Transcript

Implementation of K-matrix formalism in the

amplitude modelBy Rudin Petrossian-Byrne

Supervisors: Dr. Marco Gersabeck & Stefanie Reichert

CERN Summer Student Programme 2014

Before The Physics…. Hi!

My name is Rudin

from Dublin

studying Physics (Undergraduate)

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The big pictureMixing and CPV

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The big pictureMixing and CPV

Mixing

strange quark

bottom quark

mixing

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The big pictureMixing and CPV

Mixing

me

mixing

strange quark

bottom quark

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The big pictureMixing and CPV with Charm

2007 – First Evidence from BaBar and Belle for mixing in charmed neutral mesons

𝒙=𝑀 1βˆ’π‘€ 2

Ξ“

Charm Quark

∝ (10βˆ’ 2 )π’š=Ξ“ 1βˆ’ Ξ“2

2 Ξ“

No significant evidence for CPV in charm to date

β€’ Mixing parameters very small

2012 – LHCb find evidence for mixing in a single measurement

β€’ SM β€˜predicts’ small CPV

β†ͺObservation at current sensitivity would imply New Physics

R

Phys. Rev. Lett. 110 (2013) 101802

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π‘«πŸŽ{π’„π’π’–π‘«πŸŽβ†’π‘² 𝒔 𝝅+ΒΏπ…βˆ’ΒΏ

(π‘šπ‘œπ‘‘π‘’π‘Ÿπ‘›π‘›π‘œπ‘‘π‘Žπ‘‘π‘–π‘œπ‘›)

Allows measuring x and y parameters directly

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π‘«πŸŽ{π’„π’π’–π‘«πŸŽβ†’π‘² 𝒔 𝝅+ΒΏπ…βˆ’ΒΏ

(π‘šπ‘œπ‘‘π‘’π‘Ÿπ‘›π‘›π‘œπ‘‘π‘Žπ‘‘π‘–π‘œπ‘›)

Allows measuring x and y parameters directly

P P

Protons collide in the VELO

Very short life-time of charm quark travels mm, then decays

π‘«πŸŽ

𝝅+ΒΏ ΒΏ

π…βˆ’

𝑲 𝒔

{π‘žπ‘Žπ‘ŽDetected by TT tracker.

Bend through magnet. Detected by T1, T2, T3.

𝝅+ΒΏ ΒΏ

π…βˆ’

{π‘Ž decay in VELO as well decay outside VELO harder to reconstruct𝝅+ΒΏ ΒΏ

π…βˆ’

π…βˆ’

𝝅+ΒΏ ΒΏ

𝑲 𝒔

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π‘«πŸŽβ†’π‘² 𝒔 𝝅+ΒΏπ…βˆ’ΒΏ

Allows measuring x and y parameters directly

3-Body Decay Unlike 2-body decays, energy of daughter particles not well-defined Range of possible values.

(π‘šπ‘œπ‘‘π‘’π‘Ÿπ‘›π‘›π‘œπ‘‘π‘Žπ‘‘π‘–π‘œπ‘›)

π‘«πŸŽ

𝑲 𝒔

π…βˆ’

𝝅+ΒΏ ΒΏ

β†ͺ

π‘«πŸŽ{𝒄𝒏𝒖

LHCb Simulation

π’Žπ‘²π’” 𝝅¿ ΒΏ

π’Žπ‘²π’”π…

βˆ’

𝟐

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What we observe:Dalitz plot is characterised by Resonances + non-resonant background

Resonances (bands of high )Corresponds to

↑Intermediate particle, e.g.

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Not homogenously populated with events Some daughter energies more probable

P

π‘«πŸŽβ†’π‘² 𝒔 𝝅+ΒΏπ…βˆ’ΒΏ

LHCb Simulation

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Resonant decay treated as a superposition of 2-body decays e.g. and

Approximate by a relativistic Breit–Wigner probability distribution function

is clearly affected by resonances

Each resonance has a probability amplitude

π‘«πŸŽβ†’π‘² 𝒔 𝝅+ΒΏπ…βˆ’ΒΏ

THE ISOBAR MODEL

𝑀=βˆ‘π‘Ÿ

π‘Žπ‘Ÿπ‘€π‘Ÿ

𝑴𝒓= βŸ¨πœ‹+ΒΏπœ‹βˆ’ΒΏπ‘Ÿ ⟩ πœŸπ’“ ΒΏ

Great for isolated Resonances!

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PROBLEMIf Resonances overlapTotal probability 1

β†ͺNot good

β†ͺTheorists are unhappy

β†ͺShould probably do something about that…

Great for isolated Resonances!

BAD for overlappingresonances

π’Žπ…π…πŸ

π’Žπ…π…πŸ

Curtis A. Meyer, Carnegie Mellon University, β€˜A k-matrix tutorial’ (2008)

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ALTERNATIVE MODEL

Makes use of K-Matrix formalism to describe resonances with

Assumption: equivalent dynamics to scattering off

Need to consider all possible decays of r in the analysis

π‘«πŸŽ

𝝅+ΒΏ ΒΏ

π…βˆ’

𝝅+ΒΏ ΒΏ

π…βˆ’

π‘«πŸŽ

𝑲 𝒔

𝑲 𝒔

𝒓

𝒓

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P

K-Matrix Formulation

Pseudo-propagatorComes from scatteringdata.

K - Matrix phase-space factor

Production VectorDescribes Couplings of resonances to

Upholds unitarity by construction!Curtis A. Meyer, Carnegie Mellon University, β€˜A k-matrix tutorial’ (2008)

π’Žπ…π…πŸ

π’Žπ…π…πŸ

─ Breit-Wigner─ K-matrix

─ Breit-Wigner─ K-matrix

𝑴𝒓= βŸ¨πœ‹+ΒΏπœ‹βˆ’ΒΏπ‘Ÿ ⟩ 𝑭 ⟨𝐾 π‘ π‘Ÿ|𝐷0 ⟩

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My Job: Implement K-matrix description in fitting code for

Implementation: CODING

Programming language: CUDA ( C++

Running on a GPU (Graphical Processing Unit)

implement P fit to data

extremely fast parallelisation

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What are we fitting to data?

21 floating variables

and are complex

𝑃 𝑗=βˆ‘π›Ό

𝛽𝛼0 𝑔𝛼 𝑗

0

π‘šπ›Ό2 βˆ’π‘šπœ‹πœ‹

2 + 𝑓 πœ‹πœ‹ π‘—π‘π‘Ÿ 1 βˆ’π‘ 0

π‘π‘Ÿ

π‘šπœ‹πœ‹2 βˆ’π‘ 0

π‘π‘Ÿ

P

K-matrix: comes entirely from scattering data

phase space matrix: depends only on masses

production vector: describes coupling to resonances

LHCb Simulation

Need to fit

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Wrestling with errors

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STATUS

This Week: Code Working on a CPU!

β€’ Positive cross-checks (e.g. decay time )

Implementation complete

β€’ Observing things (printing to screen) changes variables.

memory issues probably to blame

GPU memory issues currently being addressed

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THANK YOU

Questions?

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Spare Slides

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What are we fitting to data?

21 floating variables and are complex both real and imaginary parts need to be fitted

K-Matrix

Production vector

Sum over poles

Non resonant term

Correction term

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Outline Background: Mixing and CP violation in the charm sector

Parametrisations:

Implementation & Results

Onto the Physics….

β€’ Isobar model β€’ K-matrix

β€’ Detectionβ€’ Dalitz Plot & Resonances


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