t - - PowerPoint PPT Presentation

t
SMART_READER_LITE
LIVE PREVIEW

t - - PowerPoint PPT Presentation

t r sttt rt Pss rst


slide-1
SLIDE 1

❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

▼❛r❝✐♥ ❇❛❞③✐❛❦

■♥st✐t✉t❡ ♦❢ ❚❤❡♦r❡t✐❝❛❧ P❤②s✐❝s✱ ❯♥✐✈❡rs✐t② ♦❢ ❲❛rs❛✇

❘❡♥❝♦♥tr❡s ❞❡ ▼♦r✐♦♥❞✱ ▲❛ ❚❤✉✐❧❡✱ ✶✼t❤ ▼❛r❝❤ ✷✵✶✶ ❜❛s❡❞ ♦♥ t❤❡ ✇♦r❦ ✇✐t❤ ▼❛r❡❦ ❖❧❡❝❤♦✇s❦✐ ❛♥❞ ❙t❡❢❛♥ P♦❦♦rs❦✐ ♣r❡❧✐♠✐♥❛r② r❡s✉❧ts

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-2
SLIDE 2

▼✐♥✐♠❛❧ ❙❖✭✶✵✮ ❛♥❞ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥

❋♦r ❛ ❣✐✈❡♥ ❣❡♥❡r❛t✐♦♥ ❛❧❧ ♠❛tt❡r ❢❡r♠✐♦♥s✱ ✐♥❝❧✉❞✐♥❣ ν❘✱ s✐t ✐♥ ♦♥❡ ✶✻ ❞✐♠✳ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❙❖✭✶✵✮ ❇♦t❤ ▼❙❙▼ ❍✐❣❣s ❞♦✉❜❧❡ts ❛r❡ ✐♥ t❤❡ ✶✵ ❞✐♠✳ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❙❖✭✶✵✮ ❨✉❦❛✇❛ ✐♥t❡r❛❝t✐♦♥s ❛r❡ ❣✐✈❡♥ ❜② ❲ = ❤ ✶✻ ✶✵ ✶✻ ✇❤✐❝❤ ✐♠♣❧② ✉♥✐✜❝❛t✐♦♥ ♦❢ t − ❜ − τ ❨✉❦❛✇❛ ❝♦✉♣❧✐♥❣ ❛t ▼●❯❚✳

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-3
SLIDE 3

❊①♣❧❛✐♥✐♥❣ (❣ − ✷)µ ❛♥♦♠❛❧② ❛♥❞ ❨✉❦❛✇❛ ✉♥✐✜❝❛t✐♦♥

❨✉❦❛✇❛ ✉♥✐✜❝❛t✐♦♥ ♣r❡❢❡rs µ < ✵ ❜✉t ✉s✉❛❧❧② µ > ✵ ✐s ❝♦♥s✐❞❡r❡❞✳ ❲❤②❄ (❣ − ✷)❙▼

µ

♠♦r❡ t❤❛♥ ✸σ ❜❡❧♦✇ ❡①♣❡r✐♠❡♥t❛❧ ✈❛❧✉❡✳ (❣ − ✷)❙❯❙❨

µ

∼ s❣♥(µ▼✷) ⇒ (❣ − ✷)µ ♣r❡❢❡rs µ > ✵ ❢♦r ✉♥✐✈❡rs❛❧ ❣❛✉❣✐♥♦ ♠❛ss❡s ❜✉t ❯♥✐✈❡rs❛❧ ❣❛✉❣✐♥♦ ♠❛ss❡s ❛r❡ ♥♦t ♦❜❧✐❣❛t♦r② ✐♥ ❙❯❙❨ ●❯❚s ❖✉r ❙tr❛t❡❣② ❈♦♥s✐❞❡r µ < ✵ ❛♥❞ ♥♦♥✲✉♥✐✈❡rs❛❧ ❣❛✉❣✐♥♦ ♠❛ss❡s ✇✐t❤ ▼✷ < ✵

