Lecture 11: FCNC and

“Penguin” Diagrams

http://faculty.physics.tamu.edu/kamon/teaching/phys627/1

“Penguin” Diagrams

The goal of this lecture is to understand Flavor Changing NeutralCurrents (FCNCs) and its power in probing new physics.

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Goal

Charged & Neutral Currents

B Mesons

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We focus on a rare decay of Bs today.

𝑩𝟎 ഥ𝒃𝒅

𝑩𝒔𝟎 ഥ𝒃𝒔

𝑩+ ഥ𝒃𝒖

𝑩𝒄+ ഥ𝒃𝒄

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Quark Mixing & CKM Matrix

Square of each matrix element 𝑉𝑖𝑗2

expresses transition probabilitybetween 𝑖 ↔ 𝑗 with W boson exchange.

Feynman Diagram in Week Interaction

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𝒈𝑾

Propagator for W boson:

V-A Charged Current:

−𝑔𝑊

2ҧ𝑐𝐿𝛾

𝜇𝑊𝜇+𝑠𝐿

′

−𝑔𝑊

2ҧ𝜈𝐿𝛾

𝜇𝑊𝜇+𝑒𝐿

Quark Mixing

𝛾𝜇1

21 − 𝛾5

𝒃

𝒄

𝑾−

𝒈𝑾𝑽𝒄𝒃

Dimensionless coupling strength 𝒈𝑾 for leptons 𝒈𝑾 × (CKM Factor) for quarks

CC and FCNC for 𝑩𝒔 → 𝝁𝝁𝑲𝑲

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CC for 𝑏 → 𝑐 transition

FCNC for 𝑏 → 𝑠 transition

“Penguin” Diagram

Note: those types of “loop” diagrams are veryimportant to search effects beyond the standardmodel, because any undiscovered particles cancontribute in the loop as a virtual state !

Doesn’t look like penguin ?

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𝑲𝟎

ഥ𝑲𝟎

Other “Penguin” Diagram in Kaon

ഥ𝑲𝟎𝝅𝟎

Deviation at 2.4𝜎 - 2.6𝜎 from the SM Compatible with other anomalies observed in

𝒃 → 𝒔𝝁𝝁 transition ⟹ ~4𝜎 tension with SM

Puzzle with Anomalies in B Decays

New contribution via 𝑋 → 𝜇+𝜇−?

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[Q] Convince yourself if the ratios should be unity. Why do we use R?

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Feynman Diagrams in the SM

[Q] Why do we use R?

Simone Bifani, Sebastien Descotes-Genon, Antonio Romero Vidal and Marie-Helene Schune,

“Review of Lepton Universality tests in B decays”, arXiv:1809.06229

𝑹𝑲(∗) =

𝒆−𝒆+

𝝁−𝝁+

= (cancelling QCD corrections)

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Neutrinos in Weak Interaction

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Rich Neutrino Physics

3 neutrino flavors. More? Non-Zero masses. Why so

light? Mass hierarchy?Oscillations. Structure of

mixing angles?Non standard interactions? Cosmology?

Seesaw mechanism is a generic model used to understand the relative sizes of observed neutrino masses, of the order of eV, compared to those of quarks and charged leptons. RH neutrinos?

Pauli (1930) Discovered by Cowan and Reines

using a nuclear reactor in 1958 Massless Neutrinos in the Standard

Model (‘60s): 𝑵𝝂 = 𝟐. 𝟗𝟖𝟒 ± 𝟎. 𝟎𝟎𝟖(LEP 2006)

Evidence for neutrino mass from SuperK (1998) and SNO (2002)

First evidence that the “minimal” Standard Model of particle physics is incomplete!

2002 Nobel to pioneers: Davis and Koshiba:

Neutrino Cosmology: o Can be a (hot) dark matter, but it

cannot be the dominant cold dark (non-relativistic) matter components.

o Prediction by the hot Big Bang agrees with observations (e.g., the power spectrum of Cosmic Microwave Background (CMB) anisotropies), which would fail dramatically without a Cosmic Neutrino Background (C𝜈B) with properties matching closely those predicted by the standard neutrino decoupling process (i.e., involving only weak interactions).

o 𝒎𝒕𝒐𝒕𝒂𝒍 = σ𝒊𝒎𝝂𝒊 ≲ 𝟏 𝐞𝐕; 𝑵𝐞𝐟𝐟 ≈ 𝟑. 𝟏

o Matter-antimatter asymmetry?

Tiny Neutrinos, Huge Player

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Tiny masses, but a very big player in particle physics andcosmology…

Neutrino Flavor Mixing

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𝜈𝑒𝜈𝜇𝜈𝜏

=

𝑈𝑒1 𝑈𝑒2 𝑈𝑒3𝑈𝜇1 𝑈𝜇2 𝑈𝜇3𝑈𝜏1 𝑈𝜏2 𝑈𝜏3

𝜈1𝜈2𝜈3

3 flavors of 𝜈 in SM

3 mass eigenstate of 𝜈

PMNS matrix(1962)

• Pontecorvo• Maki• Makagawa• Sakaga

Atmospheric & accelerator: 𝜃23~45

°

∆𝑚232~2 × 10−3 eV2

Interference:𝜃13~9

°

and 𝛿𝐶𝑃= ??

