Stefan Leupold Hyperon-photon physics

Hyperon-photon physics

Stefan Leupold

Uppsala University

NoSTAR 2017, Columbia, SC, August 2017

1 Stefan Leupold Hyperon-photon physics Table of Contents

1 Motivation: structure of matter

2 Theory for low-energy form factors

3 Summary and outlook

2 n p  T  q q T  T Σ− Λ Σ0 T Σ+ T  q T q  q T  T  and from Ξ− Ξ0 Gell-Mann’s multiplets q q − 0 + ++ containing strange hadrons ∆ ∆ ∆ ∆ T  q T q q  q T  , expect valuable information T Σ∗− Σ∗0 Σ∗+ → from combining T  q T q  q electromagnetism and T  strangeness T Ξ∗− Ξ∗0 T  , complements information q T  q → T  from nucleon form factors TΩ− q

Stefan Leupold Hyperon-photon physics Historical remark first hints for compositeness of proton came from non-trivial gyromagnetic ratio = 2 6

3 Stefan Leupold Hyperon-photon physics Historical remark n p  T first hints for compositeness  q q T of proton came from  T Σ− Λ Σ0 T Σ+ non-trivial gyromagnetic T  q T q  q ratio = 2 T  6 T  and from Ξ− Ξ0 Gell-Mann’s multiplets q q − 0 + ++ containing strange hadrons ∆ ∆ ∆ ∆ T  q T q q  q T  , expect valuable information T Σ∗− Σ∗0 Σ∗+ → from combining T  q T q  q electromagnetism and T  strangeness T Ξ∗− Ξ∗0 T  , complements information q T  q → T  from nucleon form factors TΩ− 3 q Stefan Leupold Hyperon-photon physics Electromagnetic form factors of hyperons

to large extent terra incognita

electron-hyperon scattering complicated instead: + − ¯ reactions e e hyperon anti-hyperon (Y1 Y2) BESIII , form factors and→ transition form factors → 2 2 for large time-like q > (mY1 + mY2 ) (time-like means q2 > 0, i.e. energy transfer > momentum transfer) + − decays Y1 Y2 e e HADES+PANDA → 2 2 , transition form factors for small time-like q < (mY1 mY2 ) → − 4 Stefan Leupold Hyperon-photon physics Theory for baryon low-energy form factors

ideally as model independent as possible , use (if possible) effective field theories (EFTs) → and general QFT principles (unitarity, analyticity, . . . ) existing (in EFT spirit): for octet: chiral perturbation theory (EFT), Kubis/Meißner, Eur. Phys. J. C 18, 747 (2001) , predictions for electric and magnetic radii → (= slopes of form factors) , shortcomings: no explicit decuplet, no explicit vector mesons ,→ for curvatures one already needs vector mesons → for transitions decuplet-octet: chiral perturbation theory for ∆-N, Pascalutsa/Vanderhaeghen/Yang, Phys. Rept. 437, 125 (2007) , no vector mesons and not for hyperons → 5 Stefan Leupold Hyperon-photon physics Theory for hyperon low-energy form factors new approach: hadronic chiral perturbation theory plus dispersion theory , easier to include decuplet → , dispersion theory includes ρ meson as measured in π-π → Σ0-Λ transition form factors: C. Granados, E. Perotti, SL, Eur.Phys.J. A53, 117 (2017) , some results on next slides → decuplet-octet transitions: E. Perotti, O. Junker, SL, work in progress very similar in spirit: J.M. Alarc´on, A.N. Hiller Blin, M.J. Vicente Vacas, C. Weiss, Nucl.Phys. A964, 18 (2017)

6 Stefan Leupold Hyperon-photon physics

( ) Hyperon transition form factors Σ ∗ for Σ/Σ∗ Λ e+e− need transition form factors → Λ dispersive framework: at low energies q2 dependence is governed by lightest intermediate states ( ) Σ ∗ π+ , obtain from → π − Λ π+ , need pion vector form factor (measured) → π− ( ) π Σ ∗

and hyperon-pion scattering amplitudes

π Λ 7 Stefan Leupold Hyperon-photon physics Hyperon-pion scattering amplitudes

( ) π Σ ∗

contain

π Λ π Σ( ) “right-hand cuts” (pion rescattering) π ∗ , straightforward from → unitarity and analyticity π (and experimental pion phase shift) π Λ

( ) and rest: π Σ ∗ left-hand cuts, polynomial terms , not straightforward = ? ,→ use three-flavor baryon chiral → perturbation theory π Λ

