Particle Physics and Fundamental Physics Studies with VERITASrene/VERITAS/ESAC2011/Buckley-FundPhysics.pdf · Particle Physics and Fundamental Physics Studies with VERITAS Jim Buckley

Particle Physics and Fundamental Physics Studies

with VERITASJim Buckley for

the VERITAS collaboration

Friday, February 25, 2011

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ESAC 2011 VERITAS James Buckley

Outline

• Dark Matter searches

• Galactic Center

• Dwarf Galaxies

• Intergalactic Magnetic Field constraints

• Tests of Lorentz-invariance violation

• Diffuse Extragalactic Background

• Axion-Like Particles


Dark Matter


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Dark Matter Observing Plan• Dwarf galaxies: 100 hours/season - Goal: move to within one order of magnitude of

generic predictions, constrain scenarios with Sommerfeld or astrophysical boost

• Concentrate on 3 promising Dwarf galaxies. More than one source to spread out over RA, average over systematic uncertainties in DM distribution.

• Systematics limit an individual observation to ~150-200 hours. Stacking could reduce systematics . We propose acquiring 500 hours on 3 sources in 5 years with 100 hours per source

• Fermi Unidentified Sources: 35 hours per season - Goal: identify astrophysical sources, potential for discovery of subhalo

• Follow up observations of hard-spectrum, steady, high lattitude (possibly extended) Fermi UIDs

• Galactic Center: 20 hours per season ON-OFF data on annulus around GC - Goal: obtain upper limits on generic models at high mass (greater than a few TeV) to complement LHC, only modest astophysical boost required


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Gamma-rays from DM

• Line-of-sight integral for MW-like halo in VL Lactea II simulation (M. Kuhlen, et al.)

• Sommerfeld enhancement larger for colder (lower velociy dispersion) dwarf halos

!0 q

!0

p

"0

K

q

"+

#

#

1

EγΦγ(θ) ≈ 10−10

�Eγ,TeV

dN

dEγ,TeV

� ��σv�

10−26cm−3s−1

� �100 GeV

Mχ

�2

� �� particle physics

J(θ)�� erg cm−2s−1sr−1

J(θ) =1

8.5 kpc

�1

0.3 GeV/cm3

�2 �

line of sightρ2(l)dl(θ)

� �� astrophysics

σ ∝ 1/v2


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LZA Observations

• At LZA, showers appear smaller (farther away), dimmer (light more spread out) and are visible over a larger effective area. Standard reconstruction stops working as well for angular resolution - use length, width (elongation) - get same angular resolution at LZA as SZA!


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VERITAS GC Detection

• Preliminary Results - 11 sigma excess at GC, some evidence for other HESS sources. All in 15 hours of data!


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GC Spectrum

• Spectrum has a similar shape to HESS spectrum(consistent with a cutoff, comparable errors for 15 hours not 100 hours of data!)

]

-1 s

-2 d

N/dE

[erg

cm

2 E-1310

-1210

-1110

Energy [eV]1210 1310

VERI

TAS

H.E.

S.S.Crab

galactic center

Crab (H.E.S.S.)

Crab (VERITAS, z>55deg)

Crab (VERITAS, z>60deg)

SgrA, VERITAS


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DM Limit from GC

• Estimated sensitivity with new PMTs, LZA observations for 5 years for a generic DM model, including x20 Sommerfeld enhancements.


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Dwarf Galaxy Limits

• Improvements from threshold, dedication of observing time, can come within an order of magnitude of generic predictions


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Sommerfeld Enhancement

• At high mass, expect Sommerfeld enhancement from W, Z exchange for standard neutralinos can give large enhancement in cross section, larger at small velocities

!"#$%&'$()*+",-.%

the indices i, j run over the possible initial two-particlestates. Let us consider for definiteness the case of thewinolike neutralino: the possible initial states aref!0!0;!!!"g. The neutralino and the chargino are as-sumed to be quasidegenerate, since they are all membersof the same triplet. What we will say can anyway be easilygeneralized to the case of the Higgsinolike neutralino. Letus also focus on two particular annihilation channels: theW!W" channel and the e!e" channel. It can be assumedthat, close to a resonance, d1 # d2. This can be inferred, forexample, using the square well approximation as inRef. [11], where it is found that, in the limit of smallvelocity, d1 ’

!!!2

p$cos

!!!2

ppc%"1 "

!!!2

p$coshpc%"1 and d2 ’

$cos!!!2

ppc%"1 ! 2$coshpc%"1, where pc &

!!!!!!!!!!!!!!!!!!!!!!2"2m=mW

p.

