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Massive photinos: Unstable and interesting
Volume 105B, number 2,3
PHYSICS LETTERS
1 October 1981
MASSIVE PHOTINOS: UNSTABLE AND INTERESTING N. CABIBBO Istituto di Fisica, Universit~ di Roma, INFN, Sezione di Roma, Italy G.R. F A R R A R Rutgers University, New Brunswick, NJ, USA and INFN, Sezione di Roma, Italy and L. MAIANI Istituto di Fisica, Universitk di Roma, 1NFN, Sezione di Roma, Italy Received 7 July 1981
Massive photinos decay into a photon and a goldstino with a calculable lifetime. Cosmological arguments indicate that photinos are either eight, m~'< 30 eV or heavy, m~.> 0.3 MeV. Light photi.nos could provide the missing mass in the galaxy and give rise to an observable UV background. Photino searches in high-energy experiments can be affected by photino decay.
The existence of a spontaneously broken supersymmetry [ 1 - 3 ] is a very attractive possibility, particularly if the scale of the breaking is relatively low [4], i.e. comparable to that of the breaking of SU(2) ® U(1). A scheme of this kind could give a natural explanation for the existence of the low-mass (~100 GeV) scalar particles needed to implement internal symmetry breaking. In the simplest case, N = 1 supersymmetry, the familiar quarks and leptons have spin-0 partners with masses in the 1 5 - 4 0 GeV range and the photon and gluons have spin-l/2 partners, the photino and gluinos - which are likely to be light or massless [4] * 1. In addition, spontaneous supersymmetry breaking requires the existence of a massless goldstone fermion, the goldstino Xg. The scale o f supersymmetry breaking can be characterized by an order parameter d, defined through the goldstino to vacuum matrix element of the supersymmetry current, S t : (0IS~IXg >= d3,~Ug.
(1)
they are necessarily unstable, and decay according to* 2 ~r --~ ~kg + 7, with a calculable lifetime r~ = 87rd2/(m~ ) 5 .
(2)
This result, which has interesting consequences for the behaviour of photinos in astrophysics and in high-energy processes is very simply derived. The p h o t i n o photon-goldstino coupling can be determined using standard current-algebra arguments. Gauge invariance requires this coupling to have the form: L etf = hXgF, v3~TvX 7.
(3)
The value of h is determined by the condition that the p h o t i n o - p h o t o n matrix element of S t ,
+ dh,yt~-, 1FpaTo ,ya u(X~,),
(4)
In this note we show that if photinos, X7, are massive, .1 For recent developments of this model, see ref. [5 ]. 0 031-9163/81/0000-0000/$ 02.75 © 1981 North-Holland
.2 We are assuming that photinos are not so heavy as to be able to decay into, e.g. an electron and its scalar partner. 155
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PHYSICS LETTERS
be divergenceless. Eq. (4) is obtained by adding to the standard p h o t i n o - p h o t o n supersymmetry current [3] the contribution of the goldstino pole derived from eqs. (1) and (3). The divergence condition leads to h = m,~12d
(5)
and to the expression in eq. (2) for z~,. The previous considerations shed some light on the problem of the photino mass. The effective coupling h has dimension (mass) - 1 , so that L e tf cannot be present at the tree level in a renormalizable theory. L etf* 3 may appear in higher order [6], or as a nonrenormalizable interaction related to a change of regime of the theory at some large mass A (grand unification?). In this case, eq. (5) can be read as m~, = 2d/A, which may suggest a very light photino *4. For discussing the consequences of eq. (2) we need some assumption on the value o f d . There is a lower limit [8] d >~ 90 GeV 2,
(6)
resulting from the experimental upper bound on ff unseen neutrals, interpreted (see, however, below) as a limit on ~ kg + k 7. The lower bound, eq. (6), leads to z~, >t 1.3 X 102611 eV/m~,] 5 s.
(7)
The particularly attractive hypothesis that the breaking of supersymmetry is related to that of SU(2). ® U(1) leads to a guess for the value of d which is substantially higher than the lower limit in eq. (6): d ~
(50 GeV)2-(200 GeV)2.