8 Stefan Leupold Hyperon-photon physics Input for hyperon-pion scattering amplitudes

ideally use data , available for pion-nucleon, but not for pion-hyperon → , instead: three-flavor baryon chiral perturbation theory (χPT) → at leading and next-to-leading order (NLO) including decuplet states (optional for Σ0 Λ transition, but turns out to be important!) →

( ) π Σ ∗

( ) π Σ ∗ ( ) π Σ ∗

Σ/Σ∗ + ≈ π π Λ Λ

π Λ

9 Stefan Leupold Hyperon-photon physics χPT input for hyperon-pion scattering amplitudes three-point couplings fairly well known, but how to determine NLO four-point coupling constants?

only one parameter (b10) for Σ-Λ transition , but not very well known → “resonance saturation” estimates Meißner/Steininger/Kubis, Nucl.Phys. B499, 349 (1997); π Σ( ) Eur.Phys.J. C18, 747 (2001) ∗

or from fit to πN and KN scattering data with π Λ coupled-channel Bethe-Salpeter approach Lutz/Kolomeitsev, Nucl.Phys. A700, 193 (2002) maybe in the future: cross-check from lattice QCD parameter is directly related to magnetic transition radius of Σ-Λ 10 Stefan Leupold Hyperon-photon physics Transition form factors Σ-Λ

0.01 2.5 small hA, cutoff la. hA, sm. b10, sm. cut. 0.005 radius adjust. sm. hA, sm. b10, la. cut. large hA, cutoff 2 la. hA, av. b10, sm. cut. 0 sm. hA, av. b10, la. cut. la. hA, la. b10, sm. cut. -0.005 1.5 sm. hA, la. b10, la. cut. -0.01 1 E -0.015 M G G 0.5 -0.02

-0.025 0 -0.03 -0.5 -0.035 -0.04 -1 -1 -0.8 -0.6 -0.4 -0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0 q2 [GeV2] q2 [GeV2] electric transition form factor very small over large range , what one might measure at low energies is → magnetic transition form factor , data integrated over Λ-e− angle, but differential in q2 might be → sufficient 2 2 2 note: Dalitz decay region 4me < q < (mΣ mΛ) hardly visible here − 11 Stefan Leupold Hyperon-photon physics Magnetic transition form factor Σ-Λ 2.5 la. hA, sm. b10, sm. cut. sm. hA, sm. b10, la. cut. 2 la. hA, av. b10, sm. cut. sm. hA, av. b10, la. cut. la. hA, la. b10, sm. cut. 1.5 sm. hA, la. b10, la. cut.

1 M G 0.5

0

-0.5

-1 -1 -0.8 -0.6 -0.4 -0.2 0 q2 [GeV2]

large uncertainty

, directly related to uncertainty in NLO low-energy constant b10 → , can be determined from measuring magnetic transition radius → 12 Stefan Leupold Hyperon-photon physics Summary exploring structure of hadrons learned a lot about hadrons from electromagnetic probes . . . from strangeness , high time to combine these lines of research → electromagnetic (transition) form factors of hyperons + − at low energies: Dalitz decays YA YB e e → complementary theory program: combining dispersion theory with baryon octet+decuplet chiral perturbation theory , first results: → electric form factor of Σ-Λ transition very small (also found in recent quark–Dyson-Schwinger calculations, Sanchis-Alepuz/Alkofer/Fischer, arXiv:1707.08463 [hep-ph]) magnetic form factor in spacelike region can be predicted if radius is measured in timelike region (Dalitz decay)

13 Stefan Leupold Hyperon-photon physics

backup slides

14 Stefan Leupold Hyperon-photon physics 0 + Σ Λ e e− → basic: branching ratio (QED prediction 5 10−3) · advanced: differential distribution; resolve effect from non-trivial transition form factors GE , GM

2 d Γ n 2 2 2 2 2 2 2 2 o GE (q ) (mΛ+mΣ) (1 z )+ GM (q ) q (1+z ) dq2 dz ∼ | | − | | as compared to (leading-order) QED prediction

d 2Γ QED µ2 q2 (1 + z 2) dq2 dz ∼ ΣΛ

0 with transition magnetic moment µΣΛ (known from Σ Λ γ) → note: proportionality factor is function of q := pe+ + pe− , but not of z :=cos(angle(e−, Λ) in dilepton rest frame)