The elements of the ! matrix for the annihilation into apair of W bosons are #"2

2=m2!, so that we can write the

following order of magnitude estimate:

#v$!0!0 ! W!W"% # jd1j2"22

m2!: (9)

On the other hand, the nonenhanced neutralino annihila-tion cross section to an electron-positron pair !22 #"22m

2e=m

4!, so that it is suppressed by a factor $me=m!%2

with respect to the gauge boson channel. This is a well-known general feature of neutralino annihilations to fer-mion pairs and is due to the Majorana nature of theneutralino. The result is that all low-velocity neutralinoannihilation diagrams to fermion pairs have amplitudesproportional to the final state fermion mass. The charginoannihilation cross section to fermions, however, does notsuffer from such an helicity suppression, so that it is again!11 # "2

2=m2! ' !22. Then:

#v$!0!0 ! e!e"% # jd1j2"22

m2!: (10)

Then we have that, after the Sommerfeld correction, theneutralino annihilates to W bosons and to e!e" pairs (andindeed to all fermion pairs) with similar rates, apart fromO$1% factors. This means that while the W channel isenhanced by a factor jd1j2, the electron channel is en-hanced by a factor jd1j2m2

!=m2e. The reason is that the

annihilation can proceed through a ladder diagram like

the one shown in Fig. 4, in which basically the electron-positron pair is produced by annihilation of a chargino pairclose to an on shell state. This mechanism can be similarlyextended to annihilations to other charged leptons, neutri-nos, or quarks.

IV. CDM SUBSTRUCTURE: ENHANCING THESOMMERFELD BOOST

There is a vast reservoir of clumps in the outer halowhere they spend most of their time. Clumps should sur-vive perigalacticon passage over a fraction (say $) of anorbital time scale, td ( r=vr, where vr is the orbital ve-locity (given by v2

r ( GM=r%. It is reasonable to assumethat the survival probability is a function of the ratiobetween td and the age of the halo tH, and that it vanishesfor td ! 0. Thus, at linear order in the (small) ratio td=tH, afirst guess at the clump mass fraction as a function ofgalactic radius would be fclump / td. We conservativelyadopt the clump mass fraction %cl ( $rv"1

r t"1H with $ (

0:1–1. This gives a crude but adequate fit to the highestresolution simulations, which find that the outermost halohas a high clump survival fraction, but that near the Sunonly 0.1%–1% survive [17]. In the innermost galaxy, es-sentially all clumps are destroyed.Suppose the clump survival fraction S$r% / fclump / r3=2

to zeroth order. The annihilation flux is proportional to&2 ) Volume) S$r% / S$r%=r. This suggests we shouldexpect to find an appreciable gamma-ray flux from theouter galactic halo. It should be quasi-isotropic with a#10% offset from the center of the distribution. The fluxfrom the Galactic center would be superimposed on this.High resolution simulations demonstrate that clumps ac-count for as much luminosity as the uniform halo [18,19].However much of the soft lepton excess from the inner halowill be suppressed due to the clumpiness being much lessin the inner galaxy.We see from the numerical simulations of our halo,

performed at a mass resolution of 1000M* that the subhalocontribution to the annihilation luminosity scales asM"0:226

min [19]. For Mmin ( 105M*, this roughly equatesthe contribution of the smooth halo at r ( 200 kpc fromthe center. This should continue down to the minimumsubhalo mass. We take the latter to be 10"6M* clumps,corresponding the damping scale of a binolike neutralino[20,21]. We consider this as representative of the dampingscale of neutralino dark matter, although it should be notedthat the values of this cutoff for a general weakly interact-ing massive particle (WIMP) candidate can span severalorders of magnitude, depending on the details of the under-lying particle physics model [22,23]. It should also betaken into account that the substructure is a strong functionof the galactic radius. Since the dark matter density dropsprecipitously outside the solar circle (as r"2), the clumpcontribution to boost is important in the solar neighbor-hood. However absent any Sommerfeld boost, it amounts

FIG. 4. Diagram describing the annihilation of two neutralinosinto a charged lepton pair, circumventing helicity suppression.

