensing

mass

Contains Mass Profile Information

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Lensing Effect on Background Lensing Effect on Background GalaxiesGalaxies

ForegroundCluster

BackgroundSourceshapeNote: the effect has been greatly exaggerated here

(Orig Figure: S.Dodelson)

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Simulations of COWL Simulations of COWL (Cosmological Weak Lensing)(Cosmological Weak Lensing)

Field on the right has higher Field on the right has higher _m

(Orig Figure: S.Dodelson)

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Several Upcoming COWL Several Upcoming COWL SurveysSurveys

Panstarrs

LSST

LBT-OWLS

Dark Energy Survey

SNAP

(Orig Figure: S.Dodelson)OSU

?

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Photometric RedshiftPhotometric Redshift We may ultimately use several We may ultimately use several

bands to obtain zp estimates bands to obtain zp estimates and increase weak lensing and increase weak lensing signalsignal

But so far, in the Winter Run it But so far, in the Winter Run it looked unpromising to use 3 looked unpromising to use 3 band information for this – band information for this – better to get more clusters and better to get more clusters and source galaxies source galaxies [Dec 2 update : [Dec 2 update : see next page!]see next page!]

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Use Photometric Redshift to Use Photometric Redshift to Strengthen Lensing Signal ?Strengthen Lensing Signal ?

Number of galaxies From HyperZ (photoZ code): # of entries vs. zp3-zp5

Where: zp3 = 3-band photoZ, zp5 = 5-band photoZ

Looks promising potentially, but we found only about 60% of zp3<0.3 matched zp5<0.3, which would not strengthen our weak lensing signal dramatically

So we are not planning for the Winter run to do 3 band observing[ Update: Dec 2 – new work by P. Martini indicates it may in fact be useful, so we will use 3 bands! ]

[Thanks for discussions to: N. Morgan, R. Assef]

zp3 – zp5

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CLWL (Cluster Weak Lensing)CLWL (Cluster Weak Lensing)

We can determine some of the We can determine some of the CDM CDM params from CLWL, using params from CLWL, using

1. Total Mass of cluster at a given z1. Total Mass of cluster at a given z2. Radial mass profiles 2. Radial mass profiles

z = 7 z = 5 z = 3

z = 1 z = 0.5 z = 0

dark matterdark matter

timetime

5 MpcKravtsov

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LBT OWLS ProjectionsLBT OWLS Projections

Projections for LBT with several clusters Projections for LBT with several clusters by next Autumnby next Autumn

(Plot: J. Yoo)

Assumes lensing using 50 richest clusters in observed 250 degree squared field with all background (lensed) galaxies at z=0.6

Colors are 1,2,3 sigma countours

Here: sigma_8 vs. Omega_m

We may be getting first data as early as JANUARY – need full weak lensing pipeline set up by then – this is my priority at the moment!

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Other Parameters from OWLSOther Parameters from OWLS

(Plot: J. Yoo)

Here: w vs. Omega_m and w vs. sigma_8

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DES Projection for Sky CoverageDES Projection for Sky Coverage

Blanco 4-m Optical Telescope at CTIO: 5000 sq. deg. Dark Energy Survey

(Fig: J.Frieman)

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Summing Up: HEP + Cosmology Summing Up: HEP + Cosmology makes a “power duo”makes a “power duo”

We are entering a bold new era: where We are entering a bold new era: where “Large” is the name of the game“Large” is the name of the game

Potential to make progress on some of Potential to make progress on some of the fundamental questions of our timethe fundamental questions of our time

LHC and LBT+friends both have LHC and LBT+friends both have profound potential to reveal a whole new profound potential to reveal a whole new level of information about our Universelevel of information about our Universe

Dream Big, friends. :->Dream Big, friends. :-> [ CMS construction video ][ CMS construction video ]

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END!END!

Go to backup slides……………..Go to backup slides……………..

