QCD RADIATIVE CORRECTIONS TO HIGGS PHYSICS

Taushif Ahmed Feb 21, 2017 Talk to Defend My Thesis

Thesis Advisor: Prof. V. Ravindran

1

MOTIVATIONS

• It is an interesting era for High energy physics

2012’s Discovery of SM-Higgs-like particle

Excess in 750 GeV

• Confirming these demand more data at LHC and precise theoretical predictions

• Is it new physics or the SM?

• QCD radiative corrections are crucial

2

MOTIVATIONS

LO is a crude approximation

3LO prediction is unreliable: Huge scale uncertainty

MOTIVATIONS

Reliable Result

4

at N3LO

WHAT IS NEXT?

Precise predictions in Higgs, pseudo-Higgs & DY production channels

This thesis arises in this context

5

PUBLICATIONS

1. Higgs Boson Production Through Annihilation At Threshold QCD

bbN3LO

JHEP 1410, 139 (2014) TA, Rana & Ravindran

2. Rapidity Distribution In Drell-Yan & Higgs Productions at Threshold QCD N3LO

Phys.Rev.Lett. 113, 212003 (2014) TA, Mandal, Rana & Ravindran

3. Pseudo Scalar Form Factors At 3-Loop QCDTA, Gehrmann, Mathews, Rana & RavindranJHEP 1511, 169 (2015)

TA, Kumar, Mathews, Rana & RavindranEur. Phys. J. C (2016) 76:355

4. Pseudo-scalar Higgs Boson Production at Threshold and QCD

N3LON3LL

6

PUBLICATIONS (NOT INCLUDED IN THESIS)5. Two-Loop QCD Correction to massive spin-2 resonance → 3-gluons

JHEP 1405, 107 (2014) TA, Mahakhud, Mathews, Rana & Ravindran6. Drell-Yan Production at Threshold to Third Order in QCD

Phys.Rev.Lett. 113, 112002 (2014) TA, Mahakhud, Rana & Ravindran

TA, Mahakhud, Mathews, Rana & RavindranJHEP 1408, 075 (2014)7. Two-loop QCD corrections to Higgs → amplitudeb+ b+ g

TA, Mandal, Rana & RavindranJHEP 1502, 131 (2015)8. Higgs Rapidity Distribution in Annihilation at Threshold in QCD bb N3LO

9. Spin-2 Form Factors at Three Loop in QCDJHEP 1512, 084 (2015) TA, Das, Mathews, Rana & Ravindran

Eur.Phys.J. C76 (2016) no.12, 663 TA, Bonvini, Kumar, Mathews, Rottoli, Rana & Ravindran10. Pseudo-scalar Higgs boson production at N3LOA +N3LL0

11. NNLO QCD Corrections to the Drell-Yan Cross Section in Models of TeV- Scale GravityTA, Banerjee, Dhani, Kumar, Mathews, Rana & RavindranEur.Phys.J. C77 (2017) no.1, 22

TA, Das, Kumar, Mathews, Rana & RavindranarXiv:1505.07422 [hep-ph]15. RG improved Higgs boson production to N3LO in QCD

12. The two-loop QCD correction to massive spin-2 resonance ! qqgEur.Phys.J. C76 (2016) no.12, 667 TA, Das, Mathews, Rana & Ravindran

N = 413. Konishi Form Factor at Three Loop in SYM arXiv:1610.05317 [hep-th] (Under consideration in PRL) TA, Banerjee, Dhani, Rana, Ravindran & Seth

14. Three loop form factors of a massive spin-2 with non-universal coupling arXiv:1612.00024 [hep-ph] (Appeared to be in PRD) TA, Banerjee, Dhani, Mathews, Rana & Ravindran

7

HIGGS BOSON PRODUCTION THROUGH ANNIHILATION AT THRESHOLD QCD N3LO

JHEP 1410, 139 (2014) TA, Rana & Ravindran

bb

8

MOTIVATIONS:

Higgs boson production

Dominant Sub-dominant

• Yukawa coupling: small in SM, can be enhanced in MSSM

• Measurements of Higgs couplings are underway at LHC

• In precision studies nothing is unimportant

QCD RADIATIVE CORRECTIONS ARE CRUCIAL

bb ! H

9

Give % of bB channel contribution

MOTIVATIONS: SV

• Going beyond LO: challenginglarge no of diagrams

Phase space integrals

Loop integrals

• Often fail to compute complete fixed order result

• Alternative approach to catch dominant contributions

virtual & soft gluons

Soft-virtual corrections10

SOFT-VIRTUAL

�(z) = �sing(z) +�hard(z)

�sing(z) ⌘ �SV(z) = �SV� �(1� z) +

1X

j=0

�SVj Dj

Dj ⌘ lnj(1� z)

1� z

!

