# Presentation: 002157

## ESTIMATING THE MASSES OF ELEMENTARY PARTICLES

**Rajan Gupta**
** ****Los Alamos National Laboratory**

## A FASCINATING STORY OF THE DISCOVERY AND IDENTIFICATION OF ELEMENTARY PARTICLES,  AND THE SUBSEQUENT DETERMINATION OF THEIR MASSES.

## Elementary Particles

- With our current understanding, the world of elementary particles is first encountered at the level of atoms (10-10 m)

-  Electrons
-  Nucleus

- nucleons (protons, neutrons)

- quarks and gluons

## Slide 4

## Standard Model

***L ****= ****L****(QCD)**  +  ****L ****(SU(2)**L** ****  U(1)**Y **)** + ****L ****(Higgs) + ****L ****(Y)** *

*L**(QCD) =*  *-* 1/4 Ga Ga  +  Q ( i  + gaAa  )Q

***L ****(SU(2)**L** ****  U(1)**Y **) = -* 1/4 Wa Wa  *-* 1/4 B B
- 			                   + L (g2aWa   + g1Y B  ) L
- 				 + R (g2aWa   + g1Y B  )  R
- 				 +  L (i  ) L

***L ****(Higgs)  = **(**D** **** **)*†*(**D** **** **) **-** **(**-****h**2** ** **** *†***   +  ****h **/4** (***†***)**2** ** )** *

***L ****(Y) = * Q Mq* *Q +  L Ml L* + **M**q**/v**  *QHQ + Ml/ *v* LHL* *

## History of the Standard Model 

_**History of the Standard Model **_

- Electro- 	Coulomb, Faraday, Maxwell (1864)	magnetism
- QED	Tomonaga, Schwinger, Feynman 1949
- Weak	Fermi 1934 (Fermi Theory) 				Marshak & Sudarshan,  Feynman & 			Gell-mann 1958 (V-A)
- Electro- 	Glashow, Salam, Weinberg 1969; 	weak 	‘t Hooft & Veltman 1972 (renormalizable)
- QCD	Gellmann,  Zweig 1963 (quarks)			Quarks and gluons (dynamics) 1972			Politzer, Gross & Wilczek (1973 asymptotic freedom)

## KEY IDEAS IN THE THEORY 

_**KEY IDEAS IN THE THEORY **_

- Relativity: 	Einstein 1905-1915
- Quantum 		Bohr, Born, de Broglie, Heisenberg, Mechanics: 	Pauli, Schrodinger, 1913-1927
- Antimatter:	Dirac 1928
- Non-abelian	Yang & Mills, 1954
- Higgs		Higgs 1964

## WHERE ARE THE ELEMENTARY PARTICLES

**ELECTRONS (****e****), MUONS (********), THEIR NEUTRINOS (**e , **),  PHOTONS (********), ARE THE ONLY ELEMENTARY PARTICLES THAT EXIST COPIOUSLY IN NATURE.**
**ALL OTHERS HAVE TO BE CREATED IN HIGH ENERGY ACCELERATORS AND THEN STUDIED IN COMPLEX DETECTORS**

## PARTICLE ACCELERATORS

_**PARTICLE ACCELERATORS**_

*E* increases E by E = Fd = qV = q*E*d
- Constant *B* bends beam in a circle of radius  = pc/q*B*

- V=*E*d

******E = qV**

- Accelerators are based on 2 properties of the electromagnetic force F = q(*E* + v*B*)

## SLAC (e-, e+)

**OTHER** **(****e****-****, e****+****) MACHINES: CORNELL, DESY, LEP**

## FERMILAB (p,p)

**OTHER** **(p,********p) MACHINES: CERN (LHC)**

## PARTICLE DETECTORS

- COMPLEX, MULTILAYERED & HUGE

- Electronics on beam pipe

- CDF in collision hall

- Inserting the silicon vertex tracker in the 2000 ton central detector. West plug also shown

