The Standard Model

R. Barbieri

Zuoz, August 14-20, 2016

The Standard Model

I. The SM and its status, as of 2016

II. Problems of (questions for) the SM III. Mirror Twin Higgs World

and (some of) its extensions

IV. Anomalies in B-decays

V. Axion searches by way of their coupling to the spin

to the electron spin

Axion searches by way of their coupling

Thanks to the QUAX collaboration

A quick introduction

µ

J

=

c

G

G ˜

+ c

F

F ˜

d

x L d

x

J

= + argdetM

Embed the chiral symmetry into an exact classical

U(1)-symmetry (PQ) spontaneously broken at a scale f

DFSZ ^{L = SH}

^H

^{+ Y}

^{QH ¯}

^{u + Y}

^{QH ¯}

^{d + Y}

^{QH ¯}

^e KSVZ

The axion a(x) is the corresponding (pseudoGB) 1. Due to the triangle anomaly

L = G

G ˜

2. In spite of being a 4-divergence is physical 3. Actually

4. To solve the strong CP problem

L = S T T ¯ + ¯ T

D

T + M T T ¯

L

=

a

f

J

+ a f

S

8 G

G ˜

+ a

f

8 c

F

F ˜

q e

q T rQ

= 1

L^{a µ}a

f_a (J_µ^{P Q} q¯ _{µ 5}Q_aq) + a

f_a 8 c_emF_µ F˜^µ q¯_LM˜_q(a)q_R

M ˜

(a) = e

M

e

V (a,

) < a >= 0

m²_a = m_um_d m_u + m_d

m² f² f_a²

The axion a(x) is the corresponding (pseudoGB)

Relic abundance of the QCD axion

¨

a + 3H a ˙ + m

a = 0

i

= a

/f

H = T

/M

a

= m

a

T

1/R

3H m

m

m

f_a ( ^QCD

T )^{4 m}_f

a

T > _QCD T < _QCD

i.e. cold Dark Matter

i2

=

i

= a

3 f

QCD Axions in cosmology

a

h

0.16( m

10

eV )

m

f

10

eV · 10

GeV

(Axion Like Particles: and unrelated) m f

P_iso(a) H_I²

2f_a² _i²

The dynamical field, a, is the “axion”

axion mass

and is very intensively searched for

inverse axion coupling

(with the most interesting region still unaccessible)

Olive et al, 2104

The coupling to spin 1

NRL:

L

4

a

f

G

G ˜

(g

= 10

g

GeV m )

d · E d 10

a

f

(e · cm)

A coupling to the spin and to the Electric field

B _{ef f} ·

DFSZ

g

= A m

f

= e 2m

g

(e) 1

g

(e) 10

The axion as a source of an effective 1 B

1. By the DM axion wind

B

= g

e a = g

e m

v a

cos m

t

(as reference)

m

10

eV f

10

GeV

coherence length

= m

100 GHz v 10

coherence time _a

2

m

v

10

sec B

10

T esla m

10

eV

(1000 bigger on nucleons)

m

a

0.3 GeV /cm

Ca

1

m

v 10 m

2. From a static source

U

g

g

m

m

e

r

·

E

(2)

B

·

a nuclear spin

r

º

º ^{1 2}

U

g

g

m

e

r

r ˆ ·

E

(2)

B

·

B

1

2

g

g

m

m

n

e

10

T ( m

10

eV )

n

10

/cm

e

B

1

2

g

g

m

n

e

10

T m

10

eV

n

10

/cm

e

Moody, Wilczek 1984

The axion as a source of an effective 2 B

Comparing numbers

(From the DM axion wind)

Need to work on some resonant phenomenon

(Gabrielse et al)

versus, e.g.

(CASPEr)

d E 10

eV E

10

V /cm

d

< 10

e · cm d

E 10

eV E

10

V /cm (g 2)

< 10

B 10

eV B

5 T esla

e

B

(e)

B

(N ) 10

eV m

10

eV

Proposal 1

Arvanitaki, Geraci 2014

the axion wind case

but smaller than in B

!! !! w = 200 Hz

(a static force from a rotating source)