+

z =q2

s

�hard(z) : polynomial in ln(1� z) sub-leading

Leading in z ! 1

Partonic X-section

11

MOTIVATIONS: SV

�sing(z) ⌘ �SV(z) = �SV� �(1� z) +

1X

j=0

�SVj Dj

�(z) = �sing(z) +�hard(z)Dj ⌘

lnj(1� z)

1� z

!

+

z =q2

s

�hard(z) : polynomial in ln(1� z) sub-leading

Leading in z ! 1

Partonic X-section: expand around z ! 1

Our focus12

GOAL

SV corrections to bb ! H cross sectionN3LOat QCD

Existing result: NNLO and partial SV [’03, ’06]

Next obvious and necessary extension

N3LO

13

THE PRESCRIPTION

Many methods

1. Direct evaluation of diagrams

14

THE PRESCRIPTION

Many methods

1. Direct evaluation of diagrams

{

{15

THE PRESCRIPTION

Many methods

1. Direct evaluation of diagrams

2. Use factorisation, RGE & Sudakov resum

16

THE PRESCRIPTION

Many methods

1. Direct evaluation of diagrams

2. Use factorisation, RGE & Sudakov resum

{

{ Will not compute these!!

Symmetry

17

MASTER FORMULA

with

• Operator renormalisation• Form factors• Soft-collinear distribution• Mass factorisation kernel

Required up to N3LO

[Ravindran]

18

MASTER FORMULA

with

• Operator renormalisation• Form factors• Soft-collinear distribution• Mass factorisation kernel

[Gehrmann, Kara ’14]

[Ravindran]

[TA, Mahakhud, Rana, Ravindran ’14]

19

FORM FACTORS & SOFT-COLLINEAR DISTR

Form Factors

[Gehrmann, Kara ’14]

Real emission diagrams|gg!H , Real emission diagrams|bb!H

�|gg!H =CA

CF�|bb!H

Soft-Collinear Distr

[Ravindran ’06]• Established up to NNLO[TA, Mahakhud, Rana, Ravindran ’14]• We postulated the relation even at N3LO

• Verified in case of Drell-Yan [Catani et. al., von Monteuffel et. al. ’14]

20

RESULTS

Analytical results at N3LO

Most accurate result till date!

• is the new result• Uplift the theoretical precision• Reduces scale uncertainties

�SV|�

21

RAPIDITY DISTRIBUTION IN DRELL-YAN & HIGGS PRODUCTIONS AT THRESHOLD QCD N3LO

Phys.Rev.Lett. 113, 212003 (2014) TA, Mandal, Rana & Ravindran

22

MOTIVATIONS

• DY & Higgs: very important processes

• DY: 1. One of the cleanest processes 2. Crucial role in determining PDF• Higgs: Yet to confirm the identities of 2012’s particle

23

MOTIVATIONS

• DY & Higgs: very important processes

• DY: 1. One of the cleanest processes 2. Crucial role in determining PDF• Higgs: Yet to confirm the identities of 2012’s particle

• Differential rapidity distributions: important observable

• Will be measured at the LHC

24

MOTIVATIONS

• DY & Higgs: very important processes

• DY: 1. One of the cleanest processes 2. Crucial role in determining PDF• Higgs: Yet to confirm the identities of 2012’s particle

• Differential rapidity distributions: important observable

• Will be measured at the LHC

• Often fail to compute complete fixed order result• Going beyond LO: challenging• Call for more precise theoretical results

25

MOTIVATIONS

• DY & Higgs: very important processes

• DY: 1. One of the cleanest processes 2. Crucial role in determining PDF• Higgs: Yet to confirm the identities of 2012’s particle

• Differential rapidity distributions: important observable

• Will be measured at the LHC

• Often fail to compute complete fixed order result• Going beyond LO: challenging• Call for more precise theoretical results

Catch dominant contributions through SV approx26

SOFT-VIRTUAL

Rapidity Distribution

z1 ! 1, z2 ! 1

zi =x

0i

xi

Y ⌘ 1

2

log

✓x

01

x

02

◆⌧ ⌘ x

01x

02

�Y (z1, z2) = �singY (z1, z2) +�hard

Y (z1, z2)

�SVY = �SV

Y |���(1� z1)�(1� z2) +2j�1X

j=0

�SVY |�Dj�(1� z2)Dj

+2j�1X

j=0

�SVY |�Dj

�(1� z2)Dj +X

j,l

�SVY |DjDl

DjDl .