Solar & reactor:𝜃12~34

°

∆𝑚122~8 × 10−5 eV2

3-flavor mixing describes (almost) all neutrino oscillation phenomena (3 mixing angles, 2 independent mass splittings, 1 CPV phase). And “matter effect” … Neutrino oscillations change when in media in comparison to vacuum oscillations due to the scattering of neutrinos on matter constituents, electrons particularly. This can be easily described by introducing new effective matter mixing angles and squared mass-splittings.

Neutrino Detections

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Bubble Chambers Emulsion Chambers IceCube

MINOS, NOvA T2KSuper-Kamiokande

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Feynman Diagrams for 𝑩𝒔 → 𝝁𝝁

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[Q] What is inside the circle?

𝑩𝒔 → 𝝁𝝁 (Cont’d)

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XX

[Q] Gluon doesn’t work. What else?

𝑩𝒔 → 𝝁𝝁 (Cont’d)

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[Q] Phone doesn’t work. For bs. Any solution?

𝑩𝒔 → 𝝁𝝁 (Cont’d)

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[Q] FCNC for 𝑠 → 𝑏 transition?

Standard Model FCNC for 𝑩𝒔 → 𝝁𝝁

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m

m

𝜸/𝒁

b

s

_

b

SM

𝒕

𝑾−

Supersymmetric FCNC for 𝑩𝒔 → 𝝁𝝁

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m

m

H/A0

b

s

_

c+~

t~

b

SUSY

tan𝜷𝟏/ cos𝜷

tan𝜷

∝ tan𝛽 𝟔

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Inquiry/classification on superymmetric diagram

Power of 𝑩𝒔 → 𝝁𝝁

This is one of interesting rare decays to test new physicssuch as SUSY:

Br(Bsmm)SM ~ 3 x 10-9

Br(Bsmm)SUSY ~ Br(Bsmm)SM x (10 ~ 1000)

Within the SM, we will not see any events even with 100 x 1012

collisions at the Tevatron.

In the SUSY models (large tanb), the decay can be enhanced by up to1,000.

But the SUSY particle masses are expected to be of orderof 1000 GeV. But the Bs mass is ~5 GeV.

How can one possibly test SUSY models using Bs mesondecays? This is a main topic of this lecture.

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Why 𝑩𝒔 → 𝝁𝝁 ? [1990’s] LEP results on the measurements of couplings indicate

SUSY with two Higgs doublets gives a possibility of unification offundamental forces. This motivates me to work on a particular channel (“trilepton”) at theTevatron.

[1998] There were two SUSY/Higgs workshops at Fermilab toexplore a feasibility and a potential of discovery of Higgs andSUSY at the Tevatron. An importance of large tanb SUSYscenarios is highlighted. This motivated me to work on large tanb scenario of SUSY where tauleptons are the key in SUSY discovery.

[2002] The WMAP measurement of the dark matter content (23%)in the universe strongly indicates a few SUSY scenarios. One ofthem is a scenario at large tanb where one can explore at theTevatron using the Bsmm decays This is the beginning of TAMU’s PPC program.

[2013] Observation at the SM expectation.

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Teruki Kamon 25PPC 2017

CBS comedy “Big Bang Theory”

(Season 1 Episode 15)

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The poster was designed during lunch meetings …

PPC 2007 and Big Bang Theory

Rare 𝑩𝒔 Meson Decay

CKM matrix

b t

s t

Vtb … transition between t and b

Vts … transition between t and s

PLB 538 (2002) 121

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𝑩𝒔 → 𝝁𝝁

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PLB 538 (2002) 121

FCNC in 𝑩𝒔 → 𝝁𝝁

Br(𝑩𝒔 → 𝝁𝝁 )

2

+

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𝑩𝒔(𝒅) → 𝝁𝝁 Candidate at CDF

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Run 198082 Event 8264441:- M(mm) = 5.375 GeV- ct = 236mm - pT(m

+) = 4.6 GeV- pT(m

-) = 2.4 GeV

m+m-

1st Round Analysis

PRL 93 (2004) 032001

First 2-side 90%CL Limit

SM Expectation

PRL 93 (2004) 032001PRL 95 (2005) 221805 PRL 100 (2008) 101802PRL 107 (2011) 191801PRD 87 (2013) 072003

PLB 538 (2002) 121

170 pb-1 ~ 8.5 x 1012 collisions

2002 2013

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Data in Bs signal window

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We see an excess over the background-only expectation in the Bs signal region and have set the first two-sided bounds on BR(Bs→ m+m-)

A fit to the data, including all uncertainties, yields

Data in the B0 search window are consistent with background expectation, and the world’s best limit is extracted:

Conclusion (2011)

81.19.0 108.1)(

-+-

-+ mmsBBR

89109.3)(106.4

--+- mmsBBR at 90% C.L.