- Curtsey of FNAL & CDF collaboration

## WHAT IS MASS

- E2 = p2c2 + m2c4  & p = mv
- E = h and p = h/
- Pole in the propagator
- Axial Symmetry  relation between currents

**knowing E & p gives m**

## DETERMINING MASSES

- Are the particles sufficiently “long-lived” to leave a measurable track
- Are they electrically charged
- Do they have well-defined decay channels

**PROPERTIES THAT FACILITATE DETECTION**

## e Tracks in B field

**e, ******** LEPTONS ARE EASY TO PRODUCE & DETECT**

## CHARGED LEPTONS

- e+ , e-		0.511 MeV	Stable
- +, -	105.7 MeV	2.197 × 10-6 sec
- +,  -		 1777 MeV		290.6 × 10-15 sec

_***Mass***_

_***Mean life time***_

- Experiments utilize incident beams of e+, e- and of  +, -

## HISTORY OF CHARGED LEPTONS

_**HISTORY OF CHARGED LEPTONS**_

- e+ , e-	J. J. Thompson using cathode tube at 			Cavendish in 1897. Millikan measured 		the basic unit of charge in 1909
- +, -	Neddermeyer and Anderson in cosmic 		ray experiments in 1937(also Stevenson 		& Street and Nishina Group)
- +, -	Martin Perl at SLAC in 1976

## FORCE CARRIERS

-  (photon)		0			Stable
- g (gluons)		0			Confined
- W+, W-	 80.42 GeV	2.12 GeV (3.1 × 10-25 sec )
- Z		 91.19 GeV	2.50 GeV (2.6 × 10-25 sec )

_***Mass***_

_***Width |Mean life time***_

**Experiments can create photon beams**

## HISTORY OF FORCE CARRIERS

_**HISTORY OF FORCE CARRIERS**_

- 	Antiquity. 						Planck introduced “quanta” in 1900.	 	Einstein established particle nature by 	describing photoelectric effect in 1905.
- g	3 jet events reported at DESY in 1979; 	the third jet interpreted as due to a gluon
- W, Z	Discovered at CERN in 1982 (Rubbia)

## Examples of 2-jet and 3-jet events observed in the JADE detector at the PETRA e+  e-  collider at 30, 31 GeV in cm (DESY)

- q

- q

- g

- Examples of 2-jet and 3-jet events observed in the JADE detector at the PETRA e+  e-  collider at 30, 31 GeV in cm (DESY)

- e+

- e-

- e-

- e+

## 4-JET EVENT

## JETS  GLUONS

- Three or more jets signify production of **qq** and additional particles (gluons within the framework of QCD) that also form jets.
- The ratio of 3-jet/2-jet (and 4-jet/2-jet, ...) cross-sections is consistent with gluon production in QCD
- The change in these ratios of cross-sections with energy is consistent with QCD

## States produced as resonances in e+e- Annihilation

**R = ****N****c**** **** ********i**** e****i****2****  = **

- s = cm energy, GeV

- e+

- l,  q

***X***

- l,  q

****** ****,** **Z****0**

- e-

**States produced as resonances in e****+****e****-**** Annihilation**

- (e+e-  hadrons)
- (e+e-  +  - )

- s = cm energy, GeV

- Vector boson resonances

## Resonance in p+p- Interactions

**g, ******** ,** **Z****0**

- q

- q

***X***

**Resonance in p****+****p****-**** Interactions**

##  e+e- final state

## + -  final state

## 2-JET EVENT

## RESONANCES PARTICLES

- +  -
- +  -
- W+  W-
- Z0
- Charmonium  (J/, ....)
- Bottomonium (  /  // , .....)
- Top

**LEAD TO THE DISCOVERY/PRODUCTION OF**

## CHARMONIUM (cc) 

**SLAC (Richter, 1974)**

**BNL (Ting, 1974)**

- p + Be  J/  + anything
- 	              e+e-

- Such experiments gave the masses of cc  bound states.  mc?

