The Curvature of Higgs Field Space Rodrigo Alonso In collaboration - - PowerPoint PPT Presentation

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The Curvature of Higgs Field Space Rodrigo Alonso In collaboration with E.E. Jenkins & A.V. Manohar HEFT 2015 - Chicago The Nature of the New Scalar Composite? Elemental? Mass Stabilization? Effective Field Theories helps us stay

SLIDE 1

The Curvature of Higgs Field Space

Rodrigo Alonso In collaboration with E.E. Jenkins & A.V. Manohar

HEFT 2015 - Chicago

SLIDE 2

The Nature of the New Scalar

Composite? Elemental? Mass Stabilization? Effective Field Theories helps us stay agnostic A tool to frame the BEH scalar This talk: a different view of (H)EFTs

SLIDE 3

Part I: Curvature

SLIDE 4

Started from the bottom

W,Z Massive Gauge Bosons living in: SU(2) xU(1) /U(1) One needs fields that live in the broken group to be sacrificed in the gauge bosons altar: a three sphere S parametrized as:

L Y Q 3

SLIDE 5

Started from the bottom

W,Z Massive Gauge Bosons living in: SU(2) xU(1) /U(1) One needs fields that live in the broken group to be sacrificed in the gauge bosons altar: a three sphere S parametrized as:

L Y Q 3

SLIDE 6

Started from the bottom

Defines the Gauge Covariant Derivative Three Massive Gauge Bosons living in: SU(2) xU(1) /U(1) a three sphere S

L Y Q 3

SLIDE 7

Started from the bottom

The most general transformation is given by the Killing Vectors Three Massive Gauge Bosons living in: SU(2) xU(1) /U(1) a three sphere S

L Y Q 3

SLIDE 8

Started from the bottom

So that we have a Gauge Covariant Derivative: Three Massive Gauge Bosons living in: SU(2) xU(1) /U(1) a three sphere S

L Y Q 3

and a Kinetic term:

SLIDE 9

It is a singlet of the EW symmetry and appears where the NGB are, is it maybe the ‘radius’? Then the sphere S gets expanded to R we have the SM Higgs doublet

Now the Higgs is here

3 4

The Field Space turns FLAT but u still transforms non-linearly!

SLIDE 10

Let’s give him a kinetic term

What Higgs is it?

For Example:

SLIDE 11

How is the space the 4 scalars live on? # of GB, 3 Functions of the singlet h characterizing Curvature

Riemann Curvature

2 1

SLIDE 12

The Curvature and Physical Observables

E.g. in an HEFT longitudinal boson scattering is not fully unitarized: Which means new resonances are required at (NDA):

[Barbieri, Bellazzini, Rychkov & Varagnolo; ’07]

SLIDE 13

Connection with Composite Models

take O(5)/O(4) and therefore a 4-sphere, S

and curvature: where the function of the singlet in the metric:

[Agashe, Contino Pomarol; ‘05]

SLIDE 14

Part II: Curvature is useful

SLIDE 15

Functional Methods

Partition Function and Effective Action: expanding the action around the classical solution 1-loop result:

SLIDE 16

Functional Methods

1-loop result:

[t’Hooft; ‘73]

SLIDE 17

Second variation of the action of HEFT Non-Invariant term!

Functional Methods: HEFT

SLIDE 18

The problem is we do not know how to take derivatives Or equivalently we must use geodesics to deviate from the background field

Covariant Formalism

So the second variation of the action is:

[Honerkamp; ’72] [Tataru; ‘75]

SLIDE 19

HEFT at one-loop

Introduce:

SLIDE 20

HEFT at one-loop

times

[Guo, Ruiz-Femenia & Sanz-Cillero; ’15] [RA,Jenkins, Manohar]

SLIDE 21

Non-invariant terms

[Appelquist & Bernard; ‘81] [Gavela, Machado, Kanshin, Saa; ‘14]

They are calculable with functional methods: and we can compare with the literature:

SLIDE 22

The Limits of HEFT

SM Higgs; Flat Technicolor; Curved (=1/v) Composite Higgs; Curved (tunable) Dilaton; Flat to first order

SLIDE 23

Measure the Curvature

Two curvature magnitudes: The second is hard to measure

2 1

quite constrained e.g.

SLIDE 24

Is the Earth Higgs field round?

. v f

SLIDE 25

–Thank You

Is the Earth Higgs field round?

. v f