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-4
SLIDE 4

❚❤❡ ♠♦❞❡❧

µ < ✵ ◆♦♥✲✉♥✐✈❡rs❛❧ s❝❛❧❛r ♠❛ss❡s✿ ♠✷

❍❞ = ♠✷ ✶✵ + ✷❉

♠✷

❍✉ = ♠✷ ✶✵ − ✷❉

♠✷

◗,❯,❊ = ♠✷ ✶✻ + ❉

♠✷

❉,▲ = ♠✷ ✶✻ − ✸❉

◆♦♥✲✉♥✐✈❡rs❛❧ ❣❛✉❣✐♥♦ ♠❛ss❡s ❣❡♥❡r❛t❡❞ ❜② ❋✲t❡r♠ tr❛♥s❢♦r♠✐♥❣ ❛s ✺✹ ❞✐♠✳ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❙❖✭✶✵✮✿ ▼✶ = −✶ ✷♠✶/✷ ▼✷ = −✸ ✷♠✶/✷ ▼✸ = ♠✶/✷ ❯♥✐✈❡rs❛❧ tr✐❧✐♥❡❛r ❝♦✉♣❧✐♥❣s✿ ❆❯ = ❆❉ = ❆❊ = ❆✵ ✺ ♣❛r❛♠❡t❡rs ✰ t❛♥ β

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-5
SLIDE 5

▼❡t❤♦❞♦❧♦❣②

❚❤❡ s♦❢t ❙❯❙❨ ❜r❡❛❦✐♥❣ ♠❛ss❡s ❛r❡ ✐♠♣♦s❡❞ ❛t t❤❡ ●❯❚ s❝❛❧❡ ❛♥❞ r✉♥ ❞♦✇♥ t♦ t❤❡ ❡❧❡❝tr♦✇❡❛❦ s❝❛❧❡ ✇✐t❤ ❘●❊ ❝♦❞❡ ❙❖❋❚❙❯❙❨✳ ❲❡ ✐♠♣♦s❡ t❤❡ ❝♦♥❞✐t✐♦♥ ♦❢ ❘❊❲❙❇✱ ♥❡✉tr❛❧ ▲❙P✱ ♣❛rt✐❝❧❡ ♠❛ss ❜♦✉♥❞s ❛♥❞ t❤❡ ❡①♣❡r✐♠❡♥t❛❧ ❝♦♥str❛✐♥ts ❢♦r t❤❡ ❢♦❧❧♦✇✐♥❣ ♦❜s❡r✈❛❜❧❡s✿ t❤❡ r❡❧✐❝ ❛❜✉♥❞❛♥❝❡ ♦❢ ❞❛r❦ ♠❛tt❡r Ω❉▼❤✷ ❛µ ≡ (❣ − ✷)µ/✷ ❇❘✭❜ → sγ✮ ❇❘✭❇s → µ+µ−✮ ✇❤✐❝❤ ✇❡ ❝❛❧❝✉❧❛t❡ ✉s✐♥❣ ▼✐❝r❖▼❊●❆s✳ ❲❡ ❤❛✈❡ ♣❡r❢♦r♠❡❞ r❛♥❞♦♠ s❝❛♥ ❢♦r t❤❡ ❢♦❧❧♦✇✐♥❣ r❛♥❣❡s ♦❢ ♣❛r❛♠❡t❡rs✿ ✵ ♠✶✻ ✷✵✵✵ ●❡❱ ✵ ♠✶/✷ ✷✵✵✵ ●❡❱ ✵.✶ ♠✶✵/♠✶✻ ✷ ✵ ❉/♠✷

✶✻ ✵.✸

−✸ ❆✵/♠✶✻ ✸ ✹✵ t❛♥ β ✺✺

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-6
SLIDE 6

❲✐❞❡ r❛♥❞♦♠ s❝❛♥ ❢♦r ❨✉❦❛✇❛✲✉♥✐✜❡❞ s♦❧✉t✐♦♥s

❘ ≡ ♠❛① (❤t, ❤❜, ❤τ) ♠✐♥ (❤t, ❤❜, ❤τ) ❜ → sγ ❡①❝❧✉❞❡❞ ❜ → sγ ♦❦ ❨✉❦❛✇❛ ✉♥✐✜❝❛t✐♦♥ ✭❘ ≈ ✶✮ ❝❛♥ ❜❡ ♦❜t❛✐♥❡❞ ❢♦r ❛ ✈❡r② ✇✐❞❡ r❛♥❣❡s ♦❢ ♣❛r❛♠❡t❡rs ❜✉t ♠❛❥♦r✐t② ♦❢ ♣♦✐♥ts ✇✐t❤ ❣♦♦❞ ②✉❦❛✇❛ ✉♥✐✜❝❛t✐♦♥ ❡①❝❧✉❞❡❞ ❜② ❜ → sγ✳