CAN THE WIMP ANNIHILATION BOOST FACTOR . . . PHYSICAL REVIEW D 79, 083523 (2009)

083523-5

Lattanzi and Silk, PRD 79, 083523 (2009), Profumo

(2005)

At sufficiently high neutralino masses, the W and Z can act as carriers of a long-range (Yukawa-like) force, resulting in a velocity dependent enhancement in cross section ( 1/v or even 1/v2 enhancement near resonance)

(Courtesy Matthieu Vivier)


Tests of Lorentz Invariance Violation


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LIV Observing Plan

• No explicit observation time, will be covered by other observing programs

• AGN observations

• GRB observations

• Crab pulsar


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Lorentz Invariance Violation• The goal of this slide is to show my ignorance on the subject, and to

provoke a clarification by Alan Kostelecky!

• Usually we start with a Hamiltonian that obeys Lorentz invariance, then derive the classical equations of motion for the generalized coordinates/field, and then derive a quantum field theory that hopefully obeys unitarity. Consider the free photon energy momentum relationship

E2 = c

2p2

or H = cp

From hamiltonian mechanics : x =∂H

∂p= c

Now add a Lorentz violating term that kicks in at some very high energy, Mplanck

do this by adding a function of energy E in a specific frame, e.g., the rest frameof the CMB.

H = cp + E[1 + f(E/Mplanck)]Now, assume Hamiltonian mechanics applies, and expand in powers of E/Mplanck

x =∂H

∂p∼ c

�1± ξ

E

Mpl+O

�E

Mpl

�2�


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L1

The Astrophysical Journal, 689: L1–L4, 2008 December 10! 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.

ASTROPHYSICAL TESTS OF LORENTZ AND CPT VIOLATION WITH PHOTONS

V. Alan Kostelecky1 and Matthew Mewes2

Received 2008 September 17; accepted 2008 October 21; published 2008 November 13

ABSTRACTA general framework for tests of Lorentz invariance with electromagnetic waves is presented, allowing for

operators of arbitrary mass dimension. Signatures of Lorentz violations include vacuum birefringence, vacuumdispersion, and anisotropies. Sensitive searches for violations using sources such as active galaxies, gamma-raybursts, and the cosmic microwave background are discussed. Direction-dependent dispersion constraints areobtained on operators of dimension 6 and 8 using gamma-ray bursts and the blazar Markarian 501. Stringentconstraints on operators of dimension 3 are found using 5 year data from the Wilkinson Microwave AnisotropyProbe. No evidence appears for isotropic Lorentz violation, while some support at 1 j is found for anisotropicviolation.Subject headings: cosmic microwave background — galaxies: active — gamma rays: bursts — gravitation —

relativity

Recent years have seen a resurgence in tests of relativity,spurred in part by the prospect of relativity violations arisingin a unified description of nature (Kostelecky & Samuel 1989;Kostelecky & Potting 1991). Experimental searches for vio-lations of Lorentz invariance, the symmetry underlying rela-tivity, have been performed in a wide range of systems (fordata tables see Kostelecky & Russell 2008). Historically, ex-periments probing the behavior of light have been central inconfirming relativity. Contemporary versions of the classic Mi-chelson-Morley and Kennedy-Thorndike experiments (Lipa etal. 2003; Antonini et al. 2005; Muller et al. 2007) remain amongthe most sensitive tests today.

Some tight constraints on relativity violations have beenachieved by seeking tiny changes in light that has propagatedover astrophysical distances. Many of these search for a changein polarization resulting from vacuum birefringence, usingsources such as galaxies (Carroll et al. 1990; Colladay & Kos-telecky 1998; Kostelecky & Mewes 2001, 2002), gamma-raybursts (GRBs; Mitrofanov 2003; Jacobson et al. 2004; Kos-telecky & Mewes 2006; Kahniashvili et al. 2006; Fan et al.2007), and the cosmic microwave background (CMB; Feng etal. 2006; Gamboa et al. 2006; Kostelecky & Mewes 2007;Cabella et al. 2007; Komatsu et al. 2009; Xia et al. 2008;Kahniashvili et al. 2008). Others seek a frequency-dependentvelocity arising from vacuum dispersion, using GRBs, pulsars,and blazars (Amelino-Camelia et al. 1998; Kostelecky &Mewes 2002; Boggs et al. 2004; Martınez & Piran 2006; Elliset al. 2006; Lamon et al. 2008; Albert et al. 2008). Here, wepresent a general theoretical framework that characterizes Lor-entz-violating effects on the vacuum propagation of electro-magnetic waves and includes operators of all mass dimensions.We discuss several techniques that can be used to search forthe unconventional signals of Lorentz violation, Using vacuum-dispersion constraints from GRBs and the blazar Markarian501, we place new direction-dependent limits on several com-binations of coefficients for Lorentz violation. We also performa search for Lorentz violations in the 5 year results from theWilkinson Microwave Anisotropy Probe (WMAP; Komatsu etal. 2009; Hinshaw et al. 2009; Nolta et al. 2009), finding some

