New particle mass spectrometry at the LHC : Resolving combinatoric - - PowerPoint PPT Presentation

New particle mass spectrometry at the LHC : Resolving combinatoric endpoints

Won-Sang Cho (IPMU)

• 2010. 05. 10

PHENO 2010

Resolving every meaningful endpoints hidden in inclusive signature (1) Amplification of the endpoint structure

Ref: arXiv0912.2354 [W.Cho, J.E. Kim, J. Kim]

(2) General combinatoric endpoints

[Work in progress with M. M. Nojiri]

New particle mass spectrometry at the LHC

Amplification of MT2 endpoints

• MCT2 ?? [ref) arXiv:0912.2354, Cho, Kim, Kim]

2 2 1 2 2 2 2 2 2 2 2

V(p)+χ(k) + V(p)+χ(k) min[max{ = visible transverse momenta min&max over a ( ), ( )}] 2 | | | | ll possi , bl 2

CT CT CT CT V CT V

Y Y M M Y M Y M M m m m m

χ χ

→ ≡ ≡ + + + + ⋅ +

T T T T T

p for k p k p in the LAB frame i i e invisible missing momentum

T

k

Endpoint structures are amplified. for buried in several backgrounds. Amplification factor is controlled by test mass Good

• accentuating

several break points i i

qq gq gq qqq qqq χ χ → →

• i

Endpoint from squark decay Endpoint from gluino decays

A ccentuating the buried break points in N -jet events

max max

Systematic errors for physical constraints reduced by O(1/J ) in local fitting of break points. J : Jacobian factor near the endpoint region →

This enhances our observability for several endpoints. (Previously) Impose hard cut, and remove the BG events near the endpoint. (Now) Well, moderate cut & irreducible BGs are okay, as long as there exist dim BPs from signal endpoints. We can magnify it !

Then, what endpoints are to be amplified by MCT2 projection ???

Complex new physics event topology at the LHC P P

: from ISR or Decays

T

δ

• : System of interest with N

M decay steps

T

δ − ×

• 1

α

i

α

N

α

1

β

j

β

M

β Missing new physics particles

i j

, =Visible or Invisible SM particles α β

1

A

i

A

N

A

1

B

j

B

M

B

i j

A /B =Intermediate new particles

Decay chain crossing two particle endpoint functions as basic building blocks for mass reconstruction in N×M decay chains.

1

α

i

α

N

α

1

β

j

β

M

β

1

A

i

A

N

A

1

B

j

B

M

B

i i+1 j j+1 i j

max i j A A B B 2 2

CM Energy is not bounded in a event by event basis. ( , ) (??)=> M ,M ,M ,M ~ , , .... ~ ( : dot product )

T CT CT

f f M M M P P Euclidean

α β

α β i i

i j k m

max i j m A A B B

CM Energy is bounded above by decayed mother particles in a decay chain ( , / , ) => M ,M ,M ,M ....

k

M M α α β β ≤ Along the decay lines Crossing the decay lines Why two ?

2

• 1. Smallest combinatorics in NxM visibles
• 2. No internal combinatorics for
• 3. Single massless SM particle in each decay chains

=> Simple and Good for endpoint amplification for C-M

CT

f Combinatoric M = −

CT2

1 i N 1 j N i j

[work in progress] Let's take a system of interest with transverse momentum, ( ) ( ,... ... / ... ... /New physics missing PTLs) ( ) ( + (ass umed o . t

T T

δ α α α β β β δ α β → + → + pp

CT2 i j T

Combinatoric - M (α - β )

• δ

i+1 j+ T 2 2 i j 2 2 1 2

be) missing particles(E ')) (i=1..N, j=1..M) (

• )

min[m = visible transverse momenta A ax{ ( ), ( )}] 2 | | | | 2 , & B ( in

CT CT i CT j CT

C M M A M B M α β χ χ χ / − ≡ ≡ + + ⋅ +

T T T T T

p k p p k = universal test mass for i i

i+1 j+1

A B

general M M ) min&max over all possible invisible missing momentum α β ≠ = /

T T T

k ( ) + k ( ) = -( + ) - k

iT jT T T

α β δ E ' i i

Universal test mass, χ = Controlling parameter of the amplification Utilizable for complex event topologies with additional missing particles C-MCT2(αi-βj) has well-defined (amplified) endpoint value for general non-zero δT and univeral test mass, χ

CT2

If 2, all of the M+1 masses can be determined with C-M . M ≥

CT2

If ( 1)( 1) 3, all the masses can be measured

• nly with C-M

M N − − ≥ Totally asymmetric system Totally symmetric case, N=M & intermediate particles with same masses. The additional vertical constraints (M /M ) can be helpful, also.

αα ββ

P P

MET : 2 WIMPs missing Mass scale

1 1

( ) ( ) ( ) ( ) gg q q q q qq qq χ χ → + + + → +

• Simple Example :

1

α

2

α

1

β

2

β

4jets 6 possible pairs of jets / 3 Independent decay crossing pairs exist 1) α(1)-β(1) 2) α(1)-β(2)/α(2)-β(1) 3) α(2)-β(2)

1 1

( ) ( ) gq qq q χ χ → +

• 3 jets 3 pairs /

2 Independent decay crossing pairs exist 2) α(1)-β(2)/α(2)-β(1) 3) α(2)-β(2)

Partonic level results : C-MT2

T2

C-M Endpoint by DC pair-(1)

T2

C-M Endpoint by DC pair-(2)

T2

C-M Endpoint by DC pair-(3)

2

Combinatoric-

T

M

Partonic level results : C-MCT2

2

Combinatoric-

CT

M

T2

C-M Endpoint by DC pair-(1)

2

Combinatoric-

CT

M

T2

C-M Endpoint by DC pair-(2)

T2

C-M Endpoint by DC pair-(3)

• MCT2 : impressive endpoint structure

enhancement.

• Small slope discontinuities are amplified by J(x)2,

accentuating the breakpoint structures clearly.

• Extract the various constraints hidden in complex inclusive

signatures

• Combinatoric-MCT2 has well-defined endpoints and

power to accentuate them.

• With C-MCT2, ordinary combinatoric background is not only

background anymore. It provides mass information to be analyzed.

• Thus, C-MCT2 can be a useful tool for every new particle mass

measurement in generic complex event topologies.

Conclusion

Back up slides

• IF mvis~ 0, MCT2 (x) projection can have significantly

amplified endpoint structure (x = Trial missing ptl mass)

• Jmax(x) ⇒ ∞ as x ⇒ 0
• One can control Jmax(x) by choosing proper value of x

• A faint BP(e.g. signal endpoint) with small slope difference

amplified by large Jacobian factor : Δa ⇒ Δa` = Jmax

2(x) Δa

With the accentuated BP structure, the fitting scheme (function/range) can be elaborated, and it can significantly reduces the systematic uncertainties in extracting the position of the BPs !

2 2 2

~

BP

a σ δ Δ