Resonance and Mass Resonances (Lecture 08)people.physics.tamu.edu/.../Lec08_phys823_Resonance... ·...
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Resonances (Lecture 08) PHYS 823 1 R Resonance: short lived state with fixed mass, and well defined quantum numbers particle e.g., Production and two-body decay A + B R C+D Resonance and Mass 2 2 2 2 2 2 ) ( ) ( p E p p E E M M D C D C D C resonance 2 X Z pp ) ( e.g., Z boson production and leptonic decay at the LHC PDFs p 1 p 2 Z p p X X (e.g.) Dimuon Resonances (~70 x 10 12 p pp collisions) Jun. 14, 2011 3 H Hadron colliders (vs. Lepton colliders): we have to include parton distribution functions (PDFs). Hadron Colliders X Z pp ) ( e.g., Z boson production and leptonic decay at the LHC PDFs p 1 p 2 Z p p X X 5 PDFs All the fractions x have to add up to 1, where f i p(n) (x)dx is the number of parton i in the proton (neutron) that carry a fractional momentum x in the range x x+dx. The functions, f i p(n) (x), are called parton distribution functions (PDFs). Structure functions probed by electron-nucleon collisions: ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 9 1 ) ( ) ( 9 4 ) ( ) ( ) ( ) ( ) ( 9 1 ) ( ) ( 9 4 ) ( x d x d x d x u x u x u x s x s x u x u x d x d x x F x s x s x d x d x u x u x x F n n n n n n en p p p p p p ep s(ea) v(alence) s(ea) v(alence) s s s s 2 s s s s 2 where 1 ] ) ( [ ) ( i n p i x f x dx Illustration of PDFs 6 ) ( ), ( x g x q x ) ( ), ( x g x q x ?
Transcript of Resonance and Mass Resonances (Lecture 08)people.physics.tamu.edu/.../Lec08_phys823_Resonance... ·...
Resonances(Lecture 08)
PHYS 823
1
RResonance: short lived state with fixed mass, and welldefined quantum numbers � particle
e.g., Production and two-body decay A + B � R � C + D
Resonance and Mass
222222 )()( pEppEEMM DCDCDCresonance���
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2
XZpp ��� �� )( ��e.g., Z boson production and leptonic decay at the LHC
�
PDFs
p
pp1
p2
Z
p
p
X
X
((e.g.) DDimuon RResonances
(~70 x 1012 ppp collisions)
Jun. 14, 2011
3
HHadron colliders (vs. Lepton colliders): we have to includeparton distribution functions (PDFs).
Hadron CColliders
XZpp ��� �� )( ��e.g., Z boson production and leptonic decay at the LHC
�
PDFs
p
pp1
p2
Z
p
p
X
X
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PPDFs
All the fractions x have to add up to 1, where fip(n)(x)dx is thenumber of parton i in the proton (neutron) that carry a fractionalmomentum x in the range x �� x+dx. The functions, fip(n)(x), arecalled parton distribution functions (PDFs).
Structure functions probed by electron-nucleon collisions:
� �
� �
)()()()()()(
)()()()(91)()(
94)(
)()()()(91)()(
94)(
xdxdxdxuxuxu
xsxsxuxuxdxdxxF
xsxsxdxdxuxuxxF
nnnnnnen
ppppppep
s(ea)v(alence)
s(ea)v(alence)
ssss2
ssss2
where
��
��
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������
1])([ )( ���i
npi xfxdx
IIllustration of PDFs
66
)(),( xgxq
x
)(),( xgxq
x
?
77
Illustration of PDFs PProbing Proton Structure Functions
88
99
�
PDFs
p
pp1
p2
Cross Section
How one can express the cross section?
110
CCross Section (I)
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CCross Section (II)
112
CCross Section (III)
QQuick Quiz
113
Zp
p
X
X
TThe quark discription of a proton is (uud). Z bosons arecopiously produced in proton-proton collisions at the LHC.However, an annihilation of a quark and an anti-quark isresponsible for the production of the Z boson. See below.
a) Is the quark diagram wrong? Yes or No?b) Why?
)(ˆ)()( //,
���� � �� qqxfxfxdxd BqAqqq�
HW 8 Problem
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HHW 8 Problem (cont’d)
115 116
QQuantum Numbers
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SSpace--ttime Picture of pp Collision�TThe wave function describing a decaying state is:
wwith ER = resonance energy and � = lifetime
�The Fourier transform gives:
�The amplitude as a function of E is then:
where K = constant, ER = central value of the energy ofthe state
� ��
� �2/2/ )0()0()( ��� ��� ���� �� RR iEttti eeet
� � dtetg ti��
�0
)( ���
� �
� �� � �����
��
���
����
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!"�
2/)0()()( 2
���
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iEEKdtedtetEAR
EEitiEt R
)()(* EAEA � �# $4/4/
22
2
max ��
����
�REE
Breit--Wigner Shape (I)
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�EE � W, ER � W0
Breit--Wigner Shape (II)
4/)()( 22
0 ����
WWKWN
�Mean value of the Breit-Wigner shape is the mass of theresonance: M = ER. Here, � is the width of a resonanceand is inverse mean lifetime of a particle at rest: � = 1/�
19 220
DDecay Widths
%% RResonance in eep SScattering
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%% RResonances in &&pp Scattering
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“quark diagram”
EExotic Resonances in &&pp Scattering
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�““Hypothetical” resonance
(*) Thanks to Ji-Gwang Hwang to provide a reference talk.
IIsospin ((I)
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IIsospin ((II)
225
IIsospin ((III)
226
227
~200 mb
~60 mb
~20 mb
228
TTesting Quark Models
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''()
**
+)(1)()(2)(dpdn
,�,�,�,�
330
((1)
331
NNew particle (= resonance): short lived state with fixedmass, and well defined quantum numbers within aframework beyond the Standard Model.
e.g., Supersymmetry (or SUSY)e.g., Universal Extra Dimenssion (or UED)e.g., Littlest Higgs with T parity (or LHT)e.g., ...
New Particles
332
[WW�e,] Distribution peaks just belowmW and falls sharply just below mW.
W Mass: W�� e,,
)cos1(2TTTT misseE
misse EEM -%��
data
� One heavy object, followed by two-body decay
� One missing ,
�� One kinemarical template to characterize the decay of the W boson
)(GeV/ 2T cM
33
HHow about SUSY?� Two heavy objects,
followed by two-body decays
� Two missing objects
� Many kinemaricaltemplates to characterize the decay of the SUSY particles
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(ee.g.) SUSY Decays
335
((e.g.) SSquark DDecay
11) Find W in W�jj2) Find the squark in J+W
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Dijet mass distribution forany two-jet pairs in theevent.
BG-subtracted Dijet massdistribution has still residualBG, but, much easier toextract the ���.
Clearly we can see the Wevents and sideband BG.
Dijet mass distribution forany two-jet pairs in themixed events.
Bii-EEvent SSubtraction TTechnique
Powerful tool to remove combinatorial background
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Phys. Lett. B 703 (2011); hep-ph/1104.2508
SSquark MMass : “JW”
Endpoint = 774 GeVTrue = 739 GeV (.4
0)
MJW
True = 739 GeV (.40)
True = 714 GeV (.1+/�)
True
[Vetoing events with any �’ s with pT > 20 GeV]
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FFuture BEST iin SUSY
mjWmjj
? ?
39 440
441
~~200 mb
~60 mb
~20 mb
elastictotal �� *
inelasticelastictotal ��� �*
Why different?