1 Physics Department, Indiana University, Bloomington, IN 47405.2 Physics Department, Marquette University, Milwaukee, WI 53201.

evidence for anisotropic violations but no support for isotropicviolations.

At attainable energies, violations of Lorentz invariance aredescribed by a framework called the standard-model extension(SME; Colladay & Kostelecky 1997, 1998; Kostelecky 2004)that is based on effective field theory (Kostelecky & Potting1995). Approaches outside field theory also exist (Amelino-Camelia 2008). The SME characterizes all realistic violationsaffecting known particles and fields, while incorporating oth-erwise established physics. Much of the work on Lorentz vi-olation has focused on the minimal SME, which restricts at-tention to gauge-invariant operators of renormalizabledimension. In this work, we consider the gauge-invariant pure-photon sector of the full SME with Lorentz-violating operatorsof arbitrary dimension, which has Lagrange density (Koste-lecky & Mewes 2007)

1 1 1 klmnmn klmn ˆ ˆ( ) ( )L p ! F F " e A k F ! F k F , (1)mn l AF mn kl F mnk4 2 4

where is the 4-potential with field strength . In a flatA Fm mn

background with energy-momentum conservation, the Lorentzviolation arises through the differential operators

a …a1 (d!3)(d)k p k ! … ! , (2)( ) ( )!AF AF a a1 (d!3)k kdpodd

klmn klmna …a1 (d!4)(d)k p k ! … ! . (3)( ) ( )!F F a a1 (d!4)dpeven

The constant coefficients and char-a …a klmna …a1 (d!3) 1 (d!4)(d) (d)k k( ) ( )AF Fk

acterize the degree of Lorentz violation. The former controlCPT-odd operators and are nonzero for odd dimension ,d ! 3while the latter control CPT-even operators and are restrictedto even .d ! 4

The Lagrange density (eq. [1]) yields modified Maxwellequations. At leading order in coefficients for Lorentz violation,two plane-wave solutions exist. The corresponding two mod-ified dispersion relations can be written in the form

2 2 20 1 2 3"p(q) " 1 " " # " " " " " q, (4)( ) ( ) ( )[ ]

Lorentz Invariance Violation• In the past, there was a big focus on specific scenarios (e.g., John Ellis’ “quantum

gravity” idea with scalar first order, delay terms only.

• Since there is no complete theory, it is useful to follow the framework of Kostelecky and collaborators, where one considers generic terms in the Electromagnetic sector of the Lagrangian:

L2 KOSTELECKY & MEWES Vol. 689

where p and q are the wavenumber and frequency, respectively.It follows that electromagnetic waves generically contain twopropagating modes with different velocities and polarizations.The symbols !0, !1, !2, and !3 represent certain combinationsof coefficients for Lorentz violation, and they depend on thefrequency q and direction of propagation . With convenientpnormalizations, !1, !2, and !3 are the Stokes parameters 1s p

, , and of the faster mode, while !0 is a scalar2 3Q s p U s p Vcombination analogous to the intensity . These four com-0s p Ibinations completely control the leading-order effects of Lor-entz violation on light propagating through empty space. Thecombination !3 depends only on the coefficients ,

a …a1 (d!3)(d)k( )AFk

while !0, !1, and !2 depend only on the coefficients.

klmna …a1 (d!4)(d)k( )F

It is convenient to identify a minimal set of coefficient com-binations that affect light propagating in vacuo. This can beaccomplished through spherical-harmonic decomposition.Since !0 and !3 are rotation scalars while !1 and !2 are rotationtensors, their decomposition must involve some form of tensorspherical harmonics. The spin-weighted harmonics pro-ˆY (p)s jm

vide a well-understood set (Newman & Penrose 1966; Gold-berg 1967). The index s is the spin weight, which up to a signis equivalent to helicity. Decomposing yields

0 d!4 (d)ˆ! p q Y (n)k ,! 0 jm (I)jmdjm

1 2 d!4 (d) (d)ˆ ( )! ! i! p q Y (n) k " ik ,! !2 jm (E)jm (B)jmdjm

3 d!4 (d)ˆ! p q Y (n)k , (5)! 0 jm (V )jmdjm

where and is a unit vector pointing to theˆ ˆj ! d ! 2 n p !psource in astrophysics tests.