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SM Math Simplified SM Math Simplified 1: QED & QCD Parts – “easy” 1: QED & QCD Parts – “easy”

partpart We will list only type 3 (interaction) terms – all We will list only type 3 (interaction) terms – all

cyan circles surround couplings known i.t.o. cyan circles surround couplings known i.t.o. basic SM parametersbasic SM parameters

QED LL: All chemistry, Solid state physicsAnd much of astrophysics:

QCD L :L :Nuclear physics,Neutron stars, etc. :

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SM Math Simplified SM Math Simplified 2: Electroweak Part: matter2: Electroweak Part: matter

Next: Electroweak theory of fermions Next: Electroweak theory of fermions (l,(l,,q) and ,q) and spin-1 bosons (W+, W-, Z)spin-1 bosons (W+, W-, Z)

WW

W

WolfensteinForm of CKMMatrix:

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4646

SM Math Simplified SM Math Simplified 3: Electroweak Part: with Higgs3: Electroweak Part: with Higgs

We know every single parameter (quite well) – except for We know every single parameter (quite well) – except for is what determines the HIGGS MASS (as )is what determines the HIGGS MASS (as )

v

All functions of Known SM params:

v

All 18 SM Params:(NB: Strong CP Problem ignored Here)

Page 47: 1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill OSU Astronomy Department Colloquium Thursday, November.

4747

CKM matrix unitarity significanceCKM matrix unitarity significance

Page 48: 1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill OSU Astronomy Department Colloquium Thursday, November.

4848

Getting to Unitarity TriangleGetting to Unitarity Triangle

Page 49: 1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill OSU Astronomy Department Colloquium Thursday, November.

4949

B0 Mesonpositron

electron50% Matter50% Anti-Matter

ColliderCollider Level Diagram Level Diagram

Anti-B0 Meson

Page 50: 1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill OSU Astronomy Department Colloquium Thursday, November.

5050

General Categories of HEP General Categories of HEP ExperimentsExperiments

Accelerator-based: [e, p], n, Accelerator-based: [e, p], n, Collider and fixed-targetCollider and fixed-targetNon-accelerator: proton decay, Non-accelerator: proton decay,

neutrinoless double beta decayneutrinoless double beta decayCosmic-ray: charged particlesCosmic-ray: charged particlesCosmic-ray: neutrinosCosmic-ray: neutrinos

Page 51: 1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill OSU Astronomy Department Colloquium Thursday, November.

5151

Definite new physics: massive nu’sDefinite new physics: massive nu’s

Massive nu’s not accounted for in SMMassive nu’s not accounted for in SM Even if you added just a RH partner, it Even if you added just a RH partner, it

doesn’t couple as the other SM charged RH doesn’t couple as the other SM charged RH partners dopartners do

ONLY a left-handed nu couples to WONLY a left-handed nu couples to W Also: mass scale is pointing to a different Also: mass scale is pointing to a different

mechanism for mass, like the see-saw mechanism for mass, like the see-saw

eV

atm

atm

solar

solar

eV 0.009 Δm

eV 0.05Δm

2sun

2atm

NO

RM

AL

INV

ER

TE

D

Page 52: 1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill OSU Astronomy Department Colloquium Thursday, November.

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Allowed EqsAllowed Eqs

2

2

]1[akc

tot

2mc=EPaul M. told me this is the only equation I’m actually allowed to put into a talk:

Since I’ve already broken the rule, I’ll put in at least the natural extension of this, From SR GR, we get the Friedmann Eq. – and we sum up the contents and structureof the Universe in one eq.:

Page 53: 1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill OSU Astronomy Department Colloquium Thursday, November.

5353

Timeline of Structure Formation In The Universe

3410 sect

Quantum Mechanical Fluctuations

during Inflation

( )V

Perturbation Growth: Pressure

vs. Gravity

t ~100,000 years

Matter perturbations grow into non-

linear structures observed today

, ,reion dez w

Photons Photons freestream: freestream: Inhomogeneities Inhomogeneities turn into turn into anisotropiesanisotropies

m, r , b , f(slide credit: S. Dodelson)

Page 54: 1 From the Littlest to the Largest: QCD to the LBT The intersection of HEP and Cosmology M.S.S. Gill OSU Astronomy Department Colloquium Thursday, November.

5454

Graphic Illustration of CausticsGraphic Illustration of Caustics

Sources are magnified and distorted by Sources are magnified and distorted by lenslens

Source plane vs. image planeSource plane vs. image plane