## BOTTOMONIUM (bb)

**p + Be, Cu, Pt**
** ******** ********+  ****+**** ********- ****+ anything**

**FNAL (1977)**

**CLEO at CESR**

- The   /  //  are not resolved in the broad peak

- e+e-    hadrons
- 	          e+e- ,  +-

## (t t ) too short lived to form onia

- p+ p-  t  + t  +  anything
- 	               W-  b
-                           W+  b

**W ******** e ******
**W ******** ******** ******
**W ******** q q ******** jet**

**b, b ********  jet**

- Artist’s view of top event at CDF

## QUARKS

- u	up	2-4 MeV	 QCD
- d	down	4-6 MeV	 QCD
- s	strange	70-120 MeV	 QCD
- c	charm	1.15-1.5 GeV
- b	bottom	4.0 - 4.4 GeV
- t	top 	168+10 GeV

_***Mass ***_(MS)

_***quark***_

_***Name***_

- -7

**1963**

**1974**

**1977**

**1995**

## MASSES OF QUARKS

- Quarks are not seen as asymptotic states but confined within hadrons!
- Experiments provide masses of mesons (, K, , /, , , J/, ,...) and baryons (N, , , , , ...)
- Decays products are heavier than the quarks due to hadronization! Quarks always dressed by gluons
- The QCD coupling is large, s 1, at hadronic scales. Gluon effects are large (~ 300 MeV ~ QCD)

**How do we measure quark masses?**

## RESORT TO THEORY AND RELATE HADRON MASSES TO QUARKS

- QCD: Cannot solve it analytically in the low energy region. USE
- Chiral Lagrangian: Low energy effective theory of , K,  mesons. Same symmetries as QCD. 		Quark masses are parameters.

**LATTICE QCD**

**QCD SUM RULES**

## CHIRAL PERTURBATION THEORY

- Parameters of this effective theory include quark masses.
- Determine these parameters by fitting the observed meson masses and decays to predictions of PT
- Can extract only ratios of light quark masses (mu/md, md/ms) as theory has an overall unknown scale.

## DEFINITION OF mq in QCD

-  (A12) = (m1 + m2) P12
-  (V12) = (m1 - m2)  S12

**CURRENT CONSERVATION IN QCD**

**Calculate 2-point correlation functions**

**(J is a source for pions)**

## QCD SUM-RULES

****** ** (A12) (x,t)    (A12) (0,0)** ********  = **

- (m1 + m2)2 ****** ** P12 (x,t) P 12 (0,0) ****

- Spectral function

**OPERATOR PRODUCT EXPANSION**
**+ PERTURBATION THEORY**

## SOLVE QCD NUMERICALLY

- masses of quarks
- the gauge coupling

**Solve for the spectrum of mesons and baryons using Monte Carlo simulations of  **_**LATTICE QCD**_** with input values for **

**Tune m****quark**** until masses of all hadrons agree with experimental values.**

## LATTICE QCD

- Generate background gauge configurations {U(x)} distributed with probability given by the QCD action
- Calculate Feynman quark propagators SF[U] on these background configurations
- Average correlation functions constructed out of {U(x)} and SF[U] over these  configurations (do the functional integral)

**Field theory in Euclidean space**

## LATTICE QCD

**LATTICE QCD**

**	****GAUGE CONFIGURATIONS**

**	****QUARK**** ****PROPAGATORS**

**QCD (g, m****u****, m****d****, m****s****, m****c****, m****b****)**

**$**

**Statistical errors**

**Systematic errors**

## QUARK MASSES (MS)

- mu (2GeV)	2.2-2.7 MeV	2.4-3.8 MeV
- md (2GeV) 	4.3-6.9 MeV	4.3-6.9 MeV
- ms (2GeV) 	78-100 MeV	83-130 MeV
- Mc (Mc)		1.2-1.6 GeV	1.25(10) GeV
- Mb (Mb)		4.3(1)   GeV	4.2(1)   GeV

_***LQCD***_

_**Sum Rules**_

**Chiral Perturbation theory**

-   mu  / md          = 0.55(4)
- 2ms / (mu +md) = 24.4(1.5)

## NEUTRINOSe,e,,,,

- Electrically neutral
- Have only weak interactions
- Masses very small

## Neutrino interactions are weak

- e-

- e

- W-

- e

- e-

- e-

- e

- e

- e-

- Z

- +

- very small!