With this decomposition, all types of Lorentz violations forpropagation in vacuo can now be simply characterized usingfour sets of spherical coefficients, , , and for(d) (d) (d)k k k(I)jm (E)jm (B)jm

CPT-even effects and for CPT-odd effects. For each co-(d)k (V )jm

efficient, the underlying Lorentz-violating operator has massdimension d and eigenvalues of total angular momentum givenby jm, as usual. For light from astrophysical sources, dispersionarises when the speed of propagation depends on frequency,which occurs for any nonzero coefficient with . Bire-d ( 4fringence results when the usual degeneracy among polariza-tions is broken, for which at least one of , , or(d) (d)k k(E)jm (B)jm

is nonzero. For example, all operators producing light-(d)k (V )jm

speed corrections that are linear in the energy have andd p 5are necessarily birefringent. The only coefficients for nonbi-refringent dispersion are therefore with even . Since(d)k d " 6(I)jm

birefringence tests using polarimetry are typically many ordersof magnitude more sensitive than dispersion tests using timing,in the following discussion of dispersion we focus only oncoefficients for nonbirefringent dispersion.

Tests for vacuum dispersion seek differences in the velocityof light at different wavelengths. In the present context withzero birefringent coefficients, the change in velocity is dv "

. We see from equation (5) that the velocity generically0!!depends on the direction as well as the frequency q. Typicalnanalyses study explosive or pulsed sources of radiation pro-ducing light over a wide wavelength range in short time periods,comparing the arrival times of different wavelengths. This ideahas been the focus of many searches based on modified dis-persion relations (Amelino-Camelia et al. 1998; Kostelecky &Mewes 2002; Boggs et al. 2004; Martınez & Piran 2006; Ellis

et al. 2006; Lamon et al. 2008; Albert et al. 2008). Many ofthese studies assume isotropic violations, which correspondsto the limit . However, at each dimension d, thisj p m p 0isotropic restriction misses possible effects from2(d ! 2d ! 2)anisotropic violations.

To calculate arrival-time differences in an expanding universe,some care is required (Jacob & Piran 2008). In the present case,the photons propagate between two comoving objects, so the rel-evant coordinate interval is . Here,dl p (1 # z)dl p !v dz/Hc p zz

is the particle velocity at redshift z, and 4v H p H (Q z #z 0 rz

with is the Hubble expansion3 2 1/2Q z # Q z # Q ) z p 1 # zm k L

rate at z in terms of the present-day Hubble constant H "0

km s!1 Mpc!1, radiation density , matter density71 Q " 0r

, vacuum density , and curvature densityQ " 0.27 Q " 0.73m L

. The total coordinate distance is theQ p 1 ! Q ! Q ! Qk r m L

same for all wavelengths, but the travel times may differ. In-tegrating from the same initial time to the two arrival timesdlc

for the two velocities gives a relation for the arrival-time dif-ference , which depends on the two energies and the sourceDtlocation on the sky. For the present case with Lorentz violationat dimension d, we find

z d!4(1 # z)d!4 (d)ˆDt # !Dq dz Y (n)k , (6)!# 0 jm (I)jmH jm0 z

where is the difference in between the twod!4 d!4Dq qfrequencies.