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-7
SLIDE 7

(❣ − ✷)µ ✈s ❜ → sγ

❙tr♦♥❣ ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ (❣ − ✷)µ ❛♥❞ ❜ → sγ ❋♦r t❤❡ ♣♦✐♥ts ♥♦t ❡①❝❧✉❞❡❞ ❜② ❜ → sγ✱ (❣ − ✷)µ t②♣✐❝❛❧❧② ✈❡r② s♠❛❧❧ ❍♦✇ t♦ ❞✐s❡♥t❛♥❣❧❡ (❣ − ✷)µ ❢r♦♠ ❜ → sγ❄ ❲❡ ❤❛✈❡ ✐❞❡♥t✐✜❡❞ ✷ ❝❧❛ss❡s ♦❢ s♦❧✉t✐♦♥s ✇✐t❤ ❣♦♦❞ ②✉❦❛✇❛ ✉♥✐✜❝❛t✐♦♥✱ ❝♦♥s✐st❡♥t ✇✐t❤ ❛❧❧ t❤❡ ❡①♣❡r✐♠❡♥t❛❧ ❝♦♥str❛✐♥ts ✭✐♥❝❧✉❞✐♥❣ ❜ → sγ✮ ✇✐t❤ ❧❛r❣❡ ❙❯❙❨ ❝♦♥tr✐❜✉t✐♦♥ t♦ (❣ − ✷)µ

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-8
SLIDE 8

❙♦❧✉t✐♦♥ ✶

▲❛r❣❡ ❉✲t❡r♠s t♦ ♣✉s❤ ✉♣ ♠❍± ❛♥❞ s✉♣♣r❡ss ❍✐❣❣s ❝♦♥tr✐❜✉t✐♦♥ t♦ ❇❘(❜ → sγ) ❆t ≈ ✵ ❛t ▼❊❲ ✭t❤✐s r❡q✉✐r❡ ❧❛r❣❡ ♣♦s✐t✐✈❡ ❆✲t❡r♠s ❛t ▼●❯❚✮ t♦ s✉♣♣r❡ss ❝❤❛r❣✐♥♦✲st♦♣ ♠✐①✐♥❣ ❝♦♥tr✐❜✉t✐♦♥ t♦ ❇❘(❜ → sγ) ✇✐t❤♦✉t s✉♣♣r❡ss✐♥❣ ❝❤❛r❣✐♥♦ ❝♦♥tr✐❜✉t✐♦♥ t♦ (❣ − ✷)µ ❜✐♥♦✲❧✐❦❡ ▲❙P ✇✐t❤ t❤❡ r❡❧✐❝ ❛❜✉♥❞❛♥❝❡ s❛t✐s❢②✐♥❣ ❲▼❆P ❜♦✉♥❞ ❞✉❡ t♦ st❛✉ ❝♦❛♥♥✐❤✐❧❛t✐♦♥s (❣ − ✷)µ ✇✐t❤✐♥ ✷σ ❢r♦♠ ❡①♣✳ ✈❛❧✉❡ ✭✶σ r❡❧❛①✐♥❣ ❍✐❣❣s ♠❛ss ❜♦✉♥❞✮

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-9
SLIDE 9

❙♦❧✉t✐♦♥ ✷

♠✶/✷ ≪ ♠✶✻ ⇒ ❧✐❣❤t ❣❧✉✐♥♦s ✭✺✵✵✲✼✵✵ ●❡❱✮ ▲❛r❣❡ ❝❤❛r❣✐♥♦ ♠✐①✐♥❣ ✭▼✷ ≈ µ ❛t ▼❊❲✮ ✇❤✐❝❤ r❡s✉❧ts ✐♥ ♥❡❣❛t✐✈❡ ❝❤❛r❣✐♥♦ ❝♦♥tr✐❜✉t✐♦♥ t♦ ❇❘(❜ → sγ) ❜✐♥♦✲❧✐❦❡ ▲❙P ✇✐t❤ ♥♦♥✲♥❡❣❧✐❣✐❜❧❡ ❤✐❣❣s✐♥♦ ❝♦♠♣♦♥❡♥t ✇❤✐❝❤ ❛❧❧♦✇s ❢♦r r❡s♦♥❛♥t ❛♥♥✐❤✐❧❛t✐♦♥s t❤r♦✉❣❤ ❤✵ ♦r ❩ ❜♦s♦♥s (❣ − ✷)µ ✇✐t❤✐♥ ✷σ ❢r♦♠ ❡①♣✳ ✈❛❧✉❡ ✭✶σ r❡❧❛①✐♥❣ ❍✐❣❣s ♠❛ss ❜♦✉♥❞✮