15 Stefan Leupold Hyperon-photon physics Challenge to extract form factors

Σ0 Λ e+e− does not produce large e− invariant→ masses for the lepton pair, 2 2 q < (77 MeV) 0 Σ e+ , transition form factor is close to unity → (normalization at photon point) Λ , need high precision in experiment and → theory to deduce transition form factor , expect effects on 1-2% level → e−

, effects from form factor compete with 0 Σ + → QED corrections e , tedious but calculable → Λ (T. Husek and SL, in preparation)

16 Stefan Leupold Hyperon-photon physics Full formulae for differential distribution double differential decay width Σ0 Λ e+e−: → 2  2 1/2 d Γ 1 1/2 2 2 4me 2 = 3 3 λ (mΣ, s, mΛ) 1 ds dz (2π) 64mΣ − s |M|

4 2 e 2 = 2((mΣ mΛ) s) |M| s2 − −   2   n 2 2 4me 2 GE (s) (mΛ + mΣ) 1 1 z | | − − s 2 2 2 2 o + GM (s) (s (1 + z ) + 4m (1 z )) . | | e − note: electron mass neglected in main presentation independent kinematical variables defined on next slide

17 Stefan Leupold Hyperon-photon physics Full formulae for differential distribution, cont. independent kinematical variables: 2 2 s := (pe+ + pe− ) = q z is cos of angle between e− and Λ in rest frame of dilepton ∆m2 z := 2 (∆m )max 2 2 2 with ∆m := (pe+ + pΛ) (p − + pΛ) and − e r 4m2 ∆m2
:= λ1/2(m2 , s, m2 ) 1 e . max Σ Λ − s kinematical variables cover the ranges 2 2 z [ 1, 1] and 4m s (mΣ mΛ) ∈ − e ≤ ≤ −

K¨all´enfunction λ(a, b, c) := a2 + b2 + c2 2(ab + bc + ac) − 18 effective theories are systematic phenom. models are not ↔ “systematic” means that one can estimate the theory uncertainty/precision dispersion theory uses data instead of phenomenological models , (improvable) data uncertainties instead of → (not improvable) model uncertainties but: not for every problem there exists an effective theory; dispersion theory not of practical use if one has to deal with too many channels, too many particles

Stefan Leupold Hyperon-photon physics Theory for low-energy form factors

Confessions of a theorist: every theorist has favorite toys mine are at the moment effective field theories (EFT) and dispersion theory , some arguments in favor of this choice: →

19 but: not for every problem there exists an effective theory; dispersion theory not of practical use if one has to deal with too many channels, too many particles

Stefan Leupold Hyperon-photon physics Theory for low-energy form factors

Confessions of a theorist: every theorist has favorite toys mine are at the moment effective field theories (EFT) and dispersion theory , some arguments in favor of this choice: → effective theories are systematic phenom. models are not ↔ “systematic” means that one can estimate the theory uncertainty/precision dispersion theory uses data instead of phenomenological models , (improvable) data uncertainties instead of → (not improvable) model uncertainties

19 Stefan Leupold Hyperon-photon physics Theory for low-energy form factors

Confessions of a theorist: every theorist has favorite toys mine are at the moment effective field theories (EFT) and dispersion theory , some arguments in favor of this choice: → effective theories are systematic phenom. models are not ↔ “systematic” means that one can estimate the theory uncertainty/precision dispersion theory uses data instead of phenomenological models , (improvable) data uncertainties instead of → (not improvable) model uncertainties but: not for every problem there exists an effective theory; dispersion theory not of practical use if one has to deal with too many channels, too many particles

19 ? , if (1) is not completely correct, then how accurate is it? → , phenomenological model cannot answer this, → effective theory can

credits for this example: Emil Ryberg, Gothenburg

Stefan Leupold Hyperon-photon physics Example: effective theory phenom. model ↔

determine potential energy of object with mass m and height h above ground

figure from wikipedia , develop phenomenological model: → Vpheno(h) = m g h (1) perform measurements for some h (and m) to determine g , obtain predictive power for any h →

20 Stefan Leupold Hyperon-photon physics Example: effective theory phenom. model ↔

determine potential energy of object with mass m and height h above ground

figure from wikipedia , develop phenomenological model: → Vpheno(h) = m g h (1) perform measurements for some h (and m) to determine g , obtain predictive power for any h? → , if (1) is not completely correct, then how accurate is it? → , phenomenological model cannot answer this, → effective theory can credits for this example: Emil Ryberg, Gothenburg 20 Stefan Leupold Hyperon-photon physics Example: effective theory phenom. model ↔ determine potential energy of object with mass m and height h above ground , effective theory (systematic): → 2 3 Veff (h) = m (g h + g2 h + g3 h + ...) (2) how to use it: truncate (2) e.g. after (h2) and perform measurements to O determine g and g2 2 theory uncertainty/accuracy ∆V g2 h if unsatisfied with accuracy ≈ | | , truncate (2) only after (h3) and perform (more!) → O measurements to determine g, g2 and g3 ... , systematically improvable → (but requires more and more measurements to gain predictive power) 21 Stefan Leupold Hyperon-photon physics Example: effective theory and fundamental theory effective theory