As an illustration, consider the bright gamma-ray burst GRB021206 at right ascension 240" and declination !9.7". Overenergies from 3 to 17 MeV, arrival-time differences are nomore than ms for this source at (Boggs et al.Dt ! 4.8 z " 0.32004). Numerical integration of equation (6) leads to a boundon one direction-specific combination of the 25 independentcoefficients for nonbirefringent dispersion with ,d p 6

(6) !16 !2Y (99.7", 240")k ! 1 # 10 GeV . (7)! 0 jm (I)jmjm

For the 63 independent nonbirefringent dispersive operatorswith , we obtaind p 8

(8) !13 !4Y (99.7", 240")k ! 3 # 10 GeV . (8)! 0 jm (I)jmjm

Operators with higher d can be treated similarly. Note that manysources are required to constrain fully the coefficient space fora given d. In contrast, only one source is needed to constrainfully the corresponding coefficient in the restrictive isotropiclimit . In this limit, the bounds from equations (7)j p m p 0and (8) reduce to and(6) !16 !2 (8)k ! 4 # 10 GeV k ! 9 #(I)00 (I)00

, respectively.!13 !410 GeVAs another example, consider Markarian 501, which lies at

. This source produces flares with photon energies inz " 0.03the TeV range, making it particularly sensitive to an energy-dependent velocity and also to threshold analyses (Amelino-Camelia & Piran 2001). A recent analysis of observations bythe MAGIC collaboration found some evidence for a nonbi-refringent velocity defect of the form ordv p !q/M dv p

(Albert et al. 2008). The first case is incompatible with2 2!q /Mthe present treatment; a reanalysis incorporating the necessarybirefringence could yield comparatively weak but compatiblenew bounds. The second case suggests dispersion with M "

GeV, assuming an arrival-time lag due entirely to#5 10(6 ) # 10!1

L1

The Astrophysical Journal, 689: L1–L4, 2008 December 10! 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.

ASTROPHYSICAL TESTS OF LORENTZ AND CPT VIOLATION WITH PHOTONS

V. Alan Kostelecky1 and Matthew Mewes2

Received 2008 September 17; accepted 2008 October 21; published 2008 November 13

ABSTRACTA general framework for tests of Lorentz invariance with electromagnetic waves is presented, allowing for

operators of arbitrary mass dimension. Signatures of Lorentz violations include vacuum birefringence, vacuumdispersion, and anisotropies. Sensitive searches for violations using sources such as active galaxies, gamma-raybursts, and the cosmic microwave background are discussed. Direction-dependent dispersion constraints areobtained on operators of dimension 6 and 8 using gamma-ray bursts and the blazar Markarian 501. Stringentconstraints on operators of dimension 3 are found using 5 year data from the Wilkinson Microwave AnisotropyProbe. No evidence appears for isotropic Lorentz violation, while some support at 1 j is found for anisotropicviolation.Subject headings: cosmic microwave background — galaxies: active — gamma rays: bursts — gravitation —

relativity

Recent years have seen a resurgence in tests of relativity,spurred in part by the prospect of relativity violations arisingin a unified description of nature (Kostelecky & Samuel 1989;Kostelecky & Potting 1991). Experimental searches for vio-lations of Lorentz invariance, the symmetry underlying rela-tivity, have been performed in a wide range of systems (fordata tables see Kostelecky & Russell 2008). Historically, ex-periments probing the behavior of light have been central inconfirming relativity. Contemporary versions of the classic Mi-chelson-Morley and Kennedy-Thorndike experiments (Lipa etal. 2003; Antonini et al. 2005; Muller et al. 2007) remain amongthe most sensitive tests today.

Some tight constraints on relativity violations have beenachieved by seeking tiny changes in light that has propagatedover astrophysical distances. Many of these search for a changein polarization resulting from vacuum birefringence, usingsources such as galaxies (Carroll et al. 1990; Colladay & Kos-telecky 1998; Kostelecky & Mewes 2001, 2002), gamma-raybursts (GRBs; Mitrofanov 2003; Jacobson et al. 2004; Kos-telecky & Mewes 2006; Kahniashvili et al. 2006; Fan et al.2007), and the cosmic microwave background (CMB; Feng etal. 2006; Gamboa et al. 2006; Kostelecky & Mewes 2007;Cabella et al. 2007; Komatsu et al. 2009; Xia et al. 2008;Kahniashvili et al. 2008). Others seek a frequency-dependentvelocity arising from vacuum dispersion, using GRBs, pulsars,and blazars (Amelino-Camelia et al. 1998; Kostelecky &Mewes 2002; Boggs et al. 2004; Martınez & Piran 2006; Elliset al. 2006; Lamon et al. 2008; Albert et al. 2008). Here, wepresent a general theoretical framework that characterizes Lor-entz-violating effects on the vacuum propagation of electro-magnetic waves and includes operators of all mass dimensions.We discuss several techniques that can be used to search forthe unconventional signals of Lorentz violation, Using vacuum-dispersion constraints from GRBs and the blazar Markarian501, we place new direction-dependent limits on several com-binations of coefficients for Lorentz violation. We also performa search for Lorentz violations in the 5 year results from theWilkinson Microwave Anisotropy Probe (WMAP; Komatsu etal. 2009; Hinshaw et al. 2009; Nolta et al. 2009), finding some