(8)
We can then rewrite eq. (2) as ~-~- = 1.65 X 1030 [d/(100 GeV)2]2(1 eV/m~,) 5.
156
(9)
In the following discussion we will take d = (100 GeV) 2 as a guideline, but the reader should keep in mind that the uncertainty on d implies a very large uncertainty on the value of r~, for a given value of m~,. Eq. (9), or the lower bound in eq. (7), leads to interesting consequences for the behaviour of photinos in astrophysics and in high-energy experiments. The possible cosmological relevance of photinos derives from the fact that their low-energy interactions are Fermi-like with a strength comparable to those of neutrinos [9]. Along with a neutrino sea originating frorfi the big bang we thus expect a photino sea of a comparable number density so that standard cosmological arguments can be used, together with eqs. (7) or (9), to exclude a certain range of values for m~,. The lower end of this range is given by the CowsickMcLelland bound [ 10] : m~, < 33 eV (H0/50 km s -1 Mpc-1) 2,
(10)
where H 0 is the Hubble constant. The bound applies since photinos lighter than this have a lifetime which is longer than the present age of the universe. Photinos heavier than this bound must have a lifetime short enough to have disappeared early in the history of the universe. The basic requirement is that the decay photons from big-bang photinos have had time to thermalize and merge into the 3 K background. According to ref. [14] lifetimes shorter than 103 s are required, which leads to: m~, > 30 keV,
(11)
if we use the bound eq. (7), or: m~, > 0.3 MeV,
*a Left can be easily completed into a fully supersymmetric and gauge invariant interaction, where the vector supersymmetric multiplet associated with "yand h~, is coupled to a scalar multiplet containing the goldstino and two additional scalar fields. In the notation of ref. [3], this interaction is the F-component of the superfield h l,~Wa~, where Wa is the gauge invariant 3'h,,/chiral superfield and q~is the chiral superfield containing hg. Besides L etf given in eq. (3), [WatCaq~]F contains a term F~_-~h7 where F is one of the auxiliary fields in ¢. When (F) 0 = d eq. (5) is again obtained. ,4 This is very reminiscent of the arguments of ref. [7] for neutrino masses.
1 October 1981
(12)
in correspondence to the value in eq. (9). From this argument we learn that photinos are either very light, or relatively heavy. In the first case, it is an appealing possibility that the photino mass is close to the upper bound in eq. (10). In this case (say if 10 eV ~< m~, ~ 30 eV) photinos could contribute a large fraction of the mass density in the universe. At the same time, a halo of photinos clustered around the galaxy could provide the solution to the hidden-mass problem [12]. In this situ-
Volume 105B, number 2,3
PHYSICS LETTERS
ation the galactic photinos would decay giving rise to a sharp UV line at h¢o = m~/2. The intensity of the radiation depends upon the photino lifetime, which in turn depends critically upon m~, and d. As an example, m~, = 15 eV and d = (100 GeV) 2 would correspond to ~-~, ~ 1017 yr. The importance of UV galactic photons was first stressed by De R6jula and Glashow [13], in connection with the possible decay of massive relic neutrinos. Their analysis directly applies to photinos: a photino lifetime of 1017 yr leads to the average monochromatic photon flux q~~ 105 photons/cm 2
(13)
for photinos clustered in the galaxy. Present data on the UV background radiation [14] at wavelengths between 1230 A and 1800 A have been analyzed in terms of neutrino decay in ref. [ 15] ,5. This analysis applies equally well to photinos; the main results are: (i) The data require r~, > 1015 yr for photinos uniformly distributed in the universe. (ii) The rather uncertain evidence for a rise of the spectrum in the 1680-1800 A region could be interpreted as originating from galaxy-clustered photinos with a mass of 14 eV and with r~ ~ 1017 yr. Improved UV measurements should be able to detect the photons from 10-30 eV photinos; by contrast, all reasonable estimates [12] give a neutrino lifetime larger than 1023 yr and lead to unobservably small UV photon fluxes. If no such signal is found, the possibility that relatively light photinos provide the bulk of the galactic mass would be excluded. However, if such a signal is observed it not only will have enormous cosmological importance for the missing mass problems, but also will provide the first concrete support for the spontaneously broken supersymmetry hypothesis and give precious information on the value of m~ and d. If the photino mass is higher than the values (11) or (12), photino instability may be relevant for the analysis of photino searches in high-energy experiments. Photinos are expected to be produced in hadronic collisions, as a result of the fast decay of gluino-containing hadrons. It has been proposed [17] to look for photino effects in calorimeter experiments (looking *s For a more recent analysis, see ref. [16].