Leading in

: polynomial in sub-leading�hardY (z1, z2) ln(1� zi)

27

GOAL

SV corrections to rapidity for 1. Higgs in 2. Leptonic pair in DY

N3LOat QCD

Existing result: NNLO and partial SV [’03, ’07]

Next obvious and necessary extension

N3LO

gg ! H

28

THE PRESCRIPTION

Many methods

1. Direct evaluation of diagrams

29

THE PRESCRIPTION

Many methods

1. Direct evaluation of diagrams

{

{30

THE PRESCRIPTION

Many methods

1. Direct evaluation of diagrams

2. Use factorisation, RGE & Sudakov resum

31

THE PRESCRIPTION

Many methods

1. Direct evaluation of diagrams

2. Use factorisation, RGE & Sudakov resum

{

{ Will not compute these!!

Symmetry

32

MASTER FORMULA

• Operator renormalisation• Form factors• Soft-collinear distribution• Mass factorisation kernel

Required up to N3LO

[Ravindran]�

SMY (z1, z2, q

2, µ2R, µ

2F ) = C exp

⇣ Y

�z1, z2, q

2, µ2R, µ

2F , ✏

� ⌘���✏=0

Y =

✓lnhZ(as, µ

2R, µ

2, ✏)i2

+ ln���F(as, Q

2, µ2, ✏)���2◆�(1� z1)�(1� z2)

+ 2�Y (as, q2, µ2, z1, z2, ✏)� C ln�(as, µ

2, µ2F , z1, ✏)�(1� z2)

� C ln�(as, µ2, µ2

F , z2, ✏)�(1� z1) .

33

MASTER FORMULA

• Operator renormalisation• Form factors• Soft-collinear distribution• Mass factorisation kernel

[Ravindran]�

SMY (z1, z2, q

2, µ2R, µ

2F ) = C exp

⇣ Y

�z1, z2, q

2, µ2R, µ

2F , ✏

� ⌘���✏=0

Y =

✓lnhZ(as, µ

2R, µ

2, ✏)i2

+ ln���F(as, Q

2, µ2, ✏)���2◆�(1� z1)�(1� z2)

+ 2�Y (as, q2, µ2, z1, z2, ✏)� C ln�(as, µ

2, µ2F , z1, ✏)�(1� z2)

� C ln�(as, µ2, µ2

F , z2, ✏)�(1� z1) .

Unavailable

34

SOFT-COLLINEAR DISTRIBUTION

• Demanding finiteness of rapidity & RG invariance

• Determining finite part

poles of SCD

requires explicit computations

• However, it has been found �Y , �Xsection

• SCD for Xsection is used to obtain at N3LO�Y[TA, Mandal, Rana, Ravindran]

[Ravindran, van Neerven, Smith]

35

RESULTS

Analytical results at N3LO

• is the new result • Uplift the theoretical precision• Reduces scale uncertainties

�SVY |��

Numerical Impacts for Higgs

has the largest contribution!�SVY |��

36

RESULTS

Most accurate results till date!

37

PSEUDO SCALAR FORM FACTORS AT 3-LOOP QCD

TA, Gehrmann, Mathews, Rana & RavindranJHEP 1511, 169 (2015)

TA, Kumar, Mathews, Rana & RavindranEur. Phys. J. C (2016) 76:355

38

MOTIVATIONS

h,H,A• MSSM has richer Higgs sector

5 physical Higgs bosons H±

neutral

charged: CP evenh,H

A : CP odd{• Pseudo-scalar: important at the LHC

similar to scalar Higgs

• Searches at the LHC demands precise theoretical predictions

• New resonance at 750 GeVNew scalar / Spin-2 / Pseudo-scalar?