1 Physics Department, Indiana University, Bloomington, IN 47405.2 Physics Department, Marquette University, Milwaukee, WI 53201.

evidence for anisotropic violations but no support for isotropicviolations.

At attainable energies, violations of Lorentz invariance aredescribed by a framework called the standard-model extension(SME; Colladay & Kostelecky 1997, 1998; Kostelecky 2004)that is based on effective field theory (Kostelecky & Potting1995). Approaches outside field theory also exist (Amelino-Camelia 2008). The SME characterizes all realistic violationsaffecting known particles and fields, while incorporating oth-erwise established physics. Much of the work on Lorentz vi-olation has focused on the minimal SME, which restricts at-tention to gauge-invariant operators of renormalizabledimension. In this work, we consider the gauge-invariant pure-photon sector of the full SME with Lorentz-violating operatorsof arbitrary dimension, which has Lagrange density (Koste-lecky & Mewes 2007)

1 1 1 klmnmn klmn ˆ ˆ( ) ( )L p ! F F " e A k F ! F k F , (1)mn l AF mn kl F mnk4 2 4

where is the 4-potential with field strength . In a flatA Fm mn

background with energy-momentum conservation, the Lorentzviolation arises through the differential operators

a …a1 (d!3)(d)k p k ! … ! , (2)( ) ( )!AF AF a a1 (d!3)k kdpodd

klmn klmna …a1 (d!4)(d)k p k ! … ! . (3)( ) ( )!F F a a1 (d!4)dpeven

The constant coefficients and char-a …a klmna …a1 (d!3) 1 (d!4)(d) (d)k k( ) ( )AF Fk

acterize the degree of Lorentz violation. The former controlCPT-odd operators and are nonzero for odd dimension ,d ! 3while the latter control CPT-even operators and are restrictedto even .d ! 4

The Lagrange density (eq. [1]) yields modified Maxwellequations. At leading order in coefficients for Lorentz violation,two plane-wave solutions exist. The corresponding two mod-ified dispersion relations can be written in the form

2 2 20 1 2 3"p(q) " 1 " " # " " " " " q, (4)( ) ( ) ( )[ ]Dispersion relation (momentum versus frequency)

Non-birefringent components

CPT odd

CPT even

Related to Stokes Parameters

{}

ζ1 = Q, ζ2 = U, ζ3 = V


! !

1

! ! ! !


Spherical Harmonics

• Combine many measurements of the shortest variability timescales of AGN at different points in the sky to obtain limits on the coefficients of the Ylm

• In general one must allow scalar terms, subluminal and superluminal terms in the dispersion, polarization dependent terms, and anisotropic terms (coefficients in a spherical harmonic expansion indicating, e.g., a prefered direction in space)


! !

1

! ! ! !


LIV

• For standard first-order terms, and nearby sources (in the Newtonian limit) one obtains a rough idea of the sensitivity of Fermi and VERITAS to different astrophysical sources

Lorentz invariance violation in VHE data

• Limits on Lorentz invariance violation can be derived from astrophysical observations when a fast feature in the light curve can be detected.

• The deviation of the speed of light as a function of energy is usually parametrized by a linear and a quadratic term:

• Given a light curve feature with characteristic time !t detected up to energies !E from a source at distance dL can be estimated by:


Probes of Intergalactic Magnetic Fields


! !