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-10
SLIDE 10

❈♦♥❝❧✉s✐♦♥s

❨✉❦❛✇❛ ❝♦✉♣❧✐♥❣ ✉♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ❝♦♥s✐st❡♥t ✇✐t❤ ❛❧❧ t❤❡ ♣❤❡♥♦♠❡♥♦❧♦❣✐❝❛❧ ❝♦♥str❛✐♥ts ✐s ♠✉❝❤ ♠♦r❡ ♥❛t✉r❛❧ ❢♦r µ < ✵✳ Pr♦♣❡r ❘❊❲❙❇ r❡q✉✐r❡s ♥♦♥✲✉♥✐✈❡rs❛❧ s❝❛❧❛r ♠❛ss❡s ❛t ▼●❯❚ ✇❤✐❝❤ ✐s ❣❡♥❡r✐❝ ✐♥ t❤❡ ❙❖✭✶✵✮ ●❯❚ → ❉✲t❡r♠ s♣❧✐tt✐♥❣✱ ❘● r✉♥♥✐♥❣ ❜❡t✇❡❡♥ ▼P❧ ❛♥❞ ▼●❯❚ ◆♦♥✲✉♥✐✈❡rs❛❧ ❣❛✉❣✐♥♦ ♠❛ss❡s ✇✐t❤ ▼✷ < ✵✱ ❛s r❡q✉✐r❡❞ ❜② (❣ − ✷)µ ❝♦♥str❛✐♥t✱ ❝❛♥ ❜❡ ❣❡♥❡r❛t❡❞ ❜② t❤❡ ❋✲t❡r♠ ✐♥ ✺✹ r❡♣✳ ♦❢ ❙❖✭✶✵✮ (❣ − ✷)µ ❝❛♥ ❜❡ ❞✐s❡♥t❛♥❣❧❡❞ ❢r♦♠ ❜ → sγ ❛♥❞ ❝♦♠♣❛t✐❜❧❡ ✇✐t❤ t❤❡ ❡①♣❡r✐♠❡♥t❛❧ ✈❛❧✉❡ ❛t ✶σ ❧❡✈❡❧✳ ❯♣♣❡r ❧✐♠✐t ❢♦r (❣ − ✷)µ ✐s s❡t ❜② t❤❡ ▲❊P ❜♦✉♥❞ ♦♥ ♠❤✵✳ ❨✉❦❛✇❛ ✉♥✐✜❝❛t✐♦♥ ✐♥ ❙❖✭✶✵✮ ✇✐t❤ ❧✐❣❤t ❙❯❙❨ s♣❡❝tr✉♠✿ ▲✐❣❤t ❣❧✉✐♥♦s ❢♦r t❤❡ ❡❛r❧② ▲❍❈

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-11
SLIDE 11

❇❛❝❦✉♣ s❧✐❞❡s

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-12
SLIDE 12

❙♦❧✉t✐♦♥ ✶✿ t②♣✐❝❛❧ s♣❡❝tr✉♠

h H A H Χo Χo Χo Χo g Χ Χ ΝeeL eR dR uR uLdL ΝΜΜL ΜR sR cR cLsL Τ1 ΝΤ Τ2 b1 t1 b2t2