39

CP evenInclusive production cross section at QCDN3LO

CP oddInclusive production cross section at NNLO QCD

What is next?Go beyond NNLO for CP odd!requires

1. Virtual correction at 3-loop2. Real corrections at N3LO

[Anastasiou, Duhr, Dulat, Furlan, Herzog, Mistlberger]

[Harlander, Kilgore; Anastasiou, Melnikov]

MOTIVATIONS

40

GOAL

CP evenInclusive production cross section at QCD

CP oddInclusive production cross section at

N3LO

NNLO QCD

What is next?Go beyond NNLO for CP odd!requires

1. Virtual correction at 3-loop2. Real corrections at N3LO

Our GOAL

[Anastasiou, Duhr, Dulat, Furlan, Herzog, Mistlberger]

[Harlander, Kilgore; Anastasiou, Melnikov]

41

EFFECTIVE LAGRANGIAN

OJ(x) = @µ� �µ�5

�OG(x) = Gµ⌫

a Ga,µ⌫ ⌘ ✏µ⌫⇢�Gµ⌫a G⇢�

a

CG = �as254G

12F cot� CJ = �

asCF

✓3

2� 3 ln

µ2R

m2t

◆+ a2sC

(2)J + · · ·

�CG

Effective Theory Simplifications occur if mA << 2mt

effective theory by int out top loopmassless QCD

LAe↵ = �A

h� 1

8CGOG � 1

2CJOJ

i

[Chetyrkin, Kniehl, Steinhauser and Bardeen]

Original Theory Pseudo scalar couples to quarks through Yukawa

42

FEYNMAN DIAGRAMS

1586

447

244

400

+

+

2

+

6

+

+

+

4

FGq

+

+

+

7

type

type

type

type

Qgraf [P. Nogueira]

43

PRESCRIPTION

• Lorentz & Dirac algebra in d-dimensions

• Color simplification in SU(N) theory } in-house codes

• What about �5 ?"µ⌫⇢�&

inherently 4-dimensional

problem of defining in d ( ) dimensions 6= 4

[’t Hooft and Veltman]

"µ1⌫1�1�1 "µ2⌫2�2�2 = 4!�µ2

[µ1· · · ��2

�1]

�5 = i1

4!"⌫1⌫2⌫3⌫4�

⌫1�⌫2�⌫3�⌫4Prescription

Treat in d-dimensions

{�5, �µ} 6= 0

�5

44

IBP & LI • Removing unphysical DOF of gluons

1. Internal: Ghost loops

2. External: Polarization sum in axial gauge

• ResultsThousands of 3-loop scalar integrals!

22 Master Integrals (topologically different)

IBP & LI identities[Chetyrkin,Tkachov; Gehrmann, Remeddy]

45

MIS

b41 b51 b52

b61

b62 b81c61

c81

a51 a52 a61

a62

a63 a71 a72

a73a74

a75

a81a91

a92a94

Master Integrals [Gehrmann, Huber & Maitre ’05; Gehrmann, Heinrich, Huber & Studerus ’06; Heinrich, Huber & Maitre ’08; Heinrich, Huber, Kosower & Smirnov ’09; Lee, Smirnov & Smirnov ’10]

Unrenormalized 3-loop FF in power series of ✏ (d = 4 + ✏)

Results

46

COUPLING CONS RENORM

• Coupling Constant Renorm

• Dimensional Regularization

d = 4 + ✏

asS✏ =

✓µ2

µ2R

◆✏/2

Zasas

Zas = 1 + as

2

✏�0

�+ a2s

4

✏2�20 +

1

✏�1

�+ a3s

8

✏3�30 +

14

3✏2�0�1 +

2

3✏�2

�+ · · ·

�i QCD beta functions

47

OPERATOR RENORM

• Overall Operator Renorm

OG OJ& requires additional renorm

[OG]R = ZGG [OG]B + ZGJ [OJ ]B

[OJ ]R = Zs5Z

sMS

[OJ ]B

mixes under renormOG

Zs5 �5 prescriptionFinite renorm

Universal IR pole structure Zij

48

RESULTS

• 3-loop pseudo-scalar FF

• Operator renormalisation constants

• Corresponding anomalous dimensions

µ2R

d

dµ2R

Zij ⌘ �ikZkj

• Using these, we obtain renormalised FF

Most accurate results till date!49

AXIAL ANOMALY RELATION

Axial Anomaly

RG Invariance

Our results are in agreement with this in

Crucial check

50

APPLICATIONS

N3LO• Soft-virtual cross section at

Threshold resum cross section at N3LLand

[TA, Kumar, Mathews, Rana & Ravindran]

N3LL0

• For total inclusive production cross section, it is an important ingredient.

51

• Approximate + cross section using SCET N3LO

[TA, Bonvini, Kumar, Mathews, Rottoli, Rana & Ravindran]

CONCLUSIONS

Most precise predictions for

1. Xsection of Higgs production in bottom annihilation2. Rapidity of Higgs and DY pair3. Pseudo-scalar Form Factors at 3-loop

These will play important role at the LHC

Scale dependence is under control

52

53