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IGMF Observing Strategy

• VERITAS observations of sources like 1ES0229 (very hard and steady) with Fermi counterpart. In 5 years and 25 hours/year could obtain a limit like BIGMF > 10-18 to 10-16 Gauss

• Obtain high and low state data on nearby AGN (e.g., PG1553???, Mrk501) and search for difference in angular extent, evidence for halo. With ~20 hours per year for next 5 years could provide a measurement of a halo that would be a signature of a 10-15 to 10-12 Gauss IGMF

• With on the order of 150 hours over 5 years of a source like PKS1222+216 might see time delay of spectral hardening that could reveal an IGMF field in the range of 10-11 to 10-17 Gaus


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IGMF

(courtesy Tim Arlen and Vladimir Vassiliev)

Eγ (TeV) <Dist> (Mpc)

100 2

10 90

1 175

0.1 500

primary γ−ray (E > 100 GeV)

BIGMF < 10−9 G

Eelec(TeV) Dist (Mpc)

1 ~ 1

10 – 100 ~ 0.01 – 0.1

IGMF

ZintZ = 0

CMB

CMBEBL (UV-IR)

e+

e−

γGeV−TeV

γGeV−TeV


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Method 1: Cascade Spectra

• From TeV emission spectrum, expect a cascade spectrum visible with Fermi. Since it may take hundreds of years for the full cascade to form, robust upper limits come from simultaneous measurements and the predicted minimum prompt cascade signal.


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Method 2: Pair Halos

• Cascade emission (up to 100 GeV - mostly Fermi up to low energy VERITAS) may have a finite angular extent.


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Method 3:Temporal Decay

• Cascade emission (up to 100 GeV - mostly Fermi up to low energy VERITAS) may have a finite angular extent. Expect spectral harding and finite decay time.???


EBL and ALPs


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Extragalactic Background Light

April 16, 2004VERITAS ESAC Meeting, Amado

Cosmic Infrared Background

e-gIR

gTe

V

AGN

Jet

The DIRBE team has reported detection

of EBL at 140 and 240 mm, and has setonly

upper limits to its brightness at eightother wavelengths-

1.25, 2.2, 3.5, 4.9, 12, 25, 60 and 100

mm.

Hauser et al., 1998, ApJ, 508, 25

GLAST+VERITAS will measure the

line of sight integral of EBLabsorption

γ TeV

γ IR

e−

e+

• Pair-production in intergalactic space causes absorption and spectral cutoffs that move to lower energy as the redshift increases.

• If one knows something about the source spectrum, can constrain, even measure, the spectrum of the EBL.

• Can do cosmology by constraining star formation history (e.g., Pop III stars), and any new particle physics scenarios that yield a contribution to the EBL (e.g. neutrino decay, electromagnetic signatures from annihilation of DM over a large mass range)


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Photon-Axion MixingPhoton-Axion mixing

• Axionlike particles (ALPs) can oscillate into photons and vice versa in the presence of an electric or magnetic field.

• This effect will happen for high energy photons: in the X-ray and !-ray band.

• The oscillation of photons into axions could modify the spectra and luminosities of cosmological X-ray and !-ray sources.

• VHE !-ray observations of extragalactic sources could eventually be sensitive to the effects of photon-ALP oscillations.


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Photon-Axion MixingPhoton-ALP mixing in VHE spectra

• Photon-ALP mixing can happen at the source, or during photon propagation in the presence of intergalactic magnetic field.

• One signature of this effect will be a relatively sharp drop of ~30% in the spectrum between 1 and 100 GeV.

• Another effect is that mixing could make some photons travel to Earth as axions and then convert back to photons. Axions would not be attenuated by EBL. Therefore, one could expect to see less EBL absorption than expected at E~1TeV for distant sources. The boost effect could be of factor ~100 in the most optimistic scenarios.

Sanchez-Conde, Paneque, Bloom, Prada & Dominguez, Phys. Rev. D 79 (2009) 123511

The flux increase due to axions propagating through EBL could be tested with VERITAS by observing distant sources. The effect could be disentangled from our ignorance of EBL density by seeing the effect in multiple sources at different z.


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Conclusions/Questions

• We plan to make fundamental physics a high priority, commensurate with DOE contribution to the project.

• Best contributions will only come with dedicated observing time for dark matter searches, but for other fundamental physics goals there is a high degree of overlap with other VERITAS astrophysics programs.

• While many of these programs are high risk, they have potentially large scientific payoffs contributing to questions like the nature of the Dark Matter, origin of extragalactic magnetic fields, and new physics at energy scales well above the reach of terrestrial experiments.

• We hope for suggestions by the ESAC to refine our strategy.


Particle Physics and Fundamental Physics Studies with VERITASrene/VERITAS/ESAC2011/Buckley-FundPhysics.pdf · Particle Physics and Fundamental Physics Studies with VERITAS Jim Buckley

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