2 3 Veff (h) = m (g h + g2 h + g3 h + ...)

figure from wikipedia for this physics problem (potential energy . . . ) Newton provided the fundamental theory: G M m G M m V (h) = + fund − h + R R

, parameters g, g2 , . . . can be calculated instead of measured → , just Taylor expand in h/R → , range of applicability of effective theory is h R →  effective theories always have a limited range of applicability 22 Stefan Leupold Hyperon-photon physics Back to hadrons

fundamental theory: QCD effective field theory at low energies (below resonances): chiral perturbation theory there exist plenty of phenomenological models (and some colleagues call them “effective theories” :-( for region of hadronic resonances there is no established effective field theory (yet) (active field of research: Lutz, Kolomeitsev, SL, Scherer, Meißner, . . . ) , is there a way to get controlled theory uncertainties in the → resonance region? , dispersion theory! (sometimes) →

23 Stefan Leupold Hyperon-photon physics Dispersion theory

if a resonance 180 is important data set 1 160 data set 2

(e.g. vector mesons for 140 electromagnetic reactions) 120 100 ] ° [ is known from rather well δ 80 measured phase shifts 60 40 does not have too many 20 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 decay channels √s [GeV]

, use phase shifts instead of modeling → , dispersion theory → based on fundamental principles of local quantum field theory

24 Stefan Leupold Hyperon-photon physics Unitarity and analyticity

constraints from local quantum field theory: partial-wave amplitudes for reactions/decays must be unitary:

SS† = 1 , S = 1 + iT 2 ImT = TT † ⇒ , note that this is a matrix equation: → P † ImTA→B = X TA→X TX →B in practice: use most relevant intermediate states X analytical(dispersion relations):

∞ q2 Z ImT (s) T (q2) = T (0) + ds π s (s q2 i) −∞ − −

can be used to calculate whole amplitude from imaginary part 25 Stefan Leupold Hyperon-photon physics Right- and left-hand cuts

X † ImTA→B = TA→X TX →B X ∞ q2 Z ImT (s) T (q2) = T (0) + ds π s (s q2 i) −∞ − − can be used to calculate whole amplitude from imaginary part , but need to know imaginary part for all values of s, → not only for physical ones restricted by thresholds sthr of A, B, X for instance, if X = 2π then s 4m2 = s is physical range ≥ π thr ∞ Z , ds ... “right-hand cut” → sthr

26 Stefan Leupold Hyperon-photon physics Right- and left-hand cuts

∞ q2 Z ImT (s) T (q2) = T (0) + ds π s (s q2 i) −∞ − −

crossing symmetry: imaginary part in s sthr leads in crossed channel to imaginary part in Mandelstam≥ variable t (or u) but condition t s is in crossed channel related to s ˜s ≥ thr ≤ thr ˜s Zthr , ds ... “left-hand cut” → −∞ note: name “cut” is related to fact that amplitude has logarithmic structure , Riemann sheets and cuts → 27 Stefan Leupold Hyperon-photon physics Hyperon transition form factors

( ) Σ ∗ for Σ/Σ∗ Λ e+e− need transition form factors → Λ , separate long- from short-range physics, → universal from quark-structure specific features , use dispersion theory and encode short-range physics in → subtraction constants ( ) Σ ∗ π+ , obtain from → π − Λ

28 Stefan Leupold Hyperon-photon physics Pion vector form factor

2 10 π+

1 10 Belle data [25] Ref. [23] Ref. [24] 2 |

) Fit π− s ( 0 V π 10 F | π+ ↓+ -1 10 π

-2 10 π− 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 π− √s [GeV] pion phase shift very well known; fits to pion vector form factor Sebastian P. Schneider, Bastian Kubis, Franz Niecknig, Phys.Rev.D86:054013,2012

29 Stefan Leupold Hyperon-photon physics χPT input for hyperon-pion scattering amplitudes how to determine three-point coupling constants:

( ) Σ-Λ-π and Σ-Σ-π related to weak octet π Σ ∗ decays (F and D parameter) Σ/Σ∗ ∗ ∗ ∗ Σ -Λ-π and Σ -Σ-π from Σ decays (hA) π Λ interesting observations: pole of Σ-exchange contribution is close to 2π threshold , creates structure, i.e. energy dependence, → that is not covered by simple vector-meson dominance models see also Frazer/Fulco, Phys.Rev. 117, 1609 (1960) in general (away from threshold): large cancelation between Σ- and Σ∗-exchange , inclusion of decuplet is not an option but a necessity → 30 Stefan Leupold Hyperon-photon physics Uncertainties of input

parameter variations: 2.2 < hA < 2.4 0.85 < b10 < 1.35 (in inverse GeV) (Lutz/Kolomeitsev value is at lower edge) cut off formal ΣΛ¯ π+π− amplitude when other channels except for 2π become→ important , physically at KK¯ threshold, but at the latest at ΣΛ¯ threshold → , vary cutoff in range 1-2 GeV (mild effect) → NNLO corrections not yet calculated , no reliable uncertainty estimates yet → variations in input for pion phase shift not explored yet, but expected to be small

Colangelo/Gasser/Leutwyler, Nucl.Phys. B603, 125 (2001) Garcia-Martin/Kaminski/Pelaez/Ruiz de Elvira/Yndurain, Phys.Rev. D83, 074004 (2011) 31 Stefan Leupold Hyperon-photon physics First results 450 full Born 400 full NLO+res bare Born 350 bare NLO+res 300

] 250 -2 200 [GeV

E 150

Re T 100 50 0 -50 -100 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 √s [GeV] shows electric (helicity non-flip) part of formal ΣΛ¯ π+π− p-wave amplitude (real part, sub threshold) impact→ of ρ meson visible when comparing “full” (dispersive) vs. “bare” (χPT input) inclusion of decuplet exchange (“res”) important 32 Stefan Leupold Hyperon-photon physics Comparison to nucleon case

How well does formalism work for nucleon where data (note that one needs the isovector form factors) and fully dispersive analysis of pion-nucleon scattering amplitudes Hoferichter/Ruiz de Elvira/Kubis/Meißner, Phys.Rept. 625, 1 (2016) exist?

based on SL, arXiv:1707.09210 [hep-ph]

33 Stefan Leupold Hyperon-photon physics Pion-nucleon amplitudes

7000 2500 MO NLO+res MO NLO+res RS band RS band 6000 2000 5000 1500 ] ] -2

4000 -2 [GeV 3000 [GeV 1000 M M

2000 Im T Re T 500 1000 0 0

-1000 -500 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 √s [GeV] √s [GeV] , good agreement → “RS” (Roy-Steiner equation): fully dispersive analysis “MO”: pion rescattering by solving Muskhelishvili-Omn`es equation “NLO+res”: nucleon+Delta chiral perturbation theory at next-to-leading order

34 Stefan Leupold Hyperon-photon physics Magnetic isovector form factor of nucleon

25 2.5 RS analysis Λ = 1 GeV Λ= 1.8 GeV Λ = 1.8 GeV Λ= 1 GeV Kelly param. lower limit 20 2 Kelly param. upper limit

15 1.5 M M

10 G

Im G 1 5 0.5 0

0 -5 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 q2 [GeV2] √s [GeV] , low-energy framework works up to q2 0.4 GeV2 → | | ≈ “RS” (Roy-Steiner equation): fully dispersive analysis “Kelly param.”: parametrization of form factor data J.J. Kelly, Phys.Rev.C 70, 068202 (2004)

based on SL, arXiv:1707.09210 [hep-ph]

35 Stefan Leupold Hyperon-photon physics Comparison MO vs. N/D

Pion rescattering is treated differently in Granados/Perotti/SL, Eur.Phys.J. A53, 117 (2017) , solving a Muskhelishvili-Omn`es(MO) equation → and in Alarc´on/HillerBlin/Vicente Vacas/Weiss, Nucl.Phys. A964, 18 (2017) , variant of N/D →

, How much do results differ (for nucleon)? → based on SL, arXiv:1707.09210 [hep-ph]

36 Stefan Leupold Hyperon-photon physics Comparison MO vs. N/D for nucleon

90 MO LO 80 MO NLO MO NLO+res 70 N/D LO N/D NLO 60 N/D NLO+res

50 M 40 Im G 30

20

10

0

-10 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 √s [GeV] , very different in ρ-meson peak region → (note: MO agrees with fully dispersive πN analysis)

37