1 October 1981
for the missing energy carried away by them) or in beam-dump experiments (where long-lived photinos would give rise to an excess of neutral current-like events downstream of the shielding). If the photino lifetime is short enough, r~, < 10 -8 s (which corresponds to m~ > 100 MeV for E~- = 30 GeV) the sensitivity of calorimeter experiments is severely affected, in that only goldstinos escape the calorimeter, reducing by a factor of two the average missing energy. As for beam-dump experiments, photinos would not reach the detectors for z~ < 10 - 6 s (i.e. m~, > 60 MeV for E~, = 30 GeV). In this case, however, one could still observe an excess of neutral current-like events with a considerably lower visible energy from goldstino interactions in the detectors. Although very speculative, we cannot exclude the possibility that this is the origin of the excess of low-energy neutral-current events seen recently by the CHARM collaboration [18]. For lifetimes in the range r~ = 1 0 - 6 - 1 0 - 4 s, one could attempt to observe directly file decay of photinos emerging from the beam dump (decay beam dump). In view of the very steep dependence: r~ = const × (m~,) - 6 , this experiment is sensitive only to a very narrow window in m~-. Finally, the photino instability suggests that an investigation of the reaction $ ~ Xg + X~, and of the related one for the T (10 GeV), be carried out not only by looking for $ ~ unobserved neutrals, but also for ~b~ photon + unobserved neutrals, the photon energy going up to one half of the ~b mass.
References [ 1] Yu.A. Gel'fand and E.P. Likhtman, JETP Lett. 13 (1971) 323; D.V. Volkov and V.P. Akulov, Phys. Lett. 46B (1973) 109; Teor. Mat. Fiz. (USSR) 18 (1974) 39; J. Wess and B. Zumino, Nuel. Phys. B70 (1974) 39. [2] P. Fayet and J. Iliopoulos, Phys. Lett. 51B (1974) 461. [3] For a general review see, e.g.P. Fayet and S. Ferrara, Phys. Rep. 32C (1977) 249. [4] P. Fayet, Phys. Lett. 69B (1977) 489. [5] P. Fayet, in: Supersymmetry, particle physics and gravitation, eds. by S. Ferrara, J. Ellis and P. Van Nieuwenhuizen (Plenum, New York, 1980). [6] P. Fayet, Phys. Lett. 78B (1978) 417. [7] M. GeU-Mann,P. Ramond and R. Slansky, Rev. Mod. Phys. 50 (1978) 721. [8] P. Fayet, Phys. Lett. 84B (1979) 421. [9] P. Fayet, Phys. Lett. 86B (1979) 272. 157
Volume 105B, number 2,3
PHYSICS LETTERS
[10] R. Cowsick and J. McLelland, Phys. Rev. Lett. 29 (1972) 669. [11] J.E. Gunn, B.W. Lee, I. Lerche, D.N. Schramm and G. Steigman, Astrophys. J. 223 (1978) 1015. [12] S.M. Faber and J.S. GaUagher, Ann. Rev. Astron. Astrophys. 17 (1979) 135. [13] A. De Rfijula and S. Glashow, Phys. Rev. Lett. 45 (1980) 942.
158
1 October 1981
[14] P.C. Anderson et al., Astrophys. J. 233 (1979) L39; 234 (1979) 415. [15] F.W. Stecker, Phys. Rev. Lett. 45 (1980) 1460; [16] R. Kimble, S. Bowyer and P. Jakobsen, Phys. Rev. Lett. 46 (1981) 80. [17] G.R. Farrar and P. Fayet, Phys. Lett. 76B (1978) 575; 79B (1978) 442. [18] CHARM CoUab., M. Jonker et al., Phys. Lett. 96B (1980) 435.