B_{ef f} /T 10 ²³ M_T /T 10 ²⁰

B, Cerdonio, Fiorentini, Vitale 1989 on electron spins

Proposal 2 (axion DM wind)

on nucleon spins

Graham, Rajendram 2010 CASPEr 2014

Solving Block eq.s, at resonance

m

=

2 _N B^ext 10 ⁷ eV B^ext T 2 _eB^ext 10 ⁴ eV B^ext

T

10 ¹⁹T (m_a = 10 ⁷ eV, = 0.1 sec) 10 ²¹T (m_a = 10 ⁴ eV, = 10 ⁶ sec) M_T = _e,N² B_e,N^{ef f} n_S cos (m_at)

n_S = 10²²/cm³ e

N

e N

= min( _a, _rel, _R) dM

dt = M B 1

T₁, T₂ M

On the same line (axion DM wind in NMR)

d 10

a

f

(e · cm) d · E

Graham, Rajendram 2010 CASPEr 2014

M_T = _N d · E n_S cos (m_at) = 10 ¹⁷T (m_a = 10 ⁷ eV, = 0.1 sec)

since

N B_N^{ef f} 10² m_a 10 ⁷ eV

QUaerere AXions

Use the coupling to the electron spin (to avoid the frequency cutoff) and (try to) detect the RF power emitted by the coherent

magnetic dipole oscillating at

w = m

INFN (PD, Legnaro, TO), Birmingham, Moscow

About “radiation dumping”

Back to the transverse magnetization

M

=

B

n

cos (m

t)

large, hence negligible, for NMR exp.s (CASPEr, static force)

R

seriously relevant for EMR

R

= min( _a, _rel, _R)

a

2

m_av² 10 ⁴ sec 10 ⁴ eV

m_a ^rel 10 ⁶ sec f or EM R

0.1 sec f or N M R (for axion wind only)

w = 200 Hz 10 ³ sec f or N M R 10 ⁹ sec f or EM R

R = 1

2n_Sw³V (10 ⁴eV

w )³ mm³ V

10²²/cm³ n_S

Bloom 1957

H = (w

i

2 )m

m + (w

i

2 )a

a + (w

i

2 )c

c+

g

(ma

+ m

a) + g

(mc

+ m

c)

g_mc = e

m_e (n_Sw_cV /V_c)^1/2

Working in a cavity

axion-magnon coupling g_am = v_a

f (n_Sw_a)^1/2 magnon-cavity mode coupling

a = axion mode c = cavity mode m = magnon mode

z = 1

(2w_c)^1/2 (c + c⁺)

RF power exiting from the cavity

P

=

2 < z ˙

>=

w

w

g

g

N

| (w

w

+ i

)(w

w

+ i

) g

|

= P

(

>>

,

)f

f (w

= w

± g

) = 4

(

+

)

Looks OK, since no and R

RAD dumping in free space

Hybrid width

RF power and counting rate

Using realistic numbers for and

n

V

R_a = P_out

a

= 2.6 10 ³ m_a

2 · 10 ⁴ eV

2 V_s 1 liter

n_S

10²⁸/m³

min

10 ⁶ s Hz

P

10

W att( n

10

/cm

)( V

10

cm

)(

10

sec )( m

2 · 10

eV )

¯

n = 1

e

1 R

= ¯ n/

N = (R

+ R

)t

SNR = R

t

(R

+ R

)t

= R

R

+ R

t

Maximal expected sensitivity

Ultimate noise from the termal bath

Number of counts in a time t

R

< R

R

t

SNR

1 = 1.6 R

4 10

Hz

Working at and w = 48 GHz

= 1 µs

requires T

< 13 mK

Given above, for SNR > 3 R

Some very preliminary measurements

Using a sphere of YIG

of about ^{20 mm}

Graham et al, 2106

still a bit far from the desired sensitivity

Atomic transitions from DM wind

Sikivie 2014

axion wind tuned laser

- - -

0

e

B

E

m

= 10

eV eV

excited level

(

)

Photon rate from de-excited atoms:

dN

dt n

10

Hz min(t, t

,

) 10

sec

Requires:

T 10 mK ( m

10

eV )

to depopulate the higher spin state in absence

of axion wind

N

e

< 0.1

(Some) proposed experiments using NMR/EMR

CASPEr axion wind/NMR

limited in frequency (mass) but size of the effect OK

frequency OK but effect smaller

ARIADNE static source/NMR

frequency OK

QUAX axion wind/EMR

B_{ef f} /T 10 ²³ M_T /T 10 ²⁰

B_{ef f} /T 10 ²² M_T /T 10 ²¹ (m_a/eV = 10 ⁴, = 0.1sec)

(m_a/eV = 10 ⁴, = 10 ⁶sec) (m_a/eV = 10 ⁷, = 0.1sec)

B_{ef f} /T 10 ²² M_T /T 10 ¹⁹

for question time

P

= w(M

V )B

P

= w

(M

V )

M_T = ²B_T n_S

P

= P

= 1

2

w

V n

=

Another way to understand R

Incoming power

RF power emitted by the oscillating macroscopic dipole

Transverse oscillating magnetization

Energy conservation

Bloembergen, Pound 1954

The classic search

Not easy to explore the most relevant

region

10 ⁴ m_a/eV 10 ³

Rybka

ADMX