**Charged current**

**Neutral current**

## DECTECTING NEUTRINOS

- THE INCIDENT NEUTRINO IS INVISIBLE. DETECTORS “SEE” THE CHARGED PRODUCTS

## e type event

- _e type event_

- Curtsey: B Blumenfeld, JHU

##  type event

- ___ __type event_

- Curtsey: B Blumenfeld, JHU

## NEUTRINOS

- e		< 3 eV		 > 7 109 sec/eV
- 		< 0.19 MeV	 > 15.4 sec/eV
- 	 	< 18.2 MeV

_***Mass***_

******/m******

- Experiments utilize incident beams of e  e    

## History of Neutrino Physics

**1914: Chadwick finds ******** decay spectrum to be continuous**
**1930:****	****W. Pauli proposed ‘neutron’ as an explanation**
**1936:****	****Fermi-Gamow-Teller theory with a “neutrino”**
**1956:****	****Cowan and Reines observe ********e**** interactions**
**1958: V-A theory of weak processes**
**1962:****	****Danby et al, observe ************ interactions**
**1990: Precisely 3 light neutrinos exist in nature**
**2000:****	****DONUT collaboration observes ************  interactions**

## NEUTRINO MASSES

- e : End point of the tritium beta decay spectrum

**n **** p + e + ********e**

-  : End point of the pion decay spectrum

****** ******** ******** **********

## M from missing energy

- Beta decay spectrum for molecular tritium

## MASSES FROM OSCILLATIONS

- 

- 

- 

- 

- 2

- 2

- 2

- 2

- 2

- 2

- sin

- 2

- sin

*a*

*b*

*e*

*osc*

*m*

*m*

*m*

*where*

*E*

*L*

*m*

*P*

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

**

**

**

**

**

**

*L*= 1.27  distance in meters
**= mixing angle between the 2 **
*E*= Energy of **in**MeV

**(eV)****2**

## MASSES FROM OSCILLATIONS

- LSND
- Accelarator:   e

- Superkamiokande
- SOLAR:  e  x

- Detecting Cherenkov light from electron produced in interaction

## The LSND Experiment

- 800 MeV protons
- 1 mA
- 6% duty ratio

- L = 30 meters

- CH2

- ee )

- _Neutrino Targets in  CH__2__ :_
- 	  e  :   neutrons in 12C  +  electrons
- e  :   protons  in 12C  +  electrons  +  free protons

- 167 tons CH2
- 1220 PMT’s
- Active Veto Shield

- Cu Beam Dump

- Target

## CURRENT PICTURE

- There are three signals of neutrino oscillations:

*With three flavors there are *
*only two independent ****m**2** !*

## # OF LIGHT NEUTRINOS?

- Z  ee  ,    , 
- Z  e+e- ,  +- ,  +-
- Z  q q

**The total Z width depends on the number of light neutrinos. Current data restricts the number to 3**

## Possible solutions

- One of the experimental value is wrong or the effect is not due to neutrino oscillations
- There are additional (sterile) neutrinos lurking in the universe
- Oscillations are not due to mass but due to the effects of extra dimensions /string theory.

*It is crucial to verify whether all three*
***m**2** measurements are due to oscillations. *

## FUTURE

- Refine the mass estimates of quarks
- Masses and mixing of neutrinos
- Discover the Higgs particle
- Look for supersymmetric particles