PHYSICS LETTERS
1 October 1981
MASSIVE PHOTINOS: UNSTABLE AND INTERESTING N. CABIBBO Istituto di Fisica, Universit~ di Roma, INFN, Sezione di Roma, Italy G.R. F A R R A R Rutgers University, New Brunswick, NJ, USA and INFN, Sezione di Roma, Italy and L. MAIANI Istituto di Fisica, Universitk di Roma, 1NFN, Sezione di Roma, Italy Received 7 July 1981
Massive photinos decay into a photon and a goldstino with a calculable lifetime. Cosmological arguments indicate that photinos are either eight, m~'< 30 eV or heavy, m~.> 0.3 MeV. Light photi.nos could provide the missing mass in the galaxy and give rise to an observable UV background. Photino searches in high-energy experiments can be affected by photino decay.
The existence of a spontaneously broken supersymmetry [ 1 - 3 ] is a very attractive possibility, particularly if the scale of the breaking is relatively low [4], i.e. comparable to that of the breaking of SU(2) ® U(1). A scheme of this kind could give a natural explanation for the existence of the low-mass (~100 GeV) scalar particles needed to implement internal symmetry breaking. In the simplest case, N = 1 supersymmetry, the familiar quarks and leptons have spin-0 partners with masses in the 1 5 - 4 0 GeV range and the photon and gluons have spin-l/2 partners, the photino and gluinos - which are likely to be light or massless [4] * 1. In addition, spontaneous supersymmetry breaking requires the existence of a massless goldstone fermion, the goldstino Xg. The scale o f supersymmetry breaking can be characterized by an order parameter d, defined through the goldstino to vacuum matrix element of the supersymmetry current, S t : (0IS~IXg >= d3,~Ug.
(1)
they are necessarily unstable, and decay according to* 2 ~r --~ ~kg + 7, with a calculable lifetime r~ = 87rd2/(m~ ) 5 .
(2)
This result, which has interesting consequences for the behaviour of photinos in astrophysics and in high-energy processes is very simply derived. The p h o t i n o photon-goldstino coupling can be determined using standard current-algebra arguments. Gauge invariance requires this coupling to have the form: L etf = hXgF, v3~TvX 7.
(3)
The value of h is determined by the condition that the p h o t i n o - p h o t o n matrix element of S t ,
+ dh,yt~-, 1FpaTo ,ya u(X~,),
(4)
In this note we show that if photinos, X7, are massive, .1 For recent developments of this model, see ref. [5 ]. 0 031-9163/81/0000-0000/$ 02.75 © 1981 North-Holland
.2 We are assuming that photinos are not so heavy as to be able to decay into, e.g. an electron and its scalar partner. 155
Volume 105B, number 2,3
PHYSICS LETTERS
be divergenceless. Eq. (4) is obtained by adding to the standard p h o t i n o - p h o t o n supersymmetry current [3] the contribution of the goldstino pole derived from eqs. (1) and (3). The divergence condition leads to h = m,~12d
(5)
and to the expression in eq. (2) for z~,. The previous considerations shed some light on the problem of the photino mass. The effective coupling h has dimension (mass) - 1 , so that L e tf cannot be present at the tree level in a renormalizable theory. L etf* 3 may appear in higher order [6], or as a nonrenormalizable interaction related to a change of regime of the theory at some large mass A (grand unification?). In this case, eq. (5) can be read as m~, = 2d/A, which may suggest a very light photino *4. For discussing the consequences of eq. (2) we need some assumption on the value o f d . There is a lower limit [8] d >~ 90 GeV 2,
(6)
resulting from the experimental upper bound on ff unseen neutrals, interpreted (see, however, below) as a limit on ~ kg + k 7. The lower bound, eq. (6), leads to z~, >t 1.3 X 102611 eV/m~,] 5 s.
(7)
The particularly attractive hypothesis that the breaking of supersymmetry is related to that of SU(2). ® U(1) leads to a guess for the value of d which is substantially higher than the lower limit in eq. (6): d ~
(50 GeV)2-(200 GeV)2.