..%)90(%9510)0.5(0.6)(90

LCatBBR --+ mm

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3/14: Approval … postponed

6/09: Collaboration Review (I)

6/22: Collaboration Review (II)

6/30: Approved!

7/10: Submission to PRL!!

7/15: Fermilab-Today

7/26: PRL referee report

8/19: Re-submission

9/07: PRL referee report (II)

9/08: RE-Re-submission

9/09: Accepted by PRL!!!

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Results opened atEPS 2011

What we will seebeyond our horizon ?

Stay tuned !

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2011.07.13

PRL 107 (2011) 191802

PRL 107 (2011) 191801

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CDF

CMS

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CMS Event in 2011

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But, on November 2012

LHCb at HCP2012 𝑩𝒔 → 𝝁𝝁

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LHCb at HCP2012 𝑩𝒔 → 𝝁𝝁

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<4.2x10-9

CMS PAS BPH-12-009

LHCb CONF-2012-017

<8.1x10-10

𝑩𝒔 → 𝝁𝝁

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CMS: PRL 111 (2013) 101804

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LHCb 2017

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ATLAS 2016

𝟏𝝈2𝝈

3𝝈

[Q] LHCb and CMS results are shown in a combined form, while it is notfor ATLAS. What is the reason?

Collider Detectors

ATLAS CMS CDF II D0 II

Magnetic

field

2 T solenoid +

toroid (0.5 T barrel

1 T endcap)

4 T solenoid +

return yoke

1.4T solenoid 2T solenoid

+ toroid (1.8T)

Tracker Si pixels, strips +

TRT

σ/pT ≈ 5x10-4 pT +

0.01

Si pixels, strips

σ/pT ≈ 1.5x10-4 pT +

0.005

Si strips + drift

chamber

Si strips +

scintillating fiber

EM

calorimeter

Pb+LAr

σ/E ≈ 10%/√E +

0.007

PbWO4 crystals

σ/E ≈ 3%/√E 0.003

Pb+scintillator

σ/E ≈ 13.5%/√E

0.015 in barrel

U+LAr

Hadronic

calorimeter

Fe+scint. / Cu+LAr

(10 λ)

σ/E ≈ 50%/√E

0.03

Brass+scintillator

(7 λ + catcher)

σ/E ≈ 100%/√E

0.05

Iron+scintillator

σ/E ≈ 50%/√E 0.03

in barrel

U+LAr (Cu or

stainless in outer

hadronic)

Muon σ/pT ≈ 2% @ 50GeV

to 10% @ 1TeV

(ID+MS)

σ/pT ≈ 1% @ 50GeV

to 10% @ 1TeV

(DT/CSC+Tracker)

Rapidities to 1.4 Rapidities to 2.0

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What we learned from 𝑩𝒔 → 𝝁𝝁 ?

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[Q] What can we conclude on SUSY?

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FCNC Processes

Check List

1) Describe FCNC and list a few key decay modes; draw a few Penguin diagrams

2) Draw Feynman diagrams for 𝑩𝒔 → 𝝁𝝁 in the SM

3) Draw Feynman diagrams for 𝑩𝒔 → 𝝁𝝁 in SUSY. See Br(𝑩𝒔 → 𝝁𝝁 ) being

proportional to tan6b4) Survey 95% and 90% C.L. limits on Br(𝑩𝒔 → 𝝁𝝁 ) from major experiments

(CLEO, BELLE, BABAR, CDF and D0).

5) D0’s muon detector has an excellent coverage. [Check the pseudo-rapidity

coverage for muons in D0 and CDF.] However, D0 limits on Br(𝑩𝒔 → 𝝁𝝁 ) is

weaker than the CDF limits. Why?

6) CLEO, BELLE, BABAR do not have limits on Br(𝑩𝒔 → 𝝁𝝁 ). Why?

7) Below are three CDF papers on search for 𝑩𝒔 → 𝝁𝝁 . Summarize the analysis

and result in each paper by identifying how the analysis technique was

improved.

CDF (171 pb-1) Br < 7.5E-7 [hep-ex/0403032; PRL 93 (2004) 032001 ]

CDF (364 pb-1) Br < 2.0E-7 [hep-ex/0508036; PRL 95 (2005) 221805]

CDF (2000 pb-1) Br < 5.8E-8 [arXiv:0712.1708 [hep-ex] and PRL 100 (2008) 101892]

8) Survey the results from ATLAS, CMS and LHCb

9) How do we measure Br?

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Flavor Changing Neutral Currents (FCNCs) are powerful tool to probe newphysics.

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But, FCNC …

Summary

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Experimentally, …

Samples of 𝝅’s and 𝑲’s

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Decay-In-Flight

K+ K+

pT = 3 GeVpT = 2 GeV

K+ m+~100 cm

~10 cm

0

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Impact Parameter

Anatomy of 𝑩𝒔 → 𝝁𝝁

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Anatomy of Amplitude of 𝑩𝒔 → 𝝁𝝁

m

m

H/A0

b

s

_

c+~

t~

tan6b

b

SUSY

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