500 1000 1500 masses GeV

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-13
SLIDE 13

❙♦❧✉t✐♦♥ ✷✿ t②♣✐❝❛❧ s♣❡❝tr✉♠

h H A H Χo Χo Χo Χo g Χ Χ ΝeeL dR eRuRuLdL ΝΜ ΜL sR ΜRcRcLsL b1 t1 ΝΤΤ1b2t2 Τ2

500 1000 1500 masses GeV

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-14
SLIDE 14

❙♦✉r❝❡s ♦❢ ♥♦♥✲✉♥✐✈❡rs❛❧ s❝❛❧❛r ♠❛ss❡s

❘● r✉♥♥✐♥❣ ❢r♦♠ t❤❡ P❧❛♥❝❦ s❝❛❧❡ ■♥ ❣r❛✈✐t② ♠❡❞✐❛t✐♦♥ s♦❢t ❙❯❙❨ ❜r❡❛❦✐♥❣ t❡r♠s ❛r❡ s✉♣♣♦s❡❞ t♦ ❜❡ ❣❡♥❡r❛t❡❞ ❛r♦✉♥❞ ▼P❧✳ ❘✉♥♥✐♥❣ ❢r♦♠ t❤❡ P❧❛♥❝❦ s❝❛❧❡ t♦ t❤❡ ●❯❚ s❝❛❧❡ s♣❧✐ts ✶✵ ❛♥❞ ✶✻✳ ❲❡ ♣❛r❛♠❡t❡r✐③❡ t❤✐s ❡✛❡❝t ❜② s❡tt✐♥❣ ♠✶✵ ❢♦r ❍✐❣❣s❡s ❛♥❞ ♠✶✻ ❢♦r sq✉❛r❦s ❛t ▼●❯❚✳ ❉✲t❡r♠ ❝♦♥tr✐❜✉t✐♦♥ ❲❤❡♥ t❤❡ ❣❛✉❣❡ s②♠♠❡tr② ✐s ❜r♦❦❡♥ ❛♥❞ ✐ts r❛♥❦ ✐s r❡❞✉❝❡❞✱ s♦❢t s❝❛❧❛r ♠❛ss❡s ❛❝q✉✐r❡ ♥❡✇ ❝♦♥tr✐❜✉t✐♦♥ ❢r♦♠ ❉✲t❡r♠s ♦❢ t❤❡ ❜r♦❦❡♥ ❯✭✶✮ ✇❤✐❝❤ ✐s ♣r♦♣♦rt✐♦♥❛❧ t♦ ❝❤❛r❣❡s ♦❢ t❤❡ ❜r♦❦❡♥ ❯✭✶✮ ❋♦r ❙❖✭✶✵✮ → ●❙▼✿ ♠✷

❍❞ = ♠✷ ✶✵ + ✷❉

♠✷

❍✉ = ♠✷ ✶✵ − ✷❉

♠✷

◗,❯,❊ = ♠✷ ✶✻ + ❉

♠✷

❉,▲ = ♠✷ ✶✻ − ✸❉

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚

slide-15
SLIDE 15

◆♦♥✲✉♥✐✈❡rs❛❧ ❣❛✉❣✐♥♦ ♠❛ss❡s ❢r♦♠ ♥♦♥✲s✐♥❣❧❡t ❋✲t❡r♠s

  • ❛✉❣✐♥♦ ♠❛ss❡s ✐♥ ❙❯●❘❆ ❝❛♥ ❛r✐s❡ ❢r♦♠ ❞✐♠❡♥s✐♦♥ ✺ ♦♣❡r❛t♦r✿

L ⊃ − ❋ ❛❜ ✷▼P❧❛♥❝❦ λ❛λ❜ + ❝.❝. ❋ ❛❜ ♠✉st tr❛♥s❢♦r♠ ❛s ❛ s✐♥❣❧❡t ✉♥❞❡r t❤❡ ❙▼ ❣❛✉❣❡ ❣r♦✉♣ ❜✉t ❝❛♥ ❜❡ ✐♥ ❛ ♥♦♥✲s✐♥❣❧❡t r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❙❖✭✶✵✮ ◆♦♥✲③❡r♦ ❣❛✉❣✐♥♦ ♠❛ss❡s ❛r✐s❡ ❢r♦♠ ❋ ❛❜ r❡♣r❡s❡♥t❛t✐♦♥s ✐♥ t❤❡ s②♠♠❡tr✐❝ ♣❛rt ♦❢ t❤❡ ❞✐r❡❝t ♣r♦❞✉❝t ♦❢ t❤❡ ❛❞❥♦✐♥t r❡♣r❡s❡♥t❛t✐♦♥✿ (✹✺ × ✹✺)❙ = ✶ + ✺✹ + ✷✶✵ + ✼✼✵ ■❢ ❋ ❛❜ tr❛♥s❢♦r♠s ❛s ✺✹✱ ❣❛✉❣✐♥♦ ♠❛ss❡s ❛r❡ ❞❡t❡r♠✐♥❡❞ ❜②✿

▼❛rt✐♥✱ ✷✵✵✾

▼✶ : ▼✷ : ▼✸ = −✶ ✷ : −✸ ✷ : ✶ ▼✷ < ✵ ⇒ µ < ✵ ❝❛♥ ❜❡ ❝♦♥s✐st❡♥t ✇✐t❤ (❣ − ✷)µ ❝♦♥str❛✐♥t✦

▼❛r❝✐♥ ❇❛❞③✐❛❦ ❨✉❦❛✇❛ ❯♥✐✜❝❛t✐♦♥ ✐♥ ❙❯❙❨ ❙❖✭✶✵✮ ●❯❚