Determining Spin in Hadron Colliders

Itay Yavin

In collaboration with Lian-Tao Wang

Harvard University

The road ahead

• Introduction

• Simple decays, developing some tools.

• HERWIG – simulating spin correlations

• Where shall spin be found

• Conclusions

IntroductionThe LHC is about to go on-line very soon and discerning new physics is not going to be easy.

-Resonances

-End points

-Edges

-Lepton, jets

-what have you.

LNSM

for a recent accessment of the challanges in correctly interpreting the data, see:

N.Arkani-Hamed, G.L.Kane, J.Thaler and L.T.Wang, arXiv:hep-ph/0512190

We are also not the first to think about spin determination:A. Barr hep-ph/0405052 , hep-ph/05111115

P. Meade and M. Reece, hep-ph/0601124

Cascades

Observable

Unobservable

Observable

Observable

Unobservable

Observable

In this talk I will concentrate on measuring the spin through cascade decays.

Spin???

Rules for spin correlations

-1 -0.5 0.5 1

0.2

0.4

0.6

0.8

1

cos

Circular Longitudinal

cos-1 -0.5 0.5 1

1.2

1.4

1.6

1.8

2

Longitudinal Circular

LH, RH (RH) (LH)2

2

Em

-1 -0.5 0.5 1

0.5

1

1.5

2

cos121 P

cos121

When do particles get polarized?To understand how a particle might get polarized consider its rest frame

1) Production through Z0:Z0

ZaZa cc

RL

2) Decay through massive gauge-boson

Z’

RH

RH

long. dominate

RH LH

circ. dominate

3) Decay through a Majoranna fermion

RH

LH

LH

RH

LH

RH

LH

a)

b)

different

4) Decay through a Dirac fermion – must involve chiral interactions

Both must be chiral vertices

Approximations with MC simulators: (not with MadGraph and CompHEP)

The spin information in the propagator’s numerator is lost:

)(1 22

22222mp

mmmp

NWA

22 mp

mp

Narrow width approximation:

Monte-Carlo SimulatorsThere are many available: Pythia, HERWIG, ISAWIG, MadGraph, CompHEP

SPIN CORRELATIONS IN MONTE CARLO SIMULATIONS, Peter Richardson, JHEP 0111:029,2001 and references therein

Designed to simulate hadronic emissions with special emphasis on gluon interference.

HERWIG1

Utilizes a spin-correlations algorithms:

inoutinoutinpropout NWA

ininoutoutinpropout ''',

2

ininD '

',',

outoutD '',

[1] G. Marchesini, B.R. Webber, G. Abbiendi, I.G. Knowles, M. H. Seymour and L. Stanco, HERWIG: a Monte Carlo event generator for simulating hadron emission reactions with interfering gluons. Version 5.1 - april 1991, Comput. Phys. Commun. 67 (1992) 465.

Massive Gauge-BosonsIn order to implement spin-correlations for massive gauge-bosons in HERWIG, we need to write the polarization in terms of massive spinors:

)()()(2121 22

1),( pvpup

m

And massive spinors can be expressed in terms of mass-less spinors as usual and implemented into Herwig.

021

),(),(

L ),( R ),(

Implemented diagrams

+ permutations

Coming soon:

Tedious but done.

Where shall spin be found?We will assume for the moment that no leptonic partners are light enough to be produced.

Vs.

q~~kkW

2coslongP

012

2

2amama qwqw M

2)( Wqqw ppm

LaP cos121 Racos12

1

0222)( amaa qwRL MVs.

Comparison of theory with MC

2

22222~

max 4

),,()( 21

M

mmMMmm LSPWq

qw

Theory MC

1001 M

5002 M

80010tan

1000~ qm

Observing the Lepton

Farther study required

KK SS1001 M

5002 M

80010tan

1000~ qm

Do we need to tell apart Jetfar from Jetnear?

)( 2P

2M

M1=180

160

120

100

We performed an initial scan of the parameters M1 and M2 keeping all the other parameters (mq, , tan) fixed

bins i

KKi

SSi nn

22

GeVHT 300

4.0R

Why is it a good channel?

1. Very sharp contrast between SUSY and KK signal.

2. Results in only few jets so combinatorics is not terrible.

3. 2 of the jets can (in principle) be set apart from the rest by reconstructing the W.

4. The signal is still strong even when averaged over Jnear and Jfar.

5. Assume no sleptons in the spectrum so fairly generic.

6. Standard model background?

Using SleptonsA. Barr originally considered,

q~ q~

q

2

l

l

LSP

q

2

l

l

LSP

Process 1 Process 2

Two problems:

1) You don’t know which lepton is which.

2) There is an equivalent chain starting with an anti-squark having all the arrows opposite which tends to wash out correlations

q~

q

l

LSP

q~

q

l

LSP

We can solve the second problem by considering instead:

Information about the charge is kept in the leptons.

1001 M

5002 M

800

10tan

1000~ qm

300~ l

m

KK

2lqm

SS

2lqm

Conclusions• The tools to investigate the possibility of measuring spin are available.• The channels we considered seem promising, but farther study (background, cuts,

smearing etc.) is warranted. • Spin determination through production channels (ala’ A. Barr) might prove to be a

cleaner signal.• Global studies combining different methods to cover the full parameter regions are

needed.• Gluon partner’s spin? Seems pretty hard!!!

Jet OverlapHow close the jets are to each other? 22 R

Jnear - JfarJfar - JW

Jnear - JW JW1 – JW2

Jets seem well separated, but farther study is certainly necessary