(8)
We can then rewrite eq. (2) as ~-~- = 1.65 X 1030 [d/(100 GeV)2]2(1 eV/m~,) 5.
156
(9)
In the following discussion we will take d = (100 GeV) 2 as a guideline, but the reader should keep in mind that the uncertainty on d implies a very large uncertainty on the value of r~, for a given value of m~,. Eq. (9), or the lower bound in eq. (7), leads to interesting consequences for the behaviour of photinos in astrophysics and in high-energy experiments. The possible cosmological relevance of photinos derives from the fact that their low-energy interactions are Fermi-like with a strength comparable to those of neutrinos [9]. Along with a neutrino sea originating frorfi the big bang we thus expect a photino sea of a comparable number density so that standard cosmological arguments can be used, together with eqs. (7) or (9), to exclude a certain range of values for m~,. The lower end of this range is given by the CowsickMcLelland bound [ 10] : m~, < 33 eV (H0/50 km s -1 Mpc-1) 2,
(10)
where H 0 is the Hubble constant. The bound applies since photinos lighter than this have a lifetime which is longer than the present age of the universe. Photinos heavier than this bound must have a lifetime short enough to have disappeared early in the history of the universe. The basic requirement is that the decay photons from big-bang photinos have had time to thermalize and merge into the 3 K background. According to ref. [14] lifetimes shorter than 103 s are required, which leads to: m~, > 30 keV,
(11)
if we use the bound eq. (7), or: m~, > 0.3 MeV,
*a Left can be easily completed into a fully supersymmetric and gauge invariant interaction, where the vector supersymmetric multiplet associated with "yand h~, is coupled to a scalar multiplet containing the goldstino and two additional scalar fields. In the notation of ref. [3], this interaction is the F-component of the superfield h l,~Wa~, where Wa is the gauge invariant 3'h,,/chiral superfield and q~is the chiral superfield containing hg. Besides L etf given in eq. (3), [WatCaq~]F contains a term F~_-~h7 where F is one of the auxiliary fields in ¢. When (F) 0 = d eq. (5) is again obtained. ,4 This is very reminiscent of the arguments of ref. [7] for neutrino masses.
1 October 1981
(12)
in correspondence to the value in eq. (9). From this argument we learn that photinos are either very light, or relatively heavy. In the first case, it is an appealing possibility that the photino mass is close to the upper bound in eq. (10). In this case (say if 10 eV ~< m~, ~ 30 eV) photinos could contribute a large fraction of the mass density in the universe. At the same time, a halo of photinos clustered around the galaxy could provide the solution to the hidden-mass problem [12]. In this situ-
Volume 105B, number 2,3
PHYSICS LETTERS
ation the galactic photinos would decay giving rise to a sharp UV line at h¢o = m~/2. The intensity of the radiation depends upon the photino lifetime, which in turn depends critically upon m~, and d. As an example, m~, = 15 eV and d = (100 GeV) 2 would correspond to ~-~, ~ 1017 yr. The importance of UV galactic photons was first stressed by De R6jula and Glashow [13], in connection with the possible decay of massive relic neutrinos. Their analysis directly applies to photinos: a photino lifetime of 1017 yr leads to the average monochromatic photon flux q~~ 105 photons/cm 2
(13)
for photinos clustered in the galaxy. Present data on the UV background radiation [14] at wavelengths between 1230 A and 1800 A have been analyzed in terms of neutrino decay in ref. [ 15] ,5. This analysis applies equally well to photinos; the main results are: (i) The data require r~, > 1015 yr for photinos uniformly distributed in the universe. (ii) The rather uncertain evidence for a rise of the spectrum in the 1680-1800 A region could be interpreted as originating from galaxy-clustered photinos with a mass of 14 eV and with r~ ~ 1017 yr. Improved UV measurements should be able to detect the photons from 10-30 eV photinos; by contrast, all reasonable estimates [12] give a neutrino lifetime larger than 1023 yr and lead to unobservably small UV photon fluxes. If no such signal is found, the possibility that relatively light photinos provide the bulk of the galactic mass would be excluded. However, if such a signal is observed it not only will have enormous cosmological importance for the missing mass problems, but also will provide the first concrete support for the spontaneously broken supersymmetry hypothesis and give precious information on the value of m~ and d. If the photino mass is higher than the values (11) or (12), photino instability may be relevant for the analysis of photino searches in high-energy experiments. Photinos are expected to be produced in hadronic collisions, as a result of the fast decay of gluino-containing hadrons. It has been proposed [17] to look for photino effects in calorimeter experiments (looking *s For a more recent analysis, see ref. [16].
1 October 1981
for the missing energy carried away by them) or in beam-dump experiments (where long-lived photinos would give rise to an excess of neutral current-like events downstream of the shielding). If the photino lifetime is short enough, r~, < 10 -8 s (which corresponds to m~ > 100 MeV for E~- = 30 GeV) the sensitivity of calorimeter experiments is severely affected, in that only goldstinos escape the calorimeter, reducing by a factor of two the average missing energy. As for beam-dump experiments, photinos would not reach the detectors for z~ < 10 - 6 s (i.e. m~, > 60 MeV for E~, = 30 GeV). In this case, however, one could still observe an excess of neutral current-like events with a considerably lower visible energy from goldstino interactions in the detectors. Although very speculative, we cannot exclude the possibility that this is the origin of the excess of low-energy neutral-current events seen recently by the CHARM collaboration [18]. For lifetimes in the range r~ = 1 0 - 6 - 1 0 - 4 s, one could attempt to observe directly file decay of photinos emerging from the beam dump (decay beam dump). In view of the very steep dependence: r~ = const × (m~,) - 6 , this experiment is sensitive only to a very narrow window in m~-. Finally, the photino instability suggests that an investigation of the reaction $ ~ Xg + X~, and of the related one for the T (10 GeV), be carried out not only by looking for $ ~ unobserved neutrals, but also for ~b~ photon + unobserved neutrals, the photon energy going up to one half of the ~b mass.
References [ 1] Yu.A. Gel'fand and E.P. Likhtman, JETP Lett. 13 (1971) 323; D.V. Volkov and V.P. Akulov, Phys. Lett. 46B (1973) 109; Teor. Mat. Fiz. (USSR) 18 (1974) 39; J. Wess and B. Zumino, Nuel. Phys. B70 (1974) 39. [2] P. Fayet and J. Iliopoulos, Phys. Lett. 51B (1974) 461. [3] For a general review see, e.g.P. Fayet and S. Ferrara, Phys. Rep. 32C (1977) 249. [4] P. Fayet, Phys. Lett. 69B (1977) 489. [5] P. Fayet, in: Supersymmetry, particle physics and gravitation, eds. by S. Ferrara, J. Ellis and P. Van Nieuwenhuizen (Plenum, New York, 1980). [6] P. Fayet, Phys. Lett. 78B (1978) 417. [7] M. GeU-Mann,P. Ramond and R. Slansky, Rev. Mod. Phys. 50 (1978) 721. [8] P. Fayet, Phys. Lett. 84B (1979) 421. [9] P. Fayet, Phys. Lett. 86B (1979) 272. 157
Volume 105B, number 2,3
PHYSICS LETTERS
[10] R. Cowsick and J. McLelland, Phys. Rev. Lett. 29 (1972) 669. [11] J.E. Gunn, B.W. Lee, I. Lerche, D.N. Schramm and G. Steigman, Astrophys. J. 223 (1978) 1015. [12] S.M. Faber and J.S. GaUagher, Ann. Rev. Astron. Astrophys. 17 (1979) 135. [13] A. De Rfijula and S. Glashow, Phys. Rev. Lett. 45 (1980) 942.
158
1 October 1981
[14] P.C. Anderson et al., Astrophys. J. 233 (1979) L39; 234 (1979) 415. [15] F.W. Stecker, Phys. Rev. Lett. 45 (1980) 1460; [16] R. Kimble, S. Bowyer and P. Jakobsen, Phys. Rev. Lett. 46 (1981) 80. [17] G.R. Farrar and P. Fayet, Phys. Lett. 76B (1978) 575; 79B (1978) 442. [18] CHARM CoUab., M. Jonker et al., Phys. Lett. 96B (1980) 435.